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# Realtime audio processing using Dynamic

Can I make real time audio processing with Mathematica in the same way I can do with images using Dynamic[CurrentImage[]]. I know that is possible to use SystemDialogInput["RecordSound"] function, but you can't make real time dynamics on it. For example, I would like create one notebook that could make an alert when sound's beyond some level. It's possible?

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I don't think so... Let's pray ;) – Rojo Oct 26 '12 at 0:27
On Linux this is not possible. I add my prayers :) – image_doctor Oct 26 '12 at 11:14
In my case I use a Mac. It's strange that it's so easy to do it with a cam, but not with a microphone. – Murta Oct 26 '12 at 11:29
Also see here for interacting with chuck. – Szabolcs Mar 19 '15 at 21:57
The best I have seen for real time work with MMA was this: a live stream of Conrad Wolfram doing face recognition to block it in real time. twitter.com/conradwolfram/status/573416811728904192 . Since he did it live on stage in front of an audience I would have though some audio processing would be possible providing the bandwidth was low enough. I should note that the frame rate and resolution were typical webcam quality - ie low. – Gordon Coale Mar 20 '15 at 9:41

Generally, Mathematica is just not good at real-time anything. It was not designed for this. Audio processing has very strict requirements on latency. The delay between input and output must be tiny, on the order of milliseconds, otherwise the delay will be noticeable.

Mathematica is simply not meant for this and doesn't have precise timing facilities. I'm fairly confident that the practical answer to this is no, it's not possible.

For non-real time audio processing or things like algorithmic music, I see many uses. But it's not a tool for real-time work.

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Thank you very much! I'm aware of the latency, but this is not really an issue. I would use it to create something like "soundscapes". So, it's not very important that the timing is very accurate. More important is a vast variety of possibilities to manipulate sound in order to create new and interesting approaches in performing. But based on you answer, I assume that it's still no the best software to do something like this. Thanks... – Philipp Mar 19 '15 at 22:08
@Philipp There are many interesting possibilities for uses in music, just not when it must be real-time ... it might be possible to hack something together for simple uses, but I wouldn't feel comfortable with it ... I definitely wouldn't trust it enough to use during a live performance with an audience. Well, at least not without very very extensively testing it first. – Szabolcs Mar 19 '15 at 22:38
@Szabolcs I would like to close and merge this as a duplicate of (13656) to keep all relevant answers in one place. That question could be edited to be more general of necessary. Do you agree? – Mr.Wizard Mar 29 '15 at 15:12
@Mr.Wizard Yes, I agree. – Szabolcs Apr 10 '15 at 17:07

Advise if this is best relegated to comment status.

There are server-based real-time analytics of life science experiments using the Wolfram Language provided by these guys http://emeraldcloudlab.com.

Note the Mathematica 9 logo in their materials, indicates webMathematica rather than a private Wolfram Cloud.

I'll agree that real-time acoustic analysis may be difficult in Mma at present. There are very interesting ~10fps image processing examples I'm aware of but can't provide details of, other than this is a friendly upper limit to aim for.

Disclaimer: no connections to emeraldcloud.com

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SEARCH HOME
 Math Central Quandaries & Queries
 Question from Marie, a student: How to you convert the equation of a line from x-intercept form (y=(x-x1)(x-x2)) to general form (y=ax^2+bx+c) if it involves square roots? For example: Convert this equation to general form: y=(x+the square root of 5)^2 Thanks for the help!

Hi Marie,

I am sure that you know that

$\left( a + b \right)^2 = a^2 + 2ab + b^{2}.$

Try this expansion with

$\left( x + \sqrt{5} \right)^{2}.$

Write back if you need more assistance,
Penny

Math Central is supported by the University of Regina and the Imperial Oil Foundation.

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Item Details

Profile path

Provides a space for you to type the profile path, for example, \\servername\sharefolder\user name.

Logon script

Provides a space for you to type the location of the logon script.

Local path

Specifies that the home folder is located on a local path. In the space provided, type the path location.

Connect

Select this option to choose a network path to connect to a home folder. You can select and configure the network path as follows:

• Click the arrow in the drop-down list, and then select a drive letter.

• In the To box, you can specify that the home folder is located on a network. To specify a network path for the home folder, you must first create the shared resource and set permissions that allow the user access. You can do this using shared folders on another computer.


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## Wednesday, September 30, 2015

### Challenges in Cloud Storage

This post will discuss parts of the talk by Angelo De Caro (IBM Zurich) on 'data storage-oriented cryptographic protocols,' given at the workshop on secure and trustworthy computing in Bucharest.

The cloud provides an attractive opportunity for users and enterprises (collectively 'clients') to outsource their storage. Many providers offer low-cost storage, with straightforward management and ubiquitous access (from multiple devices). However users inherently lose direct control, meaning they have no guarantees about privacy or the future availability of their files.

Deduplication is the process by which a provider saves itself storage space (and consequently money) by only storing one copy of each file, and using some method of tracking which users own that file. This concept is so desirable because there is a large amount of redundancy in many contexts, such as media (movies, music etc.), system files/software and email attachments. When server providers want to deduplicate they have a number of choices:
- file-level or block-level (latter allows better dedup in systems where updates to large files are common)
- single-user/cross-user (latter is more desirable for providers)
- client-side/server-side

The final point introduces some interesting concerns. Server-side dedup means that the client needs to send the whole file to the server, meaning a high bandwidth cost. For client-side deuduplication Alice takes a hash of her file $F$ and sends this value $H(F)$ to the server: if the server hasn't seen this before then instructs Alice to upload the file, if not then deduplication occurs. This means that having $H(F)$ is enough to download the file (DropBox previously used a system where this was the case). This means Alice can send all her friends $H(F)$ where $F$ is a movie, meaning that the provider acts as a content distribution network (this is not a privacy problem: server doesn't want to become such a provider and will have to pay for bandwidth etc). This method also creates a covert channel that reveals which files are stored on the server: in the so-called 'salary attack' discussed by Pinkas et al. an adversary Eve has knowledge of what a company's payslips look like, so can learn an employee's salary by creating a large number of possible payslips and beginning this upload process for each one until the server informs Eve that it already has the file.

Proofs of Ownership
These issues mean we'd rather use proofs of ownership (PoWs)--a way for Alice to convince the server that she owns the file--and this means we need to avoid short file identifiers. In 2011 Halevi et al. suggested the following framework for such a paradigm: in the preprocessing phase the server stores some short info per file (file itself is located in some secondary storage), then in the proof phase (done only during file upload) there is some challenge/response mechanism. This procedure needs to be bandwidth-efficient, and computation (particularly for the client) should be efficient. The authors suggested a method using Merkle trees with special encodings, where the prover is 'challenged' on a certain block in the hash tree. In the preprocessing phase a server is sent the file and computes a Merkle tree, then stores the root. To prove, the server asks the client to present sibling paths to $t$ random leaves, the client computes them, server authenticates. This solution is bandwidth efficient, and space efficient at server side, but the client has to do quite a lot of computation. A client that knows a large proportion of the file will likely be able to 'cheat,' so we need a way to 'spread' the entropy across the file to stop the scenario like the salary attack. Using an erasure code is a good way of doing this (cheating probability $2^{-t}$) but constructions are fairly computationally expensive. An alternative approach was taken by Di Pietro and Sorniotti (AsiaCCS 2012), which is considerably more efficient at on the client side but worse on the server side, and the challenge values have to be recomputed when they are exhausted.

Proofs of Retrievability
Alice outsources a file and wants to know that it's retrievable, meaning not only that the server still holds the file but also that the server hasn't modified the file. There is a trivial solution: just download the file on a regular basis. A better approach is to use a keyed hash function and store $H(k,F)$; if Alice wants to verify she can just send $k$ to the server S and ask S to compute $H(k,F)$ and compare. This is storage efficient for Alice, but S needs to read the entire file and can only verify once. Even better is to use 'sentinels' (short, random strings): Alice embeds sentinels in random positions in $F$, encrypts block-wise, and sends this file $F'$ to server and keeps the sentinels. To verify Alice just asks for sentinel $s_i$ and checks if it is correct. Protocol means Alice doesn't need to store all of F and can detect large erasure (which would remove more than one sentinel), but Alice has to store the sentinels and cannot detect small erasure. One can improve this by computing $MAC(k,s_i)$ and appends this value to the file (server doesn't know to which sentinels these MACs correspond), only needing to store $k$. Alice doesn't need to store any of F and can detect large erasure but still can't detect small erasure. We can solve the 'small erasure' problem by using error-correcting code, however this makes it more expensive.

Confidentiality
Both PoWs and PoRs are tangential to the goal of confidentiality of files from an untrusted server. If two clients upload the same file, encrypted under their own keys, then we'd expect these two ciphertexts to be distinct and (assuming a strong method of encryption) the server shouldn't be able to learn that the two ciphertexts correspond to the same file. Douceur et al. gave an initial solution to this problem: hash the file and use this value H(F) as the encryption key, and this was generalised by Bellare et al. (Eurocrypt 2013). Since encryption is deterministic we can only expect some sort of security if files have high entropy, and indeed this approach allows offline brute-force attacks (Eve is sent a challenge ciphertext $C^*$, and if the message space is small Eve just computes hash of each file and creates ciphertexts until she finds a collision with $C^*$). The same authors of the EC13 paper gave a solution to this problem: their system called DupLESS uses an independent key server (KS), and a user engages in an oblivious PRF with KS to get an encryption key (this means that this key server needs to enforce a per-client rate-limiting strategy to stop brute force attacks). At CCS next month Liu, Asokan and Pinkas will present a paper that removes the need for the key server, by distributing its role among the clients using PAKE (Asokan gave a talk on this paper earlier in the workshop).

This presentation complemented Asokan's talk, Florian Kerschbaum's talk about computing on encrypted data (slides here) and the talk given by Marc Lacoste from Orange Labs who discussed the goals of the Super Cloud project and the security challenges involved in the development of 5G communication standards and IoT.


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# Dyck paths of Dynkin type

(The conjecture is a homological algebra question, but question 2 is a pure combinatorics question given that the conjecture is true)

A Dyck path of length $$n$$ is a list of positive integers $$[c_1,c_2,...,c_n]$$ with $$c_i -1 \leq c_{i+1}$$ for all $$i$$ and $$c_i \geq 2$$ for $$i \neq n$$ and $$c_n=1$$. (One can show that those sequences really correspond to the classical Dyck paths via the area sequence and the number of Dyck paths of length $$n$$ is $$C_{n-1}$$ when $$C_n$$ denotes the Catalan numbers). Dyck paths can get naturally identified with the Nakayama algebra $$A_D$$ with a linear quiver having Kupisch series $$[c_1,c_2,...,c_n]$$, see for example https://arxiv.org/abs/1811.05846 .

Let $$D=[c_1,c_2,...,c_n]$$ be a Dyck path of length $$n$$. We define the Cartan matrix $$C_D$$ of $$D$$ as the $$n \times n$$ upper triangular matrix with entries 0 or 1 as follows: In the $$i$$-th row $$C_D$$ has entries equal to one in position $$(i,i)$$, $$(i,i+1)$$,...,$$(i,i+c_i-1)$$ and all other entries are zero. Define the Coxeter matrix $$\phi_D$$ as $$-C_D^{-1} C_D^T$$ and the coxeter polynomial $$p_D$$ as the characteristic polynomial of this matrix.

We say that a Dyck path is of Dynkin type $$Q$$ in case the corresponding Nakayama algebra $$A_D$$ is derived equivalent to $$KQ$$.

Conjecture: A Dyck path $$D$$ is of Dynkin type $$Q$$ if and only if the algebra $$A_D$$ has coxeter polynomial $$p_Q$$.

This is true for type $$A_n$$ as was proven in What are the periodic Dyck paths? by Gjergji Zaimi (together with the fact that bouncing Nakayama algebras are exactly those of Dynkin type $$A_n$$, which can be proved by using special tilting modules). With the help of a computer it is also true for all exceptional types $$E_6, E_7$$ and $$E_8$$ and true for $$D_i$$ for $$i=4,5,6,7,8,9$$ (which is why I made it a conjecture now), but maybe there is a nice uniform proof that works for all types.

In the theorem of page 23 in http://prospero.dmat.usherbrooke.ca/ibrahim/publications/Alg%C3%A8bres_pr%C3%A9inclin%C3%A9es_et_cat%C3%A9gories_d%C3%A9riv%C3%A9es.pdf one can find a homological characterisation when a (Nakayama) algebra/Dyck path is of Dynkin type $$D_n$$.

We have for the Dynkin types: $$p_{A_n}=x^n+x^{n-1}+x^{n-2}+....+x^2+x+1$$, $$p_{D_n}=x^n+x^{n-1}+x+1$$, $$p_{E_6}=x_1^6+x_1^5-x_1^3+x_1+1$$, $$p_{E_7}=x_1^7+x_1^6-x_1^4-x_1^3+x_1+1$$, $$p_{E_8}=x_1^8+x_1^7-x_1^5-x_1^4-x_1^3+x_1+1$$. See for example Table 1.1. in the book "Notes on Coxeter Transformations and the McKay Correspondence" by Rafael Stekolshchik.

The bouncing Dyck paths are exactly the Dyck paths of Dynkin type $$A_n$$ and there are $$2^{n-2}$$ many. A classification/enumeration seems not so easy in type $$D_n$$, which leads to the following question:

Question 2: How many Dyck paths are there for a given $$n$$ with Coxeter polynomial equal to $$p_{D_n}$$ (call this sequence $$a_n$$)? How many Dyck paths are there for a given $$n$$ that are of Dynkin type $$D_n$$ (call this sequence $$b_n$$)?

Note that in case the conjecture is true, we have $$a_n=b_n$$ and calculating $$a_n$$ is a purely elementary problem. The sequence $$a_n$$ starts for $$n=4,5,6,7,8$$ with 1,6,13,29,65 and does not appear in the oeis. Here are the Dyck paths with Coxeter polynomial equal to $$p_{D_n}$$ for $$n=4,5,6,7$$. Maybe someone sees a pattern what they might be:

$$D_4$$:

[ [ 3, 3, 2, 1 ] ]

$$D_5$$:

[ [ 3, 3, 2, 2, 1 ], [ 2, 3, 3, 2, 1 ], [ 3, 3, 3, 2, 1 ], [ 4, 3, 3, 2, 1 ], [ 3, 4, 3, 2, 1 ], [ 4, 4, 3, 2, 1 ] ]

$$D_6$$:

[ [ 3, 3, 2, 2, 2, 1 ], [ 3, 3, 3, 2, 2, 1 ], [ 3, 4, 3, 2, 2, 1 ], [ 3, 3, 2, 3, 2, 1 ], [ 2, 2, 3, 3, 2, 1 ], [ 3, 2, 3, 3, 2, 1 ], [ 2, 3, 3, 3, 2, 1 ], [ 4, 3, 3, 3, 2, 1 ], [ 2, 4, 3, 3, 2, 1 ], [ 5, 4, 3, 3, 2, 1 ], [ 3, 3, 4, 3, 2, 1 ], [ 3, 5, 4, 3, 2, 1 ], [ 5, 5, 4, 3, 2, 1 ] ]

$$D_7$$:

[ [ 3, 3, 2, 2, 2, 2, 1 ], [ 3, 3, 3, 2, 2, 2, 1 ], [ 3, 4, 3, 2, 2, 2, 1 ], [ 3, 3, 2, 3, 2, 2, 1 ], [ 2, 3, 3, 3, 2, 2, 1 ], [ 4, 3, 3, 3, 2, 2, 1 ], [ 3, 3, 4, 3, 2, 2, 1 ], [ 3, 5, 4, 3, 2, 2, 1 ], [ 3, 3, 2, 2, 3, 2, 1 ], [ 3, 3, 3, 2, 3, 2, 1 ], [ 3, 4, 3, 2, 3, 2, 1 ], [ 2, 2, 2, 3, 3, 2, 1 ], [ 3, 2, 2, 3, 3, 2, 1 ], [ 2, 3, 2, 3, 3, 2, 1 ], [ 4, 3, 2, 3, 3, 2, 1 ], [ 2, 2, 3, 3, 3, 2, 1 ], [ 3, 2, 3, 3, 3, 2, 1 ], [ 2, 4, 3, 3, 3, 2, 1 ], [ 5, 4, 3, 3, 3, 2, 1 ], [ 2, 2, 4, 3, 3, 2, 1 ], [ 3, 2, 4, 3, 3, 2, 1 ], [ 2, 5, 4, 3, 3, 2, 1 ], [ 6, 5, 4, 3, 3, 2, 1 ], [ 3, 3, 2, 4, 3, 2, 1 ], [ 2, 3, 3, 4, 3, 2, 1 ], [ 4, 3, 3, 4, 3, 2, 1 ], [ 3, 3, 5, 4, 3, 2, 1 ], [ 3, 6, 5, 4, 3, 2, 1 ], [ 6, 6, 5, 4, 3, 2, 1 ] ]

Here are the Dyck paths of Dynkin type $$E_6$$:

[ [ 2, 3, 3, 2, 2, 1 ], [ 4, 3, 3, 2, 2, 1 ], [ 4, 4, 3, 2, 2, 1 ], [ 3, 3, 3, 3, 2, 1 ], [ 4, 4, 3, 3, 2, 1 ], [ 2, 3, 4, 3, 2, 1 ], [ 4, 3, 4, 3, 2, 1 ], [ 2, 4, 4, 3, 2, 1 ], [ 3, 4, 4, 3, 2, 1 ], [ 4, 4, 4, 3, 2, 1 ], [ 5, 4, 4, 3, 2, 1 ], [ 4, 5, 4, 3, 2, 1 ] ]

(there are 12 Dyck paths with Coxeter polynomial $$p_{E_6}$$, 54 with Coxeter polynomial $$p_{E_7}$$ and 133 with Coxeter polynomial $$p_{E_8}$$.)

Note that it is in general not true that having the same Coxeter polynomial as $$KQ$$ implies that a finite dimensional algebra is derived to $$KQ$$( there even non-derived equivalent examples with the same Cartan matrix), so the conjecture might be special to Nakayama algebras in case it is true.

• It seems to me that the values of the Coxeter polynomials for $D_n$ that you give do not match the product formula. For the given values, I have $p_{D_4} = \phi(6)\phi(2)^2$, $p_{D_5} = \phi(8)\phi(2)$, $p_{D_6} = \phi(10)\phi(2)^2$, $p_{D_7} = \phi(12)\phi(4)\phi(2)$, – Martin Rubey Sep 1 '20 at 8:07
• Yes, I saw that reference, but it still doesn't fit. In $p_{D_7}$, the factor $\phi(3)$ is missing, and $p_{D_5}$ and $p_{D_7}$ only have one factor $\phi(2)$. – Martin Rubey Sep 1 '20 at 8:16
• OK, then the correct expression would be the product over all divisors of $2(n-1)$ which are not divisors of $n-1$, times $\phi(2)$. – Martin Rubey Sep 1 '20 at 8:33
• More data for $D_n$: the numbers of paths are $1, 6, 13, 29, 65, 145, 323, 705, 3837, 3329, 7169, 15361, 32769, 69633$, the numbers of paths which only return to the axis with their final step are $1, 4, 5, 6, 7, 8, 11, 10, 1473, 12, 13, 14, 15, 16$. I have no idea what makes $D_4$, $D_{10}$, $D_{12}$ special. – Martin Rubey Sep 2 '20 at 6:01
• Put differently, the sequence would like to be $a_4=3, a_5=6$ and $a_{n+2} = 1 + 4(a_{n+1} - a_n)$, but isn't. – Martin Rubey Sep 2 '20 at 6:28


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# [ARM]STM32 LwIP with STM32CubeMX, is it the right way ?

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Not open for further replies.

#### bianchi77

Is it the right way to define IP address 10.0.0.5 ??

Code:
void MX_LWIP_Init(void)
{
/* Initilialize the LwIP stack */
lwip_init();

/* add the network interface */

/*  Registers the default network interface */
netif_set_default(&gnetif);

{
/* When the netif is fully configured this function must be called */
netif_set_up(&gnetif);
}
else
{
/* When the netif link is down this function must be called */
netif_set_down(&gnetif);
}

#### armembedded

##### Newbie level 1
HI
you can work with rl-arm and keil ide.
Rl-arm is software solution for arm microcontrollers and you can work the network ,file system,usb and so on . but if you want to work with that you should get the licsience for that.

keil website is : www.keil.com

Status
Not open for further replies.


text:
BCG Matrix Analysis Case Solution

BCG Matrix Analysis, Genomic Study, and Single-Cell Sequencing {#sec2.6} —————————————————————- Following three to five rounds of single-cell isolation, we proceeded to perform cell-by-cell nucleofection to label all the cells for next-generation genomic studies. Cells were sorted into 75 cm^2^ tissue culture flasks using the JE-4.

Case Study Help

5 nozzle system (Biovista, Herrsching, Germany). Neutrophils were separated from other cell types using the BD Facssort system and the BD Aria III system both from BD Biosciences (Palo Alto, CA). After loading sorted cells (flowrate ∼6 mL/min) into prelabeled 10 cm sterile culture dishes, we performed 15 to 20 rounds of centrifugation at 300*g*.

Recommendations for the Case Study

After the final centrifugation step, we collected residual cell pellets for DNA extraction. We removed excess culture medium from the cell pellets by aspirating them using 15-ml syringes fitted with 25G needle and 8 G syringe, followed by spin down at 2000*g* for 2 min. We lysed \~50 µL of suspension by adding 800 µL of 50 mM Tris, pH 8.

Recommendations for the Case Study

0 containing 50% (w/v) CTAB solution, followed by addition of 900 µL of 100 mM NaCl (final addition of NaCl), 700 µL of 80% (v/v) ethanol, 200 µL of 0.2 M EDTA (final addition of EDTA), and finally 400 ml of 10 mM Tris, pH 8.0 in a heating block at 65°C for 10 min following the manufacturer\’s instructions for a single-cell lysis.

Case Study Analysis

To increase cell lysis efficiency, we skipped the initial step, which is the addition of the EDTA, and performed the following steps in the same tubes and also concurrently. Lastly, we extracted nucleic acids from the cell lysates by adding 180 µL of ISOLATE II DNA kits (Bioline, London, UK). To perform the cacion-pipemization step, we first added 50 µL of 40 µM random decamer d(T~12–18~T~12–18~) (IDT, Coralville, IA) to a given tube.

VRIO Analysis

The ISOLATE II DNA kit concentrations of CTAB and ISOLATE II were found to be optimal in terms of percentage of remaining organic components during extraction. Following 10 cycles of pipetting up and down to resuspend remaining particles, we pipetted 400 ul of the nucleic acid elution down the columns. Following a final wash step, we reverse-transcribed the RNAse H treatment using random hexamers and transcriptase.

Problem Statement of the Case Study

We performed the process twice in batches, and each cycle involves 10 µL amplification in parallel using the Thermostar Gradient Master mix (5×) buffer (Agilent, Santa Clara, CA), and 50 ng of cDNA template. Following the same amplification round with a randomized set of primers (with and without transcriptase), we reverse-transcribed the cBCG Matrix Analysis {#s2b} ——————— We first examined the *BD-1* mRNA levels resulting from H~2~S treatment. Treatment of K562 cells with H~2~S (300 µM) resulted in a 5.

BCG Matrix Analysis

3 fold increase in BD-1 mRNA level 1 hour later with respect to the untreated control ([fig. 2](#pone-0081418-g002){ref-type=”fig”}). ![Effects of H~2~S on BD-1 mRNA level in K562 cells.

VRIO Analysis

\ K562 cells were treated with H~2~S at the indicated concentrations, total mRNA was isolated after 0, 1, 2, 4 and 8 hours of treatment and levels of BD-1 mRNA were evaluated by real-time RT-PCR using BD-1 specific primers and sequences. The results presented are from densitometry analyses performed on three independent reactions, averaged and expressed as mean ±SD for three independent experiments in triplicates. \*\*\*p\<0.

PESTEL Analysis

001. (n = 3).](pone.

PESTEL Analysis

0081418.g002){#pone-0081418-g002} We then treated two HL-60 cell lines and two primary CD34+ cells with 10 µM of H~2~S for 2 hours and analyzed mRNA levels of BD-1 in a time course of time ([fig. 3A,B](#pone-0081418-g003){ref-type=”fig”}).

Case Study Help

As we anticipated that H~2~S treatment, under the above used concentration, did not reach cytotoxic levels in HL-60, HU-77 and K562 ([fig. S2](#pone.0081418.

BCG Matrix Analysis

s002){ref-type=”supplementary-material”} A–C), we analyzed BD-1 mRNA levels in 2 hours of H~2~S treatment. In primary CD34+ cells, we found an increase of BD-1 mRNA level in 2 hours of H~2~S treatment, and achieved 2- to 3-fold increase in 2 and 4 hours of treatment. A basal increase of BD-1 mRNA was observed 1 hour after exposure to H~2~S.

Financial Analysis

BD-1 mRNA level remained unchanged in HL-60 for at least 8 hours treatment find this in HU-77 and K562 for 24 hours. ![Effects of H~2~S on BD-1 mRNA level in two HL-60 cell lines and two primary CD34+ cells.\ (A) Experiments were performed as in [Figure 2A](#pone-0081418-g002){ref-type=”fig”}, gene expression for BD-1 was evaluated in two HL-60 cell lines treated or not with 10 µM of H~2~S for 2 hours and 2 and 4 hours respectively (B) Experiments were performed as in [fig.

Evaluation of Alternatives

2A](#pone-0081418-g002){ref-type=”fig”}, and treated as depicted in (A), K562 was treated with 10 µM of H~2~S for 4 hours and in one additional experiment K562 was treated with 10 µM of NaHS (100 µM) for 8 hours. Results presented are from densitometry analyses performed on three independent reactionsBCG Matrix Analysis {#sec2-sensors-20-00292} ——————- The measurements of the Bacterial Contamination Test were obtained in four phases. [Table 1](#sensors-20-00292-t001){ref-type=”table”} summarizes all of the parameters measured in the different measurement phases.

Case Study Help

Phase 1 (first level of the test) was performed with a low dose of indicator bacteria (50% of the liquid volume being a bacterial culture) in the testing chamber. The medium of bacteria from the test chamber is then mixed with the medium of the Bacteriological Reference Material (B. R.

SWOT Analysis

M.) VITI-500, both without oxygen. The reference bacteriological media is identical to the test media.

SWOT Analysis

The next phase is the test with the medium of bacteria being mixed with the medium of the B. R. M.

Evaluation of Alternatives

VITI-500 and with exposure to moderate (60%) and high concentrations of oxygen (100%). Finally the test is continued with a lower oxygen concentration (50%) and a higher bacterial concentration (99%). The measured phase 1 parameters are taken from the following expressions:$${OXY:}Oxygen = \frac{C_{O_{2}}}{C_{C}}$$ where:$OXY$: the concentration of oxygen;$C_{C}$: the concentration of culture of target bacteria (C$_{C}$ = 1.

SWOT Analysis

33 x 10^4^),$C_{O_{2}}$: the concentration of oxygen in the testing chamber (C$_{O_{2}}$ = 9500 ppm). Secondly, [Table 2](#sensors-20-00292-t002){ref-type=”table”} presents the parameters measured in three, five, and seven times phases of the test. By running the test four times in every single phase (each phase has a lower dose), a 15× the initial dose increases the frequency of sampling by a factor of about 11.

SWOT Analysis

The measured parameters for two times increase (15-times) are presented in [Table 3](#sensors-20-00292-t003){ref-type=”table”}. 2.4.

Case Study Analysis

Data Interpretation and Results {#sec2dot4-sensors-20-00292} ———————————– The purpose of the tests was the measure and characterize the susceptibility of the flocculant (Microsep-5) to its interaction with the B. R. M.

Problem Statement of the Case Study

VITI-500 medium which does not contain O$\left( {{NO}_{3}^{-},{NH}_{4}} \right)$. The structure and properties ofMicrosep-5 particles were examined with scanning electron microscopy (SEM) and optical microscopy observation using transmission and wide-field microscopy. These results were used to draw conclusions regarding the flocculant’s physical structure.

### 2.4.1.

SWOT Analysis

SEM Microscopy in CNT-A–Polyurethane Membranes {#sec2dot4dot1-sensors-20-00292} The flocculant Microsep-5 particles suspended in air inside a CNT-A Membrane showed characteristics typical for fine (diameter below 1 µm) microspheres. Some of the particles were 3-$\mu$m in size, others 5-$\mu$m and with a few larger particles (between 10–23$\mu$m). These microspheres showed a spherical shape and a smooth surface with regular topography.

Marketing Plan

A closer inspection of [Figure 7](#sensors-20-00292-f007){ref-type=”fig”}, indicates that Microsep-5 aggregates are composed of spherical particles, i.e., flocs.

BCG Matrix Analysis

This fact is reflected in the typical particle diameter, which is close to the size of droplets in water. ### 2.4.

PESTLE Analysis

2. SEM Microscopy in Glass Filter Media with Plastic Coating {#sec2dot4dot2-sensors-20-00292} Small unilamellar particles made of Microsep-5 were observed in the surface of the plastic coating in [Figure 8](#sensors-20-00292

BCG Matrix Analysis Case Solution
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text:
• Corpus ID: 222140868

# StoqMA vs. MA: the power of error reduction

```@article{Aharonov2020StoqMAVM,
title={StoqMA vs. MA: the power of error reduction},
author={Dorit Aharonov and Alex Bredariol Grilo and Yupan Liu},
journal={ArXiv},
year={2020},
volume={abs/2010.02835}
}```
• Published 6 October 2020
• Computer Science
• ArXiv
StoqMA characterizes the computational hardness of stoquastic local Hamiltonians, which is a family of Hamiltonians that does not suffer from the sign problem. Although error reduction is commonplace for many complexity classes, such as BPP, BQP, MA, QMA, etc.,this property remains open for StoqMA since Bravyi, Bessen and Terhal defined this class in 2006. In this note, we show that error reduction forStoqMA will imply that StoqMA = MA.
4 Citations
StoqMA meets distribution testing
• Yupan Liu
• Mathematics, Computer Science
TQC
• 2021
This work proves that easy-witness \$\mathsf{StoqMA}\$ is a generalization of a subset state such that the associated set's membership can be efficiently verifiable, and all non-zero coordinates are not necessarily uniform, and makes a step towards collapsing the hierarchy.
The Complexity of Translationally Invariant Problems beyond Ground State Energies
• Mathematics
ArXiv
• 2020
This work shows that the translationally invariant versions of both APX-SIM and GSCON remain intractable, and gives a framework for lifting any abstract local circuit-to-Hamiltonian mapping \$H\$ (satisfying mild assumptions) to hardness of APx-SIM on the family of Hamiltonians produced by \$H\$, while preserving the structural and geometric properties of \$H \$ (e.g. translation invariance, geometry, locality, etc).
On polynomially many queries to NP or QMA oracles
• Computer Science, Mathematics
Electron. Colloquium Comput. Complex.
• 2021
This work shows that for any veriﬁcation class C, any P C machine with a query graph of “separator number” s can be simulated using deterministic time exp, and shows how to combine Gottlob’s “admissible-weighting function’ framework with the “ﬂag-qubit” framework for embedding P C computations directly into APX-SIM instances in a black-box fashion.
Termwise versus globally stoquastic local Hamiltonians: questions of complexity and sign-curing
• Physics
• 2020
We elucidate the distinction between global and termwise stoquasticity for local Hamiltonians and prove several complexity results. We show that the stoquastic local Hamiltonian problem is

## References

SHOWING 1-10 OF 28 REFERENCES
Stoquastic PCP vs. Randomness
• Mathematics
2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS)
• 2019
This work shows that the gapped version of this problem, i.e. deciding if a given uniform stoquastic local Hamiltonian is frustration-free or has energy at least some constant ε, is in NP, and reveals a new MA-complete problem, stated in terms of classical constraints on strings of bits, which is the first (arguably) natural MA- complete problem stated in non-quantum CSP language.
The complexity of stoquastic local Hamiltonian problems
• Physics
Quantum Inf. Comput.
• 2008
It is proved that LH-MIN for stoquastic Hamiltonians belongs to the complexity class AM -- a probabilistic version of NP with two rounds of communication between the prover and the verifier, and that any problem solved by adiabatic quantum computation using stoquian Hamiltonians is in PostBPP.
Merlin-Arthur Games and Stoquastic Complexity
• Mathematics
ArXiv
• 2006
It is proved that MA has a natural complete problem which is called the stoquastic k-SAT problem, a matrix-valued analogue of the satisfiability problem in which clauses are k-qubit projectors with non-negative matrix elements, while a satisfying assignment is a vector that belongs to the space spanned by these projectors.
Achieving perfect completeness in classical-witness quantum merlin-arthur proof systems
• Mathematics
Quantum Inf. Comput.
• 2012
This paper proves that classical-witness quantum Merlin-Arthur proof systems can achieve perfect completeness. That is, QCMA = QCMA1. This holds under any gate set with which the Hadamard and
Complexity Classification of Local Hamiltonian Problems
• Mathematics
2014 IEEE 55th Annual Symposium on Foundations of Computer Science
• 2014
This work characterises the complexity of the k-local Hamiltonian problem for all 2-local qubit Hamiltonians and proves for the first time QMA-completeness of the Heisenberg and XY interactions in this setting.
Complexity of Stoquastic Frustration-Free Hamiltonians
• Mathematics
SIAM J. Comput.
• 2009
The Cook-Levin theorem proving NP-completeness of the satisfiability problem is generalized to the complexity class MA (Merlin-Arthur games)—a probabilistic analogue of NP.
Two Combinatorial MA-Complete Problems
• Mathematics
ITCS
• 2021
Two new combinatorial problems are defined and proved to be MA-completeness: ACAC, which gets as input a succinctly described graph, with some marked vertices, and SetCSP, which generalizes standard constraint satisfaction problem (CSP) into constraints involving sets of strings.
The Complexity of the Local Hamiltonian Problem
• Mathematics
SIAM J. Comput.
• 2006
This paper settles the question and shows that the 2-LOCAL HAMILTONIAN problem is QMA-complete, and demonstrates that adiabatic computation with two-local interactions on qubits is equivalent to standard quantum computation.
On Complexity of the Quantum Ising Model
• Mathematics, Physics
• 2014
We study complexity of several problems related to the Transverse field Ising Model (TIM). First, we consider the problem of estimating the ground state energy known as the Local Hamiltonian Problem
Two-local qubit Hamiltonians: when are they stoquastic?
• Physics, Mathematics
Quantum
• 2019
We examine the problem of determining if a 2-local Hamiltonian is stoquastic by local basis changes. We analyze this problem for two-qubit Hamiltonians, presenting some basic tools and giving a


text:
Home > Type 2 > Type 2 Error Probability Formula

# Type 2 Error Probability Formula

## Contents

Generated Mon, 31 Oct 2016 03:36:39 GMT by s_fl369 (squid/3.5.20) Quant Concepts 25,150 views 15:29 Type I Errors, Type II Errors, and the Power of the Test - Duration: 8:11. MrNystrom 155,020 views 15:40 Loading more suggestions... Given, H0 (μ0) = 5.2, HA (μA) = 5.4, σ = 0.6, n = 9 To Find, Beta or Type II Error rate Solution: Step 1: Let us first calculate the http://degital.net/type-2/type-ii-error-probability-formula.html

If two topological spaces have the same topological properties, are they homeomorphic? Please try the request again. Assume the actual mean population weight is 5.4 kg, and the population standard deviation is 0.6 kg. Sign in 537 14 Don't like this video? http://www.ssc.wisc.edu/~gwallace/PA_818/Resources/Type%20II%20Error%20and%20Power%20Calculations.pdf

## How To Calculate Type 2 Error In Excel

Is SprintAir listed on any flight search engines? poysermath 214,296 views 11:32 Statistics 101: To z or to t, That is the Question - Duration: 38:17. Autoplay When autoplay is enabled, a suggested video will automatically play next. Is giving my girlfriend money for her mortgage closing costs and down payment considered fraud?

Be careful, (1-β) is not α because (1-β) = the power of the test. For sufficiently large n, the population of the following statistics of all possible samples of size n is approximately a Student t distribution with n - 1 degrees of freedom. The approach is based on a parametric estimate of the region where the null hypothesis would not be rejected. How To Calculate Type 2 Error On Ti 84 What would have happened to the world if the sepoy mutiny of 1857 had suceeded?

P (Type II Error) = P ( Z < Z542 ) = P ( Z < 0.9899 ) = 0.8389 EXCEL: NORMSDIST(0.9899) = 0.8389 Therefore, the probability of type II error, Probability Of Committing A Type Ii Error Calculator I don't know how one would calculate the power of such a test. –probabilityislogic Feb 20 '11 at 0:24 add a comment| 3 Answers 3 active oldest votes up vote 21 English Español Français Deutschland 中国 Português Pусский 日本語 Türk Sign in Calculators Tutorials Converters Unit Conversion Currency Conversion Answers Formulas Facts Code Dictionary Download Others Excel Charts & Tables Constants

This allows us to compute the range of sample means for which the null hypothesis will not be rejected, and to obtain the probability of type II error.

jbstatistics 450,631 views 5:44 Calculating Statistical Power Tutorial - Duration: 29:19. Probability Of Type 2 Error Beta Brandon Foltz 67,177 views 37:43 16 videos Play all Hypothesis Testingjbstatistics Calculating Power - Duration: 12:13. Generated Mon, 31 Oct 2016 03:36:39 GMT by s_fl369 (squid/3.5.20) ERROR The requested URL could not be retrieved The following error was encountered while trying to retrieve the URL: http://0.0.0.10/ Connection Sign in 15 Loading...

## Probability Of Committing A Type Ii Error Calculator

They are different. http://stats.stackexchange.com/questions/7402/how-do-i-find-the-probability-of-a-type-ii-error Question How do I calculate the probability of a Type II error involving a normal distribution, where the standard deviation is known? How To Calculate Type 2 Error In Excel Watch QueueQueueWatch QueueQueue Remove allDisconnect Loading... Probability Of Type 2 Error Two Tailed Test In this example: Ho: μ0 = 500  Ha: μ > 500 μ = 524 Draw a normal curve with population mean μ = 524, and sample mean found which is x

Using Tables to Find Areas and Percentiles (Z, t, X2, F) 4. Solution We begin with computing the standard error estimate, SE. > n = 35                # sample size > s = 2.5               # sample standard deviation > SE = s/sqrt(n); SE    # standard error estimate [1] 0.42258 We next compute the lower and upper bounds of sample means for which the null hypothesis μ = 15.4 would Type II errors arise frequently when the sample sizes are too small and it is also called as errors of the second kind. this content Formula: Example : Suppose the mean weight of King Penguins found in an Antarctic colony last year was 5.2 kg.

Please try again later. How To Calculate Type 2 Error In Hypothesis Testing ANOVA 12. Sign in to add this video to a playlist.

## I assume a one-sided $H_{1}: \mu_{1} > \mu_{0}$.

Related 64Is there a way to remember the definitions of Type I and Type II Errors?1How to interpret type-II error probability while doing A/B testing?2Computing type II error $\beta$0How to compute The probability of avoiding a type II error is called the power of the hypothesis test, and is denoted by the quantity 1 - β . This feature is not available right now. Type Ii Error Calculator Proportion In this example, Z542 = (x bar - μ)/(σ/√n ) = (542 - 524)/(115/√40) = 0.9899 Then use this Z value to compute the probability of Type II Error based on

Loading... Are assignments in the condition part of conditionals a bad practice? NurseKillam 46,470 views 9:42 Stats: Hypothesis Testing (Traditional Method) - Duration: 11:32. http://degital.net/type-2/type-ii-error-probability.html asked 5 years ago viewed 13954 times active 5 years ago Get the weekly newsletter!

Sign in Transcript 122,646 views 536 Like this video? Required fields are marked * Name * Email * Website Comment Current [email protected] * Leave this field empty Chapters1. The probability of a type II error is then derived based on a hypothetical true value. Please try the request again.

How to remove calendar event WITHOUT the sender's notification - serious privacy problem Why does Deep Space Nine spin? The system returned: (22) Invalid argument The remote host or network may be down. Hypothesis Testing 7. Discrete Probability Distributions 2.

Since we assume that the actual population mean is 15.1, we can compute the lower tail probabilities of both end points. > mu = 15.1             # assumed actual mean > p = pt((q - mu)/SE, df=n-1); p [1] 0.097445 0.995168 Finally, the probability of type II error is the jbstatistics 56,904 views 13:40 Super Easy Tutorial on the Probability of a Type 2 Error! - Statistics Help - Duration: 15:29. StoneyP94 58,444 views 12:13 Factors Affecting Power - Effect size, Variability, Sample Size (Module 1 8 7) - Duration: 8:10. Working...


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Four friends have been doing really well in their Calculus class: they have been getting top grades for their homework and on the midterm. So, when it's time for the final, they decide not to study on the weekend before, but to drive to another friend's birthday party in another city - even though the exam is scheduled for Monday morning. As it happens, they drink too much at the party, and on Monday morning, they are all hung over and oversleep. When they finally arrive on campus, the exam is already over.

They go to the professor's office and offer him an explanation: "We went to our friend's birthday party, and when we were driving back home very early on Monday morning, we suddenly had a flat tire. We had no spare one, and since we were driving on backroads, it took hours until we got help."

The professor nods sympathetically and says: "I see that it was not your fault. I will allow you to make up for the missed exam tomorrow morning." When they arrive early on Tuesday morning, the students are put by the professor in a large lecture hall and are seated so far apart from each other that, even if they tried, they had no chance to cheat. The exam booklets are already in place, and confidently, the students start writing.

The first question - five points out of one hundred - is a simple exercise in differentiation, and all four finish it within ten minutes.

When the first of them has completed the problem, he turns over the page of the exam booklet and reads on the next one:

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text:
Getting started with the computational analysis of games:

Playing "stripped down" poker

Theodore L. Turocy
University of East Anglia

EC'16 Workshop 24 July 2016

In [1]:
import gambit

Gambit version 16.0.0 is the current development version. You can get it from http://www.gambit-project.org.

In [2]:
gambit.__version__

Out[2]:
'16.0.0'

Inspecting a game¶

The game that we will use as our starting point is one which many of you may have encountered in some variation. Myerson's (1991) textbook refers to this as a one-card poker game; Reiley et at (2008) call this "stripped-down poker."

There is a deck consisting of two types of cards: Ace and King. There are two players, Alice and Bob. Both start by putting 1 in the pot. One player (Alice) draws a card; initially assume the cards are in equal proportion in the deck. Alice sees her card, and then decides whether she wants to raise (add another 1 to the pot) or fold (and concede the pot to Bob). If she raises, play passes to Bob, who much decide whether to meet her raise (and add another 1 to the pot) or pass (and concede the pot to Alice). If Alice raises and Bob meets, Alice reveals her card: If it is an Ace, she takes the pot, whereas if it is a King, Bob does.

Here is what the game looks like in extensive form (as drawn by Gambit's graphical viewer, which we will touch on separately):

In [3]:
g = gambit.Game.read_game("poker.efg")

Gambit's .efg format is a serialisation of an extensive game. The format looks somewhat dated (and indeed it was finalised in 1994), but is fast: recently I loaded a game with about 1M nodes in under 2s.

In [4]:
g

Out[4]:
EFG 2 R "A simple poker example" { "Alice" "Bob" }
""

c "" 1 "" { "A" 1/2 "K" 1/2 } 0
p "" 1 1 "a" { "R" "F" } 0
p "" 2 1 "b" { "M" "P" } 0
t "" 1 "Alice wins big" { 2, -2 }
t "" 2 "Alice wins" { 1, -1 }
t "" 3 "Bob wins" { -1, 1 }
p "" 1 2 "k" { "R" "F" } 0
p "" 2 1 "b" { "M" "P" } 0
t "" 4 "Bob wins big" { -2, 2 }
t "" 2 "Alice wins" { 1, -1 }
t "" 3 "Bob wins" { -1, 1 }

The game offers a "Pythonic" interface. Most objects in a game can be accessed via iterable collections.

In [5]:
g.players

Out[5]:
[<Player [0] 'Alice' in game 'A simple poker example'>, <Player [1] 'Bob' in game 'A simple poker example'>]

All objects have an optional text label, which can be used to retrieve it from the collection:

In [6]:
g.players["Alice"]

Out[6]:
<Player [0] 'Alice' in game 'A simple poker example'>

In this game, Alice has two information sets: when she has drawn the Ace, and when she has drawn the King:

In [7]:
g.players["Alice"].infosets

Out[7]:
[<Infoset [0] 'a' for player 'Alice' in game 'A simple poker example'>, <Infoset [1] 'k' for player 'Alice' in game 'A simple poker example'>]

The chance or nature player is a special player in the players collection.

In [8]:
g.players.chance

Out[8]:
<Player [CHANCE] in game 'A simple poker example'>
In [9]:
g.players.chance.infosets

Out[9]:
[<Infoset [0] '' for player '' in game 'A simple poker example'>]

Gambit does sorting of the objects in each collection, so indexing collections by integer indices also works reliably if you save and load a game again.

In [10]:
g.players.chance.infosets[0].actions

Out[10]:
[<Action [0] 'A' at infoset '' for player '' in game 'A simple poker example'>, <Action [1] 'K' at infoset '' for player '' in game 'A simple poker example'>]

We can assign particular game objects to variables for convenient referencing. In this case, we will explore the strategic effects of changing the relative probabilities of the Ace and King cards.

In [11]:
deal = g.players.chance.infosets[0]

In the original version of the game, it was assumed that the Ace and King cards were equally likely to be dealt.

In [12]:
deal.actions["A"].prob

Out[12]:
$\frac{1}{2}$
In [13]:
deal.actions["K"].prob

Out[13]:
$\frac{1}{2}$

Computing Nash equilibria¶

Gambit offers a variety of methods for computing Nash equilibria of games, which we will discuss in more detail separately. This is a two-player game in extensive form, for which we can use Lemke's algorithm applied to the sequence form of the game.

In the Python interface, solution methods are offered in the gambit.nash module. Each method also is wrapped as a standalone command-line binary.

In [14]:
result = gambit.nash.lcp_solve(g)

The result of this method is a list of (mixed) behaviour profiles. (Future: the return value will be encapsulated in a results class retaining more detailed metadata about the run of the algorithm.)

In this game, there is a unique (Bayes-)Nash equilibrium.

In [15]:
len(result)

Out[15]:
1

A behaviour profile looks like a nested list. Entries are of the form profile[player][infoset][action].

In [16]:
result[0]

Out[16]:
$\left[\left[\left[1,0\right],\left[\frac{1}{3},\frac{2}{3}\right]\right],\left[\left[\frac{2}{3},\frac{1}{3}\right]\right]\right]$
In [17]:
result[0][g.players["Alice"]]

Out[17]:
$\left[\left[1,0\right],\left[\frac{1}{3},\frac{2}{3}\right]\right]$
In [18]:
result[0][g.players["Bob"]]

Out[18]:
$\left[\left[\frac{2}{3},\frac{1}{3}\right]\right]$

We can compute various interesting quantities about behaviour profiles. Most interesting is perhaps the payoff to each player; because this is a constant-sum game, this is the value of the game.

In [19]:
result[0].payoff(g.players["Alice"])

Out[19]:
$\frac{1}{3}$
In [20]:
result[0].payoff(g.players["Bob"])

Out[20]:
$\frac{-1}{3}$

Bob is randomising at his information set, so he must be indifferent between his actions there. We can check this.

In [21]:
result[0].payoff(g.players["Bob"].infosets[0].actions[0])

Out[21]:
$-1$
In [22]:
result[0].payoff(g.players["Bob"].infosets[0].actions[1])

Out[22]:
$-1$

As we teach our students, the key to understanding this game is that Alice plays so as to manipulate Bob's beliefs about the likelihood she has the Ace. We can examine Bob's beliefs over the nodes (members) of his one information set.

Given the structure of the betting rules, Bob becomes indifferent to his actions when he thinks there is a 3/4 chance Alice has the Ace.

In [23]:
result[0].belief(g.players["Bob"].infosets[0].members[0])

Out[23]:
$\frac{3}{4}$
In [24]:
result[0].belief(g.players["Bob"].infosets[0].members[1])

Out[24]:
$\frac{1}{4}$

Construction of the reduced normal form¶

The call to lcp_solve above uses the sequence form rather than the (reduced) strategic form of the game. This representation takes advantage of the tree structure, and can avoid (in many games of interest) the exponential blowup of the size of the strategic form relative to the extensive form. (More details on this in a while!)

Nevertheless, the reduced strategic form of a game can be of interest. Gambit implements transparently the conversions between the extensive and strategic representations. For games in extensive form, the reduced strategic form is computed on-the-fly from the game tree; that is, the full normal form payoff tables are not stored in memory.

Each player has a data member strategies which lists the reduced normal form strategies (s)he has.

In [25]:
g.players["Alice"].strategies

Out[25]:
[<Strategy [0] '11' for player 'Alice' in game 'A simple poker example'>, <Strategy [1] '12' for player 'Alice' in game 'A simple poker example'>, <Strategy [2] '21' for player 'Alice' in game 'A simple poker example'>, <Strategy [3] '22' for player 'Alice' in game 'A simple poker example'>]
In [26]:
g.players["Bob"].strategies

Out[26]:
[<Strategy [0] '1' for player 'Bob' in game 'A simple poker example'>, <Strategy [1] '2' for player 'Bob' in game 'A simple poker example'>]

We can also do a quick visualisation of the payoff matrix of the game using the built-in HTML output (plus Jupyter's inline rendering of HTML!)

Disclaimer: There's a bug in the 16.0.0 release which prevents the correct generation of HTML; this will be corrected in 16.0.1 (and is corrected in the 'master' branch of the git repository already).

In [27]:
import IPython.display; IPython.display.HTML(g.write('html'))

Out[27]:

A simple poker example

 1 2 11 0,0 1,-1 12 1/2,-1/2 0,0 21 -3/2,3/2 0,0 22 -1,1 -1,1

Bonus note: Gambit also supports writing out games using Martin Osborne's sgame LaTeX style: https://www.economics.utoronto.ca/osborne/latex/. This doesn't have auto-rendering magic in Jupyter, but it's all ready to cut-and-paste to your favourite editor.

In [28]:
print g.write('sgame')

\begin{game}{4}{2}[Alice][Bob]
&1 & 2\\
11 &  $0,0$  &  $1,-1$ \\
12 &  $1/2,-1/2$  &  $0,0$ \\
21 &  $-3/2,3/2$  &  $0,0$ \\
22 &  $-1,1$  &  $-1,1$
\end{game}

We can convert our behaviour profile to a corresponding mixed strategy profile. This is indexable as a nested list with elements [player][strategy].

In [29]:
msp = result[0].as_strategy()
msp

Out[29]:
$\left[\left[\frac{1}{3},\frac{2}{3},0,0\right],\left[\frac{2}{3},\frac{1}{3}\right]\right]$

Of course, Alice will receive the same expected payoff from this mixed strategy profile as she would in the original behaviour profile.

In [30]:
msp.payoff(g.players["Alice"])

Out[30]:
$\frac{1}{3}$

We can also ask what the expected payoffs to each of the strategies are. Alice's last two strategies correspond to folding when she has the Ace, which is dominated.

In [31]:
msp.strategy_values(g.players["Alice"])

Out[31]:
[Fraction(1, 3), Fraction(1, 3), Fraction(-1, 1), Fraction(-1, 1)]

Automating/scripting analysis¶

The real gain in having libraries for doing computation in game theory is to be able to script computations. For example, we can explore how the solution to the game changes, as we change the probability that Alice is dealt the Ace.

Payoffs and probabilities are represented in games in Gambit as exact-precision numbers, which can be either rational numbers of (exact-precision) decimals. These are called gambit.Rational and gambit.Decimal, and are compatible with the Python fractions.Fraction and decimal.Decimal classes, respectively. (In Gambit 16.0.0, they are derived from them.)

Caveat/Tip: This means one cannot set a payoff or probability to be a floating-point number. We justify this based on the principle "explicit is better than implicit." In two-player games, the extreme points of the set of Nash equilibria are rational numbers, whenever the data of the game are rational, and the Gambit equilibrium computation methods take advantage of this. If the payoff of a game were specified as a floating-point number, e.g. 0.333333 instead of 1/3, surprising results can occur due to rounding.

In [32]:
import pandas
probs = [ gambit.Rational(i, 20) for i in xrange(1, 20) ]
results = [ ]
for prob in probs:
g.players.chance.infosets[0].actions[0].prob = prob
g.players.chance.infosets[0].actions[1].prob = 1-prob
result = gambit.nash.lcp_solve(g)[0]
results.append({ "prob": prob,
"alice_payoff": result.payoff(g.players["Alice"]),
"bluff": result[g.players["Alice"].infosets[1].actions[0]],
"belief": result.belief(g.players["Bob"].infosets[0].members[1]) })
df = pandas.DataFrame(results)
df

Out[32]:
alice_payoff belief bluff prob
0 -13/15 1/4 1/57 1/20
1 -11/15 1/4 1/27 1/10
2 -3/5 1/4 1/17 3/20
3 -7/15 1/4 1/12 1/5
4 -1/3 1/4 1/9 1/4
5 -1/5 1/4 1/7 3/10
6 -1/15 1/4 7/39 7/20
7 1/15 1/4 2/9 2/5
8 1/5 1/4 3/11 9/20
9 1/3 1/4 1/3 1/2
10 7/15 1/4 11/27 11/20
11 3/5 1/4 1/2 3/5
12 11/15 1/4 13/21 13/20
13 13/15 1/4 7/9 7/10
14 1 1/4 1 3/4
15 1 1/5 1 4/5
16 1 3/20 1 17/20
17 1 1/10 1 9/10
18 1 1/20 1 19/20
In [33]:
import pylab
%matplotlib inline
pylab.plot(df.prob, df.bluff, '-')
pylab.xlabel("Probability Alice gets ace")
pylab.ylabel("Probability Alice bluffs with king")
pylab.show()

In [34]:
pylab.plot(df.prob, df.alice_payoff, '-')
pylab.xlabel("Probability Alice gets ace")
pylab.ylabel("Alice's equilibrium payoff")
pylab.show()

In [35]:
pylab.plot(df.prob, df.belief, '-')
pylab.xlabel("Probability Alice gets ace")
pylab.ylabel("Bob's equilibrium belief")
pylab.ylim(0,1)
pylab.show()

As a final experiment, we can also change the payoff structure instead of the probability of the high card. How would the equilibrium change if a Raise/Meet required putting 2 into the pot instead of 1?

In [36]:
deal.actions[0].prob = gambit.Rational(1,2)

In [37]:
deal.actions[1].prob = gambit.Rational(1,2)

The outcomes member of the game lists all of the outcomes. An outcome can appear at multiple nodes. Outcomes, like all other objects, can be given text labels for easy reference.

In [38]:
g.outcomes["Alice wins big"]

Out[38]:
<Outcome [0] 'Alice wins big' in game 'A simple poker example'>
In [39]:
g.outcomes["Alice wins big"][0] = 3

In [40]:
g.outcomes["Alice wins big"][1] = -3

In [41]:
g.outcomes["Bob wins big"][0] = -3

In [42]:
g.outcomes["Bob wins big"][1] = 3

Once again, solve the revised game using Lemke's algorithm on the sequence form.

In [43]:
result = gambit.nash.lcp_solve(g)

In [44]:
len(result)

Out[44]:
1
In [45]:
result[0]

Out[45]:
$\left[\left[\left[1,0\right],\left[\frac{1}{2},\frac{1}{2}\right]\right],\left[\left[\frac{1}{2},\frac{1}{2}\right]\right]\right]$

The value of the game to Alice is now higher: 1/2 instead of 1/3 with the original payoffs.

In [46]:
result[0].payoff(g.players["Alice"])

Out[46]:
$\frac{1}{2}$

Bob's equilibrium belief about Alice's hand is also different of course, as he now is indifferent between meeting and passing Alice's raise when he thinks the chance she has the Ace is 2/3 (instead of 3/4 before).

In [47]:
result[0].belief(g.players["Bob"].infosets[0].members[0])

Out[47]:
$\frac{2}{3}$

Serialising the game in other formats¶

We already saw above some of the formats that can be used to serialise games. There are a few other standard options. For example, Gambit also has a format for games in strategic (or normal) form. You can get the reduced normal form of the extensive game in this format directly:

In [48]:
print g.write('nfg')

NFG 1 R "A simple poker example" { "Alice" "Bob" }

{ { "11" "12" "21" "22" }
{ "1" "2" }
}
""

0 0
1 -1
-2 2
-1 1
1 -1
0 0
0 0
-1 1

Also, we can write the game out in the XML format used by Game Theory Explorer:

In [49]:
print g.write('gte')

<gte version="0.1">
<gameDescription/>
<display>
<color player="1">#FF0000</color>
<color player="2">#0000FF</color>
Times
<strokeWidth>1</strokeWidth>
<nodeDiameter>7</nodeDiameter>
<isetDiameter>25</isetDiameter>
<levelDistance>75</levelDistance>
</display>
<players>
<player playerId="1">Alice</player>
<player playerId="2">Bob</player>
</players>
<extensiveForm>
<node>
<node player="Alice" prob="1/2" move="A">
<node iset="b" player="Bob" move="R">
<outcome move="M">
<payoff player="Alice">3</payoff>
<payoff player="Bob">-3</payoff>
</outcome>
<outcome move="P">
<payoff player="Alice">1</payoff>
<payoff player="Bob">-1</payoff>
</outcome>
</node>
<outcome move="F">
<payoff player="Alice">-1</payoff>
<payoff player="Bob">1</payoff>
</outcome>
</node>
<node player="Alice" prob="1/2" move="K">
<node iset="b" player="Bob" move="R">
<outcome move="M">
<payoff player="Alice">-3</payoff>
<payoff player="Bob">3</payoff>
</outcome>
<outcome move="P">
<payoff player="Alice">1</payoff>
<payoff player="Bob">-1</payoff>
</outcome>
</node>
<outcome move="F">
<payoff player="Alice">-1</payoff>
<payoff player="Bob">1</payoff>
</outcome>
</node>
</node>
</extensiveForm>
</gte>


text: See your article appearing on the GeeksforGeeks main page and help other Geeks. Second, we will use the corrcoeff method to create the … You used the tag numpy but you are using lists. If you have any doubts in the tutorial, mention them in the comment section. It's straightforward with the NumPy library. Computing a Correlation Matrix in Python with NumPy. It is also used for multidimensional arrays and as we know matrix is a rectangular array, we will use this library for user input matrix. For example, a matrix of shape 3x2 and a matrix of shape 2x3 can be multiplied, resulting in a matrix shape of 3 x 3. in a single step. close, link acknowledge that you have read and understood our, GATE CS Original Papers and Official Keys, ISRO CS Original Papers and Official Keys, ISRO CS Syllabus for Scientist/Engineer Exam, Adding new column to existing DataFrame in Pandas, How to get column names in Pandas dataframe, Python program to convert a list to string, Reading and Writing to text files in Python, isupper(), islower(), lower(), upper() in Python and their applications, Taking multiple inputs from user in Python, Python | Program to convert String to a List, Python | Split string into list of characters, Multiplication of two Matrices in Single line using Numpy in Python, Python | Numpy numpy.ndarray.__truediv__(), Extracting the real and imaginary parts of an NumPy array of complex numbers, Using NumPy to Convert Array Elements to Float Type, Different ways to create Pandas Dataframe, Write Interview Result of a*b : 1 4 9 3 8 15 5 12 21 . Its only goal is to solve the problem of matrix multiplication. share | improve this question | follow | edited Nov 26 '18 at 16:25. ktv6. With the help ofnumpy.matrix.I() function we can get the multiplicative inverse of the same size as of our given matrix.. Syntax : numpy.matrix.I() Return : [matrix object] If self is non-singular, ret is such that ret * self == self * ret == np.matrix(np.eye(self[0, :].size) all return True.Return multiplicative inverse of given matrix. We can see in above program the matrices are multiplied element by element. brightness_4 We will be using the numpy.dot () method to find the product of 2 matrices. Multiplication of Matrices. Using this library, we can perform complex matrix operations like multiplication, dot product, multiplicative inverse, etc. 0. Experience. Active 11 months ago. Multiplication is the dot product of rows and columns. So for doing a matrix multiplication we will be using the dot function in numpy. Python @ Operator. How to Multiply Two Matrices using Python? Podcast 279: Making Kubernetes work like it’s 1999 with Kelsey Hightower. It has a method called dot for the matric multiplication. Multiplizieren zweier Matrizen – Theorie: Damit zwei Matrizen miteinander multipliziert werden können, muss die Spaltenzahl der ersten Matrix (hier: A) mit der Anzahl der Zeilen der zweiten Matrix (hier: B) übereinstimmen. The product between a1 and a2 will be calculated parallelly, and the result will be stored in the mul variable. Multiplication operator (*) is used to multiply the elements of two matrices. I find for loops in python to be rather slow (including within list comps), so I prefer to use numpy array methods whenever possible. Always use numpy arrays, and not numpy matrices. Python Numpy Matrix Multiplication. Let us now do a matrix multiplication of 2 matrices in Python, using NumPy. Multiplication of matrix is an operation which produces a single matrix by taking two matrices as input and multiplying rows of the first matrix to the column of the second matrix. edit In Python numpy.dot() method is used to calculate the dot product between two arrays. The numpy.matmul() function returns the matrix product of two arrays. See what the numpy docs say about this. The Overflow Blog How to communicate more deliberately and efficiently when working remotely. For example, for two matrices A and B. The following runs a quick test, multiplying 1000 3×3 matrices together. In this tutorial, we are going to learn how to multiply two matrices using the NumPy library in Python. Im using python 2.7 if it is relevant to an issue. In this post, we will be learning about different types of matrix multiplication in the numpy library. Example: import numpy as np Matrix_A = np.array( [[1,2,3], [4,5,7], [8,9,10]]) Matrix_B = np.array([[11,12,13], [14,15,16], [17,18,19]]) print("Matrix_A * Matrix_B is :") print(Matrix_A.dot(Matrix_B)) print("\nMatrix_B * Matrix_A … mat1 = np.matrix([[1,2,3],[4,5,6]]) … die Matrix-Multiplikation zur Verfügung stellen. Ein Unterschied besteht darin, dass die NumPy-Matrizen streng 2-dimensional sind, während NumPy arrays von beliebiger Dimension sein können, also n-dimensional. No. Zu di… The matmul function implements the semantics of the @ operator introduced in Python 3.5 following [0, 1]]) >>> b = np.array([1, 2]) >>> np.matmul(a, b) array([1, In Python, we can implement a matrix as nested list (list inside a list). Example 1 : Matrix multiplication of 2 square matrices. code. While it returns a normal product for 2-D arrays, if dimensions of either argument is >2, it is treated as a stack of matrices residing in the last two indexes and is broadcast accordingly. Use numpy arrays and it will work – Sembei Norimaki Nov 26 '18 at 16:24. A = [ [1, 2], [2, 3]] B = [ [4, 5], [6, 7]] So, A.B = [ [1*4 + 2*6, 2*4 + 3*6], [1*5 + 2*7, 2*5 + 3*7] So the computed answer will be: [ [16, 26], [19, 31]] Using explicit for loops: This is a simple technique to multiply matrices but one of the expensive method for larger input data set.In this, we use nested for loops to iterate each row and each column. Zu diesem Zweck kann man natürlich eine for-Schleife nutzen. In this tutorial, we will learn how to find the product of two matrices in Python using a function called numpy.matmul(), which belongs to its scientfic computation package NumPy. Matrix-Multiplikation in reinem python. It has a method called dot for the matric multiplication. By using our site, you Also note that from python 3.5+, you can use @ for matrix multiplication with numpy arrays, which means there should be absolutely no good reason to use matrices over arrays. In this tutorial, we are going to learn how to multiply two matrices using the NumPy library in Python. Python program multiplication of two matrix. In the above image, 19 in the (0,0) index of the outputted matrix is the dot product of the 1st row of the 1st matrix and the 1st column of the 2nd matrix. Two matrices can be multiplied using the dot() method of numpy.ndarray which returns the dot product of two matrices. It’s a little crude, but it shows the numpy.array method to be 10 times faster than the list comp of np.matrix. A product of an $m \times p$ matrix $A = [a_{ij}]$ and an $p \times n$ matrix $B = [b_{ij}]$ results in … Matrix Multiplication in NumPy is a python library used for scientific computing. np.dot(a,b) a.dot(b) for matrix multiplication … Eine Möglichkeit besteht darin, die Punktelementfunktion von numpy.ndarray zu verwenden. Strengthen your foundations with the Python Programming Foundation Course and learn the basics. Let us see how to compute matrix multiplication with NumPy. We will be using the numpy.dot() method to find the product of 2 matrices. Python program to print a checkboard pattern of n*n using numpy. NumPy Mathematics Exercises, Practice and Solution: Write a NumPy program to multiply a 5x3 matrix by a 3x2 matrix and create a real matrix product. Let's see the steps involved in the program. We will use np.random.randint() method to generate the numbers. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. Wie kann man zu einer numerischen Liste einen Skalar addieren, so wie wir es mit dem Array v getan hatten? This can be done from the below code block: Here, I have shown how to iterate across the rows and columns to input the values for the first matrix. We can treat each element as a row of the matrix. SciPy uses dot for matrix multiplication too, in their own examples on sparse matrices page.So you can use dot consistently like . Please use ide.geeksforgeeks.org, generate link and share the link here. In this section, you will learn how to do Element wise matrix multiplication. We can either write. Attention geek! Im folgenden addieren wir 2 zu den Werten dieser Liste: Obwohl diese Lösung funktioniert, ist sie nicht elegant und pythonisch. Rows of the 1st matrix with columns of the 2nd; Example 1. It's straightforward with the NumPy library. Beginnen wir mit der skalaren Addition: Multiplikation, Subtraktion, Division und Exponentiation sind ebenso leicht zu bewerkstelligen wie die vorige Addition: Wir hatten dieses Beispiel mit einer Liste lst begonnen. Please write to us at contribute@geeksforgeeks.org to report any issue with the above content. Currently, no builtin Python types implement the new operator, however, it can be implemented by defining __matmul__(), __rmatmul__(), and __imatmul__() for regular, reflected, and in-place matrix multiplication. Multiply the matrices with numpy.dot(matrix_1, matrix_2) method and store the result in a variable. But before that let’s create a two matrix. Multiplication of two Matrices in Single line using Numpy in Python, Multiplication of two Matrices using Java. Let’s replicate the result in Python. In Python, there exists a popular library called NumPy. We use cookies to ensure you have the best browsing experience on our website. We’ll randomly generate two matrices of dimensions 3 x 2 and 2 x 4. PEP 465 adds the @ infix operator for matrix multiplication. x.dot(A.dot(y)) or A.dot(y).dot(x) although the latter is harder to read because x is out of place.. Note that we have to ensure that the number of rows in the first matrix should be equal to the number of columns in the second matrix. w3resource . home Front End HTML CSS JavaScript HTML5 Schema.org php.js Twitter Bootstrap Responsive Web Design tutorial Zurb Foundation 3 tutorials Pure CSS HTML5 Canvas JavaScript Course Icon Angular React Vue Jest Mocha NPM Yarn … Different Types of Matrix Multiplication . As NumPy is famous for the support of Mathematic tools, so to perform matrix multiplication we do not need to write an algorithm NumPy provides users with an inbuilt dot() method which can multiply two matrices. Multiplication of two Matrices in Single line using Numpy in Python; Python program to multiply two matrices; Median of two sorted arrays of different sizes; Median of two sorted arrays of same size; Median of two sorted arrays with different sizes in O(log(min(n, m))) Median of two sorted arrays of different sizes | Set 1 (Linear) As Paul Panzer said, x @ A @ y is most readable and works as expected (requires Python 3.5+ and NumPy 1.10+). Two matrices can be multiplied using the dot() method of numpy.ndarray which returns the dot product of two matrices. Now, we are going to get into some details of NumPy’s corrcoef method. Example 2 : Matrix multiplication of 2 rectangular matrices. Just execute the code below. The numpy.multiply () function will find the product between a1 & a2 array arguments, element-wise. Der größte Vorteil von Matrizen liegt darin, dass sie eine komfortable Notation für verschiedene Matrizenoperationen, wie z.B. numpy.matmul — NumPy v1.19 Manual, After matrix multiplication the prepended 1 is removed. If you execute the above program, you will get the following results. Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below. This library is a fundamental library for any scientific computation. PEP 465 - A dedicated infix operator for matrix multiplication¶. Browse other questions tagged python numpy matrix-multiplication or ask your own question. Matrix b : 1 2 3 . 311 1 1 gold badge 3 3 silver badges 11 11 bronze badges. First, we will load the data using the numpy.loadtxt method. – Praveen Oct 14 '16 at 5:03 Note, that this will be a simple example and refer to the documentation, linked at the beginning of the post, for more a detailed explanation. NumPy matrix multiplication with @ in pythontex. Scientific Programming. Let us see how to compute matrix multiplication with NumPy. C++ Program to Check Multiplicability of Two Matrices, Python Program to check if two given matrices are identical. In NumPy, you can create a matrix using the numpy.matrix() method. You can install the NumPy library with the following command. Photo by Daniil Kuželev on Unsplash. Matrixmultiplikation in Python mit numpy . asked Nov 26 '18 at 16:22. ktv6 ktv6. So is this the method we should use whenever we want to do NumPy matrix multiplication? python python-2.7 numpy numpy-ufunc. Matrix multiplication is not commutative. So, the solution will be an array with the shape equal to input arrays a1 and a2. The @ operator was introduced to Python’s core syntax from 3.5 onwards thanks to PEP 465. Ask Question Asked 1 year, 1 month ago. Die Matrixmultiplikation kann mit der Punktfunktion auf zwei gleichwertige Arten erfolgen. We’ve saved the best ‘till last. Matrix Multiplication in Python nested loop using Numpy array Thus, the array of rows contains an array of the column values, and each column value is initialized to 0. Code #2: Using map() function and Numpy. def matmult(m1,m2): r= [] m= [] for i in range(len(m1)): for j in range(len(m2[0])): sums=0 for k in range(len(m2)): sums=sums+ (m1[i] [k]*m2[k] [j]) r.append(sums) m.append(r) r= [] return m. Informationsquelle Autor der Antwort Prateek Khandelwal. If matrix1 is a n x m matrix … Methods to multiply two matrices in python 1. NumPy Matrix Multiplication in Python. To begin with, your interview preparations Enhance your Data Structures concepts with the Python DS Course. Viewed 165 times 0. Writing code in comment? Dedicated infix operator for matrix multiplication each element as a row of the matrix method. To generate the numbers for doing a matrix multiplication in the comment section Lösung funktioniert ist... 10 times faster than the list comp of np.matrix matrices in Python matrix … NumPy matrix multiplication in NumPy a! Verschiedene Matrizenoperationen, wie z.B generate the numbers adds the @ operator introduced... To Python ’ s 1999 with Kelsey Hightower ) method 3 3 silver badges 11 bronze! With NumPy 15 5 12 21 and b n using NumPy year, 1 month ago Python to! Used to multiply the elements of two arrays … matrix b: 2!, die Punktelementfunktion von numpy.ndarray zu verwenden be calculated parallelly, and not NumPy matrices im addieren! At 5:03 let us see how to compute matrix multiplication in Python numpy.dot ( ) method of which... ’ s create a two matrix a2 array arguments, element-wise numpy.dot ( ) method and store the will. Returns the dot product of two matrices, Python program to print a checkboard pattern of *. * ) is used to multiply two matrices a and b see in above the. Concepts with the Python DS Course to find the product of 2 matrices in Python, dass eine. 4 9 3 8 15 5 12 21 dass sie eine komfortable Notation für verschiedene Matrizenoperationen, wie.. Clicking on the GeeksforGeeks main page and help other Geeks with columns of the 2nd ; example 1 matrix!, während NumPy arrays and it will work – Sembei Norimaki Nov 26 '18 16:24! Operator ( * ) is used to multiply the elements of two a! Returns the matrix product of two matrices, Python program to Check Multiplicability of two matrices the... Own question geeksforgeeks.org to report any issue with the Python Programming Foundation Course and learn the basics will. Scientific computing in NumPy is a fundamental library for any scientific computation to compute matrix multiplication Python... | edited Nov 26 '18 at 16:24 is initialized to 0 follow | edited Nov 26 '18 at ktv6. Shows the numpy.array method to find the product of 2 matrices you have the best browsing on., your interview preparations Enhance your data Structures concepts with the above program, you can dot. Question Asked 1 year, 1 month ago doubts in the tutorial, we be... Die Matrixmultiplikation kann mit der Punktfunktion auf zwei gleichwertige Arten erfolgen Kubernetes work like it ’ create! Use the corrcoeff method to find the product between a1 & a2 array arguments element-wise!, also n-dimensional, so wie wir es mit dem array v getan hatten core syntax from 3.5 onwards to. To Python ’ s a little crude, but it shows the numpy.array to. Matrix multiplication of 2 matrices in Single line using NumPy array Matrixmultiplikation in Python, exists! The dot product of two matrices Oct 14 '16 at 5:03 let us see how to more... Question | follow | edited Nov 26 '18 at 16:24 share | Improve article. Using the dot product of 2 matrices two arrays podcast 279: Kubernetes... Matrixmultiplikation kann mit der Punktfunktion auf zwei gleichwertige Arten erfolgen matrices can be multiplied using the NumPy library addieren so. 1St matrix with columns of the matrix product of 2 rectangular matrices can see in above program the are. Pep 465 adds the @ operator was introduced to Python ’ s core syntax from 3.5 onwards thanks pep. Zu einer numerischen Liste einen Skalar addieren, so wie wir es mit dem array v getan?... Function will find the product of 2 rectangular matrices to find the product of matrices. Wir 2 zu den Werten dieser Liste: Obwohl diese Lösung funktioniert ist... 2Nd ; example 1: matrix multiplication in NumPy in Single line using NumPy, generate link share... Can treat each element as a row of the matrix product of two matrices NumPy! Incorrect by clicking on the ` Improve article '' button below for the multiplication! Of two matrices find the product between a1 and a2 the product of 2 matrices von numpy.ndarray zu.. Install the NumPy library we are going to get into some details of ’... Wie wir es mit dem array v getan hatten now, we will use corrcoeff... Matrices can be multiplied using the numpy.matrix ( ) method to find the product between arrays! 5 12 21 be 10 times faster than the list comp of np.matrix own examples sparse! S a little crude, but it shows the numpy.array method to generate numbers... Month ago 1 4 9 3 8 15 5 12 21 numpy.matmul — NumPy v1.19,! Multiplication in NumPy, you can create matrix multiplication in python with numpy two matrix some details of NumPy ’ s corrcoef method Matrixmultiplikation Python! How to compute matrix multiplication there exists a popular library called NumPy Python... Ve saved the best browsing experience on our website data Structures concepts with the Python DS Course to 10!, generate link and share the link here page.So you can create a matrix... Inverse, etc 11 11 bronze badges element by element was introduced to Python ’ a. Contribute @ geeksforgeeks.org to report any issue with the Python DS Course your data Structures concepts the. With the above content 26 '18 at 16:25. ktv6 data using the dot product between two arrays m matrix NumPy... Dedicated infix operator for matrix multiplication with NumPy value is initialized to 0 store the will. Us at contribute @ geeksforgeeks.org to report any issue with the above content der auf... First, we will use np.random.randint ( ) method to create the … matrix b: 1 2 3 darin! It shows the numpy.array method to be 10 times faster than the list comp of np.matrix your preparations! 1,2,3 ], [ 4,5,6 ] ] ) … Matrix-Multiplikation in reinem Python operator was to! Arrays and it will work – Sembei Norimaki Nov 26 '18 at.. X 4 use cookies to ensure you have any doubts in the program badges 11 11 bronze badges use to! Contains an array with the following results dimensions 3 x 2 and 2 x.... The numpy.multiply ( ) function returns the dot product of two matrices the. Numpy.Multiply ( ) method is used to multiply the elements of two matrices values, each., dass die NumPy-Matrizen streng 2-dimensional sind, während NumPy arrays von beliebiger Dimension sein,! Result in a variable tutorial, mention them in the tutorial, we can each! ] ] ) … Matrix-Multiplikation in reinem Python create a two matrix is to the. It has a method called dot for matrix multiplication¶ you have any doubts in the tutorial, we will an... Preparations Enhance your data Structures concepts with the Python DS Course scipy uses for. Werten dieser Liste: Obwohl diese Lösung funktioniert, ist sie nicht elegant und pythonisch so the. The basics 1999 with Kelsey Hightower and each column value is initialized to 0 matrix multiplication¶ see your appearing. So wie wir es mit dem array v getan hatten any scientific computation [! Mit dem array v getan hatten solution will be using the dot function in NumPy, can! Matrices together funktioniert, ist sie nicht elegant und pythonisch are going get... Numpy.Loadtxt method '' button below wir 2 zu den Werten dieser Liste: diese! Link here [ 4,5,6 ] ] ) … Matrix-Multiplikation in reinem Python you find incorrect! Of NumPy ’ s 1999 with Kelsey Hightower faster than the list comp of np.matrix Nov 26 at. Numpy-Matrizen streng 2-dimensional sind, während NumPy arrays, and each column value is initialized to 0 column values and. The list comp of np.matrix multiplicative inverse, etc matrix1 is a library! Generate the numbers following runs a quick test, multiplying 1000 3×3 matrices together but! Of NumPy ’ s corrcoef method result in a variable their own examples on sparse matrices page.So can... Matrix product of rows contains an array of the column values, and each column is... Matric multiplication be using the dot ( ) method die NumPy-Matrizen streng 2-dimensional sind, NumPy... Perform complex matrix operations like multiplication, dot product, multiplicative inverse etc... This tutorial, mention them in the program 3 x 2 and 2 x.. A little crude, but it shows the numpy.array method to be 10 times faster than the list comp np.matrix. Matrizen liegt darin, dass sie eine komfortable Notation für verschiedene Matrizenoperationen, wie z.B on matrices. Inverse, etc own question wir es mit dem array v getan hatten 2 zu den Werten Liste! Library used for scientific computing you will get the following runs a quick test multiplying! Enhance your data Structures concepts with the Python DS Course 1 year, 1 month ago is... Dimension sein können, also n-dimensional and the result will be calculated parallelly, and each column is! The 1st matrix with columns of the matrix NumPy v1.19 Manual, After multiplication... The list comp of np.matrix us see how to multiply the elements of two can. 1 4 9 3 8 15 5 12 21 tutorial, we be! Rows of the matrix to generate the numbers pattern of n * using! Oct 14 '16 at 5:03 let us see how to compute matrix multiplication in Python nested loop using array., we can see in above program the matrices are multiplied element by element here... Not NumPy matrices write to matrix multiplication in python with numpy at contribute @ geeksforgeeks.org to report any issue with the Python Foundation. Getan hatten share the link here in their own examples on sparse matrices page.So you use.


text:
Title: A particle based model to simulate the micromechanics of single plant cells and aggregates Authors: Van Liedekerke, Paul ×Ghysels, PieterTijskens, EngelbertSamaey, GiovanniSmeets, BartRoose, DirkRamon, Herman # Issue Date: 26-May-2010 Publisher: Institute of Physics Pub. Series Title: Physical Biology vol:7 Article number: 026006 Abstract: This paper is concerned with addressing how plant tissue mechanics is related to the micromechanics of cells. To this end, we propose a meshfree particle method to simulate the mechanics of both individual plant cells (Parenchyma) and cell aggregates in response to external stresses. The model considers two important features in the plant cell: (1) the cell protoplasm, the interior liquid phase inducing hydrodynamic phenomena, and (2) the cell wall material, a viscoelastic solid material that contains the protoplasm. In this particle framework, the cell fluid is modeled by Smoothed Particle Hydrodynamics (SPH), a meshfree method typically used to address problems with gas and fluid dynamics. In the solid phase (cell wall) on the other hand, the particles are connected by pairwise interactions holding them together and preventing the fluid to penetrate the cell wall. The cell wall hydraulic conductivity (permeability) is built in as well through the SPH formulation. Although this model is also meant to be able to deal with dynamic and even violent situations (leading to cell wall rupture or cell-cell debonding), we have concentrated on quasi-static conditions. The results of single cell compression simulations show that the conclusions found by analytical models and experiments can be reproduced at least qualitatively. Relaxation tests revealed that plant cells have short relaxation times ($\unit[1]{\mu{s}}$ - $\unit[10]{\mu{s}}$) compared to mammalian cells. Simulations performed on cell aggregates indicated an influence of the cellular organization to the tissue response, as was also observed in experiments done on tissues with a similar structure. ISSN: 1478-3967 Publication status: published KU Leuven publication type: IT Appears in Collections: Division of Mechatronics, Biostatistics and Sensors (MeBioS)Numerical Analysis and Applied Mathematics SectionMechanical Engineering - miscellaneous
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# Drainage formula (Water Overlay)

Depending on whether the drainage is passive or active, the formula for either passive or active drainage is used.

## Drainage passive

First the flow capacity is calculated

${\displaystyle Q_{p}=\Delta t\cdot q_{t}}$

${\displaystyle Q_{b}=A_{d}\cdot f_{s}\cdot {\frac {||w_{d}-w_{w}||\cdot A_{w}}{A_{d}\cdot f_{s}+A_{w}}}}$

if ${\displaystyle w_{d}>w_{w}}$ then:

${\displaystyle Q_{d}=A_{d}\cdot (w_{d}-z_{d})\cdot f_{s}}$

${\displaystyle Q_{t}=min(Q_{p},Q_{b},Q_{d})}$

else:

${\displaystyle Q_{w}=A_{w}\cdot (w_{w}-z_{w})}$

${\displaystyle Q_{t}=min(Q_{p},Q_{b},Q_{w})}$

Where:

${\displaystyle q_{t}}$ is the DRAINAGE_Q of the Drainage at time t.
${\displaystyle \Delta t}$ is the computational timestep.
${\displaystyle w_{d}}$ is the ground water level, above the drainage, in meters.
${\displaystyle w_{w}}$ is the water level in the waterway.
${\displaystyle z_{d}}$ is the drainage datum height in meters.
${\displaystyle z_{w}}$ is the max waterway height.
${\displaystyle A_{d}}$ is the drainage area size in square meters.
${\displaystyle A_{w}}$ is the waterway area size in square meters.
${\displaystyle f_{s}}$ is the average storage percentage of the ground above the drainage.
${\displaystyle Q_{p}}$ is the possible amount of water drained, or pumped back when negative, based on the DRAINAGE_Q of the Drainage and timestep Δt.
${\displaystyle Q_{b}}$ is the amount transferred for a balanced ground and surface water level.
${\displaystyle Q_{d}}$ is the amount of water available in the ground above the drainage.
${\displaystyle Q_{w}}$ is the amount of water available in the waterway.
${\displaystyle Q_{t}}$ is the actual drained, or infiltrated backwards, volume at time t.

## Drainage active

Case 1: Active Draining:

If a positive DRAINAGE_Q is defined:

${\displaystyle Q_{p}=\Delta t\cdot q_{t}}$
${\displaystyle Q_{d}=(w_{d}-z_{d})\cdot f_{s}}$

If an overflow threshold ${\displaystyle T_{o,t}}$ is defined as well:

${\displaystyle Q_{o}=max(0,T_{o,t}-w_{w})}$

The actual water pumped out of the drainage system is calculated. If any of the terms are undefined, they are not included.

${\displaystyle Q_{t}=max(0,min(Q_{d},Q_{o},Q_{p}))}$

Case 2: Active Reverse Draining:

If a negative DRAINAGE_Q is defined:

${\displaystyle Q_{p}=\Delta t\cdot q_{t}}$
${\displaystyle Q_{w}=min(0,z_{w}-w_{t,w})}$

If an overflow threshold ${\displaystyle T_{o,t}}$ is defined as well:

${\displaystyle Q_{o}=min(0,T_{o,t}-w_{t,w})}$

The actual water pumped into the drainage system is calculated. If any of the terms are undefined, they are not included.

${\displaystyle Q_{t}=max(0,max(Q_{p},Q_{w},Q_{o}))}$

Where:

${\displaystyle q_{t}}$ is the DRAINAGE_Q of the Drainage at time t.
${\displaystyle \Delta t}$ is the computational timestep.
${\displaystyle Q_{p}}$ is the possible amount of water drained, or pumped back when negative, based on the DRAINAGE_Q of the Drainage and timestep Δt.
${\displaystyle w_{d}}$ is the ground water level, above the drainage, in meters.
${\displaystyle w_{w}}$ is the water level in the waterway.
${\displaystyle z_{d}}$ is the drainage datum height in meters.
${\displaystyle z_{w}}$ is the waterway's datum height.
${\displaystyle f_{s}}$ is the average storage percentage of the ground above the drainage.
${\displaystyle Q_{d}}$ is the amount of water available in the ground above the drainage.
${\displaystyle T_{o,t}}$ is the overflow threshold in meters at time t.
${\displaystyle Q_{o}}$ is the possible amount of water at time t, that can be added to the waterway until the overflow threshold is reached.
${\displaystyle Q_{w}}$ is the amount of water available in the waterway.
${\displaystyle Q_{t}}$ is the actual drained (or pumped) volume at time t.

## Notes

• A negative DRAINAGE_Q can potentially raise the ground water level at the drainage so much that it reaches the surface above the drainage.

## Related

The following topics are related to this formula.

Structures
Drainage (Water Overlay)
Models
Surface model (Water Overlay)
Underground model (Water Overlay)


text:
0
Research Papers

# Microindentation Test for Assessing the Mechanical Properties of Silicone Rubber Exposed to a Simulated Polymer Electrolyte Membrane Fuel Cell Environment

[+] Author and Article Information
Jinzhu Tan1

College of Mechanical and Power Engineering, Nanjing University of Technology, Nanjing, Jiangsu 210009, China

Y. J. Chao2

Department of Mechanical Engineering, University of South Carolina, 300 Main Street, Columbia, SC 29208chao@sc.edu

Xiaodong Li

Department of Mechanical Engineering, University of South Carolina, 300 Main Street, Columbia, SC 29208

J. W. Van Zee

Department of Chemical Engineering, University of South Carolina, Columbia, SC 29208

1

Present address: University of South Carolina, Columbia, SC 29208.

2

Corresponding author.

J. Fuel Cell Sci. Technol 6(4), 041017 (Aug 18, 2009) (9 pages) doi:10.1115/1.3008030 History: Received July 11, 2007; Revised April 02, 2008; Published August 18, 2009

## Abstract

The elastomeric materials used as seals and gaskets in polymer electrolyte membrane (PEM) fuel cells are exposed to acidic environment, humid air, and hydrogen, and subjected to mechanical compressive load. The long-term mechanical and chemical stability of these materials is critical to both sealing and the electrochemical performance of the fuel cell. In this paper, mechanical degradation of two elastomeric materials, Silicone S and Silicone G, which are potential gasket materials for PEM fuel cells, was investigated. Test samples were subjected to various compressive loads to simulate the actual loading in addition to soaking in a simulated PEM fuel cell environment. Two temperatures, $80°C$ and $60°C$, were selected and used in this study. Mechanical properties of the samples before and after exposure to the environment were studied by microindentation. Indentation load, elastic modulus, and hardness were obtained from the loading and unloading curves. Indentation deformation was studied using Hertz contact model. Dynamic mechanical analysis was conducted to verify the elastic modulus obtained by Hertz contact model. It was found that the mechanical properties of the samples changed considerably after exposure to the simulated environment over time. The temperature and the applied compressive load play a significant role in the mechanical degradation. The microindentation method is proved to provide a simple and efficient way to evaluate the mechanical properties of gasket materials.

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## Figures

Figure 1

Schematic of the specimen preparation under compressive load and soaked in the ADT solution

Figure 2

Schematic of the indentation test showing the contact between the indenter tip (rigid ball) and the sample surface

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Hysteresis loss energy for the Silicone G samples: a before exposure, b after 45week exposure at 60°C, c after 45week exposure at 80°C, d after 47week exposure at 80°C with an applied pressure of 0.18MPa, e after 47week exposure at 80°C with an applied pressure of 0.36MPa, and f after 47week exposure at 80°C with an applied pressure of 0.77MPa

Figure 8

Hysteresis loss energy for the Silicone S samples: a before exposure, b after 45week exposure at 60°C, c after 45week exposure at 80°C, d after 47week exposure at 60°C with an applied pressure of 0.18MPa, and e after 47week exposure at 60°C with an applied pressure of 0.36MPa

Figure 9

Indentation load versus displacement curves at the indentation depth of 0.30mm for Silicone G samples: a before exposure, b after 45week exposure at 80°C, c after 47week exposure at 80°C with the applied pressure of 0.18MPa, d after 47week exposure at 80°C with the applied pressure of 0.36MPa, and e after 47week exposure at 80°C with the applied pressure of 0.77MPa

Figure 10

Indentation load versus displacement curves at a peak indentation depth of 0.30mm for Silicone G samples: a before exposure, b after 47week exposure at 60°C with the applied pressure of 0.18MPa, c after 47week exposure at 60°C with the applied pressure of 0.36MPa, d after 47week exposure at 60°C with the applied pressure of 0.77MPa, and e after 45week exposure at 60°C without any load

Figure 11

Bar charts of indentation load at a peak depth of 0.30mm for Silicone G samples: A before exposure, B after exposure at 60°C without any load, C after exposure at 80°C without any load, D after exposure at 60°C with a compressive pressure of 0.18MPa, E after exposure at 80°C with a compressive pressure of 0.18MPa, F after exposure at 60°C with a compressive pressure of 0.36MPa, G after exposure at 80°C with a compressive pressure of 0.36MPa, H after exposure at 60°C with a compressive pressure of 0.77MPa, and I after exposure at 80°C with a compressive pressure of 0.77MPa

Figure 12

Indentation load versus displacement curves at a peak depth of 0.15mm for the Silicone S samples: a before exposure, b after 47week exposure at 60°C with the applied pressure of 0.18MPa, c after 45week exposure at 60°C without any load, d after 47week exposure at 60°C with the applied pressure of 0.36MPa, and e after 45week exposure at 80°C without any load

Figure 13

Bar charts of indentation load at a peak depth of 0.15mm for the Silicone S samples: A before exposure, B after 47week exposure at 60°C with the applied pressure of 0.18MPa, C after 47week exposure at 60°C with the applied pressure of 0.36MPa, D after 45week exposure at 60°C, and E after 45week exposure at 80°C

Figure 14

Indentation loading curves obtained by microindentation and Hertz contact model for the Silicone G samples before exposure (unexposed) and after 47week exposure at 80°C with an applied pressure of 0.18MPa (C10SG80)

Figure 15

Elastic moduli for the Silicone G samples A before exposure, B after exposure at 60°C without any load, C after exposure at 80°C without any load, D after exposure at 60°C with an applied pressure of 0.18MPa, E after exposure at 80°C with an applied pressure of 0.18MPa, F after exposure at 60°C with an applied pressure of 0.36MPa, G after exposure at 80°C with an applied pressure of 0.36MPa, H after exposure at 60°C with an applied pressure of 0.77MPa, and I after exposure at 80°C with an applied pressure of 0.77MPa

Figure 16

Elastic moduli for the Silicone S samples: A before exposure, B after exposure at 60°C with the compressive pressure of 0.18MPa, C after exposure at 60°C with the compressive pressure of 0.36MPa, D after exposure at 60°C without any load, and E after exposure at 80°C without any load

Figure 17

The mean contact pressure at the peak depth of 0.30mm for Silicone G samples: A before exposure, B after 45week exposure at 60°C, C after 45week exposure at 80°C, D after 47week exposure at 80°C with an applied pressures of 0.18MPa, E after 47week exposure at 80°C with an applied pressures of 0.36MPa, and F after 47week exposure at 80°C with an applied pressures of 0.77MPa

Figure 18

The mean contact pressure at the peak depth of 0.20mm for Silicone S samples: A before exposure, B after 47week exposure at 60°C with the applied pressure of 0.18MPa, C after 47week exposure at 60°C with the applied pressure of 0.36MPa, D after 45week exposure at 60°C, and E after 45week exposure at 80°C

Figure 19

Modulus and tanδ versus temperature for Silicone S sample obtained by DMA

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