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Your last observation is correct! But it is not written properly: in fact $$\lim_n \mathsf E[\cdot \mid S_n,S_{n+1},\dots]\neq \mathsf E[\cdot \mid\varnothing]. $$The limit of conditioning on $S_n,S_{n+1},\dots$ should be understood as the limit of sigma-algebras$$\mathcal F_n = \sigma(S_n,S_{n+1},\dots).$$Why $\mathca... |
\[x \in \{0\} \cup [\ell,u]\]
I also see sometimes \(x \in 0 \cup [\ell,u]\). I am not sure which version is more correct. We assume \(0 \le \ell \le u\) (negative bounds are not very well defined in conjunction with semi-continuous variables).
Semi-continuous variables are often used in situations where we don’t like ... |
Strong convergence theorems for asymptotically k-strictly pseudocontractive maps Abstract
Let $C$ be a nonempty closed convex subset of a real Hilbert space, $H$ and let $ T: C \rightarrow C $ be an asymptotically $k$-strictly pseudo-contractive mapping with a nonempty fixed-point set, $F(T)=\{x\in C: Tx=x\}$. Let $\{t... |
A so-called leaky integrator is a first-order filter with feedback. Let's find its transfer function, assuming that the input is $x(t)$ and the output $y(t)$:
$$\frac{dy(t)}{dt} + Ay(t) = x(t)$$
$$\mathcal{L}\left\{\frac{dy(t)}{dt} + Ay(t)\right\} = \mathcal{L}\left\{x(t)\right\}$$
where $\mathcal{L}$ denotes applicati... |
I am reading a paper Okuguchi,1981 with a Ramsey growth model. There is a constant population growth $n$ such as $L(t)=e^{nt}$. The way he writes the Hamiltonian is quite interesting (equation 5 on page 658.)
$$H=e^{-(\rho+n\left(1-\sigma\right))t}\left[\frac{C^{1-\sigma}}{1-\sigma}+\psi AG+\phi\left(Q-C\right)\right]+... |
(after having spent some time working in the wrong region):
The statement of the boundaries is ambiguous, because they apply equally well to the blue or the green region shown in the graph above. But it wasn't a complete waste of time to integrate in the wrong place, as I will describe below.
The equation of the circle... |
If I were to cover the Fibonacci Sequence in introducing sequences to Calculus students, I would probably avoid some of the more obscure properties. I would focus on what early Calculus students should know: for example, how to prove that a sequence converges, and if it does, then how to find what it converges to.
(Not... |
2.1. Data Manipulation¶
In order to get anything done, we must have some way to manipulate data.Generally, there are two important things we need to do with data: (i)acquire them and (ii) process them once they are inside the computer.There is no point in acquiring data if we do not even know how to storeit, so let us ... |
I am trying to use backwards finite difference method to numerically solve a pair of partial differential equations:
$\frac{\partial \left(pv\right)}{\partial x}+\frac{\partial p}{\partial t}=0$ $\frac{\partial \left(pv^2\right)}{\partial x}+\frac{\partial \left(pv\right)}{\partial t}+c\frac{\partial p}{\partial x}=0$
... |
Introduction¶
When it comes to quick out-of-the-box predictive modeling, methods based on Decision Trees are still hand-down one of the easiest to apply yet highly efficient models. Tree ensembles like Random Forests or Boosting achieve high accuracy results without much fine-tuning or feature engineering. One of the d... |
where =SUMIF(X,">0")-SUMIF(X,"<0") Xis a range. This looks like a strange construct. It is meant to implement the sum of absolute values\[||x||_1=\sum_i |x_i|\] also known as the L1-norm. The L2-norm \[||x||_2 = \sqrt{\sum_i x_i^2}\] is easy to do in Excel: =SQRT(SUMSQ(X))
Strangely, there is no obvious (that is, obvio... |
Treewidth is NP-hard to compute on co-bipartite graphs, indeed the original NP-hardness proof of treewidth of Arnborg et al. shows this. Additionally, Bodlaender and Thilikos showed that it is NP-hard to compute the treewidth of graphs of maximum degree $9$. Finally, for any graph of treewidth at least $2$,
subdividing... |
Visiting addressNiels Henrik Abels hus Moltke Moes vei 35 (map)
0851 OSLO
Norway
Abstract: We discuss a way of constructing noncommutative projective manifolds as inductive and projective limits, generalizing the so-called Berezin quantization for ordinary compact Kähler manifolds. We first review the physical motivati... |
This question already has an answer here:
How to prove a language is regular? 8 answers
I am asked to find
Prove that the following languages are regular languages:
(a) $\{a^nb^ma^k \mid n\geq3,m\geq1,k\geq1\}$
(b) $\{a^n \mid n\neq3 \text{ and } n\not\equiv2 \mod7\}$
(c) $\{a^nb \mid n\geq2\}\cup\{ab^m \mid m≥3\}$
I h... |
I know there is this paper but I wanted to do a special case proof for just IMP for fun. So the theorem is:
$$ \langle P , \sigma \rangle \to_{Big} \langle \{ \} , \sigma' \rangle \iff \exists N \in \mathbf N: \langle P , \sigma \rangle \to^N_{Small} \langle \{ \} , \sigma' \rangle $$
in words; the program P in state $... |
The Johnson graph $J(n,k)$ has as its vertices the $k$-subsets of $\{1, 2, \dots, n\}$ where two vertices are adjacent iff their intersection has size $k-1$. A graph is
Hamilton-connected if every two vertices are joined by a Hamiltonian path. A recent paper by Alspach shows that Johnson graphs are Hamilton-connected.
... |
Update: problem reformulation
Following the advice in comments, I now restate my problem using Voronoi tessellation.
Given a unit hypercube $H_n=\{(x_1,\ldots,x_n)\in \mathbb{R}^n: 0\leq x_i\leq 1\}$, generate $K$ random points in $H_n$ using uniform Poisson point process with intensity 1.
Let $V_k$ be the $k$-th Voron... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
Search
Now showing items 1-3 of 3
D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC
(Elsevier, 2017-11)
ALICE measured the nuclear modification factor ($R_{AA}$) and elliptic flow ($\nu_{2}$) of D mesons ($D^{0}$, $D^{+}$, $D^{⁎+}$... |
I've learned sum of exponential random variables follows Gamma distribution.
But everywhere I read the parametrization is different. For instance, Wiki describes the relationship, but don't say what their parameters actually mean? Shape, scale, rate, 1/rate?
Exponential distribution: $x$~$exp(\lambda)$ $$f(x|\lambda )=... |
Consider the definition of entropy in the microcanonical ensemble:
$$S=k_B \log \Omega(N,V,E)$$
where
$$\Omega(N,V,E)=\frac 1 {N! h^{3N}} \int_{\mathcal H<E} d^N\mathbf p \ d^N \mathbf q \tag{1}\label{1}$$
is the microcanonical partition function. $\mathcal H$ is the hamiltionian of the system, which depends on all the... |
I am trying to optimize a constrained-problem with a discrete, non-linear objective function. Evaluating this function is also fairly expensive. Nevertheless, despite the above two factors, I hope, that it can still be solved efficiently, since the structure of the constrained parameter space should be helpful.
To be m... |
Evidence for the production of three massive vector bosons with the ATLAS detector
Pre-published on: 2019 August 22
Published on: —
Abstract
The search for the production of three massive vector bosons in proton$-$proton collisions, performed using data at $\sqrt{s}$ = 13 TeV recorded with the ATLAS detector at the Lar... |
Given that we want to find the Value at Risk for a portfolio of stocks only, there are two main methods to proceed. In the problem, we also assume that stocks follow a geometric Brownian motion.
A full scale simulation:
simulate normal deviates B; plug into $S_t = S_0 e^{(\mu-0.5\sigma^2)t + \sigma t B_t}$; pick the 1%... |
Estimate the kinetic energy of the following particles after their material interactions: a) a muon with \(E_{\text{kin}}\) = 400MeV traverses a 10 cm iron target, b) a proton with \(E_{\text{kin}}\) = 200MeV traverses a 20 cm iron target, c) a charged pion with \(E_{\text{kin}}\) = 1GeV traverses a 20 cm iron target.
... |
Consider the following Sturm–Liouville (SL) eigenvalue problem defined in $(-\infty,0]$ or $[0,\infty)$ or $(-\infty,+\infty)$ $$(py')'-qy=-\lambda^2wy,$$ in which $p(x)=x^2$, $w(x)=1$, and $q(x)=(x/2+a)^2+a$ with parameter $a>0$. It has a regular singularity $x=0$. We basically hope for something like homogeneous Diri... |
As title suggests, what is the size limit by volume for a rocky planet, if any? Some ideas are discussed here, but I'm wondering if there is more concrete, expert evidence to point either way. If possible, it should be at least large enough to host one or more entities that eat Earth-sized planets (a future question in... |
My book is An Introduction to Manifolds by Loring W. Tu. The following is an entire subsection (Subsection 22.5) of the section that introduces manifolds with boundary (Section 22, Manifolds with Boundary).
Note: I believe that all manifolds with or without boundary referred in this subsection have unique dimensions by... |
Consider fix point of \( R(z) = z^2 – z \) .
Which is the solution of $$ R(z) = z \\ \Rightarrow z^2 – z =z \\ \Rightarrow z^2 – 2z =0 \\ \Rightarrow z(z -2) =0 $$
Now , consider the fix point of \( R^2(z) \) . \( \\ \) $$ i.e. R^2(z) = R . R(z) = R(z^2 -z)\\ \Rightarrow (z^2 -z)^2 – z^2 +z =z \\ \Rightarrow z^4 -2z^3 ... |
The GNS construction allows one to represent a $C^*$-algebra as the algebra of bounded operators on a Hilbert space when a state is fixed, this state being represented as a vector on the Hilbert space. Another state will be represented as a vector on a
different Hilbert space. I am trying to find back the usual quantum... |
Here is my understanding of your question, I might have oversimplified your problem, and made some hypothesis that were not yours.
Assuming we are talking about a bond paying $1$ each day until $T$ or default event if occuring before $T$.
Let's write the risky coupon bond payment in a continous time manner:
$$\int_0^T ... |
I would suggest trying to read at least the introduction of the article because I think Drew did a really great job motivating the beauty of the subject and setting the stage for the main results of the paper. While Brant and I did help implement a few modifications to Drew's exposition, the introduction is for the mos... |
The orthogonal group, consisting of all proper and improper rotations, is generated by reflections. Every proper rotation is the composition of two reflections, a special case of the Cartan–Dieudonné theorem.
Yeah it does seem unreasonable to expect a finite presentation
Let (V, b) be an n-dimensional, non-degenerate s... |
I found it difficult to explain the difference between the fraction a / b and the ratio a : b. This subject is for pupils of grade 5. So is there a real difference between them and how to explain the difference in simple way ?!
This paragraph from Adding It Up is a good overview of the context of this question. Rationa... |
If $f \colon C \to C'$ is a dominant morphism of smooth projective curves, there is a norm map $f_\ast = \mathrm{Nm} \colon JC \to JC'$ between their Jacobians, and we can consider the abelian subvariety $Z = (\ker \mathrm{Nm})^0$ and the polarization on $Z$ induced from $JC$. In two particularly interesting cases this... |
... h a GUI. The figure below shows data for steering angle history/prediction.Project DetailsBeginning date: 01 Feb 2006Ending date: 31 Jul 2009Funding: European Commission (FP6-IST-FET, contra ...
... priced scanner "for the masses", that can be used by, for example, 3D artists, game designers, 3D printing community ... |
Definition: Let $\kappa$ be an $\aleph$ cardinal, we say that $\langle f_\alpha\colon\alpha\to\kappa\mid\alpha<\kappa^+\rangle$ is a ladder if every $f_\alpha$ is injective.
Equivalently this is the range of a choice function from every injection of $\alpha$ into $|\alpha|$ (for $\alpha<\kappa$ we can always assume the... |
Consider fix point of \( R(z) = z^2 – z \) . Which is the solution of $$ R(z) = z \\ \Rightarrow z^2 – z =z \\ \Rightarrow z^2 – 2z =0 \\ \Rightarrow z(z -2) =0 $$ Now , consider the fix point of \( R^2(z) \) . \( \\ \) $$ i.e. R^2(z) = R . R(z) =...
And suppose that R has no periodic points of period n . Then (d, n) i... |
Bubbling transition
Peter Ashwin (2006), Scholarpedia, 1(8):1725. doi:10.4249/scholarpedia.1725 revision #137426 [link to/cite this article]
The
bubbling transition is a bifurcation in certain nonlinear dynamical systems where a change in parameter results in a qualitative change in the way the attractor responds to no... |
Consider the word $abab$. It has two derivation trees (rendered using syntree):
Hence your grammar is ambiguous. In order to make an unambiguous grammar, we have to force the parse to be unique. We identify the word with a path in which $a$ corresponds to $\nearrow$ and $b$ to $\searrow$. We're looking for a non-empty ... |
Given the base case $a_0 = 1$, does $a_n = a_{n-1} + \frac{1}{\left\lfloor{a_{n-1}}\right \rfloor}$ have a closed form solution? The sequence itself is divergent and simply goes {$1, 2, 2+\frac{1}{2}, 3, 3+\frac{1}{3}, 3+\frac{2}{3}, 4, 4+\frac{1}{4}, 4+\frac{2}{4}, 4+\frac{3}{4}, . . .$} and so forth. It seems like it... |
Amsler, C; Bösiger, K; Caminada, L; Canelli, F; Chiochia, V; de Cosa, A; Galloni, C; Hreus, T; Kilminster, B; Lange, C; Maier, R; Ngadiuba, J; Pinna, D; Robmann, P; Taroni, S; Yang, Y; et al, (2017).
Characterisation of irradiated thin silicon sensors for the CMS phase II pixel upgrade. European Physical Journal C - Pa... |
An array $\mathcal{A}$ of $n$ distinct integers $\{a_1,a_2,\ldots,a_n\}$ is given. I'm asked to design a randomized (esp. Las Vegas) algorithm to make a Binary Search Tree out of these elements, such that the height of the tree is $\lceil \log{_{2-\epsilon}n}\rceil$, where $\epsilon=\frac{2}{9}$.
If we had to make a
pe... |
Let's say $p_1, p_2, p_3, \ldots $ is the increasing sorted sequence of all prime numbers. Prove that there exists a constant $n_0 \in \mathbb{N}$, so that for all $n \ge n_0$: $$K(p_n) < \log_2(p_n) − 2.$$ Hint: Prime number theorem: $p_n \in \Theta (n \ln n)$.
I think, I could have a program A, which generates $p_n$ ... |
Let $X$ be a complex analytic space. It is a 'well known fact' that the categories of local systems on $X$ (i.e. locally constant sheaves with stalk $C^n$), and of (holomorphic) vector bundles on $X$ with flat connection, are equivalent. I've been looking for a proof of this, but every reference I can find merely says ... |
We have \(n\) groups of volunteers. Groups have different sizes (number of volunteers). There are \(m\) volunteer sites with a certain demand for volunteers. Try to assign volunteers to sites such that we don't split up groups if not needed.
We can recognize a
transportation modelin the description of the problem. We h... |
On reading the section 12.1 of Peskin and Schroeder's (P&S) QFT on "Wilson's Approach to Renormalization Theory", I gathered the impression that in the Wilsonian approach, one starts by analyzing a Lagrangian containing all possible terms compatible with some given symmetry
and having mass dimension $\leq 4$. For examp... |
Are there any famous problems/algorithms in scientific computing that cannot be sped up by parallelisation? It seems to me whilst reading books on CUDA that most things can be.
The central issue is the length of the critical path $C$ relative to the total amount of computation $T$. If $C$ is proportional to $T$, then p... |
If I know the chemical shift tensor (from ab initio methods), $\sigma$, for each atom in my structure, is it possible to construct an NMR spectra for my system? If yes, how and what mathematical implementations do I need?
Yes, it is possible. It is done often. The solution depends on the dynamics and orientation(s) of ... |
Regularly I am asked “
What is the difference between Matlab and GAMS when modeling optimization problems?”. I’ll try to answer this question with some examples. Matlab
In Matlab LP and MIP models are modeled using a matrix data structure. Basically a linear optimization model is viewed as:
\[\boxed{\begin{align}\min\>... |
The pressure drop in the venturi is proportional to air density and the fuel is at ambient pressure in the float chamber, so I would expect the fuel flow to reduce proportionally with density, and that response to preserve the fuel-air ratio over changing altitude.
But in practice that does not seem to be the case. Pro... |
This question already has an answer here:
I'm no physicist so it might be a stupid question but is there a maximum energy a single photon can have?
My idea was, that there might be restriction for the minimum wavelength and I thought about the Planck length: $1.616 · 10^{−35}$ m
So my hypothetical photons energy would ... |
I'm working out of the 3rd edition CLRS Algorithms textbook and in Chapter 3 a discussion begins about asymptotic notation which starts with $\Theta$ notation. I understood the beginning definition of:
$$\Theta(g(n)) = \{ f(n)\,|\, \exists\, c_1, c_2 > 0, n_0 \in \mathbb{N}: 0 \leq c_1 g(n) \leq f(n) \leq c_2 g(n)\ \ \... |
Let $n \in \mathbb N$ be arbitrary. Does the integral
$$\int_{0}^{1} |\ln (x)|^n \, dx$$ converge? I asked myself this question and I have no idea of a proof or counter example. Someone can give me a help?
The only problem is at $0$. The absolute value is irrelevant (just multiply by $(-1)^{n+1}$ the final result when ... |
In some degenerate cases there may be no such a one point (for instance, if all the lines are parallel). However there's a single solution in the general case.
I assume you're trying to solve a more general problem where all the lines are not required to intersect exactly (otherwise there's a much simpler solution than... |
Automata Theory- Brzozowski Algebraic Method
A LaTeX typeset copy of this tutorial is below for download:
Brzozowski_Algebraic_Method.pdf
(126.4K)
Number of downloads: 1388
I. Introduction
Recall that a language is regular if and only if it is accepted by some finite state automaton. In other words, each regular expres... |
It is well-known that bounded error quantum query complexity of the function $OR(x_1,x_2,\ldots, x_n)$ is $\Theta(\sqrt{n})$. Now the question is what if we want our quantum algorithm to succeed for every input with probability $1-\epsilon$ rather than the usual $2/3$. Now in terms of $\epsilon$ what would be the appro... |
Is it necessary for someone to write
$$\int (x^2+2x) \,\mathrm{d}x$$
Instead of
$$\int x^2+2x \,\mathrm{d}x$$
With the second one, it's quite obvious which terms we are taking the integral of. Is it still necessary to use brackets in this case?
Mathematics Stack Exchange is a question and answer site for people studyin... |
Here is a version of continuity of the roots.
Consider the monic complex polynomial $f(z)=z^n+c_1z^{n-1}+...+c_n\in \mathbb C[z]$ and factor it as $$f(z)=(z-a_1)...(z-a_n) \quad (a_k\in \mathbb C)$$ where the roots $a_k$ are arranged in some order, and of course needn't be distinct. Then for every $\epsilon \gt 0$, the... |
The solution of the model contains constant: $k = \alpha K$, it relates to: (i) probability of getting a fill ($\alpha$) and (ii) market impact ($K$).
Estimating (i). The author proposes that the market order sizes follow a power law distribution:
$$f(x)^Q \propto x^{-1-\alpha}$$
So no problem estimating this.
Estimati... |
The Basic Model
Aghion and Howitt assume that the economy is populated by a continuous mass, L, of infinitely lived individuals with linear preferences, who discount the future at rate ρ. Each individual is endowed with one unit of labor per unit of time, which she can allocate between production and research: in equil... |
Found this on Complexity Zoo warning expired certificate check NP Over The Complex Numbers.
[BCS+97] show the following striking result. For a positive integer $n$, let $t(n)$ denote the minimum number of additions, subtractions, and multiplications needed to construct $n$, starting from 1. If for every sequence ${n_k}... |
Question
I have a sequence of natural numbers $0 = k_0 < k_1 < k_2 < \dots < k_n$ and we want to find the set of numbers which satisfy some property, so we want to find (in function of $n$): $$ \mathcal{A}_n := \{ (k_1,\dots,k_n) \in \mathbb{N}^{n} \mid (k_0,\dots,k_n) \mbox{ satisfy property }A\} $$ The property $A$ w... |
Given a Hamiltonian $H$, how can I relate the collapse operator for the Lindblad equation to a given environmental effect? Also, how can I relate the constant $\gamma$ in front of the sum of the collapse operators to the full Hamiltonian?
For reference, the lindblad equation is:
$$\dot \rho = -i[H, \rho] + \left( \gamm... |
I am trying to find a way to compare two real numbers (actually floating-point) with a tolerance, i.e. test $|r-s|\le\epsilon$. Without loss of generality, $\epsilon=1$.
I want to do this by replacing the numbers by a discrete key computed on them in such a way that when two keys differ, they map two significantly dist... |
Let $V$ be a vector space over a field $k$. Let $T$ be a $k$-linear transformation from $V$ to itself. Without using the notion of characteristic polynomial or Cayley-Hamilton theorem from Linear Algebra, how can I show that there exists a unique monic polynomial $p_T(X) \in k[X]$ such that $p_T(T)$ is the zero transfo... |
Circular motion in special relativity is somewhat tricky: Note that for circular motion, the acceleration in the spaceship travelling in a circle is
not zero, so the spaceship is not in a single frame of inertia.
Here is an interesting thought: Distances
perpendicular to the direction of motion are not subject to contr... |
Model the dashed line h(x)
We want to model that the costs are represented by the function \(h(x)\) (the dashed curve in the picture). Let's make a few assumptions:
The function \(f(x)\) is a quadratic function while \(g(x)\) is linear. \(f(x)\) is convex We are minimizing cost (or maximizing profit) Update: I also ass... |
Disclaimer: these are just opinions, I do not necessarily have authoritative knowledge in this topic.
If you consider the traditional Sharpe definition:
$$S = \frac{reward}{risk}$$where reward is the expected return (above risk free rate) and risk is the standard deviation of reward, it is not clear to me how your augm... |
fskilnik wrote:
GMATH
practice exercise (Quant Class 7)
In the figure shown, AB = AC = 12. Which of the following is closest to the area of the circle with center O that is tangent, at points M, N, and P, to the circular sector ABPC with center A and central angle of 60 degrees?
(A) 40.1
(B) 43.7
(C) 46.8
(D) 50.2
(E) ... |
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Free keywords: General Relativity and Quantum Cosmology, gr-qc,Astrophysics, Cosmology and Extragalactic Astrophysics, astro-ph.CO, Astrophysics, High Energy Astrophysical Phenomena, astro-ph.HE, Astrophysics, Instrumentation and Methods for Astrophysics, astro-ph.IM
Abstract: We employ gravitational-wave radiomet... |
After looking through some literature I'm answering my own question. I'll wait on accepting for a few days in case anyone else has a better answer.
First of all, the problem is equivalent to solving,$$A x = \sqrt{A}b,$$so the only square root part needed is computing $\sqrt{A}b$, after which it is a normal solve.
The f... |
4.5. Weight Decay¶
Now that we have characterized the problem of overfitting and motivated the need for capacity control, we can begin discussing some of the popular techniques used to these ends in practice. Recall that we can always mitigate overfitting by going out and collecting more training data, that can be cost... |
Analysis Seminar – Simon Bortz (University of Washington)
Title: Sobolev contractivity of the gradient flow maximal function Abstract: In 2013, Carneiro and Svaiter showed that the heat flow maximal function is contractive in $\dot{W}^{1,2}(\mathbb{R}^n)$ for $W^{1,2}(\mathbb{R}^n)$ functions. In other words, if $K_t$ ... |
... h systems almost always employ conventional control strategies. Biological systems, on the other hand, learn. In the beginning they are functional only at a very basic level from which they improve the ...
I just noticed that there is a bug in the code that manifests itself in "later" versions of Matlab. The bug is... |
Introduction¶
In my last post I replaced the original features of a simulated 2-dimensional classification problem with the matrix of euclidean distances between all data-points. This meant that the distances to all points in the training set became the new features for the learner - formally speaking we performed the ... |
Early in 2011, I spent a few months as an exchange student in the University of Melbourne. Although I was writing my thesis at the time, I was looking for topics for a small-scale research, as I had to turn in some written assignment as part of the exchange program. I can't remember why, but I thought a bit about power... |
Given $ U, V, C $ are three distinct digits, figure them out from the following relation:
$$ \overline{CCC} = \overline{UVUVUV} \div \left ( \overline{UV} \times \overline{UV} \right) $$
Puzzling Stack Exchange is a question and answer site for those who create, solve, and study puzzles. It only takes a minute to sign ... |
Well, what you find is that the introduction of stochastic vol changes the delta of your options. So what does this mean? If the new delta reduces the variance of your hedged portfolio versus the pure local vol model , then it means that the introduction of stochastic vol has resulted in a better description of market ... |
I am having the following equation:
\begin{equation} Q(\lambda,\hat{\lambda}) = -\frac{1}{2} P(O \mid \lambda ) \sum_s \sum_m \sum_t \gamma_m^{(s)} (t) \left( n \log(2 \pi ) + \log \left| C_m^{(s)} \right| + \left( \mathbf{o}_t - \hat{\mu}_m^{(s)} \right) ^T C_m^{(s)-1} \left(\mathbf{o}_t - \hat{\mu}_m^{(s)}\right) \ri... |
On some graph transformations that preserve sgn$(\lambda_2-2)$ Bojana Mihailović University of Belgrade - School of Electrical Engineering, Belgrade, Serbia Marija RasajskiPDF University of Belgrade - School of Electrical Engineering, Belgrade, Serbia Minisymposium:SPECTRAL GRAPH THEORY Content:For a simple graph $G$ (... |
Question.Suppose $\kappa$ is a supercompact cardinal and $\lambda > \kappa$ is measurable (or even larger large cardinal if necessary). Is there a set generic extension of the universe in which $\kappa$ remains supercompact, $\lambda$ is preserved and $cf(\lambda)=\omega?$ Remark 1. By Gitik-Shelah indestructibility re... |
I recently started learning about Algebraic Lattices because I was interested in how they relate to Automata Theory. It turns out they’re fundamental to a bunch of other things that I’ve always wanted to learn more about, like CRDTs and Type Theory.
I stumbled upon an interesting property about lattices that reminded m... |
I'm sorry if this is too easy for MO.
Let $S$ be a locally noetherian scheme, flat over $\mathrm{Spec}\,\mathbb{Z}$, $X$ and $Y$ be flat $S$-schemes locally of finite presentation, and let $f:X\to Y$ be a map over $S$. Suppose that the differential $df: f^* \Omega^1_{Y/S}\to \Omega^1_{X/S}$ is an isomorphism.
Can we co... |
I wanted to derive length contraction from the Lorentz transformation, but I keep getting stuck on problems with simultaneity in my derivation. At some point, I came across Wikipedia's article on Length Contraction where, in the section labeled "Derivation", it states
In an inertial reference frame $S^\prime$, $x_1^{\p... |
As my question states, I want to calculate the Fourier transform $F(q)$ of a radial function $f(r)$ (defined on $[0,\infty)$ and which decays like an exponential $\exp(-Ar+b)$ at large $r$) as accurately as possible in Fortran. The function values come from a data file (which I can easily interpolate through cubic inte... |
The Annals of Statistics Ann. Statist. Volume 21, Number 4 (1993), 1982-2000. Random Discriminants Abstract
Let $X_1, X_2, \cdots, X_n$ be a random sample from a continuous univariate distribution $F$, and let $\Delta = \prod_{1 \leq i < j \leq n}(X_i - X_j)^2$ denote the discriminant, or square of the Vandermonde dete... |
Benzophenone is a notorious case where prompt fluorescence, phosphorescence and delayed fluorescence can mix. Have a look at
Modern Molecular Photochemistry by N.J. Turro for some general information and Prompt and delayed fluorescence from benzophenone by R.E. Brown and L.A. Singer for the original reference.
\[\begin... |
It is easier to understand the geometry of linear maps in terms of matrices. Let $\mathbb{R}^2$ be equipped with its canonical base. Then all linear maps $\varphi : \mathbb{R}^2 \to \mathbb{R}^2$ can be written as
$$ \varphi(x) = Ax $$
for some suitable, real $2 \times 2$ -matrix $A$ with respect to the canonical (or a... |
I am trying to follow lecture notes regarding the Kalman Filter from a course taught at Stanford. The lecture notes can be found here.
The linear Gaussian state space model (LGSSM) is introduced as \begin{align*} z_0 &\sim N(0, \Sigma_0) \\ z_t &= A z_{t-1} + w_{t-1} &&\text{ for independent } &&w_{t-1} \sim N(0,Q) &\f... |
I have tried to show that every metric space $(X,d)$ is homeomorphic to a bounded metric space. My book gives the hint to use a metric $d'(x,y)=\mbox{min}\{1,d(x,y)\}$.
If we can show that $d(x,y) \le c_1 \cdot d'(x,y)$ with $c_1$ some positive constant and $d'(x,y) \le c_2 \cdot d(x,y)$ for $c_2$ some positive constan... |
I'm going through Kerr metric, and following the 'Relativist's toolkit' derivation of the surface gravity, I've come to a part that I don't understand.
Firstly, the metric is given by
$$\mathrm{d}s^2=\left(\frac{\Sigma}{\rho^2}\sin^2\theta\omega^2-\frac{\rho^2\Delta}{\Sigma}\right)\mathrm{d}t^2-2\frac{\Sigma}{\rho^2}\s... |
Suppose you have an infinite thin sheet of charge with a certain charge density. By symmetry we know the electric field is perpendicular to the sheet. You can calculate the field using this method:http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elesht.html
$E = \dfrac{\sigma}{2\epsilon_0}$
This field is constant ev... |
Does the frictional force increase as the normal force increases, or does the coefficient of friction get smaller in value?
The coefficient of friction should in the majority of cases, remain constant no matter what your normal force is. When you apply a greater normal force, the frictional force increases, and your co... |
between each X variable and Y. Security Patch SUPEE-8788called beta (b ) weights.If the correlation between X1 and X2 is of Why did my electrician put metal plates wherever the stud is drilled through?
Please help, I
just is a straight-forward generalization of the case for one independent variable. We can do this inte... |
Let $\mathcal{M}(\mathbb R)$ be the space of Radon measures, equipped with topology $\tau$ generated by the following "weak convergence":
$$ \mu_n \rightarrow \mu \quad \text{iff} \quad \int f d\mu_n \rightarrow \int f d\mu \quad $$ for all continuous function $f$ with quadratic growth: $|f(x)|\leq C(1+|x|^2)$ for some... |
Difference between revisions of "Algebraic Geometry Seminar Spring 2015"
(→Spring 2015 Schedule)
(→Spring 2015 Schedule)
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|April 17
|April 17
|Lee McEwan (OSU, Mannsfield)
|Lee McEwan (OSU, Mannsfield)
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|Max and Gonzalez Villa
|Max and Gonz... |
For a model (1) I needed to calculate the cumulative distribution function \(F(x)\) of the Gamma distribution. There is no uniform consensus: the Gamma distribution has different parametrizations. I use the \(k, \theta\) parametrization from (2). This would yield (3):
\[F(x) = \gamma( \frac{x}{\theta},k)\]
where \(\gam... |
Problem Data meanis just the average of the \(x\)- and \(y\)-coordinates. NLP Model
Unconstrained NLP Model \[\min \sum_i \sqrt{\sum_c (\color{darkred}x_c-\color{darkblue}p_{i,c})^2 }\]
We use \(c = \{x,y\}\), i.e. we have \(x\) and \(y\)-coordinates. Note that we use \(x\) in two different contexts: element of set \(c... |
The Kolmogorov complexity of a string $x$ is the size of the smallest Turing machine $M$ that started on empty tape produces $x$. To make it computable, we can add a bound on the time used by $M$ to produce $x$:
$C^{t}(x) = \min \{|M| : U(M) = x$ in less than $t(n)$ steps $ n = |x| \}$
And for a nice function $f(n) < n... |
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