Showing papers by "University of Waterloo published in 1972"

Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems

Abstract: This paper presents new algorithms for the maximum flow problem, the Hitchcock transportation problem, and the general minimum-cost flow problem. Upper bounds on the numbers of steps in these algorithms are derived, and are shown to compale favorably with upper bounds on the numbers of steps required by earlier algorithms. First, the paper states the maximum flow problem, gives the Ford-Fulkerson labeling method for its solution, and points out that an improper choice of flow augmenting paths can lead to severe computational difficulties. Then rules of choice that avoid these difficulties are given. We show that, if each flow augmentation is made along an augmenting path having a minimum number of arcs, then a maximum flow in an n-node network will be obtained after no more than ~(n a - n) augmentations; and then we show that if each flow change is chosen to produce a maximum increase in the flow value then, provided the capacities are integral, a maximum flow will be determined within at most 1 + logM/(M--1) if(t, S) augmentations, wheref*(t, s) is the value of the maximum flow and M is the maximum number of arcs across a cut. Next a new algorithm is given for the minimum-cost flow problem, in which all shortest-path computations are performed on networks with all weights nonnegative. In particular, this algorithm solves the n X n assigmnent problem in O(n 3) steps. Following that we explore a "scaling" technique for solving a minimum-cost flow problem by treating a sequence of derived problems with "scaled down" capacities. It is shown that, using this technique, the solution of a Iiitchcock transportation problem with m sources and n sinks, m ~ n, and maximum flow B, requires at most (n + 2) log2 (B/n) flow augmentations. Similar results are also given for the general minimum-cost flow problem. An abstract stating the main results of the present paper was presented at the Calgary International Conference on Combinatorial Structures and Their Applications, June 1969. In a paper by l)inic (1970) a result closely related to the main result of Section 1.2 is obtained. Dinic shows that, in a network with n nodes and p arcs, a maximum flow can be computed in 0 (n2p) primitive operations by an algorithm which augments along shortest augmenting paths. KEY WOl¢l)S AND PHP~ASES: network flows, transportation problem, analysis of algorithms CR CATEGOI{.IES: 5.3, 5.4, 8.3

Correlation Problems in Atomic and Molecular Systems. IV. Extended Coupled-Pair Many-Electron Theory and Its Application to the B H 3 Molecule

Abstract: The equations of the coupled-pair many-electron theory (CPMET) are extended to incorporate the effect of both unlinked and linked triexcited clusters. The minimal basis correlation energy of the B${\mathrm{H}}_{3}$ molecule in the ground state is calculated using the ordinary as well as extended CPMET in various degrees of approximation, and the relative importance of linked and unlinked triexcited clusters is studied. The results afford an unambiguous conclusion for closed-shell systems that, in contrast to the situation with tetraexcited states, unlinked triexcited clusters are negligible relative to the linked ones. It is shown that the extended CPMET reproduces the full configuration-interaction results to a very high degree of accuracy.

Distribution functions of multi-component fluid mixtures of hard spheres

Abstract: A simple algorithm for obtaining accurate pair distribution functions gij of hard-sphere mixtures is proposed. This generalizes the pure-fluid procedure of Verlet and Weis for improving the Percus-Yevick distribution functions. Two theorems are proved concerning the distribution functions yij =exp (uij/kT)gij , and an approximation for these functions is proposed. Finally, a method for computing direct correlation functions, given the pair distribution functions, is described.

Effectiveness factors for immobilized-enzyme reactions

Abstract: The effect of intraparticle diffusion in artificial membranes on the kinetic behavior of immobilized enzymes has been considered theoretically in terms of an effectiveness factor. When the immobilized enxymes obey a Michaelis-Menten relationship, an approximate equation is proposed for the effectiveness factor. For a substrate inhibited enzymatic reaction, the effectiveness factor may exceed unity and display multiple steady-state behavior. Thus, the over-all rate of reaction in the artificial membrane is faster in this case than that when the substrate concentration in the interior is at the same as that at the exterior surface. In the case of a product inhibited enzymatic reaction, the effectiveness factor is always less than that which corresponds to a Michaelis-Menten relationship. On a etudie theoriquement, en fonction d'un facteur d'efficacite, l'effet que produit la diffusion entre particules dans les membranes artificielles sur le comportement cinetique d'enzymes immobilisees. Lorsque les enzymes immobilisees obeissent a une relation de Michaelis et Menten, on propose une equation d'approximation pour le facteur d'efficacite. Dans le cas d'une reaction enzymatique inhibee par le substrat, le facteur d'efficacite peut ětre plus grand que 1 et indiquer un comportement de regimes permanents multiples; aussi, la vitesse globale de reaction dans la membrane artificielle est-elle plus considerable dans ce cas que lorsque la concentration du substrat a la surface interieure est la měme que celle qu'on note a la surface exterieure. Dans le cas d'une reaction enzymatique inhibee par un produit, le facteur d'efficacite est toujours moindre que celui qui correspond a une relation de Michaelis et Menten.

Codes over certain rings

Abstract: Given an integer m which is a product of distinct primes p i , a method is given for constructing codes over the ring of integers modulo m from cyclic codes over GF ( p i ). Specifically, if we are given a cyclic ( n , k i ) code over GF ( p i ) with minimum Hamming distance d i , for each i , then we construct a code of block length n over the integers modulo m with π i p k i i codewords, which is both linear and cyclic and has minimum Hamming distance min i d i .

The Universe as a Black Hole

Abstract: SINCE Einstein applied his general theory of relativity to study the structure of the universe as a whole1, cosmologists have wondered if the universe is geometrically closed or open. Neither theory nor observation has been able to settle this question unambiguously. Several authors have hoped that the universe may after all be a closed, yet unbounded, system. This would solve many problems regarding the nature and origin of the universe, and would fit many of the observations of distant sources made at radio, optical and other wavelengths2. Here I demonstrate that the universe may not only be a closed structure (as perceived by its inhabitants at the present epoch) but may also be a black hole, confined to a localized region of space which cannot expand without limit.

Implementing Clenshaw-Curtis quadrature, II computing the cosine transformation

Abstract: In a companion paper to this, “I Methodology and Experiences,” the automatic Clenshaw-Curtis quadrature scheme was described and how each quadrature formula used in the scheme requires a cosine transformation of the integrand values was shown. The high cost of these cosine transformations has been a serious drawback in using Clenshaw-Curtis quadrature. Two other problems related to the cosine transformation have also been troublesome. First, the conventional computation of the cosine transformation by recurrence relation is numerically unstable, particularly at the low frequencies which have the largest effect upon the integral. Second, in case the automatic scheme should require refinement of the sampling, storage is required to save the integrand values after the cosine transformation is computed.This second part of the paper shows how the cosine transformation can be computed by a modification of the fast Fourier transform and all three problems overcome. The modification is also applicable in other circumstances requiring cosine or sine transformations, such as polynomial interpolation through the Chebyshev points.

Predictive equations for self‐diffusion in liquids: A different approach

Abstract: Simple relationships have been obtained which can be used to predict self-diffusion coefficients of liquids with an average error of ±4%. In addition to the customary parameters, one of these equations contains the critical volume whereas the other uses Lennard-Jones potential parameters Both relations were derived by using a general relation between transport coefficients of pure fluids and a molecular-kinetic-model of liquids. No use has been made either of the Stokes-Einstein relation or the absolute rate theory. By applying the same relation between transport coefficients of pure fluids to gases, an equation has been obtained which can be used to calculate consistently molecular diameters in gases as a function of temperature, using Lennard-Jones potential parameters.

A directed-divergence function of type β*

Abstract: A new concept of directed-divergence function of type β is introduced in this paper This concept is used in obtaining a directed-divergence of type β which generalizes Kullback's directed-divergence and has a relation with REnyi's information-gain of order β This relation can be used to give another characterization of information-gain of order β A characterization theorem for the directed-divergence of type β is proved with the help of a functional equation

Graph-Theoretical Models for Pipe Network Analysis

Abstract: Graph-theoretic models were developed for the analysis of nonlinear pipe networks. Both symbolic formulation procedures as well as illustrative examples were presented. The topological information contained in the continuity equations together with the component characteristics are used to derive the minimum set of independent equations in a systematic manner. In contrast to conventional methods, the nonlinearities associated with components in the network are treated as an integral part of the formulation procedures and thus they do not require any special treatment. One of the main advantages of the graph-theoretic approach is that the formulation procedure is independent of the numerical technique used to solve the resulting set of nonlinear equations. In other words, once the equations are formulated, a suitable numerical method for solution can be chosen. The graph-theoretic formulation procedures are highly computer worthy.

Implementing Clenshaw-Curtis quadrature, I methodology and experience

Abstract: Clenshaw-Curtis quadrature is a particularly important automatic quadrature scheme for a variety of reasons, especially the high accuracy obtained from relatively few integrand values. However, it has received little use because it requires the computation of a cosine transformation, and the arithmetic cost of this has been prohibitive.This paper is in two parts; a companion paper, “II Computing the Cosine Transformation,” shows that this objection can be overcome by computing the cosine transformation by a modification of the fast Fourier transform algorithm. This first part discusses the strategy and various error estimates, and summarizes experience with a particular implementation of the scheme.

Phenotypic and Genetic Relations Between Initial Response to Electric Shock and Rate of Avoidance Learning in Mice

Abstract: The first experiment was designed to determine what proportion of the between-strain variation in rate of avoidance learning could be attributed to strain differences in sensitivity and response topography to electric shock. Measures of jumping at six shock intensities for four inbred strains were collected in a pretest of shock sensitivity. They were then used to derive a shock intensity for each strain which yielded the same amount of jumping for all strains. Avoidance training was administered to other mice of the same age and strains using the same apparatus and shock source as in the pretest. When training was given with a 180 pa shock, significant strain differences were observed in latency of the first escape and total errors to a learning criterion during both jump-out and one-way avoidance training. A large strain by training procedure interaction was found, as well. When training was administered with shock levels which yielded equal jumping in the pretest, strain differences in latency of the first escape were totally eliminated. However, the magnitude of strain differences in the rate of avoidance learning was not changed substantially. A second experiment examined two F1 hybrid strains and a four-way cross of the inbred strains tested in the first experiment. Results indicated that initial response to shock is characterized by intermediate inheritance, while rate of avoidance learning exhibits significant dominant inheritance. Although significant genetic differences in both initial response to shock and rate of avoidance learning were detected in the present experiments, it is concluded that the former cannot account for the latter.

A freezing core method for describing the vertical distribution of sediments in a streambed

Abstract: A new technique is described for obtaining in situ samples of substrate from stony streambeds, using liquid nitrogen to freeze the substrate around a standpipe driven into the bed. Various physical parameters are calculated for the substrate obtained. (10 refs.)

The Hadamard Maximum Determinant Problem

Abstract: (1972). The Hadamard Maximum Determinant Problem. The American Mathematical Monthly: Vol. 79, No. 6, pp. 626-630.

Real-Time Simulation of Multihead Tape Units

Abstract: The main result of this paper is that, given a Turing machine with several read-write heads per tape, one can effectively construct an equivalent multitape Turing machine with a single read-write head per tape, which runs at precisely the same speed. This result implies that serial storage may be used to handle files requiring several points of immediate two-way read-write access without interruptions for rewinds, etc. It also yields simplified proofs of several results in the literature of computational complexity.

The blending efficiencies of some impellers in batch mixing

Abstract: Mixing times for the blending of viscous liquids with tracer materials have been measured in a mechanically agitated tank using two conventional agitutor types (turbine, helical ribbon) and a series of novel tubular-type agitators. The range of conditions studied were: viscosity = 1 to 70,000 cP, agitator Reynolds number = 5 to 105, tank diameter = 11.5 in. It was found that in terms of agitator power requirement, the tubular agitators were generally more efficient for viscosities greater than 100cP than the others for the blending process. The effects of pseudoplastic non-Newtonian fluid behavior, of tank-baffles, and of tank size on mixing times have also been examined in several of the above cases.

Response of Large Stratified Lakes to Wind

Abstract: The response of a simple Great Lake model to wind stress is studied theoretically. The model is of constant depth and of circular shape, continuously stratified with a thermocline region of linear density distribution. The excitation of natural modes of oscillation is calculated for a suddenly imposed uniform wind stress and for one acting for a finite period. The results show that strong Kelvin-type (shore-bound) waves are generated in the first few baroclinic modes, which give rise to “coastal jets” of a width of order 5 km and less, the combination of several baroclinic modes resulting in a complex structure for these jets. In the central portions of the lake model the response consists of Poincare-type waves of near-inertial frequency. The qualitative features of the theoretical results agree quite well with observational evidence from the Great Lakes.

Simplified computer-aided analysis of double-diffused transistors including two-dimensional high-level effects

Abstract: An approximate two-dimensional numerical analysis has been developed for studying double- (or triple-) diffused transistors. The program supplies dc and hf terminal characteristics (e.g., h fe , r bb , f T , I B , V BE ) over a wide range of operating collector currents and voltages for a given set of physical device parameters (mask dimensions, impurity profile, etc.). The approach is based on obtaining a set of differential equations describing current flow in the longitudinal (emitter-collector) direction and a separate differential equation describing current flow in the lateral direction. The assumption is made of space-charge or space-charge-neutral regions with current- and voltage-dependent boundaries. The equations are valid for arbitrary injection levels and automatically include such high-level effects as conductivity modulation, base widening, and emitter current crowding. Both theoretical and experimental results are given for transistors with f T values between 100 MHz and 3 GHz. The validity of the approach is confirmed and some areas requiring further study are outlined. The technique described is felt to be particularly attractive for the design and optimization of high-power microwave devices, due to the small computer execution time and memory requirements.

History of Nevada

Abstract: When the first edition of History of Nevada was published in 1973, the critics wrote: 'This is an immensely absorbing book about a ruggedly beautiful and wholly intriguing state' - "American West". 'The appearance of History of Nevada is a major event in Nevada historiography' - Richard C. Lillard, "Nevada Historical Society Quarterly". 'Well-written, extensively documented and carefully indexed, [this work] is a valuable contribution for the study of a state too often mentioned only for gold and silver rushes, atomic bomb testing, or the opulent honky tonk of Las Vegas and its ilk' - "Pacific Historian".This updated edition of "History of Nevada" is still the most comprehensive one-volume economic, political, and social history of a state that was once thought of as "a bridge to somewhere else." It will be welcomed by students and general readers. Russell R. Elliott is the author of "Nevada's Twentieth-Century Mining Boom", and William D. Rowley is the author of "U.S. Forest Service Grazing" and "Rangelands: A History". Elliott is a professor of history emeritus and Rowley a professor of history at the University of Nevada-Reno.