Search results for "FACTORIZATION"
showing 10 items of 221 documents
Model building on the non-factorisable type IIA T6/(Z4×ΩR) orientifold
2016
We construct global semi-realistic supersymmetric models with intersecting D6-branes on the non-factorisable orientifold . The non-factorisable structure gives rise to differences compared to the factorisable case: additional conditions for the three-cycles to be Lagrangian and extra constraints on the wrapping numbers for building fractional cycles.
Deciphering genomic heterogeneity and the internal composition of tumour activities through a hierarchical factorisation model
2021
Genomic heterogeneity constitutes one of the most distinctive features of cancer diseases, limiting the efficacy and availability of medical treatments. Tumorigenesis emerges as a strongly stochastic process, producing a variable landscape of genomic configurations. In this context, matrix factorisation techniques represent a suitable approach for modelling such complex patterns of variability. In this work, we present a hierarchical factorisation model conceived from a systems biology point of view. The model integrates the topology of molecular pathways, allowing to simultaneously factorise genes and pathways activity matrices. The protocol was evaluated by using simulations, showing a hi…
A Non-antisymmetric Tensor Contraction Engine for the Automated Implementation of Spin-Adapted Coupled Cluster Approaches
2015
We present a symbolic manipulation algorithm for the efficient automated implementation of rigorously spin-free coupled cluster (CC) theories based on a unitary group parametrization. Due to the lack of antisymmetry of the unitary group generators under index permutations, all quantities involved in the equations are expressed in terms of non-antisymmetric tensors. Given two tensors, all possible contractions are first generated by applying Wick's theorem. Each term is then put down in the form of a non-antisymmetric Goldstone diagram by assigning its contraction topology. The subsequent simplification of the equations by summing up equivalent terms and their factorization by identifying co…
Classifying Healthy Children and Children with Attention Deficit through Features Derived from Sparse and Nonnegative Tensor Factorization Using Even…
2010
In this study, we use features extracted by Nonnegative Tensor Factorization (NTF) from event-related potentials (ERPs) to discriminate healthy children and children with attention deficit (AD). The peak amplitude of an ERP has been extensively used to discriminate different groups of subjects for the clinical research. However, such discriminations sometimes fail because the peak amplitude may vary severely with the increased number of subjects and wider range of ages and it can be easily affected by many factors. This study formulates a framework, using NTF to extract features of the evoked brain activities from time-frequency represented ERPs. Through using the estimated features of a ne…
Testing mode-coupling theory for a supercooled binary Lennard-Jones mixture
1995
Abstract We have performed a molecular dynamics computer simulation study to investigate the dynamical behavior of a supercooled simple liquid for comparison with the predictions of mode-coupling theory (MCT). By scaling the intermediate scattering function by the α-relaxation time r we find that the correlators fall onto a master curve extending over several decades in time. Thus we find that the time temperature superposition principle holds. In the late β-relaxation regime this master curve can be fitted very well by a master curve predicted by the idealized version MCT. However, there is no evidence for the presence of the critical decay predicted by the theory for the early part of the…
Sampling methods for low-frequency electromagnetic imaging
2007
For the detection of hidden objects by low-frequency electromagnetic imaging the linear sampling method works remarkably well despite the fact that the rigorous mathematical justification is still incomplete. In this work, we give an explanation for this good performance by showing that in the low-frequency limit the measurement operator fulfils the assumptions for the fully justified variant of the linear sampling method, the so-called factorization method. We also show how the method has to be modified in the physically relevant case of electromagnetic imaging with divergence-free currents. We present numerical results to illustrate our findings, and to show that similar performance can b…
Recent progress in electrical impedance tomography
2003
We consider the inverse problem of finding cavities within some body from electrostatic measurements on the boundary. By a cavity we understand any object with a different electrical conductivity from the background material of the body. We survey two algorithms for solving this inverse problem, namely the factorization method and a MUSIC-type algorithm. In particular, we present a number of numerical results to highlight the potential and the limitations of these two methods.
The factorization method for real elliptic problems
2006
The Factorization Method localizes inclusions inside a body from mea- surements on its surface. Without a priori knowing the physical parameters inside the inclusions, the points belonging to them can be characterized using the range of an auxiliary operator. The method relies on a range characterization that relates the range of the auxiliary operator to the measurements and is only known for very particular applications. In this work we develop a general framework for the method by considering sym- metric and coercive operators between abstract Hilbert spaces. We show that the important range characterization holds if the difference between the inclusions and the background medium satisfi…
A component-based approximation for trend detection of intense rainfall in the Spanish Mediterranean coast
2022
Rainfall behavior is a fundamental issue in areas with scarce and irregular amounts, such as the Spanish Mediterranean region. We identified 12 spatial patterns that characterized 899 torrential precipitation events (≥150 mm in 24 h) that occurred in the 3,537 rainy precipitation series in the period 1950–2020. Three of these components––eastern and ESE––showed positive and significant trends in their accumulated volumes. We then characterized the mean synoptic causes of the 10 most intense events in each component at both mean sea-level pressure and 500 hPa geopotential height, and also the integrated water-vapor transport between 1,000 and 300 hPa. We found a clear spatial distribution of…
A NEW COMPLEXITY FUNCTION FOR WORDS BASED ON PERIODICITY
2013
Motivated by the extension of the critical factorization theorem to infinite words, we study the (local) periodicity function, i.e. the function that, for any position in a word, gives the size of the shortest square centered in that position. We prove that this function characterizes any binary word up to exchange of letters. We then introduce a new complexity function for words (the periodicity complexity) that, for any position in the word, gives the average value of the periodicity function up to that position. The new complexity function is independent from the other commonly used complexity measures as, for instance, the factor complexity. Indeed, whereas any infinite word with bound…