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Of course, the curves may neither converge nor diverge. An extreme case of such case is they may evolve more or less parallel to each other.
My problem is to recognize the convergence and the divergence patterns. This may be trivial as done visually by human, but I want to automate the task using an algorithm, and like... | CommonCrawl |
Opis: Single tungsten oxide aerogels (WO3), binary oxide aerogels (WO3-Al2O3) and ternary oxide aerogels (WO3-SiO2-Al2O3) were prepared using standard sol-gel route. Tungsten oxide tetraethoxide (WO(OCH2CH3)4) was used as the sol-gel precursor. The excellent properties of the gels obtained by the sol-gel synthesis were... | CommonCrawl |
$s^ n_ i = (s^ n_ i, s^ n_ i)$.
In other words, $V \times _ U W$ is the fibre product of the presheaves $V$ and $W$ over the presheaf $U$ on $\Delta $.
In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the followin... | CommonCrawl |
A 0-definable set $ D $ in a structure $ M $ is said to be stably embedded if every $ M $-definable subset of $ D^n $, for any $ n $, is $ D $-definable.
In a stable theory, every definable set is stably embedded. This fact is sometimes called the Parameter Separation Theorem, e.g., by Bruno Poizat. More generally, in ... | CommonCrawl |
15:00 to 16:00 Elvira Zappale Lower semicontinuity and relaxation of nonlocal $L^\infty$ functionals.
16:30 to 17:15 Kirill Cherednichenko Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties.
13:30 to 14:10 Julia Yeomans Bacteria: self-motile liquid crys... | CommonCrawl |
Here we are finding number of state less than energy E for particle trapped in 3D harmonic potential .For large value of E as compare to hw , we assumed energy levels as continuous.And we introduces coordinate system in terms of which surface of constant energy is plane E = E_1 + E_2 + E_3 .Number of state with energy ... | CommonCrawl |
We propose a new provable method for robust PCA, where the task is to recover a low-rank matrix, which is corrupted with sparse perturbations. Our method consists of simple alternating projections onto the set of low rank and sparse matrices with intermediate de-noising steps. We prove correct recovery of the low rank ... | CommonCrawl |
The question is "Let $X$ be a metric space, find a closed subset $A$ such that $A'\neq \emptyset$ and $(A')' = \emptyset $"
Well in $\mathbb R$ with the standard topology, $\mathbb Q$ is close and open simultaneously (hope I'm not wrong with that) therefore it answers the demands. Yet I can't find an example in which $... | CommonCrawl |
We study the semiclassical propagation of a class of wavepackets for large times on manifolds of negative curvature. The time evolution is generated by the Laplace-Beltrami operator and the wavepackets considered are Lagrangian states. The principal result is that these wavepackets become weakly equidistributed in the ... | CommonCrawl |
Bagchi, Biman and Chandra, Amalendu and Rice, Stuart A (1990) An interpretation of the bifurcation of orientational relaxation processes in a supercooled liquid. In: Journal of Chemical Physics, 93 (12). pp. 8991-9001.
The orientational relaxation of molecules in a supercooled liquid is known to exhibit interesting dyn... | CommonCrawl |
Rodrigo Platte's primary research interests are in computational mathematics, numerical analysis, and approximation theory. A recurring theme in his research is sampling. Today's world is increasingly rich in data, but working with large data sets can be computationally expensive and, in some cases, even detrimental to... | CommonCrawl |
Schubert calculus is the study of flag varieties, which are quotients of algebraic groups (usually complex semisimple, but sometimes over the real numbers or even finite fields) by parabolic subgroups.
Reference for Grassmann and Schubert varieties for Beginners .
I need some references to understand Grassmann and Schu... | CommonCrawl |
Industry vs Kaggle challenges. Is collecting more observations and having access to more variables more important than fancy modelling?
What must someone know in statistics and machine learning?
What is the probability that $X<Y$ given $\min(X,Y)$?
Why is computing ridge regression with a Cholesky decomposition much qu... | CommonCrawl |
The expression with n terms is (1/2)(2/3)(3/4)...)((n-1)/n)=1/n. The limit is obviously 0.
(n-1)*(n-2)*(n-3)!/n*(n-1)*(n-2)*(n-3)!. Now I understand the result.
Last edited by skipjack; October 4th, 2018 at 11:28 PM.
Is it okay how I solve it? I wanted to know where the result 1/n appeared from.
The result comes intuit... | CommonCrawl |
You are given two integers $N$ and $K$. Find all ways to represent $N$ as the sum of exactly $K$ distinct positive integers $x_1,x_2, \ldots,x_K$ — in other words.
How to code to generate these combinations in any language?
Are you currently participating in SnackDown Round 1B, Then you should not ask this question bef... | CommonCrawl |
50 Requesting someone to give up their seat to me on public transport if I have an invisible disability?
23 Is there any combination of two airports that are connected via taxiways?
11 No Lie algebra over $\Bbb R$ or $\Bbb C$ can have a unit element.
9 Why are $L^p$ spaces for $p\not=1,2,\infty$ important?
6 Can GHC wa... | CommonCrawl |
We study charmonium spectral functions at finite temperature by using stochastic reconstruction methods. Our quenched lattice QCD simulations are performed with the standard plaquette gauge and the $O(a)$-improved Wilson fermion actions on 192$^3 \times N_\tau$ lattices with $N_\tau$ = 96--32, which corresponds to temp... | CommonCrawl |
3. It is smaller than $7\times 4$.
You might like to print off this sheet of the problem.
Addition & subtraction. Factors and multiples. Working systematically. Visualising. Combinations. Odd and even numbers. Interactivities. Place value. Generalising. Investigations. | CommonCrawl |
The first edition of Bourbaki's General Topology (chapter I, §9, p. 56) contains the following theorem.
Proposition 3. Soient $E$, $F$ deux espaces topologiques, $R$ une relation d'équivalence dans $E$, $S$ une relation d'équivalence dans $F$. L'application canonique de l'espace produit $(E/R) \times (F/S)$ sur l'espac... | CommonCrawl |
M-theory and string theory predict the existence of many six-dimensional SCFTs. In particular, type IIA brane constructions involving NS5-, D6- and D8-branes conjecturally give rise to a very large class of N=(1,0) CFTs in six dimensions. We point out that these theories sit at the end of RG flows which start from six-... | CommonCrawl |
You may have noticed that I am back to publishing regular blog posts! My goal for now is a blog post every second Wednesday. I am now also trying to answer forum questions promptly. I want to thank the readers who took up the slack for the last year and a half in answering questions in the forums. In particular, I'd li... | CommonCrawl |
As you probably know, a Sudoku puzzle is a $9\times 9$ grid divided into nine $3\times 3$ subgrids. Some of the cells in the grid contain a symbol: usually the symbols are the numbers $1,2,\ldots, 9$.
Here I revisit a topic I have written on several times before, and which furthermore continues the theme of my last col... | CommonCrawl |
by Lorenzo Di Paola. Published on 28 January 2016.
the risk of a financial breakdown.
Making the best decisions means not only using the available data and the right model, but also understanding its implications and limitations. Then, companies can take the risks that could lead them to them the best possible outcomes... | CommonCrawl |
A $3 \times 3 \times 3$ cube may be reduced to unit cubes ($1 \times1 \times1$ cubes) in six saw cuts if you go straight at it.
What about a cube of any size (an $n \times n \times n$ cube)?
Visualising. Interlocking cubes. Creating and manipulating expressions and formulae. Squares. Games. Interactivities. Cubes & cub... | CommonCrawl |
Description: Górecki and Łuczak describe an approach for using a weighted combination of raw series and first-order differences for NN classification with either the Euclidean distance or full-window DTW. They find the DTW distance between two series and the two differenced series. These two distances are then combined... | CommonCrawl |
What is a good introduction to integrable models in physics?
What is known about first return times to Markov partitions for Anosov diffeomorphisms?
the ability to give explicit solutions.
These guidelines whould be interpreted in a very broad sense."
Very good answers! I'd love to see more angles to this important iss... | CommonCrawl |
This question was previously titled "Finding residues of a huge multivariable rational function."
First I want to solve for $u_1$ in the denominator and find those roots (poles) that have $x_1$ as below.
Then I will loop through the roots and compute the residue of $f$ w.r.t. $u_1$ at those poles.
Then I replace $f$ wi... | CommonCrawl |
Let $T:Σ^*\to Σ^*$ be an operation such that $T(L)$ is regular for all regular languages $L \in Σ^*$.
Is it possible to prove $T^∞(L)$ is regular?
Colleague Apass Jack already warned about the dangers of infinity, and he also indicated a very simple example that shows that a very simple iteration leads to a non-regular... | CommonCrawl |
It is recently been shown that the spin Hall effect (SHE) in $\beta $-Ta generates a transverse spin current that is sufficient for efficiently reversing the moment of adjacent thin film nanomagnets through the spin torque (ST) mechanism. Here we report the existence of an even larger SHE in $\beta $-W thin films. Usin... | CommonCrawl |
Purpose: In this tutorial we will learn how to perform a time-dependent density-functional (TDDFT) calculation using different xc-kernels. Two examples will be proposed: One for the BSE derived xc kernel and other for the LRC kernel. As a test case, the optical spectrum of LiF will be studied.
Before starting, be sure ... | CommonCrawl |
Abstract: We analyze eight epochs of Hubble Space Telescope H$\alpha$+[N II] imaging of Eta Carinae's outer ejecta. Proper motions of nearly 800 knots reveal that the detected ejecta are divided into three apparent age groups, dating to around 1250 A.D., to around 1550 A.D., and to during or shortly before the Great Er... | CommonCrawl |
of two constants ($\alpha_2$ and $\alpha_1$) of the model.
in radicals. The explicit solution for $m = l$ is presented in Appendix. Imposing certain restrictions on $x$, we prove the stability of the solutions in a class of cosmological solutions with diagonal metrics.
We also consider a subclass of solutions with smal... | CommonCrawl |
Thank you and well done to everyone who submitted solutions to this problem. There were lots and lots of correct solutions, so we couldn't mention you all. In fact, choosing between them was difficult!
$10A+B=(A+B)\times4$, because $A$ has to be multiplied by ten to make it a 2 digit number.
$10A+B=4A+4B$, because you ... | CommonCrawl |
The goal of the project is to better understand and well formalize the effects of complex environments on the dynamics of the interconnections, as well as to develop methods and tools for the analysis and control of such systems.
The applications deal with medecine (chronic and acute myeloid leukaemias), microbial ecol... | CommonCrawl |
Maximum protection of your sensitive data thanks to the security algorithm Rijndael 256-Bit!
Instead of passwords like "toothbrush" or "Rover", which can both be cracked in a few minutes, you now use passwords like "g\/:1bmV5″£$p'}=8>,,/2¬%`CN?\A:y:Cwe-k)mUpHiJu:[email protected]<i" (with a 1-GHz-Pentium-PC, it takes a... | CommonCrawl |
Inspired by @DEEM's Grandpa Mystery puzzles (e.g. here and here). Be sure to check them out!
Now we all know that Grandpa is a genius... but sometimes he says the most absurd things!
Did you know that $6$ is prime?
$6$ is not a prime number, as it is equal to $3\times 2$. Oh wait, are you referring to the gesture your ... | CommonCrawl |
In Button Up, the focus was on working in a systematic way. This follow-up problem will allow children to consolidate their understanding of working systematically, but the main objective is to encourage them to identify and explain patterns, which will lead to generalisations.
Here you can see a response from a school... | CommonCrawl |
Figure 1:Shape collections typically come with inconsistent orientations (a). PCA-based alignment (b), or aligning to an arbitrarily chosen base model (c) is prone to error. The problem with pairwise alignments is attributed to several minima in alignment distances (Epair), arising due to near-symmetries of shapes. We ... | CommonCrawl |
My question has survived. Therefore I try another one. Consider some elementary operations on closed compact 3-manifold $M \subset R^4$. These elementary operations are e.g. $0$-surgery or $1$-surgery such that corresponding disk of dimension $1$ or $2$ is nicely embedded in $R^4$ (not intersecting manifold except the ... | CommonCrawl |
A positive integer is called a "prime-factor prime" when the number of its prime factors is prime. For example, $12$ is a prime-factor prime because the number of prime factors of $12 = 2 \times 2 \times 3$ is $3$, which is prime. On the other hand, $210$ is not a prime-factor prime because the number of prime factors ... | CommonCrawl |
Why does the result of cutting a Möbius strip down the middle lengthwise have two full twists in it? I can account for one full twist--the identification of the top left corner with the bottom right is a half twist; similarly, the top right corner and bottom left identification contributes another half twist. But where... | CommonCrawl |
Schur complement based preconditioners are well-established and studied for classical saddle point problems in $\mathbb The method is applied to two sets of problems: \begin Both methods are robust with respect to mesh size and the later one is also robust with respect to spline degree. By combining these smoothers, a ... | CommonCrawl |
All stores are offering amazing deals for Black Friday. Dan wants to buy a huge TV, a Home Theater system, and a sofa at a store. The regular price for the TV is $\$1100$; the regular price for the Home Theater system is $\$1600$; and the regular price for the sofa is $\$450$. This store is offering a deal where they w... | CommonCrawl |
44 Why is Lebesgue integration taught using positive and negative parts of functions?
13 Formerly good at math, but after 12 years I've lost most of my skills. Now I need them once again. Any advice to grow them back?
11 Why do we care about $L^p$ spaces besides $p = 1$, $p = 2$, and $p = \infty$?
9 Why should one stil... | CommonCrawl |
The RosetteSep™ Human Monocyte Enrichment Cocktail is designed to isolate monocytes from whole blood by negative selection. Unwanted cells are targeted for removal with Tetrameric Antibody Complexes (TAC) recognizing non-monocyte cells and red blood cells (RBCs). When centrifuged over a buoyant density medium such as L... | CommonCrawl |
Vol. 22, no. 2, pp. 357-387, 2018. Regular paper.
Abstract We define the visual complexity of a plane graph drawing to be the number of basic geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g., one needs only one line segment to draw a path with an arbitrar... | CommonCrawl |
Abstract: We consider a scale invariant extension of the standard model (SM) with a combined breaking of conformal and electroweak symmetry in a strongly interacting hidden $SU(n_c)$ gauge sector with $n_f$ vector-like hidden fermions. The (pseudo) Nambu-Goldstone bosons that arise due to dynamical chiral symmetry brea... | CommonCrawl |
Abstract: An upper estimate is obtained for the growth exponent of the set of all uncancellable words equal to $1$ in a group given by a system of defining relations with the Dehn condition. By a theorem of Grigorchuk, this yields a sufficient test for the transience of a random walk on a group given by a system of def... | CommonCrawl |
This paper is concerned with entropy methods for linear drift-diffusion equations with explicitly time-dependent or degenerate coefficients. Our goal is to establish a list of various qualitative properties of the solutions. The motivation for this study comes from a model for molecular motors, the so-called Brownian r... | CommonCrawl |
The shape of the cow figurine is described by an $N \times N$ grid of characters like the one below ($3 \leq N \leq 8$), where '#' characters are part of the figurine and '.' characters are not.
Unfortunately, right before FJ can make his purchase, a bull runs through the shop and breaks not only FJ's figurine, but man... | CommonCrawl |
Z. Kiguradze, T. Jangveladze, M.Aptsiauri. On the Stabilization of Solution as $t\to\infty$ and Convergence of the Corresponding Finite Difference Scheme for One Nonlinear Integro-Differential Equation. Rep. Enl. Sess. Sem. of I.Vekua Inst. Appl. Math. 2008წ. V.22, p.15-19.
Z. Kiguradze. On the Stationary Solution for ... | CommonCrawl |
An internal kink instability has been observed to grow and saturate in the Rotating Wall Machine Experiment. Detailed measurements show that an ideal, line-tied kink mode begins growing when the safety factor drops sufficiently below 1 inside the plasma; the saturated state corresponds to a rotating helical equilibrium... | CommonCrawl |
The $k$-Even Set problem is a parameterized variant of the Minimum Distance Problem of linear codes over $\mathbb F_2$, which can be stated as follows: given a generator matrix $\mathbf A$ and an integer $k$, determine whether the code generated by $\mathbf A$ has distance at most $k$. Here, $k$ is the parameter of the... | CommonCrawl |
Diffie-Hellman key exchange works by agreeing on two publicly shared values: a large prime number $q$ and a primitive root $g$. Alice and Bob each generate a secret key—a large random number—$x_a$ and $x_b$ respectively, and each raise the primitive root to the power of the secret key, modulo the large prime number.
Th... | CommonCrawl |
In addition to numpy, we need a module to handle sparse matrics. scipy.sparse has all of what we need.
How much memory does a dense matrix of double precision numbers of size $10^6 \times 10^6$ occupy?
How much memory does a sparse identity matrix of the same size occupy? | CommonCrawl |
Abstract: The idea of topological quantum computation (TQC) is to store and manipulate quantum information in an intrinsically fault-tolerant manner by utilizing the physics of topologically ordered phases of matter. Currently, one of the most promising platforms for a topological qubit is in terms of Majorana fermion ... | CommonCrawl |
Is it possible to integrate a matrix?
Can this be done or do we think I went wrong somewhere?
Matrices form a vector space. Therefore, you can simply integrate them componentwise.
There is a more sophisticated operation, in case the matrix in question belongs to a Lie algebra: ordered exponentiation. It is to integrati... | CommonCrawl |
Theorem 4.1: $ L^p\cong (L^q)^* $ when $ \frac1p+\frac1q=1,1\le p-<\infty $.
We have a natural injection $ L^q\hookrightarrow (L^p)^*, g\mapsto \left(\ell:f\mapsto \int_X fg\,d\mu\right) $ by Holder's inequality. We want $ ||\ell||=||g||_q $, which is equivalent to showing that equality can be attained (or become arbit... | CommonCrawl |
The structure of atom was first given by the plum pudding model of J.J. Thomson before the experiment of Ernest Rutherford. The plum pudding model explained an atom as a positive charge body which contains small negatively charged particles which are called electrons. He also described that the negative charge in atom ... | CommonCrawl |
In this note, we establish a general result on the existence of global attractors for semigroups $S(t)$ of operators acting on a Banach space $\mathcal X$, where the strong continuity $S(t)\in C(\mathcal X,\mathcal X)$ is replaced by the much weaker requirement that $S(t)$ be a closed map.
Keywords: global attractors, ... | CommonCrawl |
Abstract: We consider a continuum model of active viscoelastic matter, whereby an active nematic liquid-crystal is coupled to a minimal model of polymer dynamics with a viscoelastic relaxation time $\tau_C$. To explore the resulting interplay between active and polymeric dynamics, we first generalise a linear stability... | CommonCrawl |
Abstract: This is an edited version of an unpublished 1979 EFI (U. Chicago) preprint: "The U(N) lattice gauge theory in 2-dimensions can be considered as the statistical mechanics of a Coulomb gas on a circle in a constant electric field. The large N limit of this system is discussed and compared with exact answers for... | CommonCrawl |
This lecture will present a short overview on kinetic MHD. The advantages and drawbacks of kinetic versus fluid modelling will be summarized. Various techniques to implement kinetic effects in the fluid description will be introduced with increasing complexity: bi-fluid effects, gyroaverage fields, Landau closures. Hyb... | CommonCrawl |
The basic example works fairly well because the two systems can be decomposed in two fairly distinct rays of the Hilbert space. But in the case of a quantum field theory, how does one define an observer? Any "realistic" object (especially for interactive QFTs) will likely be a sum of every state of the Fock space of th... | CommonCrawl |
How does one compute all the solutions to this system?
I have the following method in place for computing solutions given the initial condition that $$x_1^2 + x_2^2 = y^2$$ for some integer $y$.
One can make the standard Pythagorean triple reduction given this condition and then repeat the reduction again thus generati... | CommonCrawl |
Bessie likes sightseeing, and today she is looking for scenic valleys.
Of interest is an $N \times N$ grid of cells, where each cell has a height. Every cell outside this square grid can be considered to have infinite height.
A valley is a region of this grid which is contiguous, has no holes, and is such that every ce... | CommonCrawl |
$A,B,C,D$ and $E$ are five persons who are to be seated around a circular table such that $A$ and $B$ must sit together and $C$ and $D$ must never sit together. In how many ways can they be seated?
First we make $(AB)$ and $E$ sit which can be done in $2$ ways since $A$ and $B$ can arrange themselves in $2!=2$ ways.
On... | CommonCrawl |
Files are identified by filenames, which are represented in GAP as strings. Filenames can be created directly by the user or a program, but of course this is operating system dependent.
Filenames for some files can be constructed in a system independent way using the following functions. This is done by first getting a... | CommonCrawl |
Find some upper and lower bounds for the integral given that $f:\mathbb R\mapsto\mathbb R$ is continuous, increasing, and that $f(f(x))=e^x$.
This is an interesting problem that I came up with while investigating half-exponential functions. I last investigated this type of function in this post about fractional iterate... | CommonCrawl |
A conference was held recently at the University of New South Wales to celebrate the ninetieth birthday of well-known local mathematician George Szekeres.
The 'Happy End' problem is a geometrical problem that has permeated George Szekeres' life.
On 26 October 2001 a large block of ice was unveiled inside an ice fridge ... | CommonCrawl |
We extend the Adaptive Aggregation Based Domain Decomposition Multigrid (DD-$\alpha$AMG) algorithm to $N_f=2$ twisted mass fermions. We show numerical results for an $N_f=2$ ensemble of twisted fermions with a clover term simulated at the physical value of the pion mass. We fine-tuned the parameters to achieve a speedu... | CommonCrawl |
We consider the geodesic flow defined by periodic Eaton lens patterns in the plane and discover ergodic ones among those. The ergodicity result on Eaton lenses is derived from a result for quadratic differentials on the plane that are pull backs of quadratic differentials on tori. Ergodicity itself is concluded for $\m... | CommonCrawl |
by Steve Chien, Prahladh Harsha, Alistair Sinclair and Srikanth Srinivasan.
The two conflicting results (i.e., hard vs easy) as summarized in the first part of the 2nd paragraph, speak for themselves. The third result (i.e., dichotomy) identifies a parameter of algebras that governs the complexity of computing the dete... | CommonCrawl |
Abstract: We study representation stability in the sense of Church and Farb of sequences of cohomology groups of complements of arrangements of linear subspaces in real and complex space as $S_n$-modules. We consider arrangement of linear subspaces defined by sets of diagonal equalities $x_i = x_j$ and invariant under ... | CommonCrawl |
Highly irregular : fractal objects tend to be highly irregular and fill the space in which it is embedded.
Self-similarity : an object that displays the same basic pattern at all scales. The simplest fractals are deterministic, and are generated using recursive or iterative procedures.
Fractal Dimension : the character... | CommonCrawl |
Afshari, H., Sajjadmanesh, M. (2015). Fixed point theorems for $\alpha$-contractive mappings. Sahand Communications in Mathematical Analysis, 02(2), 65-72.
Hojjat Afshari; Mojtaba Sajjadmanesh. "Fixed point theorems for $\alpha$-contractive mappings". Sahand Communications in Mathematical Analysis, 02, 2, 2015, 65-72.
... | CommonCrawl |
DrawVib is a powerful graphical interface to visualise and analyze the vibrational spectra together with the atomic displacements of the vibrational normal modes calculated by a quantum chemistry program.
Analyze one particular QM result calculated by Gaussian, Gamess US.
Show both the structure of the molecule (as wel... | CommonCrawl |
You are an elephant working for peanuts. The job that you do is to walk around the packing plant and make sure that peanuts are being packed correctly. Peanuts at your plant are packed by size — small, medium, and large. You walk around and note every peanut that is packed in the wrong type of box, or that is not packe... | CommonCrawl |
Given a $N \times N$ grid of integers, we can choose a combination of $N$ numbers where no two in the same row and no two in the same column. We aim to find a combination of $N$ numbers whose minimum is maximized.
The first line of input consists of an integer $N$, where $1 \leq N \leq 30$. The next $N$ lines each cont... | CommonCrawl |
Also, the set of vectors are independent because splitting $\bf x$ will always produce non-zero vectors, hence $a_1 a_2 ... I suggest you start here if you are interested in how this is done in a computationally efficient and of course provably correct way.
Perhaps the VDI error is just a symptom of a repairable disk c... | CommonCrawl |
Abstract: Neural time-series data contain a wide variety of prototypical signal waveforms (atoms) that are of significant importance in clinical and cognitive research. One of the goals for analyzing such data is hence to extract such 'shift-invariant' atoms. Even though some success has been reported with existing alg... | CommonCrawl |
Fifteen $2 \times 1$ dominoes can be used to tile a $6 \times 5$ rectangle. In tiling the rectangle we might generate what are known as fault-lines. A fault-line is any horizontal or vertical line that divides a tiling, without cutting through any of the domino pieces, so as to form a tiling consisting of two sub-recta... | CommonCrawl |
Abstract: In the abelian sandpile model on a graph $G = (V,E)$ with sink $s$, there are a non-negative number of chips $\sigma(v)$ at each non-sink vertex $v$. If $\sigma(v) \geq \deg(v)$, the vertex can 'topple' passing one chip to each neighbor. Any chips which fall on the sink are lost from the model. A configuratio... | CommonCrawl |
Abstract: We study the problem of decomposing a volume bounded by a smooth surface into a collection of Voronoi cells. Unlike the dual problem of conforming Delaunay meshing, a principled solution to this problem for generic smooth surfaces remained elusive. VoroCrust leverages ideas from $\alpha$-shapes and the power ... | CommonCrawl |
Why is there a deep mysterious relation between string theory and number theory (Langlands program), elliptic curves, modular functions, the exceptional group $E_8$, and the Monster group as in Monstrous Moonshine?
Surely it's not just a coincidence in the Platonic world of mathematics.
Granted this may not be fully an... | CommonCrawl |
How should I approach using two 8s and two 3s to make the number 24?
Use two $8$s, two $3$s, and basic arithmetic operators ($ +, -, \times , \div$, parentheses) to make the number $24$.
I don't know how to start besides just trying to find the correct answer. Is there a way you can make this equation through small ste... | CommonCrawl |
A common practice in Reinforcement Learning is to go from a continuous space towards a discrete space. What does this mean? Take for example a range of numbers between $]-3, 3[$, if we want to represent all the numbers that fit in this range as a state then we would have $\infty$ numbers being represented or $\infty$ s... | CommonCrawl |
Department of Math & Stat, KFUPM, POBox 119, Dhahran 31261, KSA.
B.Sc. Mathematics (1986) King Saud University, Riyadh, Saudi Arabia.
Calculus , Linear Algebra, Introduction to Differential Equations and Linear Algebra, Engineering Mathematics, Introduction to Numerical Computing, Numerical Analysis, Linear and Nonline... | CommonCrawl |
Are there any theories being developed which study structures with many operations and many distributive laws?
"Algebraic structure" will mean a set with some n-ary operations defined on it. This does not include vector spaces for example.
During my study of algebra I have encountered mostly algebraic structures with o... | CommonCrawl |
We study the limiting distribution of the height in a generalized trie in which external nodes are capable to store up to $b$ items (the so called $b$-tries). We assume that such a tree is built from $n$ random strings (items) generated by an unbiased memoryless source. In this paper, we discuss the case when $b$ and $... | CommonCrawl |
How can we be sure that for every $A$, $A^\dagger A$ has a positive square root?
Mostly I'm confused over whether the common convention is to use +$i$ or -$i$ along the anti-diagonal of the middle $2\times 2$ block.
What are theta, phi and lambda in cu1(theta, ctl, tgt) and cu3(theta, phi, lam, ctl, tgt)? What are the ... | CommonCrawl |
This node exports several files from a mask. The images are exported as gray levels, each pixel having a value between 0 and 1. The generated images have the resolution of the mask as its size, and the gray levels (0 is the min value and 1 is the max value) determine the value of each point.
The advantage of exporting ... | CommonCrawl |
Does a diode block current but not voltage?
Does it mean a diode blocks current but not voltage ?
Figure 3 from the 1N4148 datasheet.
Diodes have very small leakage current. At 3 V this will be between 3.5 and 10 nA.
The 2N7000 has a gate−body leakage current, Forward of -10 nA max.
The diode also has about 4 pF capaci... | CommonCrawl |
Formulas are derived which relate strength and asymmetry between magnet top and bottom poles of ferrite and compensator to the strength and temperature compensation of the magnetic field and the skew quadrupole moment and its temperature dependence in dipole or gradient dipole magnets. Applying these formulas will allo... | CommonCrawl |
You are currently browsing the archive for the Deep Belief Networks category.
This is a great intro and I highly recommend it.
If you want more information, check out Ng's lecture notes, Honglak Lee's 2010 NIPS slides, and Hinton's Videos ( ).
Nuit Blanche's article "The Summer of the Deeper Kernels" references the two... | CommonCrawl |
Generalized entropic functionals are in an active area of research. Hence lower and upper bounds on these functionals are of interest. Lower bounds for estimating Rényi conditional $\alpha$-entropy and two kinds of non-extensive conditional $\alpha$-entropy are obtained. These bounds are expressed in terms of error pro... | CommonCrawl |
"Kernel density estimation" is a convolution of what?
I am trying to get a better understanding of kernel density estimation.
Let's take $K()$ to be a rectangular function which gives $1$ if $x$ is between $-0.5$ and $0.5$ and $0$ otherwise, and $h$ (window size) to be 1.
I understand that the density is a convolution ... | CommonCrawl |
Corollaries to Lebesgue's Crit. - Riemann Integrability of Bnd. Funct.
Recall from the Lebesgue's Criterion Part 1 - Riemann Integrability of a Bounded Function and Lebesgue's Criterion Part 2 - Riemann Integrability of a Bounded Function pages that if $f$ is a bounded function on $[a, b]$ and if $D$ is the set of disc... | CommonCrawl |
A model is presented which simulates the behavior of superthermal ions previously reported in the dayside ionosphere of Venus. The model considers effects of E $\times$ B and gradient drifts, charge exchange and collisions with the ambient neutral atmosphere and the possible effects of a wave-particle (anomalous) scatt... | CommonCrawl |
Abstract: The advance in RF energy transfer and harvesting technique over the past decade has enabled wireless energy replenishment for electronic devices, which is deemed as a promising alternative to address the energy bottleneck of conventional battery-powered devices. In this paper, by using a stochastic geometry a... | CommonCrawl |
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