The computer-derivation of thermodynamic equations Part III. Chemical systems

An algorithm, THERMODER4, based on Jacobians, is presented for automating the symbolic derivation of expressions for thermodynamic derivatives for chemical systems, to complement algorithms given previously for unrestricted simple and complex systems. The algorithm is implemented by a program using an augmented computer-algebra system together with a microcomputer. Examples are given to illustrate the use of the algorithm in transforming variables and in sensitivity analysis for systems at equilibrium.     

Two Dimensional Aggregation Procedure: An Alternative to the Matrix Algebraic Algorithm

The aggregation procedure is an important theoretical and empirical topic of economics. It appears in the Microeconomics and Macroeconomics, in Panel and Cross-Sectional Data Analysis, in Data Mining Analysis, in Input–Output and Agent-based Computational Economics Modelling. The question of the choice of algorithm is became important since the size of the sample data has became more important, and despite of the speed of the computers. In this paper we present the “classical” algorithm (the “matrix algebraic” one) of aggregation of the two-dimensional sample data, and compare it to the alternative algorithms (the “vectorial” one) we developed. Then we present some extensions to the multidimensional aggregation.      

Graphical fault tree analysis for fatal falls in the construction industry

The current study applied a fault tree analysis to represent the causal relationships among events and causes that contributed to fatal falls in the construction industry. Four hundred and eleven work-related fatalities in the Taiwanese construction industry were analyzed in terms of age, gender, experience, falling site, falling height, company size, and the causes for each fatality. Given that most fatal accidents involve multiple events, the current study coded up to a maximum of three causes for each fall fatality. After the Boolean algebra and minimal cut set analyses, accident causes associated with each falling site can be presented as a fault tree to provide an overview of the basic causes, which could trigger fall fatalities in the construction industry. Graphical icons were designed for each falling site along with the associated accident causes to illustrate the fault tree in a graphical manner. A graphical fault tree can improve inter-disciplinary discussion of risk management and the communication of accident causation to first line supervisors.     

Groebner基在分次代数中的应用

运用Groebner基理论，给出了K－代数A在阶滤子下和两个分次代数gr^c(A)与A的算法关系。     

Tridiagonalization of a dense symmetric matrix on multiple GPUs and its application to symmetric eigenvalue problems

For software to fully exploit the computing power of emerging heterogeneous computers, not only must the required computational kernels be optimized for the specific hardware architectures but also an effective scheduling scheme is needed to utilize the available heterogeneous computational units and to hide the communication between them. As a case study, we develop a static scheduling scheme for the tridiagonalization of a symmetric dense matrix on multicore CPUs with multiple graphics processing units (GPUs) on a single compute node. We then parallelize and optimize the Basic Linear Algebra Subroutines (BLAS)‐2 symmetric matrix‐vector multiplication, and the BLAS‐3 low rank symmetric matrix updates on the GPUs. We demonstrate the good scalability of these multi‐GPU BLAS kernels and the effectiveness of our scheduling scheme on twelve Intel Xeon processors and three NVIDIA GPUs. We then integrate our hybrid CPU‐GPU kernel into computational kernels at higher‐levels of software stacks, that is, a shared‐memory dense eigensolver and a distributed‐memory sparse eigensolver. Our experimental results show that our kernels greatly improve the performance of these higher‐level kernels, not only reducing the solution time but also enabling the solution of larger‐scale problems. Because such symmetric eigenvalue problems arise in many scientific and engineering simulations, our kernels could potentially lead to new scientific discoveries. Furthermore, these dense linear algebra algorithms present algorithmic characteristics that can be found in other algorithms. Hence, they are not only important computational kernels on their own but also useful testbeds to study the performance of the emerging computers and the effects of the various optimization techniques. Copyright © 2013 John Wiley & Sons, Ltd.     

Modeling power and energy consumption of dense matrix factorizations on multicore processors

In this paper, we propose a model for the energy consumption of the concurrent execution of three key dense matrix factorizations, with task parallelism leveraged via the Symmetric Multi‐Processing Superscalar (SMPSs) runtime, on a multicore processor. Our model decomposes the power dissipation into the system, static and dynamic components, with the former two being estimated from basic, off‐line experiments. The dynamic power, on the other hand, requires significantly more care, and we introduce a contention‐aware model that accommodates for the variability of power consumption due to memory contention. Experimental results on an Intel Xeon E5504 processor with four cores, using an internal powermeter that samples the power drawn by the mainboard with a frequency of 1 KHz, show the reliability of the energy model for the Cholesky, LU, and QR factorizations on this platform. Copyright © 2013 John Wiley & Sons, Ltd.     

Final Coalgebras And a Solution Theorem for Arbitrary Endofunctors

Every endofunctor F of Set has an initial algebra and a final coalgebra, but they are classes in general. Consequently, the endofunctor F^∞ of the category of classes that F induces generates a completely iterative monad T. And solutions of arbitrary guarded systems of iterative equations w.r.t. F exist, and can be found in naturally defined subsets of the classes TY.More generally, starting from any category , we can form a free cocompletion ^∞ of under small-filtered colimits (e.g., Set^∞ is the category of classes), and we give sufficient conditions to obtain analogous results for arbitrary endofunctors of .     

Robbins algebra: Conditions that make a near-boolean algebra boolean

Some problems posed years ago remain challenging today. In particular, the Robbins problem, which is still open and which is the focus of attention in this paper, offers interesting challenges for attack with the assistance of an automated reasoning program; for the study presented here, we used the program OTTER. For example, when one submits this problem, which asks for a proof that every Robbins algebra is a Boolean algebra, a large number of deduced clauses results. One must, therefore, consider the possibility that there exists a Robbins algebra that is not Boolean; such an algebra would have to be infinite. One can instead search for properties that, if adjoined to those of a Robbins algebra, guarantee that the algebra is Boolean. Here we present a number of such properties, and we show how an automated reasoning program was used to obtain the corresponding proofs. Additional properties have been identified, and we include here examples of using such a program to check that the corresponding hand-proofs are correct. We present the appropriate input for many of the examples and also include the resulting proofs in clause notation.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.     

A portable implementation of a modular multiprocessing database programming language

This paper introduces the database programming language RAPP, which is an integration of the data type relation and relational algebraic operations with the modular multiprocessing language Pascal Plus. A portable version of the RAPP compiler has been implemented and is described.     

Axiomatisations of functional dependencies in the presence of records,lists, sets and multisets

We investigate functional dependencies in databases that support complex values such as records, lists, sets and multisets. Therefore, an abstract algebraic framework is proposed that classifies data models according to the underlying types they support. This allows to emphasise the impact of the data types rather than the specifics of a particular data model.