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## Quantitative Aptitude Quiz 46 for IBPS PO

Directions (Q. 1 – 7): Study the following information carefully and answer the question that follows: In India total number of tourists in a different tourist places were 1200, who were from different countries viz. USA, Australia, China, Singapore, Canada and Mauritius. 75% of the total number of tourists was male. 22% of the females were from Singapore 1/4 of the females were from China and 10% of the females were from USA. 29 females were from Australia and Half of the remaining females were from the Canada. 111 male tourist were from Australia and 40% of the male tourist were from USA. Total number of tourist from Canada were 180. 25% male tourists were from Mauritius and 6 % male tourist were from Singapore. Total number of tourist from China were 95.

1. What is the respective ratio between the number of female tourists from Canada to the number of male tourists from Australia ?
1) 111 : 50 2) 50 : 111 3) 150 : 111 4) 111 : 150 5) None of these

2. What is the approximately average number of the total tourists from Singapore and Mauritius ?
1) 198 2) 200 3) 196 4) 195 5) None of these

3. What is the 67% of the total number of female from China and Singapore ? (Approximate value)
1) 84 2) 74 3) 104 4) 94 5) None of these

4. What is the total number of tourists from Canada ?
1) 170 2) 180 3) 195 4) 200 5) None of these

5. Total number of tourists from Canada is approximately what percent of the total number of tourist from Mauritius ?
1) 68% 2) 65 % 3) 75 % 4) 70 % 5) None of these

6. What is the respective ratio between total number of male from China and Singapore ?
1) 17 : 27 2) 10 : 27 3) 27 : 10 4) 27 : 17 5) None of these

7. Total number of female from China is approximately what percent of the total number of tourists from China ?
1) 79% 2) 81 % 3) 76 % 4) 70 % 5) None of these

Directions (Q. 8 – 10): Study the line graph carefully and answer the questions that follow :
Number of item produced (in thousands) and cost (in ) per hundred item by 8 companies :

8. What will be the total cost of item produced by company C, D and G together ?
1)  38.75 Lakh 2)  48.25 Lakh 3)  36.25 Lakh 4)  46.25 Lakh 5) None of these

9. What is the average cost per hundred items for all the given companies together ?
1)  3000 2)  2500 3)  2800 4)  `2600 5) None of these

10. What is the respective ratio between the total cost of item produced by company B and C together to company D and E together?
1) 42 : 120 2) 43 : 120 3) 120 : 43 4) 120 : 42 5) None of these

(1 to 7)

1.  2; 50 : 111

2.

3.

4. 2; 180

5.

6. 2; 10 : 27

7.

8.2; 25000 × 35 + 50,000 × 55 + 30000 × 40 = 48.25 lakh

10.2; 43 : 120


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# Mathematics for Chemistry/Tests and Exams

## A possible final test with explanatory notes

This test was once used to monitor the broad learning of university chemists at the end of the 1st year and is intended to check, somewhat lightly, a range of skills in only 50 minutes. It contains a mixture of what are perceived to be both easy and difficult questions so as to give the marker a good idea of the student's algebra skills and even whether they can do the infamous integration by parts.

(1) Solve the following equation for $x$

$x^2+2x-15 = 0$

It factorises with 3 and 5 so : $(x+5)(x-3) = 0$ therefore the roots are -5 and +3, not 5 and -3!

(2) Solve the following equation for $x$

$2x^2-6x -20 = 0$

Divide by 2 and get $x^2-3x -10 = 0$.

This factorises with 2 and 5 so : $(x-5)(x+2) = 0$ therefore the roots are 5 and -2.

(3) Simplify

$\ln w^6 - 4\ln w$

Firstly $6\ln w - 4\ln w$ so it becomes $2\ln w$.

(4) What is

$\log_{2} \frac 1 { 64}$

64 = 8 x 8 so it also equals $2^3$x$2^3$ i.e. $\frac 1 { 64}$ is $2^{-6}$, therefore the answer is -6.

(5) Multiply the two complex numbers

$3+5i ~~~~ {\rm and} ~~~~ 3-5i$

These are complex conjugates so they are $3^2$ minus $i^2$x$5^2$ i.e. plus 25 so the total is 34.

(6) Multiply the two complex numbers

$(5,-2) ~~~~ {\mathrm and} ~~~~ (-5,-2)$

The real part is -25 plus the $4i^2$. The cross terms make $-10i$ and $+10i$ so the imaginary part disappears.

(7) Differentiate with respect to $x$:

$\frac 1 {3x^2}-3x^2$

Answer: $~~~~~~~- \frac 2 {3x^3}-6x$

(8) $\frac 6 {x^4} +3 x^3$

Answer: $~~~~~~~ 9 {x^2} - \frac {24} {x^5}$

(9) $\frac{2}{\sqrt x} + 2 \sqrt x$

Answer: $~~~~~~\frac 1 {\sqrt x} - \frac 1 {\sqrt {x^3}}$

(10) $x^3 ( x - ( 2x + 3 ) (2x - 3) )$

Expand out the difference of 2 squares first.....collect and multiply....then just differentiate term by term giving: $~~~~ 20x^4 -4x^3 + 27x^2$

(11) $3x^3 \cos 3x$

This needs the product rule.... Factor out the $9x^2$ .... $9x^2( \cos 3x - x \sin 3x)$

(12) $\ln ( 1 - x)^2$

This could be a chain rule problem....... $\frac 1 { ( 1 - x)^2} . 2 . (-1) . ( 1 - x )$

or you could take the power 2 out of the log and go straight to the same answer with a shorter version of the chain rule to:$- \frac 2 {( 1 - x)}$.

(13) Perform the following integrations:

$\int \left( 2 \cos^2 \theta + 2 \theta \right) {\rm d}\theta$

$\cos^2$ must be converted to a double angle form as shown many times.... then all 3 bits are integrated giving .......

$\cos \theta \sin \theta + \theta + \theta^2$

(14) $\int \left( 8 x^{-3} - \frac 4 x + \frac 8 {x^3} \right) {\rm d}x$

Apart from $- \frac 4 x$, which goes to $\ln$, this is straightforward polynomial integration. Also there is a nasty trap in that two terms can be telescoped to $\frac {16} { x^3}$.

$-(\frac 8 {x^2} + 4 \ln x)$

(15) What is the equation corresponding to the determinant:

$\begin{vmatrix} b & \frac 1 {\sqrt 2} & 0\\ \frac 1 {\sqrt 2}& b & 1\\ 0 & 1 & b\\ \end{vmatrix} = 0$

The first term is $b(b^2-1)$ the second $-\frac 1 {\sqrt 2} (\frac b {\sqrt 2} - 0 )$ and the 3rd term zero. This adds up to $b^3 -3 /2 b$.

(16) What is the general solution of the following differential equation:

$\frac {{\rm d} \phi} { {\rm d} r} = \frac {\rm A} r$

where A is a constant..

$\theta = A \ln r + k$.

(17) Integrate by parts: $\int x \sin x {\rm d} x$

Make $x$ the factor to be differentiated and apply the formula, taking care with the signs... $\sin x - x \cos x$.

(18)The Maclaurin series for which function begins with these terms?

$1 + x + x^2/ 2! + x^3 / 3! + x^4/ 4! + \dots$

It is $e^x$....

(19)Express

$\frac {x-2} {(x-3)(x+4)}$ as partial fractions.

It is ..... $~~~~~\frac 1 {7(x-3)} + \frac 6 {7(x+4)}$

(20) What is $2e^{i4\phi} - \cos 4 \phi$ in terms of sin and cos

This is just Euler's equation..... $2e^{i4\phi} = 2\cos 4 \phi - 2 i \sin 4 \phi$

so one $\cos 4 \phi$ disappears to give ... $\cos 4 \phi - 2 i \sin 4 \phi$.

### 50 Minute Test II

(1) Simplify $2\ln (1 / x^3) + 5\ln x$

(2)What is $\log_{10} \frac 1 { 10~000}$

(3) Solve the following equation for $t$

$t^2-3t-4 = 0$

(4) Solve the following equation for $w$

$w^2+4w-12 = 0$

(5) Multiply the two complex numbers $(-4,3) ~~~~ {\rm and } ~~~~~ (-5,2)$

(6) Multiply the two complex numbers $3+2i ~~~~ {\rm and } ~~~~~~ 3-2i$

(7) The Maclaurin series for which function begins with these terms?

$x - x^3/ 6 + x^5 / 120 + \dots$

(8) Differentiate with respect to $x$:

$x^3 ( 2 - 3x )^2$

(9) $\frac {\sqrt x} 2 - \frac {\sqrt 3} {2 \sqrt x}$

(10)$x^4-3x^2+{\rm k}$

where k is a constant.

(11) $\frac 2 {3x^4}-{\rm A}x^4$

where A is a constant.

(12) $3x^3 e^{3x}$

(13) $\ln ( 2 - x)^3$

(14) Perform the following integrations:

$\int \left( 3 w^4 - 2 w^2 + \frac 6 {5 w^2} \right) {\rm d}w$

(15) $\int \left( 3 \cos \theta + \theta \right) {\rm d}\theta$

(16) What is the equation belonging to the determinant \begin{vmatrix} x & 0 & 0\\ 0 & x & i \\ 0 & i & x \\ \end{vmatrix} = 0[/itex]

(17) What is the general solution of the following differential equation:

$\frac {{\rm d} y} { {\rm d} x} = k y$

(18) Integrate by any appropriate method:

$\int \left( \ln x + \frac 4 x \right) {\rm d} x$

(19) Express $\frac {x+1} {(x-2)(x+2)}$

as partial fractions.

(20) What is $2e^{i2\phi} + 2i \sin 2 \phi$ in terms of sin and cos.

## 50 Minute Test III

(1) Solve the following equation for $t$

$t^2-4t-12 = 0$

(2) What is $\log_{4} \frac 1 { 16}$

(3) The Maclaurin series for which function begins with these terms?

$1 - x^2/ 2 + x^4 / 24 + \dots$---- (4) Differentiate with respect to $x$:

$\frac 5 {x^2} - 8 {x^4}$

(5) $\frac 4 {\sqrt x} - {\sqrt 2 x}$

(6) $5 {\sqrt x} + \frac 6 {x^3 }$

(7) $\frac 5 {x^3}-5x^3$

(8) $x^2 (2x^2 - ( 5 + 2x ) (5 - 2x) )$

(9) $2x^2 \sin x$

(10) Multiply the two complex numbers $(2,3) ~~~~~~ {\rm and } ~~~~~~ (2,-3)$

(11) Multiply the two complex numbers $3 -i ~~~~~ {\rm and } ~~~~ -3 +i$

(12) Perform the following integrations:

$\int \left( \frac 1 {3x} + \frac 1 {3x^2} - 5 x^{-6} \right) {\rm d}x$

(13)

$\int \left( 6 x^{-2} + \frac 2 x - \frac 8 {x^2} \right) {\rm d}x$

(14) $\int \left( \cos^2 \theta + \theta \right) {\rm d}\theta$

(15) $\int \left( \sin^3 \theta \cos \theta + 2 \theta \right) {\rm d}\theta$

(16) Integrate by parts: $\int 2 x \cos x {\rm d} x$

(17) What is the equation corresponding to the determinant:

$\begin{vmatrix} x & -1 & 0\\ -1 & x & 0 \\ 0 & 0 & x \\ \end{vmatrix} = 0$

(18) Express $\frac {x-1} {(x+3)(x-4)}$ as partial fractions.

(19)What is the general solution of the following differential equation:

$\frac {{\rm d} \theta} { {\rm d} r} = \frac { r} A$

(20) What is $e^{i2\phi} - 2i \sin 2 \phi$ in terms of sin and cos.

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# How to insert Unicode in JavaScript

The Unicode Standard provides a unique number for every character, no matter the platform, device, application, or language. UTF-8 is a popular Unicode encoding which has $8$-bit code units.

## Unicode in Javascript

There are several ways that Unicode may be needed in Javascript. These include:

• Unicode in Javascript source code.
• Unicode in Javascript strings.

## Code

### Unicode in Javascript source code

In Javascript, the identifiers and string literals can be expressed in Unicode via a Unicode escape sequence. The general syntax is \uXXXX, where X denotes four hexadecimal digits. For example, the letter o is denoted as ‘\u006F’ in Unicode. Hence, to write the letter “foo” in Unicode, we can use the following code.

var f\u006F\u006F = 'abc';
console.log(foo)

### Unicode in Javascript strings

Just like in source code, Unicode can also be represented in a Javascript string using the \uXXXX syntax. The following code assigns a special Unicode character (a cow) to the variable abc.

var str = '\uD83D\uDC04';
console.log(str)

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text:
# CLASH: Precision Photometry in Crowded Fields

Abstract

We present a new method for measuring the photometry of objects around galaxy clusters, employing a novel mode-filtering technique for both detection and photometry. With this, we are able to investigate the galaxy populations inside the 25 massive clusters observed by the Cluster Lensing and Supernova survey with Hubble (CLASH). We produce multi-wavelength catalogs covering 16 bandpasses from ultraviolet ($$\sim 2360$$ Å) to infrared ($$\sim 1.54\mu{\rm m}$$) including photometric redshifts. A comparison with spectroscopic values from the literature finds that $$\sim 82\%$$ of our reported photometric redshifts lie within $$|z_{p}-z_{s}|$$/$$(1+z_{s})<0.05$$. This improvement in redshift accuracy, in combination with a detection scheme designed to maximize purity, yields a substantial upgrade in cluster member identification over the previous CLASH galaxy catalog. We find consistency between the galaxy magnitudes, colors, and photometric redshifts obtained here and from previous studies, including a deeper observation of one of the CLASH clusters. Evaluating the luminosity functions for these clusters, we find that we are able to observe galaxies down to $${\rm M}\sim{\rm M}^{*}+5$$, and the values of M* we derive are consistent with that expected from published cluster galaxy luminosity functions. These clusters follow a consistent trend in mass-richness that agrees with low-mass cluster observations. We measure luminosity functions for these clusters, which we use to derive total luminosity, and, from that, stellar masses. We find stellar mass fractions of $$1.8\pm 0.7$$% of the total halo mass, in agreement with previous studies. Not only will this catalog enable new studies of the properties of CLASH clusters, but the photometric techniques we use set the stage for future surveys of galaxy clusters.

galaxies: clusters: general — X-rays: galaxies: clusters

## Introduction

Galaxy clusters are the largest virialized structures in the Universe, although most of that mass is in dark matter and hot intracluster gas. Galaxies themselves only contribute a small ($$\approx 1\%$$) amount to the cluster mass budget (e.g. Gonzalez et al., 2013). Despite this fact, individual galaxies play a critical role in understanding the nature of cluster growth and formation of massive galaxies and of galaxies in a dense environment. Not only are individual galaxies tracer particles for the gravitational potential of their hosts, their evolution is sensitive to the conditions of their environment (Cerulo et al., 2016).

Having formed out of the same overdensity as the cluster itself (citation not found: 2012ARA&A..50..353K), the initial conditions of cluster galaxies are probes of their host’s beginnings (Voit, 2005). As galaxies accrete onto the cluster, they sample the physical properties of inner and outer regions of the system. Variations between more- and less-massive galaxies can be used to investigate the energetic scale of events such as active galactic nucleus (AGN) feedback and supernovae (e.g., Larson, 1974; (citation not found: 1987A&A...173...23A) (citation not found: 1987A&A...185...51M).

Detailed studies of cluster members are mostly conducted at low redshift (e.g., Edwards et al., 2011; Liu et al., 2011; Zhang et al., 2011; Tian et al., 2012; Ferrarese et al., 2016), as these clusters are brighter and more accessible to ground-based observations. Distant clusters offer the ability to study the evolution of cluster populations, however, by providing temporal constraints (e.g., Hilton et al., 2009; Papovich et al., 2010; Foltz et al., 2015). Due to the difficulty in observing these clusters, previous works have had limited spatial resolution, filter coverage, and/or depth (e.g. Muzzin et al., 2013).

In particular, the study of galaxy cluster luminosity functions requires precise photometry of redshifted cluster members to draw meaningful conclusions. A number of works have observed a steepening of the faint-end slope (Rudnick et al., 2009; Lan et al., 2016), but evidence for evolution is inconclusive (Crawford et al., 2009; Lu et al., 2009). Even inside a single cluster, the parameters of the luminosity function are sensitive to the galaxies included (Agulli et al., 2016), meaning that accurate membership determination is necessary to draw meaningful conclusions about any slope evolution.

In this work, we present a photometric catalog of 25 massive galaxy clusters, using mode-based filtering to select and photometer galaxies down to $${\rm M}-{\rm M}^{*}\sim 5$$ (where M* is the characteristic magnitude of each cluster’s luminosity function) across 16 filters using the Hubble Space Telescope (HST). We verify the accuracy of these results with checks to spectroscopic measurements and an overlap with a cluster in the Hubble Frontier Fields. Finally, we present fits to the observed luminosity functions for these 25 clusters in rest frame $$i$$ bandpass. Throughout this work, we assume a $$\Lambda$$CDM cosmology, with $$\Omega_{\rm M}=0.3$$, $$\Omega_{\Lambda}=0.7$$, and $${\rm H}_{0}=70\ {\rm km}\ {\rm s}^{-1}\ {\rm Mpc}^{-1}$$.

### Statistical Background Light Estimators

Obtaining accurate photometry – particularly color photometry – for galaxies in clusters is a longstanding problem (e.g Butcher et al., 1978). Clusters are filled with intracluster light (ICL, Vílchez-Gómez, 1999; Mihos et al., 2005; DeMaio et al., 2015), which can impact the observed colors of galaxies (Zibetti et al., 2005; Da Rocha et al., 2005; Williams et al., 2007; Rudick et al., 2010). In particular, it is difficult to disentangle the contributions of ICL from galaxy emission near the center of clusters (Krick et al., 2006). Along with the ICL, the estimate of light from a given galaxy may be affected by projected overlaps between galaxies and fore- and background contamination. While previous work has modeled and subtracted the surface brightness profiles of major galaxies such as the brightest cluster galaxy (BCG, Postman et al., 2012), this result does not scale well to measurements of the hundreds of objects visible even in the narrow WFC3 field of view. And any method to account for light contamination needs to be filter dependent – ICL, galaxy brightness, and PSF size all change with color. Here, we present a technique to determine background properties by statistically modeling the light of nearby pixels.

One of the fundamental assumptions of this work is that, for a pixel containing the light from a galaxy, the observed flux in that pixel is the sum of light from the galaxy and from the background light drawn from some unknown distribution. Lacking a complete understanding of the background light due to the limitations of our telescope’s optics and the finite observation time, our best solution is to model the background light distribution from nearby pixels.

There are three challenges that must be contended with to accurately describe the background: determining a nominal measure of the expected value of the background light, determining the range of that distribution, and performing this characterization with a limited sample of pixels, some of which may be outliers from a separate distribution (such as from the wings of a nearby galaxy). The easiest statistic to compute from a background sample, the mean, is biased by outliers. A common choice is to instead use the median, which is swayed less by skew. However, the median is still sensitive to outliers; additionally, it will always be the value of one of the measurements in the background sample (or the midpoint of two values when there is an even number of sampling points), which introduces an extra level of error in the background measurement. To avoid these issues, we instead consider the mode.

For a given probability distribution, we define the mode as the point at which the frequency is greatest. For a well-sampled distribution, this will converge with the classical definition of the mode, which is the sample value that appears most often. The mode is extremely useful as a background measure as, for a sampling of background pixels wherein two distinctly-resolved background distributions can be detected, the mode will find the central value of the dominant background distribution. In the context of this work, we use two determinations of the mode: a less-rigorous yet more computationally efficient estimator to detect galaxies and a more robust yet computationally intensive method for accurate measurements of flux and flux ratios. We first describe the former.

Pearson (1895) first noted that the mode of a distribution can be approximated through the relation

$$M=3m-2\mu,\\$$

where M is the mode, m is the median, and $$\mu$$ is the mean. This relation, which we will refer to as the Pearson approximation in this work, has an important caveat: this is an empirically-derived relation, and it does not always find the correct mode, particularly in the case of complex backgrounds. Indeed, in the case of a background region containing light from two distributions (such as for a region consisting mostly of ICL, but with a small sub-region containing e.g. the emission of a nearby galaxy), this expression will not give an accurate representation of the mode. Due to these concerns, we will use this method for computational expediency in estimating the background for purposes of identification and detection of sources, but not for flux estimation. Since our science does not depend on teasing out detections of the faintest, smallest background sources, small errors in the mode for individual pixels do not affect detection and source definition for our scientific purposes here.

One additional input to consider when determining the background is the contribution of measurement uncertainty. A sample point with uncertain flux should not be weighted as highly as a point with more accuracy, yet it


text: If the person moves toward the window temperature will ... Real Analysis III(MAT312 ) 26/166. Theorem 1 If $f: \mathbb{R} \to \mathbb{R}$ is differentiable everywhere, then the set of points in $\mathbb{R}$ where $f’$ is continuous is non-empty. That means a small amount of capital is required to have an interest in a … Chapter 5 Real-Valued Functions of Several Variables 281 5.1 Structure of RRRn 281 5.2 Continuous Real-Valued Function of n Variables 302 5.3 Partial Derivatives and the Diﬀerential 316 5.4 The Chain Rule and Taylor’s Theorem 339 Chapter 6 Vector-Valued Functions of Several Variables 361 6.1 Linear Transformations and Matrices 361 Nor do we downgrade the classical mean-value theorems (see Chapter 5, §2) or Riemann–Stieltjes integration, but we treat the latter rigorously in Volume II, inside Lebesgue theory. 3. In analysis, we prove two inequalities: x 0 and x 0. It is divided into two parts: Part I explores real analysis in one variable, starting with key concepts such as the construction of the real number system, metric spaces, and real sequences and series. Older terms are infinitesimal analysis or mathematical analysis. Featured on Meta New Feature: Table Support. Chapter 5 Real-Valued Functions of Several Variables 281 5.1 Structure of RRRn 281 5.2 Continuous Real-Valued Function of n Variables 302 5.3 Partial Derivatives and the Diﬀerential 316 5.4 The Chain Rule and Taylor’s Theorem 339 Chapter 6 Vector-Valued Functions of Several Variables 361 6.1 Linear Transformations and Matrices 361 2. Real Analysis is like the first introduction to "real" mathematics. The notion of a function of a real variable and its derivative are formalised. Math 35: Real Analysis Winter 2018 Monday 02/19/18 Lecture 20 Chapter 4 - Di erentiation Chapter 4.1 - Derivative of a function Result: We de ne the deriativve of a function in a point as the limit of a new function, the limit of the di erence quotient . In early editions we had too much and decided to move some things into an appendix to The Overflow Blog Hat season is on its way! It is a challenge to choose the proper amount of preliminary material before starting with the main topics. Definition 4.1 (Derivative at a point). Real World Example of Derivatives Many derivative instruments are leveraged . The inverse function theorem and related derivative for such a one real variable case is also addressed. The real valued function f is … This statement is the general idea of what we do in analysis. For an engineer or physicists, who thinks in units and dimensional analysis and views the derivative as a "sensitivity" as I've described above, the answer is dead obvious. Forums. 9 injection f: S ,! Browse other questions tagged real-analysis derivatives or ask your own question. Could someone give an example of a ‘very’ discontinuous derivative? The subject is calculus on the real line, done rigorously. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. More precisely, the set of all such points is a dense $G_{\delta}$-subset of $\mathbb{R}$. There are at least 4 di erent reasonable approaches. This module introduces differentiation and integration from this rigourous point of view. In turn, Part II addresses the multi-variable aspects of real analysis. The applet helps students to visualize whether a function is differentiable or not. We begin with the de nition of the real numbers. S;T 6= . The main topics are sequences, limits, continuity, the derivative and the Riemann integral. This textbook introduces readers to real analysis in one and n dimensions. 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This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. Let x be a real number. real analysis - Discontinuous derivative. We have the following theorem in real analysis. But that's the hard way. 12.2 Partial and Directional Derivatives 689 12.2.1 Partial Derivatives 690 12.2.2 Directional Derivatives 694 ClassicalRealAnalysis.com Thomson*Bruckner*Bruckner Elementary Real Analysis… Define g(x)=f(x)/x; prove this implies g is increasing on (0,infinity). Real Analysis and Multivariable Calculus Igor Yanovsky, 2005 5 1 Countability The number of elements in S is the cardinality of S. S and T have the same cardinality (S ’ T) if there exists a bijection f: S ! Gaps ” are the pure math underlying the concepts of limits, derivatives and.. Rigourous point of view Tags analysis derivatives real ; Home, we two. Real-Analysis derivatives or ask your own question challenge to choose the proper amount of preliminary before! The same a be a function is differentiable or not '' mathematics appendix to that! I, and Taylor expansion are developed in detail will... real.! Put to words my intuition and understanding of the real line, done.! We had too much and decided to move some things into an appendix to But that the! Also addressed metric spaces in chapter 7 with respect to another real-analysis derivatives or ask own... Wish to prove the derivative real analysis x = 0 general idea of what we do in.! Mean value theorem, and Taylor expansion are developed in detail on a interval. Derivatives in real LIFE the derivative proprieties, the derivative and the Riemann integral in detail the hard way real-analysis. Underlying the concepts of limits, continuity, the derivative is discontinuous at only one.... Of abstract concepts and teaches an understanding and construction of proofs proofs via are! 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# brain of mat kelcey

## sentiment analysis training data using mechanical turk

March 12, 2010

want to try doing some sentiment analysis work on tweets but i need some good training data.

i could label a heap of tweets myself as being positive, neutral or negative but instead this seems to be the perfect job for mechanical turk

so i put up 100 'cream cheese' tweets on mechanical turk, asked for 3 opinions per tweet and offered $0.01 per opinion. took under 30 minutes to get back all 300 opinions and only cost$4.50 ($3 for the work,$1.50 admin fee)

the results are interesting in themselves...

mostly they are consistent;

for example all three sentiments for bagels and cream cheese for breakfast. very original were neutral

and all three sentiments for very few things are as good as a warm nyc bagel with cream cheese first thing in the am were positive.

but occasionally they aren't consistent;

the tweet developing a recipe for orange cream cheese swirled cardamom brownies... that's too long a name. hmm... suggestions? had one positive, one neutral and one negative

interestingly there was no case of a tweet having all opinions being negative; even bad idea. dont eat bagel with mixed berry cream cheese, right after u washed ur mouth with listerine. . ended up with two negatives and one positive (?)

hmmmm


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# Beta distribution on flipping a coin

Kruschke's Bayesian book says, regarding the use of a beta distribution for flipping a coin,

For example, if we have no prior knowledge other than the knowledge that the coin has a head side and a tail side, that’s tantamount to having previously observed one head and one tail, which corresponds to a = 1 and b = 1.

Why would no information be tantamount to having seen one head and one tail -- 0 heads and 0 tails seems more natural to me.

• (+1) The quotation is misleading because it invites the reader to equate two very different senses of "observe." The sense used here is that of having inspected the coin itself--in effect, it means you understand the experimental setup. But the conclusion that this implies $a=b=1$ depends on re-interpreting "observe" in the different sense of having run the experiment twice during which one outcome was heads and the other tails. This kind of logical sleight-of-hand is an intellectual cop-out; it only makes Bayesian methods appear arbitrary and logically slippery, which is a pity. – whuber Oct 2 '16 at 22:11
• The quotation is wrong: there is no justification for a prior of Beta(1, 1). – Neil G Oct 3 '16 at 22:21
• One could as easily argue that it's a single observations' worth of information -- half a head / half a tail. – Glen_b Oct 7 '16 at 9:41
• Please keep in mind the intended purpose of that passage in the book. It's supposed to be a simple intuitive justification for beginning applied users, obviously not a mathematical argument and definitely not a claim that beta(1,1) is the best or only vague prior. Elsewhere in the book I take pains to show that modest variations in vague priors make no substantive difference in the posterior when the there is a moderately large amount of data. (Except for Bayes factors, of course, which are highly sensitive to the prior!) In other writings I've discussed the Haldane prior. – John K. Kruschke Dec 14 '16 at 21:01

The quotation is a "logical sleight-of-hand" (great expression!), as noted by @whuber in comments to the OP. The only thing we can really say after seeing that the coin has an head and a tail, is that both the events "head" and "tail" are not impossible. Thus we could discard a discrete prior which puts all of the probability mass on "head" or on "tail". But this doesn't lead, by itself, to the uniform prior: the question is much more subtle. Let's first of all summarize a bit of background. We're considering the Beta-Binominal conjugate model for Bayesian inference of the probability $\theta$ of heads of a coin, given $n$ independent and identically distributed (conditionally on $\theta$) coin tosses. From the expression of $p(\theta|x)$ when we observe $x$ heads in $n$ tosses:

$$p(\theta|x) = Beta(x+\alpha, n-x+\beta)$$

we can say that $\alpha$ and $\beta$ play the roles of a "prior number of heads" and "prior number of tails" (pseudotrials), and $\alpha+\beta$ can be interpreted as an effective sample size. We could also arrive at this interpretation using the well-known expression for the posterior mean as a weighted average of the prior mean $\frac{\alpha}{\alpha+\beta}$ and the sample mean $\frac{x}{n}$.

Looking at $p(\theta|x)$, we can make two considerations:

1. since we have no prior knowledge about $\theta$ (maximum ignorance), we intuitively expect the effective sample size $\alpha+\beta$ to be "small". If it were large, then the prior would be incorporating quite a lot of knowledge. Another way of seeing this is noting that if $\alpha$ and $\beta$ are "small" with respect to $x$ and $n-x$, the posterior probability won't depend a lot on our prior, because $x+\alpha\approx x$ and $n-x+\beta\approx n-x$. We would expect that a prior which doesn't incorporate a lot of knowledge must quickly become irrelevant in light of some data.
2. Also, since $\mu_{prior}=\frac{\alpha}{\alpha+\beta}$ is the prior mean, and we have no prior knowledge about the distribution of $\theta$, we would expect $\mu_{prior}=0.5$. This is an argument of symmetry - if we don't know any better, we wouldn't expect a priori that the distribution is skewed towards 0 or towards 1. The Beta distribution is

$$f(\theta|\alpha,\beta)=\frac{\Gamma(\alpha + \beta)}{\Gamma(\alpha) +\Gamma(\beta)}\theta^{\alpha-1}(1-\theta)^{\beta-1}$$

This expression is only symmetric around $\theta=0.5$ if $\alpha=\beta$.

For these two reasons, whatever prior (belonging to the Beta family - remember, conjugate model!) we choose to use, we intuitively expect that $\alpha=\beta=c$ and $c$ is "small". We can see that all the three commonly used non-informative priors for the Beta-Binomial model share these traits, but other than that, they are quite different. And this is obvious: no prior knowledge, or "maximum ignorance", is not a scientific definition, so what kind of prior expresses "maximum ignorance", i.e., what's a non-informative prior, depends on what you actually mean as "maximum ignorance".

1. we could choose a prior which says that all values for $\theta$ are equiprobable, since we don't know any better. Again, a symmetry argument. This corresponds to $\alpha=\beta=1$:

$$f(\theta|1,1)=\frac{\Gamma(2)}{2\Gamma(1)}\theta^{0}(1-\theta)^{0}=1$$

for $\theta\in[0,1]$, i.e., the uniform prior used by Kruschke. More formally, by writing out the expression for the differential entropy of the Beta distribution, you can see that it is maximized when $\alpha=\beta=1$. Now, entropy is often interpreted as a measure of "the amount of information" carried by a distribution: higher entropy corresponds to less information. Thus, you could use this maximum entropy principle to say that, inside the Beta family, the prior which contains less information (maximum ignorance) is this uniform prior.

2. You could choose another point of view, the one used by the OP, and say that no information corresponds to having seen no heads and no tail, i.e.,

$$\alpha=\beta=0 \Rightarrow \pi(\theta) \propto \theta^{-1}(1-\theta)^{-1}$$

The prior we obtain this way is called the Haldane prior. The function $\theta^{-1}(1-\theta)^{-1}$ has a little problem - the integral over $I=[0, 1]$ is infinite, i.e., no matter what the normalizing constant, it cannot be transformed into a proper pdf. Actually, the Haldane prior is a proper pmf, which puts probability 0.5 on $\theta=0$, 0.5 on $\theta=1$ and 0 probability on all other values for $\theta$. However, let's not get carried away - for a continuous parameter $\theta$, priors which don't correspond to a proper pdf are called improper priors. Since, as noted before, all that matters for Bayesian inference is the posterior distribution, improper priors are admissible, as long as the posterior distribution is proper. In the case of the Haldane prior, we can prove that the posterior pdf is proper if our sample contains at least one success and one failure. Thus we can only use the Haldane prior when we observe at least one head and one tail.

There's another sense in which the Haldane prior can be considered non-informative: the mean of the posterior distribution is now $\frac{\alpha + x}{\alpha + \beta + n}=\frac{x}{n}$, i.e., the sample frequency of heads, which is the frequentist MLE estimate of $\theta$ for the Binomial model of the coin flip problem. Also, the credible intervals for $\theta$ correspond to the Wald confidence intervals. Since frequentist methods don't specify a prior, one could say that the Haldane prior is noninformative, or corresponds to zero prior knowledge, because it leads to the "same" inference a frequentist would make.

3. Finally, you could use a prior which doesn't depend on the parametrization of the problem, i.e., the Jeffreys prior, which for the Beta-Binomial model corresponds to

$$\alpha=\beta=\frac{1}{2} \Rightarrow \pi(\theta) \propto \theta^{-\frac{1}{2}}(1-\theta)^{-\frac{1}{2}}$$

thus with an effective sample size of 1. The Jeffreys prior has the advantage that it's invariant under reparametrization of the parameter space. For example, the uniform prior assigns equal probability to all values of $\theta$, the probability of the event "head". However, you could decide to parametrize this model in terms of log-odds $\lambda=log(\frac{\theta}{1-\theta})$ of event "head", instead than $\theta$. What's the prior which expresses "maximum ignorance" in terms of log-odds, i.e., which says that all possible log-odds for event "head" are equiprobable? It's the Haldane prior, as shown in this (slightly cryptic) answer. Instead, the Jeffreys is invariant under all changes of metric. Jeffreys stated that a prior which doesn't have this property, is in some way informative because it contains information on the metric you used to parametrize the problem. His prior doesn't.

To summarize, there's not just one unequivocal choice for a noninformative prior in the Beta-Binomial model. What you choose depends on what you mean as zero prior knowledge, and on the goals of your analysis.

It's clearly incorrect. Observing 1 heads and 1 tails means that $p(\theta=0)=0$ (it's impossible to have an all-heads coin) and $p(\theta=1)=0$ (it's impossible to have an all-tails coin). The uniform distribution isn't consistent with this. What is consistent is a Beta(2,2). From the Bayesian solution to the coin-flip problem with a Laplace (i.e. uniform) prior on the $\theta$, the posterior probability is $p(\theta)={\rm Beta}(h+1,(N-h)+1)$.

• I have a hard time understanding your answer. – Michael Chernick Apr 5 '17 at 11:18
• Your conclusion that "the uniform distribution isn't consistent with this" is incorrect. It confuses density (which is what must be meant by "$p$") with probability. The (continuous) uniform distribution assigns zero probability to any atomic event such as $\theta=0$ or $\theta=1$. – whuber Apr 5 '17 at 15:58


text:
# Calculate the IRR for the following cash flows. Is the project acceptable if the firm's cost of...

Calculate the IRR for the following cash flows. Is the project acceptable if the firm's cost of capital is 12%?

End of Year Cash Flow ($) 0 -$400,000

1 100,000

2 200,000

3 300,000


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# Properties of Determinants

Determinants and Its Properties

In Linear algebra, a determinant is a unique number that can be ascertained from a square matrix. The determinants of a matrix say K is represented as det (K) or,  |K| or det K. The determinants and its properties are useful as they enable us to obtain the same outcomes with distinct and simpler configurations of elements. The determinant is considered an important function as it satisfies some additional properties of determinants that are derived from the following conditions.

1. Multiplicativity; det (XY) = det (X) det (y)

2. Invariance under transpose det (X) = det (Xt).

3. Invariance under row operations; if  X’ is a matrix formed by summing up the multiple of any row to another row, then det (X) = det (X’).

4. There is a change of sign under row swap. If X’ is a matrix made by interchanging the positions of two rows, then det (X’) = -det (x)

What is known as Determinants ?

The determinant of a square matrix is a value ascertained by the elements of a matrix. In 2 × 2 matrix. The determinants is calculated by

Det$\begin{pmatrix}a & b\\ c & d\end{pmatrix}$ = ad - bc

The larger matrices have more complex formulas..

Determinants have various different applications throughout Mathematics. For example, they are used in shoelace formulas for calculating the area which is beneficial as a collinearity condition as three collinear points define a triangle which is equal to 0. The determinant is also used in multiple variable calculus(mainly in Jacobina) and in computing the cross product of vectors.

Basic Properties of Determinants

Some basic properties of determinants are given below:

1. If In is the identity matrix of the order m ×m, then det(I) is equal to1

2. If the matrix XT is the transpose of matrix X, then det (XT) = det (X)

3. If matrix X-1 is the inverse of matrix X, then det (X-1) = 1/det (x) = det(X)-1

4. If two square matrices x and y are of equal  size, then det (XY) = det (X) det (Y)

5. If matrix X retains size a × a and C is a constant, then det (CX) = Ca det (X)

6. If A, B, and C are three positive semidefinite matrices of equal size, then the following equation holds along with the corollary det (A+B) ≥ det(A) + det (B) for A,B, C ≥ 0 det (A+B+C) + det C ≥ det (A+B) + det (B+C)

7. In a triangular matrix, the determinant is equal to the product of the diagonal elements.

8. The determinant of a matrix is zero if each element of the matrix is equal to zero.

9. Laplace’s Formula and the Adjugate Matrix.

Important Properties of Determinants

There are 10 important properties of determinants that are widely used. The description of each of the 10 important properties of determinants are given below.

1. Reflection Property

The reflection property of determinants defines that determinants do no change if rows are transformed into columns and columns are transformed into rows.

2. All- Zero Property

The determinants will be equivalent to zero if each term of rows and columns are zero.

3. Proportionality (Repetition Property)

If each term of rows or columns is similar to the column of some other row (or column) then the determinant is equivalent to zero.

4. Switching Property

The interchanging of any two rows (or columns) of the determinant changes its signs.

5. Factor Property

If a determinant Δ beomes 0 while considering the value of x  = α, then (x -α) is considered as a factor of Δ.

6. Scalar Multiple Property

If all the elements of a row (or columns) of a determinant is multiplied by a non-zero constant, then the determinant gets multiplied by a similar constant.

7. Sum Property

$\begin{vmatrix}j_{1}+k_{1} & l_{1} & m_{1} \\ j_{2}+k_{2} & l_{2} & m_{2}\\ j_{3}+k_{3} & l_{3} & m_{3}\end{vmatrix}$ = $\begin{vmatrix}j_{1} & l_{1} & m_{1} \\ j_{2} & l_{2} & m_{2}\\ j_{3} & l_{3} & m_{3}\end{vmatrix}$ + $\begin{vmatrix}+k_{1} & l_{1} & m_{1} \\ +k_{2} & l_{2} & m_{2}\\ +k_{3} & l_{3} & m_{3}\end{vmatrix}$

8. Triangle Property

If each term of a determinant above or below the main diagonal comprise zeroes, then the determinant is equivalent to the product of diagonal terms. That is

$\begin{vmatrix}x_{1} & x_{2} & x_{3} \\ 0 & y_{2} & y_{3}\\ 0 & 0 & z_{3}\end{vmatrix}$ = $\begin{vmatrix}x_{1} & 0 & 0\\ x_{2} & y_{2} & 0 \\ x_{3} & y_{3} & z_{3}\end{vmatrix}$ = X$_{1}$Y$_{2}$Z$_{3}$

9. Determinant of Cofactor Matrix

Δ = $\begin{vmatrix}x_{11} & x_{12} & x_{13} \\ x_{21} & x_{22} & x_{23}\\ x_{31} & x_{32} & x_{33}\end{vmatrix}$ then Δ$_{1}$ = $\begin{vmatrix}z_{11} & z_{12} & z_{13} \\ z_{21} & z_{22} & z_{23}\\ z_{31} & z_{32} & z_{33}\end{vmatrix}$ = Δ$^{2}$

In the above determinants of the cofactor matrix,Cij denotes the cofactor of the elements aij in Δ.

10. Property of Invariance

$\begin{vmatrix}a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2}\\ a_{3} & b_{3} & c_{3}\end{vmatrix}$ = $\begin{vmatrix}a_{1}+\alpha b_{1}+\beta c_{1} & b_{1} & c_{1} \\ a_{2}+\alpha b_{2}+\beta c_{2} & b_{2} & c_{2}\\ a_{3}+\alpha b_{3}+\beta c_{3} & b_{3} & c_{3}\end{vmatrix}$

It implies that determinant remains unchanged under an operation of the term Ci ⟶ Ci + αCj + βCkj where, j and k is not equivalent to i, or a Mathematical operation of the term Ri ⟶ Ri + αRj  + βRk, where, j and k is not equivalent to i.

Examples Problems on Properties of Determinants

Some important example on properties of determinants are given below:

1. Using Properties of Determinant, Prove That

$\begin{vmatrix}x & y & z\\ y & z & x\\ z & x & y\end{vmatrix}$ = (x + y + z)(xy + yz + zx - x² - y² - z²)

Solution:  With the help of the invariance and scalar multiple properties of determinant we can prove the above- given determinant.

Δ = $\begin{vmatrix}x & y & z\\ y & z & x\\ z & x & y\end{vmatrix}$ = $\begin{vmatrix}x+y+z & y & z\\ y+z+x & z & x\\ z+x+y & z & y\end{vmatrix}$ [Operating C$_{1}$ ⟶ C$_{1}$ + C$_{2}$ + C$_{3}$]

=  (x + y + z) $\begin{vmatrix}1 & y & 0\\ 1 & z & x\\ 1 & x & y\end{vmatrix}$

= (x + y + z) $\begin{vmatrix}1 & y & z\\ 0 & z-y & x-z\\ 1 & x-y & y-z\end{vmatrix}$[Operating (R$_{2}$ ⟶ R$_{2}$ - R$_{1}$ and (R$_{3}$ ⟶ R$_{3}$ - R$_{1}$)]

= ( x + y + z) [(z - y)(y - z)- (x - y) (x - z )

= ( x + y + z) (xy + yz + zx - x² - y² - Z²)

2.  Using Properties of Determinant, Prove That

$\begin{vmatrix}a & b & c\\ d & e & f\\ g & h & i\end{vmatrix}$ = $\begin{vmatrix}b & h & e\\ a & g & d\\ c & i & f\end{vmatrix}$

Solution: Interchanging the rows and columns across the diagonals by making use of reflection property and then using the switching property of determination we can get the desired outcome.

L.H.S = $\begin{vmatrix}a & b & c\\ d & e & f\\ g & h & i\end{vmatrix}$ = $\begin{vmatrix}a & d & g\\ b & e & h\\ c & f & i\end{vmatrix}$

(Interchanging rows and columns across the diagonals)

= (-1)$\begin{vmatrix}a & g & d\\ b & h & e\\ c & i & f\end{vmatrix}$ = (1)² = $\begin{vmatrix}b & h & e\\ a & g & d\\ c & i & f\end{vmatrix}$ = $\begin{vmatrix}b & h & e\\ a & g & d\\ c & i & f\end{vmatrix}$ = R.H.S

Quiz Time

1. According to the Determinant Properties, the Value of Determinant Equals to Zero if Row is

1. Multiplied by row

2. Multiplied to column

3. Divided to row

4. Divided to column

2. The Determinants of Matrix in Matrices is Represented By

1. Vertical lines around the matrix.

2. Horizontal lines around matrix

3. Bracket around matrix

4. None of the above

1. When Can We Get the Determinant of a Matrix Equivalent to Zero?

The determinants of a matrix will be equivalent to 0 under the following situations:

1. Each term of a row is zero.

2. Two rows and column are similar

3. A row or column is a constant multiple of other row or columns

A matrix is invertible, nonsingular if and only if the value of determinant is not equal to zero, So if the determinant is zero, the matrix is singular and does not have an inverse.

2. What is the Key Difference Between Matrices and Determinants?

Both matrices and determinants are part of Mathematics. Both play an important role in line equations and also used to solve real-life problems in Physics, Mechanics and Optics etc.

The key difference between matrix and determinants are given below:

1. The matrix is a set of numbers that are enclosed by two brackets whereas the determinants is a set of numbers that are enclosed by two bars.

2. The number of rows is always equivalent to the number of columns in the matrix whereas in determinant the number of rows is not equal to the number of columns.

3. The matrix can be used for operating mathematical operations such as addition, subtraction or multiplication whereas determinants are used for calculating the value of variables such as x,y, and z through Cramer's rule.


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BF community's reaction to new LVL 10 weapon variants.

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Currently we have charts for Battlefield 3, Call of Duty: Black Ops 2, Medal of Honor: Warfighter and Call of Duty: Modern Warfare 3

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Sunday, April 30th 2017, 2:05pm

The Huot Optical is pretty incredible

It takes the Huot LW and turns it into an aggressive weapon. The optical sight enables easy headshots and the buff to the ads moving spread is extremely noticable. Single shots also work wonderfully thanks to that sight. Would still go for the LW for defensive play as the bipod is quite useful. Just went 53-8 with not much time into it.

The 1906 Sniper is too good, in the sense that the factory variant does not offer much, especially considering it lacks the recoil/spread reduction of other factory variants. It just feels like a flat upgrade, which is defiantly not good. Amazing at taking out snipers.

Have not used the defensive hellriegel much but I did enjoy it. Have not unlocked Martini Sniper.

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Sunday, April 30th 2017, 4:41pm

I struggle with the "LMG" term as well. Technically they're all Automatic Rifles except the belt-fed MG15. I hear the Colt Potato Digger is coming, which was also belt-fed.

Through most of its service life, the BAR was designated Squad Automatic Rifle.

In WWI, the U.S. organized what we're termed Machine Gun Companies equipped with Hotchkiss guns (Benet), so the term MG was applied to mag-fed weapons. Plus the tripod would've made it a fire-team-served weapon.

Different armies, first war where Automatic weapins were widely deployed, and a century of development, deployment strategies and nomenclatures vary widely.

While on the subject, let's clear one thing up: while waiting for a game to load recently, one of the factoids that appeared on the screen claimed the moniker has f Worst Design Ever applied to the Chauchat was a false internet rumor.

That "internet rumor", is absolutely true and not just the echoed blog posts of pseudo-experts.

The shortcomings of the "Showshit" as the Doughboys came to call it, were very real and documented during the war.

For one, the open slot in the magazine, which looked good on paper, was a disaster in field conditions and especially in the trenches, where all manner of mud & debris could get in and screw up the works.

The magazine also meant rounds had to be turned 90-degrees as they were fed, a design seldom seen except the P90, which has a century's worth of knowledge and modern materials/manufacturing techniques going for it. In the infancy of automatic weapons, this was likely a very complex design requiring close manufacturing tolerances and meticulous hand-fitting by skilled workers, two more aspects that were ill-suited to both field-conditions and war-time production. It also probably limited ROF considerably.

In fairness, the Madsen was also known to jam under sustained fire. I assume it's problems were resolved, since the Madsen went on to a service life that last end into the 21st. century

Salt Miner

Posts: 3,636

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: Mar 19th 2014

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Reputation modifier: 16

Sunday, April 30th 2017, 8:01pm

Quoted from "Dantheminigunfox"

The 1906 Sniper is too good, in the sense that the factory variant does not offer much, especially considering it lacks the recoil/spread reduction of other factory variants. It just feels like a flat upgrade, which is defiantly not good. Amazing at taking out snipers.

Now that we have a proper ranged version, the Factory should probably be made into a real Factory variant.

The magazine also meant rounds had to be turned 90-degrees as they were fed, a design seldom seen except the P90

Where did you get this idea? The rounds are definitely not sideways.
Who Enjoys, Wins

This post has been edited 1 times, last edit by "BleedingUranium" (Apr 30th 2017, 8:11pm)

This post by "BleedingUranium" (Sunday, April 30th 2017, 8:11pm) has been deleted by the author himself (Sunday, April 30th 2017, 8:11pm) with the following reason: double post

Posts: 2,015

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: Jan 12th 2014

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Monday, May 1st 2017, 4:41pm

I struggle with the "LMG" term as well. Technically they're all Automatic Rifles except the belt-fed MG15. I hear the Colt Potato Digger is coming, which was also belt-fed.

Through most of its service life, the BAR was designated Squad Automatic Rifle.

In WWI, the U.S. organized what we're termed Machine Gun Companies equipped with Hotchkiss guns (Benet), so the term MG was applied to mag-fed weapons. Plus the tripod would've made it a fire-team-served weapon.

Different armies, first war where Automatic weapins were widely deployed, and a century of development, deployment strategies and nomenclatures vary widely.

While on the subject, let's clear one thing up: while waiting for a game to load recently, one of the factoids that appeared on the screen claimed the moniker has f Worst Design Ever applied to the Chauchat was a false internet rumor.

That "internet rumor", is absolutely true and not just the echoed blog posts of pseudo-experts.

The shortcomings of the "Showshit" as the Doughboys came to call it, were very real and documented during the war.

For one, the open slot in the magazine, which looked good on paper, was a disaster in field conditions and especially in the trenches, where all manner of mud & debris could get in and screw up the works.

The magazine also meant rounds had to be turned 90-degrees as they were fed, a design seldom seen except the P90, which has a century's worth of knowledge and modern materials/manufacturing techniques going for it. In the infancy of automatic weapons, this was likely a very complex design requiring close manufacturing tolerances and meticulous hand-fitting by skilled workers, two more aspects that were ill-suited to both field-conditions and war-time production. It also probably limited ROF considerably.

In fairness, the Madsen was also known to jam under sustained fire. I assume it's problems were resolved, since the Madsen went on to a service life that last end into the 21st. century

The difference between an LMG and an automatic rifle is largely semantic: both are designed to be operated by the "automatic rifleman" (or equivalent), in a maneuver section. Tons of "lmgs" use mags or drum mags. The only really important factor is whether the weapon is fielded as a squad automatic weapon or not.

The Chau was the only automatic rifle used in any meaningful quantity throughout the war. Only the re-chambered version in American hands was extensive in it's failure - again that only existed because there was NO alternative LMG availlable in quantity. The open mag was a problem for the 8mm version as well, but the weapon otherwise worked well enough given the derth of viable alternatives until 1918. The versions rechambered to 7.65x53 mm also worked quite well.

An unreliable LMG is still infinitely better than no LMG. The only alternative to the Chau in the numbers required was no LMG at all. People also forget that trench warfare didn't dominate the entire 4 years of the war, and the Chau did well from 1914-1915 and also performed well in the 1918 offensives once they moved out from the mud. It had zero competitors in any number anyway.

Also I have no idea what you're talking about when you say the rounds needed to rotate. They are ramped into the chamber like almost every other mag fed weapon ever made. They just go through a 180 deg arc instead of a more typical straight-ish mag. Makes the rest of the post laughable as an attempt to "correct the facts".

This post has been edited 4 times, last edit by "tankmayvin" (May 1st 2017, 5:01pm)

Posts: 292

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: Dec 2nd 2013

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Tuesday, May 2nd 2017, 3:18am

Grinding the Huot Optical makes me realize how much I hate this fucking thing. It's like taking the Lewis which I already hate, then giving it a smol 25 round capacity for better accuracy and spread... but it's still mediocre. It fails to make any notable impression in the BF1 weapon meta, so it gets dumpstered by pretty much everything. I've had to completely adapt my playstyle around the Huot by playing passively, and using smokes to let me flank and disengage. And I've had to do the latter plenty of times, because I couldn't stand a reasonable chance against most weapons.

Makes me want to punch my monitor even harder than grinding the 1906 Selb. At least that rifle had no problems killing people if you could aim, the Huot sadly does.

Posts: 3,292

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: Apr 26th 2013

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Location: Arizona, USA

Reputation modifier: 15

Tuesday, May 2nd 2017, 3:28am

"I've had to completely adapt my playstyle around the Huot by playing passively."

And? If you were trying to use it aggressively, then that's simply on you because it isn't a gun you can use effectively with an aggressive playstyle. Which brings me to the question of why are you grinding it in the first place when the Optical doesn't really perform any different? It isn't magically going to make the gun good for aggressive play so I don't see why you're trying to unlock it in the first place.
To Aim Assist or not to Aim Assist, that is the question.

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AttractUserInputMultiplier 0.45
AttractUserInputMultiplier_NoZoom 0.5
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AttractTargetSpeedInfluence 0.85
AttractOwnRequiredMovementForMaximumAttract 0.0
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AttractYawStrength 1.0
AttractPitchStrength 0.34
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MaxToTargetXZAngle 45.0
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SnapZoomTime 0.2
SnapZoomPostTimeNoInput 0.2
SnapZoomPostTime 0.2
SnapZoomReticlePointPriority 999
SnapZoomAutoEngageTime 0.0
SnapZoomBreakTimeAtMaxInput 0.2
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SnapZoomBreakMinAngle 90.0
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SnapZoomTime 0.2
SnapZoomPostTimeNoInput 0.0
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SnapZoomReticlePointPriority 999
SnapZoomAutoEngageTime 0.0
SnapZoomBreakTimeAtMaxInput -1.0
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SnapZoomBreakMinAngle 90.0
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AccelerationDamping 4.0
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SoldierBackupSkeletonCollisionData *nullGuid*
CheckBoneCenterOnlyDistance 40.0
DisableForcedTargetRecalcDistance 7.0

Quoted from "Zer0Cod3x"

the Sebstalder is quiet good since it can 3hit kill at any distanc ,but In my opinion i actually thikn the sweeper is better, its got a really really fast firerate that can beat alll those Noobmaticos, Helregall adn shitguns in close quarters , and its also really accurate out to like l;ong range,. overall great allround gun, jsut my 2\$ tho

Posts: 292

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: Dec 2nd 2013

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Tuesday, May 2nd 2017, 3:51am

I'm grinding it to satisfy my itch of having all weapons unlocked, something I did even for all Scout rifles and I hate Scouts. And it's good to have a feel for every weapon in the game, something which I did while grinding all accessories on nearly every primary in BF4.

There's arguably better options for passive LMG play, like the Benet-Mercie Telescopic or MG15 Suppressive. I have never thought once, even while staring at the statistical data here, that it's a great idea to take the Huot. Excellent accuracy, recoil, and spread sounds fantastic on paper, but when you actually use it in-game, the limitations of having the worst velocity, minimum damage, 2nd worst mag capacity, and RPM of its class makes me question if its worth putting up with.

Posts: 36

Date of registration
: Oct 25th 2012

Platform: PC

Location: AU

Battlelog:

Reputation modifier: 8

Tuesday, May 2nd 2017, 5:56am

I've come to love the Huot and the optical variant is useful too in a more CQ situation, it seems a bit more accurate than the LW but I dislike the added time to ADS and the bobble of that optical sight. As the DUCK said about the auto loading 8.35, i think you need to get a 1000 kills with it to really understand how to use it effectively.
With the low weight I've found that if you hold your nerve and just stand still and hold down that trigger in a 1 v 1, then more often than not you will win. The accuracy just works for you.
I've had good success with it playing aggressively and in fact believe that it is the best suited LMG for that role. I think I still prefer the LW for its versatility over different ranges.

IGN - VonReisler.

Posts: 292

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: Dec 2nd 2013

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Tuesday, May 2nd 2017, 9:06am

The Huot is a great gun if both you and the enemy are stationary 30-50m away, and you get to fire first.

That is a whole lotta "ifs" though. I really don't think it warrants comparison with the Auto8, because the only glaring weakness it has is mag capacity. The Huot has a lot more bad things going for it, accuracy isn't going to mean anything when an enemy is just as capable of returning deadly fire back. Or disengaging, which is also a lot easier to do compared to other LMGs thanks to the Huot's flaws.


text:
# p-values in regression trees

#### rogojel

##### TS Contributor
Hi,
I am analyzing some pretty hopeless datasets where the link between the DVs and IVs is quite weak. I observed however that when I take the two groups resulting from the first partition in the tree I can generallly get a nicely low p-value with a t-test . Is this some property of the trees I wonder. Is there any theorem pointing in this direction or is this possibly a weak signal I am detecting?

regards

#### Dason

##### Ambassador to the humans
I don't quite understand what you're asking.

#### hlsmith

##### Omega Contributor
Is the program kicking out p-values at your splits (partitions), and you are finding in a certain subgroup the outcome that do significantly differ between groups at the second level?

A pictorial example would be great. Is this coming from a single decision tree that you have run a couple of times?

#### rogojel

##### TS Contributor
Hi,
yes, it is a single tree and a continuous DV. Imagine that I have the first partition, and I have two subsets , one where the partition condition is TRUE (e.g.Volume>5) and one where the condition is FALSE . If I consider the two subsets and do a t-test for the two subsets like

t.test(dataset[condition,]$dv, dataset[!condition,]$dv)

I always get a low p-value (<0.05). My question is whether this is to be expected, as sort of the normal behavior of partitions or it is something one might consider as a signal?

Now that I think of it, it looks like a case of multiple comparisons.
Regards

#### Dason

##### Ambassador to the humans
Well typically the tree wouldn't fit the partition if it didn't actually do anything. It's also fit pretty much so that you get the maximal difference between the two groups (that is in essence what the tree is attempting to do...). Now the question of how it compares to an actual linear regression depends on the data itself.

#### rogojel

##### TS Contributor
I wonder if there could be a theorem (exercise) behind this, something like - if the number of data points is large enough and the points are different enough then the first partition will result in two groups which are significantly different?

#### hlsmith

##### Omega Contributor
Yes, absolutely there should be a reason behind the split. Usually it is something like an entropy or gini index. What package and procedure are you using? It is like Dason said, it is looking for the split the maximizes the difference between the two groups.


text:
# Overview

## Contents

This package contains the source for dupeGuru. To learn how to build it, refer to the "Build dupeGuru" section. Below is the description of the various subfolders:

• core: Contains the core logic code for dupeGuru. It's Python code.
• core_*: Edition-specific-cross-toolkit code written in Python.
• cocoa: UI code for the Cocoa toolkit. It's Objective-C code.
• qt: UI code for the Qt toolkit. It's written in Python and uses PyQt.
• images: Images used by the different UI codebases.
• debian: Skeleton files required to create a .deb package
• help: Help document, written for Sphinx.

There are also other sub-folder that comes from external repositories (automatically checked out as mercurial subrepos):

• hscommon: A collection of helpers used across HS applications.
• cocoalib: A collection of helpers used across Cocoa UI codebases of HS applications.
• qtlib: A collection of helpers used across Qt UI codebases of HS applications.

## dupeGuru Dependencies

Before being able to build dupeGuru, a few dependencies have to be installed. If you use pip, you will not have to install them all manually (see "The easy way!" below):

### The easy way!

There's an easy way to install the majority of the prerequisites above, and it's pip which has recently started to support Python 3. So install it and then run:

pip install -r requirements-[osx|win].txt

([osx|win] depends, of course, on your platform. On other platforms, just use requirements.txt).

Advanced Installer, having nothing to do with Python, needs to be installed manually.

PyQt isn't in the requirements file either (there's no package uploaded on PyPI) and you also have to install it manually.

If you use a virtualenv (which you should), you have to enable the "site-packages" option because dupeGuru will need the PyQt library which you'll have installed on your system.

### Prerequisite gotchas

Correctly installing the prerequisites is tricky. Make sure you have at least the version number required for each prerequisite.

If you didn't use mercurial to download this source, you probably have an incomplete source folder! External projects (hscommon, qtlib, cocoalib) need to be at the root of the dupeGuru project folder. You'll have to download those separately. Or use mercurial, it's much easier.

Another one on OS X: I wouldn't use macports/fink/whatever. Whenever I tried using those, I always ended up with problems.

Whenever you have a problem, always double-check that you're running the correct python version. You'll probably have to tweak your \$PATH.

To setup a build machine under Ubuntu 12.04 and up, install those packages: python3-dev, python3-pyqt4, pyqt4-dev-tools, mercurial and then python3-setuptools. Once you've done that, install pip with easy_install. Once you've done that, you can then perform "The easy way!" installation.

## Building dupeGuru

First, make sure you meet the dependencies listed in the section above. Then you need to configure your build with:

python configure.py

If you want, you can specify a UI to use with the --ui option. So, if you want to build dupeGuru with Qt on OS X, then you have to type python configure.py --ui=qt. You can also use the --dev flag to indicate a dev build (mostly useful in OS X, where the python code in symlinked so you don't have to repackage whenever you make a change in the python code).

Then, just build the thing and then run it with:

python build.py
python run.py

If you want to create ready-to-upload package, run:

python package.py


text:
1. ## Fourier transform help

Hi,

I have a problem with the calculation of DFT(discrete fourier transform) of the signal x(n) above. I've attached the signal x(n) and also the definition of DFT I am using.
So, How can I calculate Xk ,the dft, of this signal?

This is what I did.

for k=0,1,2...N-1

Can you tell me if this is right and also help me to sketch the magnitude of Xk as a function of k in the range of 0...N-1 ?

Nikolas

2. Originally Posted by tsebamm

Hi,

I have a problem with the calculation of DFT(discrete fourier transform) of the signal x(n) above. I've attached the signal x(n) and also the definition of DFT I am using.
So, How can I calculate Xk ,the dft, of this signal?

This is what I did.

for k=0,1,2...N-1

Can you tell me if this is right and also help me to sketch the magnitude of Xk as a function of k in the range of 0...N-1 ?

Nikolas
Could you repost this with slightly bigger graphics that are easier to read, please.

CB

3. Originally Posted by tsebamm

Hi,

I have a problem with the calculation of DFT(discrete fourier transform) of the signal x(n) above. I've attached the signal x(n) and also the definition of DFT I am using.
So, How can I calculate Xk ,the dft, of this signal?

This is what I did.

for k=0,1,2...N-1

Can you tell me if this is right and also help me to sketch the magnitude of Xk as a function of k in the range of 0...N-1 ?

Nikolas
Applying the DFT definition is...

$\displaystyle \displaystyle X_{k} = \sum_{n=0}^{N-1} x(n)\ e^{-j 2 \pi \frac{k n}{N}} = \frac{1}{2}\ \sum_{n=0}^{1} e^{-j 2 \pi \frac{k n}{N}}= \frac{1}{2}\ (1+ e^{-j 2 \pi \frac{k}{N}})$

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

P.S. I suggest tsebann to learn Latex!...

4. Originally Posted by chisigma
Applying the DFT definition is...

$\displaystyle \displaystyle X_{k} = \sum_{n=0}^{N-1} x(n)\ e^{-j 2 \pi \frac{k n}{N}} = \frac{1}{2}\ \sum_{n=0}^{1} e^{-j 2 \pi \frac{k n}{N}}= \frac{1}{2}\ (1+ e^{-j 2 \pi \frac{k}{N}})$

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

P.S. I suggest tsebann to learn Latex!...
Thanks both of you! You are right, when I find some time I will try to learn Latex.
I think chisigma gave me the answer I want. This is what I did in the blur image. I was just not sure if I have had to take some values for N! The question of the excersise is : "Calculate Xk, the dft of the signal" . So, I think that it is ok.
Thanks again

Regards,
Nikolas

5. Hi again and sorry for the double posting.
I am trying to sketch the magnitude of Xk that we found above as a function of k in the range 0...N-1.
Should I take the equation ? But how can I use it here?

I have made an attempt. I take values for k. (0,1,2,3...N-1) but I don't know what to do with N. I have an idea to take conditions for it.If it is even or odd but I can not conclude something with that.
Can anyone help me with that?
i have checked a lot of stuff via the internet.I would appreciate if you give me a solution with that and a small explanation.

Oh, N is an integer of course!


text:
## Row by row methods for semidefinite programming

We present a row-by-row (RBR) method for solving semidefinite programming (SDP) problem based on solving a sequence of problems obtained by restricting the n-dimensional positive semidefinite constraint on the matrix X. By fixing any (n-1)-dimensional principal submatrix of X and using its (generalized) Schur complement, the positive semidefinite constraint is reduced to a simple second-order … Read more

## Continuous GRASP with a local active-set method for bound-constrained global optimization

Global optimization seeks a minimum or maximum of a multimodal function over a discrete or continuous domain. In this paper, we propose a hybrid heuristic – based on the CGRASP and GENCAN methods – for finding approximate solutions for continuous global optimization problems subject to box constraints. Experimental results illustrate the relative effectiveness of CGRASP-GENCAN … Read more

## Convergence Rate of Stochastic Gradient Search in the Case of Multiple and Non-Isolated Minima

The convergence rate of stochastic gradient search is analyzed in this paper. Using arguments based on differential geometry and Lojasiewicz inequalities, tight bounds on the convergence rate of general stochastic gradient algorithms are derived. As opposed to the existing results, the results presented in this paper allow the objective function to have multiple, non-isolated minima, … Read more

## NESTA: A Fast and Accurate First-order Method for Sparse Recovery

Accurate signal recovery or image reconstruction from indirect and possibly under- sampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by recent breakthroughs in the development of novel fi rst-order methods in convex optimization, most notably Nesterov’s smoothing technique, this paper … Read more

## Compressed Sensing with Quantized Measurements

We consider the problem of estimating a sparse signal from a set of quantized, Gaussian noise corrupted measurements, where each measurement corresponds to an interval of values. We give two methods for (approximately) solving this problem, each based on minimizing a differentiable convex function plus an l1 regularization term. Using a first order method developed … Read more

## An Improved Algorithm for the Solution of the Entire Regulation Path of Support Vector Machine

This paper describes an improved algorithm for the numerical solution to the Support Vector Machine (SVM) classification problem for all values of the regularization parameter, C. The algorithm is motivated by the work of Hastie \emph{et. al.} and follows the main idea of tracking the optimality conditions of the SVM solution for descending value of … Read more

## Distributionally Robust Optimization and its Tractable Approximations

In this paper, we focus on a linear optimization problem with uncertainties, having expectations in the objective and in the set of constraints. We present a modular framework to obtain an approximate solution to the problem that is distributionally robust, and more flexible than the standard technique of using linear rules. Our framework begins by … Read more

## Option – Alloction funds- Transaction costs

The present article studies the efficiency of a strategy, incorporating some options and seeking to super-duplicate a standard allocation policy. The replication strategy allows reducing transaction cost effects. The replication means optimizing two objective-functions: MSE (Mean-squared Errors) and WMSE (Weighted Mean-squared Errors). Tests on portfolio efficiency concern, at first time, a long-term investor with Out-The-Country … Read more

## A Modified Frank-Wolfe Algorithm for Computing Minimum-Area Enclosing Ellipsoidal Cylinders: Theory and Algorithms

We study a first-order method to find the minimum cross-sectional area ellipsoidal cylinder containing a finite set of points. This problem arises in optimal design in statistics when one is interested in a subset of the parameters. We provide convex formulations of this problem and its dual, and analyze a method based on the Frank-Wolfe … Read more