Search results for "Maxim"
showing 10 items of 1236 documents
Primitive sets of words
2020
Given a (finite or infinite) subset $X$ of the free monoid $A^*$ over a finite alphabet $A$, the rank of $X$ is the minimal cardinality of a set $F$ such that $X \subseteq F^*$. We say that a submonoid $M$ generated by $k$ elements of $A^*$ is {\em $k$-maximal} if there does not exist another submonoid generated by at most $k$ words containing $M$. We call a set $X \subseteq A^*$ {\em primitive} if it is the basis of a $|X|$-maximal submonoid. This definition encompasses the notion of primitive word -- in fact, $\{w\}$ is a primitive set if and only if $w$ is a primitive word. By definition, for any set $X$, there exists a primitive set $Y$ such that $X \subseteq Y^*$. We therefore call $Y$…
Bayesian inference for the extremal dependence
2016
A simple approach for modeling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the angular measure or, alternatively, the Pickands dependence function. We propose a nonparametric Bayesian model that allows, in the bivariate case, the simultaneous estimation of both functional representations through the use of polynomials in the Bernstein form. The constraints required to provide a valid extremal dependence are addressed in a straightforward manner, by placing a prior on the coefficients of the Bernstein polynomials which gives probability one to the set of valid functions. The…
Bootstrap validation of links of a minimum spanning tree
2018
We describe two different bootstrap methods applied to the detection of a minimum spanning tree obtained from a set of multivariate variables. We show that two different bootstrap procedures provide partly distinct information that can be highly informative about the investigated complex system. Our case study, based on the investigation of daily returns of a portfolio of stocks traded in the US equity markets, shows the degree of robustness and completeness of the information extracted with popular information filtering methods such as the minimum spanning tree and the planar maximally filtered graph. The first method performs a "row bootstrap" whereas the second method performs a "pair bo…
The Max-Product Algorithm Viewed as Linear Data-Fusion: A Distributed Detection Scenario
2019
In this paper, we disclose the statistical behavior of the max-product algorithm configured to solve a maximum a posteriori (MAP) estimation problem in a network of distributed agents. Specifically, we first build a distributed hypothesis test conducted by a max-product iteration over a binary-valued pairwise Markov random field and show that the decision variables obtained are linear combinations of the local log-likelihood ratios observed in the network. Then, we use these linear combinations to formulate the system performance in terms of the false-alarm and detection probabilities. Our findings indicate that, in the hypothesis test concerned, the optimal performance of the max-product a…
The DMT of Real and Quaternionic Lattice Codes and DMT Classification of Division Algebra Codes
2021
In this paper we consider the diversity-multiplexing gain tradeoff (DMT) of so-called minimum delay asymmetric space-time codes. Such codes are less than full dimensional lattices in their natural ambient space. Apart from the multiple input single output (MISO) channel there exist very few methods to analyze the DMT of such codes. Further, apart from the MISO case, no DMT optimal asymmetric codes are known. We first discuss previous criteria used to analyze the DMT of space-time codes and comment on why these methods fail when applied to asymmetric codes. We then consider two special classes of asymmetric codes where the code-words are restricted to either real or quaternion matrices. We p…
Fast Estimation of Diffusion Tensors under Rician noise by the EM algorithm
2016
Diffusion tensor imaging (DTI) is widely used to characterize, in vivo, the white matter of the central nerve system (CNS). This biological tissue contains much anatomic, structural and orientational information of fibers in human brain. Spectral data from the displacement distribution of water molecules located in the brain tissue are collected by a magnetic resonance scanner and acquired in the Fourier domain. After the Fourier inversion, the noise distribution is Gaussian in both real and imaginary parts and, as a consequence, the recorded magnitude data are corrupted by Rician noise. Statistical estimation of diffusion leads a non-linear regression problem. In this paper, we present a f…
A study on the degree of relationship between two individuals.
2000
The paper studies the likely degree of relationship between two individuals who could possibly be half sibs. The possible common ancestor was dead, which further complicated the problem. The model used was devised by Thompson [in Rao and Chakraborty (eds): Handbook of Statistics, North-Holland, Amsterdam, 1991] and establishes a correspondence between the possible degree of relationship and certain feasible probability distributions on the number of identical by descent genes. Two statistical approaches are considered: the classical one, in which the maximum likelihood estimation for the parameters of Thompson’s model are obtained, and the Bayesian one, in which the test of the hypothesis o…
Shear resistance analytical evaluation for RC beams with transverse reinforcement with two different inclinations
2020
An analysis-oriented mechanical model for shear strength evaluation of Reinforced Concrete (RC) beams with transverse reinforcement with two different inclinations, which required a numerical analysis, is turned into a design-oriented analytical model that can easily be utilized for practical purposes. The model assessed the shear resistance, according to the “lower-bound solution”, employing a numerical procedure that maximizes the element shear strength varying the stresses in the two sets of transverse reinforcement and the magnitude and inclination of the web concrete compressive stress field. The model is formulated with the aim of representing an extension of Eurocode 2 framework to R…
Competition, risk taking, and governance structures in retail banking
2005
This paper investigates the extent to which the linkages between bank performance and governance structure affect deposits market competition and risk taking incentives when commercial banks compete with organizations with objectives different from profit maximization. These organizations include savings banks whose corporate and ownership structure yields an objective function that can incorporate labour expenses. It is found that such objective function enables the savings banks to capture a greater market share of bank deposits and to take on relatively less risk in their portfolio of investments. The empirical evidence from the Spanish retail banking sector documents these conclusions.
The multiplex structure of interbank networks
2013
The interbank market has a natural multiplex network representation. We employ a unique database of supervisory reports of Italian banks to the Banca d'Italia that includes all bilateral exposures broken down by maturity and by the secured and unsecured nature of the contract. We find that layers have different topological properties and persistence over time. The presence of a link in a layer is not a good predictor of the presence of the same link in other layers. Maximum entropy models reveal different unexpected substructures, such as network motifs, in different layers. Using the total interbank network or focusing on a specific layer as representative of the other layers provides a po…