There is a heated debate about how far computers can map the complexity of text analysis compared to the abilities of the whole team of human researchers. A "deep" analysis of a given text is still ...beyond the possibilities of modern computers. In the heart of the existing computational text analysis algorithms there are operations with real numbers, such as additions and multiplications according to the rules of algebraic fields. However, the process of "comparing" has a very precise mathematical structure, which is different from the structure of an algebraic field. The mathematical structure of "comparing" can be expressed by using Boolean rings. We build on this structure and define the corresponding algebraic equations lifting algorithms of comparative text analysis onto the "correct" algebraic basis. From this point of view, we can investigate the question of {\em computational} complexity of comparative text analysis.
With the help of theoretical calculations we explain the phenomenon of nonplanarity of crystalline alternariol. We find out that the different orientations of the hydroxyl groups of alternariol ...influence its planarity and aromaticity and lead to different twists of the structure. The presence of the intramolecular hydrogen bond stabilizes the planar geometry while the loss of the bond results in a twist of over 14°. This effect is thought to be involved while cutting DNA strands by alternariol.
We consider two disjoint sets of points. If at least one of the sets can be embedded into an Euclidean space, then we provide sufficient conditions for the two sets to be jointly embedded in one ...Euclidean space. In this joint Euclidean embedding, the distances between the points are generated by a specific relation-preserving function. Consequently, the mutual distances between two points of the same set are specific qualitative transformations of their mutual distances in their original space; the pairwise distances between the points of different sets can be constructed from an arbitrary proximity function.
The aim of this paper is to investigate the rebinding effect, a phenomenon describing a "short-time memory" which can occur when projecting a Markov process onto a smaller state space. For ...guaranteeing a correct mapping by the Markov State Model, we assume a fuzzy clustering in terms of membership functions, assigning degrees of membership to each state. The macro states are represented by the membership functions and may be overlapping. The magnitude of this overlap is a measure for the strength of the rebinding effect, caused by the projection and stabilizing the system. A minimal bound for the rebinding effect included in a given system is computed as the solution of an optimization problem. Based on membership functions chosen as a linear combination of Schur vectors, this generalized approach includes reversible as well as non-reversible processes.
We consider a stochastic optimal exit time feedback control problem. The Bellman equation is solved approximatively via the Policy Iteration algorithm on a polynomial ansatz space by a sequence of ...linear equations. As high degree multi-polynomials are needed, the corresponding equations suffer from the curse of dimensionality even in moderate dimensions. We employ tensor-train methods to account for this problem. The approximation process within the Policy Iteration is done via a Least-Squares ansatz and the integration is done via Monte-Carlo methods. Numerical evidences are given for the (multi dimensional) double well potential and a three-hole potential.
Raman spectroscopy is a well established tool for the analysis of vibration spectra, which then allow for the determination of individual substances in a chemical sample, or for their phase ...transitions. In the Time-Resolved-Raman-Sprectroscopy the vibration spectra of a chemical sample are recorded sequentially over a time interval, such that conclusions for intermediate products (transients) can be drawn within a chemical process. The observed data-matrix \(M\) from a Raman spectroscopy can be regarded as a matrix product of two unknown matrices \(W\) and \(H\), where the first is representing the contribution of the spectra and the latter represents the chemical spectra. One approach for obtaining \(W\) and \(H\) is the non-negative matrix factorization. We propose a novel approach, which does not need the commonly used separability assumption. The performance of this approach is shown on a real world chemical example.
We present numerical validation studies for a concurrent multiscale method designed to combine molecular dynamics and finite element analysis targeting the simulation of solids. The method is based ...on an overlapping domaindecomposition and uses weak matching constraints to enforce matching between the finite element displacement field and the projection of the molecular dynamics displacement field on the mesh. A comparison between our method and the well-known bridging domain method by Xiao and Belytschko 22 is presented. As part of our validation study we discuss applicability of the method to the simulation of fracture propagation and show results.
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