Search results for "Theoretical Computer Science"

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…

Motivic Pattern Extraction in Symbolic Domain

2008

This chapter offers an overview of computational research in motivic pattern extraction. The central questions underlying the topic, concerning the formalization of the motivic structures, the matching strategies and the filtering of the results, have been addressed in various ways. A detailed analysis of these problems leads to the proposal of a new methodology, which will be developed throughout the study. One main conclusion of this review is that the problems cannot be tackled using purely mathematic or geometric heuristics or classical engineering tools, but require also a detailed understanding of the multiple constraints derived by the underlying cognitive context.

Topological Approach to Analgesia

1994

Mitigating DDoS using weight‐based geographical clustering

2020

Distributed denial of service (DDoS) attacks have for the last two decades been among the greatest threats facing the internet infrastructure. Mitigating DDoS attacks is a particularly challenging task as an attacker tries to conceal a huge amount of traffic inside a legitimate traffic flow. This article proposes to use data mining approaches to find unique hidden data structures which are able to characterize the normal traffic flow. This will serve as a mean for filtering illegitimate traffic under DDoS attacks. In this endeavor, we devise three algorithms built on previously uncharted areas within mitigation techniques where clustering techniques are used to create geographical clusters …

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.

A regularized Newton method for locating thin tubular conductivity inhomogeneities

2011

We consider the inverse problem of determining the position and shape of a thin tubular object, such as for instance a wire, a thin channel or a curve-like crack, embedded in some three-dimensional homogeneous body from a single measurement of electrostatic currents and potentials on the boundary of the body. Using an asymptotic model describing perturbations of electrostatic potentials caused by such thin objects, we reformulate the inverse problem as a nonlinear operator equation. We establish Frechet differentiability of the corresponding operator, compute its Frechet derivative and set up a regularized Newton scheme to solve the inverse problem numerically. We discuss our implementation…

Jacobian of solutions to the conductivity equation in limited view

2022

Abstract The aim of hybrid inverse problems such as Acousto-Electric Tomography or Current Density Imaging is the reconstruction of the electrical conductivity in a domain that can only be accessed from its exterior. In the inversion procedure, the solutions to the conductivity equation play a central role. In particular, it is important that the Jacobian of the solutions is non-vanishing. In the present paper we address a two-dimensional limited view setting, where only a part of the boundary of the domain can be controlled by a non-zero Dirichlet condition, while on the remaining boundary there is a zero Dirichlet condition. For this setting, we propose sufficient conditions on the bounda…

Hop: Histogram of patterns for human action representation

2017

This paper presents a novel method for representing actions in terms of multinomial distributions of frequent sequential patterns of different length. Frequent sequential patterns are series of data descriptors that occur many times in the data. This paper proposes to learn a codebook of frequent sequential patterns by means of an apriori-like algorithm, and to represent an action with a Bag-of-Frequent-Sequential-Patterns approach. Preliminary experiments of the proposed method have been conducted for action classification on skeletal data. The method achieves state-of-the-art accuracy value in cross-subject validation.

Towards more relevance-oriented data mining research

2008

Data mining (DM) research has successfully developed advanced DM techniques and algorithms over the last few decades, and many organisations have great expectations to take more benefit of their data warehouses in decision making. Currently, the strong focus of most DM-researchers is still only on technology-oriented topics. Commonly the DM research has several stakeholders, the major of which can be divided into internal and external ones each having their own point of view, and which are at least partly conflicting. The most important internal groups of stakeholders are the DM research community and academics in other disciplines. The most important external stakeholder groups are manager…