text: Others, like the plus, minus, times, and division symbols seem to be mere notations on a paper. DATA : WA_MARA TYPE MARA. It only takes a minute to sign up. ◻ It is a generalization of the well-known length, area and volume. Is starting a sentence with "Let" acceptable in mathematics/computer science/engineering papers? The Lebesgue measure seems like what your'e looking for. , N To achieve that, there exists a global symbol registry. The blackboard bold typeface is widely used for denoting the basic number systems. They can be displayed as Unicode characters, or in LaTeX format. Symbol Symbol Name Meaning / definition Example { } set: a collection of elements: A = {3,7,9,14}, B = {9,14,28} A ∩ B: intersection: objects that belong to set A and set B: A ∩ B = {9,14} A ∪ B: union: objects that belong to set A or set B: A ∪ B = {3,7,9,14,28} A ⊆ B: subset: A is a subset of B. set A is included in set B. The square function has many uses in geometry. Why is this symbol used to represent pi? square meter, as $m^2$? Some Unicode charts of mathematical operators and symbols: This article is in course of a major restructuring. In order to read (create if absent) a symbol from the registry, use Symbol.for(key). … site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. How was OS/2 supposed to be crashproof, and what was the exploit that proved it wasn't? , Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. area (A): Area (symbolized A ) is a two-dimensional quantity representing amount or extent of surface. These systems are often denoted also by the corresponding uppercase bold letter. This follows from the equation for the area of a rectangle (and parallelograms more generally) where A = l×w. Is my Connection is really encrypted through vpn? B It is impossible to label every single feature in words on a map, therefore we use map symbols. , Should one declare the specific meaning (eg: n = 2) or is that implied from the argument of m (ABCD seemingly representing a surface)? Letters are not sufficient for the need of mathematicians, and many other symbols are used. What are these capped, metal pipes in our yard? in combinatorics, one should immediately know that this denotes the real numbers, although combinatorics does not study the real numbers (but it uses them for many proofs). For this reason, in the entry titles, the symbol □ is used for schematizing the syntax that underlies the meaning. A measure of spread or variation of a set of values in a sample population set. is used for representing the neighboring parts of a formula that contains the symbol. Making statements based on opinion; back them up with references or personal experience. Lynn Atchison Beech Rate this symbol: (3.00 / 4 votes) To get you some ideas, you could use, for example: If you won't use other measures like lenght or volume, you can skip the "2" symbol or the double brackets. On the other hand, the last sections contain symbols that are specific to some area of mathematics and are ignored outside these areas. Reference Request: Regge Symmetry “Angle-Edge” Duality. Symbols save time and space when writing. Further information may be obtained from cursor enquiry of the query Q80 H40-43 M27.2 Limit between area of unoffi cial vector data Is there a symbol to represent the area of a given shape? For having more symbols, other typefaces are also used, mainly boldface , Example of using field symbol as work area In the below example we are going to use field symbol as work area. You will also have come across the symbol, π, in math, physics, and science classes. Understanding surface roughness symbols. The most basic symbols are the decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and the letters of the Latin alphabet. IF … The definition of a symbol is something that stands for or represents something else. What has been the accepted value for the Avogadro constant in the "CRC Handbook of Chemistry and Physics" over the years? (Sorry if this question is out of place; new here) This section will explain how to write these symbols to indicate surface textures. A Proportional symbol map is a type of Thematic map that uses map symbols that vary in size to represent a quantitative variable. Contour lines are indicators of elevation and are usually brown. The decimal digits are used for representing numbers through the Hindu–Arabic numeral system. The symbol is m 2 Example: A typical car parking space is about 12 square meters. Mass. Some were used in classical logic for indicating the logical dependence between sentences written in plain English. R a {\displaystyle \forall .}. , A mathematical notation is a writing system used for recording concepts in mathematics.. Typographical conventions and common meanings of symbols: This page was last edited on 22 December 2020, at 09:29. Can a smartphone light meter app be used for 120 format cameras? (the lower-case script face is rarely used because of the possible confusion with the standard face), German fraktur A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. Mathematical Symbols. This allows using them in any area of mathematics, without having to recall their definition. Notation for meta-variable or placeholder variable. (so for a shape defined by points $A,B,C,D$; I could represent the area as *symbol* $ABCD$ or something to that effect). For example, discs may be used to show the location of cities within the map where the size of the disc is proportional to the population of the city. b I'm not looking for a variable to contain the area, like $A$, but a representation for a given shape. $\langle \triangle ABC \rangle$, $\langle\!\langle \triangle ABC \rangle\!\rangle$. In mathematical formulas, the standard typeface is italic type for Latin letters and lower-case Greek letters, and upright type for upper case Greek letters. Description & Examples: Maps show features in a plan view as birds see it from above. MathJax reference. The internationally standardized symbols are intended to communicate their function in a language-independent manner. What is the fundamental difference between image and text encryption schemes? A green dragon, for example, is an excellent feng shui cure for the East - health feng shui area - of your home, while a golden dragon can be a great feng shui cure for wealth and abundance. Use MathJax to format equations. Finally, when there is an article on the symbol itself (not its mathematical meaning), it is linked to in the entry name. As the number of these sorts has dramatically increased in modern mathematics, the Greek alphabet and some Hebrew letters are also used. Historically, upper-case letters were used for representing points in geometry, and lower-case letters were used for variables and constants. That is, the first sections contain the symbols that are encountered in most mathematical texts, and that are supposed to be known even by beginners. To learn more, see our tips on writing great answers. [citation needed] It is defined as the area of a square with sides of 1 foot. EC identification and health marks, for animal products; Food safe symbol marking food contact … So, for finding how to type a symbol in LaTeX, it suffices to look at the source of the article. {\displaystyle \in } The average roughness is … Although you can use symbolism tools on individual symbol instances, they are most effective when used on symbol sets. B Field Symbol: A field symbol (in SAP) is a mechanism in which applications are created with flexibility. . {\displaystyle \mathbb {R} } So there's a bit of abuse of notation involved. A clear advantage of blackboard bold, is that these symbols cannot be confused with anything else. Should the helicopter be washed after any sea mission? Terminology explanation Letters are used for representing many other sort of mathematical objects. Symbol definition, something used for or regarded as representing something else; a material object representing something, often something immaterial; emblem, token, or sign. The standard unit of area in the International System of Units ( SI ) is the meter squared (m 2 ). The dragon symbol is an auspicious traditional feng shui cure and a powerful symbol of strong yang/male energy. For symbols that are used only in mathematical logic, or are rarely used, see List of logic symbols. Symbol. The use of pi is dated back to the Babylonians about 4,000 years ago with calculations for the area of a circle. Chemeketa Community College faculty affirm that the most common map symbols include contour lines, buildings, water features, and forests and clearings. Some take their origin in punctuation marks and diacritics traditionally used in typography. … Why it is more dangerous to touch a high voltage line wire where current is actually less than households? About the symbol signs This system of 50 symbol signs was designed for use at the crossroads of modern life: in airports and other transportation hubs and at large international events. When the meaning depends on the syntax, a symbol may have different entries depending on the syntax. A power symbol is a symbol indicating that a control activates or deactivates a particular device. Most symbols have two printed versions. Map symbols generally convey the appearance (shape and dimensions), location, and certain qualitative and quantitative characteristics of the objects, contours, and relief elements shown on … For the area of the shape ABCD, you could write $m(ABCD)$. This is not possible here, as there is no natural order on symbols, and many symbols are used in different parts of mathematics with different meanings, often completely unrelated. The tables will be replaced by, Abbreviation of English phrases and logical punctuation, Talk:List of mathematical symbols#WP:TNT must be applied to this article, Wreath product § Notation and conventions, Big O notation § Related asymptotic notations, Mathematical Alphanumeric Symbols (Unicode block), Table of mathematical symbols by introduction date, Mathematical operators and symbols in Unicode, Greek letters used in mathematics, science, and engineering, List of letters used in mathematics and science, Typographical conventions in mathematical formulae, Detexify: LaTeX Handwriting Recognition Tool, Range 2100–214F: Unicode Letterlike Symbols, Range 2200–22FF: Unicode Mathematical Operators, Range 27C0–27EF: Unicode Miscellaneous Mathematical Symbols–A, Range 2980–29FF: Unicode Miscellaneous Mathematical Symbols–B, Range 2A00–2AFF: Unicode Supplementary Mathematical Operators, Short list of commonly used LaTeX symbols, https://en.wikipedia.org/w/index.php?title=List_of_mathematical_symbols&oldid=995683325, Short description is different from Wikidata, Articles with unsourced statements from November 2020, Pages that use a deprecated format of the math tags, Creative Commons Attribution-ShareAlike License, The Laplace operator is a second order differential operator in n-dimensional. The set A B is represented by the hatched region. … The new symbol has been designed to convey the message "Danger — Stay Away" to anyone who sees it, regardless of their age, education, or cultural background. A So, for searching the entry of a symbol, it suffices to type or copy the unicode symbol in the search window. ; In the history of mathematics, these symbols have denoted numbers, shapes, patterns and change.The notation can also include symbols for parts of the conventional discourse between mathematicians, … By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. {\displaystyle {\mathcal {A,B}},\ldots } Symbols that indicate the surface texture of machined and structural parts are used in industrial diagrams. Symbols vary in height, length, area, or volume from place to place depending on the variable that they represent. (so for a shape defined by points A, B, C, D; I could represent the area as *symbol* A B C D or something to that effect) I'm not looking for a variable to contain the area, like A, but a representation for a given shape. The area equal to a square that is 1 meter on each side. The Key is essential since it contains what each symbol on the map stands for. For summarizing the syntax in the entry name, the symbol The square metre (international spelling as used by the International Bureau of Weights and Measures) or square meter (American spelling) is the SI derived unit of area with symbol m2. , , Graphically, the average roughness is the area between the roughness profile and its center line divided by the evaluation length (normally five sample lengths with each sample length equal to one cutoff). As a popular feng shui cure, dragons come in many sizes and variations of materials and color. (the other letters are rarely used in this face, or their use is controversial). List of mathematical symbols (Unicode and LaTeX). The pictorial representation using these symbols is defined in ISO 1302:2002. We can create symbols in it and access them later, and it guarantees that repeated accesses by the same name return exactly the same symbol. The intersection symbol ( ) denotes the intersection of two set s. It is commonly used in mathematics and engineering. The average roughness is the area between the roughness profile and its mean line, or the integral of the absolute value of the roughness profile height over the evaluation length. FIELD-SYMBOLS : TYPE MARA. When an entry name contains special characters such as [, ], and |, there is also an anchor, but one has to look at the article source to know it. Z The diagram below illustrates set intersection. Most … DATA : IT_MARA TYPE TABLE OF MARA. With the Unicode version, using search engines and copy-pasting are easier. . Thanks! Is binomial(n, p) family be both full and curved as n fixed? Linear position Similarly, when possible, the entry name of a symbol is also an anchor, which allows linking easily from another Wikipedia article. {\displaystyle {\mathfrak {a,A,b,B}},\ldots ,} ∈ C What is the reason behind writing the symbol for the unit of area i.e. , This symbol indicates, that the device is currently connected to a mobile network and visualizes the strength of the signal (relative as bars). Therefore, in this article, the Unicode version of the symbols is used (when possible) for labelling their entry, and the LaTex version is used in their description. SELECT * FROM MARA INTO TABLE IT_MARA UP TO 50 ROWS. (was also uncertain about tag). Power On (IEC 60417-5007) and Power Off (IEC 60417 … and blackboard bold script typeface Definition. Comparison of 1 square metre with some Imperial and metric units of area Given two sets A and B, the intersection of A and B, written A B, is the set C of all elements that are in both A and B. Physical Quantity. See § Brackets for examples of use. What architectural tricks can I use to add a hidden floor to a building? Such symbols may be drawings, letters, lines, shortened words or coloured areas. Name. The device is connected to another mobile network, but not to the one of your operator, and uses … Used for measuring areas of rooms, houses, blocks of land, etc. , A mathematical symbol is a figure or a combination of figures that is used to represent a … Unit. Whatever notation you use, define it, and everything should be fine. The Wild Area is an integral part of Pokémon Sword and Shield since it houses many of the creatures that you can find in the game.. It seems fairly general. Every map is accompanied by a legend or key. And then one would expect $ABCD$ to denote the set we want to find the area of. Sets A and B are denoted as circles (including their interiors). And, they have true value in real life. For these uses, see Variable (mathematics) and List of mathematical constants. Yet, symbols in math are essentially the instructions that drive this area of academics. {\displaystyle \mathbb {N,Z,R,C} } , If you want to talk about two dimensional shapes in the plane, you should say "the two-dimensional Lebesgue measure". It is a commonly known fact that the area of a square with sides of length n is equal to n 2. IAEA has said the following about the new warning symbol: It is intended for IAEA Category 1, 2, and 3 sources defined as dangerous sources capable of causing death or serious injury, such as food irradiators, teletherapy machines for cancer … The article is split in sections that are sorted by increasing level of technicality. A In other words, there's not really a. ft, sf, or ft 2; also denoted by ' 2) is an imperial unit and U.S. customary unit (non-SI, non-metric) of area, used mainly in the United States and partially in Canada, the United Kingdom, Bangladesh, India, Nepal, Pakistan, Ghana, Liberia, Malaysia, Myanmar, Singapore and Hong Kong. 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# Experiment¶

It is the responsibility of the user to define their own experiment structure. The usual definition will describe the sample of interest, the instrument configuration, and the measured data, and will provide a theory function which computes the expected data given the sample and instrument parameters. The theory function frequently has a physics component for computing the ideal data given the sample and an instrument effects component which computes the expected data from the ideal data. Together, sample, instrument, and theory function define the fitting model which needs to match the data.

The curve fitting problem can be expressed as:

$P(\text{model}\ |\ \text{data}) = {P(\text{data}\ |\ \text{model})P(\text{model}) \over P(\text{data})}$

That is, the probability of seeing a particular set of model parameter values given the observed data depends on the probability of seeing the measured data given a proposed set of parameter values scaled by the probability of those parameter values and the probability of that data being measured. The experiment definition must return the negative log likelihood as computed using the expression on the right. Bumps will explore the space of the sample and instrument parameters in the model, returning the maximum likelihood and confidence intervals on the parameters.

There is a strong relationship between the usual $$\chi^2$$ optimization problem and the maximum likelihood problem. Given Gaussian uncertainty for data measurements, we find that data $$y_i$$ measured with uncertainty $$\sigma_i$$ will be observed for sample parameters $$p$$ when the instrument is at position $$x_i$$ with probability

$P(y_i\ |\ f(x_i;p)) = \frac{1}{\sqrt{2\pi\sigma_i^2}} \exp\left(-\frac{(y_i-f(x_i;p))^2}{2\sigma_i^2}\right)$

The negative log likelihood of observing all points in the data set for the given set of sample parameters is

$-\log \prod_i{P(y_i\ |\ f(x_i;p))} = \tfrac12 \sum_i{\frac{(y_i-f(x_i;p))^2}{\sigma_i^2}} - \tfrac12 \sum_i{\log 2 \pi \sigma_i^2} = \tfrac12 \chi^2 + C$

Note that this is the unnormalized $$\chi^2$$, whose expected value is the number of degrees of freedom in the model, not the reduced $$\chi^2_R$$ whose expected value is $$1$$. The Bumps fitting process is not sensitive to the constant $$C$$ and it can be safely ignored.

Casting the problem as a log likelihood problem rather than $$\chi^2$$ provides several advantages. We can support a richer set of measurement techniques whose uncertainties do not follow a Gaussian distribution. For example, if we have a Poisson process with a low count rate, the likelihood function will be asymmetric, and a gaussian fit will tend to overestimate the rate. Furthermore, we can properly handle background rates since we can easily compute the probability of seeing the observed number of counts given the proposed signal plus background rate. Gaussian modeling can lead to negative rates for signal or background, which is fundamentally wrong. See Simple functions for a demonstration of this effect.

We can systematically incorporate prior information into our models, such as uncertainty in instrument configuration. For example, if our sample angle control motor position follows a Gaussian distribution with a target position of 3° and an uncertainty of 0.2°, we can set

$-\log P(\text{model}) = -\frac{1}{2} \frac{(\theta-3)^2}{0.2^2}$

ignoring the scaling constant as before, and add this to $$\tfrac12\chi^2$$ to get log of the product of the uncertainties. Similarly, if we know that our sample should have a thickness of 100 ± 3.5 Å based on how we constructed the sample, we can incorporate this information into our model in the same way.

## Simple experiments¶

The simplest experiment is defined by a python function which takes a list of instrument configuration and has arguments defining the parameters. For example, to fit a line you would need:

def line(x, m, b):
return m*x + b

Assuming the data was in a 3 column ascii file with x, y and uncertainty, you would turn this into a bumps model file using:

# 3 column data file with x, y and uncertainty
M = Curve(line, x, y, dy)

Using the magic of python introspection, Curve is able to determine the names of the fittable parameters from the arguments to the function. These are converted to Parameter objects, the basis of the Bumps modeling system. For each parameter, we can set bounds or values:

M.m.range(0,1)  # limit slope between 0 and 45 degrees
M.b.value = 1   # the intercept is set to 1.

We could even set a parameter to a probability distribution, using Parameter.dev for Gaussian distributions or setting parameter.bounds to Distribution for other distributions.

Bumps includes code for polynomial interpolation including B-splines, monotonic splines, and chebyshev polynomials.

For counts data, PoissonCurve is also available.

## Likelihood functions¶

If you are already have the negative log likelihood function and you don’t need to manage data, you can use it with PDF:

def nllf(m, b):
return numpy.sum(((y - (m*x + b))/dy)**2)
M = PDF(nllf)

You can use M.m and M.b to the parameter ranges as usual, then return the model as a fitting problem:

M.m.range(-inf,inf)
M.b.range(-inf,inf)
problem = FitProblem(M)

## Complex models¶

More sophisticated models, with routines for data handling and specialized plotting should define the Fitness interface. The Peak Fitting example sets up a problem for fitting multiple peaks plus a background against a 2-D data set.

Models are parameterized using Parameter objects, which identify the fitted parameters in the model, and the bounds over which they may vary. The fitness object must provide a set of fitting parameters to the fit problem using the parameters method. Usually this returns a dictionary, with the key corresponding to the attribute name for the parameter and the value corresponding to a parameter object. This allows the user of the model to guess that parameter “p1” for example can be referenced using model.p1. If the model consists of parts, the parameters for each part must be returned. The usual approach is to define a parameters method for each part and build up the dictionary when needed (the parameters function is only called at the start of the fit, so it does not need to be efficient). This allows the user to guess that parameter “p1” of part “a” can be referenced using model.a.p1. A set of related parameters, p1, p2, … can be placed in a list and referenced using, e.g., model.a.p[i].

The fitness constructor should accept keyword arguments for each parameter giving reasonable defaults for the initial value. The parameter attribute should be created using Parameter.default. This method allows the user to set an initial parameter value when the model is defined, or set the value to be another parameter in the fitting problem, or to a parameter expression. The name given to the default method should include the name of the model. That way when the same type of model is used for different data sets, the two sets of parameters can be distinguished. Ideally the model name would be based on the data set name so that you can more easily figure out which parameter goes with which data.

During an analysis, the optimizer will ask to evaluate a series of points in parameter space. Once the parameters have been set, the update method will be called, if there is one. This method should clear any cached results from the last fit point. Next the nllf method will be called to compute the negative log likelihood of observing the data given the current values of the parameters. This is usually just $$\sum{(y_i - f(x_i))^2 / (2 \sigma_i^2)}$$ for data measured with Gaussian uncertainty, but any probability distribution can be used.

For the Levenberg-Marquardt optimizer, the residuals method will be called instead of nllf. If residuals are unavailable, then the L-M method cannot be used.

The numpoints method is used to report fitting progress. With Gaussian measurement uncertainty, the nllf return value is $$\chi^2/2$$, which has an expected value of the number of degrees of freedom in the fit. Since this is an awkward number, the normalized chi-square, $$\chi^2_N = \chi^2/\text{DoF} = -2 \ln (P)/(n-p)$$, is shown instead, where $$-\ln P$$ is the nllf value, $$n$$ is the of points and $$p$$ is the number of fitted parameters. $$\chi^2_N$$ has a value near 1 for a good fit. The same calculation is used for non-gaussian distributions even though nllf is not returning sum squared residuals.

The save and plot methods will be called at the end of the fit. The save method should save the model for the current point. This may include things such as the calculated scattering curve and the real space model for scattering inverse problems, or it may be a save of the model parameters in a format that can be loaded by other programs. The plot method should use the current matplotlib figure to draw the model, data, theory and residuals.

The resynth_data method is used for an alternative monte carlo error analysis where random data sets are generated from the measured value and the uncertainty then fitted. The resulting fitted parameters can be processed much like the MCMC datasets, yielding a different estimate on the uncertainties in the parameters. The restore_data method restores the data to the originally measured values. These methods are optional, and only used if the alternative error analysis is requested.

## Linear models¶

Linear problems with normally distributed measurement error can be solved directly. Bumps provides bumps.wsolve.wsolve(), which weights values according to the uncertainty. The corresponding bumps.wsolve.wpolyfit() function fits polynomials with measurement uncertainty.

## Foreign models¶

If your modeling environment already contains a sophisticated parameter handling system (e.g. sympy or PyMC) you may want to tie into the Bumps system at a higher level. In this case you will need to define a class which implements the FitProblem interface. This has been done already for PyMCProblem and interested parties are directed therein for a working example.

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# Example of a martingale and a stopping time with $E(T)<\infty$ but $E(X_T) \neq E(X_0)$

Is there an example of a martingale in discrete time $X_0, X_1, X_2,\ldots$ and a stopping time $T$ so that $E(T) <\infty$ but $E(X_T) \neq E(X_0)$?

With added assumptions on how $X_n$ behaves, you can prove that $E(X_T)=E(X_0)$ For example if $|X_{n+1} - X_{n}| \leq c$ for some constant $c$, then we can show $E(X_T) = E(X_0)$.

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How about this: let $Y_0,Y_1,\ldots$ be independent RVs, where $$P(Y_n=2^n)=\frac{1}{2},\qquad P(Y_n=-2^n)=\frac{1}{2}.$$ For $n\geq 0$, let $X_n=\sum_{i=0}^{n}Y_i=X_{n-1}+Y_n$. This is a martingale: $$\mathbb{E}[X_n\,\mid\,X_{n-1}]=X_{n-1}+\mathbb{E}[Y_n]=X_{n-1},$$ since $X_{n-1}$ is measurable with respect to $Y_1,\ldots,Y_{n-1}$, while $Y_n$ is independent of these. Let $T$ be the minimum $n$ such that $X_n>0$, if such an $n$ exists, and $\infty$ otherwise.
Note that $T$ is also the first $n$ such that $Y_n>0$, since $2^n>1+2+\cdots+2^{n-1}$. So, $$P(T=n)=\frac{1}{2^{n+1}}\qquad\text{and}\qquad\mathbb{E}[T]=\sum_{n=0}^{\infty}\frac{n}{2^{n+1}}=1.$$ Since $\mathbb{E}[T]<\infty$, $T$ is almost surely finite, and $X_T$ is almost surely well-defined. But, since $X_n\geq 1$ if $X_n>0$, it is always the case that $X_T\geq 1$ if $T<\infty$. Combining these, $\mathbb{E}[X_T]\geq1$, whereas $\mathbb{E}[X_0]=0$.


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# SL(2,Z/N)-decomposition of space of cusp forms for Gamma(N)

Since $\Gamma(N)$ is normal in $\mathrm{SL}(2,\mathbb{Z})$, the quotient group $\mathrm{SL}(2,\mathbb{Z}/N)$ acts on the spaces of cusp forms $S_k(\Gamma(N))$. How do these spaces decompose into irreducible representations?

I can do the case $N=2$. I'm mostly interested in the case of $N$ a prime.

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I wonder if this question of mine is related: mathoverflow.net/questions/2875/… –  Ilya Nikokoshev Nov 9 '09 at 20:08

See Theorem 1.0.3 of Jared Weinstein's phd thesis (it uses equivariant Riemann Roch).

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As usual, once I spot a question on here I have anything useful to say about, somebody has already answered it.

I can sum up that part of my thesis this way: let M be the induced representation of the character (-I) --> (-1)^k of the center up to all of SL(2,Z/NZ). Then S_k(Gamma(N)) is roughly k/12 copies of M, plus some error term which can be given precisely, with some effort.

When you ask instead about Hilbert modular forms over a totally real field K, the "1/12" becomes the absolute value of zeta_K(-1).

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Thank you moonface and Jared, that's perfect. I wish I could give more than one accepted answer. :) –  Dan Petersen Nov 10 '09 at 8:35

If you think about this question in terms of automorphic representations then it sort of becomes trivial. The space $Sk(\Gamma(N))$ can be re-interpreted as the direct sum of $\pi^{U(N)}$, where $\pi$ is running through the automorphic representations of $GL_2$ which are holomorphic of weight $k$. Each factor is $SL(2,Z/NZ)$-invariant and often irreducible but sometimes has small finite length. The representation of $SL(2,Z/NZ)$ that shows up on $\pi{^U(N)}$ is the "type" of $\pi$. For explicit $\pi$s one will be able to explicitly determine this representation.

-
I'm not sure that they are irreducible (at least if I'm thinking about GL_2(F_p)) - e.g. can't I get things like the induction of the trivial character on the Borel showing up? –  TSG Nov 9 '09 at 23:48

You can almost do this with nothing more than Riemann-Hurwitz; in particular, by R-H you can compute the action of SL_2(Z/NZ) on H_1(X(N),C), which is just the sum of the representation you want with its dual.

-
The great thing about this approach is that it's completely different to the automorphic forms approach, and if the two are used together then they give information about the number of automorphic forms of a given "type". Sort of a generalisation of counting how many level 1 forms there are by computing the dimension of the space of level 1 forms by some global method. –  Kevin Buzzard Nov 10 '09 at 7:38


text:
Pi Day: March 14th

By Murray Bourne, 13 Mar 2007

Tomorrow is Pi Day, celebrated because π is approximately 3.14.

Some interesting stuff related to Pi:

Remembering the Digits of Pi

For a party trick (or if you have no life), try learning the digits of pi.

Here is George Polya's mnemonic for the first fifteen digits of π :

How I need a drink, alcoholic of course, after the heavy chapters involving quantum mechanics

[The lengths of the words are the digits. George Polya was very influential in mathematics education, especially in problem solving.]

Want to try to Remember All These?

From the BBC:

In September 2002, Pi was computed to 1,240,000,000,000 decimal places by Professor Yasumasa Kanada at the University of Tokyo. It took over 400 hours on a Hitachi Supercomputer.

New Pi Page

Getting into the spirit of the day, I added a new page to the Interactive Mathematics site today: Pi.

American Pi:

And to finish with, enjoy yourself with American Pi:

See the 1 Comment below.

Comment Preview

HTML: You can use simple tags like <b>, <a href="...">, etc.

To enter math, you can can either:

1. Use simple calculator-like input in the following format (surround your math in backticks, or qq on tablet or phone):
a^2 = sqrt(b^2 + c^2)
(See more on ASCIIMath syntax); or
2. Use simple LaTeX in the following format. Surround your math with $$ and $$.
$$\int g dx = \sqrt{\frac{a}{b}}$$
(This is standard simple LaTeX.)

NOTE: You can mix both types of math entry in your comment.

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From Math Blogs


text:
# Clock Divider IC, Using Series or Parallel Termination

I am using a 542MILF in a design.

The datasheet says the output impedance is 20Ω (not low output impedance)

Would I have to use series termination e.i. 30Ω resistor followed by 50Ω transmission line because this IC has a fairly high output impedance?

If the clock signal is going to a HiZ input could I still use parallel termination instead?

Thanks

• What is the clock frequency and what is the length of the lines connecting it to the load? – The Photon Mar 1 '17 at 2:40
• ~100kHz. The trace will be as short as possible <1". – Tony Mar 1 '17 at 2:50
• 100 kHz and 1 inch you don't need to worry about impedance matching or transmission line characteristic impedance. – The Photon Mar 1 '17 at 2:51

The datasheet is quite clear.

Clock output traces over one inch should use series termination. To series terminate a 50Ω trace (a commonly used trace impedance), place a 33Ω resistor in series with the clock line, as close to the clock output pin as possible. The nominal impedance of the clock output is 20Ω.

First I need to correct your assumptions.

20Ω typ is the lowest impedance in 5V CMOS logic drivers in existence.

• Most 3.3V Logic is 25Ω and 5V logic is around 50Ω.
• effective Z tolerance over temp and supply range is around 50% , Vol/Iol=Z

Note that this chip has a 1ns (typ) rise time and max skew of 500 ps and 1" was recommended max for path length for best performance.

## What does this mean?

It means signal integrity of clocks degrades as path length increases beyond this without impedance matching but is preserved with matching.

Transmission Line Rules for impedance matching become important when the risetime , Tr is < 15% of the propagation delay. i.e. Wavelength is $\lambda =~0.35/Tr$ thus if Tr is greater than 5% of a $\lambda$. Others use 10% as a rule of thumb with less margin on signal integrity.

Otherwise inductive tracks with distributed capacitance can cause overshoot and ringing. Parallel Loading can reduce the Q and decay time.

A true matched impedance with stripline and termination resistor is the ideal scenario at the expense of 50% reduced Vpp swing.

Obviously compromises can be made between ringing and load impedance if you know the level of ringing, but usually this is not needed as terminations can be split from Vcc to gnd to maintain proper bias around input thresholds.

Essentially these rules of Transmission Line design apply to all CMOS for rise time vs path length when these rules need to be applied. This is because is the rise time from higher output impedance drivers with higher load capacitance results in lower slew rates, longer path lengths can be used without terminations using careful controlled impedance tracks.

Microstrip:                    Stripline.:
Zo= 60-70 Ohms for w/h = 1,    0.6 times that of microstrip.
40-50 ohms for w/h = 2.    0.6 times that of microstrip.
Propagation Delay: 150 pS/in   180 pS/in
Average Propagation Delay: 2 nS/ft  between microstrip and stripline.
(Ref Henry Ott)


text:
# CDF-based nonparametric confidence interval

In statistics, cumulative distribution function (CDF)-based nonparametric confidence intervals are a general class of confidence intervals around statistical functionals of a distribution. To calculate these confidence intervals, all that is required is an independently and identically distributed (iid) sample from the distribution and known bounds on the support of the distribution. The latter requirement simply means that all the nonzero probability mass of the distribution must be contained in some known interval $\left[a,b\right]$.

## Intuition

The intuition behind the CDF-based approach is that bounds on the CDF of a distribution can be translated into bounds on statistical functionals of that distribution. Given an upper and lower bound on the CDF, the approach involves finding the CDFs within the bounds that maximize and minimize the statistical functional of interest.

## Properties of the bounds

Unlike approaches that make asymptotic assumptions, including bootstrap approaches and those that rely on the central limit theorem, CDF-based bounds are valid for finite sample sizes. And unlike bounds based on inequalities such as Hoeffding's and McDiarmid's inequalities, CDF-based bounds use properties of the entire sample and thus often produce significantly tighter bounds.

## CDF bounds

When producing bounds on the CDF, we must differentiate between pointwise and simultaneous bands.

### Pointwise band

A pointwise CDF bound is one which only guarantees their Coverage probability of $1-alpha$ percent on any individual point of the empirical CDF. Because of the relaxed guarantees, these intervals can be much smaller.

One method of generating them is based on the Binomial distribution. Considering a single point of a CDF of value $F\left(x_i\right)$, then the empirical distribution at that point will be distributed proportional to the binomial distribution with $p=F\left(x_i\right)$ and $n$ set equal to the number of samples in the empirical distribution. Thus, any of the methods available for generating a Binomial proportion confidence interval can be used to generate a CDF bound as well.

### Simultaneous Band

CDF-based confidence intervals require a probabilistic bound on the CDF of the distribution from which the sample were generated. A variety of methods exist for generating confidence intervals for the CDF of a distribution, $F$, given an i.i.d. sample drawn from the distribution. These methods are all based on the empirical distribution function (empirical CDF). Given an i.i.d. sample of size n, $x_1,ldots,x_nsim F$, the empirical CDF is defined to be

: $hat\left\{F\right\}_n\left(t\right) = frac\left\{1\right\}\left\{n\right\}sum_\left\{i=1\right\}^n1\left\{x_ile t\right\},$

where $1\left\{A\right\}$ is the indicator of event A. The Dvoretzky–Kiefer–Wolfowitz inequality, whose tight constant was determined by Massart, places a confidence interval around the Kolmogorov–Smirnov statistic between the CDF and the empirical CDF. Given an i.i.d. sample of size n from $F$, the bound states

: $P\left(sup_x|F\left(x\right)-F_n\left(x\right)|>varepsilon\right)le2e^\left\{-2nvarepsilon^2\right\}.$

This can be viewed as a confidence envelope that runs parallel to, and is equally above and below, the empirical CDF.The equally spaced confidence interval around the empirical CDF allows for different rates of violations across the support of the distribution. In particular, it is more common for a CDF to be outside of the CDF bound estimated using the Dvoretzky–Kiefer–Wolfowitz inequality near the median of the distribution than near the endpoints of the distribution. In contrast, the order statistics-based bound introduced by Learned-Miller and DeStefano allows for an equal rate of violation across all of the order statistics. This in turn results in a bound that is tighter near the ends of the support of the distribution and looser in the middle of the support. Other types of bounds can be generated by varying the rate of violation for the order statistics. For example, if a tighter bound on the distribution is desired on the upper portion of the support, a higher rate of violation can be allowed at the upper portion of the support at the expense of having a lower rate of violation, and thus a looser bound, for the lower portion of the support.

## A nonparametric bound on the mean

Assume without loss of generality that the support of the distribution is contained in $\left[0,1\right].$ Given a confidence envelope for the CDF of $F$ it is easy to derive a corresponding confidence interval for the mean of $F$. It can be shown that the CDF that maximizes the mean is the one that runs along the lower confidence envelope, $L\left(x\right)$, and the CDF that minimizes the mean is the one that runs along the upper envelope, $U\left(x\right)$. Using the identity

: $E\left(X\right) = int_0^1\left(1-F\left(x\right)\right),dx,$

the confidence interval for the mean can be computed as

: $left\left[int_0^1\left(1-U\left(x\right)\right),dx, int_0^1\left(1-L\left(x\right)\right),dx ight\right].$

## A nonparametric bound on the variance

Assume without loss of generality that the support of the distribution of interest, $F$, is contained in $\left[0,1\right]$. Given a confidence envelope for $F$, it can be shown that the CDF within the envelope that minimizes the variance begins on the lower envelope, has a jump discontinuity to the upper envelope, and then continues along the upper envelope. Further, it can be shown that this variance-minimizing CDF, F', must satisfy the constraint that the jump discontinuity occurs at $E\left[F\text{'}\right]$. The variance maximizing CDF begins on the upper envelope, horizontally transitions to the lower envelope, then continues along the lower envelope. Explicit algorithms for calculating these variance-maximizing and minimizing CDFs are given by Romano and Wolf.

## Bounds on other statistical functionals

The CDF-based framework for generating confidence intervals is very general and can be applied to a variety of other statistical functionals including
• Entropy
• Mutual information
• Arbitrary percentiles


text:
3k views

### Is Fermat's principle only an approximation?

Fermat's principle says that the path taken between two points by a ray of light is the path that can be traversed in the least time. It occurred to me today that maybe the path is actually the one ...
8k views

### How are classical optics phenomena explained in QED (Snell's law)?

How is the following classical optics phenomenon explained in quantum electrodynamics? Reflection and Refraction Are they simply due to photons being absorbed and re-emitted? How do we get to Snell'...
4k views

### Geodesics equations via variational principle

I would like to recover the (timelike) geodesics equations via the variational principle of the following action: $$\mathcal{S}[x] = -m \int d\tau = -m \int \sqrt{-g_{\mu\nu}\,dx^{\mu}\,dx^{\nu}}$$ ...
2k views


text:
0

# What is 6%23

how?

8th Apr 2017, 1:11 PM
Vikram Vijayaraj
+ 19
When you'll divide a smaller number by a larger number, the quotient will be 0 and the remainder will be the smaller number itself 6/23 = 0 6%23 = 6
8th Apr 2017, 1:13 PM
Shamima Yasmin
+ 1
I think it's 6
8th Apr 2017, 1:12 PM
Ethan Woo
+ 1
The answer is 6. This is because % returns the remainder, by saying 6/23 the whole part of the number is 0 because 6 contains number 23 zero times. For some reason this is hard to explain but lets say you are dividing 26 with 8 (this is just a random example). 26/8 = 3 //Because 26 holds the number 8 three times 26%8 = 2 26 - 3 * 8 = 2 //Therefore % returns the remainder during the division of these two numbers. In the example you gave we have 6/23 = 0 6 - 0 * 23 = 6
8th Apr 2017, 1:21 PM
Dextozz
0
how bro
8th Apr 2017, 1:13 PM
Vikram Vijayaraj


text:
New Ikea Workspace Design and Decorating Ideas

Workspace at home, is the part of home architecture, if you busy with your work at home. It will give spirit and enjoyable work, if the design and decor is comfortable and neat. New ikea catalog, also give their inspiration of workspace for your home. It’s design with a lot of furniture there, but it looks comfy. Ikea still use their old design to improve this new workspace design, into something fresh, and more comfortable. It would make your work enjoyable. Let’s see this inspiration of New Ikea Workspace Design and Decorating Ideas pictures here.

New Ikea Workspace Design and Decorating Ideas Pictures Gallery

White New Ikea Workspace Design and Decorating Ideas

Stylish New Ikea Workspace Design and Decorating Ideas

Modern New Ikea Workspace Design and Decorating Ideas

Green New Ikea Workspace Design and Decorating Ideas

Cool New Ikea Workspace Design and Decorating Ideas

Brown New Ikea Workspace Design and Decorating Ideas

tags: , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ,


text:
# 4.3.1. Supported motor types¶

Currently the controller supports stepper and DC motor types. The parameters of supported motors are described in Specifications chapter.

## 4.3.1.1. Stepper motors¶

Rated current is the main parameter of the stepper motor. The rated current is adjustable at the Settings of kinematics (stepper motor) section.

Important

The motor will gradually overheat and get physically damaged if rated current is exceeded. Make sure that the rated current value is set according to the used stage. All the settings are proper in default stage profiles.

Step division mode is another important parameter. In full step operation, the motor moves through its basic step angle (for example, a 1.8° step motor takes 200 steps per motor revolution). Microstepping can divide a motor’s basic step up to 256 times. Microstepping improves low speed smoothness and minimizes low speed resonance effects.

The following step division options are available:

• 1 (full) step
• 1/2 of the step
• 1/4 of the step
• 1/8 of the step
• 1/16 of the step
• 1/32 of the step
• 1/64 of the step
• 1/128 of the step
• 1/256 of the step

The microstep mode is set either on Settings of kinematics (stepper motor) page or by motor adjustment commands. See the Communication protocol specification and the description of the related functions in the Programming guide chapter.

Note

The controller always uses the internal step division value equal to 1/256. If the user selects a coarser step division, the software will display only the multiple of the coarser step division positions and both adjustment and transmission are possible only in that coarser step division mode. This is done for compatibility with both obsolete and actual software operating with small multiples of the step division values. On the other hand, operations with the largest step division value provides the most smooth and silent rotation at the smaller speed values.

The number of steps per revolution is the another direct parameter of the stepper motor. This setting does not affect the rotation but is used in slipping control block or with motors with the encoder feedback.

Note

The controller supports stepper motors with feedback sensor - encoder. The encoder can be used as the main position sensor (more info) and as the slippage, backlash or steps loss detector (more info). Using the encoder facilitates a stable passage of the resonant speeds without movement disruption.

## 4.3.1.2. DC motors¶

Unlike stepper motors, controlling DC motors requires feedback. Currently only encoder is supported as a feedback sensor.

Main DC motor parameters are maximum current and voltage, which can be set on Settings of kinematics (DC motor). Main encoder parameter is counts per revolution.

Important

The motor will gradually overheat and get physically damaged if rated current is exceeded. Make sure that the rated current value is set according to the used stage. All the settings are proper in default stage profiles.

Important

Setting wrong value of encoder counts per revolution will lead to the controller being unable to maintain speed correctly. In some cases it may lead to stage or reducing gear failure.

DC engine is controlled by the PID regulator. Please carefully read PID-algorithm for DC engine control before you start working with it.

Important

Wrong PID regulator settings might lead to stage failure. All supplied profiles are preset with correct PID settings. It is not recommended to alter these settings unless absolutely necessary.

## 4.3.1.3. BLDC motors¶

Firmwares 4.1.x and older support BLDC motors controlling. Like DC motors, controlling BLDC motors reqiures feedback.

Main BLDC motor parameters are maximum current and number of poles, which can be set on Settings of kinematics (BLDC motor). Main encoder parameter is counts per revolution.

Like DC, BLDC engine is controlled by the PID regulator. Please carefully read PID-algorithm for BLDC engine control before you start working with it.

Important

Like DC motors, wrong PID regulator settings, current and encoder settings might lead to stage failure

## 4.3.1.4. Engine selection criteria¶

Pulse-width modulation (PWM) is a widely used way to control winding’s current in different motor types. It leads to current oscillations at PWM switching frequency (so-called “current ripple”). Current ripple’s amplitude depends on motor characteristics like its winding inductance and resistance. Motor can heat up more than it is expected with nominal current due to current ripple, i.e. $$\frac{P_{real}}{RI_s^2} > 1$$. There is $$RI_s^2$$ - power dissipated by $$I_s$$ (stabilization current), $$P_{real}$$ - real power, dissipated in motor. For overheating estimation we recommend to use this graph:

RT/L values for some motors
Motor RT/L
20 0.19576
28 0.07253
28s 0.07168
4118L1804R 0.02715
4118S1404R 0.02844
4247 0.0273
D42.3 0.0223
5618 0.0146
5618R 0.0146
5918 0.0116
5918B 0.012
VSS42 0.029
VSS43 0.0256
ZSS 0.04248
DCERE25 0.2106

The motor’s overheat is determined by this sequence:

• $$\frac{RT}{L}$$ calculation. There is $$R, L$$ - resistance and inductance of motor winding (refer to the motor documentation). $$T$$ - PWM period time. It’s value should be 51.2 us for stepper motors and 25.6 us for DC motors.
• $$\frac{V}{RI_s}$$ calculation. This parameter shows power voltage excess under nominal voltage. There is $$V$$ - power voltage,:math:R - winding resistance, $$I_s$$ - stabilization current.
• Overheat definition. After first two steps point can be plotted at the graph. Now we should define the region, which corresponds to overheat degree. For example, the region between 1.1 and 1.2 corresponds overheat value between $$1.1 * RI_s^2$$ and $$1.2 * RI_s^2$$.

There is DCE1524 overheat calculation example:

• $$T$$ = 25.6 us
• $$R$$ = 5.1 Ohm
• $$L$$ = 70 uH
• $$\frac{RT}{L}$$ = 1.86

Now we can draw vertical line corresponds this value (look at graph) and find out overheat with different power voltages. Let’s assume $$I_s$$ = 500 mA. Nominal voltage in this case is $$R *I_s$$ = 2.55 V. If power voltage exceeds nominal more than 5 times but less than 10 times DCE1524’s overheat will be between 1.5 and 1.6. Motor overheats about 1.65 times with 30 V of power voltage.

All the major engines and their parameters have been marked in RT/L values for some motors.


text:
## GOODF - Good Aim

no tags

The heated competition of the ACM-ICPC World Finals continues, and The Team is at the top of their game! Well, okay, maybe they're not actually doing so well, according to the scoreboard, yet. But they have a plan!

The contest is taking place in a huge room with a regular grid of desks. The columns and rows are each numbered $1..10^6$, and the desk in the $x$th column and $y$th row is considered to have coordinates ($x$,$y$). The Team is sitting at coordinates ($X$,$Y$). There are $N$ ($1 \leq N \leq 10^6$) opposing teams (conveniently numbered $1..N$), with team $i$ having $m_i$ ($1 \leq m_i \leq 10^6$) members, all sitting at coordinates ($x_i$,$y_i$). No desk is occupied by more than one team, and all other desks are empty.

Now, The Team is interested in removing some of the more dangerous opponents from the competition. To accomplish this, they have a number of water balloons at their disposal (after all, where in the contest rules does it say that water balloons are not allowed?). Always conservative, they would first like to answer $Q$ ($1 \leq Q \leq 10^6$) queries - for the $i$th query, how many balloons it would theoretically take to take out all of the members of team $q_i$?

In order to do any real damage, the water balloons will of course have to be thrown extremely hard - in fact, in a perfectly straight line, and not over any obstacles besides empty desks. This means that, if team $j$ lies exactly on the line segment from The Team to team $i$, then every member of team $j$ must be dispatched before any members of team $i$ can be hit. It takes one balloon to knock one person out (the members of The Team have received plenty of training, so they're not about to miss a throw). Note that these queries are all only theoretical (for the moment) - so each should be answered assuming that all teams are still untouched.

The members of The Team will need to carefully choose with opponents to take out, based on how well they're doing and how many balloons it would take, so they're already answered all of their queries in their heads. Maybe, if you can answer them as well, you can also adopt such techniques in the future...

### Input

First line: 4 integers, $N$, $Q$, $X$, and $Y$

Next $N$ lines: 3 integers, $x_i$, $y_i$, and $m_i$, for $i = 1..N$

Next $Q$ lines: 1 integer, $t_i$, for $i = 1..Q$

### Output

$Q$ lines: 1 integer, the number of balloons that would be required to take out team $t_i$, for $i = 1..Q$.

### Example

Input:
6 6 3 2
5 6 3
2 1 5
4 4 2
4 3 1
5 4 2
7 6 1
6
5
4
3
2
1
Output:
4
3
1
2
5
5
Explanation of Sample:

The following grid shows the positions of the $N$ opposing teams (marked with their numbers), as well as The Team (marked with a "T"). The line segments represent direct lines of sight to the opponents.

As can be seen, team 6 is blocked by teams 4 and 5. Therefore, taking them out would require $1+2+1=4$ balloons in total. Similarly, team 5 is blocked by team 4, and requires $1+2=3$ balloons. Teams 4, 3, and 2 are not blocked by any others, and so only require 1, 2, and 5 balloons, respectively. Finally, team 1 is blocked by team 3, and would require $2+3=5$ balloons to dispose of.

 Added by: SourSpinach Date: 2013-05-09 Time limit: 3s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: ASM64 Resource: Own problem


text:
# Vertical space at the bottom of a page

I was thinking that vertical space added with \vspace or \addvspace was removed at begin or end of page. The following code do not add space at the top of the page but add space at the bottom.

\documentclass[a6paper]{article}
\usepackage[showframe]{geometry}
\begin{document}
\vspace{1cm}
blabla.
\vfill
blabla.
\vspace{1cm}
\end{document}

In the latex2e.pdf documentation file, we can find this.

LaTeX removes the vertical space from \vspace at a page break, that is, at the top or bottom of a page. The starred version \vspace*{...} causes the space to stay.

I would like LaTeX to remove this space at the bottom of the page as expected.


text:
# Custom metrics for multiclass classification when class errors have different weights

I have a multiclass classification problem (eg. the target variable is made by 4 different outcomes: Product A, Product B, Product C and NO Product). Not all the errors are equal: for example, if the true label is "Product A" and the prediction is "NO Product" it is not a big problem, while if the true label is "Product C" the impact of the error is much bigger. Basically, I have to insert this information into the loss function of the algorithm (I am currently using Xg-Boost, Random Forest, etc).

I know that it's possible, for example using scikit-learn to train algorithms using the parameter class_weight in a way that a specific class error is more important.

Is there the possibility to say, for example, that a miss-classification of product C in Product B is more problematic w.r.t a miss-classification of Product C to Product B? I am basically looking at something that penalize the model for making cross predictions.

Any idea? Thank you!

Use a method that outputs predictive probabilities, as:

My prediction is a probability 0.6 that this instance is product A, 0.2 for product B, 0.15 for product C and 0.05 for NO product.

Then use a proper scoring rule to evaluate these predictive probabilities. If you can tune the objective function you supply to your model fitting algorithm, you should be able to use such a proper scoring rule. (The tag may be helpful.)

Of course, all the usual caveats about overfitting apply. It would be best to do this in a cross-validation setup. Also, note whether the proper scoring rule is "positively or negatively oriented", i.e., whether larger or smaller is better - different people use different conventions.

You can find more information at Why is accuracy not the best measure for assessing classification models?, which refers to two-class classification, but my answer there applies to multiclass cases, as well.

• So if the OP is currently using XGBoost and random forest, would you suggest training them to predict probabilities rather than class labels and then using the predicted probabilities for classification based on, say, minimization of expected loss? (Also, your answer stops short of telling how to actually do classification based on estimated probabilities. But that of course is simple if one just aims at minimizing the expected loss.) Apr 8 '20 at 16:03
• Thank you for the link at your ansewer @Stephan. Is it strinctly mandatory that the output of the classification algorithms is a probability or could it be just a score? Obviously the higher the score the higher the confidence for the selected class, but, for example, the sum of all the scores could be different from 1. Do you believe it could be a problem for the application of a scoring function? Apr 8 '20 at 21:47
• Well, the point of proper scoring rules is precisely that they will be minimized (or maximized, depending on the formulation) if your predicted possibilities are the true ones. If you work with outputs that measure something different, then you only have a proxy, and you don't know whether optimizing your proper scoring rule will not lead you astray, towards biased predictions. But it will probably be better than trying to optimize accuracy. Apr 9 '20 at 5:49
• @RichardHardy: I agree that this is a very short answer. I would say it's better to have a short answer than no answer at all. Anyone who has a better answer can post it. Apr 9 '20 at 5:50
• I do not think the answer is short, no problem there. However, I think it is incomplete. What is your advice for completing the task at hand, the task being not to evaluate predictive probabilities but to optimize a classification algorithm? This brings me back to my first comment, and I am curious to learn you opinion. Apr 9 '20 at 6:13


text:
# nLab Gregg Zuckerman

Gregg Jay Zuckerman is a mathematician at Yale University.

## writings

• Action principles and global geometry , in Mathematical Aspects of String Theory, S. T. Yau (Ed.), World Scientific 1987, 259-284. (pdf)
• Construction of representations via derived functors, unpublished lecture series, Institute for Advanced Study 1978.
• Modular forms, strings, and ghosts, Proc. Sympos. Pure Math, 1989
• Semi-infinite cohomology and string theory, PNAS

category: people

Revised on July 28, 2015 16:35:37 by Urs Schreiber (89.15.236.111)


text:
CryptoDB

Paper: On Black-Box Ring Extraction and Integer Factorization

Authors: Kristina Altmann Tibor Jager Andy Rupp URL: http://eprint.iacr.org/2008/156 Search ePrint Search Google The black-box extraction problem over rings has (at least) two important interpretations in cryptography: An efficient algorithm for this problem implies (i) the equivalence of computing discrete logarithms and solving the Diffie-Hellman problem and (ii) the in-existence of secure ring-homomorphic encryption schemes. In the special case of a finite field, Boneh/Lipton and Maurer/Raub showed that there exist algorithms solving the black-box extraction problem in subexponential time. It is unknown whether there exist more efficient algorithms. In this work we consider the black-box extraction problem over finite rings of characteristic $n$, where $n$ has at least two different prime factors. We provide a polynomial-time reduction from factoring $n$ to the black-box extraction problem for a large class of finite commutative unitary rings. Under the factoring assumption, this implies the in-existence of certain efficient generic reductions from computing discrete logarithms to the Diffie-Hellman problem on the one side, and might be an indicator that secure ring-homomorphic encryption schemes exist on the other side.
BibTeX
@misc{eprint-2008-17833,
title={On Black-Box Ring Extraction and Integer Factorization},
booktitle={IACR Eprint archive},
keywords={public-key cryptography / Black Box Extraction Problem, Integer Factorization, Homomorphic Encryption},
url={http://eprint.iacr.org/2008/156},
note={ tibor.jager@rub.de 14066 received 7 Apr 2008, last revised 6 Jul 2008},
author={Kristina Altmann and Tibor Jager and Andy Rupp},
year=2008
}


text:
# Emery Cat Scratching Board

by Ivan Seeking
Tags: board, emery, scratching
P: 380
 Quote by Evo My cat didn't care if the object to scratch was lying on the floor. People think cats prefer something upright because, let's face it, most of the objects they can scratch are upright.

I don't think that "people think" that cats prefer something upright. It's my understanding that cats do prefer something upright, although they will scratch flat surfaces too. They have their own cat reasons for doing what they do. This isn't a peer reviewed journal but, it's certainly not the first I've read about cat behaviour from PH.Ds and other cat specialists.

Daniel Q. Estep, Ph.D. & Suzanne Hetts, Ph.D., Certified Applied Animal Behaviorists, Animal Behavior Associates, Inc. 4994 S. Independence Way, Littleton, CO 80123

Our neighbor has a female cat named Peaches who frequently scratches the bark on a cherry tree in their front yard. In fact, the tree has been scratched so much that there are noticeable gouges in it and small pieces of bark have accumulated on the ground underneath. Why does Peaches scratch this tree so much?

It has long been assumed that when cats scratch objects with their front paws that they are sharpening their claws. It turns out that this is only a secondary reason. Research on cat behavior suggests that the major reason for this behavior is communication. By roughing up the bark of a tree (or the leg of your favorite chair) the cat is letting other cats or people know where she is and what she is up to.

Cats tend to pick a small number of conspicuous objects in their environments to scratch such as trees, fence posts, the corner of the couch, etc., and return to them repeatedly. This is why the tree next door looks so scratched up and why your cat may find it difficult to leave your couch alone. The scratched surface leaves a highly visible mark that can be easily seen by other cats. In addition, cats have scent glands in their paws so that when they make scratching movements they leave odor cues that the cats can smell. The fact that cats leave scent marks by making scratching movements may be the reason that cats will continue to try to scratch objects even after they have been declawed. Declawed cats may still be leaving scent marks on objects they scratch.

We don’t know exactly what cats are communicating with their scratching. Both males and females do it, it is done inside and outside the home and even by cats living with no other cats around. It could be a territorial warning or just a marker that announces "Peaches lives here and is alive and well!

Cat Scratch Stuff

That's why I was curious if Ivan could experiment a bit and see if the thing curried more favour being upright.

And yes, Ivan, given the proliferation of absurd commercials, one can only extrapolate out from that and assume that the commercials are convincing someone and making someone else money. Unfortunately, or fortunately as far as I'm concerned, I know where to find China on a map.
 Emeritus Sci Advisor PF Gold P: 12,501 I'll try leaning one against the wall down here in my office and see if I can coax Little Tyke into using it. I almost forgot that we have two of them. Isaac seems to use it many times a day. I'll give it a few weeks but we should be able to tell if the thing does any good.
 Emeritus Sci Advisor PF Gold P: 12,501 The jury is in. Isaac spends a lot of time on Tsu's [my wife] lap. As a result, Tsu knows exactly how deeply into her chest his claws should sink when he's happy. She says there is no doubt that his claws are both shorter and duller than ever before. I hadn't even asked her about it yet, but today she called me in the office to tell me. So it seems the product works if a cat can be coaxed to use it. I'll mount one vertically and see how it goes. Already this is great news as Isaac is not a cooperative cat. This alone makes it worth the purchase.
 Emeritus Sci Advisor PF Gold P: 12,270 Ember doesn't care if her scratchers are flat on the floor or upright. When she has a choice, she actually seems to go for the flat ones more often. Then again, I got her a new one, and apparently the catnip that came with it is MUCH more potent than any other catnip she's ever experienced, because she was going bonkers rubbing all over it (I've never seen her actually react to catnip before...so of course I then had fun dipping all her toys in the catnip too. ) As far as I can tell, the clawing is to help shed the outer layers of claw as they grow. They seem to grow in layers with each layer shedding as ones below grow longer. If I look around the scratchers, I see lots of bits and pieces of shed claw parts. Trimming Ember's claws seems to have no effect on her scratching, just on how sharp and pointy they are when she grabs my hands when we are playing. She always prefers really rough surfaces (cardboard, sisal mats or sisal rope) rather than softer surfaces like carpet, and I think that's because she needs to really get those claws to catch on something to pluck what I imagine might be an itchy or annoying loose bit off. So, I could imagine her preferring an emery surface too. So, now the thing to wait for is how long they last with regular use and whether it's long enough to be worth the cost.
Emeritus
PF Gold
P: 12,501
 Quote by Moonbear So, now the thing to wait for is how long they last with regular use and whether it's long enough to be worth the cost.
I was checking for damage this morning. After seven days, so far, so good. Already it is doing better than that stupid cardboard scratching post thingy. I think they are made using the same material, but the abrasive coating adds strength to the cardboard.
Emeritus
PF Gold
P: 12,270
 Quote by Ivan Seeking I was checking for damage this morning. After seven days, so far, so good. Already it is doing better than that stupid cardboard scratching post thingy. I think they are made using the same material, but the abrasive coating adds strength to the cardboard.
Ember is usually happy with the cardboard scratchers that cost about $5...just a box about 6" by 18" holding corrugated cardboard. They look ragged quickly, but really last months to a year (I flip them over and use the other side when she wears out one side). The other scratchers are more expensive...about$9 each made of a plastic frame with some sort of fibrous stuff that looks a little like the wrong side of a carpet, but in multi-colors. I have three of those. Two of them she uses like a normal scratcher, and the third she likes to pluck the strings out of.
P: 380
 Quote by Ivan Seeking The jury is in. Isaac spends a lot of time on Tsu's [my wife] lap. As a result, Tsu knows exactly how deeply into her chest his claws should sink when he's happy. She says there is no doubt that his claws are both shorter and duller than ever before.
Very nifty! Even though Bean doesn't fuss getting her claws clipped, if she had something to keep the tips smooth, I'd be very happy. Bean wakes me every morning by lying on my tummy and chest and poking my face with her paw. Sharp claws catch sometimes, jarring me from a dead sleep, and I'm not overly friendly about it. Not that getting hollered at or sworn at deters my cat at all. She just pokes me again.
 Emeritus Sci Advisor PF Gold P: 12,501 One caveat: Isaac's claws barely even exist anymore! They are just stubs. I wonder if his claws broke off and were then honed smooth. They are so short that this actually concerns me a bit. I guess we'll just have to see how this averages out over time. Still waiting to see if I can coax Tyke by placing the one upright. I have so much inventory in my office right now that I don't have a place for it!
P: 589
 Quote by Ivan Seeking One caveat: Isaac's claws barely even exist anymore! They are just stubs. I wonder if his claws broke off and were then honed smooth. They are so short that this actually concerns me a bit. I guess we'll just have to see how this averages out over time.
If there is no bleeding, and the cat isn't limping or showing signs of pain, I wouldn't be concerned.
 Sci Advisor P: 5,095 My cat loves the one we have.
Emeritus
PF Gold
P: 12,501
 Quote by FredGarvin My cat loves the one we have.
What is the ball designed to do; torture them with something they can never catch! Do you recall approx. how much you paid for that one? That kitty is almost a spittin image of my Little Tyke, btw, except that Tyke is much better looking.

I have the second scratcher in my office now. I was able to coax Tyke to play with the feather thingy with the board mounted upright, but she hasn't used it to scratch yet. She did knock it over and sit on it.

 Quote by pantaz If there is no bleeding, and the cat isn't limping or showing signs of pain, I wouldn't be concerned.
Tsu is thrilled with the results with Isaac. Already the wounds on her chest are beginning to heal. I see or hear Isaac using the scratcher frequently; even now when his claws are well trimmed. So far, as near as I can tell, Jack hasn't even looked at the thing since the first day. So the tally at our house so far: One cat took to the scratcher instantly and four showed no interest at all. If they use it, it does seem to work surprising well.
 Sci Advisor P: 5,095 Sorry I didn't get back to you Ivan. I forgot about this thread. IIRC, the whole thing was about $17 or so. The only drawback is they want about$6 for replacement inserts of the scratch pad. My cat loves the ball and got good enough to learn how to pop it out of the track.
P: 9,575
 Quote by FredGarvin My cat loves the one we have.
I have this exact model for my cat and he plays with it daily! The cardboard middle for scratching is holding up quite well too.
Emeritus


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# History of Belle and some of its lesser known highlights

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### Abstract

I report on the early history of Belle, which was almost entirely focused on testing the Kobayashi Maskawa mechanism for $$CP$$ violation that predicted large matter-antimatter asymmetries in certain $$B$$ meson decay modes. Results reported by both BaBar and Belle in the summer of 2001 verified the Kobayashi Maskawa idea and led to their Nobel prizes in 2008. In addition to studies of CP violation, Belle (and BaBar) reported a large number of important results on a wide variety of other subjects, many of which that had nothing to do with B mesons. In this talk I cover three (of many) subjects where Belle measurements have had a significant impact on specific sub-fields of hadron physics but are not generally well know. These include: the discovery of an anomalously large cross sections for double charmonium production in continuum e+e- annihilation; sensitive probes of the structure of the low-mass scalar mesons; and first measurements of the Collins spin fragmentation function.

### Most cited references1

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### Comprehensive Amplitude Analysis of $$\gamma\gamma \rightarrow \pi^+\pi^-, \pi^0\pi^0$$ and $$\overline{K} K$$ below 1.5 GeV

(2014)
In this paper we perform an amplitude analysis of essentially all published pion and kaon pair production data from two photon collisions below 1.5 GeV. This includes all the high statistics results from Belle, as well as older data from Mark II at SLAC, CELLO at DESY, Crystal Ball at SLAC. The purpose of this analysis is to provide as close to a model-independent determination of the $$\gamma\gamma$$ to meson pair amplitudes as possible. Having data with limited angular coverage, typically $$|\cos \theta| < 0.6-0.8$$, and no polarization information for reactions in which spin is an essential complication, the determination of the underlying amplitudes might appear an intractable problem. However, imposing the basic constraints required by analyticity, unitarity, and crossing-symmetry makes up for the experimentally missing information. Final state interactions among the meson pairs are critical to this analysis. To fix these, we include the latest $$\pi\pi\to\pi\pi$$, $${\overline K}K$$ scattering amplitudes given by dispersive analyses, supplemented in the $${\overline K}K$$ threshold region by the recent precision Dalitz plot analysis from BaBar. With these hadronic amplitudes built into unitarity, we can constrain the overall description of $$\gamma\gamma\to\pi\pi$$ and $$\overline{K}K$$ datasets, both integrated and differential cross-sections, including the high statistics charged and neutral pion, as well as $$K_sK_s$$ data from Belle. Since this analysis invokes coupled hadronic channels, having data on both $$\gamma\gamma\to\pi\pi$$ and $$\overline{K}K$$ reduces the solution space to essentially a single form. We present the partial wave amplitudes, show how well they fit all the available data, and give the two photon couplings of scalar and tensor resonances that appear. These partial waves are important inputs into forthcoming dispersive calculations of hadronic light-by-light scattering.
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### Author and article information

###### Journal
1601.01061

High energy & Particle physics


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### Topic: Worst day of Lab  (Read 8560 times)

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#### lemonoman

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##### Worst day of Lab
« on: July 20, 2005, 01:57:30 AM »
I'm just wondering now what everybody's worst day of lab was.  Why was it terrible?  Were you killed?

I just got off a day today that was murderous.  I slept in, and so I missed a meeting with my supervisor.  Luckily, he seemed OK with it.  We got an oscillioscope, for an experiment I'm doing, and I was plugging along for a little while.  Then I tip over a retort stand, it makes a current amplifier fall to the ground and rips the wires out of my only good thermocouple.  It took 3.5 hours to fix everything after that little accident.

Then I worked a bit more, and I figured looking inside a box with a hole in the top would be easier with a light.  But no flashlights were to be found.  So I was unplugging an oldschool microscope light (from a microscope when the light was a separate fixture) and as I wobbled it back and forth (it was probably plugged in for the full 20 years before ) I felt a slight tingle.  Pffft, I'm tired, my body's making things up.  Wobble wobble BUZZ all through my thumb.  Never been shocked from an electrical outlet before...but it never hurts to try it

FInally, I was just working as usual on this GC oven.  I opened the door, moved to do something inside of it and the door just fell right off.  Nice.

It might also be interesting to note that the group beside me was doing microwave extractions, which are hardly ever a problem.  But today, they did a run and 6 of the 12 samples were ruined because the pressure inside the canister was too high and it released gas temporarily, I'm told.

So yeah, anybody wanna share their suckiest lab day with us?

#### jdurg

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##### Re:Worst day of Lab
« Reply #1 on: July 20, 2005, 09:10:06 AM »
I've had many, but I'll just list me worst four.

1):  High School Biology lab.  Dissecting a giant clam which has been preserved in a 30% formaldehyde solution for quite some time.  While standing by the mouth of the clam, my lab partner accidentally pressed down on the stomach of the clam.  A jet of formaldehyde squirts out of the clam onto the right side of my face.  Thank god I was wearing goggles, because they were covered in the formaldehyde as was my face.  The skin quickly turned 'dead' and started falling off my face in sheets.  I was raw for quite a few days after that.  Looked like a really nasty sunburn, but didn't really hurt.

2):  High school chemistry lab prep.  Making a solution of sodium silicate outside of the fume hood.  (STUPID!) and while weighing out the sample the powder kind of 'poofed' into the air right into my face.  I was coughing for quite a long time and silicates aren't good things to have in your lungs.

3):  High school chemistry lab.  Bending some glass tubing which had been used years before for bromine collection.  While heating the tubing, bromine leached out of the hot glass and vaporized into the air.  I was standing in the path going from the forming bromine to the air vent overhead.  Smelled REALLY bad and burned my sinuses.

4):  Worst one ever was college analytical lab.  I really wasn't thinking that day and I paid dearly for it.  Doing a lab involving the analysis of the nickel content of a US Nickel.  At one point in the experiment I accidentally opened up the bottle of concentrated ammonia solution outside of the fume hood.  Eyes teared up for a while and my nose wasn't too happy.  At the end of lab, when I was in a rush to get out of there, I forgot to label a beaker of concentrated H2SO4 that I had.  So when it was time to clean up, I just put my thumb into the solution thinking that it was only water.  It wasn't.    My thumbnail immediately started to fizz a bit and the burning sensation started in.  I rush over to the sink/waste bottle, still holding the beaker of acid in my hand, and in my hast put my forearm over an open bottle of concentrated nitric acid.  There was a puddle of the acid on the top of the bottle opening.  It found my forearm.  So I quickly put down the beaker and wash off the acid on my thumb.  It actually hurt more when the water made contact and I began washing it off.  In the meantime, the nitric acid was 'acting upon' my forearm and left me with a nice scar there which turned yellow-brown for a good long while.  My thumb recovered quite nicely and there are no noticeable scars on it.  I guess that's because my skin was so dry that the H2SO4 really couldn't eat the layer of dead cells.  The HNO3, meanwhile, was a bit more vicious and I have a nice little scar there.
"A real fart is beefy, has a density greater than or equal to the air surrounding it, consists

#### TakeItEasy

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##### Re:Worst day of Lab
« Reply #2 on: July 20, 2005, 09:17:49 AM »
To me it seems like a nightmare coming true.
I have seen many such accidents in lab but i've never personally experienced anything so 'nightmarish' not to mention some silly things i've done inside labs that could have resulted in ''the greatest nightmares of 20th century''
« Last Edit: July 20, 2005, 09:23:52 AM by Quark »

#### movies

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##### Re:Worst day of Lab
« Reply #3 on: July 20, 2005, 01:47:22 PM »
I've been pretty lucky in lab and haven't had too many accidents.  A couple of small fires from various things.  The most traumatic was impaling my hand with a syringe about a year ago.  It went in there pretty deep, but didn't really hurt as much as it just surprised me.  I quickly removed it, but I had to inject the stuff into a reaction or I would waste the reaction I had just spent an hour setting up, so I had to add the stuff before tending to my hand.  By the time I got a look and my hand the glove I was wearing was pretty much a balloon of blood.  Good times indeed.  The muscle in my hand really tensed up and was throbbing like crazy.  The puncture wasn't all that bad, but I lost a lot of fine motor control in my left hand for the next week or so.  I don't have a scar or anything, but I'm just hoping that the chemicals in the syringe aren't too carcinogenic because I am now the inadvertent in vivo test subject.

Another scary one was when I did a reaction that produces an equivalent of HCN.  While I was cleaning up, the flask slipped out of my hand and spilled some of the reaction sludge all over my bench.  I was really lucky since I didn't actually get any on myself, but I was just really shaken by the fact that I had lost control of this incredibly toxic material.  No harm done, but I had to go and take a walk outside before going back to lab.
« Last Edit: July 20, 2005, 01:50:11 PM by movies »

#### limpet chicken

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##### Re:Worst day of Lab
« Reply #4 on: July 20, 2005, 02:36:22 PM »
One of the scariest things to happen to me, was when I was younger, and din't quite know what I was doing, at about 13 or so, I kept a bottle of Mn2O7 in my lab, and spilled a little, without noticing, on my bench (the one I had at the time was covered in thick glass plating, so the Mn2O7 didn't go off in my face, but pooled on the glass.

About a half hour or so later, I was attempting to make PCl3, by chlorinating white P, and placed a small piece of WP on the desk, to add to a jar full of chlorine gas, only to have it suddenly explode, bright flash of light, scared the bleeding jesus out of me, and I almost dropped the jar I was using to store my lab stock of WP in on me.

Probably the worst though was a lab I did using hydrogen selenide generated by heating parraffin wax and selenium powder in a metal cab, made of an empty propane canister, with a hose through the top to vent gas into 2-propanol, I was heating the cen with a blowlamp, and after about 20 minutes, the hose burned through, and I got a great gout of H2Se spewing out, along with a dirty great big flame from burning wax vapors, I almost s#*$my pants running for my mask, I think I am lucky my amateur chemistry carreer didn't get prematurely ended. The light blinds So behold darkness as our new light In our darkness we can see So with others blindness We take flight. #### arnyk • Guest ##### Re:Worst day of Lab « Reply #5 on: July 20, 2005, 09:37:38 PM » Umm in high school chem we did sodium and water and the classroom blew up in flames. Well, maybe not "blew up" but a good portion of the room burnt down. I tried to clock in early today for work (I started at 1:30 and got there at 1:28...) since I was almost late and the entire management team caught me and lectured me for 5 minutes before I could go get ready. So all in all I was pretty late for the first time ever. Oh and I've only screwed up 4 times in my entire career, and 3 of those times a manager was right behind me, and 1 of those times the store owner was behind me. Baaaaaaaad luck I tell ya. Oh, are we still talking about labs? #### Qazzian • Regular Member • Posts: 42 • Mole Snacks: +13/-6 • Gender: • Text? We don't need no stinking text! ##### Re:Worst day of Lab « Reply #6 on: July 20, 2005, 10:27:55 PM » Hmm, nothing like that. But last term, I was testing samples, and titrated to an end point. I had to boil to expel CO2. I did all 4 samples, and was going to boil them all at the same time. I was tired, did the titrating, and dumped em. Now, I have large hands, which means I could hold all the samples at once. Which means they all went at once. As I saw the last drops come out, I noticed the hot plate I had set up, then looked from the hot plate, to the empty flasks, and back, and again, and realized what happened. 2 hours of sample prep gone. Not as bad, but really annoying: Sample of cow blood. Alot of it. Pouring into a graduated cylinder, and my hand tipped, so my left hand which was balanacing the cylinder was covered in blood. Looked like something from a horror movie. And wasn't too nice to feel either. Biochemistry student. Third Year. University of Waterloo. Canada. Hire Co-Op! #### xiankai • Chemist • Full Member • Posts: 786 • Mole Snacks: +77/-37 • Gender: ##### Re:Worst day of Lab « Reply #7 on: July 22, 2005, 01:09:02 AM » while i havent had any roller-coaster lab rides, i still have my share of annoyances during one QA test, i was supposed to add ethanol to some solution. then i took a good inhalation of the "sweet vapour". my nose instantly fired up and i had heart pains for a week after. one learns best by teaching #### woelen • Chemist • Full Member • Posts: 277 • Mole Snacks: +40/-2 • Gender: • The art of wondering makes life worth living... ##### Re:Worst day of Lab « Reply #8 on: July 22, 2005, 02:45:20 AM » ... I kept a bottle of Mn2O7 in my lab... I would not like to live nextdoors to you at those days . That stuff is ridiculously instable. I once made this stuff in the open air. I saw many specks of light (looked like little sparks) on the surface of the drop I made. I think that these little sparks were due to small dust particles touching the drop of Mn2O7/H2SO4 mix. While I was watching this, the whole mess did BOOM and I had a nice white/violet flash and many tiny droplets of brown stuff in the air. The same thing also happened to me, once I made a mix of 3 volumes of conc. H2SO4 and 1 volume of 30% H2O2. Fortunately, I also made just a large drop of this mix. I knew the dangers of it. Want to wonder? See http://www.oelen.net/science #### limpet chicken • mad scientist • Full Member • Posts: 750 • Mole Snacks: +49/-27 • Gender: • Vote Limpet for supreme emperor of the new order ##### Re:Worst day of Lab « Reply #9 on: July 23, 2005, 12:49:18 AM » Yeah, I know now of the dangers of manganese heptoxide, I didn't however, at age 12-13, if I KNEW the stuff was likely to blow up in a cloud of ozone and acidic fumes in my face at any moment, I probably wouldn't have kept it in a 2l glass bottle Often, I find, that one of the worst parts of chemistry, is those times where one needs reagents deemed suspicious by the drug-nazi governments, and where one is left waiting for several days, on edge, wondering wether what you get in the mail next is that liter of acetic anhydride you paid £40 for, or a customs McNastygram. I REALLY hate those sort of situations, even more than physical dangers in the lab, at least you will PROBABLY only cause a lot of pain and disfigurement, or a hospital visit (for which you get yummy painkilers ), rather than the dreaded investigation. Heh, I remember another incident as a kid now I think back, I used to be big into pyro, of the most obnoxious, teen wannabe "anarchist" sort, forever causing hell, at the time, I had a small arsenal of improvised rockets, and assorted explosive devices (none of which I do any more), and being inexperienced, I had under my bed, one 3 kilogram tub of a mixture of KMnO4 and sucrose, and one large container FULL of a chlorate/sulfur composition that at the time, I liked to fill pipe-bombs with, or empty CO2 canisters. I had absolutely no idea of what can happen by autocatalysed decomposition of the chlorate into ClO2, from residual acid on the sulfur, which then sets off the resulting entire damned charge, luckily, nothing came of it, but I stored the bucketful of S/NaClO3 for several months, until I eventually misused it, looking back, I am lucky some of the s#*$ in my younger days didn't take off more than just the flesh of part of my hand
The light blinds
So behold darkness as our new light
In our darkness we can see
So with others blindness
We take flight.


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# MKS GEN L looks dead

In an attempt to upgrade my Ender 3 to TMC2208, I bought an MKS GENL 1.0 board from Banggood, but it doesn't get recognized from the Windows Device Manager at all: no COM port, no "Unknown Device", no beep when connected/disconnected via USB.

I have some Arduino and electronics experience and having an USBasp I've decided to give a go to reflashing the bootloader, with no joy. I tried flashing both the stk500boot_v2_mega2560.hex and the ATmegaBOOT.hex using avrdude like the following (copy pasted from Arduino IDE):

bin\avrdude -Cetc\avrdude.conf -v -patmega2560 -cusbasp -Pusb -Uflash:w:..\..\arduino\avr\bootloaders\atmega8\ATmegaBOOT.hex:i -Ulock:w:0x0F:m

Whatever I do the board seems dead: tried alternative cables (also double checked using a plain inkjet printer to confirm it wasn't that) and also alternative PCs (all running Windows)... I believe it might be possible for me to upload Marlin via ICSP, but without USB I'll have not much use for it anyway...

It might be worth noting the board uses a CH340 USB chip (drivers already installed), which seems to be getting only 2.6 V at VCC...

When connected via USB the red power on LED D7 turns on, but nothing else happens...

I'm about to throw the board into the bin and buy another one from Amazon, unless somebody has any suggestion that might revive it...

• You might need a CH340 driver to be manually installed, although Windows normally installs that for you (whereas for OSX it is much more of a nightmare). See this for example, although, I presume (from your description) that Windows isn't even showing you an unknown device in Device Manager?. What is the error (if any) that you get when using avrdude? I've had issues like this before, and I've always been able to get them going again, usually with judicious use of the reset button and timing it just right. May 7 '19 at 20:19
• CH340 driver is installed, but as windows in not recognizing ANY device I have no COM port to specify to avrdude. The usbasp bootloader programming via ICSP seems to complete nicely (both write and verify steps completed). I would generally agree with you with regards to resetting the board, but in this case it seems it's the CH340 being gone... May 7 '19 at 21:59
• Hm, it doesn't sound good. This is a bit of a long shot, but the only thing that I can think of (at the moment) is to carefully monitor Device Manager whilst plugging in the board, and/or resetting the board. I had a mis-behaving Arduino-clone once that had a icon flash up only momentarily in the device manager (upon reset or plugging in) and if you weren't actually watching the device manager at the time you would never have known that it showed up briefly, and then disappeared. See here & its sequel. May 7 '19 at 22:09
• Presumably you've seen this: Mks Gen L and nothing! (where the solution appears to be buy a new board!) and more promisingly Marlin compile and upload fails–MKS Gen L 1.0 (SOLVED) - among the many hints and tips, possibly there is a need for a CH341SER driver (rather than a CH340[G])? May 7 '19 at 22:27
• @Greenonline the alt driver didn't help either, as I was expecting due the fact no device shows up to the device manager, not even momentarily. I also went a little to a lower level, trying to use zadiq to scan for any device having any USB signature, but the only USB devices recognized are those I already know (mouse, keyboard, USB hub, etc...) I would definitely rule out the driver problem at this stage... But thanks a lot for providing all that info and links May 8 '19 at 21:27


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## How long would it take for a human to walk one light year?

A light-year is approximately $10^{16}\rm{m}$ or ten trillion kilometres.

Human walking speed is about five kilometres per hour or, let's say, forty kilometres per day (allowing for eight hours walking, eight hours sleep, and eight hours contemplating the meaning of a long walk on each day).

That is going to take $\frac{10\,000}{40}=250$ billion days, or a bit less than a billion years (allowing for the occasional holiday at some of the places being passed).

About a fifth of the Earth's existence - thirty million human generations, and about five hundred times as long as the genus Homo has existed.

Dedicated human walkers could do it faster and, I dare say, the species at the end of those millions of generations would be considerably better walkers than the best Olympic walkers today.

Assuming we can walk about 2 mph. And assuming we go non-stop for sleep, meals, potty, etc,

One opinion : 225 million years

How Long Would It Take To Walk A Light-Year?

###### What would had happened if the earth did not revolve nor rotate?

There would be no day or night change, it would be either sunny all the time or dark all the time. One portion of the Earth would be unbearably hot and the other unbearabley cold, the only temperate zones would be on the fringes of the hot cold dividing line.

###### What are some of the monumental obstacles, that humans will have to overcome, in the coming years, if we are to survive as a species?

I don't think there are any monumental obstacles facing humanity. (Except for one very important threat, which I will mention at the end of this answer.)The world as a whole is getting more prosperous. And with the continued exponential growth in technology, which makes almost everything less expensive,

###### If you were going to die tomorrow, where would you go?

If I am going to die tomorrow, I will spend the remaining time with my MOTHER.I have only five words that I'd like to say to her. Five words that I think every parent wants to hear:Thank you, and I'm sorry.I will sleep like this baby.