All posts under tag "Mathematics"
Parameters defined via general estimating equations (GEE) can be estimated by maximizing the empirical likelihood (EL). Newey and Smith [Econometrica 72 (2004) 219--255] have recently shown that this EL estimator exhibits desirable higher-order asymptotic properties, namely, that its $O(n^{-1})$ bia
In previous work, we demonstrated how decoding of a non-binary linear code could be formulated as a linear-programming problem. In this paper, we study different polytopes for use with linear-programming decoding, and show that for many classes of codes these polytopes yield a complexity advantage f
Given a family of (almost) disjoint strictly convex subsets of a complete negatively curved Riemannian manifold M, such as balls, horoballs, tubular neighborhoods of totally geodesic submanifolds, etc, the aim of this paper is to construct geodesic rays or lines in M which have exactly once an exact
By factorization of the Hamiltonian describing the quantum mechanics of the continuous q-Hermite polynomial, the creation and annihilation operators of the q-oscillator are obtained. They satisfy a q-oscillator algebra as a consequence of the shape-invariance of the Hamiltonian. A second set of q-os
We classify Riemannian foliations of manifolds homeomorphic to CROSSes.
The walk distances in graphs are defined as the result of appropriate transformations of the $sum_{k=0}^infty(tA)^k$ proximity measures, where $A$ is the weighted adjacency matrix of a connected weighted graph and $t$ is a sufficiently small positive parameter. The walk distances are graph-geodetic,
We introduce some multiple integrals that are expected to have the same singularities as the singularities of the $ n$-particle contributions $chi^{(n)}$ to the susceptibility of the square lattice Ising model. We find the Fuchsian linear differential equation satisfied by these multiple integrals f
This book introduces special classes of Fuzzy and Neutrosophic matrices. These special classes of matrices are used in the construction of multi-expert special fuzzy models using FCM, FRM and FRE and their Neutorosophic analogues (simultaneous or otherwise, according to ones need). Using the six bas
The generalized Taylor expansion including a secret auxiliary parameter $h$ which can control and adjust the convergence region of the series is the foundation of the homotopy analysis method proposed by Liao. The secret of $h$ can't be understood in the frame of the homotopy analysis method. This i
A separated net is a set of points which is relatively dense and uniformly discrete (another name for a Delone set). We are dealing with tilings and separated nets in Euclidean spaces and with the question whether a given separated net is biLipschitz to the integer lattice. In this paper we show, as
This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applications, including the famous Netflix Prize and other similar questions in collaborative filtering. In
Two-points nonlocal problem for the first order differential evolution equation with an operator coefficient in a Banach space $X$ is considered. An exponentially convergent algorithm is proposed and justified in assumption that the operator coefficient is strongly positive and some existence and un
In this paper, first-order logic is interpreted in the framework of universal algebra, using the clone theory developed in three previous papers. We first define the free clone T(L, C) of terms of a first order language L over a set C of parameters in a standard way. The free right algebra F(L, C) o
We prove that a Hausdorff space $X$ is very $mathrm I$-favorable if and only if $X$ is the almost limit space of a $sigma$-complete inverse system consisting of (not necessarily Hausdorff) second countable spaces and surjective d-open bonding maps. It is also shown that the class of Tychonoff very $
This is an expanded version of our earlier paper. Let the $n$th partial sum of the Taylor series $e = sum_{r=0}^{infty} 1/r!$ be $A_n/n!$, and let $p_k/q_k$ be the $k$th convergent of the simple continued fraction for $e$. Using a recent measure of irrationality for $e$, we prove weak versions of ou
A $t-a$ covering array is an $mtimes n$ matrix, with entries from an alphabet of size $alpha$, such that for any choice of $t$ rows, and any ordered string of $t$ letters of the alphabet, there exists a column such that the 'values' of the rows in that column match those of the string of letters. We
We consider the problem of collaborative filtering from a channel coding perspective. We model the underlying rating matrix as a finite alphabet matrix with block constant structure. The observations are obtained from this underlying matrix through a discrete memoryless channel with a noisy part rep
The independence number of a graph G, denoted by alpha(G), is the cardinality of an independent set of maximum size in G, while mu(G) is the size of a maximum matching in G, i.e., its matching number. G is a Konig-Egervary graph if its order equals alpha(G)+mu(G). In this paper we give a new charact
We prove a converse to Moore's ``Garden-of-Eden'' theorem: a group G is amenable if and only if all cellular automata living on G that admit mutually erasable patterns also admit gardens of Eden. It had already been conjectured in that amenability could be characterized by cellular automata. We pr
In this paper we first generalize the Ostrowski inequality on time scales for k points and then unify corresponding continuous and discrete versions. We also point out some particular Ostrowski type inequalities on time scales as special cases.
A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a 'soft' bandlimitation, (2) an approximate reconstruction from sample values rather than a perfect one is obta
A greedy omnidirectional relay scheme is developed, and the corresponding achievable rate region is obtained for the all-source all-cast problem. The discussions are first based on the general discrete memoryless channel model, and then applied to the additive white Gaussian noise (AWGN) models, wit
This paper investigates the limit behavior of Markov Decision Processes (MDPs) made of independent particles evolving in a common environment, when the number of particles goes to infinity. In the finite horizon case or with a discounted cost and an infinite horizon, we show that when the number of
In this paper we first extend a generalization of Ostrowski type inequality on time scales for functions whose derivatives are bounded and then unify corresponding continuous and discrete versions. We also point out some particular integral type inequalities on time scales as special cases.
A new integrable sixth-order nonlinear wave equation is discovered by means of the Painleve analysis, which is equivalent to the Korteweg - de Vries equation with a source. A Lax representation and a Backlund self-transformation are found of the new equation, and its travelling wave solutions and ge
We show that as in the case of n- fold Cartesian product for n greater than or equal to 4, even in 3-fold Cartesian product, a related component of a good set need not be a full component.
We show that there are infinitely many binary strings z, such that the sum of the on-line decision complexity of predicting the even bits of z given the previous uneven bits, and the decision complexity of predicting the uneven bits given the previous event bits, exceeds the Kolmogorov complexity of
In this paper we present a simple method for deriving an alternative form of the functional equation for Riemann's Zeta function. The connections between some functional equations obtained implicitly by Leonhard Euler in his work 'Remarques sur un beau rapport entre les series des puissances tant di
The covariance evolution is a system of differential equations with respect to the covariance of the number of edges connecting to the nodes of each residual degree. Solving the covariance evolution, we can derive distributions of the number of check nodes of residual degree 1, which helps us to est
We consider microstructure as an arbitrary contamination of the underlying latent securities price, through a Markov kernel $Q$. Special cases include additive error, rounding and combinations thereof. Our main result is that, subject to smoothness conditions, the two scales realized volatility is r
We construct explicit generators of the K-theory and K-homology of the coordinate algebra of `functions' on quantum projective spaces. We also sketch a construction of unbounded Fredholm modules, that is to say Dirac-like operators and spectral triples of any positive real dimension.
The Turan bound is a famous result in graph theory, which relates the independence number of an undirected graph to its edge density. Also the Caro-Wei inequality, which gives a more refined bound in terms of the vertex degree sequence of a graph, might be regarded today as a classical result. We sh
A method to construct both classical and quantum completely integrable systems from (Jordan-Lie) comodule algebras is introduced. Several integrable models based on a so(2,1) comodule algebra, two non-standard Schrodinger comodule algebras, the (classical and quantum) q-oscillator algebra and the Re
The (strong) Bruhat order for permutations provides a partial ordering defined as follows: two permutations are comparable if one can be obtained from the other by a sequence of adjacent transpositions that each increase the number of inversions by $1$. Given two random permutations, what is the pro
In this paper, our primary objective is to establish the time decay properties of solutions $u(t, x)$ with initial data $u_0, u_1 in mathcal{Y}^q$ (pseudo-measure spaces) to the linear damped wave equation in the spaces $L^2left(mathbb{R}^nright)$ and $dot{H}^sleft(mathbb{R}^nright)$ (for $s leq 0$
We analyze the asymptotic behavior of sequences of random variables defined by an initial condition, a stationary and ergodic sequence of random matrices, and an induction formula involving multiplication is the so-called max-plus algebra. This type of recursive sequences are frequently used in appl
In this letter we determine the derivative of the mutual information corresponding to bit-interleaved coded modulation systems. The derivative follows as a linear combination of minimum-mean-squared error functions of coded modulation sets. The result finds applications to the analysis of communicat
We obtain an exact solution of the self-consistent relativistic magnetohydrodynamic equations for an anisotropic magnetoactive plasma in the background of a plane gravitational wave metric (PGW) with an arbitrary polarization. It is shown that, in the linear approximation in the gravitational wave a
This paper investigates the conditions under which the centralizer algebra $S_n(c,R)$ of a matrix $ cin M_n(R)$ is a (separable) Frobenius extension of the base algebra $R$. For an algebra $R$ over an integral domain $mathbb{k}$, we provide necessary and sufficient conditions for $S_n(c,R)/R$ to be
For any free partially commutative monoid $M(E,I)$, we compute the global dimension of the category of $M(E,I)$-objects in an Abelian category with exact coproducts. As a corollary, we generalize Hilbert's Syzygy Theorem to polynomial rings in partially commuting variables.
The large class of moving boundary processes in the plane modeled by the so-called Laplacian growth, which describes, e.g., solidification, electrodeposition, viscous fingering, bacterial growth, etc., is known to be integrable and to exhibit a large number of exact solutions. In this work, the boun
We consider limits over categories of extensions and show how certain well-known functors on the category of groups turn out as such limits. We also discuss higher (or derived) limits over categories of extensions.
It is generally accepted that many time series of practical interest exhibit strong dependence, i.e., long memory. For such series, the sample autocorrelations decay slowly and log-log periodogram plots indicate a straight-line relationship. This necessitates a class of models for describing such be
Discrete-time Rayleigh fading single-input single-output (SISO) and multiple-input multiple-output (MIMO) channels are considered, with no channel state information at the transmitter or the receiver. The fading is assumed to be stationary and correlated in time, but independent from antenna to ante
Within the program of finding axiomatizations for various parts of computability logic, it was proved earlier that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting's intuitionistic calculus. That sort of reduction permits unlimited reusage of the computational
This paper presents a computationally efficient decoder for multiple antenna systems. The proposed algorithm can be used for any constellation (QAM or PSK) and any labeling method. The decoder is based on matrix-lifting Semi-Definite Programming (SDP). The strength of the proposed method lies in a n
The capacity of discrete-time, non-coherent, multipath fading channels is considered. It is shown that if the delay spread is large in the sense that the variances of the path gains do not decay faster than geometrically, then capacity is bounded in the signal-to-noise ratio.
In this paper, we study network coding capacity for random wireless networks. Previous work on network coding capacity for wired and wireless networks have focused on the case where the capacities of links in the network are independent. In this paper, we consider a more realistic model, where wirel
A single source network is said to be memory-free if all of the internal nodes (those except the source and the sinks) do not employ memory but merely send linear combinations of the symbols received at their incoming edges on their outgoing edges. In this work, we introduce network-error correction
In this paper, we use various ansatzes with undetermined functions and the technique of moving frame to find solutions with parameter functions modulo the Lie point symmetries for the classical non-steady boundary layer problems. These parameter functions enable one to find the solutions of some rel
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