Search results for "IPA"

Graded algebras with polynomial growth of their codimensions

2015

Abstract Let A be an algebra over a field of characteristic 0 and assume A is graded by a finite group G . We study combinatorial and asymptotic properties of the G -graded polynomial identities of A provided A is of polynomial growth of the sequence of its graded codimensions. Roughly speaking this means that the ideal of graded identities is “very large”. We relate the polynomial growth of the codimensions to the module structure of the multilinear elements in the relatively free G -graded algebra in the variety generated by A . We describe the irreducible modules that can appear in the decomposition, we show that their multiplicities are eventually constant depending on the shape obtaine…

Scalable Ellipsoidal Classification for Bipartite Quantum States

2008

The Separability Problem is approached from the perspective of Ellipsoidal Classification. A Density Operator of dimension N can be represented as a vector in a real vector space of dimension $N^{2}- 1$, whose components are the projections of the matrix onto some selected basis. We suggest a method to test separability, based on successive optimization programs. First, we find the Minimum Volume Covering Ellipsoid that encloses a particular set of properly vectorized bipartite separable states, and then we compute the Euclidean distance of an arbitrary vectorized bipartite Density Operator to this ellipsoid. If the vectorized Density Operator falls inside the ellipsoid, it is regarded as s…

Radical Rings with Engel Conditions

2000

Abstract An associative ring R without unity is called radical if it coincides with its Jacobson radical, which means that the set of all elements of R forms a group denoted by R ∘  under the circle operation r  ∘  s  =  r  +  s  +  rs on R . It is proved that, for a radical ring R , the group R ∘  satisfies an n -Engel condition for some positive integer n if and only if R is m -Engel as a Lie ring for some positive integer m depending only on n .

Discrete Derivatives for Atom-Pairs as a Novel Graph-Theoretical Invariant for Generating New Molecular Descriptors: Orthogonality, Interpretation an…

2013

This report presents a new mathematical method based on the concept of the derivative of a molecular graph (G) with respect to a given event (S) to codify chemical structure information. The derivate over each pair of atoms in the molecule is defined as ∂G/∂S(vi  , vj )=(fi -2fij +fj )/fij , where fi (or fj ) and fij are the individual frequency of atom i (or j) and the reciprocal frequency of the atoms i and j, respectively. These frequencies characterize the participation intensity of atom pairs in S. Here, the event space is composed of molecular sub-graphs which participate in the formation of the G skeleton that could be complete (representing all possible connected sub-graphs) or comp…

Regression Wavelet Analysis for Lossless Coding of Remote-Sensing Data

2016

A novel wavelet-based scheme to increase coefficient independence in hyperspectral images is introduced for lossless coding. The proposed regression wavelet analysis (RWA) uses multivariate regression to exploit the relationships among wavelet-transformed components. It builds on our previous nonlinear schemes that estimate each coefficient from neighbor coefficients. Specifically, RWA performs a pyramidal estimation in the wavelet domain, thus reducing the statistical relations in the residuals and the energy of the representation compared to existing wavelet-based schemes. We propose three regression models to address the issues concerning estimation accuracy, component scalability, and c…

Automated detection and localization system of myocardial infarction in single-beat ECG using Dual-Q TQWT and wavelet packet tensor decomposition.

2019

Abstract Background and objective It is challenging to conduct real-time identification of myocardial infarction (MI) due to artifact corruption and high dimensionality of multi-lead electrocardiogram (ECG). In the present study, we proposed an automated single-beat MI detection and localization system using dual-Q tunable Q-factor wavelet transformation (Dual-Q TQWT) denoising algorithm. Methods After denoising and segmentation of ECG, a fourth-order wavelet tensor (leads × subbands × samples × beats) was constructed based on the discrete wavelet packet transform (DWPT), to represent the features considering the information of inter-beat, intra-beat, inter-frequency, and inter-lead. To red…

Outlier analysis and principal component analysis to detect fatigue cracks in waveguides

2009

Ultrasonic Guided Waves (UGWs) are a useful tool in structural health monitoring (SHM) applications that can benefit from built-in transduction, moderately large inspection ranges and high sensitivity to small flaws. This paper describes a SHM method based on UGWs, discrete wavelet transform (DWT), outlier analysis and principal component analysis (PCA) able to detect and quantify the onset and propagation of fatigue cracks in structural waveguides. The method combines the advantages of guided wave signals processed through the DWT with the outcomes of selecting defectsensitive features to perform a multivariate diagnosis of damage. The framework presented in this paper is applied to the de…

Application of principal component analysis and wavelet transform to fatigue crack detection in waveguides

2010

Ultrasonic Guided Waves (UGWs) are a useful tool in structural health monitoring (SHM) applications that can benefit from built-in transduction, moderately large inspection ranges and high sensitivity to small flaws. This paper describes a SHM method based on UGWs, discrete wavelet transform (DWT), and principal component analysis (PCA) able to detect and quantify the onset and propagation of fatigue cracks in structural waveguides. The method combines the advantages of guided wave signals processed through the DWT with the outcomes of selecting defect-sensitive features to perform a multivariate diagnosis of damage. This diagnosis is based on the PCA. The framework presented in this paper …

Design of innovative friction damper devices for earthquake-resilient RC frames with Hybrid Steel-Trussed Concrete Beams

2021

This thesis focuses on the design of innovative friction damper devices for earthquake-resilient Reinforced Concrete (RC) frames realized with Hybrid Steel-Trussed Concrete Beams (HSTCBs). These devices fall within the framework of the recently-proposed low-damage design strategy for structures built in earthquake-prone areas, on the basis of which the structures are designed to experience negligible damage when subjected to seismic events. The comprehensive solution proposed aims at introducing a feasible option for building earthquake-resilient RC Moment Resisting Frames (MRFs), having been proposed very few solutions for this structural scheme so far. Innovative solutions are proposed fo…

DISSIPATIVE DYNAMICS OF MULTI-STATE QUANTUM SYSTEMS IN THE WEAK TO STRONG COUPLING REGIME

In this thesis the dissipative dynamics of bistable quantum systems is studied within the path integral approach. The path integral representation of the propagator for quantum states and density matrices of discrete variable systems is described along with the Feynman-Vernon influence functional. The main approximations to the FV influence for the spin-boson model are introduced and applied to a bistable system beyond the two-level system approximation, the so-called double-doublet system. By the combined use of the Bloch-Redfield perturbative approach and of the path integral techniques, a phase diagram showing the various dynamical and dissipative regimes of the double-doublet system is …