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# CERN Preprints

2020-09-28
04:16
 The energy-dependent $\pi^+ \pi^+ \pi^+$ scattering amplitude from QCD / Hansen, Maxwell T. (CERN) ; Briceño, Raul A. (Jefferson Lab ; Old Dominion U.) ; Edwards, Robert G. (Jefferson Lab) ; Thomas, Christopher E. (Cambridge U., DAMTP) ; Wilson, David J. (Cambridge U., DAMTP) Focusing on three-pion states with maximal isospin ($\pi^+\pi^+\pi^+$), we present the first non-perturbative determination of an energy-dependent three-hadron scattering amplitude from first-principles QCD. [...] arXiv:2009.04931. - 22 p. Fulltext

2020-09-27
12:32
 Search for strong electric fields in PbPb collisions at ${\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} =$ 5.02 TeV using azimuthal anisotropy of prompt ${\mathrm{D^0}}$ and ${\mathrm{\overline{D}}{}^0}$ mesons The strong Coulomb field created in ultrarelativistic heavy ion collisions is expected to produce a rapidity-dependent difference ($\Delta v_{2}$) in the second Fourier coefficient of the azimuthal distribution (elliptic flow, $v_{2}$) between ${\mathrm{D^0}}$ ($\mathrm{\bar{u}}\mathrm{c}$) and ${\mathrm{\overline{D}}{}^0}$ ($\mathrm{u}\mathrm{\bar{c}}$) mesons. [...] CERN-EP-2020-155 ; CMS-HIN-19-008-003. - 2020. Additional information for the analysis - CMS AuthorList - Fulltext

2020-09-26
06:00
 A Highschooler’s Guide to GeV-Range Electromagnetism / Chatterji, Satchit (Unlisted, IN) ; Desai, Aayush (Unlisted, IN) ; Dwarkesh, Aditya (Unlisted, IN) ; Ganesh, Anushree (Unlisted, IN) ; Kunder, Ameya (Unlisted, IN) ; Malhotra, Pulkit (Unlisted, IN) ; Sahoo, Roshni (Unlisted, IN) ; Shah, Jinal (Unlisted, IN) ; Velmurugan, Kiranbhaskar (Unlisted, IN) ; Joos, Markus (CERN) et al. The following article has been written primarily by the high school students who make up the team “Cryptic Ontics”, one of the two winning teams in the 2018 edition of CERN’s Beamline for Schools (BL4S) competition, and is based on the set of experiments the students endeavoured to conduct over the course of a two-week period at CERN. [...] 2020. Fulltext

2020-09-26
04:14
 Gas Heating from Spinning and Non-Spinning Evaporating Primordial Black Holes / Laha, Ranjan ; Lu, Philip ; Takhistov, Volodymyr Primordial black holes (PBHs) from the early Universe constitute a viable dark matter (DM) candidate and can span many orders of magnitude in mass. [...] arXiv:2009.11837 ; CERN-TH-2020-159. - 7 p. Fulltext

2020-09-26
04:14
 MeV-scale Seesaw and Leptogenesis / Domcke, Valerie ; Drewes, Marco ; Hufnagel, Marco ; Lucente, Michele We study the type-I seesaw model with three right-handed neutrinos and Majorana masses below the pion mass. [...] arXiv:2009.11678 ; CERN-TH-2020-158 ; DESY-20-159. - 25 p. Fulltext

2020-09-26
04:14
 UPC: a powerful tool for ${\mathrm J}/\psi$ photoproduction analysis in ALICE / Ragoni, Simone Ultra-peripheral collisions (UPC) occur when the interacting nuclei or protons have an impact parameter larger than the sum of their radii. [...] arXiv:2009.11724. - 4 p. Fulltext

2020-09-25
04:09
 Optimizing large-scale structure data analysis with the theoretical error likelihood / Chudaykin, Anton ; Ivanov, Mikhail M. ; Simonović, Marko An important aspect of large-scale structure data analysis is the presence of non-negligible theoretical uncertainties, which become increasingly important on small scales. [...] arXiv:2009.10724 ; INR-TH-2020-040 ; CERN-TH-2020-154. - 41 p. Fulltext

2020-09-25
04:09
 Jet measurements with ALICE: substructure, dead cone, charm jets / Vertesi, Robert A selection of recent jet measurements are presented from the ALICE experiment at the CERN LHC in proton-proton collisions at $\sqrt{s}=13$ TeV, focusing on substructure results for inclusive and charmed jets. [...] arXiv:2009.11228. - Fulltext

2020-09-25
04:09
 Rare decays at the CERN high-intensity kaon beam facility Precision measurements of the branching ratios (BRs) for rare kaon decays can provide unique constraints on CKM unitarity and may reveal the existence of new physics. [...] arXiv:2009.10941. - Fulltext

2020-09-25
04:09
 Quarkonia production as a function of charged-particle multiplicity in pp collisions at $\sqrt{s}=13$ TeV with ALICE / Ding, Yanchun In pp collisions at LHC energies, heavy quarks are produced in initial hard scatterings and then these quarks hadronize in either open heavy-flavor hadrons or quarkonia (e.g. [...] arXiv:2009.10782. - 4 p. Fulltext


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# Lesson 9

La diferencia entre números

### Lesson Purpose

The purpose of this lesson is for students to represent and compare different subtraction methods on the number line.

### Lesson Narrative

In previous lessons, students represented addition and subtraction equations on the number line and wrote equations to match representations on a number line.

In this lesson, students deepen their understanding of subtraction as taking from and as an unknown addend problem. Students represent subtraction methods on the number line and compare how each representation shows the difference. The number line is also used to help students visualize when counting on and counting back strategies may be useful when subtracting 2 two-digit numbers. For example, $$17 - 14$$ can be solved by starting at 17 and counting back 14. It can also be solved by starting at 14 and counting on 3. In this case, counting on would likely be helpful because the numbers are close together and the structure of the number line helps show why this strategy is effective (MP7).

• Action and Expression

### Learning Goals

Teacher Facing

• On a number line, represent counting on and counting back strategies for solving subtraction equations.

### Student Facing

• Representemos formas de restar en la recta numérica.

### Required Materials

Materials to Gather

Materials to Copy

• Number Line to 100

### Required Preparation

Activity 1:

• Place the number line recording sheets in sheet protectors. They will be used in the next activity and future lessons.

### Lesson Timeline

 Warm-up 10 min Activity 1 15 min Activity 2 20 min Lesson Synthesis 10 min Cool-down 5 min

### Teacher Reflection Questions

Which students had opportunities to share their diagrams and thinking during whole-class discussion? How did you select these students?

### Suggested Centers

• Number Puzzles: Addition and Subtraction (1–4), Stage 4: Within 100 with Composing (Addressing)
• Number Line Scoot (2–3), Stage 1: Twos, Fives, and Tens (Addressing)

format: plain


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# What is "linear" in linear entropy?

Why is the linear entropy, defined by $$S_L = 1 - \textrm{Tr} \rho^2$$, called linear?

$$S_L$$ called linear because it's obtained from the usual definition of von Neumann entropy $$S = -\mathrm{Tr}(\rho \ln \rho)$$ by taking a linear approximation for the natural log $$\ln \rho = \rho - 1$$. Then $$S_L = \mathrm{Tr}(\rho(1 - \rho)) = 1 - \mathrm{Tr}(\rho^2)$$. This simplification is often useful for calculations as you can avoid having to diagonalize the density matrix. For more details, have a look at Wikipedia.


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# NCERT Solutions For Class 9 Math | Exercise 1.1

###### Chapter 1 | Number Systems | 4 Questions

Detailed solution to all exercise questions of NCERT book for CBSE Class 9 Math in Chapter 1 - Number Systems - exercise 1.1. The exercise comprises 4 questions.

Key concepts covered in this exercise include properties of rational numbers, natural numbers, whole numbers, and integers. Finding rational numbers between two numbers. Expressing rational numbers in the form $\frac{p}{q}$, where p and q are integers and q is not zero.

1. Is 0 a rational number? Can you write it in the form $\frac{p}{q}$, where p and q are integers and q ≠ 0?

Zero is a rational number.

Zero can be written in the form $\frac{p}{q}$, where p and q are integers and q ≠ 0 as $\frac{0}{1}$

2. Find six rational numbers between 3 and 4.

Step 1: To obtain six rational numbers between 3 and 4, we must multiply and divide both 3 and 4 by 7.
Why 7?
By multiplying and dividing by 7, we are increasing the gap between 3 and 4 by 7 times. So, 6 numbers can be fitted between them.
So, the rule is always to multiply and divide it by a number that is 1 more than the number of numbers to be fitted between the given numbers.

3 will consequently become $\frac{21}{7}$ and 4 will become $\frac{28}{7}$
Essentially, now we have to find 6 numbers between $\frac{21}{7}$ and $\frac{28}{7}$
Notice that between 21 and 28 we can fit 6 integers.

Step 2: Write integers from 22 to 27 and divide them by 7 to get the 6 numbers between 3 and 4.
The numbers are therefore, $\frac{22}{7}$, $\frac{23}{7}$, $\frac{24}{7}$, $\frac{25}{7}$, $\frac{26}{7}$, and $\frac{27}{7}$.

3. Find five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$.

Step 1: To obtain five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$, we must multiply and divide both $\frac{3}{5}$ and $\frac{4}{5}$ by 6.
Why 6?
By multiplying and dividing by 6, we are increasing the gap between $\frac{3}{5}$ and $\frac{4}{5}$ 6 times. So, 5 numbers can be fitted between them.

$\frac{3}{5}$ will consequently become $\frac{18}{30}$ and $\frac{4}{5}$ will become $\frac{24}{30}$
Essentially, now we have to find 6 numbers between $\frac{18}{30}$ and $\frac{24}{30}$
Notice that between 18 and 24 we have 5 integers.

Step 2: Write integers from 19 to 23 and divide them by 30 to get the 5 numbers between $\frac{3}{5}$ and $\frac{4}{5}$.
The numbers are therefore, $\frac{19}{30}$, $\frac{20}{30}$, $\frac{21}{30}$, $\frac{22}{30}$, and $\frac{23}{30}$.

4. State whether the following statements are true or false with reasons.

i): Every natural number is a whole number.
TRUE. Whole numbers include 0 as well as all the natural numbers. So, every natural number is a whole number.

ii): Every integer is a whole number.
FALSE. Negative integers are not whole numbers.
However, note that all whole numbers are integers.

iii): Every rational number is a whole number.
FALSE. Whole numbers are non-negative numbers.
Negative rational numbers and rational numbers whose denominators ≠ 1 are not whole numbers.

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text:
# Managing cycles

Usage of the Internet Computer is measured, and paid for, in cycles. The Internet Computer maintains a balance of cycles per canister smart contract. In addition, cycles can be transferred between canisters.

In Motoko programs targeting the Internet Computer, each actor represents an Internet Computer canister, and has an associated balance of cycles. The ownership of cycles can be transferred between actors. Cycles are selectively sent and received through messages, that is, shared function calls. A caller can choose to transfer cycles with a call, and a callee can choose to accept cycles that are made available by the caller. Unless explicitly instructed, no cycles are transferred by callers or accepted by callees.

Callees can accept all, some or none of the available cycles up to limit determined by their actor’s current balance. Any remaining cycles are refunded to the caller. If a call traps, all its accompanying cycles are automatically refunded to the caller, without loss.

In future, we may see Motoko adopt dedicated syntax and types to support safer programming with cycles. For now, we provide a temporary way to manage cycles through a low-level imperative API provided by the ExperimentalCycles library in package base.

note

This library is subject to change and likely to be replaced by more high-level support for cycles in later versions of Motoko.

## The ExperimentalCycles Library

The ExperimentalCycles library provides imperative operations for observing an actor’s current balance of cycles, transferring cycles and observing refunds.

The library provides the following operations:

func balance() : (amount : Nat)func available() : (amount : Nat)func accept(amount : Nat) : (accepted : Nat)func add(amount : Nat) : ()func refunded() : (amount : Nat)

Function balance() returns the actor’s current balance of cycles as amount. Function balance() is stateful and may return different values after calls to accept(n), calling a function after adding cycles, or resuming from await (reflecting a refund).

danger

Since cycles measure computational resources spent, the value of balance() generally decreases from one shared function call to the next.

Function available(), returns the currently available amount of cycles. This is the amount received from the current caller, minus the cumulative amount accepted so far by this call. On exit from the current shared function or async expression via return or throw any remaining available amount is automatically refunded to the caller.

Function accept transfers amount from available() to balance(). It returns the amount actually transferred, which may be less than requested, for example, if less is available, or if canister balance limits are reached.

Function add(amount) indicates the additional amount of cycles to be transferred in the next remote call, i.e. evaluation of a shared function call or async expression. Upon the call, but not before, the total amount of units added since the last call is deducted from balance(). If this total exceeds balance(), the caller traps, aborting the call.

note

the implicit register of added amounts, incremented on each add, is reset to zero on entry to a shared function, and after each shared function call or on resume from an await.

Function refunded() reports the amount of cycles refunded in the last await of the current context, or zero if no await has occurred yet. Calling refunded() is solely informational and does not affect balance(). Instead, refunds are automatically added to the current balance, whether or not refunded is used to observe them.

### Example

To illustrate, we will now use the ExperimentalCycles library to implement a toy piggy bank for saving cycles.

Our piggy bank has an implicit owner, a benefit callback and a fixed capacity, all supplied at time of construction. The callback is used to transfer withdrawn amounts.

import Cycles "mo:base/ExperimentalCycles";shared(msg) actor class PiggyBank(  benefit : shared () -> async (),  capacity: Nat  ) {  let owner = msg.caller;  var savings = 0;  public shared(msg) func getSavings() : async Nat {    assert (msg.caller == owner);    return savings;  };  public func deposit() : async () {    let amount = Cycles.available();    let limit : Nat = capacity - savings;    let acceptable =      if (amount <= limit) amount      else limit;    let accepted = Cycles.accept(acceptable);    assert (accepted == acceptable);    savings += acceptable;  };  public shared(msg) func withdraw(amount : Nat)    : async () {    assert (msg.caller == owner);    assert (amount <= savings);    Cycles.add(amount);    await benefit();    let refund = Cycles.refunded();    savings -= amount - refund;  };}

The owner of the bank is identified with the (implicit) caller of constructor PiggyBank(), using the shared pattern, shared(msg). Field msg.caller is a Principal and is stored in private variable owner (for future reference). See Principals and caller identification for more explanation of this syntax.

The piggy bank is initially empty, with zero current savings.

Only calls from owner may:

• query the current savings of the piggy bank (function getSavings()), or

• withdraw amounts from the savings (function withdraw(amount)).

The restriction on the caller is enforced by the statements assert (msg.caller == owner), whose failure causes the enclosing function to trap, without revealing the balance or moving any cycles.

Any caller may deposit an amount of cycles, provided the savings will not exceed capacity, breaking the piggy bank. Because the deposit function only accepts a portion of the available amount, a caller whose deposit exceeds the limit will receive an implicit refund of any unaccepted cycles. Refunds are automatic and ensured by the Internet Computer infrastructure.

Since transfer of cycles is one-directional (from caller to callee), retrieving cycles requires the use of an explicit callback (the benefit function, taken by the constructor as an argument). Here, benefit is called by the withdraw function, but only after authenticating the caller as owner. Invoking benefit in withdraw inverts the caller/caller relationship, allowing cycles to flow "upstream".

Note that the owner of the PiggyBank could, in fact, supply a callback that rewards a beneficiary distinct from owner.

Here’s how an owner, Alice, might use an instance of PiggyBank:

import Cycles = "mo:base/ExperimentalCycles";import Lib = "PiggyBank";actor Alice {  public func test() : async () {    Cycles.add(10_000_000_000_000);    let porky = await Lib.PiggyBank(Alice.credit, 1_000_000_000);    assert (0 == (await porky.getSavings()));    Cycles.add(1_000_000);    await porky.deposit();    assert (1_000_000 == (await porky.getSavings()));    await porky.withdraw(500_000);    assert (500_000 == (await porky.getSavings()));    await porky.withdraw(500_000);    assert (0 == (await porky.getSavings()));    Cycles.add(2_000_000_000);    await porky.deposit();    let refund = Cycles.refunded();    assert (1_000_000_000 == refund);    assert (1_000_000_000 == (await porky.getSavings()));  };  // Callback for accepting cycles from PiggyBank  public func credit() : async () {    let available = Cycles.available();    let accepted = Cycles.accept(available);    assert (accepted == available);  }}

Let’s dissect Alice's code.

Alice imports the PiggyBank actor class as a library, so she can create a new PiggyBank actor on demand.

Most of the action occurs in Alice's test() function:

Alice dedicates 10_000_000_000_000 of her own cycles for running the piggy bank, by calling Cycles.add(10_000_000_000_000) just before creating a new instance, porky, of the PiggyBank, passing callback Alice.credit and capacity (1_000_000_000). Passing Alice.credit nominates Alice as the beneficiary of withdrawals. The 10_000_000_000_000 cycles, minus a small installation fee, are credited to porky's balance without any further action by porky initialization code. You can think of this as an electric piggy bank, that consumes its own resources as its used. Since constructing a PiggyBank is asynchronous, Alice needs to await the result.

After creating porky, she first verifies that the porky.getSavings() is zero using an assert.

Alice dedicates 1_000_000 of her cycles (Cycles.add(1_000_000)) to transfer to porky with the next call to porky.deposit(). The cycles are only consumed from Alice’s balance if the call to porky.deposit() succeeds (which it should).

Alice now withdraws half the amount, 500_000, and verifies that porky's savings have halved. Alice eventually receives the cycles via a callback to Alice.credit(), initiated in porky.withdraw(). Note the received cycles are precisely the cycles added in porky.withdraw(), before it invokes its benefit callback, that is, Alice.credit.

Alice withdraws another 500_000 cycles to wipe out her savings.

Alice vainly tries to deposit 2_000_000_000 cycles into porky but this exceeds porky's capacity by half, so porky accepts 1_000_000_000 and refunds the remaining 1_000_000_000 to Alice. Alice verifies the refund amount (Cycles.refunded()), which has (already) been automatically restored to her balance. She also verifies porky's adjusted savings.

Alice's credit() function simply accepts all available cycles by calling Cycles.accept(available), checking the actually accepted amount with an assert.

note

For this example, Alice is using her (readily available) cycles, that she already owns.

danger

Because porky consumes cycles in its operation, it is possible for porky to spend some or even all of Alice’s cycle savings before she has a chance to retrieve them.


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# Oasis (Kingdoms)

Oases are fields on the map, which can't be settled on, but which can be captured by kingdoms and be annected by villages to increase the production. Wild oases are protected by animals, the nature troops.

As for all NPCs, one receives only 50% of the usual off points for defeating animals in an oasis.

## Appearance

Two oases on the map

Oases can be found on the map on some landscape fields. Wood oases can be found exclusively in forests, clay oases in canyons, iron oases in mountains and crop oases either in waterholes or in crop acres. Double oases (e.g. wood + crop) can be found exclusively on the non-crop-type (e.g. wood + crop in forests). Double crop oases are in crop acres. Landscape fields with oases have a resource icon on them, making it easy to distinguish from regular landscape fields.

 Type Resource Icon Landscape (example) Wood Wood + Crop Clay Clay + Crop Iron Iron + Crop Crop Double crop

Wild oases aren't distinguishable from free ones by optics alone. Wild oases have animals however, free oases don't.

## Wild Oasis

At the start, all oases in the world are wild. To make use of an oasis, it has to be freed by killing all animals with attacks first. As soon as all animals area dead, the oasis is free and can be used. If the oasis abuts on the ow kingdom (counting diagonally), it will be part of the kingdom upon freeing it.

Wild oases produce small amounts of resources and have a storage capacity of 50 per animal, which lives in the oasis.

Apart from attacks and espionages, no interactions with wild oases are possible. Reinforcing troops return immediately upon arrival. This can be used to save troops for a certain time.

## Free Oasis

An oasis without animals is a free oasis. It can be annected, reinforced and attacked.

Free oases, that are part of a kingdom, generate an one tile large area for it, containing only the oasis. The area is considered to be fully part of the kingdom, i.e. it can be used for tribute paths as well as for the capital-to-capital connection for the kingdom union. Enemy kingdoms can steal an oasis, if it abuts on their area (counting diagonally), by killing all troops in the oasis. Then, the oasis becomes a part of the enemy kingdom and generates area for that kingdom now. Existing annexations will not be dissolved thereby. Free oases of a kingdom stay part of it, even if they don't abut on it anymore, e.g. after closing a treasury. They still generate their area in this case.

Free oases become wild again after an indeterminate time. This can be prevented by sending at least one unit as reinforcement or by annecting it.

Free oases have a defense bonus for reinforcing troops, compareable to the water ditch. The defense bonus depends on the oasis type.

## Annexation

Free oases can be used to increase the resource production of a village. For that, it has to be annected in the embassy of the appropiate village by selecting an oasis of free choice in the tab oasis. As soon as an oasis is selected, it gets annected and it starts to take effect. Every village can annect up to three oases. Annected oases can be removed and replaced in the embassy at any time. Upon destruction of the embassy, all annected oases are removed.

Requirements for the annexation:

• The village has a sufficient embassy level (level 1 for the first oasis, level 10 for the second level 20 for the third).
• The oasis is free.
• No other village of the same player has already annected the same oasis.
• The oasis is inside the 7x7 area around the village (i.e. x and y coordinate may each differ by at most 3).

Oases, that belong to a foreign kingdom, can be annected normally, but troops don't produce resources and don't exert influence there.

After the annexation, the oasis increases the production of the village by a certain percentage. Two factors are taken into account, firstly the type of the oasis and secondly the rank of the player in the oasis ranking. Additionally, the oasis can be reinforced with troops to further increase the production, but there's a maximum of troops, that can produce resources in an oasis. While one can send more troops as reinforcement, some troops may not produce resources. Troops only produce resources, if the oasis belongs to the political kingdom.

The %-production bonus affects the base production of the village (i.e. it does not effect the bonus production of resource boosters or the production of troops).

### Ranking

Every oasis has a ranking, in which all players, that annected it, are listed. The more influence a player exerts on an oasis, the better is his rank. The influence of a player is the sum of the influences of his villages, that are inside the 7x7 of the oasis plus the amount (not consumption) of his troops in the oasis. Troops only exert influence, if the oasis belongs to the political kingdom. The influence of a village is calculated by the following formula: ${\displaystyle Influence={\frac {Population}{Distance\ to\ the\ oasis}}}$

The better a rank of a player in the ranking, the higher the %-production bonus and the more troops of him can produce resources there:

Rank Prod. Bonus 25% Prod. Bonus 50% Max. Troops
1 25% 50% 250
2 20% 40% 200
3 15% 30% 150
4 10% 20% 100
5+ 5% 10% 50

### Example

The production of a village with four claypits level 10, brickyard level 5, rank 2 in a clay oasis and gold production bonus is calculated like this:

Production Site Prod. by definition Calculation Result Production Type
4x Claypit level 10 200 clay per hour each 4x 200 800 clay per hour base production
Brickyard level 5 25% of the base production 25% * 800 200 clay per hour bonus production
Rank 2 in clay oasis 20% of the base production 20% * 800 160 clay per hour bonus production
Gold production 25% of the production 25% * (800 + 200 + 160) 290 clay per hour gold production
Total Sum of all productions 800 + 200 + 160 + 290 1450 clay per hour total production

## Types

Each oasis has one or two resource types, for which it grants a bonus. The defense bonus depends on the types aswell and only counts for free oases.

Type 1 Type 2 Rank 1 prod. nonus Prod. per troop Defense bonus
Wood - 25% Wood 1 Wood 50%
Wood Crop 25% Wood + 25% Crop 1 Wood + 1 Crop 25%
Clay - 25% Clay 1 Clay 50%
Clay Crop 25% Clay + 25% Crop 1 Clay + 1 Crop 25%
Iron - 25% Iron 1 Iron 100%
Iron Crop 25% Iron + 25% Crop 1 Iron + 1 Crop 50%
Crop - 25% Crop 1 Crop 0%
Crop Crop 50% Crop 2 Crop 0%

## Differences to Travian: Legends

• In Travian: Legends, each oasis can be annected by one player only, whereas in Travian Kingdoms multiple players can use the same oasis. The ranking and influence doesn't exist there.
• In Travian: Legends, there are oases with 50% wood bonus, 50% clay bonus and 50% iron bonus on regular gameworlds inside the gray natar area.
• In Travian: Legends, troops don't produce resources in oases.
• In Travian: Legends, oases have to be annected by attacking with the hero and can't be selected easily.
• In Travian: Legends, one needs a hero's mansion level 10/15/20 for 1/2/3 oases. This building is merged with the embassy in Travian Kingdoms and the level requirements has been changed to level 1/10/20.


text:
5

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Question

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3. Set up a triple integral in spherical coordinates to find the volume outside the sphere x? y? + 22 =land inside the sphere x? y? + 22 2z _ Do not evaluate the integral Your work should include some basic algebra that proves that x? +y? + 22 2zis the equation of a sphere What is its center and rad...
EorZ-LOuse: The regression model,Y 9.3X + 105.4 relates survival rate after cardiac arrest to the time between the cardiac arrest and when a defibrillator shock is administered. Xrepresents time measured in minutes_ Yis the percentage of survival 7)Interpret the slope in the context of the problem:8)Interpret the y-intercept in the context ofthe problem9)Make a prediction for X = 8 and interpret the prediction10) r? = 0.92. a) Interpret the coefficient of determination in contextb) Find the corr
EorZ-LOuse: The regression model,Y 9.3X + 105.4 relates survival rate after cardiac arrest to the time between the cardiac arrest and when a defibrillator shock is administered. Xrepresents time measured in minutes_ Yis the percentage of survival 7)Interpret the slope in the context of the problem: ...
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Tu I (oted hmm 0(: none ot te above The cquation that represents an exponential relation is Y = 2x 3 Y =X y = 2' none of (he aboveAn equivalent form of k33 ~3k Jk3 none of the above Compound interest is an example of linear growth 6 quedratio growth c) exponential growth d) constant growth none of the above 10.Which type of distribution does the graph on the right represent? a) normal distribution b) skewed to the right distribution uniform distribution d) bimodal distribution none of th
Tu I (oted hmm 0( : none ot te above The cquation that represents an exponential relation is Y = 2x 3 Y =X y = 2' none of (he above An equivalent form of k3 3 ~3k Jk3 none of the above Compound interest is an example of linear growth 6 quedratio growth c) exponential growth d) constant growth n...
Sbort answer problems_ pointa each] Suppose that for_each_natural number_P(o) is the proposition 22 + 3 nu + 4n +42 What i8 the proposition P(n + 1)?(b) Let R = {(1,5), (2,2), (3,4), (5,2)} and $= {(2,4), (3,4), (3,1), (6,5)}. Compute$ o R(c) Let A = {1,2,3} and list the ordered pairs in one relation on that i9 not reflexive, i8 symmetric and is not transitiveWhat is the domain of the relation {(2,y) â‚¬ N x N I = 4} ? State the domain precisely.What is the range of the relation {(I,y) â‚¬ Nx
Sbort answer problems_ pointa each] Suppose that for_each_natural number_P(o) is the proposition 22 + 3 nu + 4n +42 What i8 the proposition P(n + 1)? (b) Let R = {(1,5), (2,2), (3,4), (5,2)} and $= {(2,4), (3,4), (3,1), (6,5)}. Compute$ o R (c) Let A = {1,2,3} and list the ordered pairs in one rel...


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# How does this statement about the price of a prepaid forward on a stock follow?

I am self-studying for an actuarial exam on financial economics. This statement in the following problem/solution seems to imply that the prepaid forward price on a stock is the same as the prepaid forward price on a futures contract for the stock, or $F_{0, T}^P(S) = F_{0, T}^P(\text{Future}(S))$. (Not sure if this is correct notation).

So why does the second statement underlined in red follow from the first statement?

(2) If you want to buy a stock and not have to pay for it until a future delivery date T, then you enter into a "forward" or (in the United States) a "futures contract" which specifies a price F, with $F=S e^{(r-d)T}$. No money is due when you enter into this contract.
(3) There is also an odd thing called a "prepaid forward" which is not much used except to get around tax and other regulations, in which you pay now the sum P in order to get the the stock later. This is priced at $P=F e^{-(r-d)T}$. Perhaps not surprisingly we have $P=S$ since you have to pay now, just like when buying the stock outright.


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# Tag Info

23

Following up on Matthew Leingang's answer, here's the same approach tied up with some syntactic sugar. It messes around with \catcode stuff, so care needs to be taken. \documentclass{standalone} \usepackage{tikz} \newcount\contourmarkcount \newdimen\contourraise {\catcode`\|=13 \gdef\installbarmark#1\ignorespaces{% #1\ignorespaces% ...

17

I would use the famous \tikzmark macro and combine it with intersection coordinates. Here is the code: \documentclass{standalone} \usepackage{tikz} \newcommand{\tikzmark}[1]{\tikz[overlay,remember picture,baseline] \node [anchor=base] (#1) {};}% \tikzstyle{intonation}=[rounded corners=2mm,yshift=1.5ex] \begin{document} \begin{tikzpicture}[remember ...

16

This is not commonly the way trees are represented in the linguistic literature, so none of the regular tree drawing packages (qtree and tikz-qtree) do this by default. Specifically, the way trees are drawn in the linguistics literature, the terminal nodes are not drawn at the same level (i.e. with the words along a baseline and the tree growing up from ...

15

There are two ways to write IPA symbols in LaTeX. One uses regular pdfLaTeX and the tipa package; the other uses XeLaTeX or LuaLaTeX and you can enter the symbols directly into your source, assuming you have the correct fonts. The SIL Doulos font is an excellent Unicode IPA font that is widely used in Linguistics. You can download it here. I'll outline ...

13

There are good packages for numbering examples in linguistics which have been specifically designed by linguists to meet our needs. Two of the most commonly used ones are gb4e and linguex. The questions egreg linked to in the comments show some examples. A third package, ExPex is still in development, and is extremely powerful, although somewhat non-LaTeX ...

13

TeX fonts have only 256 slots. And you can't mix encodings without telling LaTeX to do it; \textcyrillic defined by babel with the russian option does this. The last specified encoding becomes the default one. This should be a complete list of sans serif fonts available also in T2A encoding (for cyrillic): \documentclass{article} ...

12

12

Both of the major linguistic example packages provide this functionality, although in different ways. I'm assuming you just want regular labelled bracketing as is normally done in articles in the literature (i.e., the brackets are all of a fixed size.) gb4e The gb4e package provides an \lb command for a labelled bracket: \documentclass{article} ...

12

Partitions similar to these, but with even higher degrees of syncing, are common in linguistics. At http://www.essex.ac.uk/linguistics/external/clmt/latex4ling/ most LaTeX resources for linguistics have been gathered. Specifically your synched texts are similar to what's called glosses in linguistics; and these can be handled by cgloss4e.sty. See ...

12

Ok, here's a quick and dirty TiKZ solution. I haven't connected be in the diagram, although I assume it actually should be connected with seront. If you want to connect them, you could make a p3 node below now in the matrix and connect will and be to that and then connect that to seront. Update I've tweaked a few parameters to make the spacing between the ...

11

I contacted the author of ExPex (John Frampton) and he was unaware of the web page issue. The issue has now been resolved, and the link in the question has been changed (although the link in the question now redirects there). He has no intentions of abandoning development of the package. It is likely that it will be uploaded to CTAN in the future. Until ...

11

it's always better to use "precomposed" characters rather than trying to cobble something together. this may involve some work with font tools, and others on this list are better able to address that than i. however, many fonts created for use within linguistics environments are available from sil international, and i suggest looking there before trying to ...

10

Since this answer might be of use to other linguists, I'm giving a detailed answer of how to effectively transfer documents from Word to TeX, assuming you are using the regular SIL phonetic fonts in Word. The modern TeX engines LuaTeX and XeLaTeX both use UTF-8 as their file encoding, and can use any OpenType font on your system. See the following for some ...

10

You can add a node with a dot and instead of using in and out angles, use the bend parameter. \documentclass{standalone} \usepackage{tikz} \usepackage{tikz-qtree} \usepackage{tikz-qtree-compat} \usetikzlibrary{positioning} \newcommand\TR[1]{\textlangle#1\textrangle} \usepackage{ textcomp } \begin{document} \begin{tikzpicture} \Tree [ .TP [ .T\1 ...

10

If you use Alexis Dimitriadis' version of cgloss4e available here as cgloss.sty you can put language information right aligned with the first line of the example. This is IMO a very nice way to format such information, and quite common in the field: \documentclass{article} \usepackage{gb4e} \usepackage{cgloss} \usepackage{lipsum} \begin{document} ...

10

It's Unicode character U+026B LATIN SMALL LETTER L WITH MIDDLE TILDE. See also The Comprehensive LaTeX Symbol List. wsuipa (PK-Fonts) \documentclass{article} \usepackage{ipa} \begin{document} \tildel \end{document} tipa \documentclass{article} \usepackage{tipa} \begin{document} \textltilde \end{document}

10

This isn't too hard to do with tikz-qtree. In order to get the movement arrow from T to C to go under the VP, I made the object DP a node and used that as a reference point to create an intermediate node that the line passes through. Thanks very much to both Peter Grill and percusse for suggesting elegant ways to avoid the VP structure. The final solution ...

9

The warnings are harmless, and the substitutions will happen automatically. If you want to get rid of the warning you could redefine the \textipa command and the IPA environments to always use Computer Modern as shown in the example below. If you decide later to change to using e.g. mathptmx then you would need to change the definition of \tiparmdefault to ...

9

Have a look at this thread, there are both tikz and tikz-qtree solutions there; this turns out to be very simple to do once you know the trick. Here's Alan Munn's final solution from there adapted for your particular question. (I didn't bother to try to get the IPA right.) \documentclass{article} \usepackage{tikz} \usepackage{tikz-qtree} ...

9

I'm not sure I put the coordinates on the right places (and reused \zzb in two points) but something like %!TEX TS-program = xelatex %!TEX encoding = UTF-8 Unicode \documentclass[a4paper,12pt, oneside]{article} \usepackage{fontspec} \defaultfontfeatures{Mapping=tex-text, Scale=MatchLowercase} \setmainfont{Charis SIL} \makeatletter ...

9

If you need to do a lot of these, the pst-asr package is extremely powerful, but somewhat complicated. Compile the following with XeLaTeX. (Since it uses pstricks it can't be compiled with pdfLaTeX directly, and either needs XeLaTeX (as in this example) or LaTeX+dvips (in which case you would use the tipa package and not load fontspec, etc.) The spacing ...

9

gb4e sets the exe environment as a regular list. Moreover, every \ex macro defaults to \item (if you don't specify an optional argument). So, you can use enumitem to emulate the display, yet set some other properties as needed. The following MWE does exactly that (I grabbed the list parameters from g4be.sty) and provides myexe as the alternative: ...

9

A completely different approach from Werner's one. Load calc package and add \makeatletter \def\myex{\setlength{\parindent}{-\leftmargin+\labelsep}\@ifnextchar [{\@ex}{\item}} \makeatother in the preamble. Then use the newly defined \myex inside the exe environments where you want the special layout, e.g. \documentclass{article} ...

8

Here's a way to do this using my version of the popular tikzmark macro, since the gb4e version of arrows is very cumbersome to use. If you need the real \tikzmark for some other purpose, you'll need to change the name of the macro in my code. Mainly this puts together bits of code from various sources. There are two issues to be solved: first connecting ...

8

xunicode (loaded by fontspec) contains the definitions of tipa.sty: \documentclass[12pt]{article} \usepackage{fontspec} \setmainfont{Charis SIL} \begin{document} Blowzy DJ frumps vex a knight QC \textturna \textipa{[\!b] [\:r] [\;B]} \end{document}

8

I love this question and spent far too much time thinking about how to answer it. I think what you need are some good symbols to use in place of the annotations. Then you can subscript with them instead. Also, I think underlining rather than bracketing will set off the annotated text a little better. I found a wavy underline under an \attitude made sense, ...

8

Depending on your actual needs, this looks very much like the kind of job for the expex package. The ExPex package provides very sophisticated glossing macros which should do what you need. Here's an example from the documentation: \documentclass{article} \usepackage{expex} \begin{document} \ex[glhangstyle=none] \let\\=\textsc \begingl \gla Hom\^{a}o sa ...

8

The numbering of examples is hardwired in linguex; you can modify it by changing the corresponding command. Here's a commented minimal document. \documentclass{article} \usepackage{linguex} % We want that the label to an example has also the section number \renewcommand{\Exarabic}{\thesection.\arabic} % We want to reset the ExNo counter at each section ...

7

There are two issues you need to consider here I suspect: the font shape itself, serif vs sans serif; and the font apparent size (MS font in particular tend to look much bigger than other fonts. For the first issue, Aerlinthe is indeed correct, the SIL fonts seem to be a good bet, especially Gentium which looks very similar to Minion Pro. For the second ...

7

As percusse has noted (answer now deleted) the problem is with completely empty nodes. Filling them with a space element such as \, would add an empty terminal node, which would remove the error, but also yields extra vertical branches in the tree, which is not really what you probably want. A better solution is to add empty node labels instead of using ...

Only top voted, non community-wiki answers of a minimum length are eligible


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# How can a mug and a torus be equivalent if the mug is chiral?

I don't know much about topology, but the other day I was thinking about the (classic?) coffee cup - donut topological equivalence. I realised that a cylinder with one open end and a handle on the side (a mug) is a chiral object in 3D space, whereas a torus/donut is achiral ("meso", as indicated by the internal planes of symmetry present in a torus).

EDIT: I just realized the mug may not in fact be chiral, due to an internal plane of symmetry (vertical, through the handle). But I will leave the post as some of the questions are still relevant, and I'm still interested in the arbitrary example of how topology handles a chiral object being transformed into an achiral object.

As an outsider, my impression is that topology is roughly "the qualitative mathematics of shapes"; is this accurate at all? I would expect such a field would be quite concerned with phenomena like chirality, the lack of superposability of two mirror-images of a 3D object. From another perspective, chirality is the reason we have a "right hand rule" convention, or the very reason we can distinguish between a right- and left-handed coordinate system. To me chirality seems to be an emergent property, an asymmetry that arises when the object/space is sufficiently complex.

So when a chiral object and achiral object are claimed to be topologically equivalent, is there some unsung caveat about chirality? Perhaps topologists truly do not care about chirality, as it does not stop their infinitely malleable material from transforming between the two shapes. If so, then my question is what is the significance of chirality in topology?

And if I may, these questions built off this train of thought:

If a 3D object that is chiral in 3D space is viewed in a four-dimensional space, would it be considered achiral ("meso")? (Analogous to a 2D object being considered achiral in 3D space, if I am not mistaken.)

Is there any usefulness to defining chirality of 2D objects in 2D space? Is there any generalized notion of chirality for an $n$-dimensional space, some "$n$-chirality"?

• Add a lump to the handle to make the mug chiral, it will remain topologically equivalent to the torus. – Taemyr Apr 30 '17 at 6:22

Other answers have said that topology cannot distinguish chirality, but this is not quite true. Topologically a left and right glove are identical, because the left-right reflection is continuous in both directions. The difference between the left and right gloves isn't intrinsic to the gloves themselves, but is in the way the gloves are embedded in three-dimensional space.

Consider this analogy: The symbols b can be turned into d, but to do it you have to lift the b out of the plane and flip it over. If you leave b and d embedded in the plane you can never turn one into the other (although you can turn b into q and d into p) so the difference is not in the shapes themselves but in the way they inhabit the plane. Left and right gloves are distinguishable if they remain in three-dimensional space. But in larger spaces, they're identical. It's easy to turn a left glove into a right glove if you can lift it into four-dimensional space and flip it over,

The branch of topology called knot theory concerns the way simple shapes like circles can be embedded into three dimensions. Topologically a knotted loop of string and an unknotted one are the same—but again, their embeddings into three-dimensional space are different. To deal with this topologically requires some extra effort. One embeds the knotted loop in space and then considers whether there is a continuous deformation of the entire space, including the loop, that transforms the knotted loop into the unknotted one. Viewed in this way one can say that a trefoil knot (shown below) is chiral, because although each is topologically equivalent to a plain circle, the left-handed trefoil knot can never be smoothly transformed into the right-handed one, in the sense of the previous paragraph, without removing it from three-dimensional space. This seems to be what you are looking for.

But what if we consider the coffee mug and torus example? The coffee mug is not chiral in this sense. It has a handle on the left side. Could we deform space to move the handle to the right side instead? Of course we could: just turn the cup around, now the handle is on the other side. No fourth dimension is required. (There are also many other ways to get the handle to the other side.)

I'm still interested in the arbitrary example of how topology handles a chiral object being transformed into an achiral object.

This never happens. Let $C$ be some chiral object and let $\bar C$ be the mirror image of the object. Since $C$ is chiral, $C$ cannot be transformed into $\bar C$ without removing it from the ambient space.

But you say that $C$ can be transformed into some achiral object $A$. But clearly $\bar C$ could be transformed into $A$ by the same method (except mirrored.) But then we can turn $C$ into $A$ using your method, and then $A$ into $\bar C$ by using the mirrored method, but in reverse. So there is a way to turn $C$ into $\bar C$ after all, and thus $C$ was never chiral in the first place.

If a 3D object that is chiral in 3D space is viewed in a four-dimensional space, would it be considered achiral ("meso")?

Yes, always. Because if $C$ and $\bar C$ are left- and right-handed versions of the same thing, then they are identical under a reflection symmetry, and in four-space this is simply a rotation, just as a reflection of the plane can be realized as a rotation of three-space.

But it may interest you to learn that there are higher-dimensional analogues of knotted circles: in four dimensions one can have knottings of a sphere which can be left- or right-handed, and which become identical when these chiral knots are lifted into five dimensions.

• Thank you for seeing through my poor approach and targeting my underlying uncertainty. The trefoil knot example was very enlightening to me. Your last two paragraphs were the very things I was hoping to learn, but didn't quite know how to ask for. Thank you again for your assistance! – electronpusher Apr 30 '17 at 5:39
• I'm glad I could help. – MJD Apr 30 '17 at 6:42
• It may also be interesting to note that if you lift the trefoil knot into 4D, you not only can turn it around to the opposite 3D-chirality, you also can unknot it into a plain circle, which isn't chiral even after re-embedding it in 3D. – celtschk Apr 30 '17 at 11:08
• Minor quibble to an otherwise very clear answer: as someone who regularly wears gloves inside-out, I have a simple mapping from left- to right-handed gloves in three dimensions. (not that I have a better suggestion) – kyle May 1 '17 at 14:19
• Related quibble: I have used, and in fact when I read this answer I was thinking of, cotton gloves (searching for "inspection gloves" seems to give some images) that have no "front" and "back", and are therefore achiral in a simpler way. (Another minor quibble: the sentence “Since $C$ is chiral, $C$ cannot be transformed into $\bar C$...” is not strictly necessary (and was a bit confusing); IMO the argument flows better without it. This may just be one of those “proof by unnecessary contradiction” things.) – ShreevatsaR May 2 '17 at 0:06

Usually it is stated that topology is "geometry minus shape", which means, we are completely ignoring the exact shape of an object. Annother classical example would be a ball (sphere + interior) being equivalent to a (solid) cube. The sphere having infinitely many symmetries, while a cube only has a finite symmetry group. Topological equivalence only cares about preserving a kind of a closeness relation between the points of an object, i.e. homeomorphism (topological "isomorphism") will not cut or rip the objects apart.

From a topological point of view, no object is distinguishable from its mirror image. The map $f:(x_1,...,x_n)\mapsto (-x_1,x_2,...,x_n)$ is a homemorphism in the most geometrically meaningful topological spaces. In the end, a topologist can determine an object only up to a continuous transformation. He will not recognize any translation, rotation, stretching, mirroring or shearing.

• Thank you for helping me better understand the focus of topology! – electronpusher Apr 30 '17 at 5:41
• "or shearing" - doesn't shearing mean "cut or rip the objects"? – wizzwizz4 May 1 '17 at 16:49
• @wizzwizz4 It means a specific kind of linear transformation, which is always continuous. – M. Winter May 1 '17 at 17:30

The mug as pictured is not chiral. It has a mirror plane through the handle and the center of where the liquid goes in. In any event topology does not depend on point group symmetry and so does not depend on chirality.

• Thanks for pointing that out, I realized it right after I posted. But the particular example of the mug is not really the heart of my question. – electronpusher Apr 30 '17 at 0:46
• Hence the second sentence in the answer. – Oscar Lanzi Apr 30 '17 at 0:50
• All that this answer says is “topology does not depend on point group symmetry and so does not depend on chirality”, which I think does not sufficiently address the question. – ShreevatsaR May 1 '17 at 6:46

So when a chiral object and achiral object are claimed to be topologically equivalent, is there some unsung caveat about chirality?

No, it's just a notion of equivalence that doesn't care about the number of symmetries the object has. Similarly, when we say that two integers are equivalent modulo two, there isn't some unstated caveat about them possibly being different sizes: we've chosen a notion of equivalence that only cares about whether the numbers are odd or even, and doesn't care about their sizes.


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## Cryptology ePrint Archive: Report 2014/537

Constrained Verifiable Random Functions

Georg Fuchsbauer

Abstract: We extend the notion of verifiable random functions (VRF) to constrained VRFs, which generalize the concept of constrained pseudorandom functions, put forward by Boneh and Waters (Asiacrypt'13), and independently by Kiayias et al. (CCS'13) and Boyle et al. (PKC'14), who call them delegatable PRFs and functional PRFs, respectively. In a standard VRF the secret key $\sk$ allows one to evaluate a pseudorandom function at any point of its domain; in addition, it enables computation of a non-interactive proof that the function value was computed correctly. In a constrained VRF from the key $\sk$ one can derive constrained keys $\sk_S$ for subsets $S$ of the domain, which allow computation of function values and proofs only at points in $S$.

After formally defining constrained VRFs, we derive instantiations from the multilinear-maps-based constrained PRFs by Boneh and Waters, yielding a VRF with constrained keys for any set that can be decided by a polynomial-size circuit. Our VRFs have the same function values as the Boneh-Waters PRFs and are proved secure under the same hardness assumption, showing that verifiability comes at no cost. Constrained (functional) VRFs were stated as an open problem by Boyle et al.

Category / Keywords: public-key cryptography / Verifiable random functions, constrained pseudorandom functions

Original Publication (with major differences): SCN 2014, Springer LNCS 8642


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# Combining lenses

1. Nov 4, 2009

### E92M3

1. The problem statement, all variables and given/known data
2 thin lenses separated by 10cm. First has a focal length of 20cm, the second has a focal length of 30cm.

2. Relevant equations
Lens transfer matrix for each lens:
$$\begin{bmatrix} 1-\frac{D_2d_{21}}{n_{t1}} &-D_1-D_2+\frac{D_1D_2d_{21}}{n_{t1}} \\ \frac{d_{21}}{n_{t1}} & 1-\frac{D_2d_{21}}{n_{t1}} \end{bmatrix}$$

3. The attempt at a solution
Since the thickness of the 2 lens is assumed to be zero we have:
$$A_1=\begin{bmatrix} 1 & \frac{-1}{f_1}\\ 0 & 1 \end{bmatrix}$$
For the first lens and
$$A_2=\begin{bmatrix} 1 & \frac{-1}{f_2}\\ 0 & 1 \end{bmatrix}$$
for the second. Therefore we have:
$$A=A_2TA_1=A_2=\begin{bmatrix} 1 & \frac{-1}{f_2}\\ 0 & 1 \end{bmatrix}\begin{bmatrix} 1 & 0\\ d & 1 \end{bmatrix}\begin{bmatrix} 1 & \frac{-1}{f_1}\\ 0 & 1 \end{bmatrix}=\begin{bmatrix} 1-\frac{d}{f_2} & \frac{-1}{f_1}-\frac{1}{f_2}+\frac{d}{f_1f_2}\\ d & 1-\frac{d}{f_1} \end{bmatrix}=\begin{bmatrix} \frac{2}{3} & \frac{-1}{15}cm^{-1}\\ 10cm & \frac{1}{2} \end{bmatrix}=\begin{bmatrix} A_{11} & A_{12}\\ A_{21} & A_{22} \end{bmatrix}$$

Since the system is assumed to be in air, the focal length is the same on both sides of the system. SO we have:

$$f=\frac{1}{-A_{12}}=15cm$$
$$\overline{H_1O_1}=(1-A_{11})f=5cm$$
$$\overline{H_2O_2}=(1-A_{22})f=7.5cm$$

Where H denotes the principle planes and O denotes the lenses.
So here's the problem, recall that the lenses are separated by only 10cm, this forces principle plane #2 to be in front (left of) principle plane #1. How can this be true? What did i do wrong?

Last edited: Nov 4, 2009


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main-content

## Swipe to navigate through the articles of this issue

01-12-2014 | Research | Issue 1/2014 Open Access

# v-TerraFly: large scale distributed spatial data visualization with autonomic resource management

Journal:
Journal of Big Data > Issue 1/2014
Authors:
Yun Lu, Ming Zhao, Lixi Wang, Naphtali Rishe
Important notes

## Electronic supplementary material

The online version of this article (doi:10.1186/2196-1115-1-4) contains supplementary material, which is available to authorized users.

## Competing interests

The authors declare that they have no competing interests.

## Authors’ contributions

YL carried out the TerraFly deployment pattern studies and v-TerraFly design, participated in the sequence experiment and drafted much of the manuscript. MZ participated the system design, advised and designed most of the experiment and analyzed the experiments results. LW participated in the VM node deployment and helped drafting the manuscript. NR developed the TerraFly technology and major algorithms, designed system layers design and partook in writing the manuscript. All authors read and approved the final manuscript.

## Introduction

With the exponential growth of the World Wide Web, there are more domains open to Geographic Information System (GIS) applications. Internet can provide information to a multitude of users, making GIS available to a wider range of public users than ever before. Web-based map services are the most important application of modern GIS systems. For example, Google Maps has more than 350 million users. There is also a rapidly growing number of geo-enabled applications which consume web map services on traditional computing platforms as well as the emerging mobile devices.
Virtual machines (VM) are powerful platforms for hosting web map service systems. VMs support flexible resource allocation to both meet web map services system demands and share resources with other applications. Virtualization is also enabling technology for the emerging cloud computing paradigm, which further allows highly scalable and cost-effective web map services hosting leveraging its elastic resource availability and pay-as-you-go economic model [ 1].
However, due to the highly complex and dynamic nature of web map service systems, it is challenging to efficiently host them using virtualized resources. First, typical web map services have to serve dynamically changing workloads, which makes it difficult to host map services on shared resources without compromising performance or wasting resources. Second, a web map service often consists of several tiers which have different intensive resource needs and result in dynamic internal resource contention. Third, for a typical web map service, both response time for requests and the freshness of the returned data are critical factors of the Quality of Service (QoS) required by users.
To address the above challenges, this paper presents v-TerraFly, an autonomic resource management approach for virtualized map service systems, which can automatically optimize the QoS (considering both response time and data freshness) while minimizing the resource cost [ 24]. First, v-TerraFly can accurately predict the workload demands of a web map service online based on a novel two-way forecasting algorithm that considers both historical hourly patterns and daily patterns. Second, based on the predicted workload, v-TerraFly can automatically estimate the resource demands of its various tiers based on performance profiles created using machine learning techniques. Third, v-TerraFly employs a new QoS model that captures the balance between response time and data freshness and uses this model to automatically optimize the resource allocation of a web map service system [ 5].
This proposed v-TerraFly system is realized on Hyper-V virtual machine environments and evaluated by experiments using real workloads collected from the production TerraFly system. The results show that the proposed two-level workload prediction method is outperforms traditional exponential smoothing prediction by 18.91%, and the system improves the QoS by 26.19% compared to traditional statically node allocation. In the meantime, it saves resource usages by 20.83% compared to traditional peak-load-based resource allocation.
In summary, this paper’s main contributions are: (1) created a VM-based map service system, v-TerraFly, which virtualizes all tiers of a typical web map service and supports dynamic resource allocations to the different tiers; (2) proposed a novel autonomic resource management approach for virtualized map services, which automatically allocates resources to different tiers of the service and optimizes the allocations based on the performance and data freshness tradeoff; (3) evaluated v-TerraFly using real workloads collected from production web map service system, which shows substantial improvement on QoS and resource efficiency.
The rest of this paper is organized as follows: Section Background presents the background and motivations; Sections v-TerraFly describes the architecture of v-TerraFly; Section Autonomic Resource Management in v-TerraFly explains the autonomic resource management of v-TerraFly; Section Evaluation presents an experimental evaluation; Section Related work examines related work; and Section Conclusions and future work concludes the paper.

## Background

### Web map services

As a promising new application of GIS, web map service exhibits its excellence in serving online map requests responsively and delivering geographical information precisely over the Internet [ 6]. A typical web map service, such as Google maps, Bing maps, and Yahoo maps [ 7], are usually built upon several major tiers (Figure  1). A Preprocessor preloads images and geographic features from raw data repository and splits them into grid format, known as image tiles, to facilitate the Processor quickly locating and fetching data. Then a tile Processor retrieves and integrates all tiles needed in a customer’s query. As its upper tier, a generic map interface accesses this imagery by geo-location, and a client app (or browser) to show the map to end-users.
In this paper, we use TerraFly as a case study of a web map system [ 1]. TerraFly serves worldwide web map requests, providing users with customized aerial photography, satellite imagery and various overlays, such as street names, roads, restaurants, services and demographic data. Following the typical architecture described above, TerraFly contains two major tiers (Figure  1): the Image Loader Tier preprocesses the raw imagery data from repository; the Image Reader Tier processes image tiles and retrieves queried images [ 8]. These tiers are further described in Section v-TerraFly.
Traditionally, web map services are hosted on dedicated physical servers with sufficient hardware resources to satisfy their expected peak workloads in order to provide responsive web services to the users. However, this becomes inefficient for real-world situations where the workloads are intrinsically dynamic in terms of their busty arrival patterns and ever changing unit processing costs [ 9]. Consequently, peak-load-based resource provision often leads to underutilization of resources for normal state workloads and causes substantial overhead.
Using VMs to host multi-tier web map services can effectively address this limitation because virtualized resources, including CPU, memory, and I/O, are decoupled from their physical infrastructures and can be flexibly allocated to different tiers of the web map system [ 10]. This approach allows the resource capacity of each tier to elastically grow and shrink to serve its dynamic. In this way, different tiers transparently share the consolidated resources with each other and/or other applications with strong isolation. Such benefits are important to the efficiency of web map service hosting in both typical data centers and emerging cloud systems. On one hand, users need to pay for only the resources their services actually consume. On the other hand, resource providers only need to allocate resources as required by the services while saving valuable resources for hosting other applications [ 11].
Virtualization also offers a new paradigm for web map service deployments. Modern web map services are sophisticated systems, where their installation and configuration require substantial domain knowledge and experience as well as considerable efforts from the administrators. VM-based web map service hosting allows carefully installed software to be distributed as simply as copying the data that represents the VMs. In addition, this approach allows web map services to be quickly replicated and distributed for performance and reliability improvements.

## Research design and methodology

### v-TerraFly Architecture

To enable the autonomic resource management in TerraFly, we leverage VM techniques to virtualize this multi-tier system, denoted as v-TerraFly. The two critical resource intensive tiers of TerraFly, the image Loader and Reader Tier s, are deployed on the VMs instead of physical servers.
Figure  2 shows the architecture of this v-TerraFly. The users interact with the application tier which handles most of the business logic and provides advanced application services, such as universal mapping and application specific mapping (e.g. real estate, water management), by sending the mapping queries including position and resolution requirements to the tiers below. Then the image Reader Tier is invoked to compute and locate associated map tiles from indexed imagery database according to the requests from the application. To maintain data freshness, the organized imagery database is updated by the Loader Tier periodically at the same time. Loader contiguously extracts the incoming raw map data from the raw imagery repository, preprocesses and organizes the raw data to destination projection, and then converts the data into the destination file type, and finally updates the data into the organized imagery database.
Virtualization in TerraFly also improves the flexibility in terms of the system reliability and scalability. VM is the computing resource in both Loader and Reader Tier s. With the load balance in both tiers, the work load of each VM is the same; therefore, the VMs in the same tier are considered identical. Since the computing resources can be partitioned through VM nodes, the network bandwidth, which is always a bottleneck in the original system, can now be well balanced among VMs. Furthermore, by pairing every two VMs as complementary Reader nodes, it is able to provide more reliable service under unexpected system failure by simply replacing the failed VM with its corresponding back-upped VM [ 12, 13].

### Motivating examples

In this section, we demonstrate both the necessity and benefits of resource consolidation in a map service system.
For web map services, the performance of Reader Tier and Loader Tier are both important. Better Reader Tier performance provides shorter page response time; better Loader Tier performance provides faster loading of new map data. But both tiers are resource-intensive and they will compete with each other on resource allocation. The goal is to balance the two tiers to achieve best quality of service when we have limited resources.
The workloads of web map service can be highly dynamic over time. Based on the analysis on the web service logs of TerraFly, it is observed that there were millions of web requests received on the Reader server over the year of 2012, i.e., more than 450 visits per second on average. However, this workload varies significantly on hourly basis. Figure  3 shows a typical one-day TerraFly workload trace. It shows that the request rate drops to 150 (visits per second) in the morning (around 9:00 am) while rising quickly up to 900 (visits per second) in the afternoon. It would be more efficient to turn off some Reader VMs at times.
Assuming the variation in workload which follows such a time-related pattern is predictable, by virtualizing the Reader Tier of TerraFly we can easily save resources when the workload intensity is low by simply turning off some Reader VMs, and as the workload intensity increases, we can bring back them online to process the additional requests.
To further quantify the resource savings, we replay this one-day trace using two deployment schemes for the Reader Tier: the static scheme deploys the Reader tier on the fixed number of computing nodes throughout the entire experiment (2, 4, 6, 8 and 10 nodes respectively); the dynamic schema only assigns sufficient nodes needed by the workload in every hour. The response time is used as the performance metric and the desired QoS target is set to (0.7 s). Figure  4 compares the average response time in every hour using different schemes. We use node-hour as the cost unit in terms of computing resource. By measuring the number N i of active nodes used in the i th hour, the total amount of the resource during certain time period T (hours) can be computed as $∑ i T N i$.
Figure  4 compared the measured response times in every hour using different deployments as well as the total resource costs needed in one day. As we can see among the static deployment configurations, only the 10-node configuration can always meet the desired target, however at the cost of the highest total resource amount (240 node-hour); others suffer different levels of QoS violation as the workload changes dynamically.
In contrast, the dynamic deployment scheme is able to track the QoS target all the time with only 148 node-hour, saving about 23% of the resources compared to the static 8-node configuration which cannot satisfy the QoS target, and saving 38% of the resources compared to the static 10-node configuration which can satisfy the QoS target. Its resource utilization is as efficient as the 6-node configuration but delivers much better performance.
The above example shows strong evidence of the importance of map service virtualization and its online resource management. Currently, our traditional TerraFly system is deployed on the 8 physical Reader Tier nodes and 2 Loader Tier nodes. It works well for supporting up to 800 concurrent users, and about 6GB fresh data can be load each hour by the 2 Loader nodes (Refer to 4.3 Resource Model); but the system scalability is limited due to its fixed physical capacity. It cannot shift resources between Reader and Loader Tier s even when one tier has idle resource and another has insufficient resources. The inability of shifting resources between tiers results the waste of resources.
However, there are several challenges to dynamic resource management of a virtualized web map service. First, the dynamics in the realistic workload causes the demand of CPU consumption change over time; second, resources also need to be dynamically allocated between the Reader Tier to optimize response time and the Loader Tier to keep the data fresh.
These challenges can be well addressed by an autonomic VM-based resource management solution which can flexibly partition shared resources and allocate resource on-demand for dynamic workload in order to guarantee performance and improve resource utilization.

## Autonomic resource management in v-TerraFly

### General approach

Figure  5 illustrates the framework of our proposed autonomic resource management system for v-TerraFly, which consists of three key modules. Please see the notes in Table 1 Parameter description. In this paper, we focus on the resource management for both Reader and Loader Tier s, since they are the most resource intensive tiers in v-TerraFly.
Table 1
Parameter description
Parameter
Description
w ( t )
rR ( t )
Reader VM CPU resource need at time t
rL ( t )
Loader VM CPU resource need at time t
$w h Des$
Horizontal double exponential smoothing prediction
$w d Des$
Vertical double exponential smoothing prediction
w
Two-level double exponential smoothing
As a workload executes on the VMs, the Workload Sensor monitors the actual workload at current time step, noted as w( t). The Workload Predictor then forecasts the future workload w( t + 1) for the next time step based on a prediction model. Based on the predicted workload, the Reader profile and Loader profile which are trained offline are used to estimate their resource demands for time t + 1, denoted by rR( t + 1) and rL( t + 1) respectively. The estimated resource demands are then used by the Resource Allocator to make the actual allocations by assigning appropriate number of VMs to the Reader Tier and Loader Tier. Together, these modules form a closed-loop which runs continuously (e.g., every hour), for v-TerraFly’s resource control and optimization. In the rest of this section, we describe the key components of this autonomic system in details.

In order to accurately and timely predict the workload on v-TerraFly, we propose new forecasting techniques to discover and exploit patterns in user visiting behaviors such as those observed in Figure  3. Specifically, we propose a new two-level time series prediction approach to build a prediction model based on the historical workload measurements, i.e., the request rate observed from the Reader Tier of v-TerraFly. Based on such a model, the workload predictor in v-TerraFly is able to estimate the workload intensity for the next time period.
Time series analysis techniques are widely applied in economic data analysis to provide statistical prediction and therefore guide business decisions. A variety of time series prediction methods are available such as the Moving Averages, Linear Regression and Exponential Smoothing [ 1416]. In this paper, the TerraFly workload prediction based on the double exponential smoothing (DES) method [ 17] which is suitable for discrete data sequence with repeated changing patterns.
DES is a smoothing-based forecasting method that can be applied to time series data, a sequence of observations with equally spaced intervals, expressed as { Y(0), Y(1),.., Y( t)}. Then in DES, the estimate for the t + 1 time intervals can be computed as:
$Y Des t + 1 = 2 S ′ t - S ″ t + α 1 - α S ′ t - S ″ t$
$S ′ t = αY t + 1 - α S ′ t - 1$
$S ″ t = α S ′ t + 1 - α S ″ t - 1$
The equation shows a linear combination of smoothing based statistics associated with a smoothing weight α. The first two components reflect the variation of mean of the overall data while the third tracks the trend of the data. S’ is denoted as the singly-smoothed series which smoothed the next measure by assigning a exponentially decreased smoothing weight to the data of the series and computing the weighted average of the observed series. More intuitively, the most recent data is of more importance to the current estimates, i.e., the weight assigned to the data k periods old is (1 -  α) k , therefore the closer to 1 of the value of α, less smoothing effect but greater weight to the recent changes. S″ is denoted as the doubly-smoothed series computed by recursively applying the same exponential smoothing operation to the singly-smoothed series S’ using the same smoothing weight.
In order to perform the time-series-based forecast in v-TerraFly, the workload can be represented as a sequence of intensity measurements that come from a continuing time series at time intervals T, denoted as {… w( t-2  T), w( t- T), w( t)}. More specifically, the workload measurement can be either the average request rate or the number of concurrent client sessions observed in every hour; the time interval T can be either one hour or one day (24 hour).
We propose a new two-level double exponential smoothing forecasting model to capture both the daily pattern and hourly pattern of v-TerraFly workload as follows.
$w ′ t + 1 = μ h w h Des t + 1 + μ d w d Des t + 1$
(1)
where $w h Des$ is the horizontal double exponential smoothing prediction based on the hourly pattern in the workload, and $w d Des$ is the vertical double exponential smoothing prediction based on the daily pattern of the workload.
$w h Des t = 2 S ′ t - 1 - S ″ t - 1 + α h 1 - α h S ′ t - 1 - S ″ t - 1$
(2)
$w d Des t = 2 S ′ t - 24 - S ″ t - 24 + α d 1 - α d S ′ t - 24 - S ″ t - 24$
(3)
More specifically, $w h Des t$, called horizontal prediction, is predicted based on {  w( t - 3),  w( t - 2),  w( t - 1)} from a hourly series; while $w d Des t$, vertical prediction, is based on the observation series {  w( t - 48),  w( t - 24),  w( t)} that are extracted vertically at the same hours but from continuing days, i.e., a 24-hour vertical time span. The associated μ factors which are set between 0 to 1 are used to balance the importance between three components.
Since each level of DES operation is associated with a smoothing weights, we denote the weights in horizontal and vertical predictions as α h and α d respectively. Then the proposed two-level DES model can be considered as a function of α h and α d , given observed workload series. Therefore the workload model is trained continuously online as soon as the new measurement is observed by optimizing both α h and α d to minimize the weighted sum of squared errors between the prediction and the actual observation. Once the model is updated, it applies to the system immediately for the next prediction.

### Performance profiling

Performance profiles relate the workload of the Reader and Loader Tier s to their resource demands according to the desired performance. Taking the predicted workload w( t + 1) as the input, these profiles are used by the Resource Allocator to allocate resources to the Reader and Loader Tier s dynamically in order to achieve the desired QoS.
For the Reader Tier, since the workload consists of online web requests, the intensity of the workload is specified by request rate w( t) as discussed in Section Workload prediction. The relevant performance metric is the average response time RT( t) of the requests completed during each control period (e.g., one hour). It can be considered as a function of the workload and the number of VM nodes rR( t) allocated to Reader Tier. Thus,
$RT t = ∅ w t , rR t$
(4)
The strategy to build this mapping is offline profiling. Given a specific workload w, we map the number of nodes n allocated to the Reader Tier to the performance RT by iterating over the allocation space and collecting corresponding performance measurements under each allocation candidate. Then we repeat the above step under different workloads by varying the number of the concurrent users in v-TerraFly. Figure  6 illustrates the mapping results by using two to ten Reader nodes to serve a workload with 40 to 240 concurrent users. Such a mapping provides the least number of VM nodes needed for a given workload to meet a specific QoS target. For example, if desired response time is set to 0.7 second, then the minimal number of VMs needed is two for a workload with about 40 users and 10 when there are more than 230 concurrent users.
In order to reduce the time required for performance profiling, we collected only a subset of the Reader configurations under a subset of the workload intensities, and use linear regression to build the Reader Tier entire performance profile. As shown in Figure  7, we got the profile mode and the R square is 0.9131.
We profiled both the CPU and I/O resource usages of the Reader Tier, as shown in Figure  7. The results show that both the CPU and I/O demands follow the exact same pattern as the workload varies, which validates the use of identical VM nodes as the resource allocation unit of the Reader Tier.

### QoS model

In this section, we propose a novel QoS model to consider both the responsiveness in serving user mapping requests and the quality of returning geographic information. In a virtualized web mapping system, both Reader and Loader VMs are usually co-hosted in a cluster/data center and compete for the common physical resources, while the former guarantees acceptable response time and the latter keeps the imagery data up to date. Since the performances from both tiers are critical, we need to well balance the importance between them especially when the total resource capacity is constrained. Therefore, a new QoS model is defined to represent the overall system performance at measuring time period t.
$QoS t = r t × f t$
(5)
where r(t) and f(t) are the performance metrics for the Reader and Loader Tier respectively.
The former QoS component r(t) is called the normalized response time, which measures the quality of web mapping services at time t and can be calculated as following:
$r t = R T ref RT t$
(6)
where RT ref is the desired average response time at Reader Tier and RT( t) is the actual performance measurement at time t. The higher of the value, the quicker the user requests served at Reader Tier.
The latter QoS component f( t) is called the cumulative data freshness which measures the quality of data-loading process at Loader Tier at time t. It is calculated recursively based on the previous data freshness value and the current data incremental rate, expressed as following:
$f t = 1 - ρ × f t - 1 + Δ D t / D ref$
(7)
where ρ is the decaying factor (predefined in the range of 0 to 1) indicating the data quality loss in terms of freshness during the past time period; D ref is the desired amount of fresh data per time period, ΔD( t) is the actual amount of data loaded during time period t. Initially phase t = 0,  f(0) =  ΔD(0)/ D ref .
For instance, assuming we need to maintain D ref  = 300 GB amount of fresh data in repository every control period and the data freshness value at previous time period was f( t - 1) = 0.9  will be reduced to 0.864 at current time t given a decaying factor of 4.0%. If there is 15GB data loaded during current time period, then the incremental rate is 0.05 and therefore the freshness value f( t) = 0.864 + 0.05 = 0.914. Intuitively, we can say the current data quality is 91.4% fresh. Note that it is evident that the data freshness can be adjusted by controlling data incremental rate via resource management at Loader Tier.
By maximizing the QoS as computed above, the v-TerraFly resource management system automatically optimize the response time and data freshness simultaneously, which are both important to the map service received by users.

## Results and discussion

### Setup

This section evaluates the proposed virtual web map service system and its autonomic resource management using the v-TerraFly prototype and real traces collected from the TerraFly production system. As a typical web application, TerraFly usually provides a variety of web services via IIS (Internet Information Services) to serve online web requests. The test bed is set up on two Dell PowerEdge 2970 servers, each with two six-core 2.4GHz AMD Opteron CPUs, 32GB of RAM, and one 1 TB 7.2 RPM SAS disk. Windows Server 2008 and Hyper-V are installed to provide the virtualization environment for v-TerraFly. The resource management system for v-TerraFly is hosted on the hypervisor’s management VM. All guest VMs including both Reader and Loader Tier of TerraFly are installed Windows Server 2008 Data Center as the OS. Each Reader and Loader VM is configured with one core CPU, 2G memory, and 64 GB disk. The resource allocation is done by starting or stopping VMs via Hyper-V PowerShell Script.

We first evaluate the accuracy of our proposed two-level DES workload prediction algorithm by comparing it to two one-level DES approaches based on hourly pattern only ( Horizontal) and daily pattern only ( Vertical) respectively, as well as history average statistics ( History Average). The evaluation is performed using a real one-month workload trace of the November 2012 extracted from the production TerraFly system’s logs. To conduct the experiment more efficiently, the real trace is replayed with a 60-fold speedup, i.e., using one minute in the experiment to simulate one hour in real world. The prediction and updates of the workload models ( smoothing weights α h and α d , refer to Eqs. 2 and 3) are performed every minute to adapt to the dynamics.
Figure  9 compares the online prediction errors of different approaches. Our proposed two-level prediction method delivers significantly better accuracy in predicting the request rate of one month workload. Overall, the 90 percentile average error rate of our two-level method is 10.01% with the lowest standard deviation of 145.3, both much lower than the other three prediction approaches which are 45.67% ( Horizontal), 28.92% ( Vertical), and 25.14% ( History Average) respectively. These results demonstrate that our proposed method can effectively exploit both the hourly pattern and daily pattern in the workload and achieve accurate workload prediction.

### Resource management of Reader Tier

As discussed in Section Performance profiling, based on the predicted workload, the v-TerraFly resource management system automatically allocates resources to the Reader and Loader Tier s in order to optimize the QoS. This section evaluates the resource management for the Reader Tier alone and demonstrates whether it can achieve the Reader Tier’s response time target with the least amount of resources.
In the experiment, a real daily workload trace of October 4th 2012 is replayed against v-TerraFly with a 60-fold speedup. The resource allocator adjusts resources allocation every 1 minute. The QoS target is set to 0.7 s in response time. Based on the profiling, the performance model of Reader Tier is R( t) = 2.4631  W( t) + 154.06, (as shown in Figure  7).
Figures  10 and 11 compare the response time and allocations of our dynamic approach to static 6, 8, 9 and 10-node deployment plans respectively. From the results, we can see that the online dynamic approach is able to achieve the response time target all the time throughout the entire experiment. Compared to the 6-node static plan which achieves 0.634 second in average page response time, the online dynamic plan improves the performance by 32.18%, i.e., 0.430 second in average response time, but at the cost of only 5.6% more resource allocation, i.e., 8 additional node-hour. There are 13 data points where its response time exceeds 0.7 second in the 6-node static plan, which causes as much as 54.17% QoS violation; in contrast, no QoS violation occurs in the dynamic plan.
Compared to the 8-node static plan, the dynamic plan saves as much as 20.83% of total resources, i.e., 40 node-hour. Although the static 8-node plan allocates substantially more with surplus resources, it still causes three QoS violations during the experiment. The 9-node static plan meets the QoS target all the time except the 19 th hour, and it costs 29.63% more total resources than the dynamic plan. The 10-node static plan is the only static plan that meets the QoS target all the time, but it costs 36.67% more total resources than the dynamic plan.
Overall, it is evident that the online dynamic deployment plan can efficiently allocate resources to the Reader Tier while at the same time meet the response time target by flexibly adjusting its VM assignments in an online manner.

This section evaluates the proposed autonomic resource management approach for both Reader and Loader Tier s. Based on the QoS model defined in Section QoS model, the importance of both tiers needs to be balanced in order to optimize an overall QoS value which not only guarantees the responsiveness of map service but also maintains the data freshness of returned maps.
In the experiment, we use the same workload trace described in Section Resource management of Reader Tier, and compare our proposed approach to the traditional static deployment plan. The traditional method allocates a fixed number of nodes to Reader Tier to satisfy average response time by past experience and gives rest nodes to Loader Tier. Specifically, it assigns 7 nodes to the Read Tier and 3 nodes to the Loader Tier in order to achieve an average response time of 0.9 second and 303.3GB fresh data per day (average f( t)  = 0.809, refer to Eq.  7).
Figures  12 and 13 compare the performance of the proposed dynamic plan to the traditional static plan in both response time of the Reader Tier and throughput of the Loader Tier. The static plan achieves an average response time of 0.897 seconds, while the dynamic plan shows slightly better 0.873 seconds. The latter also achieves higher average throughput (194.6 thousands requests per day) than the static one (185.1 thousands requests per day).
For example, as showed in Figure  15, from Hour 7 to 10, since the workload on Reader Tier is less intense, the dynamic plan allocates more resource to the Loader Tier to allow the new data to be loaded as fast as possible. As a result, the dynamic plan loads much more new data (473.3GB Per day) at a varying loading rate than the traditional plan (303.3GB Per day), which loads data at a fixed rate. And the QoS value of the dynamic plan ( Avg QoS = 1.079, refer to Eq.  5) is 26.20% higher the traditional plan ( Avg QoS = 0.855, refer to Eq.  5).
In summary, our proposed autonomic resource management approach is able to automatically optimize the tradeoff between service responsiveness and data freshness by balancing the resource allocations between the Reader and Loader Tiers.

## Related work

In the geospatial discipline, web-based map services can significantly reduce the data volume and required computing resources at the end-user side [ 18]. To the best of our knowledge, v-TerraFly is the first to study the virtualization of typical web map services and propose QoS-driven resource management for a virtualized web map service through workload forecasting and dynamic resource allocation [ 19].
Various automatic forecasting algorithms have been studied in the related work [ 20], including different kinds of exponential smoothing. The work of Brown [ 16] and Gardner [ 17] led to the use of exponential smoothing in automatic forecasting for example, like Stellwagen & Goodrich's research at 1999 [ 1517]. Hyndman (2002) developed a more general class of methods with a uniform approach to calculate the prediction interval [ 14, 15]. The workload prediction algorithm proposed in this paper is based on exponential smoothing, but it is novel in the use of two levels of double exponential smoothing to capture both hourly pattern and daily pattern in the workload, which achieves much higher accuracy than traditional exponential smoothing methods.
In particular, Dinda et al. studied prediction-based best-effort real-time service to support distributed, interactive applications in shared computing environments. Two of the examples are an earthquake visualization tool and a GIS map display tool, which were shown to benefit from the service [ 21]. However, the workload prediction is based on linear prediction which is often not sufficient for real-world dynamic workloads. In this paper, we proposed a two-level exponential smoothing algorithm which shows good prediction accuracy for real TerraFly workloads.
Various types of solutions have been studied in the literature to address the problem of autonomic VM resource management. Different machine learning algorithms have been considered to model VM resource usages [ 2225]. Although this article focused on virtualized geo-databases, we believe that our proposed VM resource allocation approach is generally applicable to the virtual resource management for other types of Big Data handling applications. The application-specific part of this approach is geo-database system applications with large numbers of users. Feedback control theory has also been used to adjust VM resource allocations, which are often based on models trained to identify the system and build the controller [ 2629]. These various solutions are complementary to this paper’s work which focuses on the management of virtualized web map services. Meanwhile, this paper proposes a unique QoS model to capture multiple important objectives and a new method to optimize resource allocation across multiple competing tiers, which has not been studied in the related work and can be applied to manage other multi-tier applications with similar characteristics.

## Conclusions and future work

Web map services become increasingly widely used for various commercial and personal uses. Virtualization can greatly facilitate the deployment of web map service systems and substantially improve their resource utilization. To fulfill this potential, the resource management of a virtualized web map system needs to be able to handle the dynamic workloads that the system typically serves and satisfy the often competing demands of the various tiers of the system.
This paper presents a solution, v-TerraFly, to address these challenges. v-TerraFly is created by virtualizing the various tiers of a typical map service system and allowing resources to be dynamically allocated across the tiers. The resource management is done by predicting the workload intensity based on historical data and estimating the resource needs of the map service’s Reader and Loader Tier s based on their performance models. A unique QoS metric is then defined to capture the tradeoff between the service responsiveness and data freshness, and it is used to optimize the resource allocation to the Reader and Loader VMs.
Experiments based on real TerraFly workload show that our system can accurately predict the workload’s resource demands online and automatically allocate the resources accordingly to meet the performance target and save substantial resource cost compared to peak-load-based resource allocation. It can also automatically optimize the tradeoff between responsiveness and data freshness by dynamically balancing the shared resources between the Reader and Loader VMs.
In our future work, we will improve the scale of v-TerraFly, conducting larger experiments and employing live VM migration as an additional mechanism for optimizing resource management. We will also explore how to apply the principle of v-TerraFly to other applications that have similar dynamic and multi-tier characteristics as a web map service.

## Acknowledgement

This material is based in part upon work supported by the National Science Foundation under Grant Nos. MRI CNS-0821345, MRI CNS-1126619, CREST HRD-0833093, I/UCRC IIP-1338922, I/UCRC IIP-0829576, RAPID CNS-1057661, RAPID IIS-1052625, MRI CNS-0959985, AIR IIP-1237818, SBIR IIP-1330943, FRP IIP-1230661, III-Large IIS-1213026, SBIR IIP-1058428, SBIR IIP-1026265, SBIR IIP-1058606, SBIR IIP-1127251, SBIR IIP-1127412, SBIR IIP-1118610, SBIR IIP-1230265, SBIR IIP-1256641, HECURA CCF-0938045, CAREER CNS-1253944. Includes material licensed by TerraFly ( http://terrafly.com) and the NSF CAKE Center ( http://cake.fiu.edu).

## Competing interests

The authors declare that they have no competing interests.

## Authors’ contributions

YL carried out the TerraFly deployment pattern studies and v-TerraFly design, participated in the sequence experiment and drafted much of the manuscript. MZ participated the system design, advised and designed most of the experiment and analyzed the experiments results. LW participated in the VM node deployment and helped drafting the manuscript. NR developed the TerraFly technology and major algorithms, designed system layers design and partook in writing the manuscript. All authors read and approved the final manuscript.
Supplementary Material
Literature


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Volume 390 - 40th International Conference on High Energy physics (ICHEP2020) - Parallel: Quark and Lepton Flavour Physics
Beauty to open charm final states at LHCb
W. Krupa* on behalf of the LHCb collaboration
*corresponding author
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Abstract
The LHCb detector at the Large Hadron Collider is designed for Physics beyond the Standard Model searches in charge-parity violation and rare decays. Decays of beauty mesons to open charm
final states also enable a wide spectrum of spectroscopy studies, especially investigation of $b\bar{b}$ and $b\bar{s}$ systems. New results, including Run 1 and Run 2 data set, with several new branching fraction measurements, are presented in this paper.
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# Digital Filters

## First order IIR filter

In my book “Embedded Software for the IoT”, there is a chapter on Statistical Process Control. This introduces a simple-filter called EWMA – Exponentially Weighted Moving Average. It is the simplest possible low-pass IIR Filter:

y[n] = \alpha* x[n] + (1-\alpha)*y[n-1]

In other words, this filter has an output that corresponds to a fraction (less than 1) of the input plus 1 minus the same fraction times the previous output. If \alpha is close to one, the filter has a short impulse-response, and as \alpha goes towards 0 the impulse-response goes towards infinity.

Typically, filters are designed from their “3 dB cutoff frequency” – f_c . If we first introduce an intermediate variable – \beta – we can calculate the constant \alpha based on the cutoff frequency and the sampling frequency f_s .

\beta = cos(2\pi f_c/f_s)

\alpha = \beta-1+\sqrt{\beta^2-4\beta+3}

The above is easily done in Excel. You can see more on this filter here.