# Mathematics Commons™

## All Articles in Mathematics

15,776 full-text articles. Page 5 of 440.

2018 The Graduate Center, City University of New York

#### The Philosophical Foundations Of Plen: A Protocol-Theoretic Logic Of Epistemic Norms, Ralph E. Jenkins

##### All Dissertations, Theses, and Capstone Projects

In this dissertation, I defend the protocol-theoretic account of epistemic norms. The protocol-theoretic account amounts to three theses: (i) There are norms of epistemic rationality that are procedural; epistemic rationality is at least partially defined by rules that restrict the possible ways in which epistemic actions and processes can be sequenced, combined, or chosen among under varying conditions. (ii) Epistemic rationality is ineliminably defined by procedural norms; procedural restrictions provide an irreducible unifying structure for even apparently non-procedural prescriptions and normative expressions, and they are practically indispensable in our cognitive lives. (iii) These procedural epistemic norms are best analyzed in ...

2018 The Graduate Center, City University of New York

#### Galois Groups Of Differential Equations And Representing Algebraic Sets, Eli Amzallag

##### All Dissertations, Theses, and Capstone Projects

The algebraic framework for capturing properties of solution sets of differential equations was formally introduced by Ritt and Kolchin. As a parallel to the classical Galois groups of polynomial equations, they devised the notion of a differential Galois group for a linear differential equation. Just as solvability of a polynomial equation by radicals is linked to the equation’s Galois group, so too is the ability to express the solution to a linear differential equation in "closed form" linked to the equation’s differential Galois group. It is thus useful even outside of mathematics to be able to compute and ...

Notes On Complexity Of Packing Coloring, 2018 KAIST

#### Notes On Complexity Of Packing Coloring, Minki Kim, Bernard Lidicky, Tomas Masarik, Florian Pfender

##### Mathematics Publications

A packing k-coloring for some integer k of a graph G = (V, E) is a mapping ϕ : V → {1, . . . , k} such that any two vertices u, v of color ϕ(u) = ϕ(v) are in distance at least ϕ(u) + 1. This concept is motivated by frequency assignment problems. The packing chromatic number of G is the smallest k such that there exists a packing k-coloring of G.

Fiala and Golovach showed that determining the packing chromatic number for chordal graphs is NP-complete for diameter exactly 5. While the problem is easy to solve for diameter 2, we show NP-completeness ...

A Symmetry-Based Explanation Of The Main Idea Behind Chubanov's Linear Programming Algorithm, 2018 University of Texas at El Paso

#### A Symmetry-Based Explanation Of The Main Idea Behind Chubanov's Linear Programming Algorithm, Olga Kosheleva, Vladik Kreinovich, Thongchai Dumrongpokaphan

##### Departmental Technical Reports (CS)

Many important real-life optimization problems can be described as optimizing a linear objective function under linear constraints -- i.e., as a linear programming problem. This problem is known to be not easy to solve. Reasonably natural algorithms -- such as iterative constraint satisfaction or simplex method -- often require exponential time. There exist efficient polynomial-time algorithms, but these algorithms are complicated and not very intuitive. Also, in contrast to many practical problems which can be computed faster by using parallel computers, linear programming has been proven to be the most difficult to parallelize. Recently, Sergei Chubanov proposed a modification of the iterative ...

Tutte-Equivalent Matroids, 2018 California State University - San Bernardino

#### Tutte-Equivalent Matroids, Maria Margarita Rocha

##### Electronic Theses, Projects, and Dissertations

We begin by introducing matroids in the context of finite collections of vectors from a vector space over a specified field, where the notion of independence is linear independence. Then we will introduce the concept of a matroid invariant. Specifically, we will look at the Tutte polynomial, which is a well-defined two-variable invariant that can be used to determine differences and similarities between a collection of given matroids. The Tutte polynomial can tell us certain properties of a given matroid (such as the number of bases, independent sets, etc.) without the need to manually solve for them. Although the Tutte ...

Identification Of Biologically Essential Nodes Via Determinative Power In Logical Models Of Cellular Processes, 2018 University of Nebraska at Omaha

#### Identification Of Biologically Essential Nodes Via Determinative Power In Logical Models Of Cellular Processes, Trevor Pentzien, Bhanwar L. Puniya, Tomáš Helikar, Mihaela T. Matache

##### Mathematics Faculty Publications

A variety of biological networks can bemodeled as logical or Boolean networks. However, a simplification of the reality to binary states of the nodes does not ease the difficulty of analyzing the dynamics of large, complex networks, such as signal transduction networks, due to the exponential dependence of the state space on the number of nodes. This paper considers a recently introduced method for finding a fairly small subnetwork, representing a collection of nodes that determine the states of most other nodes with a reasonable level of entropy. The subnetwork contains the most determinative nodes that yield the highest information ...

Genome-Wide Association Study For Variants That Modulate Relationships Between Cerebrospinal Fluid Amyloid-Beta 42, Tau, And P-Tau Levels, 2018 The George Washington University

#### Genome-Wide Association Study For Variants That Modulate Relationships Between Cerebrospinal Fluid Amyloid-Beta 42, Tau, And P-Tau Levels, Taylor J. Maxwell, Chris Corcoran, Jorge L. Del-Aguila, John P. Budde, Yuetiva Deming, Carlos Cruchaga, Alison M. Goate, John S. K. Kauwe, Alzheimer's Disease Neuroimaging Initiative

##### Mathematics and Statistics Faculty Publications

Background: A relationship quantitative trait locus exists when the correlation between multiple traits varies by genotype for that locus. Relationship quantitative trait loci (rQTL) are often involved in gene-by-gene (G×G) interactions or gene-by-environmental interactions, making them a powerful tool for detecting G×G.

Methods: We performed genome-wide association studies to identify rQTL between tau and Aβ42 and ptau and Aβ42 with over 3000 individuals using age, gender, series, APOE ε2, APOE ε4, and two principal components for population structure as covariates. Each significant rQTL was separately screened for interactions with other loci for each trait in the rQTL model ...

2018 University of Colorado at Boulder

#### Attosecond Light Pulses And Attosecond Electron Dynamics Probed Using Angle-Resolved Photoelectron Spectroscopy, Cong Chen

##### Physics Graduate Theses & Dissertations

Recent advances in the generation and control of attosecond light pulses have opened up new opportunities for the real-time observation of sub-femtosecond (1 fs = 10-15 s) electron dynamics in gases and solids. Combining attosecond light pulses with angle-resolved photoelectron spectroscopy (atto-ARPES) provides a powerful new technique to study the influence of material band structure on attosecond electron dynamics in materials. Electron dynamics that are only now accessible include the lifetime of far-above-bandgap excited electronic states, as well as fundamental electron interactions such as scattering and screening. In addition, the same atto-ARPES technique can also be used to measure the ...

Yelp’S Review Filtering Algorithm, 2018 Southern Methodist University

#### Yelp’S Review Filtering Algorithm, Yao Yao, Ivelin Angelov, Jack Rasmus-Vorrath, Mooyoung Lee, Daniel W. Engels

##### SMU Data Science Review

In this paper, we present an analysis of features influencing Yelp's proprietary review filtering algorithm. Classifying or misclassifying reviews as recommended or non-recommended affects average ratings, consumer decisions, and ultimately, business revenue. Our analysis involves systematically sampling and scraping Yelp restaurant reviews. Features are extracted from review metadata and engineered from metrics and scores generated using text classifiers and sentiment analysis. The coefficients of a multivariate logistic regression model were interpreted as quantifications of the relative importance of features in classifying reviews as recommended or non-recommended. The model classified review recommendations with an accuracy of 78%. We found that ...

2018 The University of Western Ontario

#### High Performance Sparse Multivariate Polynomials: Fundamental Data Structures And Algorithms, Alex Brandt

##### Electronic Thesis and Dissertation Repository

Polynomials may be represented sparsely in an effort to conserve memory usage and provide a succinct and natural representation. Moreover, polynomials which are themselves sparse – have very few non-zero terms – will have wasted memory and computation time if represented, and operated on, densely. This waste is exacerbated as the number of variables increases. We provide practical implementations of sparse multivariate data structures focused on data locality and cache complexity. We look to develop high-performance algorithms and implementations of fundamental polynomial operations, using these sparse data structures, such as arithmetic (addition, subtraction, multiplication, and division) and interpolation. We revisit a sparse ...

Identifying Combinatorially Symmetric Hidden Markov Models, 2018 Aberystwyth University

#### Identifying Combinatorially Symmetric Hidden Markov Models, Daniel Burgarth

##### Electronic Journal of Linear Algebra

A sufficient criterion for the unique parameter identification of combinatorially symmetric Hidden Markov Models, based on the structure of their transition matrix, is provided. If the observed states of the chain form a zero forcing set of the graph of the Markov model, then it is uniquely identifiable and an explicit reconstruction method is given.

2018 University of South Carolina Aiken

#### The Largest Eigenvalue And Some Hamiltonian Properties Of Graphs, Rao Li

##### Electronic Journal of Linear Algebra

In this note, sufficient conditions, based on the largest eigenvalue, are presented for some Hamiltonian properties of graphs.

Positive Solutions Of The System Of Operator Equations $A_1x=C_1,Xa_2=C_2, A_3xa^*_3=C_3, A_4xa^*_4=C_4$ In Hilbert $C^*$-Modules, 2018 Ferdowsi University of Mashhad

#### Positive Solutions Of The System Of Operator Equations $A_1x=C_1,Xa_2=C_2, A_3xa^*_3=C_3, A_4xa^*_4=C_4$ In Hilbert $C^*$-Modules, Rasoul Eskandari, Xiaochun Fang, Mohammad Sal Moslehian, Qingxiang Xu

##### Electronic Journal of Linear Algebra

Necessary and sufficient conditions are given for the operator system $A_1X=C_1$, $XA_2=C_2$, $A_3XA^*_3=C_3$, and $A_4XA^*_4=C_4$ to have a common positive solution, where $A_i$'s and $C_i$'s are adjointable operators on Hilbert $C^*$-modules. This corrects a published result by removing some gaps in its proof. Finally, a technical example is given to show that the proposed investigation in the setting of Hilbert $C^*$-modules is different from that of Hilbert spaces.

Proof Of A Conjecture Of Graham And Lovasz Concerning Unimodality Of Coefficients Of The Distance Characteristic Polynomial Of A Tree, 2018 Iowa State University

#### Proof Of A Conjecture Of Graham And Lovasz Concerning Unimodality Of Coefficients Of The Distance Characteristic Polynomial Of A Tree, Ghodratollah Aalipour, Aida Abiad, Zhanar Berikkyzy, Leslie Hogben, Franklin H.J. Kenter, Jephian C.-H. Lin, Michael Tait

##### Electronic Journal of Linear Algebra

The conjecture of Graham and Lov ́asz that the (normalized) coefficients of the distance characteristic polynomial of a tree are unimodal is proved; it is also shown that the (normalized) coefficients are log-concave. Upper and lower bounds on the location of the peak are established.

Extremal Octagonal Chains With Respect To The Spectral Radius, 2018 Anhui University of Science and Technology

#### Extremal Octagonal Chains With Respect To The Spectral Radius, Xianya Geng, Shuchao Li, Wei Wei

##### Electronic Journal of Linear Algebra

Octagonal systems are tree-like graphs comprised of octagons that represent a class of polycyclic conjugated hydrocarbons. In this paper, a roll-attaching operation for the calculation of the characteristic polynomials of octagonal chain graphs is proposed. Based on these characteristic polynomials, the extremal octagonal chains with n octagons having the maximum and minimum spectral radii are identified.

A Math Research Project Inspired By Twin Motherhood, 2018 Valparaiso University

#### A Math Research Project Inspired By Twin Motherhood, Tiffany N. Kolba

##### Tiffany N Kolba

The phenomenon of twins, triplets, quadruplets, and other higher order multiples has fascinated humans for centuries and has even captured the attention of mathematicians who have sought to model the probabilities of multiple births. However, there has not been extensive research into the phenomenon of polyovulation, which is one of the biological mechanisms that produces multiple births. In this paper, I describe how my own experience becoming a mother to twins led me on a quest to better understand the scientific processes going on inside my own body and motivated me to conduct research on polyovulation frequencies. An overview of ...

2018 The University of Western Ontario

#### Topological Recursion And Random Finite Noncommutative Geometries, Shahab Azarfar

##### Electronic Thesis and Dissertation Repository

In this thesis, we investigate a model for quantum gravity on finite noncommutative spaces using the topological recursion method originated from random matrix theory. More precisely, we consider a particular type of finite noncommutative geometries, in the sense of Connes, called spectral triples of type ${(1,0)} \,$, introduced by Barrett. A random spectral triple of type ${(1,0)}$ has a fixed fermion space, and the moduli space of its Dirac operator ${D=\{ H , \cdot \} \, ,}$ ${H \in {\mathcal{H}_N}}$, encoding all the possible geometries over the fermion space, is the space of Hermitian matrices ${\mathcal{H}_N}$. A distribution of ...

R\'Enyi's Quantum Thermodynamical Inequalities, 2018 University of Coimbra

#### R\'Enyi's Quantum Thermodynamical Inequalities, Natalia Bebiano, Joao Da Providencia, J.P. Da Providencia

##### Electronic Journal of Linear Algebra

A theory of thermodynamics has been recently formulated and derived on the basis of R\'enyi entropy and its relative versions. In this framework, the concepts of partition function, internal energy and free energy are defined, and fundamental quantum thermodynamical inequalities are deduced. In the context of R\'enyi's thermodynamics, the variational Helmholtz principle is stated and the condition of equilibrium is analyzed. The %obtained results reduce to the von Neumann ones when the R\'enyi entropic parameter $\alpha$ approaches 1. The main goal of the article is to give simple and self-contained proofs of important known results in ...

2018 University of Texas of the Permian Basin

#### Minimal Graphs With A Specified Code Map Image, Paul Feit

##### Theory and Applications of Graphs

Let $G$ be a graph and $e_1,\cdots ,e_n$ be $n$ distinct vertices. Let $\rho$ be the metric on $G$. The code map on vertices, corresponding to this list, is $c(x)=(\rho (x,e_1),\cdots ,\rho (x,e_n))$. This paper introduces a variation: begin with $V\subseteq\bbz^n$ for some $n$, and consider assignments of edges $E$ such that the identity function on $V$ is a code map for $G=(V,E)$. Refer to such a set $E$ as a {\em code-match.}

An earlier paper classified subsets of $V$ for which at least one code-match exists. We prove ...

Three Examples Of Mondoromy Groups, 2018 alice.wise

#### Three Examples Of Mondoromy Groups, Alice A. Wise

##### Electronic Theses and Dissertations

This thesis illustrates the notion of the Monodromy group of a global analytic function through three examples. One is a relatively simple finite example; the others are more complicated infinite cases, one abelian and one non-abelian, which show connections to other parts of mathematics.