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# An unpacking of Hurwitz’s theorem in complex analysis

Originally published at 狗和留美者不得入内. You can comment here or there.

Let’s first state it.

Theorem (Hurwitz’s theorem). Suppose $\{f_k(z)\}$ is a sequence of analytic functions on a domain $D$ that converges normally on $D$ to $f(z)$, and suppose that $f(z)$ has a zero of order $N$ at $z_0$. Then for every small enough $\rho > 0$, there is $k$ large such that $f_k(z)$ has exactly $N$ zeros in the disk $\{|z - z_0| < \rho\}$, counting multiplicity, and these zeros converge to $z_0$ as $k \to \infty$.

As a refresher, normal convergence on $D$ is convergence uniformly on every closed disk contained by it. We know that the argument principle comes in handy for counting zeros within a domain. That means

The number of zeros in $|z - z_0| < \rho$, $\rho$ arbitrarily small, goes to the number of zeros inside the same circle of $f$, provided that

$\frac{1}{2\pi i}\int_{|z - z_0| = \rho} \frac{f'_k(z)}{f_k(z)}dz \longrightarrow \frac{1}{2\pi i}\int_{|z - z_0| = \rho} \frac{f'(z)}{f(z)}dz$.

To show that boils down to a few technicalities. First of all, let $\rho > 0$ be sufficiently small that the closed disk $\{|z - z_0| \leq \rho\}$ is contained in $D$, with $f(z) \neq 0$ inside it everywhere except for $z_0$. Since $f_k(z)$ converges to $f(z)$ uniformly inside that closed disk, $f_k(z)$ is not zero on its boundary, the domain integrated over, for sufficiently large $k$. Further, since $f_k \to f$ uniformly, so does $f'_k / f_k \to f' / f$, so we have condition such that convergence is preserved on application of integral to the elements of the sequence and to its convergent value. With $\rho$ arbitrarily small, the zeros of $f_k(z)$ must accumulate at $z_0$.

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• #### 中国姓氏的南北分布

有意思的是分布是很不均匀的，也就是说好多姓是南方比例远高于北方比例或相反。从这一点，你如果知道一个人的父母的姓氏，你就可以对他是北方人还是南方人有个有点统计显著的估计。 读者可以在包含大姓分布图的…

• #### Why I think Stanford professor James Landay's piece on computing in China in 2011 exposed his idiocy

I dittoed his blog post on my LiveJournal too, see https://gmachine1729.livejournal.com/175023.html. For the original, see…

• #### China Will Overtake the US in Computing…Maybe, Someday… by Stanford professor James Landay in 2011

Original at https://dubfuture.blogspot.com/2011/12/china-will-overtake-us-in.html. [note: the following is a rough draft — I appreciate…

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# Configuring TeXnicCenter

### Introduction

TeXnicCenter is a useful program for creating and editing TeX/LaTeX documents under Windows, but it requires a little setting up the first time you use it on a new computer. It can also stop working because software it relies on (such as Adobe Reader) has been updated, in which case it often helps to run through the configuration process from the beginning. This setup must be done from each user's account individually, so I cannot do it for you unless you are present to log me into your account.

Before you begin, make sure that your computer has TeXnicCenter installed. Look under Start -> All Programs for a TeXnicCenter folder. If it does not appear to be installed please email me (it is free but takes time to install).

The process of setting up TeXnicCenter can be broken down into three stages.

1. Configure the ``back end'' (the application, usually MikTeX, which processes TeX/LaTeX files into other formats).
2. Set up the profiles (tell the computer what commands to run to convert TeX/LaTeX to DVI/PostScript/PDF).
3. Configure Windows to associate TeXnicCenter with .tex files.

### Configure the back end

 Launch TeXnicCenter via the Start menu and close the Tip of the Day. If this is your first time using TeXnicCenter on your computer, the Configuration Wizard will pop up. It can also be found under Build -> Define Output Profiles -> Wizard. Click Next and you will be asked where TeXnicCenter can find your TeX distribution. Either browse to the directory C:\Program Files\MiKTeX 2.9\miktex\bin or type it into the box. Some PCs will have 2.7 or 2.8 instead of 2.9.
Click Next again. Depending on your exact setup, you may be taken straight to a screen telling you that your profiles have been set up, or you may be asked to choose a PostScript viewer. It's probably easiest to keep clicking through until the end of the wizard and change your PostScript viewer to GSView later.

### Set up the profiles

The Configuration Wizard sets up ``profiles'' for converting LaTeX into DVI, PostScript and PDF, but some adjustments will be required (especially for the LaTeX => PDF profile) and if you work with plain TeX you will need to set up those profiles yourself. To tweak your profiles, go to the Build menu and select Define Output Profiles.

The LaTeX => PS => PDF profile can safely be removed. Highlight it in the left pane, click on Remove, and click Yes when the "Really remove" dialog box appears.

 The LaTeX => PS profile may need to be configured to use GSView to open PS files. Highlight it, select the Viewer tab and change the path of the executable to C:\Program Files\Ghostgum\gsview\gsview32.exe if necessary. The LaTeX => PDF profile needs tweaking to work properly with Adobe Reader X. Highlight it and select the Viewer tab. Do not change the path of the executable, but change the options to use command line arguments rather than DDE commands, exactly as shown in the screenshot.

Having set up the LaTeX profiles, you can now copy them to create TeX profiles. Highlight each one in turn, click Copy, and name the copies TeX => DVI, TeX => PDF and TeX => PS as appropriate. You should end up with six profiles, three for LaTeX and three for TeX.

Highlight the TeX => DVI profile and look for the box headed ``Path to the (La)TeX compiler''. Find the word ``latex'' in this box and delete the letters ``la''. Repeat with the other two TeX profiles before clicking OK.

### Associate TeXnicCenter with .tex files

Open drive H: and navigate to a directory which contains at least one .tex file. It may be helpful to configure Windows to display file extensions if this has not been done already. To do this, select Folder Options from the Tools menu and click on the View tab. Ensure that the box ``Hide extensions for known file types'' is unchecked. Click ``Apply To All Folders'' then click OK.

Right-click on a .tex file, scroll down to ``Open With'' and browse to TeXnicCenter (TEXCNTR.EXE). Tick ``Always use the selected program to open this kind of file''. The dialog box should look something like this:

Click OK. Your file will open in TeXnicCenter and from now on TeXnicCenter will run when you double-click on a .tex file.

format: plain


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Things to keep in mind when grading:

• Transparency.
• Fairness.
• Explanation. Use grading as a teaching opportunity (by giving counter-examples, etc.).

Each TA focus group will be given four (4) questions, and 3 answers to each. Each TA will then grade these 3 papers with four questions each in the stipulated time. After the time passes, the TA moderator will discuss the recommendations and best-practices of grading, specifying the traps set in each question for the TAs.

The aim of this session is the following:

• Get TAs to handle situations when the key is given, and not given
• Not to take too much time in the grading process itself
• Not to test the TAs' technical knowledge, but to test their grading skills

#### Questions 1 and 2

These questions will be either multiple choice, or having numerical answers. The TAs will be given the correct answer, but the answer sheets will also have space to show working to get the answer.

Sample question:
Given an electrical circuit, find the effective resistance between points A and B

Sample question:
Given a pulley-and-weight system, find the tension on a particular string

Sample question:
Given a system of linear equations (2 variables, 2 equations), find values of x and y

#### Questions 3 and 4

These questions will require long answers, and students will be expected to explain concepts in their answers. The challenge for the TAs is to create their own answer keys, perhaps by going through each answer, and then start grading.

Sample question
Give one of the standard mathematical paradoxes, e.g.

(1)
$$-6 = -6 -6 + 25/4 = -6 + 25/4 4 - 10 + 25/4 = 9 - 15 + 25/4 (2 - 5/2)^2 = (3 - 5/2)^2 2 - 5/2 = 3 - 5/2 2 = 3$$

And ask them to explain how it does not make sense.

Sample question
Given a standard pn junction diode in a black box with two terminals (one connected to the p side and one connected to the n side), explain how to use a digital multimeter to determine which terminal connects to the p side and which terminal connects to the n side. Hint: Consider the resistance of pn junction diodes.

Sample question
??

#### List of tricky situations

1. In a computation based question
• No working shown, small mistake in value
• Working shown, small mistake in value
1. In a long-form question


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Experimental evidence of a \varphi Josephson junction

# Experimental evidence of a φ Josephson junction

H. Sickinger Physikalisches Institut and Center for Collective Quantum Phenomena in LISA, Universität Tübingen, Auf der Morgenstelle 14, D-72076 Tübingen, Germany    A. Lipman The Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel    M. Weides Peter Grünberg Institute and JARA-Fundamentals of Future Information Technology, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany Current address: Physikalisches Institut, Karlsruher Institut für Technologie, 76131 Karlsruhe, Germany    R. G. Mints The Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel    H. Kohlstedt Nanoelektronik, Technische Fakultät, Christian-Albrechts-Universität zu Kiel, D-24143 Kiel, Germany    D. Koelle    R. Kleiner    E. Goldobin Physikalisches Institut and Center for Collective Quantum Phenomena in LISA, Universität Tübingen, Auf der Morgenstelle 14, D-72076 Tübingen, Germany
July 14, 2019
###### Abstract

We demonstrate experimentally the existence of Josephson junctions having a doubly degenerate ground state with an average Josephson phase . The value of can be chosen by design in the interval . The junctions used in our experiments are fabricated as 0- Josephson junctions of moderate normalized length with asymmetric 0 and regions. We show that (a) these Josephson junctions have two critical currents, corresponding to the escape of the phase from and states; (b) the phase can be set to a particular state by tuning an external magnetic field or (c) by using a proper bias current sweep sequence. The experimental observations are in agreement with previous theoretical predictions.

Josephson junction
###### pacs:
74.50.+r, 85.25.Cp

Josephson junctions (JJs) with a phase shift of in the ground stateBulaevskiĭ et al. (1977) attracted a lot of interest in recent yearsBaselmans et al. (1999); Ryazanov et al. (2001a); Kontos et al. (2002); Weides et al. (2006a); van Dam et al. (2006); Gumann et al. (2007). In particular, these JJs can be used as on-chip phase batteries for biasing various classicalOrtlepp et al. (2006) and quantumFeofanov et al. (2010) circuits, allowing for removing external bias lines and reducing decoherence. Currently, it is possible to fabricate simultaneously both 0 and JJs using various technologies such as superconductor-ferromagnet heterostructuresRyazanov et al. (2001b); Weides et al. (2006b); Frolov et al. (2008); Weides et al. (2007); Pfeiffer et al. (2008) or JJs based on d-wave superconductorsVan Harlingen (1995); Tsuei and Kirtley (2000); Smilde et al. (2002); Gürlich et al. (2009).

It would be remarkable to have a phase battery providing an arbitrary phase shift , rather than just 0 or . The simplest idea is to combine 0 and JJs to obtain a JJ. However, this is not as straightforward as it may seem. The balance between 0 and parts is complicated as shown in the pioneering workBulaevskii et al. (1978), where conditions for having a non-trivial -state were derived. Long artificialBuzdin and Koshelev (2003); Pugach et al. (2010) and naturalMints (1998); Il’ichev et al. (1999); Mints et al. (2002) arrays of -0--0-- JJs with short segments were analyzed in detail and suggested as systems, where a JJ could be realized. More recently, only one period of such an array, i.e., one 0- JJ, was analyzed in an external magnetic fieldGoldobin et al. (2011). In these works, the Josephson phase is considered as a sum of a constant (or slowly varying) phase and a deviation from the average phase. Then, for the average phase one obtains an effective current-phase relation (CPR) for the supercurrentGoldobin et al. (2011)

 Is=⟨Ic⟩[sin(ψ)+Γ02sin(2ψ)+Γhhcos(ψ)], (1)

where the averaged value of the critical current . The CPR (1) exactly corresponds to a JJ at zero normalized magnetic field , if , cf. Fig.1(a). Here is the total length of JJ, while and are the lengths of 0 and parts, accordingly, is the width of JJ.

It is worth noting that the term “ JJ”, introduced in Ref. Buzdin and Koshelev, 2003, refers to a JJ with a degenerate ground state phase . In the particular case of Eq. (1) at one has . The coefficients and are defined asLipman et al. (2012)

 Γ0 = −l20l2π3(jc,0−jc,π)2(jc,0l0+jc,πlπ)2, (2a) Γh = l0lπ2jc,0−jc,πjc,0l0+jc,πlπ, (2b)

where , are the lengths normalized to the Josephson length and , are the critical current densities of 0 and parts, respectively. Here is calculated using the average value of the critical current .

The physics of JJs with a CPR given by Eq. (1) is quite unusualGoldobin et al. (2007). In particular, one should observe two critical currentsGoldobin et al. (2007, 2011) at , corresponding to the escape of the phase from the left () or the right () well of the double-well Josephson energy potential

 U(ψ)=⟨EJ⟩[1−cos(ψ)+Γhhsin(ψ)+Γ02sin2(ψ)], (3)

where . The critical currents are different because the maximum slope (maximum supercurrent in Fig. 1(a)) on the rhs (positive bias) of the well is smaller than the maximum slope (maximum supercurrent in Fig. 1(a)) on the rhs of the well, see Fig. 1(b).

In this letter we present experimental evidences of a JJ made of one 0 and one segment, see Fig. 2(a).

The samples were fabricated as NbAl-AlONiCuNb heterostructuresWeides et al. (2006b, 2010). These superconductor-insulator-ferromagnet-superconductor (SIFS) JJs have an overlap geometry as shown in Fig. 2(b). Each junction consists of two parts, a conventional 0-segment and a -segment. It is well knownKontos et al. (2002); Oboznov et al. (2006); Weides et al. (2006a); Buzdin (2005) that the critical current in SFS or SIFS JJs strongly depends on the thickness of the F-layer and can become negative within some range of ( junction). Therefore, to produce the 0 and the segments, the F-layer has different thicknesses and , as shown in Fig. 2(a). To achieve this, the F-layer of thickness , corresponding to ( JJ) was fabricated first. Then the area indicated in Fig. 2(b) was etched down to , corresponding to (0 JJ). Usually one obtains asymetric valuesKemmler et al. (2010), i.e. .

We have studied 3 samples. One of them has very little asymmetry of about 5%, and , which corresponds to . In this case even 5% of asymmetry brings the sample out of the domain, see Fig. 3 for a qualitative picture. The other two JJs have and are deep inside the -domain in parameter space. Both samples show similar results. Here we present the results obtained on one of them. Its parameters are summarized in Tab. 1 and its position within the domain is indicated in Fig. 3. The values of and cannot be measured directly. In our case we have measured the dependence (see below) and then simulated it numerically using and as fitting parameters. The best fitting was obtained for the values specified in Tab. 1.

According to theoretical predictionsGoldobin et al. (2007, 2011) for a JJ at zero magnetic field one expects two critical currents (for each bias direction), corresponding to the escape of the phase from and wells of , respectively for bias current and vice versa for . The current is always observed. To observe one has to have low damping so that retrapping in the well is avoided (for positive ). The characteristic (IVC) of the investigated 0- JJ at measured at show only one critical current. Therefore the experiments were performed in a He cryostat at down to where the damping in SIFS JJs reduces drasticallyPfeiffer et al. (2008). In the temperature range from down to both and are clearly visible in the IVCs as shown in Fig. 4.

EarlierGoldobin et al. (2007) we proposed a technique that allows to choose which critical current one traces in the IVC, i.e. from which well the phase escapes. The control is done by choosing a proper bias sweep sequence. For example, if the junction is returning from the positive voltage state, the potential is tilted so that the phase slides to the right. When the tilt becomes small enough the phase will be trapped, presumably in the right well, cf. Fig. 1(c). However, this natural assumption is not always true (see below). Then, if the phase is trapped at , we can sweep the bias (a) in the positive direction and will observe escape from (to the right) at or (b) in the negative direction to observe escape from (to the left) at .

In experiment, at , when the damping is very low, the currents and are traced in random order. Recording one IVC after the other, we were able to obtain IVCs with all 4 possible combinations: (a) , (b) , (c) , (d) . Choosing a specific sweep sequence as described above does not make the outcome ( or ) predictable. We believe that in this temperature range the damping is so low that, upon returning from the positive voltage state, the phase does not simply stop in the well, but can also reflect from the barrier and find itself in a well, cf. Fig. 1(c). The absence of determinism suggests that most probably we are dealing with a system exhibiting chaotic dynamics. This issue will be investigated elsewhere. Nevertheless, at we managed to achieve deterministic behavior as described above, see Fig. 4.

Another fingerprint of a JJ is its dependence, which (a) should have the main cusp-like minima shifted off from point-symmetrically with respect to the origin, see Fig. 4 of Ref. Goldobin et al., 2011; (b) should show up to four branches in total (for both sweep polarities) at low magnetic fieldGoldobin et al. (2011). In essence, the latter feature results from the escape of the phase from two different energy minima in two different directions and is an extension of the two-critical-currents story to the case of non-zero magnetic field. Instead, the feature (a) alone cannot serve as a proof of a JJ as it is a common feature of every asymmetric 0- JJ even if its ground state is 0 or Goldobin et al. (2011).

The experimentally obtained dependence at is shown in Fig. 5. First, in the whole temperature range we observe the main minima shifted point-symmetrically to a finite field, which is . Second, at one observes the crossing of two branches and two critical currents for each bias current polarity. The left hand branches correspond to the escape of the phase out of the -well, while the right branch corresponds to the escape from the -well. Note, that at the crossing of branches is not visible. One just observes a cusp-like minimum. In this case, both cannot be seen together and the existence of two states, as should be present for a -JJ, cannot be proven.

To trace the intersection of the branches better we were applying a special value of the magnetic field during reset from the voltage state back to state, to “prepare” a specific state ( or ) of the system. Then the field was set back to the “current” value and the bias was ramped up to trace . By doing this for different values of , one is able to trace the intersection of the branches much better than without this technique, see Fig. 5. Still, in experiment we were not able to trace the branches for positive and negative up to the point where they meet, as shown in Fig. 4(a) and (b) of Ref. Goldobin et al., 2011, probably because of retrapping.

To extract some parameters of our JJ from the curve, we performed numerical simulations, by solving the full sine-Gordon equation for a 0- JJ, using the normalized length and the critical currents and as fitting parameters. The simulations were performed using StkJJGoldobin (2011). The objective was to obtain the best fit close to the origin, especially the point where the branches of cross. The best fit is shown in Fig. 5 and was obtained for and the values and from Tab. 1. Measured data in Fig. 5 are shifted along axis by to compensate for average remanent magnetization of the F-layer. To obtain an almost perfect fit we have also assumed a difference in the constant remanent magnetizations in the 0 and in the parts of , similar to earlier studiesKemmler et al. (2010); Weides et al. (2010). One can also see that one of the experimental branches after the main maximum runs parallel to the simulated curve (the experimental is not point symmetric). This shift stays the same even if we cycle the sample through of Nb, but changes if we cycle through the Curie temperature of the F-layer. We conclude that this is related to the non-uniform remanent magnetization of the F-layer.

The parameters obtained from the fit allow to see the location of our JJ on the plane, see Fig. 3. One sees that the JJ is not really short and lays quite deep in the domain. In this region the analytic resultsGoldobin et al. (2011); Lipman et al. (2012) and, in particular, Eqs. (1) and (3) are valid only qualitatively, cf., Fig. 3 in Ref. Goldobin et al., 2011. Therefore we calculated the CPR of our JJ numerically. We started with a 0- JJ with parameters , , and obtained from the fit, assumed some applied bias current and found all static solutions numerically. Then for each of these solutions we calculated and plotted all those on a plot. By repeating this procedure for different , we obtain an effective CPR shown in Fig. 1(a) together with the curve produced by the analytical formula (1). One can see that the exact effective CPR calculated numerically and the approximate CPR calculated analytically are qualitatively similar. From the numerical CPR the value of for our particular JJ is extracted.

In conclusion, we have demonstrated experimentally the realization of a Josephson junction based on a - SIFS junction. We have observed experimentally a shift of the minimum according to the effective CPR (1), as predictedGoldobin et al. (2011), as well as two critical currents close to zero magnetic field for each bias current polarity. We showed that one can choose between the states of the system using an externally applied magnetic field, which removes their degeneracy. We also showed that one can bring the system into one of the two states by properly tilting the potential using the bias current. Depending on the damping (temperature) one can achieve deterministic behavior (when damping is small enough to see the lower critical current, but large enough to trap the phase in a particular well) as well as random behavior at very low damping. The obtained JJ has at ).

We acknowledge financial support by the German Israeli Foundation (Grant No. G-967-126.14/2007) and DFG (via SFB/TRR-21, project A5 as well via project Go-1106/3). H.S. gratefully acknowledges support by the Evangelisches Studienwerk e.V. Villigst

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• Goldobin et al. (2011) E. Goldobin, D. Koelle, R. Kleiner,  and R. G. Mints, Phys. Rev. Lett. 107, 227001 (2011)1110.2326 .
• Lipman et al. (2012) A. Lipman, E. Goldobin, D. Koelle, R. Kleiner,  and R. Mints, “Josephson junction with a magnetic-field tunable current-phase relation,”  (2012), unpublished.
• Goldobin et al. (2007) E. Goldobin, D. Koelle, R. Kleiner,  and A. Buzdin, Phys. Rev. B 76, 224523 (2007)0708.2624 .
• Weides et al. (2010) M. Weides, U. Peralagu, H. Kohlstedt, J. Pfeiffer, M. Kemmler, C. Gürlich, E. Goldobin, D. Koelle,  and R. Kleiner, Supercond. Sci. Technol. 23, 095007 (2010).
• Oboznov et al. (2006) V. A. Oboznov, V. V. Bol’ginov, A. K. Feofanov, V. V. Ryazanov,  and A. I. Buzdin, Phys. Rev. Lett. 96, 197003 (2006).
• Buzdin (2005) A. I. Buzdin, Rev. Mod. Phys. 77, 935 (2005).
• Kemmler et al. (2010) M. Kemmler, M. Weides, M. Weiler, M. Opel, S. T. B. Goennenwein, A. S. Vasenko, A. A. Golubov, H. Kohlstedt, D. Koelle, R. Kleiner,  and E. Goldobin, Phys. Rev. B 81, 054522 (2010).
• Goldobin (2011) E. Goldobin, ‘‘StkJJ – User’s Reference,” http://www.geocities.com/SiliconValley/Heights/7318/StkJJ.htm (2011).
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text:
Precalculus (6th Edition) Blitzer

As the equation contains both $x^2$ and $y^2$ terms with opposite signs, the equation is a hyperbola. In terms of the coefficients, we have $A=1, C=-4$ and $AC=-4\lt0$; thus the equation is a hyperbola.


text:
# Question

The random variable x has a normal distribution with μ = 300 and σ = 30.
a. Find the probability that x assumes a value more than two standard deviations from its mean. More than three standard deviations from μ.
b. Find the probability that x assumes a value within one standard deviation of its mean. Within two standard deviations of μ.
c. Find the value of x that represents the 80th percentile of this distribution. The 10 th percentile.

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text:
# Need calculus and several books as a prerequisite for Machine Learning

1. Jan 5, 2013

### njama

Hey!

Happy New Year 2013 to all of you!

I am in good mood for learning something new so I need advice.

I'm currently watching the videos for Machine learning from Stanford University, but I'm stuck at Lagrangian multipliers and duality.

I got solid background in Calculus I and II (I read and learned from the book by Irl Bivens and I really like it) but I've never learned about Lagrange multipliers nor Matrix Calculus, and now it's time to step my Calculus up

Also I got solid basic background in Linear Algebra but never learned about Eigenvalues and Eigenvectors or Semideﬁnite Matrices.

So I need some book for self-studying:

Here are the topics that are new to me:

Matrix Calculus 20
4.1 The Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.2 The Hessian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.3 Gradients and Hessians of Quadratic and Linear Functions . . . . . . . . . . 23
4.4 Least Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.5 Gradients of the Determinant . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.6 Eigenvalues as Optimization

3.10 The Determinant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.11 Quadratic Forms and Positive Semideﬁnite Matrices . . . . . . . . . . . . . . 17
3.12 Eigenvalues and Eigenvectors . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.13 Eigenvalues and Eigenvectors of Symmetric Matrices . . . . . . . . . . . . . 19

Convex Optimization
Convex Optimization Part 2

Here are the materials from the course (there are documents in Section Notes).

Thanks a lot.

Regards.

2. Jan 6, 2013

### jasonRF

I would first look at free books online.

FOr calculus, including Hessians and basic optimization, one nice option is the book by Kenneth Kuttler to be found at:
http://www.e-booksdirectory.com/listing.php?category=4

Other books in this category may fit the bill for Hessians as well, so browse around and see what works for you. This book also covers eigenvectors and such.

Other linear algebra references can be found:
http://www.e-booksdirectory.com/listing.php?category=538
I like the books by Heffron listed there (you can buy a hardcopy via amazon for <\$20 US), as well as the book "linear algebra done wrong" by Treil (which is harder than Heffron).

Again, browse around. Good luck!

jason

3. Jan 9, 2013

### njama

Thanks a lot for the help, I have never heard about e-booksdirectory.com it's pretty cool site for free e-books.

I've found courses from Stanford on Youtube about Convex Optimization and some applied linear algebra.

Regards.

4. Jan 11, 2013


text:
# Tags

A tag is a keyword or label that categorizes your question with other, similar questions. Using the right tags makes it easier for others to find and answer your question.

 Type to find tags:
 normed-spaces× 321 A vector space $E$, generally over the field $\mathbb R$ or $\mathbb C$ with a map $\lVert \cdot\rVert\colon E\to \mathbb R_+$ satisfying some conditions. stochastic-calculus× 320 Questions on the calculus of stochastic processes, or processes that have a random component. numerical-linear-algebra× 319 Questions on the various algorithms used in linear algebra computations (matrix computations). distribution-theory× 308 for questions about Schwartz distributions, also known as Generalised Functions. For questions about "probability distributions", use (probability-distributions). For questions about dist… 3d× 306 is for things related to 3-dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For geometry that is not on a plane, but otherwise agnostic of dimensions… boolean-algebra× 303 structures which behave similar to a power set with complement, intersection and union. Questions regarding Boolean algebras as structures, or regarding functions defined from/to … regression× 301 Questions on (linear or nonlinear) regression, the fitting of functions that best approximate empirical data. inverse× 299 the process of creating the opposite. Familiar examples include multiplicative inverse $2 \mapsto 1/2$, inverting functions $f(x) \mapsto f^{-1}(x)$, matrix inverse $M \mapsto M^{-1}$ etc… tensor-products× 290 Tensor products allow us to build "linear" objects from "multilinear" ones. It can refer to: basic ones from linear algebra/module theory, or more sophisticated versions from differential/algebraic ge… vector-analysis× 288 Questions related to understanding line integrals, vector fields, surface integrals, the theorems of Gauss, Green and Stokes. Some related tags are (multivariable-calculus) and (differential-geometry)… ideals× 288 a subset of ring such that it is possible to make a quotient ring with respect to this subset. This is the most frequent use of the name ideal, but it is used in other areas of mathemat… elliptic-curves× 288 For questions regarding elliptic curves. Questions on ellipses should be tagged [conic-sections] instead. computational-geometry× 282 The study of computer algorithms which admit geometric descriptions, and geometric problems arising in association with such algorithms. The two major classes of problems are (a) efficient design of a… coordinate-systems× 281 Questions on coordinate systems, a geometric method where a point in n-dimensions is assigned a corresponding n-tuple of numbers. laplace-transform× 281 a widely used integral transform, similar to the Fourier transform. factoring× 276 For questions about finding factors of e.g. integers or polynomials riemann-surfaces× 268 For questions about Riemann Surfaces, that is compact analytic manifolds of (complex) dimension 1, and related topics. cryptography× 267 Questions on cryptography and cryptanalysis, encryption and decryption, and the making and breaking of codes and ciphers. lebesgue-integral× 265 For question about integration, where the theory is based on measures. So it's almost always used together with the tag [measure-theory], and its aim is to specify questions about integral, not only p… homotopy-theory× 262 homotopic, if one of them can by continuously deformed to another. This gives rise to an equivalence relation. A group called homotopy group can be obtained from the equivalence clas… brownian-motion× 259 Question related to Brownian motion, a stochastic process denoted $W_t$, $t\geq 0$, with independent increments, such that $W(t)-W(s)$ is normally distributed, with $0$ mean and variance $t-s$. rotations× 256 factorial× 249 Questions on the factorial function, $n!=n\times(n-1)\times\cdots\times1$. Consider using the tag (gamma-function) if dealing with noninteger arguments. divisibility× 248 for basic questions about divisibility. algebraic-curves× 248 an algebraic variety of dimension one. An affine algebraic curve can be described as the zero-locus of $n-1$ independent polynomials of $n$ variables in affine $n$-space over a f… inner-product-space× 248 a vector space equipped with an inner product. The inner product is a generalisation of the "dot" product often used in vector calculus. propositional-calculus× 246 Questions about truth tables, conjunctive and disjunctive normal forms, negation, and implication of unquantified propositions would fit very nicely under this tag. Questions about other kind of logic… partitions× 245 Questions related to the different ways of expressing an integer as a sum of integers; or, questions related to the subdivision of a set into smaller disjoint sets; questions related to the subdivisi… calculus-of-variations× 245 Questions on the calculus of variations, a subfield of calculus that deals with the optimization of functionals. ordinals× 244 transitive sets which are well-ordered by $\in$. They are canonical representatives for well-orderings under order-isomorphism. In addition to the intriguing ordinal … infinity× 242 Somewhere beyond the numbers lies the concept of Infinity. But what exactly does "infinity" mean? What rules does it obey? What interesting properties does it have? complex-geometry× 242 the study of complex manifolds and complex algebraic varieties. It is a part of both differential geometry and algebraic geometry. exponential-function× 231 For question involving exponential functions and questions on exponential growth or decay. signal-processing× 231 Questions on the mathematical aspects of signal processing. Please consider first if your question might be more suitable for http://dsp.stackexchange.com/ topological-groups× 230 a group endowed with a topology such that the group operation and inversion are continuous maps. They are useful in various areas of mathematics. Every topological vector space … gamma-function× 227 Questions on the gamma function $\Gamma(z)$ of Euler, the extension of the usual factorial $n!$ for arbitrary argument.


text:
# Move Graphics Object

I'm an artist trying out digital media. I'm very new to Mathematica, however, so excuse me if this a basic question (which I'm sure it is). I did look, though, for anything on this site related to my situation.

I've created a Graphics3D object composed of many shapes, something like

mypoly = Show[Scale[Cone[], {1, 2, 2}], Cylinder[], Rotate[Cylinder...

Everything is working properly, and it looks fine, but I'd like to move it around (rotate it and actually move it in the coordinate space). Apart from individually changing the rotation and center of each component (e.g., Sphere[{1, 0, 0}]), is there something I can do to manipulate one iteration of the whole figure?

Ultimately, I'm going to be creating a bunch of different copies of the object and combining them.

UPDATE:

My attempt at translating the whole figure inspired by this question:

unit = Show[Graphics3D[Cylinder[]], Graphics3D[Scale[Cone[]...
newUnit = Graphics3D[Translate[unit, {1, 0, 0}]]

This only gives me the error "Graphics is not a Graphics3D primitive or directive."

Rotation, however, seems to work fine, though I run into trouble with Show[]:

newUnit = Rotate[unit, 180 Degree]
Show[unit, newUnit] //Could not combine the graphics objects in Show[]

• Welcome to Mathematica.SE! I suggest the following: 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Take the tour! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! – Michael E2 Dec 17 '15 at 0:24
• Look at the various geometric transformation functions available in the documentation. Examples are TranslationTransform, RotationTransform, ScalingTransform and ReflectionTransform. A real nice feature is you can apply multiple transforms to a graphics object. – Jack LaVigne Dec 18 '15 at 0:29

You can do many things with the whole figure, f.e. rotate it

gr = Graphics3D[{Red, Opacity@0.5, Scale[Cone[], {1, 2, 2}], Blue, Cylinder[]}]

Animate[
Graphics3D[Rotate[First@gr, pi, {{1, 0, 0}, {0, 1, 0}}], Options@gr, Boxed -> False],
{pi, 0, 2 Pi}]

Update

You have to use First. With the above definition of gr

Graphics3D[Translate[First@gr, {10, 0, 0}], Axes -> True];

• Thank you for your help! This works well for rotating things. I'm having some issues, though, with translation. – Mandelbrot Jan 9 '16 at 20:50
• See update ---------------------- – eldo Jan 9 '16 at 21:16
• Awesome, thanks. Last question: Why, if I rotate an object like I did in the update section, can I not use it in show? Is there a way around this? – Mandelbrot Jan 9 '16 at 21:47
• This functions: Show[unit, Graphics3D[Rotate[First@unit, 180 Degree, {1, 0, 0}]]]. You have to specify the 3rd parameter of Rotate. – eldo Jan 9 '16 at 22:14
• Perfect. Thank you! – Mandelbrot Jan 9 '16 at 23:16


text:
Browse Questions

# If the foci of the ellipse $\large\frac{x^2}{25}+\frac{y^2}{16}=1$ and the hyperbola $\large\frac{x^2}{4}-\frac{y^2}{b^2}=1$ coincide, then $b^2=$

$(a)\;4 \quad (b)\;5 \quad (c)\;8 \quad (d)\;9$

(b) 5


text:
# Trophic state index

Trophic State Index (TSI) is a classification system designed to rate bodies of water based on the amount of biological activity they sustain.[1] Although the term "trophic index" is commonly applied to lakes, any surface body of water may be indexed.

The TSI of a body of water is rated on a scale from zero to one hundred.[1] Under the TSI scale, bodies of water may be defined as:[1]

• oligotrophic (TSI 0–40, having the least amount of biological productivity, "good" water quality);
• mesoeutrophic (TSI 40–60, having a moderate level of biological activity, "fair" water quality); or
• eutrophic to hypereutrophic (TSI 60–100, having the highest amount of biological activity, "poor" water quality).

The quantities of nitrogen, phosphorus, and other biologically useful nutrients are the primary determinants of a body of water's TSI. Nutrients such as nitrogen and phosphorus tend to be limiting resources in standing water bodies, so increased concentrations tend to result in increased plant growth, followed by corollary increases in subsequent trophic levels.[a] Consequently, a body of water's trophic index may sometimes be used to make a rough estimate of its biological condition.[2]

## Carlson's Trophic State Index

Carlson's index was proposed by Robert Carlson in his 1977 seminal paper, "A trophic state index for lakes".[3] It is one of the more commonly used trophic indices and is the trophic index used by the United States Environmental Protection Agency.[2] The trophic state is defined as the total weight of biomass in a given water body at the time of measurement. Because they are of public concern, the Carlson index uses the algal biomass as an objective classifier of a lake or other water body's trophic status.[3] According to the US EPA, the Carlson Index should only be used with lakes that have relatively few rooted plants and non-algal turbidity sources.[2]

### Index variable

Because they tend to correlate, three independent variables can be used to calculate the Carlson Index: chlorophyll pigments, total phosphorus and Secchi depth. Of these three, chlorophyll will probably yield the most accurate measures, as it is the most accurate predictor of biomass. Phosphorus may be a more accurate estimation of a water body's summer trophic status than chlorophyll if the measurements are made during the winter. Finally, the Secchi depth is probably the least accurate measure, but also the most affordable and expedient one. Consequently, citizen monitoring programs and other volunteer or large-scale surveys will often use the Secchi depth. By translating the Secchi transparency values to a log base 2 scale, each successive doubling of biomass is represented as a whole integer index number.[4] The Secchi depth, which measures water transparency, indicates the concentration of dissolved and particulate material in the water, which in turn can be used to derive the biomass. This relationship is expressed in the following equation:

${\displaystyle \left({\frac {1}{z}}\right)\left(\ln {\frac {I_{0}}{I_{z}}}\right)=k_{w}+\alpha C}$
where z = the depth at which the disk disappears,
I0 is the intensity of light striking the water's surface,
Iz is about 10% of I0 and is considered a constant,
kw is a coefficient for the attenuation of light by water and dissolved substances,
α is treated as a constant with the units of square meters per milligram and
C is the concentration of particulate matter in units for milligrams per cubic meter.[3]

## Trophic classifications

A lake is usually classified as being in one of three possible classes: oligotrophic, mesotrophic or eutrophic. Lakes with extreme trophic indices may also be considered hyperoligotrophic or hypereutrophic. The table below demonstrates how the index values translate into trophic classes.

TSI Chl P SD Trophic Class
< 30—40 0—2.6 0—12 > 8—4 Oligotrophic
40—50 2.6—20 12—24 4—2 Mesotrophic
50—70 20—56 24—96 2—0.5 Eutrophic
70—100+ 56—155+ 96—384+ 0.5— < 0.25 Hypereutrophic
Relationships between Trophic State Index (TSI), chlorophyll (Chl), phosphorus (P, both micrograms per litre), Secchi depth (SD, metres), and Trophic Class (after Carlson 1996)[4]

Oligotrophic lakes generally host very little or no aquatic vegetation and are relatively clear, while eutrophic lakes tend to host large quantities of organisms, including algal blooms. Each trophic class supports different types of fish and other organisms, as well. If the algal biomass in a lake or other water body reaches too high a concentration (say >80 TSI), massive fish die-offs may occur as decomposing biomass deoxygenates the water.

### Oligotrophic

Kurtkowiec Lake, an oligotrophic lake in the Tatra Mountains of southern Poland

An oligotrophic lake is a lake with low primary productivity, as a result of low nutrient content. These lakes have low algal production, and consequently, often have very clear waters, with high drinking-water quality. The bottom waters of such lakes typically have ample oxygen; thus, such lakes often support many fish species such as lake trout, which require cold, well-oxygenated waters. The oxygen content is likely to be higher in deep lakes, owing to their larger hypolimnetic volume.

Ecologists use the term oligotrophic to distinguish unproductive lakes, characterised by nutrient deficiency, from productive, eutrophic lakes, with an ample or excessive nutrient supply. Oligotrophic lakes are most common in cold regions underlain by resistant igneous rocks (especially granitic bedrock).

### Mesotrophic

Mesotrophic lakes are lakes with an intermediate level of productivity. These lakes are commonly clear water lakes and ponds with beds of submerged aquatic plants and medium levels of nutrients.

The term mesotrophic is also applied to terrestrial habitats. Mesotrophic soils have moderate nutrient levels.

### Eutrophic

Algal bloom in a village river in the mountains near Chengdu, Sichuan, China

A eutrophic body of water, commonly a lake or pond, has high biological productivity. Due to excessive nutrients, especially nitrogen and phosphorus, these water bodies are able to support an abundance of aquatic plants. Usually, the water body will be dominated either by aquatic plants or algae. When aquatic plants dominate, the water tends to be clear. When algae dominate, the water tends to be darker. The algae engage in photosynthesis which supplies oxygen to the fish and biota which inhabit these waters. Occasionally, an excessive algal bloom will occur and can ultimately result in fish death, due to respiration by algae and bottom-living bacteria. The process of eutrophication can occur naturally and by human impact on the environment.

Eutrophic comes from the Greek eutrophos meaning "well-nourished", from eu meaning good and trephein meaning "to nourish".[5]

### Hypereutrophic

Hypereutrophic lakes are very nutrient-rich lakes characterized by frequent and severe nuisance algal blooms and low transparency. Hypereutrophic lakes have a visibility depth of less than 3 feet (90 cm), they have greater than 40 micrograms/litre total chlorophyll and greater than 100 micrograms/litre phosphorus.

The excessive algal blooms can also significantly reduce oxygen levels and prevent life from functioning at lower depths creating dead zones beneath the surface.

Likewise, large algal blooms can cause biodilution to occur, which is a decrease in the concentration of a pollutant with an increase in trophic level. This is opposed to biomagnification and is due to a decreased concentration from increased algal uptake.

## Trophic index drivers

Both natural and anthropogenic factors can influence a lake or other water body's trophic index. A water body situated in a nutrient-rich region with high net primary productivity may be naturally eutrophic. Nutrients carried into water bodies from non-point sources such as agricultural runoff, residential fertilisers, and sewage will all increase the algal biomass, and can easily cause an oligotrophic lake to become hypereutrophic.

## Management targets

Often, the desired trophic index differs between stakeholders. Water-fowl enthusiasts (e.g. duck hunters) may want a lake to be eutrophic so that it will support a large population of waterfowl. Residents, though, may want the same lake to be oligotrophic, as this is more pleasant for swimming and boating. Natural resource agencies are generally responsible for reconciling these conflicting uses and determining what a water body's trophic index should be.


text:
• Create Account

### #ActualGavin Williams

Posted 20 January 2013 - 10:54 PM

Hi,

I've started using async / await as I'm taking a look at WinRT. But Im having a terrible time getting to grips with async usage. Suddenly all of my objects have 3 'constructor' methods ...

public someModel(string modelAsText) // the constructor
: base(modelAsText, VertexElementTypes.Position, VertexElementTypes.Normal, VertexElementTypes.Texcoord)
{
// now often empty
}

public override void Initialize(DeviceManager devices) // called when graphics data needs to be loaded and bound to the device
{
// setup any programmatic/fast data
....
LoadData(devices) // calls the async method
}

{
...
IsReady = true; // flag indicating that all data is now loaded.
}

One thing that's starting to annoy me about async is that all my constructors are emptying. And all the construction code is having to be moved into the Initialize and async LoadData methods. I can't understand why a constructor can't be asynchronous. In my mind, it absolutely should be because like any object being constructed, it is immediately identfiable but isn't ready to be used until all its parts are in place. It seems to me that the language isn't designed correctly to handle this. I've read comments on the topic of async in constructors and I understand the reasoning .. early disposal causing leaks and object usage before its ready, but I would argue that the reasoning is only necessary because the model is flawed. That discussion isn't really helping me solve the problem, but I think it's a part of the topic.

Another problem I am seeing is that even though the file accesses are asynchronous, the awaits in LoadData cause the LoadData method to be synchronous (don't they ?) and therefore the thread has to wait anyway for LoadData to complete, so what's the point. The initialize method in this case is synchronous, so all the asyncronous code in the world can't make the drive load data any faster.

I'm really not sure about this, because when I run the app, the GUI does come up and the model pops into existence when it's loaded. So it actually seems to be doing what I want. And if i remove the IsReady flag I get a few frames where the states and shaders aren't set yet. So it seems to be running asynchronously !

Q : does the LoadData call create it's own thread and does execution immediately continue ( in this case, returning from the Initialize method immediately ) while the LoadData method contiues on it's way ?

I'd like to know what patterns people are using to initialize models and resources asynchronously.

Thanks for any help or advice.  Gavin

### #3Gavin Williams

Posted 20 January 2013 - 10:53 PM

Hi,

I've started using async / await as I'm taking a look at WinRT. But Im having a terrible time getting to grips with async usage. Suddenly all of my objects have 3 'constructor' methods ...

public someModel(string modelAsText) // the constructor
: base(modelAsText, VertexElementTypes.Position, VertexElementTypes.Normal, VertexElementTypes.Texcoord)
{
// now often empty
}

public override void Initialize(DeviceManager devices) // called when graphics data needs to be loaded and bound to the device
{
// setup any programmatic/fast data
....
LoadData(devices) // calls the async method
}

{
...
IsReady = true; // flag indicating that all data is now loaded.
}

One thing that's starting to annoy me about async is that all my constructors are emptying. And all the construction code is having to be moved into the Initialize and async LoadData methods. I can't understand why a constructor can't be asynchronous. In my mind, it absolutely should be because like any object being constructed, it is immediately identfiable but isn't ready to be used until all its parts are in place. It seems to me that the language isn't designed correctly to handle this. I've read comments on the topic of async in constructors and I understand the reasoning .. early disposal causing leaks and object usage before its ready, but I would argue that the reasoning is only necessary because the model is flawed. That discussion isn't really helping me solve the problem, but I think it's a part of the topic.

Another problem I am seeing is that even though the file accesses are asynchronous, the awaits in LoadData cause the LoadData method to be synchronous (don't they ?) and therefore the thread has to wait anyway for LoadData to complete, so what's the point. The initialize method in this case is synchronous, so all the asyncronous code in the world can't make the drive load data any faster.

I'm really not sure about this, because when I run the app, the GUI does come up and the model pops into existence when it's loaded. So it actually seems to be doing what I want. And if i remove the IsReady flag I get a few frames where the states and shaders aren't set yet. So it seems to be running asynchronously !

Q : does the LoadData call create it's own thread and does execution immediately continue ( in this case, returning from the Initialize method immediately ) while the LoadData method contiues on it's way ?

I'd like to know what patterns people are using to initialize models and resources asynchronously.

Thanks for any help or advice.  Gavin

### #2Gavin Williams

Posted 20 January 2013 - 10:51 PM

Hi,

I've started using async / await as I'm taking a look at WinRT. But Im having a terrible time getting to grips with async usage. Suddenly all of my objects have 3 'constructor' methods ...

public someModel(string modelAsText) // the constructor
: base(modelAsText, VertexElementTypes.Position, VertexElementTypes.Normal, VertexElementTypes.Texcoord)
{
// now often empty
}

public override void Initialize(DeviceManager devices) // called when graphics data needs to be loaded and bound to the device
{
// setup any programmatic/fast data
....
LoadData(devices) // calls the async method
}

{
...
IsReady = true; // flag indicating that all data is now loaded.
}

One thing that's starting to annoy me about async is that all my constructors are emptying. And all the construction code is having to be moved into the Initialize and async LoadData methods. I can't understand why a constructor can't be asynchronous. In my mind, it absolutely should be because like any object being constructed, it is immediately identfiable but isn't ready to be used until all its parts are in place. It seems to me that the language isn't designed correctly to handle this. I've read comments on the topic of async in constructors and I understand the reasoning .. early disposal causing leaks and object usage before its ready, but I would argue that the reasoning is only necessary because the model is flawed. That discussion isn't really helping me solve the problem, but I think it's a part of the topic.

Another problem I am seeing is that even though the file accesses are asynchronous, the awaits in LoadData cause the LoadData method to be synchronous (don't they ?) and therefore the thread has to wait anyway for LoadData to complete, so what's the point. The initialize method in this case is synchronous, so all the asyncronous code in the world can't make the drive load data any faster.

I'm really not sure about this, because when I run the app, the GUI does come up and the model pops into existence when it's loaded. So it actually seems to be doing what I want. And if i remove the IsReady flag I get a few frames where the states and shaders aren't set yet. So it seems to be running asynchronously !

Q : does the LoadData call create it's own thread and does execution immediately continue ( in this case, returning from the Initialize method immediately ) while the LoadData method contiues on it's way ?

I'd like to know what patterns people are using to initialize models and resources asynchronously.

### #1Gavin Williams

Posted 20 January 2013 - 10:49 PM

Hi,

I've started using async / await as I'm taking a look at WinRT. But Im having a terrible time getting to grips with async usage. Suddenly all of my objects have 3 'constructor' methods ...

public someModel(string modelAsText) // the constructor
{
// now often empty
}

public override void Initialize(DeviceManager devices) // called when graphics data needs to be loaded and bound to the device
{
// setup any programmatic/fast data
....
LoadData(devices) // calls the async method
}

{
...
IsReady = true; // flag indicating that all data is now loaded.
}

One thing that's starting to annoy me about async is that all my constructors are emptying. And all the construction code is having to be moved into the Initialize and async LoadData methods. I can't understand why a constructor can't be asynchronous. In my mind, it absolutely should be because like any object being constructed, it is immediately identfiable but isn't ready to be used until all its parts are in place. It seems to me that the language isn't designed correctly to handle this. I've read comments on the topic of async in constructors and I understand the reasoning .. early disposal causing leaks and object usage before its ready, but I would argue that the reasoning is only necessary because the model is flawed. That discussion isn't really helping me solve the problem, but I think it's a part of the topic.

Another problem I am seeing is that even though the file accesses are asynchronous, the awaits in LoadData cause the LoadData method to be synchronous (don't they ?) and therefore the thread has to wait anyway for LoadData to complete, so what's the point. The initialize method in this case is synchronous, so all the asyncronous code in the world can't make the drive load data any faster.

I'm really not sure about this, because when I run the app, the GUI does come up and the model pops into existence when it's loaded. So it actually seems to be doing what I want. And if i remove the IsReady flag I get a few frames where the states and shaders aren't set yet. So it seems to be running asynchronously !

Q : does the LoadData call create it's own thread and does execution immediately continue ( in this case, returning from the Initialize method immediately ) while the LoadData method contiues on it's way ?

I'd like to know what patterns people are using to initialize models and resources asynchronously.

PARTNERS


text:
Home > Mean Square > Root Mean Square Error Vs Variance

# Root Mean Square Error Vs Variance

## Contents

By using this site, you agree to the Terms of Use and Privacy Policy. There are, however, some scenarios where mean squared error can serve as a good approximation to a loss function occurring naturally in an application.[6] Like variance, mean squared error has the New York: Springer-Verlag. Examples Mean Suppose we have a random sample of size n from a population, X 1 , … , X n {\displaystyle X_{1},\dots ,X_{n}} . useful reference

The RMSD serves to aggregate the magnitudes of the errors in predictions for various times into a single measure of predictive power. Shea Mean, Median, and Standard Deviation for Random Values Stephen Wolfram Descriptions of Univariate Data Chris Boucher Bayesian Distribution of Sample Mean Marshall Bradley ERROR The requested URL could not be Again, the quantity S = 8.641 (rounded to three decimal places here) is the square root of MSE. The estimate of σ2 shows up indirectly on Minitab's "fitted line plot." The quantity emphasized in the box, S = 8.64137, is the square root of MSE. https://en.wikipedia.org/wiki/Mean_squared_error

## Mean Square Error Example

Introduction to the Theory of Statistics (3rd ed.). They are negatively-oriented scores: Lower values are better. Online Integral Calculator» Solve integrals with Wolfram|Alpha. Compute the min, max, mean and standard deviation by hand, and verify that you get the same results as the applet.

A red vertical line is drawn from the x-axis to the minimum value of the MSE function. Click on "Next" above to continue this lesson. © 2004 The Pennsylvania State University. Recall that we assume that σ2 is the same for each of the subpopulations. Root Mean Square Error Interpretation Two or more statistical models may be compared using their MSEs as a measure of how well they explain a given set of observations: An unbiased estimator (estimated from a statistical

Koehler, Anne B.; Koehler (2006). "Another look at measures of forecast accuracy". Mean Square Error Formula Applications Minimizing MSE is a key criterion in selecting estimators: see minimum mean-square error. Are there other Pokemon with higher spawn rates right now? https://en.wikipedia.org/wiki/Mean_squared_error The best we can do is estimate it!

Submissions for the Netflix Prize were judged using the RMSD from the test dataset's undisclosed "true" values. Mean Square Error Definition Probability and Statistics (2nd ed.). Definition of an MSE differs according to whether one is describing an estimator or a predictor. Does WiFi traffic from one client to another travel via the access point?

## Mean Square Error Formula

Mean squared error is the negative of the expected value of one specific utility function, the quadratic utility function, which may not be the appropriate utility function to use under a The MSE can be written as the sum of the variance of the estimator and the squared bias of the estimator, providing a useful way to calculate the MSE and implying Mean Square Error Example The plot of our population of data suggests that the college entrance test scores for each subpopulation have equal variance. Root Mean Square Error Formula Retrieved 4 February 2015. ^ "FAQ: What is the coefficient of variation?".

Please try the request again. http://wapgw.org/mean-square/relationship-between-mean-square-error-variance.php In bioinformatics, the RMSD is the measure of the average distance between the atoms of superimposed proteins. The difference occurs because of randomness or because the estimator doesn't account for information that could produce a more accurate estimate.[1] The MSE is a measure of the quality of an Why should we care about σ2? Root Mean Square Error Example

Copyright © 2005-2014, talkstats.com Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index Interactive Entries In statistical modelling the MSE, representing the difference between the actual observations and the observation values predicted by the model, is used to determine the extent to which the model fits However, one can use other estimators for σ 2 {\displaystyle \sigma ^{2}} which are proportional to S n − 1 2 {\displaystyle S_{n-1}^{2}} , and an appropriate choice can always give this page Will we ever know this value σ2?

What does this mean? Root Mean Square Error Excel Note that, although the MSE (as defined in the present article) is not an unbiased estimator of the error variance, it is consistent, given the consistency of the predictor. In GIS, the RMSD is one measure used to assess the accuracy of spatial analysis and remote sensing.

## Princeton, NJ: Van Nostrand, pp.77-80, 1962.

so that ( n − 1 ) S n − 1 2 σ 2 ∼ χ n − 1 2 {\displaystyle {\frac {(n-1)S_{n-1}^{2}}{\sigma ^{2}}}\sim \chi _{n-1}^{2}} . Among unbiased estimators, minimizing the MSE is equivalent to minimizing the variance, and the estimator that does this is the minimum variance unbiased estimator. Predictor If Y ^ {\displaystyle {\hat Saved in parser cache with key enwiki:pcache:idhash:201816-0!*!0!!en!*!*!math=5 and timestamp 20161007125802 and revision id 741744824 9}} is a vector of n {\displaystyle n} predictions, and Y Mean Square Error Matlab MR0804611. ^ Sergio Bermejo, Joan Cabestany (2001) "Oriented principal component analysis for large margin classifiers", Neural Networks, 14 (10), 1447â€“1461.


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# Math Help - Slopes and graph questions

1. ## Slopes and graph questions

Find the direction in which a straight line must be drawn through the point (-1,2) so that it's point of intersection with the line x + y = 4 may be at a distance of 3 units from this point. Oh yeah I used graph , I'm getting a line parallel line to x- axis... How o solve this analyticaly...?

Can't solve this question du to too many unknown variables.... besides I dont think they are asking for perpendicular distance, be cause when I checked with the formula d = abs ( Ax1 + By1 + C)/SQRT(A^2 B^2)'whrer x1 = -1 , y1 = 2 ...

Q2 The hypotenuse of a right trianlge has its ends at the points (1,3) and (-4,1). Find te equaion of the legs ( perpendicular sides ) of this triangle.

I don't think there is a solution for both the legs because I feel that the hypotenuse can be considered asa diamter of a cirlce , and it subtends 90 degree at infinite points on it's circumference, but my textbook says the anser is x=1 , y=1 ... shouldnt we get a quadratic equation ??

Ice Sync

2. Originally Posted by ice_syncer
Find the direction in which a straight line must be drawn through the point (-1,2) so that it's point of intersection with the line x + y = 4 may be at a distance of 3 units from this point. Oh yeah I used graph , I'm getting a line parallel line to x- axis... How o solve this analyticaly...?

Can't solve this question du to too many unknown variables.... besides I dont think they are asking for perpendicular distance, be cause when I checked with the formula d = abs ( Ax1 + By1 + C)/SQRT(A^2 B^2)'whrer x1 = -1 , y1 = 2 ...

Q2 The hypotenuse of a right trianlge has its ends at the points (1,3) and (-4,1). Find te equaion of the legs ( perpendicular sides ) of this triangle.

I don't think there is a solution for both the legs because I feel that the hypotenuse can be considered asa diamter of a cirlce , and it subtends 90 degree at infinite points on it's circumference, but my textbook says the anser is x=1 , y=1 ... shouldnt we get a quadratic equation ??

Ice Sync

So the equatio of a circle with radius 3 centered at the point (-1,2) is

$(x+1)^2+(y-2)^2=9$ and we want to find its point of intersection with the line $x+y=4 \iff x=4-y$

So if we sub into the equation for the circle and factor we get

$(5-y)^2+(y-2)^2=9 \iff 2y^2-14y+20=0 \iff 2(y-2)(y-5)=0$

So we get $y=2 \mbox{ or } y=5$

Subbing each of these into the equation of the line we complete the ordered pairs to get the points

$(2,2)$ and $(-1,5)$

3. Originally Posted by TheEmptySet
So the equatio of a circle with radius 3 centered at the point (-1,2) is

$(x+1)^2+(y-2)^2=9$ and we want to find its point of intersection with the line $x+y=4 \iff x=4-y$

So if we sub into the equation for the circle and factor we get

$(5-y)^2+(y-2)^2=9 \iff 2y^2-14y+20=0 \iff 2(y-2)(y-5)=0$

So we get $y=2 \mbox{ or } y=5$

Subbing each of these into the equation of the line we complete the ordered pairs to get the points

$(2,2)$ and $(-1,5)$

Null Set,

well, nice idea, we weren't taught cirlce equation and all, but the qustion was.. what direction, not point of intersection.. so is the direction tan(135) ??

4. Originally Posted by ice_syncer
Null Set,

well, nice idea, we weren't taught cirlce equation and all, but the qustion was.. what direction, not point of intersection.. so is the direction tan(135) ??

If you know points of intersection how can you answer your question?

Hint: if you start at (-1,2) how do you get to the point (2,2).

If you cant see it draw a graph, and your answer is incorrect.

P.S if you use the distance forumla

$d=\sqrt{(x+1)^2+(y-2)^2}$ and set it equal to 3 and square it you get

$3=\sqrt{(x+1)^2+(y-2)^2} \iff 9=(x+1)^2+(y-2)^2$

And the solution follows just as above


text:
# MATHS BITE: Apéry’s Constant

Apéry’s constant is defined as the number

where ζ is the Riemann Zeta Function.

This constant is named after the French mathematician Roger Apéry who proved that it was irrational in 1978. However it is still unknown whether or not it is transcendental.

## History

In the 18th century, Leonhard Euler proved that in fact it did – to π^2/6. However, the limit of the following sum remained unknown:

Although mathematicians made some progress, including Euler who calculated the first 16 decimal digits of the sum, it was not known whether the number was rational or irrational, until Apéry.

Furthermore, it is currently not known specifically whether any other particular ζ(n), for n odd, is irrational. “The best we’ve got is from Wadim Zudilin, in 2001, who showed that at least one of ζ(5), ζ(7), ζ(9), ζ(11) must be irrational, and Tanguy Rivoal, in 2000, who showed that infinitely many of the ζ(2k+1) must be irrational.”

M x

# MATHS BITE: Dini’s Surface

Dini’s surface, named after Ulisse Dini, is a surface with constant negative curvature that can be created by twisting a pseudosphere (see picture below).

Pseudosphere

Dini’s surface is given by the following parametric equations:

Dini’s Surface

Dini’s surface is pictured in the upper right-hand corner of a book by Alfred Gray (1997), as well as on the cover of volume 2, number 3 of La Gaceta de la Real Sociedad Matemática Española (1999).

M x

# MATHS BITE: The Beginning of Chaos

In 1887, King Oscar II of Norway and Sweden offered a prize for the solution of the following maths problem:

Say you have a number of celestial bodies with known mass and you know the speed and direction they are moving in at some given point in time. Use Newton’s laws of motion and the universal law of gravitation to calculate the trajectories of the bodies.

After three years, the French mathematician Henri Poincaré, who restricted himself to the case where there are just three bodies, won the prize.

However, after winning the prize, Poincaré noticed a flaw in his solution putting him in an embarrassing position, as his manuscript was to be published for the King’s birthday within a few weeks’ time!

In his attempt to correct his work, Poincaré discovered that even this simple problem suffered from the Butterfly Effect: “sensitive dependence on initial conditions“. This means that the smallest variation in the initial values can build up over time to create massive discrepancies in the trajectories. Hence, you cannot reliably predict the motion of planets over time, as you can’t know the initial values with an infinite degree of accuracy.

With this discovery, Poincaré laid the foundations for Chaos theory.

M x

# MATHS BITE: The Cantor Set

The Cantor Set is constructed in the following way:

Start with the interval [0,1]. Next, remove the open middle third interval, which gives you two line segments [0,1/3] and [2/3,1]. Again, remove the middle third for each remaining interval, which leaves you now with 4 intervals. Repeat this final step ad infinitum.

The points in [0,1] that do not eventually get removed in the procedure form the Cantor set.

#### How many points are there in the Cantor Set?

Consider the diagram below:

An interval from each step has been coloured in red, and each red interval (apart from the top one) lies underneath another red interval. This nested sequence shrinks down to a point, which is contained in every one of the red intervals, and hence is a member of the Cantor set. In fact, each point in the Cantor set corresponds to a unique infinite sequence of nested intervals.

To label a point in the Cantor set according to the path of red intervals that is taken to reach it, label each point by an infinite sequence consisting of 0s and 1s.

A 0 in the nth position symbolises that the point lies in the left hand interval after the nth stage in the Cantor process.

A in the nth position symbolises that the point lies in the right hand interval after the nth stage in the Cantor process.

For example, the point 0 in [0,1] is represented by the sequence 0000…., the point 1 is represented by the sequence 1111…. and the point 1/3 is represented by the sequence 01111….

So, as there are infinite sequences consisting of 0s and 1s, there are an infinite number of elements in the Cantor set. If we place a point before any one of these infinite sequences, for example 0100010… becomes .0100010…, then we convert an infinite sequence of 0s and 1s to the binary expansion of a real number between 0 and 1. This means that the number of points in the Cantor set is the same as the number of points in the interval [0,1]. We conclude that the infinite process of removing middle thirds from the interval [0,1] has no effect on the number of points in [0,1]!

M x

# MATHS BITE: Leyland Numbers

A Leyland number is an integer of the form , where x and y are integers greater than 1. This condition is very important as, without it, every positive integer would be a Leyland number of the form x1 + 1x.

They are named after Paul Leyland, a British number theorist who studied the factorisation of integers and primality testing.

Leyland numbers are of interest as some of them are very large primes.

### Leyland Primes

A Leyland prime is a Leyland number that is also prime. The first of such primes are:

17, 593, 32993, 2097593, 8589935681, 59604644783353249, 523347633027360537213687137, 43143988327398957279342419750374600193, …

which correspond to:

32+23, 92+29, 152+215, 212+221, 332+233, 245+524, 563+356, 3215+1532, …

The largest known Leyland prime is .

M x

# MATHS BITE: Catenary

A Catenary is the idealised shape created when you suspend a chain by its ends and let it hang naturally under its own weight. Any hanging chain will naturally find its equilibrium as the forces of tension from the hooks holding the chain up and the force of gravity pulling it downwards balance out.

Robert Hooke was the first to study the catenary mathematically; in 1675 he announced that he had solved the problem of the optimal shape of an arch by publishing the solution as an encrypted anagram: “As hangs the flexible line, so but inverted will stand the rigid arch.”

Its equation was obtained in 1691 by Leibniz, Huygens and Johann Bernoulli in response to a challenge put out by Jacob Bernoulli to find the equation of the ‘chain-curve’. The curve has a U-like shape and although it is similar in appearance to a parabola, it is not quite a parabola.

Source: IntMath

The equation of the catenary is

Catenaries for different values of a | Source: Wikipedia

In 1744, Euler proved that the catenary is the curve which gives the surface of minimum surface area for the given bounding circles when rotated about the x-axis.

M x


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# ResNet50 Model is not learning with transfer learning in keras

I am trying to perform transfer learning on ResNet50 model pretrained on Imagenet weights for PASCAL VOC 2012 dataset. As it is a multi label dataset, I am using sigmoid activation function in the final layer and binary_crossentropy loss. The metrics are precision,recall and accuracy. Below is the code I used to build the model for 20 classes (PASCAL VOC has 20 classes).

img_height,img_width = 128,128
num_classes = 20
#If imagenet weights are being loaded,
#input must have a static square shape (one of (128, 128), (160, 160), (192, 192), or (224, 224))
base_model = applications.resnet50.ResNet50(weights= 'imagenet', include_top=False, input_shape= (img_height,img_width,3))
x = base_model.output
x = GlobalAveragePooling2D()(x)
#x = Dropout(0.7)(x)
predictions = Dense(num_classes, activation= 'sigmoid')(x)
model = Model(inputs = base_model.input, outputs = predictions)
for layer in model.layers[-2:]:
layer.trainable=True
for layer in model.layers[:-3]:
layer.trainable=False

#print(model.summary())

X_train, X_test, Y_train, Y_test = train_test_split(x_train, y, random_state=42, test_size=0.2)
savingcheckpoint = ModelCheckpoint('ResnetTL.h5',monitor='val_loss',verbose=1,save_best_only=True,mode='min')
earlystopcheckpoint = EarlyStopping(monitor='val_loss',patience=10,verbose=1,mode='min',restore_best_weights=True)
model.fit(X_train, Y_train, epochs=epochs, validation_data=(X_test,Y_test), batch_size=batch_size,callbacks=[savingcheckpoint,earlystopcheckpoint],shuffle=True)
model.save_weights('ResnetTLweights.h5')

It ran for 35 epochs until earlystopping and the metrics are as follows (without Dropout layer):

loss: 0.1195 - accuracy: 0.9551 - precision_m: 0.8200 - recall_m: 0.5420 - val_loss: 0.3535 - val_accuracy: 0.8358 - val_precision_m: 0.0583 - val_recall_m: 0.0757

Even with Dropout layer, I don't see much difference.

loss: 0.1584 - accuracy: 0.9428 - precision_m: 0.7212 - recall_m: 0.4333 - val_loss: 0.3508 - val_accuracy: 0.8783 - val_precision_m: 0.0595 - val_recall_m: 0.0403

With dropout, for a few epochs, the model is reaching to a validation precision and accuracy of 0.2 but not above that.

I see that precision and recall of validation set is pretty low compared to training set with and without dropout layer. How should I interpret this? Does this mean the model is overfitting. If so, what should I do? As of now the model predictions are quite random (totally incorrect). The dataset size is 11000 images.

• your high validation accuracy and low validation precision show that your validation data is skewed. Please add validation and test data class distribution. – shivam shah Oct 15 '19 at 9:17


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# Formula Technique 16 (Boat or Swimmer in Stream)

Let speed of boat is V and speed of stream is U;

1- If swimmer goes down stream then his speed id U+V

2- If swimmer goes up stream his speed is V-U

If speed of a swimmer down stream is Ds and speed upstream is Us, then in still water (negligible or slow flow of water);

1- Speed of swimmer = 1/2(Ds+Us) {i-e his average speed)

2- Speed (relative or w.r.t the swimmer) of stream = 1/2 (Ds-Us) (average of vector sum)

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All original content on these pages is fingerprinted and certified by Digiprove
Insert math as
$${}$$


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Question:

#### Mitigating Circumstances: What shall I do if I missed the assignment submission deadline?

(Last edited: Thursday, 28 October 2021, 3:46 PM)


text:
Regularity of the free boundary for the two-phase Bernoulli problem
Abstract We prove a regularity theorem for the free boundary of minimizers of the two-phase Bernoulli problem, completing the analysis started by Alt, Caffarelli and Friedman in the 80s. As a consequence, we also show regularity of minimizers of the multiphase spectral optimization problem for the principal eigenvalue of the Dirichlet Laplacian.
Authors:
; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10283057
Journal Name:
Inventiones mathematicae
Volume:
225
Issue:
2
Page Range or eLocation-ID:
347 to 394
ISSN:
0020-9910
3. Abstract We study optimal regularity and free boundary for minimizers of an energy functional arising in cohesive zone models for fracture mechanics. Under smoothness assumptions on the boundary conditions and on the fracture energy density, we show that minimizers are $$C^{1, 1/2}$$ C 1 , 1 / 2 , and that near non-degenerate points the fracture set is $$C^{1, \alpha }$$ C 1 , α , for some $$\alpha \in (0, 1)$$ α ∈ ( 0 , 1 ) .


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# Recursion

Consider unbounded H-tone spread to penult.

$\begin{array}[t]{lcl} \acute{\sigma}\sigma\sigma & \mapsto & \acute{\sigma}\acute{\sigma}\sigma \\ \sigma\acute{\sigma}\sigma\sigma\sigma\sigma & \mapsto & \sigma\acute{\sigma}\acute{\sigma}\acute{\sigma}\acute{\sigma}\sigma \\ \sigma\sigma\acute{\sigma}\sigma\sigma\sigma & \mapsto & \sigma\sigma\acute{\sigma}\acute{\sigma}\acute{\sigma}\sigma \\ \sigma\acute{\sigma}\sigma\sigma\sigma\sigma\sigma & \mapsto & \sigma\acute{\sigma}\acute{\sigma}\acute{\sigma}\acute{\sigma}\acute{\sigma}\acute{\sigma}\sigma \\ \mathrm{etc.} \end{array}$

This is an output-oriented process. That is, whether a syllable is H-toned depends on the output tonal value of the preceding syllable.

Let $$\acute{\sigma}_i(x)$$ represent the input contrast between H and non-H syllables, and $$\acute{\sigma}_o(x)$$ representing the same in the output, we can do this explicitly in BMRS using a recursive definition of $$\acute{\sigma}_o(x)$$.

The below is a first approximation, although it is a bit wrong.

$\acute{\sigma}_o(x):= \mathtt{if}~\acute{\sigma}_o(p(x))~\mathtt{then}~\top~\mathtt{else}~\acute{\sigma}_i(x)$

This works as shown below:

$\begin{array}[t]{rccccccc} \mathrm{in:} & \sigma & \acute{\sigma} & \sigma & \sigma & \sigma & \sigma \\ \acute{\sigma}_i(x) & \bot & \top & \bot & \bot & \bot & \bot \\ \acute{\sigma}_o(x) & \bot & \top & \top & \top & \top & ^*\top \\ \mathrm{out:} & \sigma & \acute{\sigma} & \acute{\sigma} & \acute{\sigma} & \acute{\sigma} & \acute{\sigma} \\ \end{array}$

The H tone spreads leftward all the way to the final syllable, as indicated by $$^*\top$$. So we preempt this in the case that $$x$$ is the final syllable:

$\acute{\sigma}_o(x):= \begin{array}[t]{l} \mathtt{if}~\mathrm{final}(x)~\mathtt{then}~\bot~\mathtt{else}\\ \mathtt{if}~\acute{\sigma}_o(p(x))~\mathtt{then}~\top~\mathtt{else}\\ \acute{\sigma}_i(x) \end{array}$

In this way, $$\mathrm{final}(x)$$ acts like a higher-ranking constraint, blocking the spread of the H tone only in the final syllable:

$\begin{array}[t]{rccccccc} \mathrm{in:} & \sigma & \acute{\sigma} & \sigma & \sigma & \sigma & \sigma \\ \acute{\sigma}_i(x) & \bot & \top & \bot & \bot & \bot & \bot \\ \acute{\sigma}_o(x) & \bot & \top & \top & \top & \top & \bot \\ \mathrm{out:} & \sigma & \acute{\sigma} & \acute{\sigma} & \acute{\sigma} & \acute{\sigma} & \sigma \\ \end{array}$


text:
2017
Том 69
№ 9

# Konsevich N. M.

Articles: 1
Article (Ukrainian)

### Best Orthogonal Trigonometric Approximations of Classes of Functions of Many Variables $L^{ψ}_{β, p}$

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 23-29

We obtain order estimates for the best orthogonal trigonometric approximations of classes of functions of many variables L β, p ψ in the space L q, 1 < p < q < ∞, q > 2.


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# Veitch diagram draw with TikZ [duplicate]

How can I make the same diagram like this in LaTeX?

I see that i could use package karnaugh but i don´t like placement of x.

## marked as duplicate by Red, Benedikt Bauer, Andrew Swann, henrique, Claudio FiandrinoOct 25 '13 at 12:32

• Is there any chance to create the same diagram in latex without package karnaugh. – Luka Toni Oct 20 '13 at 13:53

Use package karnaugh.

\documentclass{article}
\input{kvmacros}

\begin{document}
\karnaughmap{4}{$F(x_1,x_2,x_3,x_4)=$}{{$x_1$}{$x_2$}{$x_3$}{$x_4$}}{1111100100011011}{}
\end{document}

You can also draw this stuff with TikZ:

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw (0,0) grid (4,4);
\node at (.5,.5){1};
\node at (3.5,.5){1};
\node at (1.5,1.5){1};
\node at (1.5,3.5){1};
\node at (3.5,3.5){1};
\draw (0,4.3) --node[midway, above]{$x_1$} (2,4.3);
\draw (-0.3,4) --node[midway, left]{$x_2$} (-0.3,2);
\draw (1,-0.3) --node[midway, below]{$x_3$} (3,-0.3);
\draw (4.3,1) --node[midway, right]{$x_4$} (4.3,3);
\end{tikzpicture}
\end{document}

You could also use a picture environment like the karnaugh package does internally, or PSTricks, or any other lesser-known LaTeX graphics environment since the drawing required by a Karnaugh map is very simple.

• is it possible to change a possition of x ? – Luka Toni Oct 20 '13 at 10:32
• @LukaToni I don't think so. – marczellm Oct 20 '13 at 11:32


text:
Difficult Bar Charts Solved QuestionData Interpretation Discussion

Common Information

Many Asian countries including China, Japan, Kazakhstan, India, Singapore, Malaysia and Jordon participated in one or more sporting events held at the 2006 Asian Games. In each sporting event at least three countries participated.

At the end of each sporting event, the country finishing at the first, the second and the third positions were awarded a gold, a silver and a bronze medal respectively. The following bar graph shows distribution of the three types of medals.

In this graph, the parts marked by "Data Not Available" may have belonged to one or more of all the participating countries.

 Q. Common Information Question: 2/4 What was the ratio of the number of gold medals won by Singapore to the number of silver medals won by Jordon ?
 ✖ A. 21 : 31 ✖ B. 4 : 5 ✖ C. 31 : 33 ✔ D. 29 : 31 ✖ E. Cannot be determined

Solution:
Option(D) is correct

At the end of each event exactly one each of gold, silver and bronze medals were awarded hence the total number of gold or silver or bronze medals must be the same.

Let there be $N$ number each of gold, silver and bronze medals.

Number of gold medals won by Singapore:

$= \dfrac{29N}{200}$

Number of Silver medals won by Jordon:

$=\dfrac{31N}{200}$

Hence the required ratio is $29:31$


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# Convert binary (integer and a fraction) from vhdl to decimal in C code, negative value

Status
Not open for further replies.

#### wannaknow

##### Junior Member level 2
Convert binary ( integer and fraction) from vhdl to decimal in C code,negative value

HI,

I have a 14-bit data that is fed from FPGA in vhdl, The NIos II processor reads the 14-bit data from FPGA and do some processing tasks, where Nios II system is programmed in C code

The 14-bit data can be positive, zero or negative. In Altera compiler, I can only define the data to be 8,16 or 32. So I define this to be 16 bit data.

First, I need to check if the data is negative, if it is negative, I need to pad the first two MSB to be bit '1' so the system detects it as negative value instead of positive value.

Second, I need to compute the real value of this binary representation into a decimal value of BOTH integer and fraction.

I learned from this link (https://stackoverflow.com/questions...ary-floating-point-1101-11-into-decimal-13-75) that I could convert a binary (consists of both integer and fraction) to decimal values.

I am wondering if this code can be used to check for negative value? I did try with a binary string of 11111101.11 and it gives the output of 253.75...

I have two questions:

What are the modifications I need to do in order to read a negative value?
I know that I can do the bit shift (as below) to check if the msb is 1, if it is 1, I know it is negative value...

Code:
if (14bit_data & 0x2000) //if true, it is negative value

The issue is, since it involves fraction part (but not only integer), it confused me a bit if the method still works...

If the binary number is originally not in string format, is there any way I could convert it to string? The binary number is originally fed from a fpga block say, 14 bits, with msb as the sign bit, the following 6 bits are the magnitude for integer and the last 6 bits are the magnitude for fractional part.

Last edited:

#### wannaknow

##### Junior Member level 2
How to read a 16-bit data into string in C code

I have a 16-bit data that is fed from FPGA in vhdl, the NIos II processor reads the 16-bit data from FPGA and do some processing tasks, where Nios II system is programmed in C code

How could I read this 16-bit data in string?

Code:
printf("%d", 16_bit_data);
// it shows a decimal value of 15282

What should I do in order to get the result displayed as a string 0011101110110010?

Last edited:

#### xenos

##### Full Member level 4
Re: How to read a 16-bit data into string in C code

Translate to hex (sprintf("%04x",v)) and then translate each hex digit to binary, or use something like the function

#### wannaknow

##### Junior Member level 2
Re: How to read a 16-bit data into string in C code

Translate to hex (sprintf("%04x",v)) and then translate each hex digit to binary, or use something like the function

Thanks for your reply, forgive me for didnt make it clear enough.

I need to compute the real value of this binary representation into a decimal value of BOTH integer and fraction, for example, the value is 15282 (0011 1011 1011 0010), but it is not the real value, how to make sure I will get the value as -30.750015?

The 14-bit-data is defined as follow: with msb as the sign bit, the following 6 bits are the magnitude for integer and the last 6 bits are the magnitude for fractional part.

#### FvM

##### Super Moderator
Staff member

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