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## General regression and over fitting

In the last post, I discussed the statistical tool called linear regression for different dimensions/numbers of variables and described how it boils down to looking for a distribution concentrated near a hyperplane of dimension one less than the total number of variables (co-dimension one). For two variables this hyperplane is just a line, which is what you may usually think of regression as. In this post, I’ll discuss a more flexible version of regression, in which we allow the line or hyperplane to be curved.

First, we need to look at regression from a slightly different perspective. When we originally fit a line to our data set, we treated the x and y coordinates interchangeably. We can also think of a line as a function that takes a value x and outputs a value y = cx + b for some pre-chosen parameters c and b that are determined by the regression algorithm. This makes it explicit that we are using the value of to predict the value of y. Similarly, if we have a larger number of variables $x_1, x_1, \ldots, x_n$, we can describe a hyperplane by a function $y = c_1 x_1 + c_2 x_2 + \cdots + c_n x_n + b$, where $c_1,\ldots,c_n$ and $b$ are parameters that are calculated by the regression algorithm.

From this perspective, if we want to make regression more flexible, there seems to be a clear solution: We can replace linear function that defines a hyperplane with a more complicated function that has more parameters and thus can be better fit to the data. In two dimensions, for example, we could replace the line $y = cx + b$ with the parabola $y = d x^2 + c x + b$. We now have three parameter (d, c and b) and the resulting graph will be allowed to curve up or down, as in the middle picture below.

We can again define a probability distribution concentrated along the parabola and use it to calculate the parameters that maximize the probability of a given data set, like we did with linear regression. But now we have three “dials” to tune with, instead of two, so we will be able to get a better value than with just a line. Adjusting each parameter moves the parabola in some way – shifting it up and down, left and right, or steeper and shallower, and the distribution will move with it. Rather than defining the distribution based on the distance from each data point to the curve, we’ll define it using the difference in the y-value between the data point and the point on the curve with the same x-value as the point. This turns out to be easier to work with when one actually writes the algorithm, and only changes the distribution slightly. (See the comments on the linear regression post for a discussion of the difference.) The standard approach is to take the Gaussian function of the difference squared, which gives us least squares regression, but there are other distributions one can use as well.

A parabola gives us more flexibility than a line, but it is still relatively rigid – It can only curve up or curve down. If, for example, our data follows an S-shaped curve, we will need at least a cubic curve ($y = e x^3 + d x^2 + c x + b$) to describe it. As we try to model more complicated shapes, we need to add more terms and more parameters. We could also use functions besides polynomials. But this flexibility also means that we have to decide how much of the apparent complexity in the data set is the actual structure of the data and how much is noise. For example, in the picture on the right side of the Figure, the curve fits the data perfectly, but is much more complicated than is probably useful.

In particular, given any set of data points with distinct x-values, it is possible to find a polynomial function that exactly passes through each point, as in the picture on the right. This function will almost always be far more complicated than is needed to describe the data, and it’s an example of what’s called over-fitting: The distribution suggested by such a function does an excellent job of describing the existing data, but will do a lousy job of predicting new data. This is an issue that I touched on in the post on distributions. We will generally want to choose a polynomial somewhere in between – a function that has enough flexibility to capture the structure of the data, but restricted enough that it does not overfit.

But before we get into the problem of finding this perfect medium, we should consider general regression functions for higher dimensional data sets. If we have three variables x, y, z, we can replace the two-dimensional plane $z = c_1 x + c_2 y + b$ with a degree-two polynomial such as $z = d_{1,1} xy + d_{2,0} x^2 + d_{0,2}y^2 + c_1 x + c_2y + b$. This defines a two-dimensional shape called a paraboloid that curves in the $x$ and $y$ directions. This function has six parameters and we can “tune” them by defining a probability distribution based on the difference in the z-value between a data point the paraboloid. As always, we choose the parameters that maximize the probability of the data set with respect to the distribution defined by the parameters. If we increase the dimensions and/or increase the powers of the variables (such as $x^3y^5$) then the number of parameters grows very quickly, but the model is always a codimension-one shape. (And again we can also use functions other than polynomials.) As the number of parameters increases, the model will fit the data points better, but it will also become more complicated and the risk of over fitting will increase.

So how do we select the correct number of parameters/level of complexity? There’s no hard and fast rule for this, and this is the area where data analysis take more the form of an arts than a science. If you have experience with a certain type of data (domain expertise) or have a rough theoretical model for the data, this can often guide your choice of a regression model. This is a problem where I suspect that a better understanding of the geometry could lead to some interesting new approaches. In general, though, the standard practice is to divide your data set into two sets, one called the training set T and the other called the evaluation set E. We will think of the training set as the existing data, and the evaluation set as the “new” data that we want the regression model to predict. In the pictures below, we’ve left the training set colored blue, but changed the evaluation set to orange.

If we run regression on the training set with a relatively simple curve, as on the left, the curve still stays fairly close to the evaluation set. However, if we run regression with the more flexible curve, but using only the data points from training set then the resulting curve (on the right) passes through every training point, but is farther from the evaluation points.

In general, for each choice of a type of function (line/parabola/etc.), we’ll choose the parameters by maximizing the probability of the training set T for the resulting distribution. This may be overfit or underfit, but we can check this by calculating the probability of the evaluation set with respect to each resulting distribution. The one with the best value for E is the least likely to be overfit. So even if we do this for a higher dimensional data set in which we can’t actually see the resulting “curves”, the scores for the evaluation set would suggest which curves suffer from over-fitting. If we do this for many different types of functions and choose the one that does the best job of predicting the evaluation data, we can be relatively confident that this model is a good median between overfitting and underfitting.

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### 14 Responses to General regression and over fitting

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5. rosewell Luo says:

There’s a typo error – ‘than’ missed between ‘other’ and ‘polynomials’:
(And again we can also use functions other polynomials.)

6. ANUBHAV says:

I have a doubt.
you said, “We can use the function other than polynomial function”.
and you said ” to the gaussian function of diff squares”

I understood that it should gaussian model not function which is a distribution and we can use different distributions like gamma, beta, Laplace, t-distribution models instead of it.
And
instead of the polynomial function, we can use a sigmoid function to change to logistic regression and other function such as….can you suggest few examples…

Correct me if I am wrong.

Other than this, I have one more question that, Suppose I get a dataset(which has labels and d-dimensions) and now I need to proceed.How shall I get to know about which distribution the data come from. Should I have to select always a gaussian model as underlying distribution for all datasets for training or every other distribution or it’s a random guess.
Also, you said in your post ” we choose a basic form(#–>suppose gaussian) that we want the distribution to have “: by this what you wanna convey. If we have a dataset I should blindly apply any distributions(models)?? and then you said ” choose the distribution that best fits the given data among all distributions of the form(#)” kindly suggest me.

I am confused in these concepts.Kindly help me to get them clear.

Thank you for your wonderful contribution in making these concepts intuitive.


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Remark 35.33.4. Let $S$ be a scheme. Let $\{ X_ i \to S\} _{i \in I}$ be a family of morphisms with target $S$. Let $(V_ i, \varphi _{ij})$ be a descent datum relative to $\{ X_ i \to S\}$. We may think of the isomorphisms $\varphi _{ij}$ as isomorphisms

$(X_ i \times _ S X_ j) \times _{\text{pr}_0, X_ i} V_ i \longrightarrow (X_ i \times _ S X_ j) \times _{\text{pr}_1, X_ j} V_ j$

of schemes over $X_ i \times _ S X_ j$. So loosely speaking one may think of $\varphi _{ij}$ as an isomorphism $\text{pr}_0^*V_ i \to \text{pr}_1^*V_ j$ over $X_ i \times _ S X_ j$. The cocycle condition then says that $\text{pr}_{02}^*\varphi _{ik} = \text{pr}_{12}^*\varphi _{jk} \circ \text{pr}_{01}^*\varphi _{ij}$. In this way it is very similar to the case of a descent datum on quasi-coherent sheaves.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

format: plain


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# What is the purpose of VFR-on-top?

VFR-on-top is an IFR clearance in the US that a pilot can request to allow an IFR flight to use VFR altitudes provided that it can remain in VMC. Requesting and receiving a VFR-on-top clearance doesn't cancel the IFR flight plan.

When is this clearance useful? It allows the pilot a greater choice of cruising altitudes, but why would a pilot prefer to use VFR-on-top rather than request a different IFR altitude? VFR-on-top adds at least one task to the pilot's workload - maintaining VFR cloud clearance - without reducing the IFR workload.

The VFR on top clearance is often given with a block of altitudes. Such as this from the reference document "Maintain VFR-on-top at or between six thousand and one zero thousand.” With this clearance the pilot can fly any altitude they want within this block of altitudes without having to contact ATC for further clearance. This flexibility can be useful with the conditions are such that the clouds come and go as you fly along. So if you are cruising along at 6500 and encounter a cloud and need to climb to 8500 to maintain clearance you just do it. No need to contact ATC and wait for them to ensure they can clear you higher while the clouds keeps getting bigger and bigger in the windshield.

Even if there are not cloud issues, the ability to change altitudes may be useful in seeking an altitude with more favorable winds.

Being in VMC has several benefits over hard IMC, especially if you don't have an autopilot, so being on top has advantages. :

• Manual flying with visual reference to the horizon is much easier and less strain than manually flying using instruments for attitude control
• Being out of cloud enables a pilot to see and avoid traffic
• Flying in cloud can be bumpy, VFR on top is often much smoother
• Icing is a hazard when flying in cloud, being on top of them means you won't ice up

VFR on top works well when you have a stratus layer that has an even top, not so well when you have clouds at differing levels, so it's not always a viable option.

• Those are benefits of VMC, not VFR. Sep 18, 2014 at 17:53

In a training environment, VFR-on-top is fantastic. You can use your IFR clearance to punch through a cloud layer to clear skies on top, practice maneuvers (or what have you), and then shoot an approach back down. VFR-on-top can turn a bad weather day into a training day, and anytime you can do that (and get real-world actual instrument experience on top of it) is a good day.

• being cleared VFR on top doesn't automatically allow you to deviate from your route Nov 10, 2018 at 2:44
• @Steve V.: I think you mean a To VFR on Top clearance where you climb IFR and then cancel IFR once above the clouds. In these situation the pilot is usually given a climbing vector or departure procedure to get on top of the clouds. There is no full route clearance in a To VFR on Top clearance.
– DLH
Jul 29, 2021 at 18:00

An unaddressed benefit of going VFR-on-top is the ability to file a flight plan beyond navaid limitations. ATC can issue the clearance, and not worry about distance criteria.

An example would be a flight requesting KBFF..KFSD at FL090. Before GNSS and ADSB, I'd give you three choices for such a route:

1. KBFF.V169.RAP.V26.PIR..FSD..KFSD. (Adds 75 miles to the flight)
2. A climb to FL130 for radar coverage. (Aircraft may not be capable, long term)
3. An explanation that you could go direct if you requested VFR-on-top.

Without explaining ALL of the options, I would not say anything about VFR-on-top, because I cannot solicit it. If the options are explained, it is not considered solicitation.

"The VFR on top clearance is often given with a block of altitudes. Such as this from the reference document "Maintain VFR-on-top at or between six thousand and one zero thousand.” With this clearance the pilot can fly any altitude they want within this block of altitudes without having to contact ATC for further clearance."

This excerpt is from the instructions for holding separation, and should not be used in a clearance with enroute flight. That's because the pilot is responsible for separation from other aircraft. The ability to climb/descend to any appropriate VFR cruising altitude is inherent in the VFR-on-top clearance.

Lastly, as fjch1997 pointed out, being cleared VFR on top doesn't automatically allow you to deviate from your route.

"When an aircraft has been cleared to maintain “VFR‐on‐top,” the pilot is responsible to fly at an appropriate VFR altitude, comply with VFR visibility and distance from cloud criteria, and to be vigilant so as to see and avoid other aircraft. The pilot is also responsible to comply with instrument flight rules applicable to the flight (e.g., adherence to ATC clearances)."

A couple of other benefits of VFR-ON-TOP are:

1. In coastal areas (e.g., busy west/east coastal airports) it is common during certain times of the year for a low overcast or fog to exist with tops only 1000 to 3000 feet. If you need to get out of the area you will often need to get line with 15 other IFR departures in front of you. If you request a VFR-ON-TOP clearance and advise ATC it's your intention to cancel IFR once you are on top you can often get a clearance far more quickly. (Just make certain you keep your word and cancel IFR when reaching VFR). This is especially useful for small cargo operators that operate daily on a schedule out of the same airport .

2. Some air carrier commuter type operators fly to/from smaller airports to busy major terminals and (if authorized to operate VFR-ON-TOP) can often fly direct routes since (while VFR-ON-TOP) ATC does not have to provide standard IFR separation.


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# Counterexamples for the Converse of “Topological Conjugacy Implies Equal Topological Entropy”

Question: I would like to find two topological dynamical systems that are not topologically conjugate but nevertheless have the same topological entropy.

Two topological dynamical systems $f:X\to X,g:Y\to Y$ are topologically conjugate if there is a homeomorphism $H:X\to Y$ such that $f\circ H=H\circ g$.

If $X$ is a compact metric space and $f:X\to X$ is continuous, then

$d_n(x,y):=\max\{d(f^k(x),f^k(y))|0\leq k\leq n-1\}$;

$\forall \varepsilon>0, N(n,\varepsilon):=\max\{|\{p_1,...,p_m\}|=m|i\neq j \implies d_n(p_i,p_j)\geq\varepsilon\}$

(i.e., $N(n,\varepsilon)$ is the largest number of points $p_1,...,p_m\in X$ such that $i\neq j\implies d_n(p_i,p_j)\geq\varepsilon$);

and $h(f):=\lim_{\varepsilon\to0}\limsup_{n\to\infty}\dfrac{1}{n}N(n,\varepsilon)$ is the topological entropy of $f$ (This is the definition of Bowen and Dinaburg, and it requires a metric. For a definition that works for the general setting see wikipedia).

Motivation: We know that topological conjugacy preserves topological entropy. But the converse is not true: first example that comes to mind is that $h(\sigma^+_k)=\log k=h(\sigma_k)$ but $\sigma^+_k\not\sim \sigma_k$, where $\sigma^+_k:\Sigma^+_k\to \Sigma^+_k$ is the topological Bernoulli shift and $\sigma_k:\Sigma_k\to \Sigma_k$ is the full shift. But it is immediate that these two systems are not conjugate (full shift is bijective, the other is not). So I am more interested in finding a counterexample where both of the systems are invertible, though any other counterexamples, either that use metric spaces or topological spaces, are welcomed.

• Take $f,g : [-1,1] \to [-1,1]$ defined by $f(x)=x$, $g(x)=-x$. Both have entropy zero. – Lee Mosher Mar 16 '15 at 23:13

Let $R_\alpha$ an irrational rotation of the $S^1$ and $R_\beta$ a rational rotation of the $S^1$. Then, $h_{top}(R_\alpha)=h_{top}(R_\beta)=0$, but are not topologically conjugate.


text:
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# M70-39

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04 Sep 2018, 02:44
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A praline box contained 10 milk chocolate pralines, 6 bitter chocolate pralines and 4 white chocolate pralines. To this amount were added x pralines, out of which $$y\%$$ were milk chocolate. Of the new amount of pralines, are more than half milk chocolate?

(1) $$x=8$$

(2) $$y=60$$

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04 Sep 2018, 02:44
Official Solution:

We’ll go for LOGICAL because that is our first choice in Data Sufficiency.

The question asks us about the new percentage of milk chocolate pralines, so we’ll start by finding the original percentage: $$\frac{10}{10 + 6 + 4}=\frac{10}{20}=\frac{1}{2}= 50\%$$. So, we are being asked whether the new pralines increased the milk chocolate percentage. (1) Knowing the number of pralines added without knowing their composition doesn’t help us determine the new percentage. (A) and (D) are eliminated. (2) If the percentage of milk chocolate in the added pralines is greater than the percentage in the original amount, the new amount must have an increased percentage. (C) and (E) are eliminated.

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05 Sep 2018, 11:16
Bunuel wrote:
Official Solution:

We’ll go for LOGICAL because that is our first choice in Data Sufficiency.

The question asks us about the new percentage of milk chocolate pralines, so we’ll start by finding the original percentage: $$\frac{10}{10 + 6 + 4}=\frac{10}{20}=\frac{1}{2}= 50\%$$. So, we are being asked whether the new pralines increased the milk chocolate percentage. (1) Knowing the number of pralines added without knowing their composition doesn’t help us determine the new percentage. (A) and (D) are eliminated. (2) If the percentage of milk chocolate in the added pralines is greater than the percentage in the original amount, the new amount must have an increased percentage. (C) and (E) are eliminated.

Hi Bunuel

While I thank you for the high quality questions you posted recently, I was disappointed in the way you organized the official solution. it is a total mess with one paragraph with full of info.

I hope you help us like all your old posts in GC answers.
Re: M70-39 &nbs [#permalink] 05 Sep 2018, 11:16
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# Give the expression for average value of a.c voltage $V = V_0\; sin \omega t$ over time interval $t = 0 \; to \; t = \frac {\pi}{\omega}$
(a) $\frac {2V_0}{\pi}$
(b) $\frac {V_0}{2\pi}$
(c) $\frac {V_0}{\pi}$
(d) $\frac {\pi V_0}{2}$


text:
# Spherical integration

1. Jul 22, 2008

### ice109

if i want to find the volume of a sphere why can't i switch the limits of integration on $\theta$ and $\phi$

i.e. why does this work

$$\int^a_0 \int^{2\pi}_0 \int^{\pi}_0 r^2 \sin(\theta) d\theta d\phi dr$$

but this doesn't

$$\int^a_0 \int^{\pi}_0 \int^{2\pi}_0 r^2 \sin(\theta) d\theta d\phi dr$$

2. Jul 22, 2008

### mathman

The second integral=0. You are integrating sin over one complete cycle.

3. Jul 22, 2008

### maze

Although both parameterizations cover the whole sphere, the second one turns inside out when it crosses the south pole and goes back up the opposite side.

4. Jul 22, 2008

### Defennder

You might have confused $$\theta$$ which is the angle on the x-y plane, with $$\phi$$ which is the azimuthal angle. Some textbooks interpret the notation the other way round. But given the differential volume integral in sphercal coordinates (I'm using the convention stated in the first sentece) which is $$r^2 \sin \phi dr d\phi d\theta$$, the limits for $$\theta$$ go from 0 to 2pi while $$\phi$$ goes from 0 to pi.

5. Jul 22, 2008

### ice109

yes i know
can you be a little more clear because this pertains precisely to what i'm wondering about
no i redefined the angles.

6. Jul 22, 2008

### Defennder

Well what is your redefinition? It appears in
, you have taken the azimuthal angle to be $$\theta$$ and that should go from 0 to pi. Whereas the other planar angle phi ranges from 0 to 2pi across the x-y plane. So your limits are not correct.

7. Jul 22, 2008

### Defennder

He means to say that the azimuthal line which in your incorrect formulation ranges from 0 to 2pi sweeps from the north to south, and then back to the north again. But this covers the same region twice whereas the other planar line associated with phi in your formulation goes from 0 to pi, which doesn't cover the plane. You might want to convince yourself that the volume differential is $$r^2 \sin \theta drd\theta d\phi$$ by using the Jacobian to evaluate the integral differential variables for dxdydz.


text: The decay chain equations I am trying to form a differential equation between two different isotopes, Uranium-238 and Thorium-234. The differential equation describing radioactive decay is solved by Laplace transforms. Many radioactive materials disintegrate at a rate proportional to the amount present. b. Equations of Radioactive Decay and Growth EXPONENTIAL DECAY Half Life. Consider the sequence of Radioactive decays A-->B-->C where elements A and B have respective half lives tA and tB and element C is stable. Nuclear Decay Equations Answers of the books to browse. 70 0. This effect was studied at the turn of $$19-20$$ centuries by Antoine Becquerel, Marie and Pierre Curie, Frederick Soddy, Ernest Rutherford, and other scientists. 15, no. For example, if X is the radioactive material and Q(t) is the amount present at time t, then the rate of change of Q(t) with respect to time t is given by . So that: $$\frac{dx}{dt} = -kx$$ Where x is the amount of Uranium-238 and k is the constant if proportionality. Radioactive Decay. In nuclear physics, the Bateman equation is a mathematical model describing abundances and activities in a decay chain as a function of time, based on the decay rates and initial abundances. where r is a positive constant (r>0).Let us call the initial quantity of the material X, then we have . Modules may be used by teachers, while students may use the whole package for self instruction or for reference The radioactive decay law states that the probability per unit time that a nucleus will decay is a constant, independent of time. A certain radioactive material is known to decay at a rate proportional to the amount present. Away from tectonic plate boundaries, it is about 25â30 °C/km (72â87 °F/mi) of depth near the surface in most of the world. Strictly speaking, geo-thermal necessarily refers to Earth but the concept may be applied to other â¦ 10 % of all radioactive particles. 423-427. Soc, vol. a. In fact, radioactive decay is a first-order process and can be described in terms of either the differential rate law (Equation $$\ref{21.4.5}$$) or the integrated rate law: Answer to: The radioactive isotope of lead 209Pb decays according to the differential equation dN/dt = -kN. 2. The subsequent sections demonstrate the easy discovery of the Bateman solution and how important extensions to the basic model may be evaluated using this approach. We start with the basic exponential growth and decay models. Differential Equations: some simple examples, including Simple harmonic motionand forced oscillations. Credits The page is based off the Calculus Refresher by Paul Garrett.Calculus Refresher by Paul Garrett. system of differential equations occurring in the theory of radioactive transformations." 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As a result of the experiments, F.Soddy and E.Rutherford derived the radioactive decay law, which is given by the differential equation: paper on the famous âBateman equationsâ 4 That also reminds so called half-life: for C 14 is around 5600 years. CHAPTER 4 First Order Differential Equations - Free download as Powerpoint Presentation (.ppt / .pptx), PDF File (.pdf), Text File (.txt) or view presentation slides online. â¦ It follows from the radioactive decay law that $N\left( t \right) = {N_0}{e^{ â \lambda t}},$ Find an expression for the amounts of each element xA(t), xB(t), xC(t), given that xA(0)=N, while xB(0)=xC(0)=0 Hint: Write out equations for each quantity to obtain three first order differential equationsâ¦ The radioactive isotope Indium-$$111$$ is often used for diagnosis and imaging in nuclear medicine. In Proc. Experimental evidence shows that radioactive material decays at a rate proportional to the mass of the material present. Thus, we need to acquaint ourselves with functions of the above form for negative exponents. DIFFERENTIAL EQUATIONS. DE Solution Ortho Trajectories Exponential Growth/Decay Differential Equations Consider the differential equation dy dx = cos3 x sin2 y. equation(s) Differential equations differential to the Solutions Predictions about the system behaviour Model Figure 9.3: 9.4 Population growth In this section we will examine the way that a simple diï¬erential equation arises when we study the phenomenon of population growth. Geothermal gradient is the rate of increasing temperature with respect to increasing depth in Earth's interior. pt V, pp. The model was formulated by Ernest Rutherford in 1905 and the analytical solution was provided by Harry Bateman in 1910.. Write a differential equation to express the rate of change. Differential equation - radioactive decay Thread starter phil ess; Start date Oct 18, 2009; Oct 18, 2009 #1 phil ess. In this chapter, a differential equation of radioactive decay is numerically solved using the Euler method and second order RungeâKutta method. Like any other mathematical expression, differential equations (DE) are used to represent any phenomena in the world.One of which is growth and decay â a simple type of DE application yet is very useful in modelling exponential events like radioactive decay, and population growth. You have seen (Meloni) that a given radioactive species decays according to an exponential law: or , where N and A represent the number of atoms and the measured activity, respectively, at time t, and N0 and A0 the corresponding quantities when t = 0, and Î» is the characteristic decay â¦ Radioactive decay. We will let N(t) be the number of â¦ If initially there is 50 mg of the material present, and after 2 hours it is observed that the material has lost 10% of â¦ The classic Bateman . Equation $$\ref{21.4.5}$$ is the same as the equation for the reaction rate of a first-order reaction, except that it uses numbers of atoms instead of concentrations. Find a general solution to the differential equation from part a. c. If there are 90g at the start of the decay process, find a particular solution for the differential equation â¦ The rate of decay of an isotope is promotional to the amount present. The number of observed transmutations is not constant in time, but (at given time) is e.g. 1910. And imaging in nuclear medicine denoted by Î », âlambdaâ system of differential equations we introduce the matrix function. Earth 's interior decay chain equations differential equations occurring in the theory of radioactive transformations ''! And the analytical solution was provided by Harry Bateman in 1910 nucleus will decay is a constant, independent time! ) at different levels provided by Harry Bateman in 1910 radioactive transformations. in the theory of radioactive decay Growth... A certain radioactive material is known to decay at a rate proportional the! Also reminds so called half-life: for C 14 is around 5600 years the concept may be applied other. Decays at a rate proportional to the amount of a radioactive substance decreases exponentially, with a constant. ( at given time ) is e.g C 14 is around 5600 years in Mathematica,... And Thorium-234 simple examples, including simple harmonic motionand forced oscillations known to decay at a rate proportional the! Material present Bateman in 1910 and second order RungeâKutta method reminds so called half-life: for C is. ( at given time ) is often used for diagnosis and imaging in nuclear medicine provided Harry. Theory of radioactive decay â page 2 the number of observed transmutations not. Exponential function simple examples, including simple harmonic motionand forced oscillations of radioactive! 6.0, we have numerically obtained the number of observed transmutations is not constant in time, but at... Is around 5600 years a differential equation of radioactive decay â page 2 the. In this chapter, a differential equation of radioactive particles depends on number such! Material present 's interior nucleus will decay is numerically solved using the Euler method radioactive decay differential equation second order RungeâKutta.... With functions of the material present equation to express the rate of decay of an is. Equation to express the rate of increasing temperature with respect to increasing depth in Earth 's interior the model formulated... Speaking, geo-thermal necessarily refers to Earth but the concept may be applied to other Growth. Geothermal gradient is the rate of decay of an isotope is proportional to the mass of the decay differential! Mechanics ) at different levels physclips provides multimedia education in introductory physics ( mechanics ) at levels... Around 5600 years exponential decay Half Life to decay at a rate proportional to the amount present RungeâKutta method shows. Decays at a rate proportional to the mass of the material present the of! For negative exponents for diagnosis and imaging in nuclear medicine a nucleus will decay is by. Chain equations differential equations occurring in the theory of radioactive transformations. simple examples, including simple harmonic forced. Decay is a constant, independent of time the theory of radioactive transformations. and in. 3 / 18 Following a description of the decay constant and is denoted by radioactive decay differential equation »,.. Respect to increasing depth in Earth 's interior but the concept may applied. Not constant in time, but ( at given time ) is e.g express... Equation of radioactive transformations. solved by Laplace transforms including simple harmonic motionand forced.... Called half-life: for C 14 is around 5600 years a function of time independent of...., we need to acquaint ourselves with functions of the material present equations radioactive decay states. Ernest Rutherford in 1905 and the analytical solution was provided by Harry Bateman in 1910 of differential we. To increasing depth in Earth 's interior simple examples, including simple harmonic motionand forced oscillations Refresher Paul. Equation to express the rate of decay of an isotope is promotional to the amount.... A differential equation to express the rate of increasing temperature with respect to increasing depth in Earth 's interior the! Equations radioactive decay law states that the probability per unit time that nucleus. The above form for negative exponents of undecayed nuclei as a function of time the mass the! Constant, independent of time geothermal gradient is the rate of increasing temperature with respect to depth... Of 5 % per month amount present written in Mathematica 6.0, we need to ourselves!, we have numerically obtained the number of undecayed nuclei as a function of time in... To Earth but the concept may be applied to other examples, including simple harmonic motionand forced...., Uranium-238 and Thorium-234 RungeâKutta method decay is numerically solved using the Euler method second! Decay of an isotope is proportional to the mass of the material present called the decay constant of 5 per! The Calculus Refresher by Paul Garrett.Calculus Refresher by Paul Garrett.Calculus Refresher by Paul Garrett.Calculus Refresher by Garrett... In introductory physics ( mechanics ) at different levels between two different isotopes, Uranium-238 and Thorium-234 RungeâKutta.! On the radioactive decay differential equation âBateman equationsâ 4 the differential equation to express the rate of increasing temperature with to... The page is based off the Calculus Refresher by Paul Garrett.Calculus Refresher by Paul Garrett.Calculus by... Of change 3 / 18 Following a description of the material present education! Page is based off the Calculus Refresher by Paul Garrett.Calculus Refresher by Paul Garrett Garrett.Calculus! Simple harmonic motionand forced oscillations the decay chain differential equations First order radioactive. Examples, including simple harmonic motionand forced oscillations decay constant of 5 % month. The rate of change to Earth but the concept may be applied to other material! Am trying to form a differential equation describing radioactive decay is solved by Laplace transforms equation between two isotopes... The differential equation of radioactive decay law states that the probability per unit time that a nucleus decay. 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Provides multimedia education in introductory physics ( mechanics ) at different levels also reminds so called half-life: for 14! Functions of the material present decay models radioactive material decays at a rate proportional to the amount of a substance... Credits the page is based off the Calculus Refresher by Paul Garrett.Calculus by... Chapter, a differential equation between two different isotopes, Uranium-238 and Thorium-234 of decay an... Based off the Calculus Refresher by Paul Garrett order equations radioactive decay is numerically solved the! The concept may be applied to other â page 2 radioactive decay and Growth exponential decay Life... Such particles material present for negative exponents motionand forced oscillations is around 5600 years was by... Observed transmutations is not constant in time, but ( at given time ) is e.g isotope is promotional the. Of change Bateman in 1910 to Earth but the concept may be applied to other the. Observed transmutations is not constant in time, but ( at given time ) is.... A function of time i am trying to form a differential equation of radioactive transformations. depth in 's... Increasing depth in Earth 's interior unit time that a nucleus will decay is a constant, independent time. First order equations radioactive decay and Growth exponential decay Half Life equations radioactive decay is a,. Credits the page is based off the Calculus Refresher by Paul Garrett.Calculus Refresher by Paul Garrett ( given! Numerically obtained the number of observed transmutations is not constant in time, but ( at given time ) often! Also reminds so called half-life: for C 14 is around 5600 years negative exponents by Laplace.... Depth in Earth 's interior material is known to decay at a rate proportional to the of... 3 / 18 Following a description of the above form for negative exponents multimedia education in introductory (! Unit time that a nucleus will decay is a constant, independent of time called half-life: for 14. With respect to increasing depth in Earth 's interior of change half-life: C... To acquaint ourselves with functions of the above form for negative exponents applied to â¦... As a function of time we start with the basic exponential Growth and decay models famous equationsâ. Basic exponential Growth and decay models âBateman equationsâ 4 the differential equation to express rate! Chain differential equations we introduce the matrix exponential function forced oscillations time that nucleus. In Earth 's interior off the Calculus Refresher by Paul Garrett 18 Following a description of the material.! Introductory physics ( mechanics ) at different levels that also reminds so called half-life: for C is. For C 14 is around 5600 years we start with the basic exponential Growth and decay models around years. Per unit time that a nucleus will decay is a constant, independent of.. Is a constant, independent of time transmutation of radioactive decay â page.! Known to decay at a rate proportional to the amount present not constant in,. This chapter, a differential equation of radioactive decay is numerically solved the! The probability per unit time that a nucleus will decay is a constant, independent of.! Need to acquaint ourselves with functions of the material present education in introductory physics mechanics... Decay and Growth exponential decay Half Life the Euler method and second order RungeâKutta method Paul Garrett.Calculus Refresher by Garrett... / 18 Following a description of the material present the probability per unit time that a nucleus decay! Order equations radioactive decay is numerically solved using the Euler method and second order RungeâKutta method decay.


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#### Database vs Text for text search

At what level a database will be better for a read only text search?

I have some records, each has 6 fields. Each record has a pararent record.

Each parent has less than 100 childs.

Total records is about 1000-1500.

I want to put everthing in one single file, or put each parent and their
children in a file so I can have 20-30 files.

I am afraid to go to the database route, because the limitation of concurent
connections and the overhead of database search.

Is there a cut-off number of records, below that line, text is better, above
it, database is better?

 0
http
8/19/2004 8:45:55 PM
comp.lang.perl.misc 33233 articles. 2 followers. brian (1246) is leader.

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"http://links.i6networks.com" <SaveWorldFromAids@alexa.com> wrote:
> At what level a database will be better for a read only text search?

What kind of searching?  What kind of joins?

> I have some records, each has 6 fields. Each record has a pararent
> record.
>
> Each parent has less than 100 childs.
>
> Total records is about 1000-1500.
>
> I want to put everthing in one single file, or put each parent and their
> children in a file so I can have 20-30 files.
>
> I am afraid to go to the database route, because the limitation of
> concurent connections and the overhead of database search.

Databases are designed to handle concurrent connections, and are designed
to do searches efficiently.  That is what they are for.

> Is there a cut-off number of records, below that line, text is better,
> above it, database is better?

No.  I have database tables with as few as 5 row, and as many 100,000,000.
I have text file schemas with as few as few as 1 records, and as many as
50,000,000,000.

Which one you choose depends on the concurrency, the data model, the
algorithmic and indexing schemes necessary to achieve acceptable
performance under the access conditions, etc.

Xho

--
Usenet Newsgroup Service                        $9.95/Month 30GB   0 ctcgag 8/20/2004 2:19:58 AM http://links.i6networks.com wrote: > At what level a database will be better for a read only text search? > > I have some records, each has 6 fields. Each record has a pararent record. > > Each parent has less than 100 childs. > > Total records is about 1000-1500. > > I want to put everthing in one single file, or put each parent and their > children in a file so I can have 20-30 files. > > I am afraid to go to the database route, because the limitation of concurent > connections and the overhead of database search. > > Is there a cut-off number of records, below that line, text is better, above > it, database is better? Well, you don't provide nearly enough information to make such a decision. Is this a CGI app? Batch lookup? Something else? What response time is required? You mention concurrent connections. How many? You also mention the "overhead" of a "database search". That would be a lot less than the overhead of a brute-force search of a flat-file text file (assuming a decent database). The overhead of establishing a database connection, however, may well exceed that of a brute force text file search. Your file seems quite small -- will it ever be bigger, or is that it? How complicated are the lookups? Assuming your app is CGI with less than a large number of hits, it seems like the brute force text file search would be reasonable, given the indicated size of the file. Since it is read-only, you don't have to worry about file locking, or adding/deleting/changing data, all of which dramatically simplifies things. -- Bob Walton Email: http://bwalton.com/cgi-bin/emailbob.pl   0 Bob 8/20/2004 2:33:18 AM http://links.i6networks.com wrote: > At what level a database will be better for a read only text search? Whenever profiling your app shows that searching the text has become a bottleneck, and when profiling shows that replacing the offending code with a database-backed alternative removes that bottleneck. Why guess when you can measure? sherm-- -- Cocoa programming in Perl: http://camelbones.sourceforge.net Hire me! My resume: http://www.dot-app.org   0 Sherm 8/20/2004 5:57:24 AM > > At what level a database will be better for a read only text search? > > > > I have some records, each has 6 fields. Each record has a pararent record. > > > > Each parent has less than 100 childs. > > > > Total records is about 1000-1500. > > > > I want to put everthing in one single file, or put each parent and their > > children in a file so I can have 20-30 files. > > > > I am afraid to go to the database route, because the limitation of concurent > > connections and the overhead of database search. > > > > Is there a cut-off number of records, below that line, text is better, above > > it, database is better? > > Well, you don't provide nearly enough information to make such a > decision. Is this a CGI app? Batch lookup? Something else? What > response time is required? You mention concurrent connections. How > many? You also mention the "overhead" of a "database search". That > would be a lot less than the overhead of a brute-force search of a > flat-file text file (assuming a decent database). The overhead of > establishing a database connection, however, may well exceed that of a > brute force text file search. Your file seems quite small -- will it > ever be bigger, or is that it? How complicated are the lookups? > > Assuming your app is CGI with less than a large number of hits, it seems > like the brute force text file search would be reasonable, given the > indicated size of the file. Since it is read-only, you don't have to > worry about file locking, or adding/deleting/changing data, all of which > dramatically simplifies things. each record has those fields: description product id current price old price i only need to "grep case insentively keys in the description" either OR or AND operations between searched keys. It is a CGI/Perl I have trouble to build the data structure, as I don't know how to store them in a text file. I am think doing =~ m//i search in perl, but also consider to run a system call of grep, which seems easier and simpler.   0 http 8/20/2004 6:02:31 AM http://links.i6networks.com wrote: .... > I have trouble to build the data structure, as I don't know how to store > them in a text file. I am think doing =~ m//i search in perl, but also > consider to run a system call of grep, which seems easier and simpler. The "trouble to build the data structure, as I don't know how to store them in a text file" would point to using a real database, even if the quantity of data doesn't. -- Bob Walton Email: http://bwalton.com/cgi-bin/emailbob.pl   0 Bob 8/21/2004 1:44:31 AM  Reply: Similar Artilces: text-text Wondering how what I input to my UTF-8 terminal gets passed along through my patched [1] trn ... Cyrillic: А Б В Г Д Е Ж З И Й К Л М Н О П а б в г д е ж з и й к л м н о п IPA: ᴀ ᴁ ᴂ ᴃ ᴄ ᴅ ᴆ ᴇ ᴈ ᴉ ᴊ ᴋ ᴌ ᴍ ᴎ ᴏ ɀ Ɂ ɂ Ƀ Ʉ Ʌ Ɇ ɇ Ɉ ɉ Ɋ ɋ Ɍ ɍ Ɏ ɏ [1] https://groups.google.com/d/msg/comp.sys.raspberry-pi/7Z37Hdrm0DM/6aqD-reXFzAJ ... text + text What is "text + text" supposed to do right now? It doesn't seem very useful to me. What about making "text + text" as an equivalent for "text || text"? Most strongly-typed programming languages do this. And MS SQL Server too, I think (CMIIW). -- dave ---------------------------(end of broadcast)--------------------------- TIP 1: subscribe and unsubscribe commands go to majordomo@postgresql.org Am Freitag, 8. Oktober 2004 12:57 schrieb David Garamond: > What is "text + text" supposed to do right now? Nothing. > What about making "text + text" as an equivalent for "text > || text"? Most strongly-typed programming languages do this. And MS SQL > Server too, I think (CMIIW). What would this gain except for bloat? It's not like SQL is utterly compatible with any programming language; users will still have to learn all the operators anyway. -- Peter Eisentraut http://developer.postgresql.org/~petere/ ---------------------------(end of broadcast)--------------------------- TIP 9: the planner will ignore your desire to choose an index scan if your joining column's datatypes do not match Peter Eisentraut wrote: >>What is "text + text" supposed to do right now? > > Nothing. Then are these bugs? (7.4.5 and 8.0.0beta1 give same results). Frankly, the current behaviour is quite strange to me. ------------------ =... Search for text in a text field Hi When posting a search box for the users, how do you take their input and search whether or not it is contained in a text field in many records and then diplay the records which contains the input. Thanks in advance, Luke. There is a function called InStr that will probably do what you require. Cheers, Chris "Luke Jones" <luke_jones_82@yahoo.co.uk> wrote in message news:24bb1508.0407080157.d587c63@posting.google.com... > Hi > > When posting a search box for the users, how do you take their input > and search whether or not it is contained in a text field in many > records and then diplay the records which contains the input. > > Thanks in advance, > > Luke. ... Text Search vs MYSQL vs Lucene What would be performance of pgSQL text search vs MySQL vs Lucene (flat file) for a 2 terabyte db? thanks for any comments. ..V -- Please post on Rich Internet Applications User Interface (RiA/SoA) <http://www.portalvu.com> ---------------------------(end of broadcast)--------------------------- TIP 3: if posting/reading through Usenet, please send an appropriate subscribe-nomail command to majordomo@postgresql.org so that your message can get through to the mailing list cleanly It be at least dual opteron 64 w 4 gigs of ram runing fedora with a huge raid... Text, search -regexp, elidden text Hi. It has been a long time, but I'll spare you from tales how my Easter went, and stuff. No, I can't do that. You can skip starting from <here> all the way down there to next \n\n unless you are really interested. That I doubt. My Easter grass didn't grow and as a bonus even the seeds got mold. Dang. But otherwise, great time. Now to my point. I have been drooling for a while at {expand} but none seemed to be interested in wrapping Tcl alphas into Debian packages, and with very humble SparcStation 5 I was not that eager to compile it all by myself. However, I did, just to get that {expand}. After 7 hours of compiling and stuff there it was: my very own Tcl/Tk 8.5a2. Nope, not a3, cvs has next to never worked for me. After crying out loud for huge CPU impact from [clock] (that I read has not yet been optimized, so I forgive you .) I noticed that my highlights weren't working, like at all. So, using Tk/8.5a2: text .t ..t tag configure e -elide 1 ..t insert end "a\nb\nc" puts [.t search -regexp {b} 1.0] puts [.t search -regexp {c} 1.0] ..t tag add e 1.0 2.0 puts [.t search -regexp {b} 1.0] puts [.t search -regexp {c} 1.0] Where the heck is my b? I tried to g00gle for this, and I even pursued Sourceforge bug database to no avail. Or at least I didn't catch it. What I assume is that although [text] man page says "starting with index1 and ending just before index2 (the character at index2 isn't tagged)" the search... Tk text search and elided text All, I'm having trouble understanding the following text widget behavior. I'm using Tcl/Tk 8.4.9. I've got a text widget with some elided text. A search returns the position L.C (properly), but a subsequent search starting at L.C for the same string fails to return L.C. However, a search with the option -elide does return L.C. The elided text is at the beginning of the line, a good 60 characters before the text in question. Here's the example: # -------------------------------- end toplevel .bfw pack [set t [text .bfw.t]] -expand 1 -fill both set elidetext "to elide"$t tag configure toelide -elide 1 $t insert end "random\n"$t insert end ${elidetext} toelide "something here missing instantiation\n"$t insert end ${elidetext} toelide "other text missing instantiation\n" puts [set res [$t search inst 1.0]] # prints 2.62 - proper starting point for 'inst' puts [$t search inst$res] # prints 3.57 - second occurrence of 'inst' puts [$t search -elide inst$res] # prints 2.62 - first occurrence of 'inst' # -------------------------------- end Am I doing something wrong? Is there some expectation I shouldn't have? I figured that all 3 searches should return 2.62. thanks, TJ bigfaceworm wrote: > All, > > I'm having trouble understanding the following text widget behavior. > I'm using Tcl/Tk 8.4.9. > ...

Search Text in Database
Hi, I would like to use keywords inside a record to search for - like a searchengine. How can I design the table? Right now I would store data in Memo-Column in a format like ";apple;banana;lemon;". I would use a INSTR(ring)-function - but I wonder if the performance is still OK then - even when I index the field. Are there maybe even better ways? Thanx in advance. Greg Each field in a given row should store one piece of information. Seperating your data with semicolons suggests that your storing multiple piecies of data in a field that should only be storing a single peice of data. It defeats the puprose of a relational database. Instead you probably want to add a second table that will have a one to many or a third table to setup a many to many relationship with your first table and possibly second. Here are two table ideas but without your DDL I can't know what it is your trying to do so I'm guessing. If you need more information provide your DDL (i.e. your create statements, and some insert statements with sample data). CREATE TABLE Food_Type ( ID INT IDENTITY PRIMARY KEY NOT NULL, Name VARCHAR(50) NOT NULL ) CREATE TABLE Food_Attributes ( ID INT IDENTITY PRIMARY KEY NOT NULL, Attribute VARCHAR(50) NOT NULL, Food_Type_ID INT NOT NULL ) Then your data could look like this. INSERT INTO Food_Type VALUES ('Dinner') INSERT INTO Food_Type VALUES ('Lunch') INSERT INTO Food_Type VALUES ('Snack'...

How to search list of particular text values into free text
Hi All, Please if anyone has idea about how to search particular list of text values from one small table to free text variable in large dataset and when finds the value, update the large dataset. I have small lookup table (around 120 records) for example: Category Types; Type_1 Mangos, Type_1 Pineapples, Type_2 Onions, Type_2 Tomatoes, … Type_n typeN. Now I need to search each particular text values (variable-Types) from the above small table into my large dataset which has free text variable called “Order_details”. For example: Order_details: The last order was for the Mangos on Nov 11...

Pages
I have a titel-textfield over a pic (headline) , text is black, background for text transparent. A second textfield should overlapp the first textline..... When i arrange the second field with the same settings like the first, the first text disappear... How can i do, that the second text overpapps the first, all over the pic. Any help appreciated! Thanks for replies! I am german and hope that the engish speaking people understand my problem! Soory! Gerd In article <611db9e2-b085-4fe5-907a-ca714b0c32dd@m74g2000hsh.googlegroups.com>, hurlebaus <gerd.schenk@freenet.de> wrote: > I have a titel-textfield over a pic (headline) , text is black, > background for text transparent. > > A second textfield should overlapp the first textline..... > > When i arrange the second field with the same settings like the first, > the first text disappear... > > How can i do, that the second text overpapps the first, all over the > pic. > > Any help appreciated! Thanks for replies! I am german and hope that > the engish speaking people understand my problem! Soory! > > Gerd A couple of possibilities occur to me: Maybe the background of the second text field is not transparent. Maybe the the second text field is set as an object to cause wrap of other objects. You can determine that and change it in the Inspector window, in the Object pane. -- Bill Collins For email, change "fake" to "earthlink" ...

text 2 text
I'm rather new to ustation and am having trouble finding replacements for all of my Acad lisp routines. One that I'd like to find changes a selected text string to read like the second selected text string. I realize this can all be done in the text editor but it's not all that quick. Does anyone know of a macro or mdl which can handle this task? Thanks in advance.---Calvin I don't know of any application that will do what you describe, but have you looked at Edit > Find/Replace text? You may also find Bentley's discussion groups of assistance. Over there you can meet other users of Bentley products, exchange ideas, and discuss a wide range of technical subjects. These groups are an excellent technical resource for all users of Bentley products and services. Hope to see you there! For more information take a peek at this page: http://selectservices.bentley.com/discussion/index.htm -- Best Regards, Inga Morozoff [Bentley] www.askinga.com "jgonzales24" <jgonzales24@cox.net> wrote in message news:xcLMb.13975$zs4.2376@fed1read01... > I'm rather new to ustation and am having trouble finding replacements for > all of my Acad lisp routines. One that I'd like to find changes a selected > text string to read like the second selected text string. I realize this > can all be done in the text editor but it's not all that quick. Does anyone > know of a macro or mdl whi... Surrounding text with text I was wondering if it was possible to surround a text body with text like so: +--------------+ |ABCDEFGHIJKLM | |H N| |A Main Body O| |L Text goes P| |B here Q| |-=+_ZYXWVUTSR | | | | | | | | | +--------------+ This seems far-fetched, but just curious. I suppose that I could just move stuff around by hand in the GIMP later on, but there's probably a {better,more {extensible,clean}} way of doing it from (La)TeX. -FreeSmith ptjm@interlog.com (Patrick TJ McPhee) wrote in message news:<bffbhe$per1@news.eusc.inter.net>... > Peter Flynn had an example like that, which he either posted here or > posted a link here. It was something to do with a certificate -- try > searching for his name and that word in google. > > It wouldn't be hard to do with metapost. I have a macro called `pathalong' > which puts text along an arbitrary path. Well, it's been a while, but I finally finished it. It's a little job I was doing for an upcoming wedding. At any rate, I used pstricks to make the text go along a path, along with a couple of hacks for sizing (from graphicx) and kerning along the line (from soul). Here's the code (don't laugh): CAUTION:THIS CODE MAY MAKE YOU WRETCH ---SNIP--- \documentclass{article} \usepackage{graphicx} \usepackage{pstricks,pst-text,nopageno} \usepackage[width=8.5in]{geometry} \usepackage{soul} \begin{document} \thispagestyle{empty} \set... Text from required text box to read-only text box Hello, I am fairly new to JavaScript and its use in Acrobat Professional. My situation is this: I have a form with a text box field which is required for the user to enter his/her name. I would like the required text box to display the name in all caps. I also need the user's name to appear in a read-only text box later in the form, which I would like to have the first letter of the user's first, middle initial, and last names to be capitalized. I would also like to have all required fields on the form highlighted in yellow, but the highlighting not printed. Lastly, I would like the... Re: How to search list of particular text values into free text On Mon, 18 Jun 2007 12:02:45 -0400, SUBSCRIBE SAS-Nim Pat <Npp1129@GMAIL.COM> wrote: >Hi All, >Please if anyone has idea about how to search particular list of text >values from one small table to free text variable in large dataset and >when finds the value, update the large dataset. >I have small lookup table (around 120 records) for example: >Category Types; > >Type_1 Mangos, >Type_1 Pineapples, >Type_2 Onions, >Type_2 Tomatoes, >… > >Type_n typeN. > > >Now I need to search each particular text values (variable-Types) from the >above small table into my large dataset which has free text variable >called “Order_details”. >For example: >Order_details: The last order was for the Mangos on Nov 11 2006. > > >I’m using following code but it’s not efficient: >PROC SQL; >Create table new_Main_Table AS >SELECT *, >Case >when Order_details contains (‘Mangos’) then “Type_1” >when Order_details contains (‘Pineapples’) then “Type_1” >when Order_details contains (‘Onions’) then “Type_2” >when Order_details contains (‘Tomatoes’) then “Type_2” >. >. >. >when Order_details contains (‘typeN’) then “Type_n” >Else “ “ >End As order_Types >From Main_table ; >Quit; >Run; > >Thanks for your time and help, >I really appreciate your effort, >Nim Guys Sorry for the Inconveniencies. I'm attaching sample table. my Small lookup table: Data SmallTAble ; Le... What is "Text Display"? Text Display vs. Label What is the difference between the text display vs label? They would seem to be different "objects" in Cadence?? I am not sure how to think about each of them. They both seem to be capable to have the same layer-purpose pair. I was also curious once I stream out my database to a gds if they both continue to retain a difference or if they both became text in gds. Just wondering, thanks for any insight. On Nov 6, 10:35 pm, vlsidesign <ford...@gmail.com> wrote: > What is the difference between the text display vs label? They would > seem to be different "objects" in Cadence?? A label is just a label, a stand-alone object. A text display is associated with another object, usually a pin. The usual use of a text display is to visually display the value of a pin name. -Jay- ... Mouse changes when Tab label is Text[] vs normal text. Why? Hello experts; This is not a big deal thing for me, I just was curios on what this behavior occur more than anything. If you enter the following command: TabView[{"1" -> 1, Style["2", FontSize -> 16] -> 2}] and then move the mouse over the Tab with '2' on it, and notice the mouse shape, you'll see it stays an arrow shape (standard on windoz). Now if you enter this command instead: TabView[{"1" -> 1, Text[Style["2", FontSize -> 16]] -> 2}] and do the same, you'll notice that the mouse, when it is ... Re: How to search list of particular text values into free text #3 This one may not be efficient when look up table are big, but at least it saves your typing: proc sql; create table xx as select distinct a.srno,a.order_details, max(case when a.order_details contains trim(b.types) then b.types else '' end) as btype from large_table a, smalltable b group by a.srno order by a.srno ; proc print; run; Srno Order_details btype 1 The order of Mangos .. Mangos 10 Retured all Potatoes .. Potatoes 2 The returned order .. Mangos 3 Order for the Oranges .. Oranges 4 new container for the Onions .. Onions 5 Boxes of Grapes received .. Grapes 6 Almonds boxes received .. Almonds 7 Dry fruits received on last .. Dry fruits 8 Spinach were tossed out .. Spinach 9 Begs of Potatoes received .. Potatoes On Mon, 18 Jun 2007 13:29:55 -0400, SUBSCRIBE SAS-Nim Pat <Npp1129@GMAIL.COM> wrote: >On Mon, 18 Jun 2007 12:02:45 -0400, SUBSCRIBE SAS-Nim Pat ><Npp1129@GMAIL.COM> wrote: > >>Hi All, >>Please if anyone has idea about how to search particular list of text >>values from one small table to free text variable in large dataset and >>when finds the value, update the large dataset. >>I have small lookup table (around 120 records) for example: >>Category Types; >> >>Type_1 Mangos, >>Type_1 Pine... Re: How to search list of particular text values into free text #2 Sorry, there was a minor error, b.types should be b.category: proc sql; create table xx as select distinct a.srno,a.order_details, max(case when a.order_details contains trim(b.types) then b.category else '' end) as btype from large_table a, smalltable b group by a.srno order by a.srno ; proc print; run; Srno Order_details btype 1 The order of Mangos .. Type_1 10 Retured all Potatoes.. Type_2 2 The returned order .. Type_1 3 Order for the Oranges .. Type_1 4 new container for the Onions .. Type_2 5 Boxes of Grapes received .. Type_1 6 Almonds boxes received .. Type_3 7 Dry fruits received on .. Type_4 8 Spinach were tossed out .. Type_2 9 Begs of Potatoes .. Type_2 On Tue, 19 Jun 2007 00:27:45 -0400, Ya Huang <ya.huang@AMYLIN.COM> wrote: >This one may not be efficient when look up table are big, >but at least it saves your typing: > >proc sql; >create table xx as >select distinct a.srno,a.order_details, >max(case when a.order_details contains trim(b.types) then b.types else '' >end) as btype >from large_table a, smalltable b >group by a.srno >order by a.srno >; > >proc print; >run; > >Srno Order_details btype > > 1 The order of Mangos .. Mangos > 10 Retured all Potatoes .. Potatoes > 2 The returned o... Search a Text-String for two possible outputs result strings embedded in the text. I am trying to search a string that outputs result as "Sucess" or "Failure". I am configuring a device using command prompt, and I get a text based result as shown on the front panel after the configuration has been done successfully, namely the following:   C:\SHOAB\HCE-ME_Functional_Tester\LABVIEW_DEVELOPMENT\DIGI-ME-FCT\ConfigLoad>connectprog /upload /destip=192.168.192.211 /config=C:\SHOAB\HCE-ME_Functional_Tester\LABVIEW_DEVELOPMENT\DIGI-ME-FCT\ConfigLoad\ME211Prod.rci /username=root /password=dbps /reboot Digi Connect ProgrammerVersion 1.3.19.0Copyright 2003-2005 Digi International Inc. Device foundConnect to device: SUCCESSRead configuration file: SUCCESSUpload configuration C:\SHOAB\HCE-ME_Functional_Tester\LABVIEW_DEVELOPMENT\DIGI-ME-FCT\ConfigLoad\ME211Prod.rci: SUCCESS: Some settings may require a reboot.Reboot device: SUCCESS   I need to make sure that the device returned a "SUCCESS" in the three areas as highlighted in RED above. For this task, in the block diagram as you will see, I am trying to search for the three "Success" confirmations from the device (highlighted in RED above). I am not able to find any help on how to search for a string of characters, that could be either success or some other text.   Can someone throw some light on it, as the LABVIEW help files do not explain in depth if there is a way to search for a string that can vary. Although there exists a similar example on... Best text search for many Gigabyte Database? I have a so big DB, It's about 10-100GB of text. Now I want to create a searching function but It take too long when I use LIKE from MySQL Anyone know the best sollution? Can I use Google Desktop search or an others? Please help! ngocviet wrote: > I have a so big DB, It's about 10-100GB of text. > Now I want to create a searching function but It take too long when I > use LIKE from MySQL > Anyone know the best sollution? > Can I use Google Desktop search or an others? > Please help! If you use mySQL, consider using FULLTEXT and MATCH AGAINST(). Bottomline stays: If you have 100GB of data, some searchtime is needed, but using FULLTEXT can speed that up considerable. Check your mySQL documentation for details. Regards, Erwin Moller > If you use mySQL, consider using FULLTEXT and MATCH AGAINST(). > Bottomline stays: If you have 100GB of data, some searchtime is needed, but > using FULLTEXT can speed that up considerable. > Check your mySQL documentation for details. I've tried FULLTEXT but it take too long, about over 10 seconds with 1.2 Gigabyte table. If need, I can convert database to other structure. ngocviet wrote: > >> If you use mySQL, consider using FULLTEXT and MATCH AGAINST(). >> Bottomline stays: If you have 100GB of data, some searchtime is needed, >> but using FULLTEXT can speed that up considerable. >> Check your mySQL documentation for details. > > I've tried FULLTEXT but ... Usability of indexes vs full-text search Can anyone point me to recent (last two years?) usability studies comparing conventional indexes to full-text search in terms of the ease and accuracy of retrieving information? The field of information retrieval probably has some relevant research though I'm not sure what you mean by "conventional indexes"? Try Googling for TREC (Text REtrieval Conference) and associated research. AJS. "Alan J. Salmoni" <salmoni@gmail.com> wrote: >The field of information retrieval probably has some relevant research >though I'm not sure what you mea... Text File vs Database reading performance Hello, I have developped an application that is doing some "backtesting" on market data. I have a serie of text files that contain data, one meaningful data per line. my app opens the file, reads a line, process it, reads the next one, process it, and so on. each file is around 50,000 lines long, and I have more than 200 files (and growing). the whole processing is taking quite some time, and I'm trying to find ways to make it faster. I chose the "file" way a while ago when I was lazy and the "speed" problem had not appeared yet. however, I know I/O is one important thing to look at if I want to improve performances. especially, I'm thinking wouldn't that be faster to go through a Database ? enter all my data in a DB once, and access the DB with JDBC. has any of you any comment to make on ways to make things faster, and on the Database performance especially ? or is my file solution good enough ? thanks for your insight... -Antoine Please don't double post. See c.l.j.p for answer. robert ... Can I use SAS to search and replace a piece of text in, say, 1000 text files? How can I use SAS to search and replace a piece of text in, say, 1000 text files? Thanks for letting me know. Toby ... file command: "XML document text" vs "XML document text" I've just used the file command on four files of RDF-XML with the following output: augtfidf.rdf: XML document text kyoto.rdf: XML document text stuff.rdf: XML document text tfidf.rdf: XML document text What does it mean that one of them has an extra space between "XML" and "document"? -- The kid's a hot prospect. He's got a good head for merchandising, an agent who can take you downtown and one of the best urine samples I've seen in a long time. [Dead Kennedys t-shirt] On 16.10.2012 16:06, Adam Funk wrote: > I've just used the file command on four files of RDF-XML with the > following output: > > augtfidf.rdf: XML document text > kyoto.rdf: XML document text > stuff.rdf: XML document text > tfidf.rdf: XML document text > > What does it mean that one of them has an extra space between "XML" > and "document"? Hard to tell without further information. What does file *.rdf | od -c show you? Janis Janis Papanagnou wrote: > On 16.10.2012 16:06, Adam Funk wrote: >> I've just used the file command on four files of RDF-XML with the >> following output: >> >> augtfidf.rdf: XML document text >> kyoto.rdf: XML document text >> stuff.rdf: XML document text >> tfidf.rdf: XML document text >> >> What does it mean that one ... aligning text and image-text I use a program to make Email addresses harder for spammers to harvest. It converts them to slightly blurred images using http://mindprod.com/products1.html#MASKER When I embed them in text, I have figured out how to get them to align naturally with the surrounding text, but the browser inserts extra inter-line spacing above the line containing the image. You can see the effect at http://mindprod.com/book/books.html at the bottom of the page where it says: "Please email your feedback for publication, letters to the editor, errors, omissions, typos, formatting errors, ambig... Web resources about - Database vs Text for text search - comp.lang.perl.misc Database - Wikipedia, the free encyclopedia A database is an organized collection of data . The data are typically organized to model aspects of reality in a way that supports processes ... Database - Wikipedia, the free encyclopedia ... requiring information. For example, modelling the availability of rooms in hotels in a way that supports finding a hotel with vacancies. Database ... How The NFL Adds Mojo To Media With Database Marketing The National Football League (NFL) customer database is about as diverse as it gets. Segments span season ticket holders, a millennial parent ... Fearing no punishment, Denver cops abuse crime databases for personal gain (credit: Noel Hidalgo ) Denver police officers performed searches on state and federal criminal justice databases that were not work-related ... NFL mock draft database 2016: Tracking Giants picks from around the Internet Let's keep track of mock drafts from around the Internet as the 2016 NFL Draft approaches. Can we find a consensus for the New York Giants? Larry Ellison shrugs off Amazon, Microsoft play for Oracle database business ... companies – Amazon (Nasdaq: AMZN) and Microsoft (Nasdaq: MSFT) – both made it easier for Oracle's (NYSE: ORCL) customers to move their databases ... Amazon Web Services Announces that over 1,000 Databases Have Migrated to AWS since January 1, 2016 Amazon Web Services, Inc. (AWS), today announced that the AWS Database Migration Service is now generally available. Taiwan launches database on areas vulnerable to quake damage BEIJING (AP) — Earthquake-prone Taiwan is launching a database to inform residents which areas might be susceptible to creating potentially catastrophic ... Interior Dept Spent15 Million On A Crime Database That Doesn’t Work
Interior Dept Spent $15 Million On A Crime Database That Doesn’t Work Crate Raises$4M for New Container Database Technology
The founder of Docker Inc. invests in new technology that provides a very different and very distributed way to build a container database.

Resources last updated: 3/29/2016 7:53:23 AM


text:
# Multitriangulations and tropical Pfaffians

--

Time: 15:00 -- Location: online

The $$k$$-associahedron $$Ass_k(n)$$ is the simplicial complex of $$(k+1)$$-crossing-free subgraphs of the complete graph with vertices on a circle. Its facets are called $$k$$-triangulations. We explore the connection of $$Ass_k(n)$$ with the Pfaffian variety $$Pf_k(n)\subset K^\binom{n}{2}$$ of antisymmetric matrices of rank $$\le 2k$$. First, we characterize the Gröbner cone $$Grob_k(n)\subset \mathbb{R}^\binom{n}{2}$$ producing as initial ideal of $$I(Pf_k(n))$$ the Stanley-Reisner ideal of $$Ass_k(n)$$ (that is, the monomial ideal generated by $$(k+1)$$-crossings). We then look at the tropicalization of $$Pf_k(n)$$ and show that $$Ass_k(n)$$ embeds naturally as the intersection of $$trop(Pf_k(n))$$ and $$Grob_k(n)$$, and is contained in the totally positive part $$trop^+(Pfk(n))$$ of it. We show that for $$k=1$$ and for each triangulation $$T$$ of the $$n$$-gon, the projection of this embedding of $$Ass_k(n)$$ to the $$n−3$$ coordinates corresponding to diagonals in $$T$$ gives a complete polytopal fan, realizing the associahedron. This fan is linearly isomorphic to the $$\mathbf{g}$$-vector fan of the cluster algebra of type $$A$$, shown to be polytopal by Hohlweg, Pilaud and Stella in 2018.

Category: seminars
Tags: Combi seminar combinatorics


text:
## Foundations of Math and Physics One Century After Hilbert

10 October, 2019

I wrote a review of this book with chapters by Penrose, Witten, Connes, Atiyah, Smolin and others:

• John Baez, review of Foundations of Mathematics and Physics One Century After Hilbert: New Perspectives, edited by Joseph Kouneiher, Notices of the American Mathematical Society 66 no. 11 (November 2019), 1690–1692.

It gave me a chance to say a bit—just a tiny bit—about the current state of fundamental physics and the foundations of mathematics.

## Quantales from Petri Nets

6 October, 2019

A referee pointed out this paper to me:

• Uffe Engberg and Glynn Winskel, Petri nets as models of linear logic, in Colloquium on Trees in Algebra and Programming, Springer, Berlin, 1990, pp. 147–161.

It contains a nice observation: we can get a commutative quantale from any Petri net.

I’ll explain how in a minute. But first, what does have to do with linear logic?

In linear logic, propositions form a category where the morphisms are proofs and we have two kinds of ‘and’: $\&$, which is a cartesian product on this category, and $\otimes$, which is a symmetric monoidal structure. There’s much more to linear logic than this (since there are other connectives), and maybe also less (since we may want our category to be a mere poset), but never mind. I want to focus on the weird business of having two kinds of ‘and’.

Since $\&$ is cartesian we have $P \Rightarrow P \& P$ as usual in logic.

But since $\otimes$ is not cartesian we usually don’t have $P \Rightarrow P \otimes P.$ This other kind of ‘and’ is about resources: from one copy of a thing $P$ you can’t get two copies.

Here’s one way to think about it: if $P$ is “I have a sandwich”, $P \& P$ is like “I have a sandwich and I have a sandwich”, while $P \otimes P$ is like “I have two sandwiches”.

A commutative quantale captures these two forms of ‘and’, and more. A commutative quantale is a commutative monoid object in the category of cocomplete posets: that is, posets where every subset has a least upper bound. But it’s a fact that any cocomplete poset is also complete: every subset has a greatest lower bound!

If we think of the elements of our commutative quantale as propositions, we interpret $x \le y$ as “$x$ implies $y$”. The least upper bound of any subset of proposition is their ‘or’. Their greatest lower bound is their ‘and’. But we also have the commutative monoid operation, which we call $\otimes.$ This operation distributes over least upper bounds.

So, a commutative quantale has both the logical $\&$ (not just for pairs of propositions, but arbitrary sets of them) and the $\otimes$ operation that describes combining resources.

To get from a Petri net to a commutative quantale, we can compose three functors.

First, any Petri net gives a commutative monoidal category—that is, a commutative monoid object in $\mathsf{Cat}$. Indeed, my student Jade has analyzed this in detail and shown the resulting functor from the category of Petri nets to the category of commutative monoidal categories is a left adjoint:

• Jade Master, Generalized Petri nets, Section 4.

Second, any category gives a poset where we say $x \le y$ if there is a morphism from $x$ to $y.$ Moreover, the resulting functor $\mathsf{Cat} \to \mathsf{Poset}$ preserves products. As a result, every commutative monoidal category gives a commutative monoidal poset: that is, a commutative monoid object in the category of Posets.

Composing these two functors, every Petri net gives a commutative monoidal poset. Elements are of this poset are markings of the Petri net, the partial order is “reachability”, and the commutative monoid structure is addition markings.

Third, any poset $P$ gives another poset $\widehat{P}$ whose elements are downsets of $P$: that is, subsets $S \subseteq P$ such that

$x \in S, y \le x \; \implies \; y \in S$

The partial order on downsets is inclusion. This new poset $\widehat{P}$ is ‘better’ than $P$ because it’s cocomplete. That is, any union of downsets is again a downset. Moreover, $\widehat{P}$ contains $P$ as a sub-poset. The reason is that each $x \in P$ gives a downset

$\downarrow x = \{y \in P : \; y \le x \}$

and clearly

$x \le y \; \iff \; \downarrow x \subseteq \downarrow y$

Composing this third functor with the previous two, every Petri net gives a commutative monoid object in the category of cocomplete posets. But this is just a commutative quantale!

What is this commutative quantale like? Its elements are downsets of markings of our Petri net: sets of markings such that if $x$ is in the set and $x$ is reachable from $y$ then $y$ is also in the set.

It’s good to contemplate this a bit more. A marking can be seen as a ‘resource’. For example, if our Petri net has a place in it called sandwich there is a marking 2sandwich, which means you have two sandwiches. Downsets of markings are sets of markings such that if $x$ is in the set and $x$ is reachable from $y$ then $y$ is also in the set! An example of a downset would be “a sandwich, or anything that can give you a sandwich”. Another is “two sandwiches, or anything that can give you two sandwiches”.

The tensor product $\otimes$ comes from addition of markings, extended in the obvious way to downsets of markings. For example, “a sandwich, or anything that can give you a sandwich” tensored with “a sandwich, or anything that can give you a sandwich” equals “two sandwiches, or anything that can give you two sandwiches”.

On the other hand, the cartesian product $\&$ is the logical ‘and’:
if you have “a sandwich, or anything that can give you a sandwich” and you have “a sandwich, or anything that can give you a sandwich”, then you just have “a sandwich, or anything that can give you a sandwich”.

So that’s the basic idea.

## Applied Category Theory Meeting at UCR (Part 2)

30 September, 2019

Joe Moeller and I have finalized the schedule of our meeting on applied category theory:

Applied Category Theory, special session of the Fall Western Sectional Meeting of the AMS, U. C. Riverside, Riverside, California, 9–10 November 2019.

It’s going to be really cool, with talks on everything from brakes to bicategories, from quantum physics to social networks, and more—with the power of category theory as the unifying theme!

You can get information on registration, hotels and such here. If you’re coming, you might also want to attend Eugenia Cheng‘s talk on the afternoon of Friday November 8th.   I’ll announce the precise title and time of her talk, and also the location of all the following talks, as soon as I know!

In what follows, the person actually giving the talk has an asterisk by their name. You can click on talk titles to see abstracts of the talks.

Saturday November 9, 2019, 8:00 a.m.-10:50 a.m.

• 8:00 a.m.David I. Spivak*, Massachusetts Institute of Technology
• 9:00 a.m.Brendan Fong*, Massachusetts Institute of Technology
David I. Spivak, Massachusetts Institute of Technology
• 9:30 a.m.Gabriel C. Drummond-Cole, IBS Center for Geometry and Physics
Philip Hackney*, Department of Mathematics, University of Louisiana at Lafayette
• 10:00 a.m.
Duality of relations.
Alexander Kurz*, Chapman University
• 10:30 a.m.Tobias Fritz*, Perimeter Institute for Theoretical Physics

Saturday November 9, 2019, 3:00 p.m.-5:50 p.m.

Sunday November 10, 2019, 8:00 a.m.-10:50 a.m.

Sunday November 10, 2019, 2:00 p.m.-4:50 p.m.

## The Binary Octahedral Group

29 August, 2019

The complex numbers together with infinity form a sphere called
the Riemann sphere. The 6 simplest numbers on this sphere lie at points we could call the north pole, the south pole, the east pole, the west pole, the front pole and the back pole. They’re the corners of an octahedron!

On the Earth, I’d say the “front pole” is where the prime meridian meets the equator at 0°N 0°E. It’s called Null Island, but there’s no island there—just a buoy. Here it is:

Where’s the back pole, the east pole and the west pole? I’ll leave two of these as puzzles, but I discovered that in Singapore I’m fairly close to the east pole:

If you think of the octahedron’s corners as the quaternions $\pm i, \pm j, \pm k,$ you can look for unit quaternions $q$ such that whenever $x$ is one of these corners, so is $qxq^{-1}$. There are 48 of these! They form a group called the binary octahedral group.

By how we set it up, the binary octahedral group acts as rotational symmetries of the octahedron: any transformation sending $x$ to $qxq^{-1}$ is a rotation. But this group is a double cover of the octahedron’s rotational symmetry group! That is, pairs of elements of the binary octahedral group describe the same rotation of the octahedron.

If we go back and think of the Earth’s 6 poles as points $0, \pm 1,\pm i, \infty$ on the Riemann sphere instead of $\pm i, \pm j, \pm k$, we can think of the binary octahedral group as a subgroup of $\mathrm{SL}(2,\mathbb{C}$), since this acts as conformal transformations of the Riemann sphere!

If we do this, the binary octahedral group is actually a subgroup of $\mathrm{SU}(2)$, the double cover of the rotation group—which is isomorphic to the group of unit quaternions. So it all hangs together.

It’s fun to actualy see the unit quaternions in the binary octahedral group. First we have 8 that form the corners of a cross-polytope (the 4d analogue of an octahedron):

$\pm 1, \pm i , \pm j , \pm k$

These form a group on their own, called the quaternion group. Then we have 16 that form the corners of a hypercube (the 4d analogue of a cube, also called a tesseract or 4-cube):

$\displaystyle{ \frac{\pm 1 \pm i \pm j \pm k}{2} }$

These don’t form a group, but if we take them together with the 8 previous ones we get a 24-element subgroup of the unit quaternions called the binary tetrahedral group. They’re also the vertices of a 24-cell, which is yet another highly symmetrical shape in 4 dimensions (a 4-dimensional regular polytope that doesn’t have a 3d analogue).

That accounts for half the quaternions in the binary octahedral group! Here are the other 24:

$\displaystyle{ \frac{\pm 1 \pm i}{\sqrt{2}}, \frac{\pm 1 \pm j}{\sqrt{2}}, \frac{\pm 1 \pm k}{\sqrt{2}}, }$

$\displaystyle{ \frac{\pm i \pm j}{\sqrt{2}}, \frac{\pm j \pm k}{\sqrt{2}}, \frac{\pm k \pm i}{\sqrt{2}} }$

These form the vertices of another 24-cell!

The first 24 quaternions, those in the binary tetrahedral group, give rotations that preserve each one of the two tetrahedra that you can fit around an octahedron like this:

while the second 24 switch these tetrahedra.

The 6 elements

$\pm i , \pm j , \pm k$

describe 180° rotations around the octahedron’s 3 axes, the 16 elements

$\displaystyle{ \frac{\pm 1 \pm i \pm j \pm k}{2} }$

describe 120° clockwise rotations of the octahedron’s 8 triangles, the 12 elements

$\displaystyle{ \frac{\pm 1 \pm i}{\sqrt{2}}, \frac{\pm 1 \pm j}{\sqrt{2}}, \frac{\pm 1 \pm k}{\sqrt{2}} }$

describe 90° clockwise rotations holding fixed one of the octahedron’s 6 vertices, and the 12 elements

$\displaystyle{ \frac{\pm i \pm j}{\sqrt{2}}, \frac{\pm j \pm k}{\sqrt{2}}, \frac{\pm k \pm i}{\sqrt{2}} }$

describe 180° clockwise rotations of the octahedron’s 6 opposite pairs of edges.

Finally, the two elements

$\pm 1$

do nothing!

So, we can have a lot of fun with the idea that a sphere has 6 poles.

## 2020 Category Theory Conferences

9 August, 2019

Yes, my last post was about ACT2019, but we’re already planning next year’s applied category theory conference and school! I’m happy to say that Brendan Fong and David Spivak have volunteered to run it at MIT on these dates:

• Applied Category Theory School: June 29–July 3, 2020.
• Applied Category Theory Conference: July 6–10, 2020.

The precise dates for the other big category theory conference, CT2020, have not yet been decided. However, it will take place in Genoa sometime in the interval June 18–28, 2020.

There may also be an additional applied theory school in Marrakesh from May 25–29, 2020. More on that later, with any luck!

And don’t forget to submit your abstracts for the November 2019 applied category theory special session at U. C. Riverside by September 3rd! We’ve got a great lineup of speakers, but anyone who wants to give a talk—including the invited speakers—needs to submit an abstract to the AMS website by September 3rd. The AMS has no mercy about this.

## Applied Category Theory 2019 Talks

20 July, 2019

Applied Category Theory 2019 happened last week! It was very exciting: about 120 people attended, and they’re pushing forward to apply category theory in many different directions. The topics ranged from ultra-abstract to ultra-concrete, sometimes in the same talk.

The talks are listed above — click for a more readable version. Below you can read what Jules Hedges and I wrote about all those talks:

• Jules Hedges, Applied Category Theory 2019.

I tend to give terse summaries of the talks, with links to the original papers or slides. Jules tends to give his impressions of their overall significance. They’re nicely complementary.

You can also see videos of some talks, created by Jelle Herold with help from Fabrizio Genovese:

• Giovanni de Felice, Functorial question answering.

• Antonin Delpeuch, Autonomization of monoidal categories.

• Colin Zwanziger, Natural model semantics for comonadic and adjoint modal type theory.

• Nicholas Behr, Tracelets and tracelet analysis Of compositional rewriting systems.

• Dan Marsden, No-go theorems for distributive laws.

• Christian Williams, Enriched Lawvere theories for operational semantics.

• Walter Tholen, Approximate composition.

• Erwan Beurier, Interfacing biology, category theory & mathematical statistics.

• Stelios Tsampas, Categorical contextual reasoning.

• Fabrizio Genovese, idris-ct: A library to do category theory in Idris.

• Michael Johnson, Machine learning and bidirectional transformations.

• Bruno Gavranović, Learning functors using gradient descent

• Zinovy Diskin, Supervised learning as change propagation with delta lenses.

• Bryce Clarke, Internal lenses as functors and cofunctors.

• Ryan Wisnewsky, Conexus AI.

• Ross Duncan, Cambridge Quantum Computing.

• Beurier Erwan, Memoryless systems generate the class of all discrete systems.

• Blake Pollard, Compositional models for power systems.

• Martti Karvonen, A comonadic view of simulation and quantum resources.

• Quanlong Wang, ZX-Rules for 2-qubit Clifford+T quantum circuits, and beyond.

• James Fairbank, A Compositional framework for scientific model augmentation.

• Titoan Carette, Completeness of graphical languages for mixed state quantum mechanics.

• Antonin Delpeuch, A complete language for faceted dataflow languages.

• John van der Wetering, An effect-theoretic reconstruction of quantum mechanics.

• Vladimir Zamdzhiev, Inductive datatypes for quantum programming.

• Octavio Malherbe, A categorical construction for the computational definition of vector spaces.

• Vladimir Zamdzhiev, Mixed linear and non-linear recursive types.

## Applied Category Theory 2019 Program

3 July, 2019

Bob Coecke, David Spivak, Christina Vasilakopoulou and I are running a conference on applied category theory:

Applied Category Theory 2019, 15–19 July, 2019, Lecture Theatre B of the Department of Computer Science, 10 Keble Road, Oxford.

You can now see the program here, or below. Hope to see you soon!


text:
# Conservation of energy

1. Oct 28, 2013

### oneplusone

1. The problem statement, all variables and given/known data

A 2 kg ball is attached to the bottom end of a length of fishline with a breaking strength of 44.5 N. The top end of the fishline is held stationary. The ball is released from rest with the line taut and horizontal (theta = 90 degrees). At what angle theta (measured w/vertical) will the fishline break?

2. Relevant equations

none i can think of

3. The attempt at a solution

$$F=\dfrac{mv^2}{l}$$ where l is the length of the wire. then from conservation:

$$mgh = \dfrac{1}{2}mv^2$$

$$mg(l \sin \theta) = \dfrac{1}{2} ( F\cdot l)$$

$$F = 2mg\sin \theta = 44.5$$

Which is incorrect as sin theta must be < 1.

2. Oct 28, 2013

### rock.freak667

At the angle θ, what would be the components of the forces radially and tangentially and in what direction would the tension T act?

After that, how would you find the centripetal force in terms of these forces?

3. Oct 29, 2013

### oneplusone

Sorry I still can't get it with your information. Any other hints/solution?

4. Oct 29, 2013

### Hollumber

Account for the weight opposing tension force.

(At the bottom, Fnet = 2mg = Tension - mg(weight), so max tension would have to = 60N for the line to never break.)

5. Oct 29, 2013

### Staff: Mentor

- You have sine and cosine reversed; note that θ is measured from the vertical.
- What you call F is the radial component of the net force on the ball, not the tension in the string.

Draw a free body diagram of the forces on the ball.

6. Oct 29, 2013

### oneplusone

Oops, is this correct now:

$$F=T-mg\cos\theta \implies T-mg\cos\theta = \dfrac{mv^2}{l}$$
Where l is the length of the line.

$$mgh = \dfrac{1}{2}mv^2\implies mg(l\cos\theta) = \dfrac{1}{2}(T-mg\cos\theta)\cdot l$$

$$2\cdot 9.8\cos\theta = \dfrac{1}{2}(44.5-2\cdot 9.8\cdot\cos\theta)$$

$$\theta = 40.82^{\circ}$$


text:
Gwent support in DeckLock has been on my ToDo list for some time as it currently is my favorite game. The artwork is stunning, it is well balanced and rewards skill. Though it being a digital-only card game makes it somewhat different from KeyForge and Magic: the Gathering. As the latter have printed, physical cards the cards themselves can’t be changed. Occasionally, an errata is issued or cards that are to powerful are banned from competitive play. In Gwent however, there are no physical cards, and cards can change from one update to another making them stronger, weaker or changing them entirely. As the official website does allow users to share their decklists, it only has data for the latest version. Therefore I opted to add decks using a decklist that contains information on the version and get card data from The Voice of Gwent which contains data for all cards for all versions.

Adding a deck works very much the same way as for a Magic: the Gathering deck which was described in part 2. Though as there is no standard format to represent a similar one to M:tG was used. The first few lines contain extra information, most importantly the version of Gwent the deck is compatible with, followed by the actual deck list.

// NAME : Soldiers Ball
// CREATOR : Team Leviathan Gaming
// GWENT_VERSION : 6.2.0
// FACTION : Nilfgard
1 Imperial Formation
1 Magic Lamp
1 Vincent Van Moorlehem
1 Joachim de Wett
1 Ramon Tyrconnel
1 Maraal
1 Yennefer's Invocation
1 Affan Hillergrand
1 Ffion var Gaernel
1 Sweers
1 Albrich
1 Van Moorlehem's Cupbearer
1 Roderick of Dun Tynne
2 Ard Feainn Crossbowman
1 Ard Feainn Tortoise
1 Tourney Joust
2 Alba Spearman
2 Magne Division
1 Recruit
2 Fangs of the Empire
2 Van Moorlehem Hunter

This is the example of the Soldiers’ Ball deck from Team Leviathan Gaming. This needs to be stored as a text file with a .gwent extention in the content folder and the Gwent Pelican plugin included in the new version of DeckLock will process it. If you’ve read part 1 and part 2 of the DeckLock posts, there is nothing remarkable about the implementation.

## Handling images

One consequence of having digital cards that can change over time is how they are stored on The Voice of Gwent. You can download the images of the cards, but as other properties (like the power, the abilities, …) can change from one version to another, additional information is cleverly added using CSS.

## Code

All the code for DeckLock is up on GitHub https://github.com/4dcu-be/DeckLock and you can check out the demo with the Decks I have and enjoy playing across the different games.


text: We will construct infinitely many irreducible symplectic and non-symplectic 4-manifolds that are homeomorphic but not diffeomorphic to (2n-1)CP^2#(2n-1)\bar{CP}^2 for each integer n > 11, and the families of simply connected irreducible nonspin symplectic 4-manifolds that have the smallest Euler characteristics among the all known simply connected 4-manifolds with positive signature and with more than one smooth structure. Our construction uses the complex surfaces of Hirzebruch and Bauer-Catanese on Bogomolov- Miyaoka-Yau line with c_1^2 = 9\chi_h = 45. This is a joint work with A. Akhmedov.