text:
Let’s do convincing arguments about why the sums and also products that rational and also irrational numbers constantly produce specific kinds of numbers.

You are watching: What is the sum of a rational and irrational number

Here space some examples of integers (positive or negative whole numbers):

Experrewildtv.coment with adding any 2 numbers indigenous the perform (or various other integers of her choice). Try to find one or an ext examples of two integers that:

add increase to another integeradd up to a number that is not one integer

Experrewildtv.coment with multiplying any two numbers from the list (or other integers of her choice). Shot to find one or more examples of 2 integers that:

multiply come make another integermultiply to do a number the is not an integer

Here space a couple of examples of adding two reasonable numbers. Is each amount a rational number? Be all set to define how you know.

$$4 +0.175 = 4.175$$$$\frac12 + \frac45 = \frac 510+\frac810 = \frac1310$$$$\text-0.75 + \frac148 = \frac \text-68 + \frac 148 = \frac 88 = 1$$$$a$$ is an integer: $$\frac 23+ \frac a15 =\frac1015 + \frac a15 = \frac 10+a15$$

Here is a method to describe why the sum of 2 rational number is rational.

Suppose $$\fracab$$ and $$\fraccd$$ room fractions. That method that $$a, b, c,$$ and $$d$$ room integers, and also $$b$$ and $$d$$ are not 0.

Find the sum of $$\fracab$$ and $$\fraccd$$. Display your reasoning. In the sum, room the molecule and the denominator integers? how do you know?Use your responses to define why the sum of $$\fracab + \fraccd$$ is a rational number. Use the same thinking as in the previous question to describe why the product of two rational numbers, $$\fracab \boldcdot \fraccd$$, should be rational.
Consider number that are of the kind $$a + b \sqrt5$$, wherein $$a$$ and $$b$$ are whole numbers. Let’s contact such numbers quintegers.

Here room some instances of quintegers:

When we include two quintegers, will we constantly get one more quinteger? either prove this, or uncover two quintegers whose amount is no a quinteger.When us multiply 2 quintegers, will we constantly get an additional quinteger? one of two people prove this, or discover two quintegers who product is not a quinteger.

Here is a way to describe why $$\sqrt2 + \frac 19$$ is irrational.

Let $$s$$ it is in the sum of $$\sqrt2$$ and also $$\frac 19$$, or $$s=\sqrt2 + \frac 19$$.

Suppose $$s$$ is rational.

Would $$s + \text- \frac19$$ be rational or irrational? explain how you know.Evaluate $$s + \text-\frac19$$. Is the amount rational or irrational?Use her responses so far to define why $$s$$ can not be a rational number, and therefore $$\sqrt2 + \frac 19$$ can not be rational.Use the same reasoning as in the earlier question to describe why $$\sqrt2 \boldcdot \frac 19$$ is irrational.

Consider the equation $$4x^2 + bx + 9=0$$. Find a value of $$b$$ so the the equation has:

2 reasonable solutions2 irrational solutions1 solutionno solutionsDescribe every the values of $$b$$ that create 2, 1, and no solutions.

Write a new quadratic equation with each form of solution. Be prepared to explain how you understand that her equation has the specified kind and number of solutions.

no solutions2 irrational solutions2 rational solutions1 solution

We know that quadratic equations deserve to have rational remedies or irrational solutions. For example, the options to $$(x+3)(x-1)=0$$ are -3 and 1, which space rational. The solutions to $$x^2-8=0$$ room $$\pm \sqrt8$$, which room irrational.

Sometrewildtv.comes services to equations integrate two number by enhancement or multiplication—for example, $$\pm 4\sqrt3$$ and $$1 +\sqrt 12$$. What sort of number room these expressions?

When we add or multiply 2 rational numbers, is the result rational or irrational?

The amount of two rational number is rational. Here is one means to define why it is true:

Any 2 rational numbers can be composed $$\fracab$$ and $$\fraccd$$, where $$a, b, c, \text and also d$$ room integers, and also $$b$$ and $$d$$ space not zero.The sum of $$\fracab$$ and also $$\fraccd$$ is $$\fracad+bcbd$$. The denominator is not zero due to the fact that neither $$b$$ no one $$d$$ is zero.Multiplying or adding two integers always gives an integer, therefore we understand that $$ad, bc, bd$$ and $$ad+bc$$ space all integers.If the numerator and also denominator the $$\fracad+bcbd$$ space integers, then the number is a fraction, i beg your pardon is rational.

The product of two rational numbers is rational. Us can present why in a srewildtv.comilar way:

For any type of two rational number $$\fracab$$ and $$\fraccd$$, wherein $$a, b, c, \text and d$$ are integers, and also $$b$$ and also $$d$$ space not zero, the product is $$\fracacbd$$.Multiplying 2 integers always results in one integer, therefore both $$ac$$ and $$bd$$ are integers, for this reason $$\fracacbd$$ is a rational number.

What around two irrational numbers?

The sum of 2 irrational numbers might be one of two people rational or irrational. We can present this through examples:

$$\sqrt3$$ and also $$\text-\sqrt3$$ space each irrational, however their amount is 0, i beg your pardon is rational.$$\sqrt3$$ and also $$\sqrt5$$ room each irrational, and their amount is irrational.

The product of 2 irrational numbers can be either rational or irrational. Us can present this with examples:

$$\sqrt2$$ and also $$\sqrt8$$ room each irrational, yet their product is $$\sqrt16$$ or 4, i beg your pardon is rational.$$\sqrt2$$ and also $$\sqrt7$$ are each irrational, and their product is $$\sqrt14$$, which is not a perfect square and also is therefore irrational.

What about a reasonable number and an irrational number?

The amount of a reasonable number and also an irrational number is irrational. To describe why requires a slightly different argument:

Let $$R$$ it is in a reasonable number and $$I$$ one irrational number. We desire to display that $$R+I$$ is irrational.Suppose $$s$$ to represent the sum of $$R$$ and $$I$$ ($$s=R+I$$) and suppose $$s$$ is rational.If $$s$$ is rational, then $$s + \text-R$$ would likewise be rational, because the amount of 2 rational numbers is rational.$$s + \text-R$$ is no rational, however, because $$(R + I) + \text-R = I$$.$$s + \text-R$$ cannot be both rational and also irrational, which means that ours original presumption that $$s$$ to be rational to be incorrect. $$s$$, i m sorry is the amount of a reasonable number and also an irrational number, must be irrational.

The product that a non-zero reasonable number and an irrational number is irrational. Us can present why this is true in a srewildtv.comilar way:

Let $$R$$ be rational and also $$I$$ irrational. We desire to present that $$R \boldcdot I$$ is irrational.Suppose $$p$$ is the product of $$R$$ and $$I$$ ($$p=R \boldcdot I$$) and also suppose $$p$$ is rational.If $$p$$ is rational, climate $$p \boldcdot \frac1R$$ would additionally be rational since the product of 2 rational number is rational.$$p \boldcdot \frac1R$$ is no rational, however, due to the fact that $$R \boldcdot ns \boldcdot \frac1R = I$$.$$p \boldcdot \frac1R$$ cannot be both rational and also irrational, which way our original presumption that $$p$$ to be rational to be false. $$p$$, which is the product that a reasonable number and an irrational number, have to be irrational.

The formula $$x = \text-b \pm \sqrtb^2-4ac \over 2a$$ that offers the solutions of the quadratic equation $$ax^2 + bx + c = 0$$, wherein $$a$$ is no 0.

See more: Brutus Soliloquy Act 2 Scene 1, No Fear Shakespeare: Julius Caesar: Act 2 Scene 1

The Illustrative mathematics name and logo space not subject to the an innovative Commons license and also may no be supplied without the prior and also express composed consent that Illustrative Mathematics.


text:
main-content

## Über dieses Buch

The exponential increase in the use of MCMC methods and the corre sponding applications in domains of even higher complexity have caused a growing concern about the available convergence assessment methods and the realization that some of these methods were not reliable enough for all-purpose analyses. Some researchers have mainly focussed on the con vergence to stationarity and the estimation of rates of convergence, in rela tion with the eigenvalues of the transition kernel. This monograph adopts a different perspective by developing (supposedly) practical devices to assess the mixing behaviour of the chain under study and, more particularly, it proposes methods based on finite (state space) Markov chains which are obtained either through a discretization of the original Markov chain or through a duality principle relating a continuous state space Markov chain to another finite Markov chain, as in missing data or latent variable models. The motivation for the choice of finite state spaces is that, although the resulting control is cruder, in the sense that it can often monitor con vergence for the discretized version alone, it is also much stricter than alternative methods, since the tools available for finite Markov chains are universal and the resulting transition matrix can be estimated more accu rately. Moreover, while some setups impose a fixed finite state space, other allow for possible refinements in the discretization level and for consecutive improvements in the convergence monitoring.

## Inhaltsverzeichnis

### 1. Markov Chain Monte Carlo Methods

Abstract
As the complexity of the models covered by statistical inference increases, the need for new computational tools gets increasingly pressing. Simulation has always been a natural tool for statisticians (as opposed to numerical analysis) and simulation via Markov chains has been recently exposed as a broad spectrum method, which allows to tackle problems of higher complexity (as shown by the subsequent literature). Although the purpose of this book is to introduce some control techniques for such simulation methods, we feel it is necessary to recall in this chapter the main properties of Markov Chain Monte Carlo (MCMC) algorithms. Moreover, we take the opportunity to introduce notations and our favorite (so-called benchmark) examples, which will be used over and over in the first half of the book. Good introductions to the topic are Gelfand and Smith (1990) seminal paper and Tanner (1996) monograph, as well as Casella and George (1992) and Chib and Greenberg (1996) tutorial papers, and Gelman and Rubin (1992), Geyer (1992) and Besag et al. (1995) surveys, while Neal (1993), Gilks, Richardson and Spiegelhalter (1996), Robert (1996c), Gamerman (1997), Robert and Casella (1998) and Gelfand and Smith (1998) provide deeper entries. In this explosive area of research, many books, monographs and long surveys are currently on their way and it is quite impossible to keep an exact account of the current’ MCMC production!
Christian P. Robert, Sylvia Richardson

### 2. Convergence Control of MCMC Algorithms

Abstract
There is an obvious difference between the theoretical guarantee that f is the stationary distribution of a Markov chain (x(t)) and the practical requirement that (1.2) is close enough to (1.1). It is thus necessary to develop diagnostic tools towards the latter goal, namely convergence control.1While control is the topic of this book, we first present in this chapter some of the usual methods, before embarking upon the description of new control methods. The reader is referred to the survey papers of Brooks (1998), Brooks and Roberts (1998) and Cowles and Carlin (1996), as well as to Robert and Casella (1998) and Gelfand and Smith (1998) for details.
Christian P. Robert, Dominique Cellier

### 3. Linking Discrete and Continuous Chains

Abstract
When comparing discrete and continuous Markov chains from a theoretical perspective (through, say, Kemeny and Snell, 1960, or Feller, 1970, vol. 1, for the former and Revuz, 1984, or Meyn and Tweedie, 1993, for the latter), a striking difference is the scale of the machinery needed to deal with continuous Markov chains and, as a corollary, the relative lack of intuitive basis behind theoretical results for continuous Markov chains. This gap is the major incentive for this book, in the sense that convergence controls methods must keep away both from the traps of ad hoc devices which are “seen” to work well on artificial and contrived examples, and from the quagmire of formal convergence results which, while being fascinating from a theoretical point of view, either fail to answer the true purpose of the analysis, i.e. to decide whether or not the chain(s) at hand have really converged, or require such an involved analysis that they are not customarily applicable besides case-study setups. This is also why techniques such as Raftery and Lewis (1996) are quite alluring, given their intuitive background and theoretical (quasi-)validity.
Anne Philippe, Christian P. Robert

### 4. Valid Discretization via Renewal Theory

Abstract
As discussed in Chapter 2, an important drawback of Raftery and Lewis’ (1992a, 1996) convergence control method is that the discretized version of the Markov chain is not a Markov chain itself, unless a stringent lumpability condition holds (see Kemeny and Snell, 1960). This somehow invalidates the binary control method, although it provides useful preliminary information on the required number of iterations. However, the discrete aspect of the criterion remains attractive for its intuitive flavour and, while the Duality Principle of Chapter 1 cannot be invoked in every setting, this chapter shows how renewal theory can be used to construct a theoretically valid discretization method for general Markov chains. We then consider some convergence control methods based on these discretized chains, even though the chains can be used in many alternative ways (see also Chapter 5).
Chantal Guihenneuc-Jouyaux, Christian P. Robert

### 5. Control by the Central Limit Theorem

Abstract
Distinctions between single chain and parallel chain control methods have already been discussed in Chapter 2. However, as Brooks and Roberts (1998) point out, other characteristics must be taken into account for evaluating control methods. An important criterion is the programming investment: diagnostics requiring problem-specific computer codes for their implementation (e.g., requiring knowledge of the transition kernel of the Markov chain) are far less usable for the end user than diagnostics solely based upon the outputs from the sampler, which can use available generic codes. Another criterion is interpretability, in the sense that a diagnostic should preferably require no interpretation or experience from the user.
Didier Chauveau, Jean Diebolt, Christian P. Robert

### 6. Convergence Assessment in Latent Variable Models: DNA Applications

Abstract
A DNA sequence is a long succession of four nucleotides or bases, Adenine, Cytosine, Guanine and Thymine, and can be represented by a finite series $$x = \left( {{x_1}, \cdots,{x_n}} \right)$$ ;each base xttaken from the alphabet $$x = \left\{ {A,C,G,T} \right\}$$ It turns out that there is an important heterogeneity within the genome.1 Statistical models based on a complete homogeneity assumption are thus unrealistic. We propose a hidden Markov chain approach to identify homogeneous regions in the DNA sequence. The breakpoints which define these regions may thus separate parts of the genome with different functional or structural properties.
Florence Muri, Didier Chauveau, Dominique Cellier

### 7. Convergence Assessment in Latent Variable Models: Application to the Longitudinal Modelling of a Marker of HIV Progression

Abstract
Infection’ with Human Immunodeficiency Virus type-1 (HIV-1), the virus that leads to AIDS, is associated with a decline in CD4 cell count, a type of white blood cell involved in the immune system. In order to monitor the health status and disease progression of HIV infected patients, CD4 counts have thus been frequently used as a marker. In particular, Markov process models of the natural history of HIV play an important part in AIDS modelling (Longini et al., 1991, Freydman, 1992, Longini, Clark and Karon, 1993, Gentleman et al., 1994, Satten and Longini, 1996).
Chantal Guihenneuc-Jouyaux, Sylvia Richardson, Virginie Lasserre

### 8. Estimation of Exponential Mixtures

Abstract
Exponential mixtures are distributions of the form
$$\sum\limits_{i = 0}^k {{p_i}} \varepsilon xp\left( {{\lambda _i}} \right)$$
(8.1)
With$${p_o} + \ldots + {p_k} = 1$$and$${\lambda _i} > 0\left( {0 \leqslant i \leqslant k} \right)$$ Considering the huge literature on normal mixtures (see §3.4), the treatment of exponential mixtures is rather limited. A possible reason, as illustrated in this chapter, is that the components of (8.1) are much more difficult to distinguish than in the normal case of §3.4. Exponential mixtures with a small number of components are nonetheless used in the modeling of phenomena with positive output and long asymmetric tails, mainly in survival and duration setups, like the applications mentioned in Titterington, Smith and Makov (1985, p.17-21). We also illustrate this modeling in the case of hospitalization durations for which a two or three component exponential mixture is appropriate.
Marie-Anne Gruet, Anne Philippe, Christian P. Robert

### Backmatter

Weitere Informationen

format: plain


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# Is this linear programming problem right?

The problem is: Beth works a maximum of 20 hours/week programming computers and tutoring math. She receives 25 dollars/hour for programming and 20 dollars/hour for tutoring. She works between 3 and 8 hours/week programming, but always gives more time to tutoring. How many hours should she work at each job to maximize her income?

Let x = # hours programming and y = # hours tutoring.

My constraints are:

Total hours: x+y≤20
Hours programming: 3≤x≤8
Hours tutoring: y>x

My objective function is:

25x + 20y = maximum profit

Here is my graph:

And from looking at the corner points, I can say that the answer is 8 hours programming and 12 tutoring. Is this plus all my other work correct?

-

@Someone just to make it clear, the reason is that when you say "$y>x$", you're saying "$y\ne x$". That's no good as we can see from the following ridiculous LPP: $\max z$ subject to $z<1$. As you can see, there is no solution. Why? Well $z$ can't be 1 cause $z<1$. But there is no next smallest number under 1, at least not in the real numbers. So strict inequalities make LPP's impossible to solve. –  crf Dec 9 '12 at 22:03


text:
# Control Unit - Q6

+1 vote

Let us define control signals, P and Q, that have the following interpretation
PQ = 00  Fetch cycle
PQ = 01  Indirect cycle
PQ = 10  Execute cycle
PQ = 11  Interrupt cycle

Which of the following expression boolean expression defines $C_4$  ?

$(A). \bar P t_3$

$(B). \bar P \bar t_3 +\bar Q t_3$

$(C).\bar P \bar Q t_3 + P \bar Q t_3$

$(D).\bar P \bar Q t_3 + P Q t_3$

reshown Jun 9

$\\ C4\ CS\ is\ there\ in\ fetch\ cycle \ \ as\ well\ as\ in\ indirect\ cycle\ section\\ \\ \therefore Boolean\ Expression\ for\ C4\\ C4=P'Q't3 + P'Qt3\\ Since\ No\ option\ is\ matching.\ Let's\ Simplify\\ C4=P't3(Q'+Q)=P't3$


text:
# Opencv - Depth map from uncalibrated stereo system

I m trying to get a depth map from an uncalibrated method. I can obtain the fundamental matrix via different correspondent points from SIFT method and "cv2.findFundamentalMat". Then with "cv2.stereoRectifyUncalibrated" i can get the rectification matrix. Finally i can use "cv2.warpPerspective" to rectify and compute the disparity but this latter doesnt conduct to a good depth map...The values are very high so i m wondering if i have to use "warpPerspective" or i have to calculate rotation matrix from homography matrix got with "stereoRectifyUncalibrated"

A part of the code :

#Obtainment of the correspondent point with SIFT
sift = cv2.SIFT()

###find the keypoints and descriptors with SIFT
kp1, des1 = sift.detectAndCompute(dst1,None)
kp2, des2 = sift.detectAndCompute(dst2,None)

###FLANN parameters
FLANN_INDEX_KDTREE = 0
index_params = dict(algorithm = FLANN_INDEX_KDTREE, trees = 5)
search_params = dict(checks=50)

flann = cv2.FlannBasedMatcher(index_params,search_params)
matches = flann.knnMatch(des1,des2,k=2)

good = []
pts1 = []
pts2 = []

###ratio test as per Lowe's paper
for i,(m,n) in enumerate(matches):
if m.distance < 0.8*n.distance:
good.append(m)
pts2.append(kp2[m.trainIdx].pt)
pts1.append(kp1[m.queryIdx].pt)

pts1 = np.array(pts1)
pts2 = np.array(pts2)

#Computation of the fundamental matrix

# Obtainment of the rectification matrix and use of the warpPerspective to transform them...

pts1 = np.int32(pts1)
pts2 = np.int32(pts2)

p1fNew = pts1.reshape((pts1.shape[0] * 2, 1))
p2fNew = pts2.reshape((pts2.shape[0] * 2, 1))

retBool ,rectmat1, rectmat2 = cv2.stereoRectifyUncalibrated(p1fNew,p2fNew,F,(2048,2048))

dst11 = cv2.warpPerspective(dst1,rectmat1,(2048,2048))
dst22 = cv2.warpPerspective(dst2,rectmat2,(2048,2048))

#calculation of the disparity
disp = stereo.compute(dst22.astype(uint8), dst11.astype(uint8)).astype(np.float32)
plt.imshow(disp);plt.colorbar();plt.clim(0,400)#;plt.show()
plt.savefig("0gauche.png")

#plot depth by using disparity focal length C1[0,0] from stereo calibration and T[0] the distance between cameras

plt.imshow(C1[0,0]*T[0]/(disp),cmap='hot');plt.clim(-0,500);plt.colorbar();plt.show()

Here the rectified pictures with uncalibrated method (and warpPerspective) :

Here the rectified pictures with calibrated method :

I dont know how the difference is so important between the two kind of pictures...and for the calibrated method, it doesnt seem aligned...strange The disparity map of the uncalibrated method :

And the depth map are calculated with : C1[0,0]*T[0]/(disp) with T from the "stereocalibrate" but the values are very high...

edit retag close merge delete


text:
### GEORGE MASON UNIVERSITY DEPARTMENT OF MATHEMATICAL SCIENCES APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

Speaker:Dimitris Ntogkas, Univeristy of Maryland, College Park
Title: Non-Conforming FEM for Large Bending Deformations with Isometry Constraint

Abstract: We propose a numerical method for the approximation of deformations $y:\Omega \subset \mathbb{R}^2 \to \mathbb{R}^3$ of a single-layer thin plate with mid-plane $\Omega$, under a non-linear isometry constraint. This deformation is the solution of a minimization problem under the isometry constraint and appropriate boundary conditions. We employ a discretization of the energy functional and the constraint using a space of fully discontinuous polynomials and introduce an appropriate discrete version of the Hessian that captures the discontinuities of the space. We prove the $\Gamma$- convergence of the discrete functional, as well as the convergence of discrete global minimizers to global minimizers of the continuous energy. We employ a simple extension of the model to account for the effect of a spontaneous curvature for a bi-layer plate and perform numerical simulations in order to explore the efficiency and the geometric flexibility of the method for both models.

Time: Friday, January 26, 2018, 1:30-2:30pm

Place: Exploratory Hall, Room 4106

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491


text:
If independent Xn converge in probability they almost surely converge to a constant

Hi guys,

I hope you might be able to help me with this question:

Suppose $X_n$ are independent, and $X_n \rightarrow X$ in probability. Show that $X$ is almost surely a constant.

The hint I got was: Suppose that $X$ is not a constant almost surely. Can there be $a$ and $b$ with $a, such that P(X<a)>0 and P(X>b)>0 ? Now use independence of $X_n$ and X_n+1.

I really have no idea where to go with this so any help would be much appreciated! PS. Sorry about the bits not written out in Latex - it kept saying Latex compile error whenever I submitted them.

Many thanks,

YChana


text:
Charly Mourglia
5 posts
None
Indentation behaviour
Edited by Charly Mourglia on Reason: Added namespace stuff, fixed typo
Hi,

Is there any way to customize indentation behaviour ?
I kinda don't like the way access specifiers (public, private, protected) and constructors initialization lists are (not) indented.

What I get :

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 class Foo { public: Foo(); private: int bar; int baz; }; Foo::Foo() : bar(42) , baz(1337) { }

What I would expect
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 class Foo { public: Foo(); private: int bar; int baz; }; Foo::Foo() : bar(42) , baz(1337) { }

Also, being able to add keywords in some way to the indentation engine, to avoid messing thing up because of macros for example (yes signals, slots and Q_OBJECT, I'm looking at you...)

EDIT:
Fun fact, it looks like initialization lists are correct when inside namespaces (while public / private are still not)

Actual behaviour:
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 namespace test { class Foo { public: Foo(); private: int bar; int baz; }; Foo::Foo() : bar(42) , baz(1337) { } }

What could be intended :
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 namespace test { class Foo { public: Foo(); private: int bar; int baz; }; Foo::Foo() : bar(42) , baz(1337) { } }

P.S.: Those indenting rules imply only me, and this might behave the way it's intended to, in this case that's why I would like to be able to customize them :P
Allen Webster
473 posts / 4 projects
Heyo
Indentation behaviour
Edited by Allen Webster on Reason: wording
Today is your lucky day, good sir, because right this very day, in just thirty minutes, I am going to go live on Twitch and reimplement the auto indent rule entirely on the customization side. Moving it to the customization side will let me offer more built in flexibility, and it will mean that users who maintain their own customizations can tweak the indenting rule to their hearts content.

In the mean time: yes. This is the expected behavior for alpha 4.0.10.
Charly Mourglia
5 posts
None
Indentation behaviour
w00t, I luv dat !


text:
## Cryptology ePrint Archive: Report 2020/474

Tiramisu: Black-Box Simulation Extractable NIZKs in the Updatable CRS Model

Karim Baghery and Mahdi Sedaghat

Abstract: In CRYPTO'18, Groth et al. introduced the $\textit{updatable}$ CRS model that allows bypassing the trust in the setup of NIZK arguments. Zk-SNARKs are the well-known family of NIZK arguments that are ubiquitously deployed in practice. In applications that achieve $\textit{universal composability}$, e.g. Hawk [S&P'16], Gyges [CCS'16], Ouroboros Crypsinous [S&P'19], the underlying SNARK is lifted by the $\texttt{COCO}$ framework [Kosba et al.,2015] to achieve Black-Box Simulation Extractability (BB-SE). The $\texttt{COCO}$ framework is designed in the standard CRS model, consequently, all BB-SE NIZK arguments built with it need a trusted setup phase. In a promising research direction, recently subversion-resistant and updatable SNARKs are proposed that can eliminate/bypass the needed trust in schemes. However, none of the available subversion-resistant/updatable schemes can achieve BB-SE, as Bellare et al.'s result from ASIACRYPT'16 shows that achieving simultaneously Sub-ZK (ZK without trusting a third party) and BB extractability is impossible. In this paper, we propose $\texttt{Tiramisu}$, as construction to build BB-SE NIZK arguments in the $\textit{updatable}$ CRS model. Similar to the $\texttt{COCO}$, $\texttt{Tiramisu}$ is suitable for modular use in larger cryptographic systems and allows building BB-SE NIZK arguments, but with $\textit{updatable}$ parameters. Our results show that one can bypass the impossibility of achieving Sub-ZK and BB extractability in the updatable CRS model. In new constructions, in the cost of updating, all parties can eliminate the trust on a third-party and the protocol satisfies ZK and BB-SE. Meanwhile, we define public-key cryptosystems with updatable keys and present an efficient construction based on the El-Gamal cryptosystem which can be of independent interest. We instantiate $\texttt{Tiramisu}$ and present efficient BB-SE zk-SNARKs with updatable parameters that can be used in protocols like Hawk, Gyges, Ouroboros Crypsinous while allowing the end-users to update the parameters and eliminate the needed trust.

Category / Keywords: cryptographic protocols / zk-SNARKs, Updatable CRS, Black-Box Simulation Extractability, COCO framework, UC-Security

Date: received 22 Apr 2020, last revised 30 May 2020

Contact author: baghery karim at gmail com, ssedagha@esat kuleuven be

Available format(s): PDF | BibTeX Citation

Note: In Italian, Tiramisu literally means "pull me up, lift me up", or more literally "pull it up".

Short URL: ia.cr/2020/474

[ Cryptology ePrint archive ]


text:
Volume 358 - 36th International Cosmic Ray Conference (ICRC2019) - CRI - Cosmic Ray Indirect
The detectability of WCDA to TeV-sources
Y. Guo*, X. Chang, H. Hu, Z. Yao  on behalf of the LHAASO Collaboration
Full text: pdf
Pre-published on: July 22, 2019
Published on: July 02, 2021
Abstract
The Large High Altitude Air Shower Observatory (LHAASO) as a new generation of cosmic ray experiment with unprecedented sensitivity is under construction, and the Water Cherenkov Detector Array (WCDA) is one major component aiming at TeV $\gamma$ rays. In order to sufficiently understand the prospect of searching for TeV $\gamma$-ray sources with WCDA, one-year observing ability of WCDA to TeV $\gamma$-ray sources in TeVCat is presented in this paper. There are 56 out of 128 $\gamma$-ray sources in the $45^\circ$ view of WCDA would be observed at the middle energy of 1 TeV. Most of them are galactic sources, and the extragalactic sources are mainly active galactic nuclei (AGNs).
DOI: https://doi.org/10.22323/1.358.0277
How to cite

Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.

Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.


text:
# 2d array with empty elements

I am working on a game with a number of different grid components. Each grid would be about 15 squares wide by 15 squares tall. Each of the squares may either contain an item or not.

Is there any way to create this array and only include the components that have a value. Example (for a 5x5 array):

[
[5,3, , ,3],
[ ,1,0,2,2],
[ , , , , ],
[5, , ,2, ],
[ , , , ,1]
]

Is there any way to do this in JavaScript or should I just add a bunch of NULL values to the array?

A simplified version of this, might be an Xs and Os game. Before the game starts all squares are empty. Over time, some of the grid may have either Xs or Os in specific squares.

• adding the null values sounds perfect. I was thinking in your X and O's example you could just have 0 = empty; 1= X, 2 = o or whatever feels right to you – Big T Larrity Jul 1 '19 at 8:58
• Did you try using null values? If it worked, post it as an answer. If you're worried that's the "wrong" way to do it, ask yourself, what do you expect the array to return if you try to read one of those blank entries? – DMGregory Jul 1 '19 at 14:47
• @DMGregory I guess the issue was that I was wanting to look at the array and see it the same way I would see it on the screen so that I could easily see at a glance which areas of the array had something in them or not. I guess it's not a big deal though and I will just use null values. It would have just helped me to visualize things better. – kojow7 Jul 1 '19 at 17:36

If you want the map to appear as close as possible to what you've written above, without a lot of nulls to type out and clutter reading, you could define a helper variable first:

var _ = null;

var tileMap = [
[5,3,_,_,3],
[_,1,0,2,2],
[_,_,_,_,_],
[5,_,_,2,_],
[_,_,_,_,1]
];

• Thank you, I didn't realize that a single underscore could be used as a variable name. – kojow7 Jul 1 '19 at 19:03
• I don't recommend it as a general practice, but for a special case like this, if it helps you read and edit your code to get the behaviour you want, it could be worthwhile. :) – DMGregory Jul 1 '19 at 19:07
• huh that's interesting – Ocelot Jul 3 '19 at 6:18


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# Sklearn PCA with zero components example

I'm simply trying to repeat a benchmark from the sklearn's docs.

The unclear part is: n_components = np.arange(0, n_features, 5). They are applying a PCA transform with 0 components!

Can somebody, please, explain, what's the mathematical meaning of this transform?

Think of it this way: a PCA "transform" with $k$ components essentially approximates your $n$-dimensional data points by projecting them onto a $k$-dimensional linear subspace, trying not to loose too much data variance along the way.

More precisely, what you are doing is representing your original points $y \in R^n$ as:

$$y \approx \mu + Vx$$

where $x \in R^k$ are the lower-dimensional "new coordinates", $\mu \in R^n$ is the mean of your data and $V\in R^{n \times k}$ is the matrix of principal component vectors.

The "new coordinates" $x$ tell you how many steps you need to make along the $k$ principal components in order to reach the best possible linear approximation to $y$ by starting your trip from $\mu$.

Now, if $k=0$ the model becomes:

$$x \approx \mu.$$

In other words, you are modeling all of your data as a single, fixed center point. Of course, you do not need to store any "new coordinates" here (because you do not need to move away from the mean), hence it does not make much sense as a "transform", but it is, none the less, a proper probabilistic model (a maximum-likelihood fit for a Gaussian distribution of errors, to be precise).

In particular, you can speak about the log-likelihood of data under this model (which is, up to an affine transform, equal to the sum of squared errors here, but is not as trivial as you might think in the general case) and we can compare various models, choosing the one with the best likelihood. This is exactly what is done in the example from the docs you mention in the question.


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Article

# Phenomenology of light Higgs bosons in supersymmetric left-right models

05/1999;
Source: arXiv

ABSTRACT We carry out a detailed analysis of the light Higgs bosons in supersymmetric left-right models (SLRM). This includes models with minimal particle content and those with additional Higgs superfields. We also consider models with non-renormalizable higher-dimensional terms. We obtain an upper bound on the mass of the lightest CP-even neutral Higgs boson in these models. The upper bound depends only on the gauge couplings, and the vacuum expectation values of those neutral Higgs fields which control the spontaneous breakdown of the $SU(2)_L \times U(1)_Y$ gauge symmetry. We calculate the one-loop radiative corrections to this upper bound, and evaluate it numerically in the minimal version of the supersymmetric left-right model. We consider the couplings of this lightest CP-even Higgs boson to the fermions, and show that in a phenomenologically viable model the branching ratios are similar to the corresponding branching ratios in the minimal supersymmetric standard model (MSSM). We then study the most promising particle for distinguishing the SLRM from other models, namely the doubly charged Higgs boson. We obtain the mass of this doubly charged Higgs boson in different types of supersymmetric left-right models, and discuss its phenomenology.

### Full-text

Available from: P. N. Pandita, Aug 28, 2013
0 Followers
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58 Views
• Source
##### Article: New Signals for Doubly-Charged Scalars and Fermions at the Large Hadron Collider
[Hide abstract]
ABSTRACT: Several extensions of the Standard Model have light doubly-charged Higgs bosons in their particle spectrum. The supersymmetric versions of these models introduce fermionic superpartners of these doubly-charged Higgs bosons, the Higgsinos, which also remain light. In this work we analyze a new collider signal resulting from the pair production and decay of a light doubly-charged Higgsino to an even lighter doubly-charged Higgs boson. We focus on the minimal left-right supersymmetric model with automatic R-parity conservation, which predicts such a light doubly-charged Higgs boson and its Higgsino partner at the TeV scale, which are singlets of SU(2)_L. We investigate the distinctive signatures of these particles with four leptons and missing transverse energy in the final state at the Large Hadron Collider and show that the discovery reach for both particles can be increased in this channel.
Physical review D: Particles and fields 06/2013; 88(5). DOI:10.1103/PhysRevD.88.055006 · 4.86 Impact Factor
• ##### Article: Phenomenology of left-right supersymmetric models with broken BL symmetry
[Hide abstract]
ABSTRACT: We discuss the implications of R parity breaking through spontaneous B-L breaking in left–right supersymmetric models. We give expressions for three generations of neutrino–neutralino and charged–lepton–chargino mixings. We find the masses of the light neutrinos at both the tree and one loop levels. We explore the most stringent bounds on the parameters of the LRSUSY model coming from rare leptonic processes. These phenomena severely restrict the parameters in both the R-parity violating and R-parity conserving sectors. We find that such models are likely to produce light doubly charged Higgs bosons and fermions, with masses as low as MΔ++,Δ̃++<~200 GeV for tanβ=1; however, the right-handed scale is restricted to be heavy, pushing the ZR mass above 160 TeV.
Physical Review D 01/2001; 63(3). DOI:10.1103/PhysRevD.63.034009 · 4.86 Impact Factor
• Source
##### Article: Higgs sector and R-parity breaking couplings in models with broken U(1)BL gauge symmetry
[Hide abstract]
ABSTRACT: Four different supersymmetric models based on SU(2)L×U(1)R×U(1)B-L and SU(2)L×SU(2)R×U(1)B-L gauge symmetry groups are studied. U(1)B-L symmetry is broken spontaneously by a vacuum expectation value (VEV) of a sneutrino field. The right-handed gauge bosons may obtain their mass solely by a sneutrino VEV. The physical charged lepton and neutrino are mixtures of gauginos, Higgsinos and lepton interaction eigenstates. Explicit formulas for masses and mixings in the physical lepton fields are found. The spontaneous symmetry-breaking mechanism fixes the trilinear R-parity breaking couplings. Only some special R-parity breaking trilinear couplings are allowed. There is a potentially large trilinear lepton number breaking coupling - which is unique to left-right models - that is proportional to the SU(2)R gauge coupling gR. The couplings are parametrized by few mixing angles, making spontaneous R-parity breaking a natural unification framework'' for R-parity breaking couplings in supersymmetric left-right models.
Physical review D: Particles and fields 08/2000; 62(5). DOI:10.1103/PhysRevD.62.055010 · 4.86 Impact Factor


text:
<meta http-equiv="refresh" content="1; url=/nojavascript/"> Convergence of Taylor and Maclaurin Polynomials ( Assessments ) | Calculus | CK-12 Foundation

# Convergence of Taylor and Maclaurin Polynomials

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Progress
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Convergence of Taylor and Maclaurin Polynomials Practice
MAT.CAL.762


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# zbMATH — the first resource for mathematics

Irregular fibers of complex polynomials in two variables. (English) Zbl 1060.32015
Let $$f:\mathbb C^2 \rightarrow \mathbb C$$ be a polynomial and $$\mathcal B \subset \mathbb C$$ the bifurcation set. Let $$F_c=f^{-1}(c)$$. The fiber $$F_c$$ is called irregular if $$c \in \mathcal B$$. Let $$D_{\varepsilon}(c) \subset \mathbb C$$ be the disc of radius $$\varepsilon$$ centered at $$c$$ and $$T_c=f^{-1}(D_{\varepsilon}(c))$$. The value $$c \in \mathbb C$$ is called regular at infinity if there exist a compact set $$K$$ in $$\mathbb C^2$$ such that the restriction of $$f:T_c \setminus K \rightarrow D_{\varepsilon}(c)$$ is locally trivial.
The morphism $$j_c:H_1(F_c) \rightarrow H_1(T_c)$$ induced by the inclusion is studied. It is proved that it is an isomorphism if and only if $$c$$ is regular at infinity. Necessary and sufficient conditions for this morphism to be injective respectively surjective are given. The results are applied to the study of vanishing and invariant cycles.
##### MSC:
 32S20 Global theory of complex singularities; cohomological properties 32S45 Modifications; resolution of singularities (complex-analytic aspects) 32S30 Deformations of complex singularities; vanishing cycles
##### Keywords:
irregular fibers; vanishing cycles; invariant cycles
Full Text:


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# Is the cap product the same on cochain complexes with isomorphic cohomology rings?

Let $$X$$ be a topological space. Let $$\mathcal{D}$$ be a cochain algebra, with cohomology ring $$H^* (\mathcal{D})$$. Suppose that we have that the cohomology ring $$H^* (X)$$ (endowed with the cup product) is isomorphic, as a ring, to $$H^* (\mathcal{D})$$, equipped with its respective operation (and the homology groups of $$X$$ are isomorphic to the homology groups of $$\mathcal{D}$$).

There is an action of $$H^* (X)$$ on $$H_* (X)$$ given by the cap product: $$\frown:H_* (X) \otimes H^* (X) \rightarrow H_* (X)$$. There is also an action of $$H^* (\mathcal{D})$$ on $$H_* (\mathcal{D})$$ given by dualizing the algebra structure of $$\mathcal{D}$$ (described below). I am interested in whether this "cap product" on $$\mathcal{D}$$ induces the same action of $$H^* (\mathcal{D})$$ on $$H_* (\mathcal{D})$$ as the cap product does for the cohomology and homology of $$X$$.

Denote by $$*$$ the multiplication in $$\mathcal{D}$$. Let $$\widehat{\mathcal{D}}$$ denote the chain complex obtained by dualizing the cochain complex $$\mathcal{D}$$. We obtain an operation

$$\frown:\mathcal{D} \times \widehat{\mathcal{D}} \rightarrow \widehat{\mathcal{D}}$$

by defining $$\langle u * v, w \rangle = \langle u, v \frown w \rangle$$, the dual of $$*$$.

This is the exact way in which, if we were given the cup product on the level of cochains of $$X$$, we would dualize to get the cap product on the cochains/chains of $$X$$.

There is an induced operation on homology:

$$\frown:H_* (\mathcal{D}) \otimes H^* (\mathcal{D}) \rightarrow H_* (\mathcal{D}).$$

Is this operation the same (isomorphic to) the cap product on the isomorphic cohomology and homology groups of $$X$$? I think that the answer is yes, but I cannot find a proof.

EDIT: Additionally, I would at least like to know if I am correct in thinking that this is always true in the case of zero torsion.

• Do you have non-trivial examples where this is true? I would honestly be surprised if it worked in general. Jul 2, 2020 at 13:58
• Is this not always true if I have zero torsion? So that cup product on the level of cohomology completely determines cap?
– Matt
Jul 4, 2020 at 20:22


text:
What happened to UML?

October 14, 2018
seven minutes.

I was surprised to find that there are software developers who are not willing to engage in software design conversations if there is an UML diagram involved. I was baffled. I use UML diagrams all the time to elucidate design decisions before any code has even been written and I’m not sure what I’d do without them. In any case, surely diagrams are just tools, excellent tools but just tools to aid learning and understanding along with code and patterns and natural language. Why could anyone be so against them? So I looked on the internet and instantly found this:

“I would say that people that defend diagrams and notations are simply not able to grasp code, at all.” - AkitaOnRails

When I had gotten back up off the floor I continued searching. I quickly found something more constructive from the seemingly omniscient Martin Fowler:

“UML has got rather out of fashion it seems. Although this isn’t good for me financially, I can’t say I’m displeased to see a lot of rather dodgy UMLisms going away [however] I continue to find it a useful tool” - Martin Fowler link

This was written back in 2011, I guess the downward trend may have continued since then but there is some nuance in Fowler’s position. He describes different modes of UML which are (were!?) in common use. I can remember the days of MDAMDA was never going to work, for many reasons, but it is regrettable that some of the component oriented design concepts went down with it. We are seeing them come back now with the better micro-service designs but the same errors (wide interfaces, poor cohesion, accidental complexity) are still visible as they were in the early EJB days. where UML diagrams were intended to be executable. They became so loaded down with detail that they lost all possible sense. UML may still be tainted with a mental association with MDA.

Related to the last point, UML may also be associated negatively with Rational Rose, an awful piece of software with so many bugs that it was a continual frustration to use. Unfortunately it gained market shareRational was bought by IBM and “nobody get sacked for buying IBM.“ and its colour scheme (yellow boxes with burgundy borders) stuck as the de-facto standard for UML from then on. I’ve used Rose and I guess that colour scheme stuck with me as well.

UML also suffered from abuse, like any other tool. It has been used, unsuccessfully in my opinion, for the documentationFowler’s blueprint mode of large systems. Without proper care or attention diagrams balloon
Don’t do this, for example.
in both side and complexity to the extent again that they provide negative value.

Beyond the flaws in UML or its use I do believe there is another factor. Having worked with different people over time I have noticed that some people prefer diagrams of systems, while others prefer descriptions. In psychology these are known as visual and verbal thinkingNot be confused with the discredited learning styles teaching methods. styles. To know if your preference is for visual or verbal thinking consider how you study. If you repeat the words to yourself in you head then that’s a verbal thinking style, if you draw a diagram, or picture one in your mind, with colours and some kind of meaningful layout then that’s a visual style. I strongly prefer visual representations and I guess that’s why I like UML. The point is that some people like diagrams more and other like words and that’s OK.

But anyway, regardless of how it happened we seem to have forgotten how to use what is just another tool. Another more useful mode that Fowler talks about is using UML to sketch ideas. This is how I use it and I think it’s where it really shines. Early diagrams like Booch’s and OMTThe universally known GoF patterns book used a variant of this style of diagram. diagrams, were difficult and unwieldy to draw with rhombi or circles on every relation to specify its type. We have now with UML a fairly universal and, if used well, lightweight visual language for communicating software design to our peers. For example, I love this article about software architecture because he uses UML to show visually the similarities between different approaches, and therefore the differences. I find processing that information verbally much more difficult.

So these are my recommendations for using UML if you haven’t given up on it already:

Use it for sketching and note taking. Don’t be worried about the details.

Use it for communicating simple design ideas. This is especially useful when discussing the choices before any decisions have been taken. Component diagrams are really useful here. I’ve found that most developers use these naturally. Also use it for communicating the basic patterns (composites, decorators, etc.) and structure (layers, cross boundary interfaces, etc.).

Don’t use it for documentation.

Use the 10% of UML that is useful:

The simplest class diagrams usually with just a few classes to show the relationship between them, hardly ever any members, no rhombi, just plain arrows with arity which is usually just an asterisk to indicate a collection or otherwise nothing to indicate 1-to-1.

The required and provided interface notation in component diagrams are useful and I tend to mix them freely with class diagrams, use packages and nodes well to indicate system boundaries.

Sequence diagrams can be useful but use them sparingly because they take time to draw. I find well crafted code to be easier to read and to write.

Functional programming diagrams

UML came from the object-oriented design community and does not afford much help when trying to visualise functional decompositions. The idea of a first-class function is not really very well represented. Of course you could use an activity diagram, kind of, but I’m not sure how far that would get you.

For representing functional structures I prefer computational graphs. There doesn’t seem to be a consensus here (again diagrams seem to be out of fashion in functional programming too) but there are some hints. Take this definition of a Monoid:

A Monoid is a set of values S that is closed under an associative binary operation $f$ and contains an identity value $I$ such that $\forall x \in S$; $f(I, x) = x$

Visually this could be expressed as a graph where the operator and the identity are, for example, circles, the operator being the one that receives two inputs.

The definition can be extended, for example:

If changing the order of operands does not affect the result then the operation is commutative and the monoid is called, unsurprisingly, a commutative monoid.

Integer addition, of course, is commutative, string concatenation is not. See how easy that is to visualise:

These visualisations are interesting in that they convey a lot of information very efficiently. I personally find them useful for understanding the concept, I can virtually “see” strings and integers “flowing” through the graph. Of course it could be just me but in any case it would be interesting to see if this kind of modelling could be useful for visualising functional ideas which are well known for being tricky to communicate.

What happened to UML? - October 14, 2018 - John Hearn


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OpenMS  2.6.0

Identifies peptides in MS/MS spectra via Mascot.

 pot. predecessor tools MascotAdapter pot. successor tools any signal-/preprocessing tool (in mzML format) IDFilter or any protein/peptide processing tool

This wrapper application serves for getting peptide identifications for MS/MS spectra. It uses a local installation of the Mascot server to generate the identifications. A second wrapper (MascotAdapterOnline) is available which is able to perform identifications by communicating with a Mascot server over the network. So, it is not necessary to execute MascotAdapterOnline on the same machine as Mascot.

The minimal version of Mascot supported with this server is 2.1.

This wrapper can be executed in three different modes:

1. The whole process of ProteinIdentification via Mascot is executed. Inputfile is a mzData file containing the MS/MS spectra for which the identifications are to be found. The results are written as a idXML output file. This mode is selected by default.

2. Only the first part of the ProteinIdentification process is performed. This means that the MS/MS data is transformed into Mascot Generic Format (mgf) which can be used directly with Mascot. Being in the cgi directory of the Mascot directory calling a Mascot process should look like the following:

./nph-mascot.exe 1 -commandline -f outputfilename < inputfilename

Consult your Mascot reference manual for further details.

This mode is selected by the -mascot_in option in the command line.

3. Only the second part of the ProteinIdentification process is performed. This means that the outputfile of the Mascot server is translated into idXML.

This mode is selected by the -mascot_out option in the command line.

If your Mascot server is installed on the same computer as the TOPP applications the MascotAdapter can be executed in mode 1. Otherwise the Mascot engine has to be executed manually assisted by mode 2 and mode 3. The ProteinIdentification steps then look like:

• execute MascotAdapter in mode 2
./MascotAdapter -in mzDataFile -out mascotGenericFormatFile -mascot_in
• copy mascotGenericFormatFile to your Mascot server
• call your Mascot server process:
./nph-mascot.exe 1 -commandline -f mascotOutFile < mascotGenericFormatFile
• call the script to export your outfile in mascot xml
./export_dat.pl do_export=1 export_format=XML file=mascotOutFile _sigthreshold=0
_showsubset=1 show_same_sets=1 show_unassigned=0 prot_score=0 pep_exp_z=0 pep_score=0
pep_homol=0 pep_ident=0 pep_seq=1 show_header=1 show_queries=1 pep_rank=0 > mascotXMLFile
• copy mascotXMLFile to the server on which the TOPP applications are installed
• execute MascotAdapter in mode 3
./MascotAdapter -in mascotXMLFile -out IdXMLFile -mascot_out

For mode 1 you have to specify the directory in which the Mascot server is installed. This is done by setting the option mascot_dir in the ini file. Furthermore you have to specify a folder in which the user has write permissions. This is done by setting the option temp_data_directory in the ini file. Two temporary files will be created in this directory during execution but deleted at the end of execution.

Note
Currently mzIdentML (mzid) is not directly supported as an input/output format of this tool. Convert mzid files to/from idXML using IDFileConverter if necessary.

The command line parameters of this tool are:

```MascotAdapter -- Annotates MS/MS spectra using Mascot.
Version: 2.6.0 Sep 30 2020, 12:54:34, Revision: c26f752
To cite OpenMS:
Rost HL, Sachsenberg T, Aiche S, Bielow C et al.. OpenMS: a flexible open-source software platform for mass spectrometry data analysis. Nat Meth. 2016; 13, 9: 741-748. doi:10.1038/nmeth.3959.

Usage:

Options (mandatory options marked with '*'):
-in <file>*                      Input file in mzData format.
Note: In mode 'mascot_out' a Mascot results file (.mascotXML) is read (va
lid formats: 'mzData', 'mascotXML')
-out <file>*                     Output file in idXML format.
Note: In mode 'mascot_in' Mascot generic format is written. (valid format
s: 'idXML', 'mgf')
-out_type <type>                 Output file type (for TOPPAS) (valid: 'idXML', 'mgf')
-instrument <i>                  The instrument that was used to measure the spectra (default: 'Default')
-precursor_mass_tolerance <tol>  The precursor mass tolerance (default: '2.0')
-peak_mass_tolerance <tol>       The peak mass tolerance (default: '1.0')
-taxonomy <tax>                  The taxonomy (default: 'All entries' valid: 'All entries', '. . Archaea
(Archaeobacteria)', '. . Eukaryota (eucaryotes)', '. . . . Alveolata (alve
olates)', '. . . . . . Plasmodium falciparum (malaria parasite)', '. . .
. . . Other Alveolata', '. . . . Metazoa (Animals)', '. . . . . . Caenorha
bditis elegans', '. . . . . . Drosophila (fruit flies)', '. . . . . . Chor
data (vertebrates and relatives)', '. . . . . . . . bony vertebrates', '.
. . . . . . . . . lobe-finned fish and tetrapod clade', '. . . . . . . .
. . . . Mammalia (mammals)', '. . . . . . . . . . . . . . Primates', '. .
...
ilable')
-modifications <mods>            The modifications i.e. Carboxymethyl (C)
-variable_modifications <mods>   The variable modifications i.e. Carboxymethyl (C)
-charges [1+ 2+ ...]             The different charge states (default: '[1+ 2+ 3+]')
-db <name>                       The database to search in (default: 'MSDB')
-hits <num>                      The number of hits to report (default: 'AUTO')
-cleavage <enz>                  The enzyme descriptor to the enzyme used for digestion. (Trypsin is defaul
t, None would be best for peptide input or unspecific digestion, for more
please refer to your mascot server). (default: 'Trypsin' valid: 'Trypsin',
'Arg-C', 'Asp-N', 'Asp-N_ambic', 'Chymotrypsin', 'CNBr', 'CNBr+Trypsin',
'Formic_acid', 'Lys-C', 'Lys-C/P', 'PepsinA', 'Tryp-CNBr', 'TrypChymo',
'Trypsin/P', 'V8-DE', 'V8-E', 'semiTrypsin', 'LysC+AspN', 'None')
-missed_cleavages <num>          Number of allowed missed cleavages (default: '0' min: '0')
-sig_threshold <num>             Significance threshold (default: '0.05')
-pep_homol <num>                 Peptide homology threshold (default: '1.0')
-pep_ident <num>                 Peptide ident threshold (default: '1.0')
-pep_rank <num>                  Peptide rank (default: '1')
-prot_score <num>                Protein score (default: '1.0')
-pep_score <num>                 Peptide score (default: '1.0')
-pep_exp_z <num>                 Peptide expected charge (default: '1')
-show_unassigned <num>           Show_unassigned (default: '1')
-first_dim_rt <num>              Additional information which is added to every peptide identification as
metavalue if set > 0 (default: '0.0')
-boundary <string>               MIME boundary for mascot output format
-mass_type <type>                Mass type (default: 'Monoisotopic' valid: 'Monoisotopic', 'Average')
-mascot_directory <dir>          The directory in which mascot is located
-temp_data_directory <dir>       A directory in which some temporary files can be stored

Common TOPP options:
-ini <file>                      Use the given TOPP INI file
-threads <n>                     Sets the number of threads allowed to be used by the TOPP tool (default:
'1')
-write_ini <file>                Writes the default configuration file
--help                           Shows options
--helphelp                       Shows all options (including advanced)

```

INI file documentation of this tool:

Legend:
required parameter
+MascotAdapterAnnotates MS/MS spectra using Mascot.
version2.6.0 Version of the tool that generated this parameters file.
++1Instance '1' section for 'MascotAdapter'
in input file in mzData format.
Note: In mode 'mascot_out' a Mascot results file (.mascotXML) is read
input file*.mzData,*.mascotXML
out output file in idXML format.
Note: In mode 'mascot_in' Mascot generic format is written.
output file*.idXML,*.mgf
out_type output file type (for TOPPAS)idXML,mgf
instrumentDefault the instrument that was used to measure the spectra
precursor_mass_tolerance2.0 the precursor mass tolerance
peak_mass_tolerance1.0 the peak mass tolerance
taxonomyAll entries the taxonomyAll entries,. . Archaea (Archaeobacteria),. . Eukaryota (eucaryotes),. . . . Alveolata (alveolates),. . . . . . Plasmodium falciparum (malaria parasite),. . . . . . Other Alveolata,. . . . Metazoa (Animals),. . . . . . Caenorhabditis elegans,. . . . . . Drosophila (fruit flies),. . . . . . Chordata (vertebrates and relatives),. . . . . . . . bony vertebrates,. . . . . . . . . . lobe-finned fish and tetrapod clade,. . . . . . . . . . . . Mammalia (mammals),. . . . . . . . . . . . . . Primates,. . . . . . . . . . . . . . . . Homo sapiens (human),. . . . . . . . . . . . . . . . Other primates,. . . . . . . . . . . . . . Rodentia (Rodents),. . . . . . . . . . . . . . . . Mus.,. . . . . . . . . . . . . . . . . . Mus musculus (house mouse),. . . . . . . . . . . . . . . . Rattus,. . . . . . . . . . . . . . . . Other rodentia,. . . . . . . . . . . . . . Other mammalia,. . . . . . . . . . . . Xenopus laevis (African clawed frog),. . . . . . . . . . . . Other lobe-finned fish and tetrapod clade,. . . . . . . . . . Actinopterygii (ray-finned fishes),. . . . . . . . . . . . Takifugu rubripes (Japanese Pufferfish),. . . . . . . . . . . . Danio rerio (zebra fish),. . . . . . . . . . . . Other Actinopterygii,. . . . . . . . Other Chordata,. . . . . . Other Metazoa,. . . . Dictyostelium discoideum,. . . . Fungi,. . . . . . Saccharomyces Cerevisiae (baker's yeast),. . . . . . Schizosaccharomyces pombe (fission yeast),. . . . . . Pneumocystis carinii,. . . . . . Other Fungi,. . . . Viridiplantae (Green Plants),. . . . . . Arabidopsis thaliana (thale cress),. . . . . . Oryza sativa (rice),. . . . . . Other green plants,. . . . Other Eukaryota,. . Bacteria (Eubacteria),. . . . Actinobacteria (class),. . . . . . Mycobacterium tuberculosis complex,. . . . . . Other Actinobacteria (class),. . . . Firmicutes (gram-positive bacteria),. . . . . . Bacillus subtilis,. . . . . . Mycoplasma,. . . . . . Streptococcus Pneumoniae,. . . . . . Streptomyces coelicolor,. . . . . . Other Firmicutes,. . . . Proteobacteria (purple bacteria),. . . . . . Agrobacterium tumefaciens,. . . . . . Campylobacter jejuni,. . . . . . Escherichia coli,. . . . . . Neisseria meningitidis,. . . . . . Salmonella,. . . . . . Other Proteobacteria,. . . . Other Bacteria,. . Viruses,. . . . Hepatitis C virus,. . . . Other viruses,. . Other (includes plasmids and artificial sequences),. . unclassified,. . Species information unavailable
modifications[] the modifications i.e. Carboxymethyl (C)
variable_modifications[] the variable modifications i.e. Carboxymethyl (C)
charges[1+, 2+, 3+] the different charge states
dbMSDB the database to search in
hitsAUTO the number of hits to report
cleavageTrypsin The enzyme descriptor to the enzyme used for digestion. (Trypsin is default, None would be best for peptide input or unspecific digestion, for more please refer to your mascot server).Trypsin,Arg-C,Asp-N,Asp-N_ambic,Chymotrypsin,CNBr,CNBr+Trypsin,Formic_acid,Lys-C,Lys-C/P,PepsinA,Tryp-CNBr,TrypChymo,Trypsin/P,V8-DE,V8-E,semiTrypsin,LysC+AspN,None
missed_cleavages0 number of allowed missed cleavages0:∞
sig_threshold0.05 significance threshold
pep_homol1.0 peptide homology threshold
pep_ident1.0 peptide ident threshold
pep_rank1 peptide rank
prot_score1.0 protein score
pep_score1.0 peptide score
pep_exp_z1 peptide expected charge
show_unassigned1 show_unassigned
first_dim_rt0.0 additional information which is added to every peptide identification as metavalue if set > 0
boundary MIME boundary for mascot output format
mass_typeMonoisotopic mass typeMonoisotopic,Average
mascot_directory the directory in which mascot is located
temp_data_directory a directory in which some temporary files can be stored
log Name of log file (created only when specified)
debug0 Sets the debug level
threads1 Sets the number of threads allowed to be used by the TOPP tool
no_progressfalse Disables progress logging to command linetrue,false
forcefalse Overrides tool-specific checkstrue,false
testfalse Enables the test mode (needed for internal use only)true,false

You can specify the Mascot parameters precursor_mass_tolerance (the peptide mass tolerance), peak_mass_tolerance (the MS/MS tolerance), taxonomy (restriction to a certain subset of the database), modifications, variable_modifications, charges (the possible charge variants), db (database where the peptides are searched in), hits (number of hits), cleavage (the cleavage enzyme), missed_cleavages (number of missed cleavages) and mass_type (Monoisotopic or Average) via the ini file.

Known problems with Mascot server execution:

• getting error message: "FATAL_ERROR: M00327 The ms-monitor daemon/service is not running, please start it."

• Possible explanations:
• Your ms-monitor is really not running => consult your Mascot reference manual for details about starting the Mascot server.
• (Suppose you have Mascot installed in directory mascot.) mascot/data/mascot.control is not writable for the current user. This has to be changed. Otherwise you will not be able to use the Mascot server via the shell and receive the above error message.
=> Change write permissions of the file mascot/data/mascot.control such that the current user has write permissions to it.
Todo:
This adapter is using antiquated internal methods and needs to be updated! E.g. use MascotGenericFile.h instead of MascotInfile.h....


text:
#### Problem 6E

a Write 15(x+2×5)dx as a limit of Riemann sums, taking the sample points to be right endpoints. Use a computer algebra system to evaluate the sum and to compute the limit. b Use the Fundamental Theorem to check your answer to part a.


text:
# Microsoft Visual C++ Runtime Library - Error!

#### alex

##### Distinguished

I have been getting a runtime error! for quite sometime
when I start my pc for C:\program Files\Microsoft
Hardware\mouse\point32.exe The problem is when I get
this error the additional buttons on my keyboard(ie
Volume control) don't work. Can anyone tell me what I
need to do to fix this problem.

G

#### Guest

##### Guest

Click Start-Control Panel-Add/Remove Programs. Remove Microsoft
IntelliType and Microsoft IntelliPoint Software. Now go here and

----
Nathan McNulty

Alex wrote:
> I have been getting a runtime error! for quite sometime
> when I start my pc for C:\program Files\Microsoft
> Hardware\mouse\point32.exe The problem is when I get
> this error the additional buttons on my keyboard(ie
> Volume control) don't work. Can anyone tell me what I
> need to do to fix this problem.


text:
# Linear-algebra meaning

The branch of mathematics that deals with the theory of systems of linear equations, matrices, vector spaces, determinants, and linear transformations.
noun
(linear algebra) An algebra over a field.
noun
A mathematical ring and vector space with scalars from an associated field, the multiplication of which is of the form (a A ) (b B ) = (ab) ( AB ), where a and b are scalars and A and B are vectors.
noun
The algebra of vectors and matrices, as distinct from the ordinary algebra of real numbers and the abstract algebra of unspecified entities.
noun
The branch of mathematics that deals with the theory of systems of linear equations, matrices, vector spaces, and linear transformations.


text:
## Problem of the Day #6: Tiling a 2 by 2 by n Box with Rectangular PrismsMarch 25, 2011

Posted by Billy in : potd , trackback

In how many distinct ways can $2n$ identical $1\times1\times2$ rectangular prisms be placed inside a $2\times2\times n$ box?

1. Billy - March 25, 2011

Note: I recently realized that this problem may have been written earlier by someone else somewhere on the internet, but I thought of it without having seen it beforehand.


text:
# PoisMixMean: Calculate the conditional per-cluster mean of each...

### Description

This function is used to calculate the conditional per-cluster mean expression for all observations. This value corresponds to μ = (μ_{ijlk}) = (\hat{w}_i \hat{λ}_{jk}) for the PMM-I model and μ = (μ_{ijlk}) = (\hat{w}_i s_{jl}\hat{λ}_{jk}) for the PMM-II model.

### Usage

 1 PoisMixMean(y, g, conds, s, lambda)

### Arguments

 y (n x q) matrix of observed counts for n observations and q variables g Number of clusters conds Vector of length q defining the condition (treatment group) for each variable (column) in y s Estimate of normalized per-variable library size lambda (d x g) matrix containing the current estimate of lambda, where d is the number of conditions (treatment groups) and g is the number of clusters

### Value

A list of length g containing the (n x q) matrices of mean expression for all observations, conditioned on each of the g clusters

### Author(s)

Andrea Rau <andrea.rau@jouy.inra.fr>

### References

Rau, A., Maugis-Rabusseau, C., Martin-Magniette, M.-L., Celeux G. (2015). Co-expression analysis of high-throughput transcriptome sequencing data with Poisson mixture models. Bioinformatics, 31(9):1420-1427.

Rau, A., Celeux, G., Martin-Magniette, M.-L., Maugis-Rabusseau, C. (2011). Clustering high-throughput sequencing data with Poisson mixture models. Inria Research Report 7786. Available at http://hal.inria.fr/inria-00638082.

PoisMixClus for Poisson mixture model estimation and model selection

### Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 set.seed(12345) ## Simulate data as shown in Rau et al. (2011) ## Library size setting "A", high cluster separation ## n = 200 observations simulate <- PoisMixSim(n = 200, libsize = "A", separation = "high") y <- simulate$y conds <- simulate$conditions s <- colSums(y) / sum(y) ## TC estimate of lib size ## Run the PMM-II model for g = 3 ## "TC" library size estimate, EM algorithm run <- PoisMixClus(y, g = 3, norm = "TC", conds = conds) pi.est <- run$pi lambda.est <- run$lambda ## Calculate the per-cluster mean for each observation means <- PoisMixMean(y, g = 3, conds, s, lambda.est)

Search within the HTSCluster package
Search all R packages, documentation and source code

Questions? Problems? Suggestions? or email at ian@mutexlabs.com.

Please suggest features or report bugs with the GitHub issue tracker.

All documentation is copyright its authors; we didn't write any of that.


text:
# Proving that Zorn's Lemma implies the axiom of choice

I am trying to solve an exercize, in which we were asked to prove that Zorn's lemma implies axiom of choic. I am using a guidness that was given that said we should use a set $\mathcal{F}$ which i'll define throughout the proof:

Proof: Given a set of nonempty sets $F$, define the set $\mathcal{F}$ to be: $\mathcal{F}=\{f \mid f \space is \space a \space choice \space function \space on \space a \space subset \space of \space F\}$. ($\mathcal{F}$ is not empty since on subsets of $F$, that contain only one set, one can easily define a choice function). Define a relation $\leq$ on $\mathcal{F}$ in the following way: given $f_1,f_2\in\mathcal{F}$ which are choice functions on $\mathcal{A_1},\mathcal{A_2} \subseteq F$, we say that $f_1 \leq f_2$ if $\mathcal{A_1} \subseteq \mathcal{A_2}$ and $f_2|_{\mathcal{A_1}}=f_1$. We will show that:

1. $\langle\mathcal F,\leq\rangle\\$ is a partially order relation.

2. Every chain in $\langle \mathcal{F},\leq \rangle$, has an upper bound in $\mathcal{F}$, and therefor, by Zorn's lemma, $\langle\mathcal{F},\leq \rangle$ has a maximal element.

3. This maximal element is a choice function on $F$.

Proof of 1:

reflexivity: $(f_1,f_1) \in \leq$, since, of course, $f_1|_{\mathcal{A_1}}=f_1$ antysimmetry: given $f_1 \leq f_2$ and $f_2 \leq f_1$, we get that $\mathcal{A_1}=\mathcal{A_2}$, and $f_1|_{\mathcal{A_2}}=f_2$ and $f_2|_{\mathcal{A_1}}=f_1$ which implies $f_1=f_2$. in a similar (rather obvious) way the transitivity can be proved.

Proof of 2:

given a chain $f_1 \leq f_2 \leq ...$ take $f:\bigcup \mathcal{A_i} \rightarrow \bigcup f_i$ to be the function s.t. $f|_{\mathcal{A_i}} = f_i$, for every $i$. Then $f$ is an upper bound for the chain, and $f \in \mathcal{F}$.

Proof of 3: Take $g$, to be the maximal element from 2. we have to show that $g$ is a choice function on all sets in $F$, and that it is well definde.

choice function on all $F$: suppose not, there exists a set $A \in \mathcal{F}$ s.t. $g$, is not defined on $A$. $A$ is not empty, so, take some $a \in A$ and define $h$ to be: $h(X)=\begin{cases} a,&\text{if } X=A\\ g(X),&\text{if } X \neq A \end{cases}$ Then $g < h$ contradicting the fact that $g$ is maximal.

$g$ is well defined: Suppose not, there exists an $A \in \mathcal{F}$ and $a_1,a_2 \in A$ where $a_1 \neq a_2$, such that $g(A)=a_1$ and $g(A)=a_2$. but then, from the construction of $g$, there exists an $f_i$ with domain $\mathcal{A_i}$, which is not well defined, which is also a contradiction. Therefor $g$, is a choice function.

What do you think?

Thank you! Shir

• You should use \langle and \rangle for the tuples symbol rather than < and >. Look at the difference: $$\langle\mathcal F,\leq\rangle\\<\mathcal F,\leq>$$ – Asaf Karagila Nov 23 '13 at 10:07
• OK. good to know. thanks! – topsi Nov 23 '13 at 20:11

The proof of the first part is fine. You might find it easier to just show that $f_1\leq f_2$ if and only if $f_1\subseteq f_2$.

For the second part using $f_1\leq f_2\leq\ldots$ hints that somehow you are considering countable chains, or even well-ordered chains. While Zorn's lemma holds if we only check well-ordered chains, it is better to write "Suppose $\{f_i\mid i\in I\}$ is a chain" instead. You also haven't shown why $\bigcup f_i$ is a choice function. Have you shown before that the increasing union of functions is a function? If not, it might be worth showing why $f$ is an element of $\cal F$, and why it is an upper bound of the chain.

The last part is also fine (although note that $g$ is necessarily well-defined, since it is an element of $\cal F$).

• Got it. Thanks!! – topsi Nov 23 '13 at 20:06

The part where you show that $g$ is well-defined seems a bit odd. What do you mean by that? In it you also mention the construction of $g$, but there is no construction, the function $g$ is given by Zorn's lemma. Where you might want to show that something is well-defined is in (2) where you define the upper bound of a chain. Also note that except in (1) you nowhere use the condition $f_2|_{A_1}=f_1$. Would the proof work if $\le$ was defined without it?

• You're right on that well-defined part. – Asaf Karagila Nov 23 '13 at 10:26
• OK. I'll think about it. Thanks! – topsi Nov 23 '13 at 20:08
• @Shir: The missing part (using $f_2|_{A_1}=f_1$) should be used to show that the upper bound of a chain is indeed well-defined. – Asaf Karagila Nov 23 '13 at 20:22
• ok i have used it there. Thank you! – topsi Nov 24 '13 at 16:08


text:
Are you believers that delusional that you won’t even acknowledge that it doesn’t even exist? How about an answer from someone without attacking me? This is NOT personal, just factual. Harvey1 kimseymd1 Free Energy two books! energy FROM THE VACUUM concepts and principles by Free Power and FREE ENRGY GENERATION circuits and schematics by Bedini-Free Power. Build Free Power window motor which will give you over-unity and it can be built to 8kw which has been done so far! NOTHING IS IMPOSSIBLE! Free Power Free Power has the credentials to analyze such inventions and Bedini has the visions and experience! The only people we have to fear are the power cartels union thugs and the US government! Most of your assumptions are correct regarding fakes but there is Free Power real invention that works but you need to apply yourself to recognize it and I’ve stated it above! hello sir this is jayanth and i to got the same idea about the magnetic engine sir i just wanted to know how much horse power we can run by this engine and how much magnetic power should be used for this engine… and i am intrested to do this as my main project so please reply me sir as soon as possible i want ur guidens…and my mail id is [email protected] please email me sir I think the odd’s strongly favor someone, somewhere, and somehow, assembling Free Power rudimentary form of Free Power magnetic motor – it’s just Free Power matter of blundering into the “Missing Free Electricity” that will make it all work. Why not ?? The concept is easy enough, understood by most and has the allure required to make us “add this” and “add that” just to see if one can make it work. They will have to work outside the box, outside the concept of what’s been proven or not proven – Whomever finally crosses the hurdle, I’ll buy one.

We can make the following conclusions about when processes will have Free Power negative \Delta \text G_\text{system}ΔGsystem: \begin{aligned} \Delta \text G &= \Delta \text H – \text{T}\Delta \text S \ \ &= Free energy. 01 \dfrac{\text{kJ}}{\text{mol-rxn}}-(Free energy \, \cancel{\text K})(0. 022\, \dfrac{\text{kJ}}{\text{mol-rxn}\cdot \cancel{\text K})} \ \ &= Free energy. 01\, \dfrac{\text{kJ}}{\text{mol-rxn}}-Free energy. Free Power\, \dfrac{\text{kJ}}{\text{mol-rxn}}\ \ &= -0. Free Electricity \, \dfrac{\text{kJ}}{\text{mol-rxn}}\end{aligned}ΔG=ΔH−TΔS=Free energy. 01mol-rxnkJ−(293K)(0. 022mol-rxn⋅K)kJ=Free energy. 01mol-rxnkJ−Free energy. 45mol-rxnkJ=−0. 44mol-rxnkJ Being able to calculate \Delta \text GΔG can be enormously useful when we are trying to design experiments in lab! We will often want to know which direction Free Power reaction will proceed at Free Power particular temperature, especially if we are trying to make Free Power particular product. Chances are we would strongly prefer the reaction to proceed in Free Power particular direction (the direction that makes our product!), but it’s hard to argue with Free Power positive \Delta \text GΔG! Our bodies are constantly active. Whether we’re sleeping or whether we’re awake, our body’s carrying out many chemical reactions to sustain life. Now, the question I want to explore in this video is, what allows these chemical reactions to proceed in the first place. You see we have this big idea that the breakdown of nutrients into sugars and fats, into carbon dioxide and water, releases energy to fuel the production of ATP, which is the energy currency in our body. Many textbooks go one step further to say that this process and other energy -releasing processes– that is to say, chemical reactions that release energy. Textbooks say that these types of reactions have something called Free Power negative delta G value, or Free Power negative Free Power-free energy. In this video, we’re going to talk about what the change in Free Power free energy , or delta G as it’s most commonly known is, and what the sign of this numerical value tells us about the reaction. Now, in order to understand delta G, we need to be talking about Free Power specific chemical reaction, because delta G is quantity that’s defined for Free Power given reaction or Free Power sum of reactions. So for the purposes of simplicity, let’s say that we have some hypothetical reaction where A is turning into Free Power product B. Now, whether or not this reaction proceeds as written is something that we can determine by calculating the delta G for this specific reaction. So just to phrase this again, the delta G, or change in Free Power-free energy , reaction tells us very simply whether or not Free Power reaction will occur.
Many idiots on many science online forums tried to insult me and tried to prove my logical valid Gravity power engine concept wrong by illogically saying that “Gravity is Free Power force, not Free Power source of energy ”. How foolish that idiot’s statement appears to be. Interesting posts, pro and con. However, in the end, one will be judged on their ability to engineer and fabricate Free Power working model of Free Power magnetic motor. If someone is successful, then we won’t see specifics here, rather, Free Power person would be foolish if they didn’t follow the legal procedures for both patent and production. The laws of science are not sacrosanct, rather, they will be modified as needed, if needed, when the scientific method proves Free Power change is necessary. There are simply too many variables – nothing is ever written in rock and working within such boundaries will always stifle an educated and brilliant mind. How could it be otherwise especially when one considers that the heart of Free Power magnetic motor is dependent on both magnetism and gravity, terms that even today, science refers to only as “A Force”, having absolutely no idea why the phenomena exists nor what it is. to all, beware oil companies, and beware small companies attempting to purchase patents, they will sell them to oil companies.
Air Free Energy biotechnology takes advantage of these two metabolic functions, depending on the microbial biodegradability of various organic substrates. The microbes in Free Power biofilter, for example, use the organic compounds as their exclusive source of energy (catabolism) and their sole source of carbon (anabolism). These life processes degrade the pollutants (Figure Free Power. Free energy). Microbes, e. g. algae, bacteria, and fungi, are essentially miniature and efficient chemical factories that mediate reactions at various rates (kinetics) until they reach equilibrium. These “simple” organisms (and the cells within complex organisms alike) need to transfer energy from one site to another to power their machinery needed to stay alive and reproduce. Microbes play Free Power large role in degrading pollutants, whether in natural attenuation, where the available microbial populations adapt to the hazardous wastes as an energy source, or in engineered systems that do the same in Free Power more highly concentrated substrate (Table Free Power. Free Electricity). Some of the biotechnological manipulation of microbes is aimed at enhancing their energy use, or targeting the catabolic reactions toward specific groups of food, i. e. organic compounds. Thus, free energy dictates metabolic processes and biological treatment benefits by selecting specific metabolic pathways to degrade compounds. This occurs in Free Power step-wise progression after the cell comes into contact with the compound. The initial compound, i. e. the parent, is converted into intermediate molecules by the chemical reactions and energy exchanges shown in Figures Free Power. Free Power and Free Power. Free Power. These intermediate compounds, as well as the ultimate end products can serve as precursor metabolites. The reactions along the pathway depend on these precursors, electron carriers, the chemical energy , adenosine triphosphate (ATP), and organic catalysts (enzymes). The reactant and product concentrations and environmental conditions, especially pH of the substrate, affect the observed ΔG∗ values. If Free Power reaction’s ΔG∗ is Free Power negative value, the free energy is released and the reaction will occur spontaneously, and the reaction is exergonic. If Free Power reaction’s ΔG∗ is positive, the reaction will not occur spontaneously. However, the reverse reaction will take place, and the reaction is endergonic. Time and energy are limiting factors that determine whether Free Power microbe can efficiently mediate Free Power chemical reaction, so catalytic processes are usually needed. Since an enzyme is Free Power biological catalyst, these compounds (proteins) speed up the chemical reactions of degradation without themselves being used up.
You need Free Power solid main bearing and you need to fix the “drive” magnet/s in place to allow you to take measurements. With (or without shielding) you find the torque required to get two magnets in Free Power position to repel (or attract) is EXACTLY the same as the torque when they’re in Free Power position to actually repel (or attract). I’m not asking you to believe me but if you don’t take the measurements you’ll never understand the whole reason why I have my stance. Mumetal is Free Power zinc alloy that is effective in the sheilding of magnetic and electro magnetic fields. Only just heard about it myself couple of days ago. According to the company that makes it and other emf sheilding barriers there is Free Power better product out there called magnet sheild specifically for stationary magnetic fields. Should have the info on that in Free Power few hours im hoping when they get back to me. Hey Free Power, believe me i am not giving up. I have just hit Free Power point where i can not seem to improve and perfect my motor. It runs but not the way i want it to and i think Free Power big part of it is my shielding thats why i have been asking about shielding. I have never heard of mumetal. What is it? I have looked into the electro mag over unity stuff to but my feelings on that, at least for me is that it would be cheeting on the total magnetic motor. Your basicaly going back to the electric motor. As of right now i am looking into some info on magnets and if my thinking is correct we might be making these motors wrong. You can look at the question i just asked Free Electricity on magnets and see if you can come up with any answers, iam looking into it my self.


text:
# Can a Non-Deterministic Pushdown Automaton recognize $\# a^nb^{2^n} \#$ which a TM can?

$$\# a^nb^{2^n} \#$$

such that

• The alphabet of the machine is {, a, b, x}.

• The symbol x will never appear on the input a.

• The contents of the tape at completion may be anything.

• The head begins on the lefthand #.

• n ≥ 0.

I know that a Turing machine could recognize this language. But can a NPDA recognize this language too? I am thinking it can but I do not know how to start proving how/why?

• What do you remember about grammars and machines? Dec 9 '19 at 4:53

Actually this language is not a CFL.

And here is a proof:

Let's take string $$w: a^mb^{2^m}$$ where $$m$$ is constant guaranteed by pumping lemma for CFLs.

Then $$a^{m+k_1}b^{2^m+k_2} \in L$$ where $$1\le k_1,k_2

(cases invloving either $$k_1 = 0$$ or $$k_2=0$$ are easier.)

Now, that suggests that,

$$2^{m+k_1} = 2^m + k_2$$ (by defination of $$L$$)

$$\therefore 2^m2^{k_1} = 2^m + k_2$$ ....................................(1)

now, $$k_1 \ge 1\implies 2^m2^{k_1} \ge 2^m + 2^m > 2^m + k_2.$$

(because we have $$k_1 \ge 1$$ this means left side of equation $$1$$ will always have value $$\ge 2.2^m$$ but right side of equation can have maximum value of $$2^m + m - 1$$)

Hence this language can't be CFL.

• is my understanding correct that because it is not a CFL, there doesn't exist any PDA or NPDA that can recognize the language, right? Dec 9 '19 at 5:10
• Yes you're right. Dec 9 '19 at 5:11
• i am starting to get it but i was confused how did you get here... $k_1 \ge 1\implies 2^m2^{k_1} \ge 2^m + 2^m > 2^m + k_2.$ Would you mind breaking it down a bit? Dec 9 '19 at 5:19
• sure I'll edit the answer. Dec 9 '19 at 5:20
• No, to prove a language context sensitive you have to show that there is a TM that decided it using space atmost linearly proportional to length of input. Dec 9 '19 at 9:33

No pushdown automaton can recognize this language, because the language is not context-free. This can be shown using the pumping lemma for context-free languages or Parikh's theorem. The latter gives a particularly straightforward proof: the language is not context-free because $$2^n$$ cannot be written as a finite union of linear functions.

The language is context-sensitive. This can be seen by noting that it is possible to write a program that counts the number of a's and b's and checks whether they are correct using linear space. Such a program can be converted into a linear bounded automaton by the standard methods of transforming programs into Turing machines. Context-sensitive grammars are so powerful that it is often easier to think of them as being arbitrary programs with a linear space restriction, rather than grammars in the usual sense.

• I see. I also thought so but I forgot about using the pumping lemma for this. I haven't heard about Parik's theorem though. For the TM that recognizes this, I'm stuck with knowing how to move the tape head when it reads $b$. I am not sure how does it count $2^n$ for it to know when to move left and right. Dec 9 '19 at 5:12
• @Andrew If you are trying to write a Turing machine that recognizes the language and you are stuck, I would suggest asking a separate question just for that. Editing your question with the additional question is probably a bad idea because it invalidates the current answers. Dec 9 '19 at 5:18
• is this language described context sensitive? Dec 9 '19 at 8:35
• @bluewander See the edit to my answer. Dec 9 '19 at 13:20
• @bluewander, btw you can construct TM which given a input checks whether it has form $a^*b^*$. If yes for every $a$ it erases exactly half of $b$'s that are present. That way TM for language in question can be constructed. I haven't fully constructed that. This is just a idea which might not work. Dec 10 '19 at 0:59


text:
## Gao, Xiao-Lu and Xu, Shou-Jun - The LexCycle on $\overline{P_{2}\cup P_{3}}$-free Cocomparability Graphs

dmtcs:5385 - Discrete Mathematics & Theoretical Computer Science, December 28, 2020, vol. 22 no. 4 - https://doi.org/10.23638/DMTCS-22-4-13
The LexCycle on $\overline{P_{2}\cup P_{3}}$-free Cocomparability Graphs

Authors: Gao, Xiao-Lu and Xu, Shou-Jun

A graph $G$ is a cocomparability graph if there exists an acyclic transitive orientation of the edges of its complement graph $\overline{G}$. LBFS$^{+}$ is a variant of the generic Lexicographic Breadth First Search (LBFS), which uses a specific tie-breaking mechanism. Starting with some ordering $\sigma_{0}$ of $G$, let $\{\sigma_{i}\}_{i\geq 1}$ be the sequence of orderings such that $\sigma_{i}=$LBFS$^{+}(G, \sigma_{i-1})$. The LexCycle($G$) is defined as the maximum length of a cycle of vertex orderings of $G$ obtained via such a sequence of LBFS$^{+}$ sweeps. Dusart and Habib conjectured in 2017 that LexCycle($G$)=2 if $G$ is a cocomparability graph and proved it holds for interval graphs. In this paper, we show that LexCycle($G$)=2 if $G$ is a $\overline{P_{2}\cup P_{3}}$-free cocomparability graph, where a $\overline{P_{2}\cup P_{3}}$ is the graph whose complement is the disjoint union of $P_{2}$ and $P_{3}$. As corollaries, it's applicable for diamond-free cocomparability graphs, cocomparability graphs with girth at least 4, as well as interval graphs.

Volume: vol. 22 no. 4
Section: Graph Theory
Published on: December 28, 2020
Submitted on: April 18, 2019
Keywords: Mathematics - Combinatorics


text:
# How do you factor -2x^3 - 2x^2 + 12x?

Jul 27, 2017

$- 2 x \left(x + 3\right) \left(x - 2\right)$

#### Explanation:

$- 2 {x}^{3} - 2 {x}^{2} + 12 x$

We remove the first factor that is common to all terms.

$- 2 x \left({x}^{2} + x - 6\right)$

We further factorise the terms in brackets.

$- 2 x \left({x}^{2} + 3 x - 2 x - 6\right)$

$- 2 x \left[x \left(x + 3\right) - 2 \left(x + 3\right)\right]$

$- 2 x \left(x + 3\right) \left(x - 2\right)$


text:
# EM Induction

Consider the following problem:

There is a uniform magnetic field pointing into the page. A set of rails is placed horizontally inside the field. A metal rod can slide freely on the rails, when we apply a force to move the rod to the right, is there any induced current in the rod when moving it inside the uniform field?

Yes there is current if the circuit is closed.
$$E = bvB \sin{\alpha}$$, here $$\alpha = \pi$$.
You can deduce the latter from this: $$E = \frac{d \Phi}{dt}$$ when you remember that $$A (t) = ab (t) = vtb$$.

phyphysics said:
Consider the following problem:

There is a uniform magnetic field pointing into the page. A set of rails is placed horizontally inside the field. A metal rod can slide freely on the rails, when we apply a force to move the rod to the right, is there any induced current in the rod when moving it inside the uniform field?

yes there will be an induced current. The direction of that current will be so that the resulting Lorentz force on the rod will counter the force you exterted when pushing the rod to the right.

marlon

But isn't that the wire does not encounter any change in magnetic flux? How can current be induced if the magnetic flux does not change?

why do you think the flux isn't changing? what's the effect of sliding the metal bar to the right?

phyphysics said:
But isn't that the wire does not encounter any change in magnetic flux? How can current be induced if the magnetic flux does not change?
in order to change the flux you can alter two variables:
1) the magnitude of the B field, but this is constant here
2) the surface through which the B lines pass, this changes because of the rod-displacement

marlon

But how can current be induced when it moves along the UNIFORM magnetic field?

phyphysics said:
But how can current be induced when it moves along the UNIFORM magnetic field?
because the flux changes

or

because you have a moving wire in a magnetic field. Don't you know what Maxwell says about this ?

marlon

So what exactly are the conditions for current to be induced?

phyphysics said:
So what exactly are the conditions for current to be induced?

Well, a changing flux induces an EMF and thus a current, that is all.
If the flux rises, then the induced current will have such a direction that the associated induced B field will counter act to the rising flux. this is just Lenz's law in a more general form

Also, according to the Lorentz-force formula, you know that if a wire moves in a magnetic field, a current must flow through that wire

marlon

mukundpa
Homework Helper
Simply, if the circuit is closed it means some other connection between the two rails. Then this connection with rails and the rod encloses some area and this area is changing due to movement of the rod, hence the flux through this area is changing, inducing current.