Search results for "Linear Algebra."
showing 10 items of 552 documents
Periodic Classification of Local Anaesthetics (Procaine Analogues)
2006
Algorithms for classification are proposed based on criteria (information entropyand its production). The feasibility of replacing a given anaesthetic by similar ones in thecomposition of a complex drug is studied. Some local anaesthetics currently in use areclassified using characteristic chemical properties of different portions of their molecules.Many classification algorithms are based on information entropy. When applying theseprocedures to sets of moderate size, an excessive number of results appear compatible withdata, and this number suffers a combinatorial explosion. However, after the equipartitionconjecture, one has a selection criterion between different variants resulting fromc…
The Rank of Trifocal Grassmann Tensors
2019
Grassmann tensors arise from classical problems of scene reconstruction in computer vision. Trifocal Grassmann tensors, related to three projections from a projective space of dimension k onto view-spaces of varying dimensions are studied in this work. A canonical form for the combined projection matrices is obtained. When the centers of projections satisfy a natural generality assumption, such canonical form gives a closed formula for the rank of the trifocal Grassmann tensors. The same approach is also applied to the case of two projections, confirming a previous result obtained with different methods in [6]. The rank of sequences of tensors converging to tensors associated with degenerat…
Contextuality Analysis of the Double Slit Experiment (With a Glimpse Into Three Slits)
2018
The Contextuality-by-Default theory is illustrated on contextuality analysis of the idealized double-slit experiment. The experiment is described by a system of contextually labeled binary random variables each of which answers the question: has the particle hit the detector, having passed through a given slit (left or right) in a given state (open or closed)? This system of random variables is a cyclic system of rank 4, formally the same as the system describing the EPR/Bell paradigm with signaling. Unlike the latter, however, the system describing the double-slit experiment is always noncontextual, i.e., the context-dependence in it is entirely explainable in terms of direct influences of…
Systematic conformational search analysis of the SRR and RRR epimers of 7-hydroxymatairesinol
2009
An extensive and systematic conformational search was performed on the two epimers of the natural lignan 7-hydroxymatairesinol (HMR), by means of a home-made Systematic Conformational Search Analysis (SCSA) code, designed to select more and more stable conformers through sequential geometry optimization of trial structures at increasing levels of calculation theory. In the present case, the starting molecular structures were selected by the semi-empirical AM1 method and filtered – i.e. decreased in number by choosing the more stable species – on the basis of their energy calculated by the HF method and the 6-31G(d) basis set. The geometries obtained were further refined by performing densit…
Missing Curious Fraction Problems
2018
In this paper we present a study of one of the best-known types of descriptive word fraction problems. These problems have disappeared from today’s textbooks but are hugely important for developing arithmetic thinking. The aim of this paper is to examine the historical solution methods for these problems and discuss the analytical readings suggested by the authors. On the basis of this analysis we have conducted a preliminary study of the performance of 35 Spanish students who are highly trained in mathematics. Our results show that these students have a preference for algebraic reasoning, are reluctant to use arithmetic methods, and have reading comprehension difficulties that are reflecte…
Polynomial numerical indices of 𝐶(𝐾) and 𝐿₁(𝜇)
2013
We estimate the polynomial numerical indices of the spaces C ( K ) C(K) and L 1 ( μ ) L_1(\mu ) .
Calculation of excitation energies from the CC2 linear response theory using Cholesky decomposition
2014
A new implementation of the approximate coupled cluster singles and doubles CC2 linear response model is reported. It employs a Cholesky decomposition of the two-electron integrals that significantly reduces the computational cost and the storage requirements of the method compared to standard implementations. Our algorithm also exploits a partitioning form of the CC2 equations which reduces the dimension of the problem and avoids the storage of doubles amplitudes. We present calculation of excitation energies of benzene using a hierarchy of basis sets and compare the results with conventional CC2 calculations. The reduction of the scaling is evaluated as well as the effect of the Cholesky …
On the intrinsic complexity of learning
1995
A new view of learning is presented. The basis of this view is a natural notion of reduction. We prove completeness and relative difficulty results. An infinite hierarchy of intrinsically more and more difficult to learn concepts is presented. Our results indicate that the complexity notion captured by our new notion of reduction differs dramatically from the traditional studies of the complexity of the algorithms performing learning tasks.
An implicitly parallel EDA based on restricted boltzmann machines
2014
We present a parallel version of RBM-EDA. RBM-EDA is an Estimation of Distribution Algorithm (EDA) that models dependencies between decision variables using a Restricted Boltzmann Machine (RBM). In contrast to other EDAs, RBM-EDA mainly uses matrix-matrix multiplications for model estimation and sampling. Hence, for implementation, standard libraries for linear algebra can be used. This allows an easy parallelization and leads to a high utilization of parallel architectures. The probabilistic model of the parallel version and the version on a single core are identical. We explore the speedups gained from running RBM-EDA on a Graphics Processing Unit. For problems of bounded difficulty like …
A New Method of Velocity Estimation Based on Variable Temporal Basis Using Incremental Encoder
1997
Abstract This paper deals with analysis and synthesis of algorithms for digital conditioning of signals generated by incremental encoders to estimate velocity of rotating devices for control purposes. Main objectives are to obtain high accuracy at low and high velocity and low tracking delays during accelerations. A digital conditioning method is described, Which uses a polynomial of order n whose coefficients are updated so as to fit the n+1 most recent velocity data acquired on a variable temporal basis. Digital sinlulations and experimental findings are shown with the ainl to validate the proposed estimation method and compare it with other methods.