**consider:symbolic-regression**11

[1510.06890] Generalized Transformation Design: metrics, speeds, and diffusion

january 2018 by Vaguery

We show that a unified and maximally generalized approach to spatial transformation design is possible, one that encompasses all second order waves, rays, and diffusion processes in anisotropic media. Until the final step, it is unnecessary to specify the physical process for which a specific transformation design is to be implemented. The principal approximation is the neglect of wave impedance, an attribute that plays no role in ray propagation, and is therefore irrelevant for pure ray devices; another constraint is that for waves the spatial variation in material parameters needs to be sufficiently small compared with the wavelength. The key link between our general formulation and a specific implementation is how the spatial metric relates to the speed of disturbance in a given medium, whether it is electromagnetic, acoustic, or diffusive. Notably, we show that our generalised ray theory, in allowing for anisotropic indexes (speeds), generates the same predictions as does a wave theory, and the results are closely related to those for diffusion processes.

engineering-design
rather-interesting
indistinguishable-from-magic
performance-measure
representation
nudge-targets
consider:looking-to-see
consider:symbolic-regression
to-write-about
january 2018 by Vaguery

[1703.10651] Reliable Decision Support using Counterfactual Models

january 2018 by Vaguery

Making a good decision involves considering the likely outcomes under each possible action. For example, would drug A or drug B lead to a better outcome for this patient? Ideally, we answer these questions using an experiment, but this is not always possible (e.g., it may be unethical). As an alternative, we can use non-experimental data to learn models that make counterfactual predictions of what we would observe had we run an experiment. To learn such models for decision-making problems, we propose the use of counterfactual objectives in lieu of classical supervised learning objectives. We implement this idea in a challenging and frequently occurring context, and propose the counterfactual GP (CGP), a counterfactual model of continuous-time trajectories (time series) under sequences of actions taken in continuous-time. We develop our model within the potential outcomes framework of Neyman and Rubin. The counterfactual GP is trained using a joint maximum likelihood objective that adjusts for dependencies between observed actions and outcomes in the training data. We report two sets of experimental results. First, we show that the CGP's predictions are reliable; they are stable to changes in certain characteristics of the training data that are not relevant to the decision-making problem. Predictive models trained using classical supervised learning objectives, however, are not stable to such perturbations. In the second experiment, we use data from a real intensive care unit (ICU) and qualitatively demonstrate how the CGP's ability to answer "What if?" questions offers medical decision-makers a powerful new tool for planning treatment.

machine-learning
models-and-modes
rather-interesting
to-write-about
consider:symbolic-regression
january 2018 by Vaguery

[1712.00714] Spatial PixelCNN: Generating Images from Patches

december 2017 by Vaguery

In this paper we propose Spatial PixelCNN, a conditional autoregressive model that generates images from small patches. By conditioning on a grid of pixel coordinates and global features extracted from a Variational Autoencoder (VAE), we are able to train on patches of images, and reproduce the full-sized image. We show that it not only allows for generating high quality samples at the same resolution as the underlying dataset, but is also capable of upscaling images to arbitrary resolutions (tested at resolutions up to 50×) on the MNIST dataset. Compared to a PixelCNN++ baseline, Spatial PixelCNN quantitatively and qualitatively achieves similar performance on the MNIST dataset.

deep-learning
neural-networks
generative-art
generative-models
to-write-about
to-do
nudge-targets
consider:symbolic-regression
december 2017 by Vaguery

[1709.06334] On the number of representations of $n=a+b$ with $ab$ a multiple of a polygonal number

september 2017 by Vaguery

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
september 2017 by Vaguery

[1709.04068] Persistence in sampled dynamical systems faster

september 2017 by Vaguery

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
september 2017 by Vaguery

[0912.4164] Distance k-Sectors Exist

april 2017 by Vaguery

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

march 2017 by Vaguery

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

march 2017 by Vaguery

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

december 2016 by Vaguery

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

december 2013 by Vaguery

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

september 2013 by Vaguery

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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