Probability set functions

A probability set function is interpretable as a probability distribution on binary sequences of fixed length. Cumulants of probability set functions enjoy particularly simple properties which make them more manageable than cumulants of general random variables. We derive some identities satisfied by cumulants of probability set functions which we believe to be new. Probability set functions may be expanded in terms of their cumulants. We derive an expansion which allows the construction of examples of probability set functions whose cumulants are arbitrary, restricted only by their absolute values. It is known that this phenomenon cannot occur for continuous probability distributions. Some particular examples of probability set functions are considered, and their cumulants are computed, leading to a conjecture on the upper bound of the values of cumulants. Moments of probability set functions determined by arithmetical conditions are computed in a final example.Dedicated to our friend, W.A. Beyer. Financial support for this work was derived from the U.S.D.O.E. Human Genome Project, through the Center for Human Genome Studies at Los Alamos National Laboratory, and also through the Center for Nonlinear Studies, Los Alamos National Laboratory, LANL report LAUR-97-323.     

Derivative evaluation and computational experience with large bilevel mathematical programs

A bilevel program is a mathematical program involving functions defined implicitly as solutions to another mathematical program. We discuss a method for extracting derivative information on the implicit function, which is especially efficient when the lower-level problem has simple bounds on the variables and/or many inactive constraints. Computational experience on problems with up to 230 variables and 30 constraints is presented.Computational support from Robert Bivins and Myron Stein is gratefully acknowledged. We have also appreciated comments from Jon Bard and an anonymous referee. This work was supported in part by the US Department of Energy through the Los Alamos National Laboratory.     

Belavkin-Kolokoltsov watchdog effects in interactively controlled stochastic computer-graphic dynamic systems

The results of investigating the stochastic properties of the long-term behavior of a continuously observed (and interactively controlled) quantum-field top are reported. Applications for interactively controlled stochastic dynamic computer-graphics systems are discussed.A preliminary English version of the given paper is contained in the Los Alamos National Laboratory Electronic Archive on Adaptation and Self-organization under number adap-org/9410001 (October, 1994).Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 2, pp. 333–352, February, 1996.     

Ergodic computations with continued fractions and Jacobi's algorithm

Ergodic computational aspects of the Jacobi algorithm, a generalization to two dimensions of the continued fraction algorithm, are considered. By means of such computations the entropy of the algorithm is estimated to be 3.5. An approximation to the invariant measure of the transformation associated with the algorithm is obtained. The computations are tested by application to the continued fraction algorithm for which both entropy and the invariant measure are known.Work partly performed under the auspices of the U.S. Atomic Energy Commission while one of the authors (M.S.W.) was a faculty participant of the Associated Western Universities at Los Alamos Scientific Laboratory. The work was also supported in part by NSF grant GP-28313 to M. S. W.     

A two-dimensional intake manifold flow simulation

A computer flow model of an intake manifold of a four cylinder engine has been developed using a computational fluid dynamic code. This code is base on the Conchas-Spray code developed at the Los Alamos National Laboratory. The flow inside the intake manifold is assumed to be two-dimensional, unsteady, compressible, and turbulent. A simple subgrid scale (SGS) turbulence model and hypothetical boundary conditions are employed in the simulation. Atmospheric pressure is specified at the inlet and the velocities are specified at the outlets of the manifold, together with the law of the wall at all the wall boundaries. Numerical results of the simulation are presented in the form of velocity, pressure, density, and temperature fields. The model is designed in such a way that different manifold geometries may be simulated with ease. A simulation of a concept manifold “the loop-manifold” is also presented.     

Convergence rates and convergence-order profiles for sequences

We investigate a number of methods of measuring convergence rates of sequences. We clarify the relationships between these different measures of convergence rates. We present eight such measurement methods and demonstrate almost all relations among them (with two open problems remaining). We also present the notion of convergence-order profiles for sequences.The work upon which this report is based was done at the Los Alamos National Laboratory, Theoretical Division. It was supported by the U.S. Department of Energy and by grants to the second author from Associated Western Universities, Inc. and from the University of Louisville.     

Simulation of free surface flows in a distributed memory environment

A parallel technique, for a distributed memory machine, based on domain decomposition for solving the Navier-Stokes equations in cartesian and cylindrical coordinates in two dimensions with free surfaces is described. It is based on the code by Tome and McKee (J. Comp. Phys. 110 (1994) 171–186) and Tome (Ph.D. Thesis, University of Strathclyde, Glasgow, 1993) which in turn is based on the SMAC method by Amsden and Harlow (Report LA-4370, Los Alamos Scientific Laboratory, 1971), which solves the Navier-Stokes equations in three steps: The momentum and Poisson equations and particle movement. These equations are discretized by explicit and 5-point finite differences. The parallelization is performed by splitting the computation domain into vertical panels and assigning each of these panels to a processor. All the computation can then be performed using nearest neighbour communication. Test runs comparing the performance of the parallel with the serial code, and a discussion of the load balancing question are presented. PVM is used for communication between processes.     

An asymptotic analysis of two-phase fluid mixing

We study the motion of the slightly compressible multi-phase flow model proposed by Chen, Glimm, Sharp and Zhang. The interface velocity and constitutive law are analyzed by derivation of the exact quantity. Using singular perturbation theory, a formal asymptotic expansion is derived for the solution of the compressible equations. An asymptotic analysis in the incompressible limit, for slightly compressible flows supplies important new information to resolve nonuniqueness of the pressure difference between the two fluid species of the incompressible flow equations.Supported in part by the U.S. Department of Energy DE-FG02-90ER25084, DE-FG02-989ER2536, DE-FG03-98DP00206, the National Science Foundation DMS-0102480, the Army Research Office grant DAAD19-01-0642 and Los Alamos National Laboratory.Supported in part by the Clay Mathematics Institute.     

Nonexistence of spatially localized free vibrations for a class of nonlinear wave equations

We prove the nonexistence of free vibrations of arbitrary period with polynomially decreasing profiles for a large class of nonlinear wave equations in one space dimension Our class of admissible models includes examples of non integrable wave equations with certain polynomial nonlinearities, as well as examples of completely integrable ones with exponential nonlinearities related to Mikhailov's equations. Our result thus proves a particular case of a conjecture first formulated by Eleonskii, Kulagin, Novozhilova and Silin, and dispels some confusion regarding the relationship between the existence of so-called breather-solutions and the complete integrability of the wave equation. Our class of admissible nonlinearities also contains a particular instance of the nonlinear scalar Higgs' equation, but does not contain the Sine-Gordon equation which is known to possess a 2π-periodic solution in time with exponential fall-off in the spatial direction. Our results may be considered as complementary to recent results by Coron and Weinstein. Our arguments are entirely global, and rest upon methods from the calculus of variations. Work supported in part by the Los Alamos National Laboratory under contract COL-2335, by a University of Texas summer grant and by the ETH-Forschungsinstitut für Mathematik.     

Global convergence for Newton methods in mathematical programming

In constrained optimization problems in mathematical programming, one wants to minimize a functionalf(x) over a given setC. If, at an approximate solutionx _n , one replacesf(x) by its Taylor series expansion through quadratic terms atx _n and denotes byx _n+1 the minimizing point for this overC, one has a direct analogue of Newton's method. The local convergence of this has been previously analyzed; here, we give global convergence results for this and the similar algorithm in which the constraint setC is also linearized at each step.This research was supported in part by the Office of Naval Research, Contract No. N00014-67-0126-0015, and was presented by invitation at the Fifth Gatlinburg Symposium on Numerical Algebra, Los Alamos, New Mexico, 1972.     

Sets pooling designs

Pooling desings have previously been used for the efficient identification of distinguished elements of a finite setU. Group testing underlies these designs: For any , a binary result is obtainable, indicating whether or not the number of distinguished elements included inS is zero. The current generalization of pooling designs will enable the efficient identification of distinguished subsets of a finite setU. In this case, for any , a binary result is obtainable, indicating whether or not the number of distinguished subsets included inS is zero. Such designs are called sets pooling designs, comprising standard pooling designs in the special case where all the distinguished subsets are elements. The new designs are similar to the standard designs but are subject to new constraints because the set of subsets included inS is its power set. To illustrate the feasibility of constructing sets pooling designs, random, non-adaptive designs are investigated for the special case where all distinguished subsets have the same size. An optimum probability for including an object in a pool is approximated as a function of the size and number of distinguished subsets, adopting the criterion of minimizing the average number of non-distinguished subsets whose status would not be resolved by the pooling design. Deterministic and adaptive designs are also described.This work was supported by the US Department of Energy under contract W-7405-ENG-36, through a Laboratory Directed Research and Development Grant at Los Alamos National Laboratory.     

Approximation algorithms for the test cover problem

In the test cover problem a set of m items is given together with a collection of subsets, called tests. A smallest subcollection of tests is to be selected such that for each pair of items there is a test in the selection that contains exactly one of the two items. It is known that the problem is NP-hard and that the greedy algorithm has a performance ratio O(log m). We observe that, unless P=NP, no polynomial-time algorithm can do essentially better. For the case that each test contains at most k items, we give an O(log k)-approximation algorithm. We pay special attention to the case that each test contains at most two items. A strong relation with a problem of packing paths in a graph is established, which implies that even this special case is NP-hard. We prove APX-hardness of both problems, derive performance guarantees for greedy algorithms, and discuss the performance of a series of local improvement heuristics. Partially supported by the Future and Emerging Technologies Programme of the EU under contract number IST-1999-14186 (ALCOM-FT).Partially supported by a Merck Computational Biology and Chemistry Program Graduate Fellowship from the Merck Company Foundation.Also Iceland Genomics CorporationPartially supported by subcontract No. 16082-RFP-00-2C in the area of ``Combinatorial Optimization in Biology (XAXE),' Los Alamos National Laboratories, and NSF grant CCR-0105548.Mathematics Subject Classification: 90B27     

A model of professional competences in mathematics to update mathematical and didactic knowledge of teachers

This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels in urban and rural public schools of Region de Los Lagos and Region de Los Rios of southern Chile. To that effect, and by means of an advanced training project based on a professional competences model, didactic interventions based on types of problems and types of mathematical competences with analysis of contents and learning assessment were designed. The teachers’ competence regarding the didactic strategy used and its results, as well as the students’ learning achievements are specified. The project made possible to validate a strategy of lifelong improvement in mathematics, based on the professional competences of teachers and their didactic transposition in the classroom, as an alternative to consolidate learning in areas considered vulnerable in two regions of the country.     

Identification of parameters in nonlinear boundary-value problems

This paper presents a method for identification of parameters in nonlinear boundary-value problems. The successive approximations technique proposed uses the theory of Lagrange multipliers and the Newton-Raphson method. This method does not require storage of functions and is quadratically convergent. Numerical results are presented.This research was sponsored by the National Institutes of Health, Grant No. GM-16197-01. Computing assistance was obtained from the Health Sciences Computing Facility, University of California at Los Angeles, NIH Grant No. FR-3.     

Pairing stochastic processes

This paper studies stochastic distributed parameter systems with stochastic inputs. It defines the pairing of two stochastic processes; the Ito stochastic integral is a particular kind of pairing.This paper was presented at the 4th IFIP Symposium, Los Angeles, California, 1971.     

Parameter estimation from non-normal modes of soil-structure interaction

The damping in soil-structure interaction problems is known to be not proportional; thus, the mode shapes are not normal. Parameters may be estimated, however, including those associated with damping, if use is made of phase angle information. Two examples of this interaction are considered. In the first example, a one-story relatively flexible building, the interaction coefficients are estimated. Soil parameters are identified in a second example of a stiff structure modeling a nuclear reactor containment vessel. Modal information is used in both instances.This research was sponsored by the National Research Council of Canada. The author would like to thank Gary C. Hart for inviting him to visit the Mechanics and Structures Department of the University of California, Los Angeles, California, for the period in which this work was done.     

Lower semicontinuous solutions for a class of Hamilton-Jacobi-Bellman equations

The present paper is concerned with the study of a Hamilton-Jacobi-Bellman equation in finite-dimensional spaces, from both the point of view of l.s.c. viscosity solutions and the point of view of l.s.c. contingent solutions. The results have been used in the study of the uniqueness problem for the Bellman equation associated to a time-optimal control problem (Ref. 1).This paper was completed while the author was visiting the University of California at Los Angeles as a Fulbright Scholar.     

Frontier analysis in air pollution

Carbon containing aerosol is the most abundant particulate air pollutant species. It causes poor visibility and can be toxic. Tracing its origins is an important step in environmental management and control. This study analyses the carbon concentrations at Duarte, CA (a suburban site near Los Angeles) and in Lennox, CA (a site next to a Los Angeles freeway). Concentrations inside a tunnel are also available and used to derive a motor vehicle emission profile. A new approach is proposed for calculating the motor vehicle contribution to organic carbon and the amount of background carbon found at these two sites. Regression analysis provides insight in the formation of organic carbon and frontier analysis is used to calculate the motor vehicle contribution to organic carbon and the amount of background carbon in the atmosphere. The information obtained from this analysis can be used in the regulation of motor vehicle emissions and in air pollution control.     

Controllability of semilinear systems

The most general results known about controllability of semilinear systems are found in Refs. 1 and 2. The authors of these papers used different approaches, and no connection between them has ever been pointed out. The purpose of this paper is to present a general theorem under which these results easily follow.This paper is taken from a chapter of the author's doctoral thesis written at University of California, Los Angeles, California.     

Convexification procedures and decomposition methods for nonconvex optimization problems

In order for primal-dual methods to be applicable to a constrained minimization problem, it is necessary that restrictive convexity conditions are satisfied. In this paper, we consider a procedure by means of which a nonconvex problem is convexified and transformed into one which can be solved with the aid of primal-dual methods. Under this transformation, separability of the type necessary for application of decomposition algorithms is preserved. This feature extends the range of applicability of such algorithms to nonconvex problems. Relations with multiplier methods are explored with the aid of a local version of the notion of a conjugate convex function.This work was carried out at the Coordinated Science Laboratory, University of Illinois, Urbana, Illinois, and was supported by the National Science Foundation under Grant ENG 74-19332.