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# How do we know if a Killing Spinor is Time-like or Null?

How to know whether a Killing spinor orbit is time-like or null? This is present in a paper like this 29/39 here. I'm not asking for a technical answer, just a logical cliche answer chit-chat answer.

Let me go into more details here

The KSEs for $N = 1$ backgrounds have been solved using spinor bilinears. In the spinorial approach [Gillard, Gran, GP], the KSEs are solved utilizing the representatives of the two orbits. $\epsilon = f(1+e_{12345})$: Solutions admit a time-like Killing vector field and its orbit space has a SU(5) structure.

$\epsilon = 1+e_{1234}$: Solutions admit a null Killing vector field, the spacetime has a $Spin(7)\times \mathbb{R}^9$ structure and include backgrounds like pp-wave propagating in a $Spin(7)$ manifold.

To see whether a Killing spinor is timelike or null, you need to make a following combination. $$V_\mu\epsilon^{ab}=\bar{\epsilon}^a\gamma_\mu\epsilon^b\,.$$ Then using Fierz identities, you can compute the norm of the vector $V_\mu$, and see whether it is timelike or null. For example, in five-dimensional minimal supergravity, you will find that $$V_\mu V^\mu=f^2\,,$$ where $f$ is a scalar which is also constructed by using a Killing spinor $\epsilon^a$ such as $$f\epsilon^{ab}=\bar\epsilon^a\epsilon^b\,.$$

I first met this concepts of a timelike or null Killing spinor in hep-th/0209114.


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From the information given, find the quadrant in which the terminal point determined by $t$ lies. Input I, II, III, or IV.
(a) $\sin (t)<0$ and $\cos (t)<0$, quadrant ;
(b) $\sin (t)>0$ and $\cos (t)<0$, quadrant ;
(c) $\sin (t)>0$ and $\cos (t)>0$, quadrant ;
(d) $\sin (t)<0$ and $\cos (t)>0$, quadrant ;

Your overall score for this problem is

format: plain


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# Appendix. Various Details and Explanations

## Kinematic Equations in Mechanics

Kinematic equations are constrained equations found in dynamics of body. In the mechanics, the constraint that is incurred on is to have constant acceleration on a body with mass m.

 $v= v 0 +at$ A1
 $x= x 0 + v 0 t+ 1 2 a t 2$ A2
 $v 2 = v 0 2 +2a( x- x 0 )$ A3
 $v ¯ = v+ v 0 2$ A4

## Determinant

Determinant is used in eigenvalue equations and other important. The simplest case is 2 x 2 determinant,
 $| a 1 a 2 a 3 a 4 |= a 1 a 4 − a 2 a 3$ A5
In the case of 3 x 3 determinant,
 $| a 1 a 2 a 3 a 4 a 5 a 6 a 7 a 8 a 9 |= a 1 ( a 5 a 9 − a 6 a 8 )− a 2 ( a 4 a 9 − a 6 a 7 )+ a 3 ( a 4 a 8 − a 5 a 7 )$ A6
Larger determinants can be solved by similar techique used in going from 2 x 2 to 3 x 3 determinant.

## Lagrangian Dynamics

Setting up equations of motion in terms of force can be rather nuisance. It is particularly true when there are many two-body interactions. The general procedure is to set up Lagrangian equations of motion to make them into matrix form.

The Lagrangian function is defined by

 $L( q i , q ˙ i ,t )=T( q i , q ˙ i ,t )−V( q i )$ A7
where T is kinetic energy and V is potential energy. The variables are in terms of ith coordinate qi, and ${\stackrel{˙}{q}}_{i}$ is the velocity associated with qi (q with a dot and a double-dot on top indicates first derivative in time and second derivative, respecitively), and t is time.
 $T( q i , q ˙ i ,t )= 1 2 m q ˙ i 2$ A8 $V( q i )= 1 2 k ( q i − q 0 ) 2$ A9
The above equation for potential energy is for harmonic motion of masses in linear Hooke's law forces between them.

Then, the dynamical equation, called Lagrange's equation, is obtained by the following.

 $d dt ( ∂L ∂ q ˙ i )− ∂L ∂ q i =0$ A10
Let us now use an example. Let us write dynamical equation for molecular vibration in one dimension. Easiest one perhaps is the CO2, as shown below.

Figure A1. CO2 molecule and its coordinates

The Lagrangian is written as

 $L( q i , q ˙ i ,t )= 1 2 m O x ˙ 1 2 + 1 2 m C x ˙ 2 2 + 1 2 m O x ˙ 3 2 − 1 2 k ( x 2 − x 1 ) 2 − 1 2 k ( x 3 − x 2 ) 2$ A11

We now need to subject Eqn. A11 to Eqn. A10 for each of ith component. The first term on the left-hand side of A10 is

 $d dt ( ∂L ∂ q ˙ i )= ∑ i m i x ¨ i$ A12
where mi is the mass associated with xi coordinate. You can easily see it that by taking the derivative of the first three terms of the right-hand side of Eqn. A11, and subsequently taking the time-derivative.

The second term on the left-hand side of A10 is

 $∂L ∂ q i =−k( x 2 − x 1 )+k( x 2 − x 1 )−k( x 3 − x 2 )$ A13
We can rewrite Eqns. A12 and A13 into three simultaneous linear equations containing given i component,
 $m O x ¨ 1 −k( x 2 − x 1 )=0 m C x ¨ 2 +k( x 2 − x 1 )−k( x 3 − x 2 )=0 m O x ¨ 3 −k( x 3 − x 2 )=0$ A14
This gives the equations of motion to be solved.


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# 4.3. Properties Reference

This section describes the most important config properties that may be used to tune Presto or alter its behavior when required.

## General Properties

### join-distribution-type

• Type: string
• Allowed values: AUTOMATIC, PARTITIONED, BROADCAST
• Default value: PARTITIONED

The type of distributed join to use. When set to PARTITIONED, presto will use hash distributed joins. When set to BROADCAST, it will broadcast the right table to all nodes in the cluster that have data from the left table. Partitioned joins require redistributing both tables using a hash of the join key. This can be slower (sometimes substantially) than broadcast joins, but allows much larger joins. In particular broadcast joins will be faster if the right table is much smaller than the left. However, broadcast joins require that the tables on the right side of the join after filtering fit in memory on each node, whereas distributed joins only need to fit in distributed memory across all nodes. When set to AUTOMATIC, Presto will make a cost based decision as to which distribution type is optimal. It will also consider switching the left and right inputs to the join. In AUTOMATIC mode, Presto will default to hash distributed joins if no cost could be computed, such as if the tables do not have statistics. This can also be specified on a per-query basis using the join_distribution_type session property.

### redistribute-writes

• Type: boolean
• Default value: true

This property enables redistribution of data before writing. This can eliminate the performance impact of data skew when writing by hashing it across nodes in the cluster. It can be disabled when it is known that the output data set is not skewed in order to avoid the overhead of hashing and redistributing all the data across the network. This can also be specified on a per-query basis using the redistribute_writes session property.

## Memory Management Properties

### query.max-memory-per-node

• Type: data size
• Default value: JVM max memory * 0.1

This is the max amount of user memory a query can use on a worker. User memory is allocated during execution for things that are directly attributable to or controllable by a user query. For example, memory used by the hash tables built during execution, memory used during sorting, etc. When the user memory allocation of a query on any worker hits this limit it will be killed.

### query.max-total-memory-per-node

• Type: data size
• Default value: JVM max memory * 0.3

This is the max amount of user and system memory a query can use on a worker. System memory is allocated during execution for things that are not directly attributable to or controllable by a user query. For example, memory allocated by the readers, writers, network buffers, etc. When the sum of the user and system memory allocated by a query on any worker hits this limit it will be killed. The value of query.max-total-memory-per-node must be greater than query.max-memory-per-node.

### query.max-memory

• Type: data size
• Default value: 20GB

This is the max amount of user memory a query can use across the entire cluster. User memory is allocated during execution for things that are directly attributable to or controllable by a user query. For example, memory used by the hash tables built during execution, memory used during sorting, etc. When the user memory allocation of a query across all workers hits this limit it will be killed.

### query.max-total-memory

• Type: data size
• Default value: query.max-memory * 2

This is the max amount of user and system memory a query can use across the entire cluster. System memory is allocated during execution for things that are not directly attributable to or controllable by a user query. For example, memory allocated by the readers, writers, network buffers, etc. When the sum of the user and system memory allocated by a query across all workers hits this limit it will be killed. The value of query.max-total-memory must be greater than query.max-memory.

### memory.heap-headroom-per-node

• Type: data size
• Default value: JVM max memory * 0.3

This is the amount of memory set aside as headroom/buffer in the JVM heap for allocations that are not tracked by Presto.

### query.low-memory-killer.policy

• Type: string
• Default value: none

The policy used for selecting the query to kill when the cluster is out of memory (OOM). This property can have one of the following values: none, total-reservation, or total-reservation-on-blocked-nodes. none disables the cluster OOM killer. The value of total-reservation configures a policy that kills the query with the largest memory reservation across the cluster. The value of total-reservation-on-blocked-nodes configures a policy that kills the query using the most memory on the workers that are out of memory (blocked).

## Spilling Properties

### experimental.spill-enabled

• Type: boolean
• Default value: false

Try spilling memory to disk to avoid exceeding memory limits for the query.

Spilling works by offloading memory to disk. This process can allow a query with a large memory footprint to pass at the cost of slower execution times. Currently, spilling is supported only for aggregations and joins (inner and outer), so this property will not reduce memory usage required for window functions, sorting and other join types.

Be aware that this is an experimental feature and should be used with care.

This config property can be overridden by the spill_enabled session property.

### experimental.spiller-spill-path

• Type: string
• No default value. Must be set when spilling is enabled

Directory where spilled content will be written. It can be a comma separated list to spill simultaneously to multiple directories, which helps to utilize multiple drives installed in the system.

It is not recommended to spill to system drives. Most importantly, do not spill to the drive on which the JVM logs are written, as disk overutilization might cause JVM to pause for lengthy periods, causing queries to fail.

### experimental.spiller-max-used-space-threshold

• Type: double
• Default value: 0.9

If disk space usage ratio of a given spill path is above this threshold, this spill path will not be eligible for spilling.

### experimental.spiller-threads

• Type: integer
• Default value: 4

Number of spiller threads. Increase this value if the default is not able to saturate the underlying spilling device (for example, when using RAID).

### experimental.max-spill-per-node

• Type: data size
• Default value: 100 GB

Max spill space to be used by all queries on a single node.

### experimental.query-max-spill-per-node

• Type: data size
• Default value: 100 GB

Max spill space to be used by a single query on a single node.

### experimental.aggregation-operator-unspill-memory-limit

• Type: data size
• Default value: 4 MB

Limit for memory used for unspilling a single aggregation operator instance.

### experimental.spill-compression-enabled

• Type: boolean
• Default value: false

Enables data compression for pages spilled to disk

### experimental.spill-encryption-enabled

• Type: boolean
• Default value: false

Enables using a randomly generated secret key (per spill file) to encrypt and decrypt data spilled to disk

## Exchange Properties

Exchanges transfer data between Presto nodes for different stages of a query. Adjusting these properties may help to resolve inter-node communication issues or improve network utilization.

### exchange.client-threads

• Type: integer
• Minimum value: 1
• Default value: 25

Number of threads used by exchange clients to fetch data from other Presto nodes. A higher value can improve performance for large clusters or clusters with very high concurrency, but excessively high values may cause a drop in performance due to context switches and additional memory usage.

### exchange.concurrent-request-multiplier

• Type: integer
• Minimum value: 1
• Default value: 3

Multiplier determining the number of concurrent requests relative to available buffer memory. The maximum number of requests is determined using a heuristic of the number of clients that can fit into available buffer space based on average buffer usage per request times this multiplier. For example, with an exchange.max-buffer-size of 32 MB and 20 MB already used and average size per request being 2MB, the maximum number of clients is multiplier * ((32MB - 20MB) / 2MB) = multiplier * 6. Tuning this value adjusts the heuristic, which may increase concurrency and improve network utilization.

### exchange.max-buffer-size

• Type: data size
• Default value: 32MB

Size of buffer in the exchange client that holds data fetched from other nodes before it is processed. A larger buffer can increase network throughput for larger clusters and thus decrease query processing time, but will reduce the amount of memory available for other usages.

### exchange.max-response-size

• Type: data size
• Minimum value: 1MB
• Default value: 16MB

Maximum size of a response returned from an exchange request. The response will be placed in the exchange client buffer which is shared across all concurrent requests for the exchange.

Increasing the value may improve network throughput if there is high latency. Decreasing the value may improve query performance for large clusters as it reduces skew due to the exchange client buffer holding responses for more tasks (rather than hold more data from fewer tasks).

### sink.max-buffer-size

• Type: data size
• Default value: 32MB

Output buffer size for task data that is waiting to be pulled by upstream tasks. If the task output is hash partitioned, then the buffer will be shared across all of the partitioned consumers. Increasing this value may improve network throughput for data transferred between stages if the network has high latency or if there are many nodes in the cluster.

### task.concurrency

• Type: integer
• Restrictions: must be a power of two
• Default value: 16

Default local concurrency for parallel operators such as joins and aggregations. This value should be adjusted up or down based on the query concurrency and worker resource utilization. Lower values are better for clusters that run many queries concurrently because the cluster will already be utilized by all the running queries, so adding more concurrency will result in slow downs due to context switching and other overhead. Higher values are better for clusters that only run one or a few queries at a time. This can also be specified on a per-query basis using the task_concurrency session property.

### task.http-response-threads

• Type: integer
• Minimum value: 1
• Default value: 100

Maximum number of threads that may be created to handle HTTP responses. Threads are created on demand and are cleaned up when idle, thus there is no overhead to a large value if the number of requests to be handled is small. More threads may be helpful on clusters with a high number of concurrent queries, or on clusters with hundreds or thousands of workers.

### task.http-timeout-threads

• Type: integer
• Minimum value: 1
• Default value: 3

Number of threads used to handle timeouts when generating HTTP responses. This value should be increased if all the threads are frequently in use. This can be monitored via the com.facebook.presto.server:name=AsyncHttpExecutionMBean:TimeoutExecutor JMX object. If ActiveCount is always the same as PoolSize, increase the number of threads.

### task.info-update-interval

• Type: duration
• Minimum value: 1ms
• Maximum value: 10s
• Default value: 3s

Controls staleness of task information, which is used in scheduling. Larger values can reduce coordinator CPU load, but may result in suboptimal split scheduling.

### task.max-partial-aggregation-memory

• Type: data size
• Default value: 16MB

Maximum size of partial aggregation results for distributed aggregations. Increasing this value can result in less network transfer and lower CPU utilization by allowing more groups to be kept locally before being flushed, at the cost of additional memory usage.

### task.max-worker-threads

• Type: integer
• Default value: Node CPUs * 2

Sets the number of threads used by workers to process splits. Increasing this number can improve throughput if worker CPU utilization is low and all the threads are in use, but will cause increased heap space usage. Setting the value too high may cause a drop in performance due to a context switching. The number of active threads is available via the RunningSplits property of the com.facebook.presto.execution.executor:name=TaskExecutor.RunningSplits JXM object.

### task.min-drivers

• Type: integer
• Default value: task.max-worker-threads * 2

The target number of running leaf splits on a worker. This is a minimum value because each leaf task is guaranteed at least 3 running splits. Non-leaf tasks are also guaranteed to run in order to prevent deadlocks. A lower value may improve responsiveness for new tasks, but can result in underutilized resources. A higher value can increase resource utilization, but uses additional memory.

### task.writer-count

• Type: integer
• Restrictions: must be a power of two
• Default value: 1

The number of concurrent writer threads per worker per query. Increasing this value may increase write speed, especially when a query is not I/O bound and can take advantage of additional CPU for parallel writes (some connectors can be bottlenecked on CPU when writing due to compression or other factors). Setting this too high may cause the cluster to become overloaded due to excessive resource utilization. This can also be specified on a per-query basis using the task_writer_count session property.

## Node Scheduler Properties

### node-scheduler.max-splits-per-node

• Type: integer
• Default value: 100

The target value for the total number of splits that can be running for each worker node.

Using a higher value is recommended if queries are submitted in large batches (e.g., running a large group of reports periodically) or for connectors that produce many splits that complete quickly. Increasing this value may improve query latency by ensuring that the workers have enough splits to keep them fully utilized.

Setting this too high will waste memory and may result in lower performance due to splits not being balanced across workers. Ideally, it should be set such that there is always at least one split waiting to be processed, but not higher.

### node-scheduler.max-pending-splits-per-task

• Type: integer
• Default value: 10

The number of outstanding splits that can be queued for each worker node for a single stage of a query, even when the node is already at the limit for total number of splits. Allowing a minimum number of splits per stage is required to prevent starvation and deadlocks.

This value must be smaller than node-scheduler.max-splits-per-node, will usually be increased for the same reasons, and has similar drawbacks if set too high.

### node-scheduler.min-candidates

• Type: integer
• Minimum value: 1
• Default value: 10

The minimum number of candidate nodes that will be evaluated by the node scheduler when choosing the target node for a split. Setting this value too low may prevent splits from being properly balanced across all worker nodes. Setting it too high may increase query latency and increase CPU usage on the coordinator.

### node-scheduler.network-topology

• Type: string
• Allowed values: legacy, flat
• Default value: legacy

Sets the network topology to use when scheduling splits. legacy will ignore the topology when scheduling splits. flat will try to schedule splits on the host where the data is located by reserving 50% of the work queue for local splits. It is recommended to use flat for clusters where distributed storage runs on the same nodes as Presto workers.

## Optimizer Properties

### optimizer.dictionary-aggregation

• Type: boolean
• Default value: false

Enables optimization for aggregations on dictionaries. This can also be specified on a per-query basis using the dictionary_aggregation session property.

### optimizer.optimize-hash-generation

• Type: boolean
• Default value: true

Compute hash codes for distribution, joins, and aggregations early during execution, allowing result to be shared between operations later in the query. This can reduce CPU usage by avoiding computing the same hash multiple times, but at the cost of additional network transfer for the hashes. In most cases it will decrease overall query processing time. This can also be specified on a per-query basis using the optimize_hash_generation session property.

It is often helpful to disable this property when using EXPLAIN in order to make the query plan easier to read.

### optimizer.optimize-metadata-queries

• Type: boolean
• Default value: false

Enable optimization of some aggregations by using values that are stored as metadata. This allows Presto to execute some simple queries in constant time. Currently, this optimization applies to max, min and approx_distinct of partition keys and other aggregation insensitive to the cardinality of the input (including DISTINCT aggregates). Using this may speed up some queries significantly.

The main drawback is that it can produce incorrect results if the connector returns partition keys for partitions that have no rows. In particular, the Hive connector can return empty partitions if they were created by other systems (Presto cannot create them).

### optimizer.optimize-single-distinct

• Type: boolean
• Default value: true

The single distinct optimization will try to replace multiple DISTINCT clauses with a single GROUP BY clause, which can be substantially faster to execute.

### optimizer.push-aggregation-through-join

• Type: boolean
• Default value: true

When an aggregation is above an outer join and all columns from the outer side of the join are in the grouping clause, the aggregation is pushed below the outer join. This optimization is particularly useful for correlated scalar subqueries, which get rewritten to an aggregation over an outer join. For example:

SELECT * FROM item i
WHERE i.i_current_price > (
SELECT AVG(j.i_current_price) FROM item j
WHERE i.i_category = j.i_category);

Enabling this optimization can substantially speed up queries by reducing the amount of data that needs to be processed by the join. However, it may slow down some queries that have very selective joins. This can also be specified on a per-query basis using the push_aggregation_through_join session property.

### optimizer.push-table-write-through-union

• Type: boolean
• Default value: true

Parallelize writes when using UNION ALL in queries that write data. This improves the speed of writing output tables in UNION ALL queries because these writes do not require additional synchronization when collecting results. Enabling this optimization can improve UNION ALL speed when write speed is not yet saturated. However, it may slow down queries in an already heavily loaded system. This can also be specified on a per-query basis using the push_table_write_through_union session property.

### optimizer.join-reordering-strategy

• Type: string
• Allowed values: AUTOMATIC, ELIMINATE_CROSS_JOINS, NONE
• Default value: ELIMINATE_CROSS_JOINS

The join reordering strategy to use. NONE maintains the order the tables are listed in the query. ELIMINATE_CROSS_JOINS reorders joins to eliminate cross joins where possible and otherwise maintains the original query order. When reordering joins it also strives to maintain the original table order as much as possible. AUTOMATIC enumerates possible orders and uses statistics-based cost estimation to determine the least cost order. If stats are not available or if for any reason a cost could not be computed, the ELIMINATE_CROSS_JOINS strategy is used. This can also be specified on a per-query basis using the join_reordering_strategy session property.

### optimizer.max-reordered-joins

• Type: integer
• Default value: 9

When optimizer.join-reordering-strategy is set to cost-based, this property determines the maximum number of joins that can be reordered at once.

Warning

The number of possible join orders scales factorially with the number of relations, so increasing this value can cause serious performance issues.

## Regular Expression Function Properties

The following properties allow tuning the Regular Expression Functions.

### regex-library

• Type: string
• Allowed values: JONI, RE2J
• Default value: JONI

Which library to use for regular expression functions. JONI is generally faster for common usage, but can require exponential time for certain expression patterns. RE2J uses a different algorithm which guarantees linear time, but is often slower.

### re2j.dfa-states-limit

• Type: integer
• Minimum value: 2
• Default value: 2147483647

The maximum number of states to use when RE2J builds the fast but potentially memory intensive deterministic finite automaton (DFA) for regular expression matching. If the limit is reached, RE2J will fall back to the algorithm that uses the slower, but less memory intensive non-deterministic finite automaton (NFA). Decreasing this value decreases the maximum memory footprint of a regular expression search at the cost of speed.

### re2j.dfa-retries

• Type: integer
• Minimum value: 0
• Default value: 5

The number of times that RE2J will retry the DFA algorithm when it reaches a states limit before using the slower, but less memory intensive NFA algorithm for all future inputs for that search. If hitting the limit for a given input row is likely to be an outlier, you want to be able to process subsequent rows using the faster DFA algorithm. If you are likely to hit the limit on matches for subsequent rows as well, you want to use the correct algorithm from the beginning so as not to waste time and resources. The more rows you are processing, the larger this value should be.


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## LaTeX forum ⇒ Graphics, Figures & Tables ⇒ Vertical Text Alignment in circled Nodes Topic is solved

Information and discussion about graphics, figures & tables in LaTeX documents.
SAKDOSS
Posts: 14
Joined: Thu Feb 21, 2013 5:06 pm

### Vertical Text Alignment in circled Nodes

Hello,

It seems that I have a lot of questions these days.

I am drawing two ellipses and two circles with tikZ:
\begin{tikzpicture}   \node[ellipse, draw] at (0,0) {     \begin{tikzpicture}       \node at (0,0.2){$blablabla$};       \node at (0,-0.2){$b$};     \end{tikzpicture}   };    \node[ellipse, draw] at (3.5,0) {     \begin{tikzpicture}       \node at (0,0.2){$b$};       \node at (0,-0.2){$blablabla$};     \end{tikzpicture}   };    \node[circle, draw] at (0,3.5) {     \begin{tikzpicture}       \node at (0,0.2){$blablabla$};       \node at (0,-0.2){$b$};     \end{tikzpicture}   };    \node[circle, draw] at (3.5,3.5) {     \begin{tikzpicture}       \node at (0,0.2){$b$};       \node at (0,-0.2){$blablabla$};     \end{tikzpicture}   };\end{tikzpicture}

The result is here:
tikZ-text-alignment.png (19.34 KiB) Viewed 2895 times

As you can see the texts in the two ellipses are centered vertically whereas they are not in the circles. This is due to the fact that "blablabla" is longer than "b" but I don't understand why it's working for the ellipses only.

Is it possible to center vertically the texts in the circles without changing the coordinates of the nodes ?
Last edited by localghost on Sat Feb 23, 2013 7:25 pm, edited 1 time in total.
Reason: Preferably no external links (see Board Rules). Attachments go onto the forum server where possible.

SAKDOSS
Posts: 14
Joined: Thu Feb 21, 2013 5:06 pm
Again I found the solution (sorry for posting). I give the answer it may help someone:

\node (a) at (6,0.2){$b$};\node (b) at (6,-0.2){$blablabla$};\node[draw, circle, fit=(a) (b)] {};

localghost
Site Moderator
Posts: 9206
Joined: Fri Feb 02, 2007 12:06 pm
Location: Braunschweig, Germany
Thanks for sharing. However, your solution in form of a self-contained and minimal document would be preferable since it would be compilable out of the box for everybody else.

Thorsten
LaTeX Community Moderator

¹ System: openSUSE 13.1 (Linux 3.11.10), TeX Live 2013 (vanilla), TeXworks 0.5 (r1351)
² Posting stopped indefinitely due to offenses

SAKDOSS
Posts: 14
Joined: Thu Feb 21, 2013 5:06 pm
Indeed here is a compilable latex file:
\documentclass{article} \usepackage[english]{babel}\usepackage{tikz}\usetikzlibrary{fit}\usetikzlibrary{shapes} \begin{document} \begin{tikzpicture}   \node[ellipse, draw] at (0,0) {     \begin{tikzpicture}       \node at (0,0.2){$blablabla$};       \node at (0,-0.2){$b$};     \end{tikzpicture}   };    \node[ellipse, draw] at (3.5,0) {     \begin{tikzpicture}       \node at (0,0.2){$b$};       \node at (0,-0.2){$blablabla$};     \end{tikzpicture}   };    \node[circle, draw] at (0,3.5) {     \begin{tikzpicture}       \node at (0,0.2){$blablabla$};       \node at (0,-0.2){$b$};     \end{tikzpicture}   };    \node[circle, draw] at (3.5,3.5) {     \begin{tikzpicture}       \node at (0,0.2){$b$};       \node at (0,-0.2){$blablabla$};     \end{tikzpicture}   };\end{tikzpicture} \begin{tikzpicture}   \node (a) at (6,0.2){$b$}; \node (b) at (6,-0.2){$itworksperfectly!$};   \node[draw, circle, fit=(a) (b)] {};\end{tikzpicture} \end{document}

Stefan Kottwitz
Posts: 7875
Joined: Mon Mar 10, 2008 9:44 pm
Location: Hamburg, Germany
Contact:
Thanks for the solution! And in this way, I could click on "Open in writeLaTeX" and immediately test your example, very good.

Stefan


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Zbl 1005.26002
Babakhani, A.; Daftardar-Gejji, Varsha
On calculus of local fractional derivatives.
(English)
[J] J. Math. Anal. Appl. 270, No.1, 66-79 (2002). ISSN 0022-247X

{\it K. M. Kolwankar} and {\it A. D. Gangal} [Fractional differentiability of nowhere differentiable functions and dimensions'', Chaos 6, No.~4, 505-513 (1996; Zbl 1055.26504)] introduced a certain localization'' $d^\alpha f(x)$ of the Riemann-Liouville fractional derivative to study the local behaviour of nowhere differentiable functions (see reviewer's remark on this notion in the review in Zbl to the paper by {\it F. Ben Adda} and {\it J. Cresson} [About non-differentiable functions'', J. Math Anal. Appl. 263, No. 2, 721-737 (2001; Zbl 0995.26006)]). The authors study some properties of this localization'', such as the Leibniz rule for the product, the chain rule and others.
[Stefan G.Samko (Faro)]
MSC 2000:
*26A33 Fractional derivatives and integrals (real functions)

Keywords: fractional derivatives; fractional integrals

Citations: Zbl 1055.26504; Zbl 0995.26006

Highlights
Master Server


text:
Home > English, Linux & Programming > Conditional Commenting in LaTeX

Conditional Commenting in LaTeX

In my Ph.D. thesis are quite a lot of comments/reminders for myself. I defined two commands for this, one for a red footnote and one for red bold text. But if someone else is to read parts of the document, he shouldn’t necessarily see all my comments, so I was searching for a method to suppress all comments with a single flag. I found the package ifthen and it’s exactly what I was looking for. If you need to use comments for yourself in a document you’re writing, consider using the following:

Categories: Tags:
1. April 9th, 2020 at 04:10 | #1
2. April 9th, 2020 at 09:03 | #2

Incredible a lot of wonderful knowledge. canada pharmacy

3. April 9th, 2020 at 13:03 | #3
4. April 9th, 2020 at 20:44 | #4
Comment pages
1 32 33 34 209


text:
## Why in BFPRT (median of medians) algorithm the partition of the array by $7$ blocks would work but with the $3$ fail?

I am working with the median-median algorithm or BFPRT algorithm and I seek to understand why would the partition of the array by $$7$$ blocks would work but with the $$3$$ fail?

If we divide into blocks of $$7$$ then we will get: Solving it by substitution I think the following manner: It is a recursive tree. In the worst case it takes $$T(10n/14)$$ time. So in the worst case it goes down to the bottom by $$(10/14)^kn=1$$ steps; $$k=log_{14/10}n$$. At each level of recursive tree the total cost is $$\le cn$$ for some constant $$c$$. So by the simplified assumptions using substitution $$k < n$$ $$T(n)\le dn \log(n)$$

$$T(n) \le T(n / 7) + T(10n / 14) + O(n) \le d\frac{n}{7}lg(n/7)+d\frac{10n}{14}lg(10n/14)+cn \le d(\frac{n}{7}lgn – \frac{n}{7}lg7) + d(\frac{10n}{14}lgn – \frac{10n}{14}lg10/14) + cn = d\frac{12n}{14}lgn – d\frac{n}{7}lg7 – d\frac{10n}{14}lg\frac{10}{14} + cn=d\frac{12n}{14}lgn – d\frac{n}{7}lg7 – d\frac{10n}{14}lg10 – d\frac{10n}{14}lg14 + cn \le d\frac{12n}{14}lgn + cn$$

So, $$T(n) = O(nlgn)$$

The same way for blocks of size $$3$$.

$$T(n) \le T(n / 3) + T(2n / 3) + O(n)$$ we get $$T(n) = O(nlgn)$$

Now, how to show that $$T(n)$$ for 7 is also $$O(n)$$ and for 3 it can not be $$O(n)$$. Also, in general how can I guess that the $$T(n)$$ is also $$O(n)$$ because here in both cases my thoughts are they both $$O(nlogn)$$?

## Sharepoint REST call to get file by ID – GetFileById fail on 404

There are some files. when I’m trying to get their content by ID (GetFileById) I’m getting 404 Not found error. I’m getting the file unique id from the item properties and then trying to get the content, and then it fails. Interesting that, in many cases when I’m trying to get same file by relative URL GetFileByServerRelativeUrl I’m getting : The length of the URL for this request exceeds the configured maxUrlLength value error.

Thanks

## Swashbuckler rogue: does sneak attack fail if you have both advantage & disadvantage? [duplicate]

I am having a bit of an argument with my DM.

The rules say that you can have sneak attack if “you don’t have disadvantage on the attack roll”.

If I have both advantage and disadvantage, that results in a straight roll when attacking. A straight roll suggests that sneak attack is allowed.

My DM interprets it as, if I have a source of disadvantage, regardless of weather I also have advantage or not, the fact I am being disadvantaged in some way prevents sneak attack from triggering.

Can someone please let me know who has the correct interpretation?

## Installing GalliumOS kernel, adding repo seems to fail

I’m a newbie to the Linux world, and trying to get a nice linux install on my Chromebook Pixel. This, it turns out, is not easy.

I’ve been trying to follow this guide:

How to install GalliumOS Kernel onto ubuntu installation Acer Chromebook 14

But when I get to the un-elaborated step “Add the GalliumOS repo”, I run:

sudo add-apt-repository "http://apt.galliumos.org/"

I get

E: The repository ‘apt.galliumos.org bionic Release’ does not have a Release file. N: Updating from such a repository can’t be done securely, and is therefore disabled by default. N: See apt-secure(8) manpage for repository creation and user configuration details.

And then there is no /etc/apt/sources.list.d/galliumos.list to edit. I try to create a new one, but it wont let me place any files in that folder, and wont let me grant myself permission in it.

What am I doing wrong, here?

## sshfs troubleshooting: what would cause openssl to fail?

I believe sshfs requires an sftp server on the remote computer (router):

ipkg list_installed | grep -i sftp openssh-sftp-server - 5.9p1-1 - sftp-server only from a FREE version of the SSH protocol suite of network connectivity tools.

The goal is to invoke sshfs to mount a remote directory:

sshfs user@mydomain.asuscomm.com:/mnt/CRUZERFIT16/directory/ /home/user/Documents/scpbox/

This sshfs setup was working correctly in May, however, a family member reset the router. sshfs returns an error:

remote host has disconnected total 0

Attempt to remote sftp into router returned:

/opt/libexec/sftp-server: can't load library 'libcrypto.so.0.9.8' Connection closed

ipkg list_installed | grep openssl returned:

openssl – 0.9.8v-2 – Openssl provides the ssl implementation in libraries libcrypto and libssl, and is needed by many other applications and librari

openssl successfully reinstalled on router:

ipkg -force-reinstall install  openssl

and am now able to sftp & sshfs into target router. Not sure why openssl was unavailable before reinstalling. Is there a test command to determine if openssl is available for the sftp server?

## [ Politics ] Open Question : Does today’s GOP count on the stupidity of Trump supporters, and do Trump supporters never fail to live up to their own stupidity?

For Example: “Fox News personality Tomi Lahren insists that her line of athletic wear stands for American values despite the fact that it is made in China.” https://www.salon.com/2019/08/26/revealed-fox-news-personality-tomi-lahrens-line-of-patriot-yoga-pants-are-made-in-china/ “Lahren recently introduced the line of clothing, which includes yoga pants that have room for packing a firearm. Patriot yoga pants, which feature a pocket for a small weapon instead of a holster, sell for \$ 90. According to The Daily Mail, the clothing line is made in China. Lahren claims that purchasing her line is a way of “supporting your president, your country….” …because she knows you are stupid.

## Sound do not work and sound test fail HP notebook

I connected my ubuntu laptop to TV via HDMI and played movie. After that I disconnected and the sound do not work. I have seen the sound output is on internal speakers. But no use. I uninstalled pulseaudio . But still the issue is there. Then , i upgraded system. Still there is issue. Let me know what I can do

## What are all the Officially Published spells in 5th Edition D&D that permit a character to choose to fail their Saving Throw?

As per the title. What are all the spells

• In 5th Edition D&D,
• in any officially published sourcebook for 5e,

where a target is granted the option to deliberately fail their Saving Throw?

## JAVA DEPLOY – FAIL – Application already exists at path /MiProyecto

Estoy trabajando en un proyecto en Java ICEfaces, cuando trato de hacer deploy me da el siguiente error:

OK – Undeployed application at context path /MiProyecto In-place deployment at C:\MiProyecto\MiProyecto\build\web deploy?config=file:/C:/Users/JULIAN~1.COR/AppData/Local/Temp/3/context48767.xml&path=/MiProyecto FAIL – Application already exists at path /MiProyecto C:\MiProyecto\MiProyecto\nbproject\build-impl.xml:594: The module has not been deployed. BUILD FAILED (total time: 9 seconds)

Esto no me deja correr la aplicación.

## CORS requests for Instagram fail without VPN

My wife’s machine could not load any Instagram content through JavaScript because of the following error:

Cross-Origin Request Blocked: The Same Origin Policy disallows reading the remote resource at https://graph.instagram.com/logging_client_events. (Reason: CORS request did not succeed).

I tried getting it to work again, even went so far as to uninstalling Firefox, clearing any Mozilla related data and reinstalling it… same error (default settings, no plug-ins).

Then I noticed she had been logged out of the VPN service (just a commercial VPN service), so I logged her in without giving it much thought. Try Instagram again and… problem solved.

I tried to repeat the above on my own machine, same story:

• VPN service enabled -> everything works just fine.
• VPN service disabled -> CORS request for Instagram fail.

My Question(s):

• Is there any common explanation for this behaviour?
• Could this point to a compromised router or strange ISP activity?


text:
# Perimeter and Area worksheet for class 7

## myCBSEguide App

CBSE, NCERT, JEE Main, NEET-UG, NDA, Exam Papers, Question Bank, NCERT Solutions, Exemplars, Revision Notes, Free Videos, MCQ Tests & more.

## Perimeter and Areaworksheet for class 7 Important Topics

• 11.1 Triangles
• 11.2 Area of a parallelogram & triangle
• 11.3 Circles : Circumference & Area
• 11.4 Perimeter of Polygons
• 11.5 Conversion of units and its applications

## Some important Facts about Perimeter and Areaworksheet for class 7

1. Perimeter is the distance around a closed figure whereas area is the part of plane occupied by the closed figure.
2. We have learnt how to find perimeter and area of a square and rectangle in the earlier class. They are: (a) Perimeter of a square = 4 × side (b) Perimeter of a rectangle = 2 × (length + breadth) (c) Area of a square = side × side (d) Area of a rectangle = length × breadth
3. Area of a parallelogram = base × height

## NCERT class 7Mathematics Solved Worksheets

• Chapter 1 – Integers
• Chapter 2 – Fractions and Decimals
• Chapter 3 – Data Handling
• Chapter 4 – Simple Equations
• Chapter 5 – Lines and Angles
• Chapter 6 – Practical Geometry
• Chapter 7 – The Triangle and its Properties
• Chapter 8 – Congruence of triangles
• Chapter 9 – Comparing Quantities
• Chapter 10 – Rational numbers
• Chapter 11 – Perimeter and Area
• Chapter 12 – Algebraic Expressions
• Chapter 13 – Exponents and Powers
• Chapter 14 – Symmetry
• Chapter 15 – Visualizing Solid Shapes

## SQUARES AND RECTANGLES

Ayush and Deeksha made pictures. Ayush made his picture on a rectangular sheet of length 60 cm and breadth 20 cm while Deeksha made hers on a rectangular sheet of length 40 cm and breadth 35 cm. Both these pictures have to be separately framed and laminated. Who has to pay more for framing, if the cost of framing is  3.00 per cm? If the cost of lamination is  2.00 per cm2 , who has to pay more for lamination?

For finding the cost of framing, we need to find perimeter and then multiply it by the rate for framing. For finding the cost of lamination, we need to find area and then multiply it by the rate for lamination

To download Printable worksheets for class 7 Mathematics and Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through the best app for CBSE students and myCBSEguide website.

Test Generator

Create question papers online with solution using our databank of 5,00,000+ questions and download as PDF with your own name & logo in minutes.


text:
# Supplementary Page

This is the supplementary page for our latest paper: Generative Adversarial Network for Abstractive Text Summarization. Exhibiting competitive ROUGE scores with the state-of-the-art methods on the CNN/ Daily Mail dataset, experimental results show that our model is able to generate more abstractive, readable and diverse summaries.

Here's the test set output:

## Our Model

### Generative Model

The generator takes the source text $x=\{w_{1}, w_{2}, ..., w_{n}\}$ as input, and predict the summary $\hat{y} =\{\hat{y_{1}}, \hat{y_{2}}, ..., \hat{y_{m}}\}$. Here, the $n$ is the length of the source text $x$ and $m$ is the length of the predicted summary. We use a bi-directional LSTM encoder to convert the input text $x$ into a sequence of hidden states $h=\{h_{1},\dots,h_{n}\}$. We then use a single LSTM decoder, computing the decoding hidden states ${s_{t}}$ from the embedding vectors of ${y_{t}}$.

To prevent the model from attending over the same part of the input on different decoding steps, we first calculate the attention distribution at each decoding time step t as in (Bahdanau, Cho, and Bengio 2014):

$${e_{i}^t = v^{T}tanh(W_{h}h_{i} + W_{s}s_{t} + b_{attn})}$$

$${a^{t} = softmax(e^{t})}$$

where $v$, $W_{h}$, $W_{s}$ and $b_{attn}$ are learnable parameters. The attention distribution helps the decoder to decide which specific part of the input should be emphasized when producing the next word. Then we can calculate the context vector $c_{t}^e$ as the weighted sum of encoder hidden states and the vocabulary distribution over all words in vocabulary: $${c_{t}^e = \sum_{i=1}^n a_{i}^t h_{i}}$$ $${ P_{vocab}(\hat{y_t}) = softmax(V^{'}(V[s_{t}, c_{t}] + b) + b^{'}) }$$

where $V^{'}$, $V$, $b$, $b^{'}$ are learnable parameters. providing us with the final probability to predict word from vocabulary. Following the work of (See, Liu, and Manning 2017), we incorporate a switching pointer-generator network to use either word generator from fixed vocabulary or pointer copying rare or unseen from the input sequence. The generation probability $p_{gen}$ for each decoding step is calculated as:

$$p_{gen} = \sigma(w_{h}^T h_{t} + w_{s}^Ts_{t} + w_{x}^T x_{t} + b_{ptr})$$

Finally, we can get the probability $P(\hat{y_{t}})$ of each token in the target:

$$P(w) = p_{gen}P_{vocab}(w) + (1-p_{gen})\sum_{i:w_{i}=w} a_{i}^t$$

### Discriminative Model

The discriminator is a binary classifier and aim at distinguishing the input sequence as originally generated by humans or synthesized by machines. We encode the input sequence with a CNN as it shows great effectiveness in text classification (Kim 2014). We use multiple filters with varying window sizes to obtain multiple features and then apply a max-over-time pooling operation over the features. These pooled features are passed to a fully connected softmax layer whose output is the probability of being original.

## Updating Model Parameters

In the adversarial process, using the discriminator as a reward function can further improve the generator iteratively by dynamically updating the discriminator. Once we obtain more realistic and high quality summaries generated by generator $G$, we re-train the discriminator as:

$$\min_{\phi} -\mathbf{E}_{Y\sim p_{data}}[log D_{\phi}(Y)] - \mathbf{E}_{Y\sim G_{\theta}}[log(1- D_{\phi}(Y))] \nonumber$$

When the discriminator $D$ is obtained and fixed, we are ready to update the generator $G$. The loss function of our generator $G$ consists two parts: the loss computed by policy gradient (denoted by $J_{pg}$) and the maximum-likelihood loss (denoted by $J_{ml}$). Formally, the objective function of $G$ is $J=\beta J_{pg} + (1-\beta) J_{ml}$ , where $\beta$ is the scaling factor to balance the magnitude difference between $J_{pg}$ and $J_{ml}$.

The generator G is considered as a stochastic parameterized policy and the score assigned by the discriminator is used as reward. The generator is trained to maximize its expected end reward:

$$J_{pg}(\theta) = \sum_{t=1}^{T}G_{\theta} (y_{t}|Y_{1:t-1},X) R_{D}^{G_{\theta}}((Y_{1:t-1}, X), y_{t})$$

where $Y_{1:T} = y_{1}, . . . , y_{T}$ represents the generated target sequence, X is the given source sequence. $R_{D}^{G_{\theta}}$ is the action-value function of a target sentence. For example, after generating the first $T-1$ words, following the policy $G_{\theta}$, we take the action $Y_{T}$. We use the REINFORCE algorithm and take the estimated probability of being human generated by the discriminator D as the reward:

$$R_{D}^{G_{\theta}}((Y_{1:t-1}, X), y_{t}) = D(X, Y_{1:t}) - b(X, Y_{1:t})$$

$b({x, y})$ denotes the baseline value to reduce the variance of the reward while keeping it unbiased. Here we adjust it as the standard score among all data. Since the Discriminator can only score a fully generated sequence, following (Yu et al. 2016), we use Monte Carlo Tree Search (MCTS) to evaluate the reward for an intermediate state. The gradient of the objective function $J(\theta)$ is calculated as:

$$\triangledown J_{pg}(\theta) = \frac{1}{T} \sum_{t=1}^{T} \sum_{y_{t}} R_{D}^{G_{\theta}}((Y_{1:t-1}, X), y_{t}) \cdot \triangledown_{\theta}(G_{\theta}(y_{t}|Y_{1:t-1}, X)) \\ = \frac{1}{T} \sum_{t=1}^{T} \mathbf{E}_{y_{t}\in G_{\theta} } [R_{D}^{G_{\theta}}((Y_{1:t-1}, X), y_{t}) \triangledown_{\theta} logp(y_{t}|Y_{1:t-1}, X)] \\$$

### Loss of maximum-likelihood function

The most widely used and traditional method to train a sequence generation decoder is to minimize the a maximum-likelihood loss during each decoding step. Suppose $y^* = {y_{1}^*, y_{2}^*, ..., y_{n^{'}}^*}$ is the groud-truth summary sequence for source text sequence $x$. The maximum-likelihood training loss is: $$J_{ml}(\theta) = -\sum_{t=1}^T logp(y_{t}^* | y_{1}^*, y_{2}^*, ..., y_{t-1}^*, x )$$

## Experiment

### Implementation Details

We use two 128-dimensional LSTMs for the bidirectional encoder and one 256-dimensional LSTM for the decoder. We use a vocabulary of 50k words for both source and target. We don’t pretrain the word embeddings, they are learned from scratch with 100 dimensional embedding size. During training and at test time, the article is truncated to 400 tokens and length of the summary is limited to 100 tokens. When pretrain the generator,we use Adagrad with a batch size of 16 and a learning rate 0.15. For adversarial training, we change the learning rate to 0.001 and the batch size to 36. For discriminator, we use filter windows of 3, 4, 5 with 100 feature maps each, dropout rate of 0.5. (Kim 2014). At test time, the width of beam search is set to 5.

We also employ some strategies that improve response quality:

• Trigram Avoidance
Sequence-to-sequence models often include repetitive phrases. Repetition problem is especially pronounced when generating longer documents and summaries. We adopt the repeated trigram avoidance method proposed by (Paulus, Xiong, and Socher 2017). According to their observation, ground-truth summaries almost never contain the same trigram twice. During beam search, we force the decoder to never output token which would create a trigram that already exists in the previous sequence of the current beam.
Both the coverage model which is used by (See et al. 2017) and trigram avoidance increase Rouge by 3%. However, in experiment, trigram is less training time effective than coverage to reach a steady result and a shorter training time is very important to our model.
• Quotation Weight Alleviation
According to our observation, an appropriate summary contains few quotations from people’s conversation. Thus we lower the weight of the direct of conversation in source text during decoding. This method only increases Rouge by 0.02% which is very trivial. But it’s very helpful to boost the readability of summary.

### Experimental Results

• Rouge Evaluation
Our results are firstly evaluated by the full-length F-1 score of the ROUGE-1, ROUGE-2 and ROUGE-L metrics with the Porter stemmer option. One thing to note, for DeepRL (Paulus, Xiong, and Socher 2017), we select their RL+ML model which obtains second highest ROUGE score but produces summaries of highest readability, hence is more relevant for our summarization task. Although their RL model achieves the highest score, it can be detrimental to the model quality.

• Human Evaluation
We perform human evaluation additionally to ensure an increase in human readability and quality. We randomly select 50 test examples from the CNN / Daily Mail dataset. For each example, we show the human evaluator the ground-truth summary as well as summaries generated from different models. The human evaluator is unaware of the source of these summaries and needs to rank (1-5) each summary based on their readability. Rank 1 indicates the lowest level of readability.

• Novel n-grams
We also report the rate of novel n-grams (those that don’t appear in the article) in summaries, indicating the degree of abstraction. Compared to the pointer-generator network (See, Liu, and Manning 2017), our model has a better performance in generating novel n-grams and go beyond the simple sentence extraction. Our model only copies 30% the original article. The generated summaries remove unnecessary phrases, and truncate long sentences into meaningful short version.

### Real Summarization Examples

#### Reference Summary

wesley burton , a father-of-three and popular radio host at kpfa in berkeley , california , was killed in a hit-and-run on saturday .
he was driving home from work when a white dodge charger crashed into his silver mercury .
wife lucrecia has made an emotional plea for anyone with information about her husband ’s killer to come forward .
burton had three children aged between 4 and 9 and after growing up without a father his dream had been to raise his own kids .

#### ABS Summary

wesley burton , a popular radio host at UNK in berkeley , was killed in a hit-and-run in the early hours of saturday morning .
his wife UNK has made an emotional plea for anyone with information about her husband ’s killer to come forward .

#### PGC Summary

wesley burton , a father-of-three and popular radio host in berkeley , california , was driving home from work when a white dodge charger crashed into his silver mercury .
the crash occurred near the berkeley-oakland city line and police say the hit-and-run driver fled the on foot .
emergency personnel attempted life-saving measures , but burton was pronounced dead at the scene - just blocks from his home .

#### Our Summary

wesley burton was driving home from work when a white dodge charger crashed into his silver mercury .
crash occurred near the berkeley-oakland city line and police say the hit-and-run driver fled the on foot .
burton was pronounced dead at the scene - just blocks from his home .

#### Source Text

an 11-year-old chinese schoolboy has become mute after he drank a glass of water which had been laced with perfume and chalk dust as part of a prank . pupil xiao gao , from fujian province in south eastern china , has not said a word in five days after a classmate who had allegedly bullied him gave him the water , reports people ’s daily online . but medical experts are at a loss to explain his sudden inability to talk and say that the combination of water , perfume and dust - while nasty - should not have caused that type of damage . pupil xiao gao , aged 11 , ( pictured ) from fujian in south east china , has not spoken a word in five days after a classmate he ‘ does not get on with ’ gave him the water which had been laced with perfume and chalk dust . gao , who is in year two at haidu number 8 middle school , is now awaiting further medical examination as well as an appointment with a psychologist . school officials told reporters that after gao lost his voice the classmate who gave him the water ‘ became very afraid ’ and told teachers it was meant as a joke and that she did not think he would drink it . she said she only added perfume and chalk dust to the water - and not nail varnish as was rumoured . she said when gao drank the water his classmates told him to spit it out but by then he had already swallowed it . gao , who is a pupil at haidu number 8 middle school , ( pictured ) is now awaiting further medical examination . gao ’s form teacher was informed of his condition and immediately notified his family before taking him to hospital . the unnamed girl has now been excluded from the school . a doctor at fujian provincial hospital told reporters that in all the years he has practised medicine he has never seen a case like this before . qiu bin gaosu said as perfume consists mainly of alcohol , perfume fragrance and methanol , consuming a small amount would not impact the body , although a large amount would irritate the throat and stomach . he said consuming small amounts of chalk dust , which is nontoxic , should also not have this sort of effect . xiao gao ’s cousin told reporters that a number of doctors have seen gao and they found no physical abnormalities . gao claims the girl who gave him the water let him drink it and then said ‘ you will die after drinking this ’ . relatives told reporters that gao ’s mother was ill and his father worked at a vegetable market . they said the boy was well-behaved and doubted the condition was a hoax - particularly as he had been unable to speak for five days . his form teacher , mr lin , said gao was a little introverted , quiet and very honest and was often bullied by other children in his class . he said : ‘ whenever a teacher saw any bullying we would chastise the offender and teach them about why their behaviour was not acceptable . ’ gao ’s classroom - a doctor said that in all the years he has practised he has never seen a case like this before . through written messages gao told reporters that he was thirsty so he drank the water his classmate handed him - but after swallowing a couple of mouthfuls he realised something was n’t right . he claims it was then the girl took away the water and said ‘ you will die after drinking this . ’ gao told reporters that he did n’t get along with the classmate who handed him the water . the story has gone viral in china and has been reported on all the main news websites . the people ’s daily reported that the local public security bureau has sta rted an investigation into the incident .

#### Reference Summary

schoolboy xiao gao , 11 , drank water spiked with perfume and chalk dust .
he has not spoken since the prank which went wrong five days ago .
doctors ca n’t explain sudden voice loss and think it may be psychological .

#### ABS Summary

xiao gao , from fujian province , has not said a word in five days .
but medical experts are at a loss to explain his sudden inability to talk .
but medical experts are at a loss to explain his sudden inability to talk .

#### PGC Summary

pupil xiao gao has not said a word in five days after a classmate he ‘ does not get on with ’ gave him the water which had been laced with perfume and chalk dust .
but medical experts are at a loss to explain his sudden inability to talk and say that the combination of water , perfume and dust - while nasty - should not have caused that type of damage .

#### Our Summary

xiao gao , 11 , drank a glass of water which had been laced with perfume and chalk dust .
medical experts are at a loss to explain his sudden inability to talk and say that the combination of water , perfume and dust - while nasty - should not have caused that type of damage .
gao , who is in year two at haidu number 8 middle school , is now awaiting further medical examination as well as an appointment with a psychologist .

#### References

[1] Bahdanau, D.; Cho, K.; and Bengio, Y. 2014. Neural machine translation by jointly learning to align and translate. arXiv preprint arXiv:1409.0473.
[2] See, A.; Liu, P. J.; and Manning, C. D. 2017. Get to the point: Summarization with pointer-generator networks. arXiv preprint arXiv:1704.04368.
[3] Kim, Y. 2014. Convolutional neural networks for sentence classification. arXiv preprint arXiv:1408.5882.
[4] Yu, L.; Zhang, W.; Wang, J.; and Seqgan, Y. Y. 2016. Sequence generative adversarial nets with policy gradient. arXiv preprint arXiv:1609.05473 2(3):5.
[5] Paulus, R.; Xiong, C.; and Socher, R. 2017. A deep reinforced model for abstractive summarization. arXiv preprint arXiv:1705.04304.


text:
# Hexagon, coordinates, base

#### Petrus

##### Well-known member
Consider a regular hexagon ABCDEF (in order counterclockwise). Determine the coordinates of AB, AE AND AF (->) in the base (AC, AD) (->)

AB(->)=(_____,_____)
AE(->)=(_____,_____)
AF(->)=(_____,_____)

what I mean with exemple AF(->) positive way from A to F. I have draw a it but I got problem to rewrite
I got AE=EF+FA(->) I am correct?

Last edited:

#### Petrus

##### Well-known member
Re: hexagon, coordinates, base

I could uppload picture from internet but it should be insted of F it should B. In ourder counterclockwise. Well I can rewrite AE=EF+FA (->)

#### HallsofIvy

##### Well-known member
MHB Math Helper
Re: hexagon, coordinates, base

No, you have the order wrong: AE= AF+ FE.

#### Petrus

##### Well-known member
Re: hexagon, coordinates, base

No, you have the order wrong: AE= AF+ FE.
Yeah I forgot to Edit. How do I do for AF and AB? Then I got Also My base.

#### Petrus

##### Well-known member
Re: hexagon, coordinates, base

So I draw it.
We know from origo to A it is 1 and origo to D it is 1.

#### Petrus

##### Well-known member
I think I have thought wrong...
We got the base AC and AD and I put $$\displaystyle AC=(1,0)$$ and $$\displaystyle AD(0,1)$$
We know that $$\displaystyle AC=AB+BC$$ ( ->) that means $$\displaystyle AB=AC-BC <=> AB=AC-BC$$ and we know that $$\displaystyle AC=(1,0)$$ That means $$\displaystyle AB=(1,0)-BC$$ But is BC same as from A to origo?

#### Petrus

##### Well-known member
So I did wrong... After alot reading I think I got correct progress now...
We know it says regular hexagon that means from origo to any point got the lenght 1.
A circle is 360 degree and we got 8 lines. $$\displaystyle \frac{360}{8}=45$$ So we got now (look picture). we know x value is cos and y value is sin so we know
$$\displaystyle A=(1,0)$$
$$\displaystyle B=(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}})$$
$$\displaystyle C=(-\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}})$$
$$\displaystyle D=(-1,0)$$
$$\displaystyle E=(-\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}})$$
$$\displaystyle F=(\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}})$$
That means
$$\displaystyle AC=(-\frac{1}{\sqrt{2}}-1,\frac{1}{\sqrt{2}})$$
$$\displaystyle AD=(-2,0)$$
----
$$\displaystyle AB=(\frac{1}{\sqrt{2}}-1,\frac{1}{\sqrt{2}})$$
$$\displaystyle AE=(-\frac{1}{\sqrt{2}}-1,-\frac{1}{\sqrt{2}})$$
$$\displaystyle AF=(\frac{1}{\sqrt{2}}-1,-\frac{1}{\sqrt{2}})$$
So now I got all point but got problem to determine our cordinate with our base.

Last edited:


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# Sum of central binomial coefficients

I was summing up some central binomial coefficients - those of the form $$\binom{2n}{n}$$ when I noticed that $$3^{2k}$$ divides $$\sum\limits _{n=0}^{3^k-1}\binom{2n}{n}$$ and is the highest power of 3 to do so i.e. $$3^{2k+1}$$ does not.

I have verified this statement for k up to 6. Can anyone find a counterexample, or have an idea how to prove this?

Note by Ivan Stošić
4 years, 12 months ago

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Your conjecture is actually true. As illustrated in this article, the following holds $v_3\left (\sum_{k=0}^{n-1}\binom{2k}{k}\right)=v_3\left (\binom{2n}{n}\right)+2v_3(n)$

where $$v_3(n)$$ is equal to the exponent of $$3$$ in the prime factorization of $$n$$.

Your result is a direct corollary of this fact.

- 4 years, 12 months ago

Does anybody have an elementary argument? Or an elementary introduction to $$p$$-adic numbers? Could a combinatorial argument use the facts that $$3^k -1 = 2(1+3+3^2+\cdots+3^{k-1})$$ and $$3^{2k} = 9^k = (1+8)^k = \sum_j \binom{k}{j} 8^j$$ ?

- 4 years, 11 months ago


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# Are 4e monsters compatible/level equivalent without adjustment in Gamma World?

I plan on running a brief Gamma World campaign with my group, and I am wondering if 4E monsters are compatible between systems without any sort of level adjustment? From a quick perusal, it seems like PCs are considerably more powerful than 4e characters of equivalent level: adding level rather than 1/2-level to rolls, alpha mutations/tech cards, major critical bonuses, hit points are restored with a short rest, etc. At the same time they are much less "survivable": the only reliable healing is through second wind, no specialized leader roles. To be equally challenging should I treat the party as a few levels higher when building an encounter with 4e monsters? Any advice would be appreciated!

D&D 4E and Gamma World encounters can be used almost as is in the other game

Characters in Gamma World dish out more damage, and are a bit more brittle than their 4e equivalents, but that just makes fights a bit more swingy and a run a bit faster.

D&D 4E and Gamma World monsters can be used almost as is in the other game

Comparing some monsters in the two games

Gamma Word

Porker Marauder 100XP
Level 1 Soldier, 29 HP, AC 17, NADs 16, 13, 12
Melee Basic: +6 vs AC, 2d6+1 damage

Sep Thresher 200XP
Level 5 Brute, 75 HP, AC 17, NADs 18, 16, 16
Melee Basic: +10 vs AC, 2d6+6 damage

D&D 4E, Monster Vault

Dwarf Clan Guard 100XP
Level 1 Soldier, 33 HP, AC 17, NADs 15, 15, 13
Melee Basic: +6 vs AC, 1d10+3 damage

Ravenous Ghoul 200XP
Level 5 Brute, 76 HP, AC 17, NADs 18, 17, 15
Melee Basic: +10 vs AC, 3d8+4 damage

Also see this Extreme Reskinning article for an example of reskinning a white dragon from the Monster Vault into a cyborg assassin for Gamma World.


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# Antimatching in revolving door graph

$$RD^d$$ is bipartite graph in which the vertices are $$(d−1)$$-element subsets and $$d$$-element subsets of a $$(2d−1)$$-element ground set. Two vertices are adjacent if one of the corresponding sets is a subset of the other.

My question is why any edge together with its incident edges defines an antimatching of $$2d-1$$ edges? And why $$2d-1$$?

Answer probably is related to the fact that this graph is $$d$$-regular but I have problem to justify it.

Let $$G$$ be a $$d$$-regular bipartite graph. And let $$e_{uv}$$ be an edge of $$G$$.

Let $$S$$ the set of $$e_{uv}$$ and all its adjacent edges. Then the size of $$S$$ is $$2d-1$$ : They are $$d$$ edges connected at the vertex $$u$$, and $$d$$ connected at vertex $$v$$. As we double count $$e_{uv}$$, we reduce the count by one, and $$|S|=2d-1$$.

Recall that an antimatching $$A$$ of $$G$$ is a set of edges such that two edges are at most at distance 2, and that the distance between two edges is defined as the distance between corresponding vertices in $$L(G)$$ (the Line graph of $$G$$).

As all edges from $$S$$ are connected to $$e_{uv}$$, then the maximum distance between edges of $$S$$ is 2.

Therefore $$S$$ is an antimatching of size $$2d-1$$.

I think that's all to proove. (I never studied antimatching before, I might be missing something).

Note An antimatching can also be defined (equivalently) as a subgraph with no induced matching of size greater than 1. This is also clearly the case for $$S$$ :

Suppose there exist an induced matching of size 2 in $$S$$. Then it must contains one edge connected to $$u$$ and one connected to $$v$$. But then in order to be induced we would need to include $$e_{uv}$$, and would not be a matching. Hence a contradiction. Therefore the only induced matching of $$S$$ have size 1.


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Browse Questions

# $E^o_{Zn^{+2}/Zn}=0.76V,E^o_{Cu^{+2}/Cu}=0.34V$ find $\Delta G^orx_n$ of following cell $Zn/Zn^{+2}\parallel Cu^{+2}/Cu$

$\begin{array}{1 1}(a)\;200KJ\\(b)\;106.15KJ\\(c)\;212.3KJ\\(d)\;424.6KJ\end{array}$

Can you answer this question?

Cell $rx_n$ will be
$Zn+Cu^{+2}\rightleftharpoons Zn^{+2}+Cu$
$E^o_{cell}=-E^oZn^{+2}/zn+E^o_{Cu^{+2}/Cu}$
$\Rightarrow 0.76+0.34$
$\Rightarrow 1.1V$
$\Delta G^o=-nFE^0_{cell}$
$n=2$
$\Delta G^o=-2\times 96500\times 1.1J$
$\qquad=212.3KJ$
Hence (c) is the correct answer.
answered Dec 10, 2013


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### Home > PC > Chapter 8 > Lesson 8.1.1 > Problem8-16

8-16.

Multiply each term by 3.

Multiply each term by −2.

Divide each term by 5.

$\text{Substitute for each } x \text{ in the function the expression }\frac{x}{5}.$


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# Quark Matter 2018

13-19 May 2018
Venice, Italy
Europe/Zurich timezone
The organisers warmly thank all participants for such a lively QM2018! See you in China in 2019!

## Dijet, dihadron and hadron-jet correlations in resummation improved pQCD approach

15 May 2018, 17:00
2h 40m
First floor and third floor (Palazzo del Casinò)

### First floor and third floor

#### Palazzo del Casinò

Poster Correlations and fluctuations

### Speaker

Hanzhong Zhang (IOPP, CCNU)

### Description

Dijet, dihadron and hadron-jet angular correlations as well as dijet transverse momentum asymmetry have been reckoned as important probes of the transverse momentum broadening effects in relativistic nuclear collisions [1,2]. Dijets become de-correlated due to the vacuum soft gluon radiation associated with the Sudakov logarithms and the medium-induced transverse momentum broadening.

We first employ the systematic Sudakov resummation formalism to describe the dihadron and hadron-jet angular correlation data in $pp$ and central $AA$ collisions [1]. For a quark jet at RHIC top energy, a global $\chi^2$ analysis of dihadron and hadron-jet angular correlation data renders the best fit for the medium-induced broadening $\langle p_\perp^2\rangle$ and the so-called jet transport coefficient $\hat q$ in central $AA$ collisions.

Then we develop a systematic theoretical approach to dijet asymmetries in $pp$ collisions based on pQCD expansion and Sudakov resummation formalism [2]. We find that the NLO pQCD calculation is indispensable to describe experimental data, while the resummation formalism is vital near the end points where the pQCD expansion fails to converge due to appearance of large Sudakov logarithms. Utilizing our resummation-improved pQCD approach, we extract jet transport coefficient for quark-gluon plasma in $PbPb$ collisions at 2.76A~TeV.

We can also use this method to study the properites of cold nuclear matter and other related topics [3].

Further experimental and theoretical efforts along the direction of this work shall significantly advance the quantitative understanding of transverse momentum broadening and help us acquire precise knowledge of jet quenching parameter in heavy-ion collisions.

[1] L. Chen, G. Y. Qin, S. Y. Wei, B. W. Xiao and H. Z. Zhang, Phys. Lett. B 773, 672 (2017).
[2] L. Chen, G. Y. Qin, S. Y. Wei, B. W. Xiao and H. Z. Zhang, arXiv:1612.04202 [hep-ph].
[3] L. Chen, G. Y. Qin, S. Y. Wei, B. W. Xiao and H. Z. Zhang, in preparing.

Content type Theory Presenter name already specified

### Primary authors

Bowen Xiao (Central China Normal University) Hanzhong Zhang (IOPP, CCNU) Guang-You Qin (Central China Normal University) Dr Shu-yi Wei (Ecole Polytechnique) Mr Lin Chen (Central China Normal University)


text:
# A ball is tossed...

• Oct 11th 2009, 04:28 PM
mathcalculushelp
A ball is tossed...
A ball is tossed straight up into the air from a bridge,and its height above the ground t seconds after it is thrown is

f(t)=-16t^2 + 108t + 82 feet.

a.How high above the ground is the bridge?

b. Write a function A(b) that gives the average velocity of the ball from t=0 to t=b seconds.Use the function to calculate the average velocity of the ball the first two seconds it is in the air.
• Oct 11th 2009, 04:32 PM
pickslides
Quote:

Originally Posted by mathcalculushelp
A ball is tossed straight up into the air from a bridge,and its height above the ground t seconds after it is thrown is

f(t)=-16t^2 + 108t + 82 feet.

a.How high above the ground is the bridge?

Find $f(0)$
• Oct 11th 2009, 04:39 PM
Arturo_026
for b)

A(b) = (f(0) - f(b)) / (0 - b)

plug values and simplify
• Oct 11th 2009, 04:50 PM
mathcalculushelp
Help me find t...?
-16t^2 + 180t + 48...??

I am getting stuck at finding t.

Iam not able to get the factors.If I use -b_+sq rt b^2 -4ac/2a then I get complicated ans.

How should I find t?
• Oct 11th 2009, 04:53 PM
Arturo_026
I think you need to find f(0) not f(t)=0

-16(0)^2 + 180(0) + 48 = f(0) , that's how high the ball is


text:
## CRL Task 3: Counterfactual Decision Making

In the previous blog post we discussed some theory of how to select optimal and possibly optimal interventions in a causal framework. For those interested in the decision science, this blog post may be more inspiring. This next task involves applying counterfactual quantities to boost learning performance. This is clearly very important for an RL agent where its entire learning mechanism is based on interventions in a system. What if intervention isn’t possible? Let’s begin!

## This Series

1. Causal Reinforcement Learning
2. Preliminaries for CRL
3. CRL Task 1: Generalised Policy Learning
4. CRL Task 2: Interventions – When and Where?
5. CRL Task 3: Counterfactual Decision Making
6. CRL Task 4: Generalisability and Robustness
7. Task 5: Learning Causal Models
8. (Coming soon) Task 6: Causal Imitation Learning
9. (Coming soon) Wrapping Up: Where To From Here?

## Counterfactual Decision Making

A key feature of causal inference is its ability to deal with counterfactual queries. Reinforcement learning, by its nature, deals with interventional quantities in a trial-and-error style of learning.…

## CRL Task 2: Interventions – When and Where?

In the previous blog post we discussed the gorey details of generalised policy learning – the first task of CRL. We went into some very detailed mathematical description of dynamic treatment regimes and generalised modes of learning for data processing agents. The next task is a bit more conceptual and focuses on the question on how to identfy optimal areas of intervention in a system. This is clearly very important for an RL agent where its entire learning mechanism is based on these very interventions in some system with a feedback mechanism. Let’s begin!

## This Series

1. Causal Reinforcement Learning
2. Preliminaries for CRL
3. CRL Task 1: Generalised Policy Learning
4. CRL Task 2: Interventions – When and Where?
5. CRL Task 3: Counterfactual Decision Making
6. CRL Task 4: Generalisability and Robustness
7. Task 5: Learning Causal Models
8. (Coming soon) Task 6: Causal Imitation Learning
9. (Coming soon) Wrapping Up: Where To From Here?

## CRL Task 1: Generalised Policy Learning

In the previous blog post we developed some ideas and theory needed to discuss a causal approach to reinforcement learning. We formalised notions of multi-armed bandits (MABs), Markov Decision Processes (MDPs), and some causal notions. In this blog post we’ll finally get to developing some causal reinforcement learning ideas. The first of which is dubbed Task 1, for CRL can help solve. This is Generalised Policy Learning. Let’s begin.

## This Series

1. Causal Reinforcement Learning
2. Preliminaries for CRL
3. CRL Task 1: Generalised Policy Learning
4. CRL Task 2: Interventions – When and Where?
5. CRL Task 3: Counterfactual Decision Making
6. CRL Task 4: Generalisability and Robustness
7. Task 5: Learning Causal Models
8. (Coming soon) Task 6: Causal Imitation Learning
9. (Coming soon) Wrapping Up: Where To From Here?

## Generalised Policy Learning

Reinforcement learning typically involves learning and optimising some policy about how to interact in an environment to maximise some reward signal. Typical reinforcement learning agents are trained in isolation, exploiting copious amounts of computing power and energy resources.…

## Preliminaries for CRL

In the previous blog post we discussed and motivated the need for a causal approach to reinforcement learning. We argued that reinforcement learning naturally falls on the interventional rung of the ladder of causation. In this blog post we’ll develop some ideas necessary for understanding the material covered in this series. This might get quite technical, but don’t worry. There is still always something to take away. Let’s begin.

## This Series

1. Causal Reinforcement Learning
2. Preliminaries for CRL
3. CRL Task 1: Generalised Policy Learning
4. CRL Task 2: Interventions – When and Where?
5. CRL Task 3: Counterfactual Decision Making
6. CRL Task 4: Generalisability and Robustness
7. Task 5: Learning Causal Models
8. (Coming soon) Task 6: Causal Imitation Learning
9. (Coming soon) Wrapping Up: Where To From Here?

## Preliminaries

As you probably recall from high school, probability and statistics are almost entirely formulated on the idea of drawing random samples from an experiment. One imagines observing realisations of outcomes from some set of possibilities when drawing from an assortment of independent and identically distributed (i.i.d.) events.…

## Causal Reinforcement Learning: A Primer

As part of any honours degree at the University of Cape Town, one is obliged to write a thesis ‘droning’ on about some topic. Luckily for me, applied mathematics can pertain to pretty much anything of interest. Lo and behold, my thesis on merging causality and reinforcement learning. This was entitled Climbing the Ladder: A Survey of Counterfactual Methods in Decision Making Processes and was supervised by Dr Jonathan Shock.

In this series of posts I will break down my thesis into digestible blog chucks and go into quite some detail of the emerging field of Causal Reinforcement Learning (CRL) – which is being spearheaded by Elias Bareinboim and Judea Pearl, among others. I will try to present this in such a way as to satisfy those craving some mathematical detail whilst also trying to paint a broader picture as to why this is generally useful and important. Each of these blog posts will be self contained in some way.…

## Covid-19 tests: probabilities

Bayes’ Theorem is applied to medical tests, to calculate the probability of being infected with a virus, given a positive or negative test result. What drives the uncertainty is false negative results, or false positive results. In this article, I give a practical outline as to how one can interpret one’s test result, after calculating the relevant probability using Bayes’ Theorem.

To start off with, we need two estimates. For a negative covid-19 test, we need the rate of false negative results, and the current actual prevalence of the disease in the community. On the other hand, for a positive covid-19 test, we need the rate of false positives, and the current prevalence of the disease. False outcomes in tests vary according to the laboratory doing the test, and probably also the skill with which each individual test is carried out, but, for the sake of a rational understanding of the usefulness of these tests, we can use common statistics to calculate feasible probabilities.…

By | January 1st, 2021|News|0 Comments

## A simple introduction to causal inference

Introduction

Causal inference is a branch of Statistics that is increasing in popularity. This is because it allows us to answer questions in a more direct way than do other methods. Usually, we can make inference about association or correlation between a variable and an outcome of interest, but these are often subject to outside influences and may not help us answer the questions in which we are most interested.

Causal inference seeks to remedy this by measuring the effect on the outcome (or response variable) that we see when we change another variable (the ‘treatment’). In a sense, we are looking to reproduce the situation that we have when we do an designed experiment (with a ‘treated’ and a ‘control’ group). The goal here is to have groups that are otherwise the same (with regard to factors that might influence the outcome) but where one is ‘treated’ and the other is not.…

## Correlation vs Mutual Information

This post is based on a (very small) part of the (dense and technical) paper Fooled by Correlation by N.N. Taleb, found at (1)

Notes on the main ideas in this post are available from Universidad de Cantabria, found at (2)

The aims of this post are to 1) introduce mutual information as a measure of similarity and 2) to show the nonlinear relationship between correlation and information my means of a relatively simple example

Introduction

A significant part of Statistical analysis is understanding how random variables are related – how much knowledge about the value of one variable tells us about the value of another. This post will consider this issue in the context of Gaussian random variables. More specifically, we will compare- and discuss the relationship between- correlation and mutual information.

Mutual Information

The Mutual Information between 2 random variables is the amount of information that one gains about a random variable by observing the value of the other.…

## The Objective Function

In both Supervised and Unsupervised machine learning, most algorithms are centered around minimising (or, equivalently) maximising some objective function. This function is supposed to somehow represent what the model knows/can get right. Normally, as one would expect, the objective function does not always reflect exactly what we want.

The objective function presents 2 main problems: 1. how do we minimise it (the answer to this is up for debate and there is lots of interesting research about efficient optimisation of non-convex functions and 2) assuming we can minimise it perfectly, is it the correct thing to be minimising?

It is point 2 which is the focus of this post.

Let’s take the example of square-loss-linear-regression. To do so we train a linear regression model with a square loss $\mathcal{L}(\mathbf{w})=\sum_i (y_i - \mathbf{w}^Tx_i)^2$. (Where we are taking the inner product of learned weights with a vector of features for each observation to predict the outcome).…


text:
# Use specific non-unicode character in lualatex

I've looked everywhere for an answer to this question, but none could answer this specific one:

I have MinionMath font (from typoma.com, MinionMath-Regular.otf) and I want to use unicode f3a0f (under "Supplementary Private Use Area-A") but I have no idea how to get it using LuaLaTeX. I can't just use \symbol{"f3a0f} as that doesn't work... Not sure what to do.

This is a pdf file that has all the symbols. I want to use symbol f3a0f (top right of page 19) specifically (and yes, I'm aware it looks similar to |, but I want to use this particular one). I did take a look at this question but for some reason there just is no temp-minionmath file at all in the .log file. I have also looked at a number of other questions but they don't seem to work :(

I need to use LuaLaTeX only, I know how to do this in XeTeX, but I absolutely 100% need it in LuaLaTeX unfortunately. Any help would be appreciated.

Edit: Here is some "compilable" code (This is a pretty basic question so really I want to be able to use this symbol with this code as a bare minimum...)

\documentclass{article}
\usepackage{unicode-math}
\setmathfont{MinionMath-Regular.otf}
\begin{document}
$󶆽$
\end{document}

EDIT 2: It now appears I have located the MinionMath-Regular.lua file after all thanks to @UlrikeFischer 's comment, and when I find the corresponding symbol number for F3A0F (\symbol{983854}) and type that into the file / compile with LuaLaTeX, that indeed works. Now I guess the question is, how come a simpler method such as \char{"F3A0F} or ^^^^^f3a0f doesn't work with LuaLaTeX, when it should? I'd rather not have to search through the .lua file for a corresponding symbol number each time.

• Just to start, you could say how to do it in XeTeX which might help others in the future. And, as always, an small piece of compilable code is welcome (or not compilable, in this case). That way you remove the burden from other users to write the basic document to start with your problem. Welcome to TeX.SE by the way! – Manuel Nov 21 '14 at 1:33
• Hi @Manuel , this question shows how to generate a table of glyphs with XeTeX. Also, I'm not sure how useful the code would be since the question is very very basic, but sure I'll put it in. – airatin Nov 21 '14 at 1:39
• Yes, there is no longer a temp-...lua mentioned in the log-file - luaotfload has dropped this prefix. But there should be quite a lot of luaotfload messages and also the name and the path of the cache file of the font. In this folder you should find .lua and .luc (packed) files. Use the .lua file to find your symbol. – Ulrike Fischer Nov 21 '14 at 7:57
• @UlrikeFischer when I search the log file for anything that has ".lua" in it, I don't find anything that looks like "MinionMath.lua" or anything of the sort. I find plenty of .lua files but none that have MinionMath or similar for some reason... – airatin Nov 21 '14 at 11:36
• @UlrikeFischer wow... I just looked at the log file and you're right, there is a MinionMath-Regular.luc file that shows, and if I go to that file location I can find the corresponding .lua file!! So I copied that unicode's corresponding number (\symbol{983854}) and it works when written into LuaLaTeX! I can't believe I didn't try this before, thank you! Now I just wish there was some easier way for me to do this without having to look for the symbol in this file... Ah well. – airatin Nov 21 '14 at 11:51

Well, Private Use Areas are part of Unicode, they just have no predefined meaning. So you can use them like any other character, e.g. by simply typing it (if you have an appropriate input method) or using the character code either as \char"F3A0F or ^^^^^f3a0f.
• actually it turns out I could locate MinionMath-Regular.lua file and find the unicode's corresponding number (\symbol{983854}); using that, the symbol appears in LuaLaTeX. But I'm curious as to why the \char or ^^^^^ method doesn't work for LuaLaTeX when it should, would be a lot easier to use that method instead of searching the .lua file each time... Was wondering if you had any idea how come it doesn't work? If not, I'll have to use this, but thank you anyway! – airatin Nov 21 '14 at 11:55


text:
Last edited by Shaktikora
Tuesday, May 19, 2020 | History

3 edition of Long range forecasting using a combined state variable and stochastic network model found in the catalog.

Long range forecasting using a combined state variable and stochastic network model

Robert S. Sullivan

# Long range forecasting using a combined state variable and stochastic network model

## by Robert S. Sullivan

Written in English

Subjects:
• Forecasting -- Mathematical models.

• Edition Notes

Includes bibliographical references.

Classifications The Physical Object Statement Robert S. Sullivan, George B. Kleindorfer, Jack C. Hayya. Series Working paper - Graduate School of Business, University of Texas at Austin ; 78-62, Working paper (University of Texas at Austin. Graduate School of Business) ;, 78-62. Contributions Kleindorfer, George B., joint author., Hayya, Jack C., joint author. LC Classifications H61.4 .S94 Pagination 10 p. ; Number of Pages 10 Open Library OL4069847M LC Control Number 79623636

variable or a series of variables. Quantitative Methods of Forecasting –There is a causal relationship between the variable to be forecast and another variable or a series of variables. (Demand is based on the policy, e.g. cement, and build material. series –The variable to be forecast has behaved according to a specific File Size: KB. The ECMWF model, the Ensemble Prediction System (EPS), uses a combination of singular vectors and an ensemble of data assimilations (EDA) to simulate the initial probability density. The singular vector perturbations are more active in the extra-tropics, while the EDA perturbations are .

Forecasting in STATA: Tools and Tricks. Introduction. This manual is intended to be a reference guide for time-series forecasting in STATA. Working with Datasets. If you have an existing STATA dataset, it is a file with the extension “.dta”. If you double-click on the file, it will typically open a STATA window and load the datafile into. change over time. These are combined into a state vector X (a vector is an ordered list of numbers). • The dynamic equations: a set of equations or rules specifying how the state variables change over time, as a function of the current and past values of the state variables. A model’s dynamic equations may also include a vector E of File Size: KB.

3 Understanding Forecast Levels and Methods. This chapter contains the following topics: Use this method with caution because long range forecasts are leveraged by small changes in just two data points. A long term forecast is less accurate than a short term forecast because the further into the future you project the forecast, the more. Because we are examining the differenced time series, we have to use the combined model ARIMA (Autoregressive integrated moving average); thus, our model so far is ARIMA(0, 1, 1). Build a Model. Our findings in the exploratory analysis phase suggest that model ARIMA(0, 1, 1) might be the best fit.

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### Long range forecasting using a combined state variable and stochastic network model by Robert S. Sullivan Download PDF EPUB FB2

State Space Models. SSMs model the temporal structure of the data via a latent state l t 2RL that can be used to encode time series components such as level, trend, and seasonality patterns.

In the forecasting setting they are typically applied to individual times series (though multivariate exensions with multi-dimensional targets exist).

In this study, linear stochastic models known as ARIMA and multiplicative Seasonal Autoregressive Integrated Moving Average (SARIMA) models were used to forecast.

The forecasts are obtained by a linear combination of the inputs. The weights are selected in the neural network framework using a “learning algorithm” that minimises a “cost function” such as the MSE. Of course, in this simple example, we can use linear regression which is a much more efficient method of training the model.

Which variables are used for short-range forecasting, long-range forecasting, or for sful organizations are also those who are able to make relatively accurate forecasts about the future needs (inventory, facilities, capacity, manufacturing, manpower).

The basic idea of the model combination in forecasting is to use each model's unique feature to capture different patterns in the data. Both theoretical and empirical findings suggest that combining different methods can be an effective and efficient way to improve forecasts.

In neural network forecasting research, a number of combining Cited by: Combining time series models for forecasting Hui Zoua, Yuhong Yangb,* aDepartment of Statistics, Sequoia Hall, Stanford University, Stanford, CAUSA bDepartment of Statistics, Snedecor Hall, Iowa State University, Ames, IAUSA Abstract Statistical models (e.g., ARIMA models) have commonly been used in time series data analysis and forecasting.

Typically, you will ﬁt your equations in Stata and use forecast estimates to add them to the model. forecast coefvector is used to add equations obtained elsewhere.

zero or more exogenous variables declared using forecast exogenous. at least one stochastic equation or identity. optional adjustments to be made to the variables of the model declared using forecast Size: KB.

Time series modeling and forecasting has fundamental importance to various practical domains. Thus a lot of active research works is going on in this subject during several years. Many important models have been proposed in literature for improving the accuracy and effeciency of time series modeling and by: A forecasting model has produced the following forecasts: Period / Demand / Forecast January / / February / / March / / April / / May / / The mean absolute percentage deviation (MAPD) for the end of May is _____.

Ana Russo et al., [8] author uses the stochastic variables to train the artificial neural networks for predicting the air forecasts. The stochastic variable reduces the training time and provide. While there are a wide range of frequently used quantitative budget forecasting tools, in this article we focus on the top four methods: (1) straight-line, (2) moving average, (3) simple linear regression, and (4) multiple linear regression.

An optimized model using LSTM network for demand forecasting. Author links open overlay panel Hossein Abbasimehr a The main difference between an RNN and LSTM is that LSTM can store long-range time dependency information and can suitably map The aim of this study is to obtain an accurate model for demand forecasting of a furniture.

Its application in forecasting Greek long-term energy consumption for the years ahead is reported in [10]. Ref. [11] used ANN on the Egyptian electrical network for long-term peak load forecasting. Ref. [12] reported the superiority of ANN for medium and long-term load forecasting in Cited by: 4.

variables. Journal of the American Statistical Association 18–31 M. Watson Time Series: Economic Forecasting Time-series forecasts are used in a wide range of economic activities, including setting monetary and ﬁscal policies, state and local budgeting, ﬁnancial management,mentsFile Size: 72KB.

Chapter 2. Forecasting “Analysts predicted in that one million mobile phones would be used worldwide by the year They were wrong by million.” Kurt Hellstrom, president of Ericsson, in an address to Comdex (PC Magazine, Jan, p.

72). Introduction Forecasting is an essential and basic activity in any planning. Forecasting in STATA: Tools and Tricks Introduction This manual is intended to be a reference guide for time‐series forecasting in STATA. It will be updated periodically during the semester, and will be available on the course website.

Working with variables in STATA. Forecasting and estimation of causal effects are quite different objectives. For forecasting, o R2 matters (a lot!) o Omitted variable bias isn’t a problem.

o We will not worry about interpreting coefficients in forecasting models o External validity is paramount: the model estimated using historical data must hold into the (near) future. Forecasts used for new product planning, capital expenditures, facility location or expansion, and R&D typically utilize a a.

short-range time horizon b. medium-range time horizon c. long-range time horizon d. naive method, because there is no data history e.

all of the above. Prediction intervals. As discussed in Sectiona prediction interval gives an interval within which we expect $$y_{t}$$ to lie with a specified probability. For example, assuming that the forecast errors are normally distributed, a 95% prediction interval for the $$h$$-step forecast is $\hat{y}_{T+h|T} \pm \hat\sigma_h,$ where $$\hat\sigma_h$$ is an estimate of the standard.

Forecasting from a Regression Model There are several reasons why we estimate regression models, one of them being to generate forecasts of the dependent variable. I'm certainly not saying that this is the most important or the most interesting use of such models.

# Create cell state and hidden state variables to maintain the state of the LSTM c, h = [],[] initial_state = [] for li in range(n_layers): (le(([batch_size, num_nodes[li]]), trainable=False)) (le(([batch_size, num_nodes[li]]), trainable=False)) (ateTuple.

## Series modelled in differences: D1. ## Univariate lags: (1,2,3,4,5,6,7,8,10,12) ## Deterministic seasonal dummies included. ## Forecast combined using the median operator.

## MSE: The output indicates that the resulting network has 5 hidden nodes, it was trained 20 times and the different forecasts were combined using the median. An overview of time series forecasting models. This kind of forecast assumes that the stochastic model generating the time series is a random walk.

An extension of the Naïve model is given by the SNaïve The state of a LSTM network is represented through a state space : Davide Burba.


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# expected time to enter a state in birth-death process

I have a question regrading the expected time of entering a state in a birth-death process. Specifically I don't quite understand Page 378 Equation 6.3 of the book here.

In it, it says if the birth rate is $$\lambda_i$$, and death rate is $$\mu_i$$, if we define $$T_i$$ to be the time from state $$i$$ to state $$i+1$$ ( in this case the state i means population is of size i at time T). Then it says if we condition on whether the first transition from i is to i-1, or i+1, we could calculate the expected value of $$T_i$$.

Define: $$I_i = 1$$ if the first transition out of i is to i+1. And $$I_i = 0$$ if the first transition out of i is to i-1.

Then it says $$E(T_i|I_i=1) = \frac{1}{\lambda_i + \mu_i}$$.

I thought the expected Time to ANY event (in this case, either death or birth) would be $$\frac{1}{\lambda_i + \mu_i}$$ and expected time to birth be $$\frac{1}{\lambda_i}$$.

So if given $$I_i = 1$$, shouldn't expected time to the next state be the expected time to the birth event? i.e. shouldn't $$E(T_i|I_i=1) = \frac{1}{\lambda_i}$$?

But professor sheldon ross (the author) is saying it is $$E(T_i|I_i=1) = \frac{1}{\lambda_i + \mu_i}$$. Could someone kindly explain about my misunderstanding?

thanks

• $I_i=1$ doesn't mean that the next event is a birth. $I$ stands for the direction of the first transition from that state. – gunes Dec 5 '18 at 14:43
• Hello gunes, but could you explain more about what you means by "the direction of the first transition"? and how the $E(T_i | I_i=1)$ arrives at $\frac{1}{\lambda_i + \mu_i}$ – john_w Dec 7 '18 at 6:59