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## Bernoulli

• Bernoulli
• Volume 24, Number 2 (2018), 1010-1032.

### Exponential mixing properties for time inhomogeneous diffusion processes with killing

#### Abstract

We consider an elliptic and time-inhomogeneous diffusion process with time-periodic coefficients evolving in a bounded domain of $\mathbb{R}^{d}$ with a smooth boundary. The process is killed when it hits the boundary of the domain (hard killing) or after an exponential time (soft killing) associated with some bounded rate function. The branching particle interpretation of the non absorbed diffusion again behaves as a set of interacting particles evolving in an absorbing medium. Between absorption times, the particles evolve independently one from each other according to the diffusion evolution operator; when a particle is absorbed, another selected particle splits into two offsprings. This article is concerned with the stability properties of these non absorbed processes. Under some classical ellipticity properties on the diffusion process and some mild regularity properties of the hard obstacle boundaries, we prove an uniform exponential strong mixing property of the process conditioned to not be killed. We also provide uniform estimates w.r.t. the time horizon for the interacting particle interpretation of these non-absorbed processes, yielding what seems to be the first result of this type for this class of diffusion processes evolving in soft and hard obstacles, both in homogeneous and non-homogeneous time settings.

#### Article information

Source
Bernoulli, Volume 24, Number 2 (2018), 1010-1032.

Dates
Revised: March 2016
First available in Project Euclid: 21 September 2017

https://projecteuclid.org/euclid.bj/1505980887

Digital Object Identifier
doi:10.3150/16-BEJ845

Mathematical Reviews number (MathSciNet)
MR3706785

Zentralblatt MATH identifier
06778356

#### Citation

Del Moral, Pierre; Villemonais, Denis. Exponential mixing properties for time inhomogeneous diffusion processes with killing. Bernoulli 24 (2018), no. 2, 1010--1032. doi:10.3150/16-BEJ845. https://projecteuclid.org/euclid.bj/1505980887

#### References

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• [4] Cattiaux, P. and Méléard, S. (2010). Competitive or weak cooperative stochastic Lotka–Volterra systems conditioned on non-extinction. J. Math. Biol. 60 797–829.
• [5] Champagnat, N. and Villemonais, D. (2016). Exponential convergence to quasi-stationary distribution and $Q$-process. Probab. Theory Related Fields 164 243–283.
• [6] Delfour, M.C. and Zolésio, J.-P. (2011). Shapes and Geometries: Metrics, Analysis, Differential Calculus, and Optimization, 2nd ed. Advances in Design and Control 22. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
• [7] Del Moral, P. (2013). Mean Field Simulation for Monte Carlo Integration. Monographs on Statistics and Applied Probability 126. Boca Raton, FL: CRC Press.
• [8] Del Moral, P. and Doucet, A. (2004). Particle motions in absorbing medium with hard and soft obstacles. Stoch. Anal. Appl. 22 1175–1207.
• [9] Del Moral, P. and Guionnet, A. (2001). On the stability of interacting processes with applications to filtering and genetic algorithms. Ann. Inst. Henri Poincaré Probab. Stat. 37 155–194.
• [10] Del Moral, P. and Miclo, L. (2000). Branching and interacting particle systems approximations of Feynman–Kac formulae with applications to non-linear filtering. In Séminaire de Probabilités, XXXIV. Lecture Notes in Math. 1729 1–145. Berlin: Springer.
• [11] Del Moral, P. and Miclo, L. (2000). A Moran particle system approximation of Feynman–Kac formulae. Stochastic Process. Appl. 86 193–216.
• [12] Del Moral, P. and Miclo, L. (2002). On the stability of nonlinear Feynman–Kac semigroups. Ann. Fac. Sci. Toulouse Math. (6) 11 135–175.
• [13] Del Moral, P. and Miclo, L. (2003). Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups. ESAIM Probab. Stat. 7 171–208.
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• [16] Ferrari, P.A. and Marić, N. (2007). Quasi stationary distributions and Fleming–Viot processes in countable spaces. Electron. J. Probab. 12 684–702.
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• [18] Gong, G.L., Qian, M.P. and Zhao, Z.X. (1988). Killed diffusions and their conditioning. Probab. Theory Related Fields 80 151–167.
• [19] Graham, C. and Méléard, S. (1997). Stochastic particle approximations for generalized Boltzmann models and convergence estimates. Ann. Probab. 25 115–132.
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# Solving for an exponent?

$1^x = i$

I can't solve it through logs, because $\log 1 = 0$. Does this mean $x$ is undefined?

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$i^4$ = 1, but remember that in complex domain there are 4 roots of degree four, so your problem is not well-posed. –  dtldarek May 19 '12 at 12:44
What would it mean when $1^x=-1$? Impossible Farhad? –  Babak S. May 19 '12 at 13:00

## 2 Answers

As already mentioned in the comments, your problem is not well-posed. Since $i^4 = 1$, you would like to say that $1^{1/4} = i$, but this is not entirely true. In the complex domain, the root function, such as $\sqrt[4]{\cdot}$ is not a well-defined function, because it in general has 4 different values for a single input. It is what is called a multivalued function, or some variant of this.

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$(\log 1) * x = \log i$. $0 * x = \log i$. $x = \frac{\log i}{0}$Anything divided by zero is always undefined, but as you proved one possible value is 1/4. Isn't this the equivalent of giving a value to an undefined equation? Or is this simply saying something divided by zero is a multivalued function rather than undefined? –  user26649 May 19 '12 at 13:23
1) The statement $(\log 1) x = \log i$ is incorrect, again for the same reason: the logarithm function $\log$ is not a well-defined function, because for a single input it outputs (infinitely) many different values. 2) The statement "Anything divided by zero is always undefined" is incorrect; it is correct to say that "dividing by zero is an undefined operation," i.e. "dividing by zero is forbidden -- such an operation does simply not exist!" –  Rick May 19 '12 at 13:46
In short, even (erroneously) assuming that the equation $1^x = i$ is well-posed, it cannot be solved using logarithms. –  Rick May 19 '12 at 13:47
Although, of course, assuming something false can imply anything you wish... so, on a philosophical level, assuming $1^x = i$ is well-posed, it can be solved using logarithms. As well as bunnies. –  Rick May 19 '12 at 13:49

It's true that logarithms are multivalued functions. What this means is that you won't get a unique answer. However certain numbers will clearly work while others do not. What you can do to find solutions is this:

$$1^x=i$$ $$x\ln(1)=\ln(i)$$

We need to find complex values of both of these logarithms. In the following, $n \in \mathbb{Z}$.

$$\ln(1)=a+bi$$ $$1=e^{a+bi}$$ $$1=e^a(\cos(b)+i\sin(b))$$

The imaginary component must be 0 and the real component must be 1. This implies that $$b=\pi n$$ for any n. This becomes $$1=e^a(\cos(\pi n)+i\sin(\pi n))$$ $$1=e^a(-1)^n$$

From here it's clear that $a=0$ and $n$ is even, so the full solution for $\ln(1)$ is $$ln(1)=2\pi n i$$ Similarly, with $\ln(i)$: $$i=e^a(\cos(b)+i\sin(b))$$ Now the real part must be zero $$b=\frac{\pi (2n+1)}{2}$$ $$i=ie^a(-1)^n$$ So again, $a=0$ and $n$ is even. $$\ln(i)=\frac{\pi(4n+1)}{2}i$$

Subbing into your equation:

$$x\ln(1)=ln(i)$$ $$x\cdot 2\pi n i=\frac{\pi(4m+1)}{2}i$$ with $m \in \mathbb{Z}$ as well. Solving gives: $$x=\frac{4m+1}{4n}$$ for any $m,n \in \mathbb{Z}, n \neq 0$.

Saying $\ln(x)$ is undefined in the complex plane is like saying $\sqrt x$ is undefined on the reals. 'Undefined' doesn't mean that no solutions exist, but that multiple solutions exist, meaning that it isn't a function anymore ('multivalued function' is a misnomer since functions by definition only have one output value for a given input). We make it a function by defining a 'principal branch'. For $\sqrt x$ we do this by only considering the positive branch. For complex $\ln(x)$ we do this by restricting the imaginary part of the answer to be in$(-\pi,\pi]$. This would involve dividing by zero here, meaning that the only solutions to your question involve considering non-principal values of the logarithm.

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# Tag Info

Technically, say you have $K\gg X$ stocks and $X$ factors. Your (daily) returns can be written as $$dR=\frac{dS}{S}=\mu\,dt + F\,dW$$ where $\mu$ is a $K\times 1$ vector of expected returns (it is not very important since it is deterministic and will play no role in the computation of the covariance) $F$ is a $K\times X$ matrix of loadings of returns on ...


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## CryptoDB

### Yehuda Lindell

#### Publications

Year
Venue
Title
2021
JOFC
ECDSA is a standard digital signature scheme that is widely used in TLS, Bitcoin and elsewhere. Unlike other schemes like RSA, Schnorr signatures and more, it is particularly hard to construct efficient threshold signature protocols for ECDSA (and DSA). As a result, the best-known protocols today for secure distributed ECDSA require running heavy zero-knowledge proofs and computing many large-modulus exponentiations for every signing operation. In this paper, we consider the specific case of two parties (and thus no honest majority) and construct a protocol that is approximately two orders of magnitude faster than the previous best. Concretely, our protocol achieves good performance, with a single signing operation for curve P-256 taking approximately 37 ms between two standard machine types in Azure (utilizing a single core only). Our protocol is proven secure for sequential composition under standard assumptions using a game-based definition. In addition, we prove security by simulation under a plausible yet non-standard assumption regarding Paillier. We show that partial concurrency (where if one execution aborts, then all need to abort) can also be achieved.
2020
JOFC
A protocol for computing a functionality is secure if an adversary in this protocol cannot cause more harm than in an ideal computation, where parties give their inputs to a trusted party that returns the output of the functionality to all parties. In particular, in the ideal model, such computation is fair—if the corrupted parties get the output, then the honest parties get the output. Cleve (STOC 1986) proved that, in general, fairness is not possible without an honest majority. To overcome this impossibility, Gordon and Katz (Eurocrypt 2010) suggested a relaxed definition—1/ p -secure computation—which guarantees partial fairness. For two parties, they constructed 1/ p -secure protocols for functionalities for which the size of either their domain or their range is polynomial (in the security parameter). Gordon and Katz ask whether their results can be extended to multiparty protocols. We study 1/ p -secure protocols in the multiparty setting for general functionalities. Our main result is constructions of 1/ p -secure protocols that are resilient against any number of corrupted parties provided that the number of parties is constant and the size of the range of the functionality is at most polynomial (in the security parameter ${n}$ n ). If fewer than 2/3 of the parties are corrupted, the size of the domain of each party is constant, and the functionality is deterministic, then our protocols are efficient even when the number of parties is $\log \log {n}$ log log n . On the negative side, we show that when the number of parties is super-constant, 1/ p -secure protocols are not possible when the size of the domain of each party is polynomial. Thus, our feasibility results for 1/ p -secure computation are essentially tight. We further motivate our results by constructing protocols with stronger guarantees: If in the execution of the protocol there is a majority of honest parties, then our protocols provide full security. However, if only a minority of the parties are honest, then our protocols are 1/ p -secure. Thus, our protocols provide the best of both worlds, where the 1/ p -security is only a fall-back option if there is no honest majority.
2019
JOFC
Recently, there has been huge progress in the field of concretely efficient secure computation, even while providing security in the presence of malicious adversaries. This is especially the case in the two-party setting, where constant-round protocols exist that remain fast even over slow networks. However, in the multi-party setting, all concretely efficient fully secure protocols, such as SPDZ, require many rounds of communication. In this paper, we present a constant-round multi-party secure computation protocol that is fully secure in the presence of malicious adversaries and for any number of corrupted parties. Our construction is based on the constant-round protocol of Beaver et al. (the BMR protocol) and is the first version of that protocol that is concretely efficient for the dishonest majority case. Our protocol includes an online phase that is extremely fast and mainly consists of each party locally evaluating a garbled circuit. For the offline phase, we present both a generic construction (using any underlying MPC protocol) and a highly efficient instantiation based on the SPDZ protocol. Our estimates show the protocol to be considerably more efficient than previous fully secure multi-party protocols.
2018
JOFC
2018
JOFC
2018
JOFC
2018
CRYPTO
2018
CRYPTO
We present two new, highly efficient, protocols for securely generating a distributed RSA key pair in the two-party setting. One protocol is semi-honestly secure and the other maliciously secure. Both are constant round and do not rely on any specific number-theoretic assumptions and improve significantly over the state-of-the-art by allowing a slight leakage (which we show to not affect security).For our maliciously secure protocol our most significant improvement comes from executing most of the protocol in a “strong” semi-honest manner and then doing a single, light, zero-knowledge argument of correct execution. We introduce other significant improvements as well. One such improvement arrives in showing that certain, limited leakage does not compromise security, which allows us to use lightweight subprotocols. Another improvement, which may be of independent interest, comes in our approach for multiplying two large integers using OT, in the malicious setting, without being susceptible to a selective-failure attack.Finally, we implement our malicious protocol and show that its performance is an order of magnitude better than the best previous protocol, which provided only semi-honest security.
2018
PKC
In the setting of secure computation, a set of parties wish to compute a joint function of their private inputs without revealing anything but the output. Garbled circuits, first introduced by Yao, are a central tool in the construction of protocols for secure two-party computation (and other tasks like secure outsourced computation), and are the fastest known method for constant-round protocols. In this paper, we initiate a study of garbling multivalent-logic circuits, which are circuits whose wires may carry values from some finite/infinite set of values (rather than only $\mathsf {True}$True and $\mathsf {False}$False). In particular, we focus on the three-valued logic system of Kleene, in which the admissible values are $\mathsf {True}$True, $\mathsf {False}$False, and $\mathsf {Unknown}$Unknown. This logic system is used in practice in SQL where some of the values may be missing. Thus, efficient constant-round secure computation of SQL over a distributed database requires the ability to efficiently garble circuits over 3-valued logic. However, as we show, the two natural (naive) methods of garbling 3-valued logic are very expensive.In this paper, we present a general approach for garbling three-valued logic, which is based on first encoding the 3-value logic into Boolean logic, then using standard garbling techniques, and final decoding back into 3-value logic. Interestingly, we find that the specific encoding chosen can have a significant impact on efficiency. Accordingly, the aim is to find Boolean encodings of 3-value logic that enable efficient Boolean garbling (i.e., minimize the number of AND gates). We also show that Boolean AND gates can be garbled at the same cost of garbling XOR gates in the 3-value logic setting. Thus, it is unlikely that an analogue of free-XOR exists for 3-value logic garbling (since this would imply free-AND in the Boolean setting).
2017
EUROCRYPT
2017
CRYPTO
2017
ASIACRYPT
2017
TCC
2017
JOFC
2017
JOFC
2017
JOFC
2016
TCC
2016
JOFC
2015
JOFC
2015
TCC
2015
EUROCRYPT
2015
CRYPTO
2015
CRYPTO
2014
CRYPTO
2014
ASIACRYPT
2013
PKC
2013
TCC
2013
TCC
2013
CRYPTO
2013
ASIACRYPT
2013
ASIACRYPT
2013
JOFC
In this note, we show the existence of constant-round computational zero-knowledge proofs of knowledge for all $\mathcal {NP}$. The existence of constant-round zero-knowledge proofs was proven by Goldreich and Kahan (Journal of Cryptology, 1996), and the existence of constant-round zero-knowledge arguments of knowledge was proven by Feige and Shamir (CRYPTO, 1989). However, the existence of constant-round zero-knowledge proofs of knowledge for all $\mathcal {NP}$ is folklore, to the best of our knowledge, since no proof of this fact has been published.
2012
ASIACRYPT
2012
JOFC
Protocols for secure two-party computation enable a pair of parties to compute a function of their inputs while preserving security properties such as privacy, correctness and independence of inputs. Recently, a number of protocols have been proposed for the efficient construction of two-party computation secure in the presence of malicious adversaries (where security is proven under the standard simulation-based ideal/real model paradigm for defining security). In this paper, we present a protocol for this task that follows the methodology of using cut-and-choose to boost Yao’s protocol to be secure in the presence of malicious adversaries. Relying on specific assumptions (DDH), we construct a protocol that is significantly more efficient and far simpler than the protocol of Lindell and Pinkas (Eurocrypt 2007) that follows the same methodology. We provide an exact, concrete analysis of the efficiency of our scheme and demonstrate that (at least for not very small circuits) our protocol is more efficient than any other known today.
2011
JOFC
2011
TCC
2011
TCC
2011
CRYPTO
2011
CRYPTO
2011
CRYPTO
2011
CRYPTO
2011
EUROCRYPT
2011
JOFC
2011
JOFC
2011
JOFC
2010
JOFC
2010
JOFC
2009
TCC
2009
JOFC
2009
JOFC
2009
CRYPTO
2009
CRYPTO
2008
TCC
2008
JOFC
2008
JOFC
2007
EUROCRYPT
2007
TCC
2007
TCC
2006
CRYPTO
2006
JOFC
2006
JOFC
2006
JOFC
2005
CRYPTO
2005
EUROCRYPT
2005
TCC
2005
JOFC
2004
TCC
2003
EUROCRYPT
2003
EUROCRYPT
2003
EUROCRYPT
2003
JOFC
2002
JOFC
2001
CRYPTO
2001
CRYPTO
2000
CRYPTO

#### Program Committees

Eurocrypt 2018
Eurocrypt 2015
TCC 2014 (Program chair)
Crypto 2013
Eurocrypt 2012
PKC 2011
Crypto 2010
Crypto 2008
TCC 2008
Crypto 2006
TCC 2006
Crypto 2005
Eurocrypt 2004


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ACCM

The ACCM function computes the magnitude of the total relative translational acceleration between markers I and J.

ACCM (I, J, L)

Description

Time derivatives are calculated in the reference frame of marker L.

Arguments

I
The marker whose acceleration is to be computed. Must be specified.
J
The marker with respect to which the acceleration is to be computed. This argument is optional. If omitted, it defaults to the ground coordinate system.
L
Time derivatives are taken in the coordinate system of this marker. This argument is optional. If omitted, it defaults to the ground coordinate system.

Example

<Post_Request
comment             = "O_ACCXYZ"
id                  = "70000015"
type                = "EXPRESSION"
expr1               = "NULL"
expr2               = "ACCM(30103031,30102021)"
expr3               = "ACCX(30103031,30102021)"
expr4               = "ACCY(30103031,30102021)"
expr5               = "NULL"
expr6               = "ACCZ(30103031,30102021)"
expr7               = "NULL"
expr8               = "NULL"
/>


text:
+0

# Prove that these are equal using Trig identities

0
72
1

Prove that these are equal using Trig identities

Guest Oct 1, 2018
#1
+27219
+3

Remember that $$\cos^2x+\sin^2x=1$$

Rearrange this in the form:  $$\sin^2x=1-\cos^2x$$

Substitute this into the left hand side (LHS) of your identity:

LHS:  $$1-\cos^2x-cos^2x$$

Simplify

LHS: $$1-2\cos^2x$$

So LHS = RHS

.

Alan  Oct 2, 2018


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# For which gases does the ratio of PV to RT equal a constant?

By definition, $\frac{P V}{R T} = Z$ is the compressibility factor. When $Z > 1$, the gas's repulsive forces dominate (it takes up more molar volume than its ideal counterpart), and when $Z < 1$, the gas's attractive forces dominate (it takes up less volume than its ideal counterpart).


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# zbMATH — the first resource for mathematics

Computational analysis of dense gas shock tube flow. (English) Zbl 0866.76052
Summary: Nonclassical phenomena associated with the classical dynamics of real gases in a conventional shock tube are studied. A TVD predictor-corrector (TVD-MacCormack) scheme with reflective endwall boundary conditions is used for the one-dimensional Euler equations to simulate the evolution of the wave field of a van der Waals gas. Depending upon the initial conditions of the gas, wave fields are produced that contain nonclassical phenomena such as expansion shocks, composite waves, splitting shocks, etc. In addition, the interactions of waves reflected from the endwalls produce both classical and nonclassical phenomena. Wave field evolution is depicted using plots of the flow variables at specific times and with $$x-t$$ diagrams.

##### MSC:
 76M20 Finite difference methods applied to problems in fluid mechanics 76L05 Shock waves and blast waves in fluid mechanics
Full Text:
##### References:
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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.


text:
Takes the density-independent rates $$R_{di}$$ of egg production (as calculated by getRDI()) and returns reduced, density-dependent reproduction rates $$R_{dd}$$ given as $$R_{dd} = R_{di} \frac{R_{max}}{R_{di} + R_{max}}$$ where $$R_{max}$$ are the maximum possible reproduction rates that must be specified in a column in the species parameter dataframe. (All quantities in the above equation are species-specific but we dropped the species index for simplicity.)

BevertonHoltRDD(rdi, species_params, ...)

## Arguments

rdi Vector of density-independent reproduction rates $$R_{di}$$ for all species. A species parameter dataframe. Must contain a column R_max holding the maximum reproduction rate $$R_{max}$$ for each species. Unused

## Value

Vector of density-dependent reproduction rates.

## Details

This is only one example of a density-dependence. You can write your own function based on this example, returning different density-dependent reproduction rates. Three other examples provided are RickerRDD(), SheperdRDD(), noRDD() and constantRDD(). For more explanation see setReproduction().

## See also

Other functions calculating density-dependent reproduction rate: RickerRDD(), SheperdRDD(), constantEggRDI(), constantRDD(), noRDD()


text:
The chain rule is by far the trickiest derivative rule, but it’s not really that bad if you carefully focus on a few important points.

By the way, here’s one way to quickly recognize a composite function.

Whenever the argument of a function is anything other than a plain old x, you’ve got a composite function.

Here’s how to differentiate it with the chain rule:

1. You start with the outside function (the square root), and differentiate that, IGNORING what’s inside.

To make sure you ignore the inside, temporarily replace the inside function with the word stuff.

2. Multiply the result from Step 1 by the derivative of the inside function, stuff´.

Take a good look at this. All basic chain rule problems follow this basic idea. You do the derivative rule for the outside function, ignoring the inside stuff, then multiply that by the derivative of the stuff.

3. Differentiate the inside stuff.

4. Put the real stuff and its derivative back where they belong.

5. Simplify.


text:
# How To Use The Genshiro Closed Beta

October 01, 2021

We’re so pleased to welcome you to our closed beta and walk you through its functionality. We have already had a total value locked in excess of over $2 million! This is your way to take advantage of all our features before we end up securing a parachain slot. Genshiro’s closed beta participants are the first to gain access to our cross-chain DeFi products, as well as GENS staking (liquidity farming) with current APY > 25%. They will furthermore get an extra 5% APY in GENS (via liquidity farming) on their average deposit during the first three months after Genshiro launches. Get started by visiting https://genshiro.equilibrium.io. 1. First, click on “Application.” 2. Connect your wallet. Make sure that you have your Polkadot.js wallet extension installed. Then select “Mainnet.” Only closed beta participants will have access to the mainnet. 3. Click “Connect Wallet” in the sidebar. 4. You have two invites for any friends you want to bring on board. Who do you think will make a strong addition to the Genshiro community? 5. This is a sidebar where you can see all the balances stored on your Polkadot.js wallet. 6. Make a deposit. Click on any asset to get started. In this tutorial we’ll use BUSD, so click on the “Deposit” button. We should mention here that since BUSD is a BSC asset, we will top up BUSD from BSC to our Substrate, using our BSC bridge. You can read more about that right here. 7. Enter the amount of tokens you want to deposit, then click “Approve” to let the smart contract spend your tokens. Please note that you will need the Metamask browser extension for this to work. You should have BUSD (for sake of our example) and some BNB for paying fees. Don't forget to switch the network in Metamask to Binance Smart Chain — we are depositing BUSD and this is a BSC asset. 8. Then click the “Deposit” button, enter your Metamask password, and you’re all set. With the first deposit, we automatically exchange some of your funds to 100 GENS tokens so that you can interact with the Equilibrium parachain and pay transaction fees. That's it! You've made your first deposit and can now start borrowing assets. You may even wish to become a bailsman and earn a 25% bonus on whatever assets you supply to the system. Liquidity farming with APY 25% You can start GENS farming once you provide liquidity to the platform — the minimum deposit for this is$1,000 in digital assets. Current APY is > 25%! Once you’ve entered an amount, click on “Deposit to the liquidity pool” to become a Liquidity Provider supporting Genshiro — read more about this system here. This is where you can also calculate your estimated profit and start liquidity farming. You don't need to do anything else, the process is fully automatic! (You can always check your portfolio by clicking on the “Earn” tab.)

Start borrowing

You can also borrow assets on Genshiro, but you have to provide collateral in order to do so. To get set up, just click on the “Borrow” tab. In the “Liquidity portfolio” section, click on the “Add collateral,” then enter your desired amount of collateral to supply. You can then start borrowing assets!

That’s where we’re at for now! Thanks for joining us in this beta program — we look forward to adding new and enhanced functionality in the future, especially as we secure a parachain!

The window to register for this beta has closed, but each active participant can invite up to two friends to join in! Feel free to ask active users for the invitation in our chat. We are also planning some further activities that will see us give away a limited amount of passes that grant access to our closed beta. Stay tuned for these updates on our Twitter!


text:
Question 505818

Consider the three equations in pairs.  For each pair, set the RHSs equal to each other, solve for *[tex \Large x] and then substitute the value of *[tex \Large x] back into either equation to calculate the value of *[tex \Large y] for the point of intersection for the pair of equations that you selected.  Once you have determined all three points of intersection, that is the three vertices of the triangle, use the distance formula 3 times to find the measure of each of the sides of the triangle.  If the triangle is an isosceles right triangle, then the measure of two of the sides will be equal and the measure of the third side will be the square root of two times the measure of either of the equal measure sides.

Distance Formula:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ sqrt{(x_1\ -\ x_2)^2\ +\ (y_1\ -\ y_2)^2}]

where *[tex \Large \left(x_1,y_1\right)] and *[tex \Large \left(x_2,y_2\right)] are the coordinates of the given points.

John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it


text:
# SharpeRatio: calculate a traditional or modified Sharpe Ratio of Return... In PerformanceAnalytics: Econometric Tools for Performance and Risk Analysis

## Description

The Sharpe ratio is simply the return per unit of risk (represented by variability). In the classic case, the unit of risk is the standard deviation of the returns.

## Usage

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 SharpeRatio( R, Rf = 0, p = 0.95, FUN = c("StdDev", "VaR", "ES"), weights = NULL, annualize = FALSE, SE = FALSE, SE.control = NULL, ... ) SharpeRatio.modified( R, Rf = 0, p = 0.95, FUN = c("StdDev", "VaR", "ES"), weights = NULL, ... )

## Arguments

 R an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns Rf risk free rate, in same period as your returns p confidence level for calculation, default p=.95 FUN one of "StdDev" or "VaR" or "ES" to use as the denominator weights portfolio weighting vector, default NULL, see Details in VaR annualize if TRUE, annualize the measure, default FALSE SE TRUE/FALSE whether to ouput the standard errors of the estimates of the risk measures, default FALSE. SE.control Control parameters for the computation of standard errors. Should be done using the RPESE.control function. ... any other passthru parameters to the VaR or ES functions

## Details

\frac{\overline{(R_{a}-R_{f})}}{√{σ_{(R_{a}-R_{f})}}}

William Sharpe now recommends InformationRatio preferentially to the original Sharpe Ratio.

The higher the Sharpe ratio, the better the combined performance of "risk" and return.

As noted, the traditional Sharpe Ratio is a risk-adjusted measure of return that uses standard deviation to represent risk.

A number of papers now recommend using a "modified Sharpe" ratio using a Modified Cornish-Fisher VaR or CVaR/Expected Shortfall as the measure of Risk.

We have recently extended this concept to create multivariate modified Sharpe-like Ratios for standard deviation, Gaussian VaR, modified VaR, Gaussian Expected Shortfall, and modified Expected Shortfall. See VaR and ES. You can pass additional arguments to VaR and ES via ... The most important is probably the 'method' argument/

This function returns a traditional or modified Sharpe ratio for the same periodicity of the data being input (e.g., monthly data -> monthly SR)

## Author(s)

Brian G. Peterson

## References

Sharpe, W.F. The Sharpe Ratio,Journal of Portfolio Management,Fall 1994, 49-58.

Laurent Favre and Jose-Antonio Galeano. Mean-Modified Value-at-Risk Optimization with Hedge Funds. Journal of Alternative Investment, Fall 2002, v 5.

SharpeRatio.annualized
InformationRatio
TrackingError
ActivePremium
SortinoRatio
VaR
ES

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 data(managers) SharpeRatio(managers[,1,drop=FALSE], Rf=.035/12, FUN="StdDev") SharpeRatio(managers[,1,drop=FALSE], Rf = managers[,10,drop=FALSE], FUN="StdDev") SharpeRatio(managers[,1:6], Rf=.035/12, FUN="StdDev") SharpeRatio(managers[,1:6], Rf = managers[,10,drop=FALSE], FUN="StdDev") data(edhec) SharpeRatio(edhec[, 6, drop = FALSE], FUN="VaR") SharpeRatio(edhec[, 6, drop = FALSE], Rf = .04/12, FUN="VaR") SharpeRatio(edhec[, 6, drop = FALSE], Rf = .04/12, FUN="VaR" , method="gaussian") SharpeRatio(edhec[, 6, drop = FALSE], FUN="ES") # and all the methods SharpeRatio(managers[,1:9], Rf = managers[,10,drop=FALSE]) SharpeRatio(edhec,Rf = .04/12)

PerformanceAnalytics documentation built on Feb. 6, 2020, 5:11 p.m.


text:
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### Credits

All commands from sorted by
Terminal - All commands - 12,330 results
2009-05-31 07:18:01
Functions: shutdown
Tags: Linux windows
111

This will issue a shutdown command to the Windows machine. username must be an administrator on the Windows machine. Requires samba-common package installed. Other relevant commands are:

net rpc shutdown -r : reboot the Windows machine

net rpc abortshutdown : abort shutdown of the Windows machine

Type:

net rpc

to show all relevant commands

while sleep 1;do tput sc;tput cup 0 $(($(tput cols)-29));date;tput rc;done &
2011-02-17 11:13:19
Functions: sleep tput
108

A nice way to use the console in full screen without forget the current time.

you can too add other infos like cpu and mem use.

2009-03-04 06:21:22
Functions: ping
Tags: Network
108

Waiting for your server to finish rebooting? Issue the command above and you will hear a beep when it comes online. The -i 60 flag tells ping to wait for 60 seconds between ping, putting less strain on your system. Vary it to your need. The -a flag tells ping to include an audible bell in the output when a package is received (that is, when your server comes online).

history | awk '{a[$2]++}END{for(i in a){print a[i] " " i}}' | sort -rn | head 2009-02-11 13:12:29 Functions: awk sort 108 echo "You can simulate on-screen typing just like in the movies" | pv -qL 10 2010-01-14 20:17:44 Functions: echo 104 This will output the characters at 10 per second. getconf LONG_BIT 2009-08-08 21:22:19 Functions: getconf Tags: getconf 32 64 104 Easy and direct way to find this out. <alt> + <print screen/sys rq> + <R> - <S> - <E> - <I> - <U> - <B> 2009-02-20 07:28:56 104 If the machine is hanging and the only help would be the power button, this key-combination will help to reboot your machine (more or less) gracefully. R - gives back control of the keyboard S - issues a sync E - sends all processes but init the term singal I - sends all processes but init the kill signal U - mounts all filesystem ro to prevent a fsck at reboot B - reboots the system Save your file before trying this out, this will reboot your machine without warning! http://en.wikipedia.org/wiki/Magic_SysRq_key ps aux | sort -nk +4 | tail 2009-01-23 17:12:33 Functions: ps sort 98 ps returns all running processes which are then sorted by the 4th field in numerical order and the top 10 are sent to STDOUT. mv filename.{old,new} 2009-03-02 02:28:55 Functions: mv 95 pushd /tmp 2009-02-16 16:52:59 93 If are a Bash user and you are in a directory and need to go else where for a while but don't want to lose where you were, use pushd instead of cd. cd /home/complicated/path/.I/dont/want/to/forget pushd /tmp cd thing/in/tmp popd (returns you to /home/complicated/path/.I/dont/want/to/forget) \[command] 2009-02-11 19:34:21 91 e.g. if rm is aliased for 'rm -i', you can escape the alias by prepending a backslash: rm [file] # WILL prompt for confirmation per the alias \rm [file] # will NOT prompt for confirmation per the default behavior of the command lsof -i 2009-04-25 14:24:04 90 echo "!!" > foo.sh 2009-02-25 00:37:25 Functions: echo 88 Sometimes commands are long, but useful, so it's helpful to be able to make them permanent without having to retype them. An alternative could use the history command, and a cut/sed line that works on your platform. history -1 | cut -c 7- > foo.sh nc -v -l 80 < file.ext 2009-02-17 14:39:52 87 From the other machine open a web navigator and go to ip from the machine who launch netcat, http://ip-address/ If you have some web server listening at 80 port then you would need stop them or select another port before launch net cat ;-) * You need netcat tool installed diff <(sort file1) <(sort file2) 2009-02-04 22:20:13 Functions: diff sort 87 bash/ksh subshell redirection (as file descriptors) used as input to diff rm !(*.foo|*.bar|*.baz) 2010-04-13 15:13:54 Functions: rm 86 Deletes all files in a folder that are NOT *.foo, *.bar or *.baz files. Edit the pattern inside the brackets as you like. !* 2009-06-21 17:58:01 86 !* is all of the arguments to the previous command rather than just the last one. This is useful in many situations. Here's a simple example: vi cd /stuff oops! [exit vi, twice] !* expands to: cd /stuff some_very_long_and_complex_command # label 2009-09-08 05:58:27 85 When using reverse-i-search you have to type some part of the command that you want to retrieve. However, if the command is very complex it might be difficult to recall the parts that will uniquely identify this command. Using the above trick it's possible to label your commands and access them easily by pressing ^R and typing the label (should be short and descriptive). UPDATE: One might suggest using aliases. But in that case it would be difficult to change some parts of the command (such as options, file/directory names, etc). lsof -P -i -n 2009-09-19 18:28:48 84 awk '/start_pattern/,/stop_pattern/' file.txt 2009-03-28 14:28:59 Functions: awk 83 I find this terribly useful for grepping through a file, looking for just a block of text. There's "grep -A # pattern file.txt" to see a specific number of lines following your pattern, but what if you want to see the whole block? Say, the output of "dmidecode" (as root): dmidecode | awk '/Battery/,/^$/'

Will show me everything following the battery block up to the next block of text. Again, I find this extremely useful when I want to see whole blocks of text based on a pattern, and I don't care to see the rest of the data in output. This could be used against the '/etc/securetty/user' file on Unix to find the block of a specific user. It could be used against VirtualHosts or Directories on Apache to find specific definitions. The scenarios go on for any text formatted in a block fashion. Very handy.

CDPATH=:..:~:~/projects
2009-03-20 14:50:25
Tags: bash
83

CDPATH tells the cd command to look in this colon-separated list of directories for your destination. My preferred order are 1) the current directory, specified by the empty string between the = and the first colon, 2) the parent directory (so that I can cd lib instead of cd ../lib), 3) my home directory, and 4) my ~/projects directory.

echo "The date is: $(date +%D)" 2009-03-07 15:51:59 Functions: echo 82 This is a simple example of using proper command nesting using$() over . There are a number of advantages of $() over backticks. First, they can be easily nested without escapes: program1$(program2 $(program3$(program4)))

versus

program1 program2 \program3 \program4\\

Second, they're easier to read, then trying to decipher the difference between the backtick and the singlequote: `'. The only drawback $() suffers from is lack of total portability. If your script must be portable to the archaic Bourne shell, or old versions of the C-shell or Korn shell, then backticks are appropriate, otherwise, we should all get into the habit of$(). Your future script maintainers will thank you for producing cleaner code.

ifconfig | convert label:@- ip.png
2011-08-24 05:58:29
Functions: ifconfig
Tags: ImageMagick
79
man hier
2010-01-26 16:31:05
Functions: man
76

Curious about differences between /bin, /usr/bin, and /usr/local/bin? What should be in the /sbin dir? Try this command to find out.

Tested against Red Hat & OS X

vim -x <FILENAME>
2009-05-05 23:24:17
Functions: vim
76

While I love gpg and truecrypt there's some times when you just want to edit a file and not worry about keys or having to deal needing extra software on hand. Thus, you can use vim's encrypted file format.


text:
# Chapter 11 - Rational Expressions and Functions - 11-5 Solving Rational Equations - Practice and Problem-Solving Exercises - Page 684: 39

$12 \space hours$

#### Work Step by Step

Let the larger pipe fill the tank in $a$ hours and the smaller tank fill the tank in $3a$ hours. (Fraction of the tank can fill by the larger pipe in a 1 hour)+ (Fraction of the tank can fill by the smaller pipe in a 1 hour)9=1 $\implies (\dfrac{1}{a}+\dfrac{1}{3a})9=1$ $\implies (\dfrac{9}{a}+\dfrac{9}{3a}) =1$ $\implies (\dfrac{9}{a}+\dfrac{3}{a}) =1$ $\implies \dfrac{12}{a}=1$ $a=12 \space hours$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


text:
# Optimizing spiking neural networks¶

Almost all deep learning methods are based on gradient descent, which means that the network being optimized needs to be differentiable. Deep neural networks are usually built using rectified linear or sigmoid neurons, as these are differentiable nonlinearities. However, in biological neural modelling we often want to use spiking neurons, which are not differentiable. So the challenge is how to apply deep learning methods to spiking neural networks.

A method for accomplishing this is presented in Hunsberger and Eliasmith (2015). The idea is to use a differentiable approximation of the spiking neurons during the training process, which can then be swapped for spiking neurons once the optimization is complete. In this example we will use these techniques to develop a network to classify handwritten digits (MNIST) in a spiking convolutional network.

In [1]:

%matplotlib inline

from urllib.request import urlretrieve
import zipfile

import nengo
import nengo_dl
import tensorflow as tf
from tensorflow.contrib.learn.python.learn.datasets import mnist
import numpy as np
import matplotlib.pyplot as plt

First we’ll load the training data, the MNIST digits/labels.

In [2]:

data = mnist.read_data_sets("MNIST_data/", one_hot=True)

for i in range(3):
plt.figure()
plt.imshow(np.reshape(data.train.images[i], (28, 28)))
plt.axis('off')
plt.title(str(np.argmax(data.train.labels[i])));

WARNING:tensorflow:From <ipython-input-2-dcb135e6a60a>:1: read_data_sets (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.
Instructions for updating:
Please use alternatives such as official/mnist/dataset.py from tensorflow/models.
WARNING:tensorflow:From d:\miniconda3\envs\nengo_dl\lib\site-packages\tensorflow\contrib\learn\python\learn\datasets\mnist.py:260: maybe_download (from tensorflow.contrib.learn.python.learn.datasets.base) is deprecated and will be removed in a future version.
Instructions for updating:
WARNING:tensorflow:From d:\miniconda3\envs\nengo_dl\lib\site-packages\tensorflow\contrib\learn\python\learn\datasets\mnist.py:262: extract_images (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.
Instructions for updating:
Please use tf.data to implement this functionality.
Extracting MNIST_data/train-images-idx3-ubyte.gz
WARNING:tensorflow:From d:\miniconda3\envs\nengo_dl\lib\site-packages\tensorflow\contrib\learn\python\learn\datasets\mnist.py:267: extract_labels (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.
Instructions for updating:
Please use tf.data to implement this functionality.
Extracting MNIST_data/train-labels-idx1-ubyte.gz
WARNING:tensorflow:From d:\miniconda3\envs\nengo_dl\lib\site-packages\tensorflow\contrib\learn\python\learn\datasets\mnist.py:110: dense_to_one_hot (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.
Instructions for updating:
Extracting MNIST_data/t10k-images-idx3-ubyte.gz
Extracting MNIST_data/t10k-labels-idx1-ubyte.gz
WARNING:tensorflow:From d:\miniconda3\envs\nengo_dl\lib\site-packages\tensorflow\contrib\learn\python\learn\datasets\mnist.py:290: DataSet.__init__ (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.
Instructions for updating:
Please use alternatives such as official/mnist/dataset.py from tensorflow/models.

Recall that the plan is to construct the network using a differentiable approximation of spiking neurons. The spiking neuron model we’ll use is nengo.LIF, which has the differentiable approximation nengo_dl.SoftLIFRate. The parameters of nengo_dl.SoftLIFRate are the same as LIF/LIFRate, with the addition of the sigma parameter which controls the smoothness of the approximation (the lower the value of sigma, the closer SoftLIFRate approximates the true LIF/LIFRate firing curves.

In [3]:

# lif parameters
lif_neurons = nengo.LIF(tau_rc=0.02, tau_ref=0.002, amplitude=0.01)

# softlif parameters (lif parameters + sigma)
softlif_neurons = nengo_dl.SoftLIFRate(tau_rc=0.02, tau_ref=0.002, amplitude=0.01,
sigma=0.002)

# ensemble parameters
ens_params = dict(max_rates=nengo.dists.Choice([100]), intercepts=nengo.dists.Choice([0]))

# plot some example LIF tuning curves
for neuron_type in (lif_neurons, softlif_neurons):
with nengo.Network(seed=0) as net:
ens = nengo.Ensemble(10, 1, neuron_type=neuron_type)

with nengo_dl.Simulator(net) as sim:
plt.figure()
plt.plot(*nengo.utils.ensemble.tuning_curves(ens, sim))
plt.xlabel("input value")
plt.ylabel("firing rate")
plt.title(str(neuron_type))

Building network
Build finished in 0:00:00
Optimization finished in 0:00:00
Construction finished in 0:00:00
Building network
Build finished in 0:00:00
Optimization finished in 0:00:00
Construction finished in 0:00:00

We will use TensorNodes to construct the network, as they allow us to easily include features such as convolutional connections. To make things even easier, we’ll use nengo_dl.tensor_layer. This is a utility function for constructing TensorNodes that mimics the layer-based syntax of many deep learning packages (e.g. tf.layers). The full documentation for this function can be found here.

tensor_layer is used to build a sequence of layers, where each layer takes the output of the previous layer and applies some transformation to it. So when we build a tensor_layer we pass it the input to the layer, the transformation we want to apply (expressed as a function that accepts a tf.Tensor as input and produces a tf.Tensor as output), and any arguments to that transformation function. tensor_layer also has optional transform and synapse parameters that set those respective values on the Connection from the previous layer to the one being constructed.

Normally all signals in a Nengo model are (batched) vectors. However, certain layer functions, such as convolutional layers, may expect a different shape for their inputs. If the shape_in argument is specified for a tensor_layer then the inputs to the layer will automatically be reshaped to the given shape. Note that this shape does not include the batch dimension on the first axis, as that will be automatically set by the simulation.

tensor_layer can also be passed a Nengo NeuronType, instead of a Tensor function. In this case tensor_layer will construct an Ensemble implementing the given neuron nonlinearity (the rest of the arguments work the same).

Note that tensor_layer is just a syntactic wrapper for constructing TensorNodes or Ensembles; anything we build with a tensor_layer we could instead construct directly using those underlying components. tensor_layer just simplifies the construction of this common layer-based pattern.

In [4]:

def build_network(neuron_type):
with nengo.Network() as net:
# we'll make all the nengo objects in the network
# non-trainable. we could train them if we wanted, but they don't
# add any representational power so we can save some computation
# by ignoring them. note that this doesn't affect the internal
# components of tensornodes, which will always be trainable or
# non-trainable depending on the code written in the tensornode.
nengo_dl.configure_settings(trainable=False)

# the input node that will be used to feed in input images
inp = nengo.Node(nengo.processes.PresentInput(data.test.images, 0.1))

# add the first convolutional layer
x = nengo_dl.tensor_layer(
inp, tf.layers.conv2d, shape_in=(28, 28, 1), filters=32,
kernel_size=3)

# apply the neural nonlinearity
x = nengo_dl.tensor_layer(x, neuron_type, **ens_params)

x = nengo_dl.tensor_layer(
x, tf.layers.conv2d, shape_in=(26, 26, 32),
filters=32, kernel_size=3)
x = nengo_dl.tensor_layer(x, neuron_type, **ens_params)

x = nengo_dl.tensor_layer(
x, tf.layers.average_pooling2d, shape_in=(24, 24, 32),
pool_size=2, strides=2)

# add a dense layer, with neural nonlinearity.
# note that for all-to-all connections like this we can use the
# normal nengo connection transform to implement the weights
# (instead of using a separate tensor_layer). we'll use a
# Glorot uniform distribution to initialize the weights.
x, conn = nengo_dl.tensor_layer(
x, neuron_type, **ens_params, transform=nengo_dl.dists.Glorot(),
shape_in=(128,), return_conn=True)
# we need to set the weights and biases to be trainable
# (since we set the default to be trainable=False)
# note: we used return_conn=True above so that we could access
# the connection object for this reason.
net.config[x].trainable = True
net.config[conn].trainable = True

x = nengo_dl.tensor_layer(x, tf.layers.dropout, rate=0.4)

# the final 10 dimensional class output
x = nengo_dl.tensor_layer(x, tf.layers.dense, units=10)

return net, inp, x

# construct the network
net, inp, out = build_network(softlif_neurons)
with net:
out_p = nengo.Probe(out)

# construct the simulator
minibatch_size = 200
sim = nengo_dl.Simulator(net, minibatch_size=minibatch_size)

Building network
Build finished in 0:00:00
Optimization finished in 0:00:00
Construction finished in 0:00:01

Now we need to train this network to classify MNIST digits. First we load our input images and target labels.

In [5]:

# note that we need to add the time dimension (axis 1), which has length 1
# in this case. we're also going to reduce the number of test images, just to
# speed up this example.
train_inputs = {inp: data.train.images[:, None, :]}
train_targets = {out_p: data.train.labels[:, None, :]}
test_inputs = {inp: data.test.images[:minibatch_size*2, None, :]}
test_targets = {out_p: data.test.labels[:minibatch_size*2, None, :]}

Next we need to define our objective (error) function. Because this is a classification task we’ll use cross entropy, instead of the default mean squared error.

In [6]:

def objective(x, y):
return tf.nn.softmax_cross_entropy_with_logits(logits=x, labels=y)

The last thing we need to specify is the optimizer. For this example we’ll use AdaDelta.

In [7]:

opt = tf.train.AdadeltaOptimizer(learning_rate=1)

In order to quantify the network’s performance we will also define a classification error function (the percentage of test images classified incorrectly). We could use the cross entropy objective, but classification error is easier to interpret.

In [8]:

def classification_error(outputs, targets):
return 100 * tf.reduce_mean(
tf.cast(tf.not_equal(tf.argmax(outputs[:, -1], axis=-1),
tf.argmax(targets[:, -1], axis=-1)),
tf.float32))

Now we are ready to train the network. In order to keep this example relatively quick we are going to download some pretrained weights. However, if you’d like to run the training yourself set do_training=True below.

In [9]:

print("error before training: %.2f%%" % sim.loss(test_inputs, test_targets,
classification_error))

do_training = False
if do_training:
# run training
sim.train(train_inputs, train_targets, opt, objective=objective, n_epochs=5)

# save the parameters to file
sim.save_params("./mnist_params")
else:
urlretrieve(
"mnist_params.zip")
with zipfile.ZipFile("mnist_params.zip") as f:
f.extractall()

print("error after training: %.2f%%" % sim.loss(test_inputs, test_targets,
classification_error))

sim.close()

error before training: 87.75%
error after training: 1.50%

Now we want to change our network from SoftLIFRate to spiking LIF neurons. We rebuild our network with LIF neurons, and then load the saved parameters.

In [10]:

net, inp, out = build_network(lif_neurons)
with net:
out_p = nengo.Probe(out, synapse=0.1)

sim = nengo_dl.Simulator(net, minibatch_size=minibatch_size, unroll_simulation=10)

Building network
Build finished in 0:00:00
Optimization finished in 0:00:00
Construction finished in 0:00:02

To test our spiking network we need to run it for longer than one timestep, since we can only get an accurate measure of a spiking neuron’s output over time. So we’ll modify our test inputs so that they present the input image for 30 timesteps (0.03 seconds).

In [11]:

n_steps = 30
test_inputs_time = {inp: np.tile(v, (1, n_steps, 1)) for v in test_inputs.values()}
test_targets_time = {out_p: np.tile(v, (1, n_steps, 1)) for v in test_targets.values()}

print("spiking neuron error: %.2f%%" % sim.loss(test_inputs_time, test_targets_time,
classification_error))

spiking neuron error: 3.50%

We can see that the spiking neural network is achieving similar accuracy as the network we trained with SoftLIFRate neurons. n_steps could be increased to further improve performance, since we would get a more accurate measure of each spiking neuron’s output.

We can also plot some example outputs from the network, to see how it is performing over time.

In [12]:

sim.run_steps(n_steps, input_feeds={inp: test_inputs_time[inp][:minibatch_size]})

for i in range(5):
plt.figure()
plt.subplot(1, 2, 1)
plt.imshow(np.reshape(data.test.images[i], (28, 28)))
plt.axis('off')

plt.subplot(1, 2, 2)
plt.plot(sim.trange(), sim.data[out_p][i])
plt.legend([str(i) for i in range(10)], loc="upper left")
plt.xlabel("time")

Simulation finished in 0:00:01

In [13]:

sim.close()


text:
# Mikala Ørsnes Jansen: Reductive Borel–Serre & Unstable algebraic K-theory

Time: Wed 2022-11-23 13.15

Location: Albano, Cramér room

Participating: Mikala Ørsnes Jansen (Köpenhamn)

Abstract

Let R by a ring. The term unstable algebraic K-theory will refer to any (family of) anima $$K(R,n)$$ built entirely out of linear algebra internal to Rn through which the canonical maps $$BGL_n(R) \to K(R)$$ factorise. A classical example is Quillen's plus-construction $$BGL_n(R)^+$$. Ideally, we want a model for unstable algebraic K-theory to be closer to $$K(R)$$ than $$BGL_n(R)$$ is in terms of its nature and properties; for example the fundamental group of the plus-construction is closer to $$K_1(R)$$ than $$GL_n(R)$$ is. The term unstable algebraic K-theory was used in the 1970's by Dennis and Stein in a survey of the functor $$K_2$$, and classically unstable algebraic K-theory has been used to derive many important computational results about ''stable'' algebraic K-theory. We introduce a new model for unstable algebraic K-theory inspired by a detailed study of the so-called reductive Borel–Serre compactification of locally symmetric spaces. In this talk I will mention the main results and calculations of this work and also attempt to shed light on the geometric origins of the model, as this is an important and interesting aspect of the story.

This is joint work with Dustin Clausen.

Belongs to: Stockholm Mathematics Centre
Last changed: Nov 18, 2022


text:
# The Hydra Problem

The nice thing about the hydra game is that Hercules cannot lose. Whatever he does, as long as he keeps cutting the heads, he will kill the hydra (but perhaps after a loooong time). The proof is not complex, but requires a bit more sophisticated machinery than basic graph theory (it is nicely summed up in the article pointed out by anorton here, if you are wondering what the mysterious symbol ωω means, check out the ordinal numbers at Wikipedia).

However, you want to show only that Herculescan kill any hydra, not that any strategy will kill any hydra. The former is much weaker statement and there is a basic proof of that.

Hints:

1. The height of the hydra tree cannot increase.
2. Make Hercules cut off any head that is as far from the root as possible.
3. Hercules can decrease the height of the hydra tree.
4. Use induction on the tree height to show that for any hydra Hercules can kill it.

If the third step is too hard, find a more detailed explanation below:

Assume the root is at the top (as in the diagram you supplied) and consider the lowest level of the tree. Group the leaves by the parent, e.g. tree $\Big(\big({\bullet}{\bullet}\big)\big(({\bullet}{\bullet}{\bullet})({\bullet}{\bullet})\big)\Big)$ would give you $({\bullet}{\bullet}{\bullet})({\bullet}{\bullet})$ or $(3,2)$ for short (the first two leaves were not taken into account because they do not belong to the lowest level). Now assign a number $4^3 + 4^2$ to it, or in general $4^{a_1} + 4^{a_2} + 4^{a_3}+\ldots$ for $(a_1, a_2, a_3, \ldots)$. Observe that when Hercules cuts any of the heads, the exponent decreases and we get two new copies. To give an example, if Hercules had cut a head in the first group, we get \begin{align}3\cdot4^{a_1-1}+4^{a_2} + 4^{a_3} + \ldots < 4^{a_1}+4^{a_2} + 4^{a_3} + \ldots \end{align} which means that the natural number we assigned decreases. It cannot decrease forever (it is a naturalnumber), so finally Hercules will manage to cut all the heads of the bottom-most level. the root is at the top (as in the diagram you supplied) and consider the lowest level of the tree.


text:
# How do you solve x^2+8x=12 using the quadratic formula?

Jul 9, 2015

$x = \left\{- 4 + 2 \sqrt{7} , - 4 - 2 \sqrt{7}\right\}$

#### Explanation:

The equation is ${x}^{2} - 8 \cdot x - 12 = 0$
$x = \frac{- b \pm \sqrt{{b}^{2} - 4 \cdot a \cdot c}}{2 \cdot a}$
Here, a = 1, b = 8, c = -12
Substituting these values,

$x = \frac{- 8 \pm \sqrt{{\left(- 8\right)}^{2} + 48}}{2 \cdot 1} = \frac{- 8 \pm \sqrt{112}}{2} = - 4 \pm 2 \sqrt{7}$

Thus the answer is $x = \left\{- 4 + 2 \sqrt{7} , - 4 - 2 \sqrt{7}\right\}$


text:
2017 4th NAFOSTED Conference on Information and Computer Science 2017
DOI: 10.1109/nafosted.2017.8108067
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“…target that enters the model, the procedure calculates the predicted value of a [49]. KNN was previously used for estimating effort and provided better results in comparison to other techniques [50], [51]. However, what distinguishes this study is that it is performed on a local set of data on a project driven by agile methodology while applying iterative effort modeling per sprint.…”
Section: K-nearest Neighbor Algorithmmentioning
confidence: 99%
“…target that enters the model, the procedure calculates the predicted value of a [49]. KNN was previously used for estimating effort and provided better results in comparison to other techniques [50], [51]. However, what distinguishes this study is that it is performed on a local set of data on a project driven by agile methodology while applying iterative effort modeling per sprint.…”
Section: K-nearest Neighbor Algorithmmentioning
confidence: 99%


text:
## Organic and Inorganic Chemistry Lesson of the Day – Optical Rotation is a Bulk Property

It is important to note that optical rotation is usually discussed as a bulk property, because it’s usually measured as a bulk property by a polarimeter.  Any individual enantiomeric molecule can almost certainly rotate linearly polarized light.  However, in a bulk sample of a chiral substance, there is usually another molecule that can rotate light in the opposite direction.  This is due to the uniform distribution of the stereochemistry of a random sample of the molecules of one compound.  (In other words, the substance consists of different stereoisomers of one compound, and the proportions of the different stereoisomers are roughly equal.)  Because one molecule’s rotation of the light can be cancelled by another molecule’s optical rotation in the opposite direction, such a random sample of the compound would have no net optical rotation.  This type of cancellation will definitely occur in a racemic mixture.  However, if a substance is enantiomerically pure, then all of the molecules in that substance will rotate linearly polarized light in the same direction – this substance is optically active.

## Determining chemical concentration with standard addition: An application of linear regression in JMP – A Guest Blog Post for the JMP Blog

I am very excited to announce that I have been invited by JMP to be a guest blogger for its official blog!  My thanks to Arati Mejdal, Global Social Media Manager for the JMP Division of SAS, for welcoming me into the JMP blogging community with so much support and encouragement, and I am pleased to publish my first post on the JMP Blog!  Mark Bailey and Byron Wingerd from JMP provided some valuable feedback to this blog post, and I am fortunate to get the chance to work with and learn from them!

Following the tradition of The Chemical Statistician, this post combines my passions for statistics and chemistry by illustrating how simple linear regression can be used for the method of standard addition in analytical chemistry.  In particular, I highlight the useful capability of the “Inverse Prediction” function under “Fit Model” platform in JMP to estimate the predictor given an observed response value (i.e. estimate the value of $x_i$ given $y_i$).  Check it out!

## Discovering Argon with the 2-Sample t-Test

I learned about Lord Rayleigh’s discovery of argon in my 2nd-year analytical chemistry class while reading “Quantitative Chemical Analysis” by Daniel Harris.  (William Ramsay was also responsible for this discovery.)  This is one of my favourite stories in chemistry; it illustrates how diligence in measurement can lead to an elegant and surprising discovery.  I find no evidence that Rayleigh and Ramsay used statistics to confirm their findings; their paper was published 13 years before Gosset published about the t-test.  Thus, I will use a 2-sample t-test in R to confirm their result.

Photos of Lord Rayleigh

Source: Wikimedia Commons


text:
## Hsia, Chun-Hsiung

Compute Distance To:
 Author ID: hsia.chun-hsiung Published as: Hsia, Chun-Hsiung External Links: MGP · ORCID
 Documents Indexed: 32 Publications since 2006 Co-Authors: 28 Co-Authors with 31 Joint Publications 742 Co-Co-Authors
all top 5

### Co-Authors

 1 single-authored 5 Jung, Changyeol 5 Ma, Tian 5 Shiue, Ming-Cheng 5 Wang, Shouhong 4 Kwon, Bongsuk 4 Lin, Chang-Shou 3 Bona, Jerry Lloyd 3 Chen, I-Kun 3 Nishida, Takaaki 2 Chen, Hongqiu 2 Chen, Shih-Hsin 2 Han, Jongmin 2 Kagei, Yoshiyuki 2 Teramoto, Yuka 2 Wadade, Hidemitsu 1 Chern, I-Liang 1 Choi, Yuncherl 1 Chuang, Ping-Han 1 Hashizume, Masato 1 Hwang, Gyeongha 1 Kawagoe, Daisuke 1 Liu, Jianguo 1 Nguyen, Thien Binh 1 Su, Jhe-Kuan 1 Ueda, Yoshihiro 1 Wang, Cheng 1 Wang, Xiaoming 1 Wang, Zhi-Qiang
all top 5

### Serials

 5 Discrete and Continuous Dynamical Systems. Series B 3 Journal of Mathematical Fluid Mechanics 2 Applicable Analysis 2 Journal of Mathematical Physics 2 Indiana University Mathematics Journal 2 Journal of Differential Equations 2 Numerische Mathematik 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Journal of Functional Analysis 1 Zeitschrift für Analysis und ihre Anwendungen 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 SIAM Journal on Mathematical Analysis 1 Methods and Applications of Analysis 1 Advances in Differential Equations 1 Discrete and Continuous Dynamical Systems 1 Nonlinear Analysis. Real World Applications 1 Communications on Pure and Applied Analysis 1 RIMS Kôkyûroku Bessatsu 1 Discrete and Continuous Dynamical Systems. Series S 1 Proceedings A. Royal Society of London
all top 5

### Fields

 25 Partial differential equations (35-XX) 14 Fluid mechanics (76-XX) 8 Dynamical systems and ergodic theory (37-XX) 6 Geophysics (86-XX) 4 Ordinary differential equations (34-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Integral equations (45-XX) 1 Numerical analysis (65-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX)

### Citations contained in zbMATH Open

27 Publications have been cited 124 times in 106 Documents Cited by Year
Revisiting an idea of Brézis and Nirenberg. Zbl 1198.35098
2010
Asymptotic symmetry and local behaviors of solutions to a class of anisotropic elliptic equations. Zbl 1388.35060
Hsia, Chun-Hsiung; Lin, Chang-Shou; Wang, Zhi-Qiang
2011
Rotating Boussinesq equations: dynamic stability and transitions. Zbl 1191.86014
Hsia, Chun-Hsiung; Ma, Tian; Wang, Shouhong
2010
Tropical atmospheric circulations with humidity effects. Zbl 1371.86020
Hsia, Chun-Hsiung; Lin, Chang-Shou; Ma, Tian; Wang, Shouhong
2015
Bifurcation analysis of the damped Kuramoto-Sivashinsky equation with respect to the period. Zbl 1342.37056
Hsia, Chun-Hsiung; Han, Jongmin; Choi, Yuncherl
2015
Dynamical bifurcation of the two dimensional Swift-Hohenberg equation with odd periodic condition. Zbl 1262.35031
Han, Jongmin; Hsia, Chun-Hsiung
2012
Attractor bifurcation of three-dimensional double-diffusive convection. Zbl 1146.35313
Hsia, Chun-Hsiung; Ma, Tian; Wang, Shouhong
2008
Asymptotic stability and bifurcation of time-periodic solutions for the viscous Burgers’ equation. Zbl 1350.35010
Chen, Shih-Hsin; Hsia, Chun-Hsiung; Jung, Chang-Yeol; Kwon, Bongsuk
2017
On the asymptotic stability analysis and the existence of time-periodic solutions of the primitive equations. Zbl 1286.35032
Hsia, Chun-Hsiung; Shiue, Ming-Cheng
2013
Regularity for diffuse reflection boundary problem to the stationary linearized Boltzmann equation in a convex domain. Zbl 1411.35058
Chen, I-Kun; Hsia, Chun-Hsiung; Kawagoe, Daisuke
2019
Singularity of macroscopic variables near boundary for gases with cutoff hard potential. Zbl 1332.35254
Chen, I-Kun; Hsia, Chun-Hsiung
2015
Hopf bifurcation for two-dimensional doubly diffusive convection. Zbl 1243.35016
Bona, Jerry L.; Hsia, Chun-Hsiung; Ma, Tian; Wang, Shouhong
2011
On a Burgers’ type equation. Zbl 1108.37052
Hsia, Chun-Hsiung; Wang, Xiaoming
2006
On time periodic solutions, asymptotic stability and bifurcations of Navier-Stokes equations. Zbl 1359.35130
Hsia, Chun-Hsiung; Jung, Chang-Yeol; Nguyen, Thien Binh; Shiue, Ming-Cheng
2017
On the synchronization theory of Kuramoto oscillators under the effect of inertia. Zbl 1419.34148
Hsia, Chun-Hsiung; Jung, Chang-Yeol; Kwon, Bongsuk
2019
On the global convergence of frequency synchronization for Kuramoto and Winfree oscillators. Zbl 1462.34080
Hsia, Chun-Hsiung; Jung, Chang-Yeol; Kwon, Bongsuk
2019
Time-periodic solutions of the primitive equations of large-scale moist atmosphere: existence and stability. Zbl 1329.35033
Hsia, Chun-Hsiung; Shiue, Ming-Cheng
2015
Structural stability and bifurcation for 2-D incompressible flows with symmetry. Zbl 1180.35410
Hsia, Chun-Hsiung; Liu, Jian-Guo; Wang, Cheng
2008
Stratified rotating Boussinesq equations in geophysical fluid dynamics: dynamic bifurcation and periodic solutions. Zbl 1144.81356
Hsia, Chun-Hsiung; Ma, Tian; Wang, Shouhong
2007
Global well-posedness and singularity propagation for the BBM-BBM system on a quarter plane. Zbl 1382.35207
Bona, Jerry L.; Chen, Hongqiu; Hsia, Chun-Hsiung
2016
The existence of positive solutions to the semilinear elliptic equation involving the Sobolev and the Sobolev-Hardy critical terms. Zbl 1236.35059
2011
Bifurcation of binary systems with the Onsager mobility. Zbl 1311.74006
Hsia, Chun-Hsiung
2010
Singular limit in Hopf bifurcation for doubly diffusive convection equations. II: Bifurcation and stability. Zbl 1467.76026
Hsia, Chun-Hsiung; Kagei, Yoshiyuki; Nishida, Takaaki; Teramoto, Yuka
2021
Singular limit in Hopf bifurcation for doubly diffusive convection equations. I: Linearized analysis at criticality. Zbl 1467.76027
Hsia, Chun-Hsiung; Kagei, Yoshiyuki; Nishida, Takaaki; Teramoto, Yuka
2021
Well-posedness for the $$BBM$$-equation in a quarter plane. Zbl 1302.35309
Bona, Jerry L.; Chen, Hongqiu; Hsia, Chun-Hsiung
2014
On the long-time stability of a temporal discretization scheme for the three dimensional viscous primitive equations. Zbl 1388.86011
Hsia, Chun-Hsiung; Shiue, Ming-Cheng
2018
Synchronization of Kuramoto oscillators with time-delayed interactions and phase lag effect. Zbl 1446.34091
Hsia, Chun-Hsiung; Jung, Chang-Yeol; Kwon, Bongsuk; Ueda, Yoshihiro
2020
Singular limit in Hopf bifurcation for doubly diffusive convection equations. II: Bifurcation and stability. Zbl 1467.76026
Hsia, Chun-Hsiung; Kagei, Yoshiyuki; Nishida, Takaaki; Teramoto, Yuka
2021
Singular limit in Hopf bifurcation for doubly diffusive convection equations. I: Linearized analysis at criticality. Zbl 1467.76027
Hsia, Chun-Hsiung; Kagei, Yoshiyuki; Nishida, Takaaki; Teramoto, Yuka
2021
Synchronization of Kuramoto oscillators with time-delayed interactions and phase lag effect. Zbl 1446.34091
Hsia, Chun-Hsiung; Jung, Chang-Yeol; Kwon, Bongsuk; Ueda, Yoshihiro
2020
Regularity for diffuse reflection boundary problem to the stationary linearized Boltzmann equation in a convex domain. Zbl 1411.35058
Chen, I-Kun; Hsia, Chun-Hsiung; Kawagoe, Daisuke
2019
On the synchronization theory of Kuramoto oscillators under the effect of inertia. Zbl 1419.34148
Hsia, Chun-Hsiung; Jung, Chang-Yeol; Kwon, Bongsuk
2019
On the global convergence of frequency synchronization for Kuramoto and Winfree oscillators. Zbl 1462.34080
Hsia, Chun-Hsiung; Jung, Chang-Yeol; Kwon, Bongsuk
2019
On the long-time stability of a temporal discretization scheme for the three dimensional viscous primitive equations. Zbl 1388.86011
Hsia, Chun-Hsiung; Shiue, Ming-Cheng
2018
Asymptotic stability and bifurcation of time-periodic solutions for the viscous Burgers’ equation. Zbl 1350.35010
Chen, Shih-Hsin; Hsia, Chun-Hsiung; Jung, Chang-Yeol; Kwon, Bongsuk
2017
On time periodic solutions, asymptotic stability and bifurcations of Navier-Stokes equations. Zbl 1359.35130
Hsia, Chun-Hsiung; Jung, Chang-Yeol; Nguyen, Thien Binh; Shiue, Ming-Cheng
2017
Global well-posedness and singularity propagation for the BBM-BBM system on a quarter plane. Zbl 1382.35207
Bona, Jerry L.; Chen, Hongqiu; Hsia, Chun-Hsiung
2016
Tropical atmospheric circulations with humidity effects. Zbl 1371.86020
Hsia, Chun-Hsiung; Lin, Chang-Shou; Ma, Tian; Wang, Shouhong
2015
Bifurcation analysis of the damped Kuramoto-Sivashinsky equation with respect to the period. Zbl 1342.37056
Hsia, Chun-Hsiung; Han, Jongmin; Choi, Yuncherl
2015
Singularity of macroscopic variables near boundary for gases with cutoff hard potential. Zbl 1332.35254
Chen, I-Kun; Hsia, Chun-Hsiung
2015
Time-periodic solutions of the primitive equations of large-scale moist atmosphere: existence and stability. Zbl 1329.35033
Hsia, Chun-Hsiung; Shiue, Ming-Cheng
2015
Well-posedness for the $$BBM$$-equation in a quarter plane. Zbl 1302.35309
Bona, Jerry L.; Chen, Hongqiu; Hsia, Chun-Hsiung
2014
On the asymptotic stability analysis and the existence of time-periodic solutions of the primitive equations. Zbl 1286.35032
Hsia, Chun-Hsiung; Shiue, Ming-Cheng
2013
Dynamical bifurcation of the two dimensional Swift-Hohenberg equation with odd periodic condition. Zbl 1262.35031
Han, Jongmin; Hsia, Chun-Hsiung
2012
Asymptotic symmetry and local behaviors of solutions to a class of anisotropic elliptic equations. Zbl 1388.35060
Hsia, Chun-Hsiung; Lin, Chang-Shou; Wang, Zhi-Qiang
2011
Hopf bifurcation for two-dimensional doubly diffusive convection. Zbl 1243.35016
Bona, Jerry L.; Hsia, Chun-Hsiung; Ma, Tian; Wang, Shouhong
2011
The existence of positive solutions to the semilinear elliptic equation involving the Sobolev and the Sobolev-Hardy critical terms. Zbl 1236.35059
2011
Revisiting an idea of Brézis and Nirenberg. Zbl 1198.35098
2010
Rotating Boussinesq equations: dynamic stability and transitions. Zbl 1191.86014
Hsia, Chun-Hsiung; Ma, Tian; Wang, Shouhong
2010
Bifurcation of binary systems with the Onsager mobility. Zbl 1311.74006
Hsia, Chun-Hsiung
2010
Attractor bifurcation of three-dimensional double-diffusive convection. Zbl 1146.35313
Hsia, Chun-Hsiung; Ma, Tian; Wang, Shouhong
2008
Structural stability and bifurcation for 2-D incompressible flows with symmetry. Zbl 1180.35410
Hsia, Chun-Hsiung; Liu, Jian-Guo; Wang, Cheng
2008
Stratified rotating Boussinesq equations in geophysical fluid dynamics: dynamic bifurcation and periodic solutions. Zbl 1144.81356
Hsia, Chun-Hsiung; Ma, Tian; Wang, Shouhong
2007
On a Burgers’ type equation. Zbl 1108.37052
Hsia, Chun-Hsiung; Wang, Xiaoming
2006
all top 5

### Cited by 143 Authors

 12 Hsia, Chun-Hsiung 7 Choi, Yuncherl 7 Guo, Zongming 6 Wan, FangShu 5 Wang, Quan 5 Wang, Shouhong 5 Zou, Wenming 4 Han, Daozhi 4 Han, Jongmin 4 Ma, Tian 4 Sengul, Mustafa Taylan 4 Shiue, Ming-Cheng 3 Chen, I-Kun 3 Guo, Zhenyu V. 3 Ha, Taeyoung 3 Hashizume, Masato 3 Hernandez, Marco 3 Jung, Changyeol 3 Kagei, Yoshiyuki 3 Wang, Chunhua 3 Wu, Fan 3 Yang, Jing 2 Bozkurt, Deniz 2 Chen, Fei 2 Chen, Hongxu 2 Chen, Shih-Hsin 2 Chen, Zhijie 2 Chern, Jann-Long 2 Deliceoğlu, Ali 2 Du, Yihong 2 Guo, Boling 2 Huang, Xia 2 Hwang, Gyeongha 2 Kwon, Bongsuk 2 Li, Jiayu 2 Li, Liang 2 Li, Limei 2 Lin, Chang-Shou 2 Liu, Honghu 2 Liu, Ruikuan 2 Nakamura, Makoto 2 Nishida, Takaaki 2 Ong, Kiah Wah 2 Özer, Saadet 2 Robert, Frédéric 2 Teramoto, Yuka 2 Wang, Liping 2 Zhong, Xuexiu 1 Arioli, Gianni 1 Ávila, Andrés I. 1 Bonheure, Denis 1 Breden, Maxime 1 Brock, Friedemann 1 Cerami, Giovanna 1 Chekroun, Mickaël D. 1 Chen, Chih-Her 1 Chen, Hongqiu 1 Chen, Mo 1 Chen, Zhimin 1 Chuang, Ping-Han 1 Cîrstea, Florica-Corina Şt. 1 Fan, Yanlong 1 Fotsin, Hilaire Bertrand 1 Gao, Fengshuang 1 Gazzola, Filippo 1 Ge, Yongbin 1 Ghoussoub, Nassif A. 1 Guan, Xiaohong 1 Guo, Yuxia 1 Haidau, Cristina A. 1 Hattori, Masanari 1 Hussein, Amru 1 Ishiwata, Michinori 1 Jeong, In-Jee 1 Jia, Lan 1 Jin, Tianling 1 Kalita, Piotr 1 Kawagoe, Daisuke 1 Khan, Arbaz 1 Kim, Chanwoo 1 Kim, Sun-Chul 1 Koch, Hans-Friedrich 1 Kondrashuk, Igor 1 Lan, Bin 1 Lee, Doo Seok 1 Lessard, Jean-Philippe 1 Li, Junyan 1 Li, YanYan 1 Lian, Xinze 1 Lods, Bertrand 1 Louodop, Patrick 1 Lu, Guichen 1 Luo, Hong 1 Ma, Shan 1 Mohan, Manil Thankamani 1 Mokhtar-Kharroubi, Mustapha 1 Nguyen, Thien Binh 1 Njougouo, Thierry 1 Notte-Cuello, Eduardo Alfonso 1 Pan, Jiaojiao ...and 43 more Authors
all top 5

### Cited in 52 Serials

 9 Discrete and Continuous Dynamical Systems. Series B 7 Journal of Mathematical Fluid Mechanics 5 Journal of Mathematical Physics 5 Communications on Pure and Applied Analysis 4 Applicable Analysis 4 Journal of Mathematical Analysis and Applications 4 Journal of Differential Equations 4 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 4 Calculus of Variations and Partial Differential Equations 3 Physica D 3 Discrete and Continuous Dynamical Systems 2 Archive for Rational Mechanics and Analysis 2 Journal of Statistical Physics 2 Chaos, Solitons and Fractals 2 Mathematische Annalen 2 Mathematische Nachrichten 2 Numerische Mathematik 2 Acta Applicandae Mathematicae 2 Communications in Partial Differential Equations 2 SIAM Journal on Mathematical Analysis 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Advanced Nonlinear Studies 2 Journal of Applied Analysis and Computation 2 Korean Journal of Mathematics 1 Journal d’Analyse Mathématique 1 Mathematical Methods in the Applied Sciences 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Journal of Functional Analysis 1 Mathematics and Computers in Simulation 1 Tôhoku Mathematical Journal. Second Series 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Journal of Nonlinear Science 1 Topological Methods in Nonlinear Analysis 1 NoDEA. Nonlinear Differential Equations and Applications 1 Advances in Differential Equations 1 Annales Academiae Scientiarum Fennicae. Mathematica 1 Abstract and Applied Analysis 1 Acta Mathematica Sinica. English Series 1 Communications in Nonlinear Science and Numerical Simulation 1 Communications in Contemporary Mathematics 1 Nonlinear Analysis. Real World Applications 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 SIAM Journal on Applied Dynamical Systems 1 Complex Variables and Elliptic Equations 1 Science China. Mathematics 1 Bulletin of Mathematical Sciences 1 Axioms 1 AIMS Mathematics 1 Electronic Research Archive 1 SN Partial Differential Equations and Applications
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### Cited in 20 Fields

 91 Partial differential equations (35-XX) 26 Fluid mechanics (76-XX) 22 Dynamical systems and ergodic theory (37-XX) 9 Ordinary differential equations (34-XX) 8 Geophysics (86-XX) 7 Statistical mechanics, structure of matter (82-XX) 5 Numerical analysis (65-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Biology and other natural sciences (92-XX) 2 Operator theory (47-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Probability theory and stochastic processes (60-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Real functions (26-XX) 1 Potential theory (31-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Systems theory; control (93-XX)


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## All Posts

One of my favorite data sources is the NYC OpenData site. A while back I noticed a really interesting data set on that site, and I’ve been mulling over what exactly to do with it for a while. The data set in question is the 2015 Street Tree Census. I knew there was some interesting question that this data could answer, I just had to think of it (or ask my girlfriend to think of it for me.

In this blog post I hope to introduce you to the powerful and simple Metropolis-Hastings algorithm. This is a common algorithm for generating samples from a complicated distribution using Markov chain Monte Carlo, or MCMC. By way of motivation, remember that Bayes' theorem says that given a prior $$\pi(\theta)$$ and a likelihood that depends on the data, $$f(\theta | x)$$, we can calculate $$\pi(\theta | x) = \frac{f(\theta | x) \pi(\theta)}{\int f(\theta | x) \pi(\theta) \; \mathrm{d}\theta}.$$ We call $$\pi(\theta | x)$$ the posterior distribution. It's this distribution that we use to make estimates and inferences about the parameter $$\theta$$. Often, however, this distribution is intractable; it can't be calculated directly. This usually happens because of a nasty integral in the denominator that isn't easily solvable. In cases like this, the best solution is usually to approximate the posterior using a Monte Carlo method.

(This is a companion to my post on Paul Gronke’s earlyvoting.net) One of the first assignments we had in my Election Sciences course was to take a look at registration data from the Oregon Motor Voter program and try to find interesting patterns. For those who don’t know, Oregon Motor Voter is an automatic voter registration program in Oregon. Whenever someone interacts with the Oregon DMV, their voter eligibility is automatically checked, and if they are eligible to vote but not registered, they are automatically added to the rolls.

Looking at the spread of a measles epidemic using social networks.


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occasional meanderings in physics' brave new world

Name:
Location: New Zealand

Marni D. Sheppeard

## Wednesday, May 14, 2008

### M Theory Lesson 188

The 1997 Broadhurst and Kreimer paper shows how knot crossing numbers correspond to the weight of the MZV. For example, the positive braid in $B_{2}$ defined by the word $\sigma_{1}^{5}$ is decorated with three chords, and this corresponds to $\zeta (5)$ at weight $w = 5$. The trefoil knot $\sigma_{1}^{3}$ is the simplest $B_{2}$ knot, which gives a three loop chord diagram (well, Feynman diagram, actually) using only two chords. The pattern of crossing and non-crossing chords gets more interesting for braids with $s$ strands where $s > 2$, via the relations of the MZV algebra, where depth corresponds to $(s - 1)$ (this is why the example of $\zeta (5)$ only has one argument). Who would have thought it was so easy to do QED with knots and number theory? Once upon a time physicists admitted that group and gauge theory was a complicated, messy business, so why bother with it? M Theory is much more fun. Observe that the number of points on the circle of the chord diagram is $2n$ (or $w + 1$) where $n$ is the number of chords, so $\zeta (5)$ is really a decorated hexagon, our favourite polygon, often used to label the vertices of the three dimensional associahedron.

a quantum diaries survivor said...

Hi Marni,

just wanted to let you know that I mentioned you and your blog in my video (in italian!!!) on scientific divulgation, for the sci.bzaar.net event I discussed a few times in my blog recently.

You were taken as an example of how one can make scientific divulgation while keeping intact the content, and of a very particular style of blogging - you have a book online by now!

Cheers,
T.

May 15, 2008 6:17 AM
Kea said...

Oh, Tommaso, that's naughty of you! But thank you very much. Yes, I would like to write a book, but as I have said previously, I will first need some sort of stable existence.

May 15, 2008 8:51 AM
Anonymous said...

Jeez, what a word, "divulgation"! I just had to Google it because I've never heard it before. It's synonymous with "publication", silly me. Kea, if you're really desperate for stability, get married!

May 15, 2008 10:02 AM
Kea said...

Dear anonymous, and how would getting married (to some random person I don't care about) improve my status as a role model for young women who dream of ripping apart the patriarchal establishment with the new tool of Web II, aka Big Sister?

May 15, 2008 10:25 AM
CarlBrannen said...

I think it's best to model the external world rather than to mold oneself into being a model. And Madame Curie did okay despite getting hitched. (And what was her maiden name, anyway?)

May 15, 2008 11:00 AM
Kea said...

Ah, Carl, but that was then and this is now ....

May 15, 2008 11:02 AM
CarlBrannen said...

Kea, well you're not alone. I've got my buddy's TV on while I use his internet to put together my lecture for next week's APSNW 2008 meeting. The program right now is Ax Men, which is about loggers in the Pacific Northwest.

The show reminds me of my job (which is also outdoors in the NW). Heavy equipment. Risk of death from various things. Bunch of rough guys whose language is so bad that the audio is a series of bleeps. Working in really bad weather, cold or rainy. Equipment getting stolen.

At least we've never had anyone severely injured or killed on the job. But I know how it happens.

And along this line, Tesla dug ditches in New York City after the market crash in 1929 (he was 73 years old). He had also worked construction back just after his fued with Edison started. By the way, my somewhat infamous great grandfather was a buddy of Tesla.

So soldier on. It's a rough planet. But history has been rather kind to Tesla.

May 15, 2008 5:58 PM
Kea said...

Oh, I'm not complaining, Carl. Your Tesla connection is cool. I quite liked the portrayal of him in the recent movie The Prestige.

May 15, 2008 6:15 PM
CarlBrannen said...

I saw Prestige, great movie.

When Edison lost the "current wars" over DC versus AC, a bunch of equipment went surplus and my ggf Elliott bought a generator to provide his house with electricity. He also built his own refrigerator before the commercial models were available.

He hooked up a motor to rotate the family Christmas tree. This annoyed his wife because it involved cutting a hole in the floor.

Back then, I would guess that most electrical engineers had knowledge that now is concentrated in just a small number, such as how to wind motors.

May 16, 2008 10:57 AM
Kea said...

Carl, that's an amazing family history you have! The only ggf of mine that I know anything about spent most of his life in prison for attempting to murder the whole family (my grandfather included). That was a WWI incident, related to the difficulty of being German in the South Pacific at the time.

May 16, 2008 11:53 AM
CarlBrannen said...

Kea, I have a few of those too, LOL. I'm going to structure my speech tomorrow at the APS meeting around solutions for QCD bound states.

May 17, 2008 10:16 AM
L. Riofrio said...

Fascinating history you have, carl. For Kea: In Australia having convict ancestors is a matter of pride! Tasmania has a tour called "Louisa's Walk" following the footsteps of woman prisoners.

May 18, 2008 2:32 AM
Kea said...

Hi Louise! Yes, in fact I am also descended from early Australian convicts.

May 18, 2008 6:25 AM
CarlBrannen said...

I recently read a most fascinating description of a few, I think Tasmanian, convicts who pirated a ship and sailed it to South America. A nasty life back then.

Hey, they're making the "word verification" things harder and harder.

May 19, 2008 1:27 PM


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# Exam-Style Question on Kinematics

## A mathematics exam-style question with a worked solution that can be revealed gradually

##### List Of QuestionsExam-Style QuestionMore Kinematics QuestionsMore on this Topic

Question id: 616. This question is similar to one that appeared on an IB AA Standard paper in 2021. The use of a calculator is allowed.

The widest river in the world has a width of 11km at its widest point. Suppose there were a straight length of this river near Awkwardville (A) as shown in the diagram below. Points A and P lie on opposite banks, such that AP is the shortest distance across the river. Point B represents the centre of Bumblingburg which is located on the southern riverbank.

$$PB = 40km, AP = 11km \text{ and angle } A \hat{P}B = 90°$$

A boat travels at an average speed of $$12km h^{-1}$$.
A bus travels along the straight road between P and B at an average speed of $$30kmh^{-1}$$.

(a) Find the travel time, in hours, from A to B given that the boat is taken from A to P, and the bus from P to B.

(b) Find the travel time, in hours, from A to B given the boat travels directly to B.

There is a point D which lies on the road from P to B. such that $$BD = x km$$.

(c) If the boat travels from A to D and the bus travels from D to B, find an expression, in terms of $$x$$, for the travel time T, from A to B, passing through D.

(d) Find the value of $$x$$ so that T is a minimum.

An excursion involves renting the boat and the bus. The cost to rent the boat is £50 per hour and the cost to rent the bus is £35 per hour.

(e) Find the new value of $$x$$ so that the total cost to travel from A to B via D is a minimum.

(f) Write down the minimum total cost for this journey.

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# Curried

Now we are looking on the crossword clue for: Curried.
it’s A 7 letters crossword puzzle definition.
Next time, try using the search term “Curried crossword” or “Curried crossword clue” when searching for help with your puzzle on the web. See the possible answers for Curried below.

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### Random information on the term “Curried”:

In mathematics, the tensor-hom adjunction is that the tensor product and Hom functors − ⊗ X {\displaystyle -\otimes X} and Hom  ( X , − ) {\displaystyle \operatorname {Hom} (X,-)} form an adjoint pair:

This is made more precise below. The order “tensor-hom adjunction” is because tensor is the left adjoint, while hom is the right adjoint.

Say R and S are (possibly noncommutative) rings, and consider the right module categories (an analogous statement holds for left modules):

Fix an (R,S) bimodule X and define functors F: D → C and G: C → D as follows:

Then F is left adjoint to G. This means there is a natural isomorphism

This is actually an isomorphism of abelian groups. More precisely, if Y is an (A, R) bimodule and Z is a (B, S) bimodule, then this is an isomorphism of (B, A) bimodules. This is one of the motivating examples of the structure in a closed bicategory.[1]

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