Search results for "Number"
showing 10 items of 3939 documents
Gray visiting Motzkins
2002
We present the first Gray code for Motzkin words and their generalizations: k colored Motzkin words and Schroder words. The construction of these Gray codes is based on the observation that a k colored Motzkin word is the shuffle of a Dyck word by a k-ary variation on a trajectory which is a combination. In the final part of the paper we give some algorithmic considerations and other possible applications of the techniques introduced here.
Introduction to the GiNaC Framework for Symbolic Computation within the C++ Programming Language
2002
AbstractThe traditional split into a low level language and a high level language in the design of computer algebra systems may become obsolete with the advent of more versatile computer languages. We describe GiNaC, a special-purpose system that deliberately denies the need for such a distinction. It is entirely written in C++and the user can interact with it directly in that language. It was designed to provide efficient handling of multivariate polynomials, algebras and special functions that are needed for loop calculations in theoretical quantum field theory. It also bears some potential to become a more general purpose symbolic package.
Population Games with Vector Payoff and Approachability
2016
This paper studies population games with vector payoffs. It provides a new perspective on approachability based on mean-field game theory. The model involves a Hamilton-Jacobi-Bellman equation which describes the best-response of every player given the population distribution and an advection equation, capturing the macroscopic evolution of average payoffs if every player plays its best response.
Support Vector Machine and Kernel Classification Algorithms
2018
This chapter introduces the basics of support vector machine (SVM) and other kernel classifiers for pattern recognition and detection. It also introduces the main elements and concept underlying the successful binary SVM. The chapter starts by introducing the main elements and concept underlying the successful binary SVM. Next, it introduces more advanced topics in SVM for classification, including large margin filtering (LMF), SSL, active learning, and large‐scale classification using SVMs. The LMF method performs both signal filtering and classification simultaneously by learning the most appropriate filters. SSL with SVMs exploits the information contained in both labeled and unlabeled e…
Learning by the Process of Elimination
2002
AbstractElimination of potential hypotheses is a fundamental component of many learning processes. In order to understand the nature of elimination, herein we study the following model of learning recursive functions from examples. On any target function, the learning machine has to eliminate all, save one, possible hypotheses such that the missing one correctly describes the target function. It turns out that this type of learning by the process of elimination (elm-learning, for short) can be stronger, weaker or of the same power as usual Gold style learning.While for usual learning any r.e. class of recursive functions can be learned in all of its numberings, this is no longer true for el…
Influence Diagnostics for Meta-Analysis of Individual Patient Data Using Generalized Linear Mixed Models
2014
In meta-analysis, generalized linear mixed models (GLMMs) are usually used when heterogeneity is present and individual patient data (IPD) are available, while accepting binary, discrete as well as continuous response variables. In the present paper some measures of influence diagnostics based on log-likelihood are suggested and discussed. A known measure is approximated to get a simpler form, for which the information matrix is no more necessary. The performance of the proposed measure is assessed through a diagnostic analysis on simulated data reproducing a possible meta-analytical context of IPD with influential outliers. The proposed measure is showed to work well and to have a form sim…
Integer Weighted Regression Tsetlin Machines
2020
The Regression Tsetlin Machine (RTM) addresses the lack of interpretability impeding state-of-the-art nonlinear regression models. It does this by using conjunctive clauses in propositional logic to capture the underlying non-linear frequent patterns in the data. These, in turn, are combined into a continuous output through summation, akin to a linear regression function, however, with non-linear components and binary weights. However, the resolution of the RTM output is proportional to the number of clauses employed. This means that computation cost increases with resolution. To address this problem, we here introduce integer weighted RTM clauses. Our integer weighted clause is a compact r…
Theory of Heterogeneous Circuits With Stochastic Memristive Devices
2022
We introduce an approach based on the Chapman-Kolmogorov equation to model heterogeneous stochastic circuits, namely, the circuits combining binary or multi-state stochastic memristive devices and continuum reactive components (capacitors and/or inductors). Such circuits are described in terms of occupation probabilities of memristive states that are functions of reactive variables. As an illustrative example, the series circuit of a binary memristor and capacitor is considered in detail. Some analytical solutions are found. Our work offers a novel analytical/numerical tool for modeling complex stochastic networks, which may find a broad range of applications.
Total Variation Regularization in Digital Breast Tomosynthesis
2013
We developed an iterative algebraic algorithm for the reconstruction of 3D volumes from limited-angle breast projection images. Algebraic reconstruction is accelerated using the graphics processing unit. We varied a total variation (TV)-norm parameter in order to verify the influence of TV regularization on the representation of small structures in the reconstructions. The Barzilai-Borwein algorithm is used to solve the inverse reconstruction problem. The quality of our reconstructions was evaluated with the Quart Mam/Digi Phantom, which features so-called Landolt ring structures to verify perceptibility limits. The evaluation of the reconstructions was done with an automatic LR detection a…
Boolean Networks: A Primer
2021
Abstract Autism Spectrum Disorders (ASDs) stand out as a relevant example where omics-data approaches have been extensively and successfully employed. For instance, an outstanding outcome of the Autism Genome Project relies in the identification of biomarkers and the mapping of biological processes potentially implicated in ASDs’ pathogenesis. Several of these mapped processes are related to molecular and cellular events (e.g., synaptogenesis and synapse function, axon growth and guidance, etc.) that are required for the development of a correct neuronal connectivity. Interestingly, these data are consistent with results of brain imaging studies of some patients. Despite these remarkable pr…