consider:symbolic-regression   8

[1709.06334] On the number of representations of $n=a+b$ with $ab$ a multiple of a polygonal number
In this paper, we study the number of representations of a positive integer n by two positive integers whose product is a multiple of a polygonal number.
number-theory  combinatorics  algebra  nudge-targets  consider:looking-to-see  consider:symbolic-regression 
7 weeks ago by Vaguery
[1709.04068] Persistence in sampled dynamical systems faster
We call a continuous self-map that reveals itself through a discrete set of point-value pairs a sampled dynamical system. Capturing the available information with chain maps on Delaunay complexes, we use persistent homology to quantify the evidence of recurrent behavior, and to recover the eigenspaces of the endomorphism on homology induced by the self-map. The chain maps are constructed using discrete Morse theory for Cech and Delaunay complexes, representing the requisite discrete gradient field implicitly in order to get fast algorithms.
nonlinear-dynamics  inference  statistics  rather-interesting  algorithms  to-understand  nudge-targets  consider:symbolic-regression  consider:performance-measures 
7 weeks ago by Vaguery
[0912.4164] Distance k-Sectors Exist
The bisector of two nonempty sets P and Q in a metric space is the set of all points with equal distance to P and to Q. A distance k-sector of P and Q, where k is an integer, is a (k-1)-tuple (C_1, C_2, ..., C_{k-1}) such that C_i is the bisector of C_{i-1} and C_{i+1} for every i = 1, 2, ..., k-1, where C_0 = P and C_k = Q. This notion, for the case where P and Q are points in Euclidean plane, was introduced by Asano, Matousek, and Tokuyama, motivated by a question of Murata in VLSI design. They established the existence and uniqueness of the distance trisector in this special case. We prove the existence of a distance k-sector for all k and for every two disjoint, nonempty, closed sets P and Q in Euclidean spaces of any (finite) dimension, or more generally, in proper geodesic spaces (uniqueness remains open). The core of the proof is a new notion of k-gradation for P and Q, whose existence (even in an arbitrary metric space) is proved using the Knaster-Tarski fixed point theorem, by a method introduced by Reem and Reich for a slightly different purpose.
computational-geometry  generalization  rather-interesting  to-write-about  nudge-targets  consider:symbolic-regression 
april 2017 by Vaguery
[1203.3373] Dense packings of spheres in cylinders I. Simulations
We study the optimal packing of hard spheres in an infinitely long cylinder, using simulated annealing, and compare our results with the analogous problem of packing disks on the unrolled surface of a cylinder. The densest structures are described and tabulated in detail up to D/d=2.873 (ratio of cylinder and sphere diameters). This extends previous computations into the range of structures which include internal spheres that are not in contact with the cylinder.
phyllotaxis  packing  rather-interesting  parametric-sweep  to-write-about  nudge-targets  consider:symbolic-regression 
march 2017 by Vaguery
[1406.5213] How many ways can you make change: Some easy proofs
Given a dollar, how many ways are there to make change using pennies, nickels, dimes, and quarters? What if you are given a different amount of money? What if you use different coin denominations? This is a well known problem and formulas are known. We present simpler proofs in several cases. We use recurrences to derive formulas if the coin denominations are {1,x,kx,rx}, and we use a simple proof using generating functions to derive a formula for any coin set.
mathematical-recreations  puzzles  number-theory  nudge-targets  consider:looking-to-see  consider:symbolic-regression  consider:novelty-search 
march 2017 by Vaguery
[1606.03225] In a search for a shape maximizing packing fraction for two-dimensional random sequential adsorption
Random sequential adsorption (RSA) of various two dimensional objects is studied in order to find a shape which maximizes the saturated packing fraction. This investigation was begun in our previous paper [Cie\'sla et al., Phys. Chem. Chem. Phys. 17, 24376 (2015)], where the densest packing was studied for smoothed dimers. Here this shape is compared with a smoothed n-mers, spherocylinders and ellipses. It is found that the highest packing fraction out of the studied shapes is 0.58405±0.0001 and is obtained for ellipses having long-to-short axis ratio of 1.85, which is also the largest anisotropy among the investigated shapes.
packing  simulation  looking-to-see  granular-materials  rather-interesting  phase-transitions  nudge-targets  consider:looking-to-see  consider:symbolic-regression  consider:robustness 
december 2016 by Vaguery
[1310.1553] A Workflow-Forecast Approach To The Task Scheduling Problem In Distributed Computing Systems
The aim of this paper is to provide a description of deep-learning-based scheduling approach for academic-purpose high-performance computing systems. The share of academic-purpose distributed computing systems (DCS) reaches 17.4 percents amongst TOP500 supercomputer sites (15.6 percents in performance scale) that makes them a valuable object of research. The core of this approach is to predict the future workflow of the system depending on the previously submitted tasks using deep learning algorithm. Information on predicted tasks is used by the resource management system (RMS) to perform efficient schedule.
deep-learning  operations-research  scheduling  algorithms  prediction  nudge-targets  consider:symbolic-regression 
december 2013 by Vaguery
[1211.4909] Fast Marginalized Block Sparse Bayesian Learning Algorithm
The performance of sparse signal recovery from noise corrupted, underdetermined measurements can be improved if both sparsity and correlation structure of signals are exploited. One typical correlation structure is the intra-block correlation in block sparse signals. To exploit this structure, a framework, called block sparse Bayesian learning (BSBL), has been proposed recently. Algorithms derived from this framework showed superior performance but they are not very fast, which limits their applications. This work derives an efficient algorithm from this framework, using a marginalized likelihood maximization method. Compared to existing BSBL algorithms, it has close recovery performance but is much faster. Therefore, it is more suitable for large scale datasets and applications requiring real-time implementation.
signal-processing  learning-from-data  sparse-stuff  nudge-targets  algorithms  consider:symbolic-regression 
september 2013 by Vaguery

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algebra  algorithms  combinatorics  computational-geometry  consider:looking-to-see  consider:novelty-search  consider:performance-measures  consider:robustness  deep-learning  generalization  granular-materials  inference  learning-from-data  looking-to-see  mathematical-recreations  nonlinear-dynamics  nudge-targets  number-theory  operations-research  packing  parametric-sweep  phase-transitions  phyllotaxis  prediction  puzzles  rather-interesting  scheduling  signal-processing  simulation  sparse-stuff  statistics  to-understand  to-write-about 

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