All posts under tag "Mathematics"
A simple lower bound to the capacity of the discrete-time Poisson channel with average energy $es$ is derived. The rate ${1/2}log(1+es)$ is shown to be the generalized mutual information of a modified minimum-distance decoder, when the input follows a gamma distribution of parameter 1/2 and mean $es
The paper studies decentralized optimization over networks, where agents minimize a sum of {it locally} smooth (strongly) convex losses and plus a nonsmooth convex extended value term. We propose decentralized methods wherein agents {it adaptively} adjust their stepsize via local backtracking proced
In previous work, we showed that there are appropriate model category structures on the category of simplicial categories and on the category of Segal precategories, and that they are Quillen equivalent to one another and to Rezk's complete Segal space model structure on the category of simplicial s
In the setting of additive regression model for continuous time process, we establish the optimal uniform convergence rates and optimal asymptotic quadratic error of additive regression. To build our estimate, we use the marginal integration method.
A hyperbolic 3-simplex reflection group is a Coxeter group arising as a lattice in the isometry group of hyperbolic 3-space, with fundamental domain a geodesic simplex (possibly with some ideal vertices). The classification of these groups is known, and there are exactly 9 cocompact examples, and 23
In this thesis, we consider semi-algebraic sets over a real closed field $R$ defined by quadratic polynomials. Semi-algebraic sets of $R^k$ are defined as the smallest family of sets in $R^k$ that contains the algebraic sets as well as the sets defined by polynomial inequalities, and which is also c
We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining `information'. We discuss the extent to which Kolmogorov's and Shannon's information theory have a common purpose, and where they are
In this paper we review the properties of families of numbers of the form $6npm1$, with $n$ integer (in which there are all prime numbers greater than 3 and other compound numbers with particular properties) to later use them in a new sieve that allows the separation of numbers $n$ that generate pri
We present an Hilbert space formulation for a set of implied volatility models introduced in cite{BraceGoldys01} in which the authors studied conditions for a family of European call options, varying the maturing time and the strike price $T$ an $K$, to be arbitrage free. The arbitrage free conditio
In this paper we investigate the probability distribution of the sum $Y$ of $ell$ independent identically distributed random variables taking values in $mathbb{Z}_p$. Our main focus is the regime of small values of $ell$, which is less explored compared to the asymptotic case $ell to infty$. Start
This paper shows how to use Computational Algebra techniques, namely the decomposition of rational functions in one variable, to explore a certain set of modular functions, called replicable functions, that arise in Monstrous Moonshine. In particular, we have computed all the rational relations with
In this note, I present a simple PSLQ code for finding null linear combinations, with the best rational coefficients, of mathematical constants, within some prescribed precision. As an example, I explore approximate expressions for the Ap'{e}ry's constant $,zeta{(3)} = sum_{nge1}{,1/n^3}$, an irrati
In this article we present a continuous time model for natural gas and crude oil future prices. Its main feature is the possibility to link both energies in the long term and in the short term. For each energy, the future returns are represented as the sum of volatility functions driven by motions.
We work in the context of the infinitely many alleles model. The allelic partition associated with a coalescent process started from n individuals is obtained by placing mutations along the skeleton of the coalescent tree; for each individual, we trace back to the most recent mutation affecting it a
In the first part, we further advance the study of category theory in a strong balanced factorization category C [Pisani, 2008], a finitely complete category endowed with two reciprocally stable factorization systems such that X to 1 is in M iff it is in M'. In particular some aspects related to 'in
The purpose of this paper is to develop a theory of bimonads and Hopf monads on arbitrary categories thus providing the possibility to transfer the essentials of the theory of Hopf algebras in vector spaces to more general settings. There are several extensions of this theory to {em monoidal} catego
In this paper, we investigate geometrical properties of the rank metric space and covering properties of rank metric codes. We first establish an analytical expression for the intersection of two balls with rank radii, and then derive an upper bound on the volume of the union of multiple balls with
Combinatorics on multisets is used to deduce new upper and lower bounds on the number of numerical semigroups of each given genus, significantly improving existing ones. In particular, it is proved that the number $n_g$ of numerical semigroups of genus $g$ satisfies $2F_{g}leq n_gleq 1+3cdot 2^{g-3}
The purpose of this work is to provide details about the construction of the Chern character for categorical sheaves mentioned in our previous work 'Chern character, loop spaces and derived algebraic geometry'. For this, we introduce and study the notion of rigid symmetric monoidal infty-category. W
A k-noncrossing RNA pseudoknot structure is a graph over ${1,...,n}$ without 1-arcs, i.e. arcs of the form (i,i+1) and in which there exists no k-set of mutually intersecting arcs. In particular, RNA secondary structures are 2-noncrossing RNA structures. In this paper we prove a central and a local
In many channel measurement applications, one needs to estimate some characteristics of the channels based on a limited set of measurements. This is mainly due to the highly time varying characteristics of the channel. In this contribution, it will be shown how free probability can be used for chann
A d-dimensional framework is a graph and a map from its vertices to E^d. Such a framework is globally rigid if it is the only framework in E^d with the same graph and edge lengths, up to rigid motions. For which underlying graphs is a generic framework globally rigid? We answer this question by prov
Cirquent calculus is a new proof-theoretic and semantic framework, whose main distinguishing feature is being based on circuits, as opposed to the more traditional approaches that deal with tree-like objects such as formulas or sequents. Among its advantages are greater efficiency, flexibility and e
We classify complactly generated t-structures on the derived category of modules over a commutative Noetherian ring R in terms of decreasing filtrations by supports on Spec(R). A decreasing filtration by supports phi : Z -> Spec(R) satisfies the weak Cousin condition if for any integer i in Z, the s
This paper studies compactifications of moduli spaces involving closed Riemann surfaces. The first main result identifies the homeomorphism types of these compactifications. The second main result introduces orbicell decompositions on these spaces using semistable ribbon graphs extending the earlier
We give, for each level of complexity L, a Hurewicz-like characterization of the Borel subsets with countable sections of a product of two Polish spaces that cannot become in L by changing the two Polish topologies.
There currently exists no algebraic algorithm for computing twisted conjugacy classes in free groups. We propose a new technique for deciding twisted conjugacy relations using nilpotent quotients. Our technique is generalization of the common abelianization method, but admits significantly greater r
Difference triangle sets are useful in many practical problems of information transmission. This correspondence studies combinatorial and computational constructions for difference triangle sets having small scopes. Our algorithms have been used to produce difference triangle sets whose scopes are t
In this note we contrast two transformation-based methods to deduce absolute extrema and the corresponding extremizers. Unlike variation-based methods, the transformation-based ones of Carlson and Leitmann and the recent one of Silva and Torres are direct in that they permit obtaining solutions by i
This paper addresses the problem of forbidden states for safe Petri net modeling discrete event systems. We present an efficient method to construct a controller. A set of linear constraints allow forbidding the reachability of specific states. The number of these so-called forbidden states and cons
Counting problems, determining the number of possible states of a large system under certain constraints, play an important role in many areas of science. They naturally arise for complex disordered systems in physics and chemistry, in mathematical graph theory, and in computer science. Counting pro
Let alpha(G) be the cardinality of a independence set of maximum size in the graph G, while mu(G) is the size of a maximum matching. G is a Konig--Egervary graph if its order equals alpha(G) + mu(G). The set core(G) is the intersection of all maximum independent sets of G (Levit & Mandrescu, 2002).
Semimodules over idempotent semirings like the max-plus or tropical semiring have much in common with convex cones. This analogy is particularly apparent in the case of subsemimodules of the n-fold cartesian product of the max-plus semiring it is known that one can separate a vector from a closed su
The problem of decentralized sequential detection with conditionally independent observations is studied. The sensors form a star topology with a central node called fusion center as the hub. The sensors make noisy observations of a parameter that changes from an initial state to a final state at a
In this article we generalize the results of the previous article with the same title [arXiv:0901.3308] for the case of an arbitrariy linear representation and non-normal stationary subgroup.
We introduce S-DUDE, a new algorithm for denoising DMC-corrupted data. The algorithm, which generalizes the recently introduced DUDE (Discrete Universal DEnoiser) of Weissman et al., aims to compete with a genie that has access, in addition to the noisy data, also to the underlying clean data, and c
Near optimal decoding of good error control codes is generally a difficult task. However, for a certain type of (sufficiently) good codes an efficient decoding algorithm with near optimal performance exists. These codes are defined via a combination of constituent codes with low complexity trellis r
Thomassen famously proved that every planar graph is 5-choosable. We explore variants of this result, focusing on finding disjoint correspondence colorings, in the more general class of $K_5$-minor-free graphs. Correspondence colorings generalize list colorings as follows. Given a graph $G$ and a po
Historically the finite volume methods have been developed for the numerical integration of conservation laws. In this study we present some recent results on the application of such schemes to dispersive PDEs. Namely, we solve numerically a representative of Boussinesq type equations in view of imp
We show that the Lusternik-Schnirelmann category of a simple, simply connected, compact Lie group G is bounded above by the sum of the relative categories of certain distinguished conjugacy classes in G corresponding to the vertices of the fundamental alcove for the action of the affine Weyl group o
Protection of the sensitive content is crucial for extensive information sharing. We present a technique of information concealing, based on introduction and maintenance of families of repeats. Repeats in DNA constitute a basic obstacle for its reconstruction by hybridization.
In this note we show that the known relation between double groupoids and matched pairs of groups may be extended, or seems to extend, to the triple case. The references give some other occurrences of double groupoids.
Let K be a global field of characteristic not 2. Let Z be a symmetric variety defined over K and S a finite set of places of K. We obtain counting and equidistribution results for the S-integral points of Z. Our results are effective when K is a number field.
We show how to protect a stream of quantum information from decoherence induced by a noisy quantum communication channel. We exploit preshared entanglement and a convolutional coding structure to develop a theory of entanglement-assisted quantum convolutional coding. Our construction produces a Cald
We define the epsilon-distortion complexity of a set as the shortest program, running on a universal Turing machine, which produces this set at the precision epsilon in the sense of Hausdorff distance. Then, we estimate the epsilon-distortion complexity of various central Cantor sets on the line gen
We present a way of constructing and deforming diffeomorphisms of manifolds endowed with a Lie group action. This is applied to the study of exotic diffeomorphisms and involutions of spheres and to the equivariant homotopy of Lie groups.
In this paper, we investigate the error correction capability of column-weight-three LDPC codes when decoded using the Gallager A algorithm. We prove that the necessary condition for a code to correct $k geq 5$ errors is to avoid cycles of length up to $2k$ in its Tanner graph. As a consequence of t
This work concerns estimation of linear autoregressive models with Markov-switching using expectation maximisation (E.M.) algorithm. Our method generalise the method introduced by Elliot for general hidden Markov models and avoid to use backward recursion.
In this note, we give some explicit upper and lower bounds for the summation $sum_{0<gammaleq T}frac{1}{gamma}$, where $gamma$ is the imaginary part of nontrivial zeros $rho=beta+igamma$ of $zeta(s)$.
In this paper, we derive an explicit formula for constructing the confidence interval of binomial parameter with guaranteed coverage probability. The formula overcomes the limitation of normal approximation which is asymptotic in nature and thus inevitably introduce unknown errors in applications. M
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