Search results for "Decomposition"
showing 10 items of 766 documents
Algorithms on Graphs
1988
In this chapter we shall develop some basic algorithms for directed graphs and relations which will be of use in later chapters, where the efficient construction of parsers is considered. The constructions needed can be expressed as the computing of certain “relational expressions”. These are expressions whose operands are relations and whose operators are chosen from among multiplication, closure, union and inverse. For this purpose we need to develop an algorithm for computing the closure of a relation. In view of the nature of our applications, the most appropriate way to do this is by a depth-first traversal of the graph that corresponds to the given relation. Other ways of computing th…
On a Quantitative Measure for Modularity Based on Information Theory
2005
The concept of modularity appears to be crucial for many questions in the field of Artificial Life research. However, there have not been many quantitative measures for modularity that are both general and viable. In this paper we introduce a measure for modularity based on information theory. Due to the generality of the information theory formalism, this measure can be applied to various problems and models; some connections to other formalisms are presented.
On the regularity and defect sequence of monomial and binomial ideals
2018
When S is a polynomial ring or more generally a standard graded algebra over a field K, with homogeneous maximal ideal m, it is known that for an ideal I of S, the regularity of powers of I becomes eventually a linear function, i.e., reg(Im) = dm + e for m ≫ 0 and some integers d, e. This motivates writing reg(Im) = dm + em for every m ⩾ 0. The sequence em, called the defect sequence of the ideal I, is the subject of much research and its nature is still widely unexplored. We know that em is eventually constant. In this article, after proving various results about the regularity of monomial ideals and their powers, we give several bounds and restrictions on em and its first differences when…
Tower sets and other configurations with the Cohen-Macaulay property
2014
Abstract Some well-known arithmetically Cohen–Macaulay configurations of linear varieties in P r as k-configurations, partial intersections and star configurations are generalized by introducing tower schemes. Tower schemes are reduced schemes that are a finite union of linear varieties whose support set is a suitable finite subset of Z + c called tower set. We prove that the tower schemes are arithmetically Cohen–Macaulay and we compute their Hilbert function in terms of their support. Afterwards, since even in codimension 2 not every arithmetically Cohen–Macaulay squarefree monomial ideal is the ideal of a tower scheme, we slightly extend this notion by defining generalized tower schemes …
Preparation of polymeric foams with a pore size gradient via Thermally Induced Phase Separation (TIPS)
2015
Abstract Foams with a pore size gradient are promising materials for tissue engineering applications where a complex architecture involving morphological variations in space must be mimicked, e.g. in bone tissue repair. In this paper, a technique to obtain a porous scaffold with a pore size gradient is presented. The preparation procedure is based on Thermally Induced Phase Separation (TIPS), by imposing a different thermal history on the two sides of a polymeric solution. In this way, a gradient in thermal history is produced, which will generate a pore size monotonously varying along scaffold thickness. By controlling some parameters easy to manipulate, such as demixing temperature and/or…
Complete Measurement of the Λ Electromagnetic Form Factors.
2019
The exclusive process e+e−→ΛΛ¯, with Λ→pπ− and Λ¯→p¯π+, has been studied at s=2.396 GeV for measurement of the timelike Λ electric and magnetic form factors, GE and GM. A data sample, corresponding to an integrated luminosity of 66.9 pb−1, was collected with the BESIII detector for this purpose. A multidimensional analysis with a complete decomposition of the spin structure of the reaction enables a determination of the modulus of the ratio R=|GE/GM| and, for the first time for any baryon, the relative phase ΔΦ=ΦE−ΦM. The resulting values are R=0.96±0.14(stat)±0.02(syst) and ΔΦ=37°±12°(stat)±6°(syst), respectively. These are obtained using the recently established and most precise value of …
Multilinear sparse decomposition for best spectral bands selection
2014
Optimal spectral bands selection is a primordial step in multispectral images based systems for face recognition. In this context, we select the best spectral bands using a multilinear sparse decomposition based approach. Multispectral images of 35 subjects presenting 25 different lengths from 480nm to 720nm and three lighting conditions: fluorescent, Halogen and Sun light are groupped in a 3-mode face tensor T of size 35x25x2 . T is then decomposed using 3-mode SVD where three mode matrices for subjects, spectral bands and illuminations are sparsely determined. The 25x25 spectral bands mode matrix defines a sparse vector for each spectral band. Spectral bands having the sparse vectors with…
Empirical Orthogonal Function and Functional Data Analysis Procedures to Impute Long Gaps in Environmental Data
2016
Air pollution data sets are usually spatio-temporal multivariate data related to time series of different pollutants recorded by a monitoring network. To improve the estimate of functional data when missing values, and mainly long gaps, are present in the original data set, some procedures are here proposed considering jointly Functional Data Analysis and Empirical Orthogonal Function approaches. In order to compare and validate the proposed procedures, a simulation plan is carried out and some performance indicators are computed. The obtained results show that one of the proposed procedures works better than the others, providing a better reconstruction especially in presence of long gaps.
Information decomposition in the frequency domain: a new framework to study cardiovascular and cardiorespiratory oscillations
2021
While cross-spectral and information-theoretic approaches are widely used for the multivariate analysis of physiological time series, their combined utilization is far less developed in the literature. This study introduces a framework for the spectral decomposition of multivariate information measures, which provides frequency-specific quantifications of the information shared between a target and two source time series and of its expansion into amounts related to how the sources contribute to the target dynamics with unique, redundant and synergistic information. The framework is illustrated in simulations of linearly interacting stochastic processes, showing how it allows us to retrieve …
Locally optimal invariant detector for testing equality of two power spectral densities
2018
This work addresses the problem of determining whether two multivariate random time series have the same power spectral density (PSD), which has applications, for instance, in physical-layer security and cognitive radio. Remarkably, existing detectors for this problem do not usually provide any kind of optimality. Thus, we study here the existence under the Gaussian assumption of optimal invariant detectors for this problem, proving that the uniformly most powerful invariant test (UMPIT) does not exist. Thus, focusing on close hypotheses, we show that the locally most powerful invariant test (LMPIT) only exists for univariate time series. In the multivariate case, we prove that the LMPIT do…