In this paper we give a computer proof of a new polynomial identity, which extends a recent result of Alladi and the first author. In addition, we provide computer proofs for new finite analogs of Jacobi and Euler for...
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In this paper we give a computer proof of a new polynomial identity, which extends a recent result of Alladi and the first author. In addition, we provide computer proofs for new finite analogs of Jacobi and Euler formulas. All computer proofs are done with the aid of the new computer algebra package qMultiSum developed by the second author. qMultiSum implements an algorithmic refinement of Wilf and Zeilberger's multi-q-extension of Sister Celine's technique utilizing additional ideas of Verbacten and Wegschaider. (C) 2002 Elsevier Science (USA).
A primary goal of quantum computer science is to find an explanation for the fact that quantum computers are more powerful than classical computers. In this paper I argue that to answer this question is to compare alg...
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A primary goal of quantum computer science is to find an explanation for the fact that quantum computers are more powerful than classical computers. In this paper I argue that to answer this question is to compare algorithmic processes of various kinds and to describe the possibility spaces associated with these processes. By doing this, we explain how it is possible for one process to outperform its rival. Further, in this and similar examples little is gained in subsequently asking a how-actually question. Once one has explained how-possibly, there is little left to do.
Atrial fibrillation (AF) is a common cardiac arrhythmia, but its mechanisms are incompletely understood. The identification of phase singularities (PSs) has been used to define spiral waves involved in maintaining the...
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Atrial fibrillation (AF) is a common cardiac arrhythmia, but its mechanisms are incompletely understood. The identification of phase singularities (PSs) has been used to define spiral waves involved in maintaining the arrhythmia, as well as daughter wavelets. In the past, PSs have often been identified manually. Automated PS detection algorithms have been described previously, but when we attempted to apply a previously developed algorithm we experienced problems with false positives that made the results difficult to use directly. We therefore developed a tool for PS identification that uses multiple strategies incorporating both image analysis and mathematical convolution for automated detection with optimized sensitivity and specificity, followed by manual verification. The tool was then applied to analyze PS behavior in simulations of AF maintained in the presence of spatially distributed acetylcholine effects in cell grids of varying size. These analyses indicated that in almost all cases, a single PS lasted throughout the simulation, corresponding to the central-core tip of a single spiral wave that maintained AF. The sustained PS always localized to an area of low acetylcholine concentration. When the grid became very small and no area of low acetylcholine concentration was surrounded by zones of higher concentration, AF could not be sustained. The behavior of PSs and the mechanisms of AF were qualitatively constant over an 11.1-fold range of atrial grid size, suggesting that the classical emphasis on tissue size as a primary determinant of fibrillatory behavior may be overstated. (C) 2002 American Institute of Physics.
Background Artificial intelligence (AI) is increasingly being used in medical practice. Especially in the image-based diagnosis of skin cancer, AI shows great potential. However, there is a significant discrepancy bet...
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Background Artificial intelligence (AI) is increasingly being used in medical practice. Especially in the image-based diagnosis of skin cancer, AI shows great potential. However, there is a significant discrepancy between expectations and true relevance of AI in current dermatological practice. Objectives This article summarizes promising study results of skin cancer diagnosis by computer-based diagnostic systems and discusses their significance for daily practice. We hereby focus on the analysis of dermoscopic images of pigmented and unpigmented skin lesions. Materials and methods A selective literature search for recent relevant trials was conducted. The included studies used machine learning, and in particular "convolutional neural networks", which have been shown to be particularly effective for the classification of image data. Results and conclusions In numerous studies, computer algorithms were able to detect pigmented and nonpigmented neoplasms of the skin with high precision, comparable to that of dermatologists. The combination of the physician's assessment and AI showed the best results. computer-based diagnostic systems are widely accepted among patients and physicians. However, they are still not applicable in daily practice, since computer-based diagnostic systems have only been tested in an experimental environment. In addition, many digital diagnostic criteria that help AI to classify skin lesions remain unclear. This lack of transparency still needs to be addressed. Moreover, clinical studies on the use of AI-based assistance systems are needed in order to prove its applicability in daily dermatologic practice.
A new algorithm is described for the simulation of the organization processes that lead from an isotropic liquid to a crystal structure. The algorithm is based on a hybrid, pseudo-Monte Carlo technique that lets a mol...
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A new algorithm is described for the simulation of the organization processes that lead from an isotropic liquid to a crystal structure. The algorithm is based on a hybrid, pseudo-Monte Carlo technique that lets a molecular assembly evolve under Metropolis conditions subject to forcing the decrease of asymmetry parameters that quantify the deviation from intermolecular alignment. This procedure was applied to the simulation of the liquid-solid transformation in n-hexane. Starting from liquid n-hexane with a significant population of gauche molecular conformations, a crystalline molecular assembly with parallel all-trans aliphatic chains is generated. This structure is very similar to the real crystal structure, except for a small difference in molecular orientation within layers. The process apparently involves an activation energy of a few kJ mol(-1) and a very minor volume activation that could be associated with density fluctuations due to the need for extra space as long molecules undergo a large conformational rearrangement. Although some detailed quantitative aspects of the simulation may be open to discussion, this is one of the very few examples of individuation of a continuous all-atom trajectory linking the liquid and the solid state of a large polyatomic molecule. The results confirm the viability of the symmetry bias for the generation of new crystal structures, and provide valuable working hypotheses on the mechanism of crystallization.
Background and study aims: Early neoplasia in Barrett's esophagus is difficult to detect and often overlooked during Barrett's surveillance. An automatic detection system could be beneficial, by assisting endo...
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Background and study aims: Early neoplasia in Barrett's esophagus is difficult to detect and often overlooked during Barrett's surveillance. An automatic detection system could be beneficial, by assisting endoscopists with detection of early neoplastic lesions. The aim of this study was to assess the feasibility of a computer system to detect early neoplasia in Barrett's esophagus. Patients and methods: Based on 100 images from 44 patients with Barrett's esophagus, a computer algorithm, which employed specific texture, color filters, and machine learning, was developed for the detection of early neoplastic lesions in Barrett's esophagus. The evaluation by one endoscopist, who extensively imaged and endoscopically removed all early neoplastic lesions and was not blinded to the histological outcome, was considered the gold standard. For external validation, four international experts in Barrett's neoplasia, who were blinded to the pathology results, reviewed all images. Results: The system identified early neoplastic lesions on a per-image analysis with a sensitivity and specificity of 0.83. At the patient level, the system achieved a sensitivity and specificity of 0.86 and 0.87, respectively. A trade-off between the two performance metrics could be made by varying the percentage of training samples that showed neoplastic tissue. Conclusion: The automated computer algorithm developed in this study was able to identify early neoplastic lesions with reasonable accuracy, suggesting that automated detection of early neoplasia in Barrett's esophagus is feasible. Further research is required to improve the accuracy of the system and prepare it for real-time operation, before it can be applied in clinical practice.
This paper presents a multimodal network design model with a computer algorithm to solve it. The selection of link improvements in the network is assumed to affect practical capacities as well as mean free times. The ...
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This paper presents a multimodal network design model with a computer algorithm to solve it. The selection of link improvements in the network is assumed to affect practical capacities as well as mean free times. The equilibrium flows and the modal shares are affected accordingly. The improvements are assumed to be continuous variables with concave marginal costs. This provided a good approximation for the behaviour of the discrete model. The algorithm is based on Hooke and Jeeves' Optimization Methodology which requires a solution of a multimodal equilibrium assignment problem for each functional evaluation. The algorithm is implemented in such a way that only some functional evaluations need a solution of an equilibrium problem, implying efficiency for large-scale problems. Computational results show that although flow congestion decreased due to link improvements, modal shares may change towards private users. The latter contributes to congestion again and possibly makes the overall decrease in congestion less significant. [ABSTRACT FROM AUTHOR]
This paper applies mathematical ideas which arise from differential geometry and control theory to computer programming theory. For the sake of simplicity, most questions of logic and language are put to the side. A c...
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This paper applies mathematical ideas which arise from differential geometry and control theory to computer programming theory. For the sake of simplicity, most questions of logic and language are put to the side. A computer program is regarded as a collection of data, considered as a collection of cross-sections of a fiber space whose base is a discrete space. These distinguished cross-sections are called the trajectories of the computer program system. For the simplest von Neumann type of program, the base space is the nonnegative integers: The trajectories may then often be thought of as the orbits of a discretetime dynamical system. Feedback control theory enters when one attempts to provide a ‘rational’ way of generating such dynamical systems, satisfying certain conditions, such as termination and correctness. The greatest common divisor and bubble sort programs — standard examples in computer science textbooks — are treated as models for the development of a general theory.
Geometrically, we will also consider them as the discrete analogue of what are called path systems in differential geometry. These examples can also be treated as the analogue of closed-loop feedback control systems — themselves a sort of path system — that are ‘driven’ to the final answer by a process that is similar to the way that Lyapunov theory is used in the linear regulator problem of control theory. This use of the Lyapunov ideas of dynamical system theory gives a technique for proving the correctness and termination of some programs. In order to provide a mathematical structure to a programming theory that is, in some sense, analogous to the group-theoretic structure of fiber bundle differential geometry, an algebraic structure of a category which acts on the fiber space is associated with such programs. The computation of the binomial coefficients will also be treated as an example of a system of partial difference equations, leading to the description of some features of concur
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