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Some Properties of Thinness and Fine Topology with Relative CapacityFeb 14 2019In this paper, we introduce a thinness in sense to a type of relative capacity for weighted variable exponent Sobolev space. Moreover, we reveal some properties of this thinness and consider the relationship with finely open and finely closed sets. We ... More

Quantum computing, Seifert surfaces and singular fibersFeb 13 2019The fundamental group $\pi_1(L)$ of a knot or link $L$ may be used to generate magic states appropriate for performing universal quantum computation and simultaneously for retrieving complete information about the processed quantum states. In this paper, ... More

Constructing Selections Stepwise Over Cones of Simplicial ComplexesFeb 08 2019It is given a simplified proof of a natural generalisation of Uspenskij's selection characterisation of paracompact $C$-spaces. The method is also applied to give a simplified proof of a similar characterisation of paracompact finite $C$-space. Another ... More

A new characterization of partial metric completenessFeb 08 2019In this article, we present a new characterization of the completeness of a partial metric space--which we call \textit{orbital characterization}-- using fixed point results.

Partial quasi-metric completeness via Kannan-type fixed pointsFeb 08 2019In this short note, we obtain partial quasi-metric versions of Kannan's fixed point theorem for self-mappings. Moreover, we use these fixed points results to characterize a certain type of completeness in partial quasi-metric spaces. We have reported ... More

Chatterjea type fixed point in Partial $b$-metric spacesFeb 08 2019In this paper, we give and prove two Chatterjea type fixed point theorems on partial $b$-metric space. We propose an extension to the Banach contraction principle on partial $b$-metric space which was already presented by Shukla and also study some related ... More

An approach to harmonic analysis on non-locally compact groups I: level structures over locally compact groupsFeb 08 2019We define a class of spaces on which one may generalise the notion of compactness following motivating examples from higher-dimensional number theory. We establish analogues of several well-known topological results (such as Tychonoff's Theorem) for such ... More

Two-Step market clearing for local energy trading in feeder-based marketsFeb 07 2019Recent innovations in Information and Communication Technologies (ICT) provide new opportunities and challenges for integration of distributed energy resources (DERs) into the energy supply system as active market players. By increasing integration of ... More

Deficient topological measures on locally compact spacesFeb 07 2019Topological measures and quasi-linear functionals generalize measures and linear functionals. We define and study deficient topological measures on locally compact spaces. A deficient topological measure on a locally compact space is a set function on ... More

Coarse structures on groups defined by $T$-sequencesFeb 06 2019A sequence $(a_{n}) $ in an Abelian group is called a $T$-sequence if there exists a Hausdorff group topology on $G$ in which $(a_{n}) $ converges to $0$. For a $T$-sequence $(a_{n}) $, $\tau_{(a_{n}) } $ denotes the strongest group topology on $G$ in ... More

Solid-set functions and topological measures on locally compact spacesFeb 05 2019A topological measure on a locally compact space is a set function on open and closed subsets which is finitely additive on the collection of open and compact sets, inner regular on open sets, and outer regular on closed sets. Almost all works devoted ... More

Topological Extensions of Rough Approximation SpacesFeb 05 2019In this work, we Extend Pawlak approximation spaces by topological spaces. Also, Rough Membership, equality and inclusion relations are extended using topological near open sets. In addition, new extended measures of accuracy and quality of approximations ... More

Hyperballeans of groupsFeb 04 2019In this paper we define some ballean structure on the power set of a group and, in particular, we study the subballean with support the lattice of all its subgroups. If $G$ is a group, we denote by $L(G)$ the family of all subgroups of $G$. For two groups ... More

Balleans, hyperballeans and idealsFeb 04 2019A ballean $\mathcal{B}$ (or a coarse structure) on a set $X$ is a family of subsets of $X$ called balls (or entourages of the diagonal in $X\times X$) defined in such a way that $\mathcal{B}$ can be considered as the asymptotic counterpart of a uniform ... More

SSGP topologies on free groups of infinite rankFeb 03 2019We prove that every free group G with infinitely many generators admits a Hausdorff group topology T with the following property: for every T-open neighbourhood U of the identity of G, each element g in G can be represented as a product g=g_1 g_2 ... ... More

Some Enumeration Problems in the Duplication-Loss Model of Genome RearrangementFeb 01 2019Tandem-duplication-random-loss (TDRL) is an important genome rearrangement operation studied in evolutionary biology. This paper investigates some of the formal properties of TDRL operations on the symmetric group (the space of permutations over an $ ... More

Adaptive Monte Carlo Multiple Testing via Multi-Armed BanditsFeb 01 2019Monte Carlo (MC) permutation testing is considered the gold standard for statistical hypothesis testing, especially when standard parametric assumptions are not clear or likely to fail. However, in modern data science settings where a large number of ... More

Fixed point sets in digital topology, 1Jan 30 2019In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results that often ... More

On the space of ends of infinitely generated groupsJan 30 2019We study the space of ends of groups. For a finitely generated group, this is a Cantor space as soon as it is infinite. In contrast, we show that for infinitely generated countable groups, it exhibits several behaviors. For instance, we show that for ... More

The cometrizability of generalized metric spacesJan 30 2019Feb 05 2019A topological space $X$ is cometrizable if it admits a weaker metrizable topology such that each point $x\in X$ has a (not necessarily open) neighborhood base consisting of metrically closed sets. We prove that the class of cometrizable spaces includes ... More

Banalytic spaces and characterization of Polish groupsJan 30 2019A topological space is defined to be banalytic (resp. analytic) if it is the image of a Polish space under a Borel (resp. continuous) map. A regular topological space is analytic if and only if it is banalytic and cosmic. Each (regular) banalytic space ... More

On the spread of topological groups containing subsets of the Sorgenfrey lineJan 30 2019We prove that any topological group $G$ containing a subspace $X$ of the Sorgenfrey line has spread $s(G)\ge s(X\times X)$. Under OCA, each topological group containing an uncountable subspace of the Sorgenfrey line has uncountable spread. This implies ... More

A Diagrammatic Approach for Determining the Braid Index of Alternating LinksJan 28 2019It is well known that the braid index of a link equals the minimum number of Seifert circles among all link diagrams representing it. For a link with a reduced alternating diagram $D$, $s(D)$, the number of Seifert circles in $D$, equals the braid index ... More

Topological games of bounded selectionsJan 27 2019We present a new variation of the classical selection principles $\mathsf{S}_\mathrm{k}(\mathcal A, \mathcal B)$ ($k\in\mathbb N$) and $\mathsf{S}_\mathrm{fin}(\mathcal A, \mathcal B)$ that lies between these two properties. Just like with the classical ... More

On the class of weakly almost contra-T*-continuous functionsJan 26 2019The aim of this paper is to introduce and investigate a new class of functions called weakly almost contra-$T^*$-continuity which is defined as a function from an operator topological space $(X, \tau, T)$ into an arbitrary topological space $(Y, \delta)$. ... More

A consistency result on long cardinal sequencesJan 25 2019For any regular cardinal $\kappa$ and ordinal $\eta<\kappa^{++}$ it is consistent that $2^{\kappa}$ is as large as you wish, and every function $f:\eta \to [\kappa,2^{\kappa}]\cap Card$ with $f(\alpha)=\kappa$ for $cf(\alpha)<\kappa$ is the cardinal sequence ... More

On densely complete metric spaces and extensions of uniformly continuous functions in $\mathbf{ZF}$Jan 25 2019A metric space $\mathbf{X}$ is called densely complete if there exists a dense set $D$ in $\mathbf{X}$ such that every Cauchy sequence of points of $D $ converges in $\mathbf{X}$. One of the main aims of this work is to prove that the countable axiom ... More

Optimal Reduction of Public Debt under Partial Observation of the Economic GrowthJan 24 2019Jan 25 2019We consider a government that aims at reducing the debt-to-gross domestic product (GDP) ratio of a country. The government observes the level of the debt-to-GDP ratio and an indicator of the state of the economy, but does not directly observe the development ... More

Counting surface branched coversJan 24 2019To a branched cover f between orientable surfaces one can associate a certain branch datum D(f), that encodes the combinatorics of the cover. This D(f) satisfies a compatibility condition called the Riemann-Hurwitz relation. The old but still partly unsolved ... More

The spread of a financial virus through Europe and beyondJan 22 2019We analyse the importance of international relations between countries on the financial stability. The contagion effect in the network is tested by implementing an epidemiological model, comprising a number of European countries and using bilateral data ... More

A generalization of a Baire theorem concerning barely continuous functionsJan 21 2019We prove that if $X$ is a paracompact space, $Y$ is a metric space and $f:X\to Y$ is a functionally fragmented map, then (i) $f$ is $\sigma$-discrete and functionally $F_\sigma$-measurable; (ii) $f$ is a Baire-one function, if $Y$ is weak adhesive and ... More

Homogenisation and the Weak Operator TopologyJan 20 2019This article surveys results that relate homogenisation problems for partial differential equations and convergence in the weak operator topology of a suitable choice of linear operators. More precisely, well-known notions like $G$-convergence, $H$-convergence ... More

On the cardinality of $π(δ)$Jan 18 2019We prove that the cardinality of transitive quasi-uniformities in a quasi-proximity class is at least $2^{2^{\aleph_0}}$ if there exist at least two transitive quasi-uniformities in the class. The transitive elements of $\pi(\delta)$ are characterized ... More

Definable V-topologies, Henselianity and NIPJan 17 2019We show that if $(K,v_1,v_2)$ is a bi-valued NIP field with $v_1$ henselian (resp. t-henselian) then $v_1$ and $v_2$ are comparable (resp. dependent). As a consequence Shelah's conjecture for NIP fields implies the henselianity conjecture for NIP fields. ... More

Quotient topology on the set of commensurability classes of hyperbolic 3-manifoldsJan 17 2019We investigate relation between Dehn fillings and commensurability of hyperbolic 3-manifolds. The set consisting of the commensurability classes of hyperbolic 3-manifolds admits the quotient topology induced by the geometric topology. We show that this ... More

Preservation of uniform continuity under pointwise productJan 16 2019Let $X$ be a uniform space and $U(X)$ the linear space of real-valued uniformly continuous functions on $X$. Our main objective is to give a number of properties characterizing the fact that $U(X)$ is stable under pointwise product in case $X$ is a metric ... More

On weakening tightness to weak tightnessJan 15 2019The weak tightness $wt(X)$ of a space $X$ was introduced in [11] with the property $wt(X)\leq t(X)$. We investigate several well-known results concerning $t(X)$ and consider whether they extend to the weak tightness setting. First we give an example of ... More

Machine learning and the Continuum HypothesisJan 15 2019Jan 30 2019We comment on a recent paper that connects certain forms of machine learning to Set Theory. We point out that part of the set-theoretic machinery is related to a result of Kuratowski about decompositions of finite powers of sets and we show that there ... More

Extensions of the Stone Duality to the category of zero-dimensional Hausdorff spacesJan 14 2019Extending the Stone Duality Theorem, we describe two categories which are dually equivalent to the category {\bf ZHaus} of zero-dimensional Hausdorff spaces and continuous maps. We find as well two categories which are dually equivalent to the category ... More

Efficient Minimum Distance Estimation of Pareto Exponent from Top Income SharesJan 08 2019We propose an efficient estimation method for the income Pareto exponent when only certain top income shares are observable. Our estimator is based on the asymptotic theory of weighted sums of order statistics and the efficient minimum distance estimator. ... More

Invest or Exit? Optimal Decisions in the Face of a Declining Profit StreamJan 06 2019Even in the face of deteriorating and highly volatile demand, firms often invest in, rather than discard, aging technologies. In order to study this phenomenon, we model the firm's profit stream as a Brownian motion with negative drift. At each point ... More

Some Baire category properties of topological groupsJan 05 2019Jan 30 2019We present several known and new results on the Baire category properties in topological groups. In particular, we prove that a Baire topological group $X$ is metrizable if and only if $X$ is point-cosmic if and only if $X$ is a $\sigma$-space. A topological ... More

On the rotation sets of generic homeomorphisms on the torus $\mathbb T^d$Jan 02 2019We study the rotation sets for homeomorphisms homotopic to the identity on the torus $\mathbb T^d$, $d\ge 2$. In the conservative setting, we prove that there exists a Baire residual subset of the set $\text{Homeo}_{0, \lambda}(\mathbb T^2)$ of conservative ... More

Geometrical representation of real and reactive powers of load demand by orbit diagrams in the Mandelbrot setDec 24 2018This paper presents the geometrical representation of the load demand by using orbits diagrams in the Mandelbrot set, to identify changing behaviors during a day period of the real and reactive powers. To perform this, different power combinations were ... More

Fractal representation of the power daily demand based on topological properties of Julia setsDec 24 2018In a power system, the load demand considers two components such as the real power (P) because of resistive elements, and the reactive power (Q) because inductive or capacitive elements. This paper presents a graphical representation of the electric power ... More

Topological properties of fractal Julia sets related to the signs and magnitudes of the real and reactive powersDec 23 2018In AC electrical systems, the power depends on the real power (P) due to resistive elements and the reactive power (Q) due to the inductive and capacitive elements, which are commonly studied by using phasor and scalar methods. Thus, this paper focuses ... More

A complete classification of hereditarily equivalent plane continuaDec 20 2018A continuum is hereditarily equivalent if it is homeomorphic to each of its non-degenerate sub-continua. We show in this paper that the arc and the pseudo-arc are the only non-degenerate hereditarily equivalent plane continua.

Non-removability of Sierpinski spacesDec 14 2018We prove that all Sierpi\'nski spaces in ${\mathbb{S}}^n$, $n\geq 2$, are non-removable for (quasi)conformal maps, generalizing the result of the first named author arXiv:1809.05605. More precisely, we show that for any Sierpi\'nski space $X\subset \mathbb{S}^n$ ... More

On the Component Factor Group G/G_0 of a Pro-Lie Group GDec 12 2018A pro-Lie group $G$ is a topological group such that $G$ is isomorphic to the projective limit of all quotient groups $G/N$ (modulo closed normal subgroups $N$) such that $G/N$ is a finite dimensional real Lie group. A topological group is almost connected ... More

Effects of forecast errors on optimal utilisation in aggregate production planning with stochastic customer demandDec 03 2018The hierarchical structure of production planning has the advantage of assigning different decision variables to their respective time horizons and therefore ensures their manageability. However, the restrictive structure of this top-down approach implying ... More

Knotting statistics for polygons in lattice tubesNov 30 2018We study several related models of self-avoiding polygons in a tubular subgraph of the simple cubic lattice, with a particular interest in the asymptotics of the knotting statistics. Polygons in a tube can be characterised by a finite transfer matrix, ... More

A Game of MartingalesNov 28 2018Dec 04 2018We consider a two player dynamic game played over $T \leq \infty$ periods. In each period each player chooses any probability distribution with support on $[0,1]$ with a given mean, where the mean is the realized value of the draw from the previous period. ... More

The $n$-dimensional Peano CurveNov 27 2018One of the most startling mathematical discoveries of the nineteen century was the existence of plane-filling curves. As is well known, the first example of such a curve was given by the Italian mathematician Giuseppe Peano in 1890. Subsequently, other ... More

Continuous projections onto ideal convergent sequencesNov 20 2018Let $\mathcal{I}\subseteq\mathcal{P}(\omega)$ be a meager ideal. Then there are no continuous projections from $\ell_\infty$ onto the set of bounded sequences which are $\mathcal{I}$-convergent to $0$. In particular, it follows that the set of bounded ... More

On the structure of abelian profinite groupsNov 20 2018A subgroup $G$ of a product $\prod\limits_{i\in\mathbb{N}}G_i$ is \emph{rectangular} if there are subgroups $H_i$ of $G_i$ such that $G=\prod\limits_{i\in\mathbb{N}}H_i$. We say that $G$ is \emph{weakly rectangular} if there are finite subsets $F_i\subseteq ... More

Weak partial $b$-metric space and Nadler's theoremNov 18 2018We study the notions of weak partial $b$-metric space and weak partial Hausdorff $b$-metric space. Moreover, we intend to generalize Nadler's theorem in weak partial $b$-metric space by using weak partial Hausdorff $b$-metric spaces. A non-trivial example ... More

Weak and weak* $I^K$-convergence in normed spacesNov 16 2018The main object of this paper is to study the concept of weak $I^K$-convergence, a generalization of weak $I^*$-convergence of sequences in a normed space, introducing the idea of weak* $I^K$-convergence of sequences of functionals where $I,K$ are two ... More

Baire categorical aspects of first passage percolation IINov 11 2018In this paper we continue our earlier work about topological first passage percolation and answer certain questions asked in our previous paper. Notably, we prove that apart from trivialities, in the generic configuration there exists exactly one geodesic ... More

Counting the Number of Quasiplatonic Topological Actions of the Cyclic Group on SurfacesNov 09 2018Define $QC(n)$ to be the number of quasiplatonic topological actions of the cyclic group $C_n$ on surfaces of genus at least two. We use formulas of Benim and Wootton to give an explicit formula for $QC(n)$. In addition, we relate the number of quasiplatonic ... More

All Parovichenko spaces are soft-ParovichenkoNov 09 2018Nov 14 2018It is shown that, assuming the Continuum Hypothesis, compact Hausdorff space of weight at most $\mathfrak{c}$ is a remainder in a soft compactification of $\mathbb{N}$. We also exhibit an example of a compact space of weight~$\aleph_1$ --- hence a remainder ... More

Two parameters bt-algebra and invariants for links and tied linksNov 08 2018Nov 20 2018We introduce a two-parameters bt-algebra which, by specialization, becomes the one-parameter bt-algebra, introduced by the authors, as well as another one-parameter presentation of it; the invariant for links and tied links, associated to this two-parameter ... More

The Affordable Care Act and the IRS Iterative Fixed Point ProcedureOct 31 2018We model the quantities appearing in Internal Revenue Service (IRS) tax guidance for calculating the health insurance premium tax credit created by the Patient Protection and Affordable Care Act, also called Obamacare. We ask the question of whether there ... More

Functional boundedness of balleansOct 29 2018Jan 21 2019We pose some open problems related to boundedness of real-valued functions on balleans and coarse spaces. Also we prove that the Bergman property of groups is a coarse invariant. A special attention is payed to balleans on groups.

Optimal electricity demand response contracting with responsiveness incentivesOct 22 2018Nov 07 2018Despite the success of demand response programs in retail electricity markets in reducing average consumption, the literature shows failure to reduce the variance of consumers' responses. This paper aims at designing demand response contracts which allow ... More

Modelling information flow in stochastic optimal control: How Meyer-$σ$-fields settle the clash between exogenous and endogenous jumpsOct 19 2018In stochastic control one seeks to find an intervention policy that optimally controls a stochastic system. Delicate issues arise when the considered system can jump due to both exogenous shocks and endogenous controls. Here one has to specify what the ... More

The normality and bounded growth of balleansOct 18 2018Nov 06 2018By a ballean we understand a set $X$ endowed with a family of entourages which is a base of some coarse structure on $X$. Given two unbounded ballean $X,Y$ with normal product $X\times Y$, we prove that the balleans $X,Y$ have bounded growth and the bornology ... More

Dynkin games with incomplete and asymmetric informationOct 17 2018Nov 03 2018We study Nash equilibria for a two-player zero-sum optimal stopping game with incomplete and asymmetric information. In our set-up, the drift of the underlying diffusion process is unknown to one player (incomplete information feature), but known to the ... More

Countably compact group topologies on non-torsion abelian groups of size continuum with non-trivial convergent sequencesOct 11 2018Under $\mathfrak{p} = \mathfrak{c}$, we answer Question 24 of \cite{dikranjan&shakhmatov3} for cardinality ${\mathfrak c}$ , by showing that if a non-torsion Abelian group of size continuum admits a countably compact Hausdorff group topology, then it ... More

Densely k-separable compacta are densely separableOct 11 2018A space has $\sigma$-compact tightness if the closures of $\sigma$-compact subsets determines the topology. We consider a dense set variant that we call densely k-separable. We consider the question of whether every densely k-separable space is separable. ... More

A General Sensitivity Analysis Approach for Demand Response OptimizationsOct 07 2018It is well-known that demand response can improve the system efficiency as well as lower consumers' (prosumers') electricity bills. However, it is not clear how we can either qualitatively identify the prosumer with the most impact potential or quantitatively ... More

Topological Connectedness and Behavioral Assumptions on Preferences: A Two-Way RelationshipOct 03 2018Oct 25 2018This paper offers a comprehensive treatment of the question as to whether a binary relation can be consistent (transitive) without being decisive (complete), or decisive without being consistent, or simultaneously inconsistent or indecisive, in the presence ... More

Hindman's finite sums theorem and its application to topologizations of algebrasOct 03 2018The first part of the paper is a brief overview of Hindman's finite sums theorem, its prehistory and a few of its further generalizations, and a modern technique used in proving these and similar results, which is based on idempotent ultrafilters in ultrafilter ... More

On the length of arcs in labyrinth fractalsOct 03 2018Labyrinth fractals are self-similar dendrites in the unit square that are defined with the help of a labyrinth set or a labyrinth pattern. In the case when the fractal is generated by a horizontally and vertically blocked pattern, the arc between any ... More

Topologies on sets of polynomial knots and the homotopy types of the respective spacesSep 25 2018A polynomial knot in $\mathbb{R}^n$ is a smooth embedding $\phi:\mathbb{R}\hookrightarrow\mathbb{R}^n$ whose component functions are polynomials with real coefficients. Let $\mathcal{P}^n$ be the set of all polynomial knots in $\mathbb{R}^n$, and let ... More

A big data based method for pass rates optimization in mathematics university lower division coursesSep 18 2018In this paper an algorithm designed for large databases is introduced for the enhancement of pass rates in mathematical university lower division courses with several sections. Using integer programming techniques, the algorithm finds the optimal pairing ... More

Generalized Fuzzy metric Spaces with an application to Colour image filteringSep 17 2018Impulsive noise is a problem encountered during the acquisition and transmission of digital images. Fuzzy metrics dealing nicely with the nonlinear nature of digital images are used in vector median-based filters for noise reduction in colour and multichannel ... More

Non-removability of Sierpinski carpetsSep 14 2018We prove that all Sierpi\'nski carpets in the plane are non-removable for (quasi)conformal maps. More precisely, we show that for any two Sierpi\'nski carpets $S,S'\subset \widehat{\mathbb{C}}$ there exists a homeomorphism $f\colon \widehat{\mathbb{C}}\to ... More

How to model fake newsSep 04 2018Oct 26 2018Over the past three years it has become evident that fake news is a danger to democracy. However, until now there has been no clear understanding of how to define fake news, much less how to model it. This paper addresses both these issues. A definition ... More

The continuity of Darboux injections between manifoldsSep 02 2018Sep 12 2018We prove that an injective map $f:X\to Y$ between connected metrizable spaces $X,Y$ is continuous if for every connected subset $C\subset X$ the image $f(C)$ is connected and one of the following conditions is satisfied: (1) $Y$ is a 1-manifold and $X$ ... More

Switching Cost Models as Hypothesis TestsAug 29 2018We relate models based on costs of switching beliefs (e.g. due to inattention) to hypothesis tests. Specifically, for an inference problem with a penalty for mistakes and for switching the inferred value, a band of inaction is optimal. We show this band ... More

Isometry group of Borel randomizationsAug 28 2018We study global dynamical properties of the isometry group of the Borel randomization of a separable complete structure. In particular, we show that if properties such as the Rohklin property, topometric generics, extreme amenability hold for the isometry ... More

Minimal covers of hypergraphsAug 24 2018Aug 27 2018For a hypergraph $H=(V,\mathcal E)$, a subfamily $\mathcal C\subseteq \mathcal E$ is called a cover of the hypergraph if $\bigcup\mathcal C=\bigcup\mathcal E$. A cover $\mathcal C$ is called minimal if each cover $\mathcal D\subseteq\mathcal C$ of the ... More

On a conjecture for $\aleph_0$-bounded groupsAug 23 2018We show that it is consistent, relative to the consistency of a strongly inaccessible cardinal, that an instance of the generalized Borel Conjecture introduced in [8] holds while the classical Borel Conjecture fails.

Meager Sets, Games and Singular CardinalsAug 21 2018We show that a statement concerning the existence of winning strategies of limited memory in an infinite two-person topological game is equivalent to a weak version of the Singular Cardinals Hypothesis.

The Bohr compactification of an abelian group as a quotient of its Stone-Čech compactificationAug 14 2018Aug 15 2018We will prove that, for any abelian group $G$, the canonical (surjective and continuous) mapping $\boldsymbol{\beta}G \to {\frak b}G$ from the Stone-\v{C}ech compactification $\boldsymbol{\beta}G$ of $G$ to its Bohr compactfication ${\frak b}G$ is a homomorphism ... More

Fast computation of the principal components of genotype matrices in JuliaAug 09 2018Finding the largest few principal components of a matrix of genetic data is a common task in genome-wide association studies (GWASs), both for dimensionality reduction and for identifying unwanted factors of variation. We describe a simple random matrix ... More

Network-based Referral Mechanism in a Crowdfunding-based Marketing PatternAug 09 2018Crowdfunding is gradually becoming a modern marketing pattern. By noting that the success of crowdfunding depends on network externalities, our research aims to utilize them to provide an applicable referral mechanism in a crowdfunding-based marketing ... More

Large irredundant sets in operator algebrasAug 04 2018Sep 02 2018A subset $\mathcal X$ of a C*-algebra $\mathcal A$ is called irredundant if no $A\in \mathcal X$ belongs to the C*-subalgebra of $\mathcal A$ generated by $\mathcal X\setminus \{A\}$. Separable C*-algebras cannot have uncountable irredundant sets and ... More

Topological properties of inductive limits of closed towers of mertrizable groupsAug 04 2018Let $\{ G_n\}_{n\in\w}$ be a closed tower of metrizable groups. Under a mild condition called $(GC)$ and which is strictly weaker than $PTA$ condition introduced in [22], we show that: (1) the inductive limit $G=\mbox{g-}\underrightarrow{\lim}\, G_n$ ... More

When the Zariski space is a Noetherian spaceJul 23 2018Jul 24 2018We characterize when the Zariski space $\mathrm{Zar}(K|D)$ (where $D$ is an integral domain, $K$ is a field containing $D$ and $D$ is integrally closed in $K$) and the set $\mathrm{Zar_{min}}(L|D)$ of its minimal elements are Noetherian spaces.

Characterization of a metrizable space $X$ such that $F_4(X)$ is Fréchet-UrysohnJul 06 2018Let $F(X)$ be the free topological group on a Tychonoff space $X$. For all natural numbers $n$ we denote by $F_n(X)$ the subset of $F(X)$ consisting of all words of reduced length $\leq n$. In \cite{Y3}, the author found equivalent conditions on a metrizable ... More

$n$-arc and $n$-circle connected graph-like spacesJul 05 2018A space $X$ is $n$-arc connected (respectively, $n$-circle connected) if for any choice of at most $n$ points there is an arc (respectively, a circle) in $X$ containing the specified points. We study $n$-arc connectedness and $n$-circle connectedness ... More

Products of Menger spaces in the Miller modelJun 27 2018Sep 21 2018We prove that in the Miller model the Menger property is preserved by finite products of metrizable spaces. This answers several open questions and gives another instance of the interplay between classical forcing posets with fusion and combinatorial ... More

Topological properties of the set of functions generated by neural networks of fixed sizeJun 22 2018Nov 08 2018We analyze the topological properties of the set of functions that can be implemented by neural networks of a fixed size. Surprisingly, this set has many undesirable properties: It is highly non-convex, except possibly for a few exotic activation functions. ... More

Complete topologized posets and semilatticesJun 07 2018In this paper we discuss the notion of completeness of topologized posets and survey some recent results on closedness properties of complete topologized semilattices.

Tangles and the Stone-Cech compactification of infinite graphsJun 01 2018We show that the space of $\aleph_0$-tangles of an arbitrary infinite connected graph $G$ is homeomorphic to the quotient of the Stone-\v{C}ech remainder $G^\ast=\beta G\setminus G$ of $G$ where each component is collapsed to a single point. Answering ... More

Hausdorff compactifications in ZFMay 24 2018For a compactification $\alpha X$ of a Tychonoff space $X$, the algebra of all functions $f\in C(X)$ that are continuously extendable over $% \alpha X$ is denoted by $C_{\alpha}(X)$. It is shown that, in a model of $\textbf{ZF}$, it may happen that a ... More

Homfly polynomials for periodic knots via state modelMay 24 2018We give criteria for oriented links to be periodic of prime order using the quantum $\mathrm{SL}(N)$-invariant. The criteria are based upon an observation on the linking number between a periodic knot and its axis of the rotation.

Equivalent Conditions for Digital Covering MapsMay 08 2018Jan 07 2019In this paper we show that a digital $(\kappa,\lambda)-$continuous surjection $p:(E,\kappa)\rightarrow (B,\lambda)$ is a digital covering map if and only if it has unique path lifting property if and only if it is a local isomorphism. Moreover, we find ... More

A Markovian genomic concatenation model guided by persymmetric matricesMay 06 2018Sobottka and Hart (2011) made use of a Markovian concatenation model to observe novel statistical symmetries in the mononucleotide and dinucleotide distributions of a collection of bacterial chromosomes. The model roughly approximates the first-order ... More