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*Please note that Lecture 4 is unavailable in a higher quality format. Instructor/speaker: Prof. Gilbert Strang View the complete course at: http://ocw.mit.edu/1806S05 This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. License: Creative Commons BYNCSA More information at http://ocw.mit.edu/terms...
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Topic: systems of equations, vector spaces, positive definite matrices, matrix theory, linear algebra,...
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This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
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Topic: systems of equations, vector spaces, positive definite matrices, matrix theory, linear algebra,...
A simulated field of gravity anomalies and secondorder gradients is used to study the recovery of gravity anomalies at ground level from measurements at flight level. The spectral properties of gravimetric quantities simulated by an array of mass points are discussed for first and second order gradients and some rules are derived for generating such fields. To study the effect of observational errors, uncorrelated normally distributed errors and correlated errors from a stationary Markov...
Topics: DTIC Archive, Schwarz,KlausPeter, OHIO STATE UNIV COLUMBUS DEPT OF GEODETIC SCIENCE, *COMPUTERIZED...
This paper studies the stationary covariance generation problem, i.e. the problem of passing from a stationary covariance function to a dynamical system which generates a process having the given covariance, in the case where the dynamical system is a finite state, continuous time, Markov process. Strictly positive definite stationary covariances can be approximated to any degree of accuracy in this way. However the number of states required may approach infinity as the covariance approaches...
Topics: DTIC Archive, Brockett,Roger W, HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS,...
To assess the effectiveness of shortterm training programs for senior national security officials, research is being conducted on two fronts. First there is the research that is required to develop a program that can serve as a suitable model, i.e. the new Harvard Executive Program in National Security. Second is that which is required to assess how effectively the program meets its basic objectives. The research to support the program itself primarily involves the development of appropriate...
Topics: DTIC Archive, Johnston, Jr, Douglas M, JOHN F KENNEDY SCHOOL OF GOVERNMENT CAMBRIDGE MA,...
Analysis of remote tower forward scatter meter measurements of extinction coefficient collected at the Air Force Geophysics Laboratory Weather Test Facility at Otis AFB, Massachusetts demonstrated the accuracy of a remote tower slant visual range (SVR) system. This report describes the final phase of the development and evaluation of a tower SVR system in which the remote tower approach has been extended to include Category I operations. Tests give additional evidence that the runway visual...
Topics: DTIC Archive, Geisler,Edward B, AIR FORCE GEOPHYSICS LAB HANSCOM AFB MA, *VISIBILITY, *AIRCRAFT...
A structural multilevel model is presented in which some of the variables cannot be observed directly but are measured using tests or questionnaires. Observed dichotomous or ordinal politicos response data serve to measure the latent variables using an item response theory model. The latent variables can be defined at any level of the multilevel model. A Bayesian procedure, the Markov Chain Monte Carlo (MCMC) procedure, to estimate all parameters simultaneously is presented. It is shown that...
Topics: ERIC Archive, Bayesian Statistics, Estimation (Mathematics), Item Response Theory, Markov...
A Ceiling/Visibility Simulation Model (WEASIM) is described to be a resident weather simulator within larger host simulation models. The weather generates synthetic observations of ceiling and visibility at multiple locations. WEASIM preserves the unconditional probabilities of occurrence of ceiling and visibility, as well as the temporal, spatial, and crossvariable correlations. The Ceiling/Visibility simulation Model is 'tuned' to a particular geographic area by inputing modelling...
Topics: DTIC Archive, Berecek,Emil M, AIR FORCE ENVIRONMENTAL TECHNICAL APPLICATIONS CENTER SCOTT AFB IL,...
Partial Contents (Abstracts Only): New Developments in the Statistical Theory of Shape; Domains of Attraction for a Family of Processes Between Suprema and Sums; Ergodicity and Inequalities for Certain Point Processes; The Role of Poisson's Equation in SteadyState Simulation Output Analysis; Quick Simulations of Networks of GI/G/1 Queues; Prophet Inequalities and Related Problems of Optimal Stopping; ReactionDiffusion Equations with Small Parameter: Probabilistic Approach; Stochastic Flow...
Topics: DTIC Archive, Iglehart, Donald L, STANFORD UNIV CA, *COMBINATORIAL ANALYSIS, *QUEUEING THEORY,...
The analysis of log data generated by online educational systems is an important task for improving the systems, and furthering our knowledge of how students learn. This paper uses previously unseen log data from Edulab, the largest provider of digital learning for mathematics in Denmark, to analyse the sessions of its users, where 1.08 million student sessions are extracted from a subset of their data. We propose to model students as a distribution of different underlying student behaviours,...
Topics: ERIC Archive, ERIC, Hansen, Christian Hansen, Casper Hjuler, Niklas Alstrup, Stephen Lioma,...
A technique to study combined influence of environmental and genetic factors on the base of changes in phenotype distributions is presented. Histograms are exploited as base analyzed characteristics. A continuous time, discrete state Markov process with piecewise constant interstate transition rates is associated with evolution of each histogram. The technique was applied to IQ longitudinal data (6 and 14year children) and made it possible to draw conclusions concerning development of...
Topics: ERIC Archive, Psychological Characteristics, Markov Processes, Intelligence Quotient, Genetics,...
This report summarizes the results of research produced under this grant, and lists titles of papers produced. (Author)
Topics: DTIC Archive, Kushner,Harold J, BROWN UNIV PROVIDENCE RI LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS,...
The research performed under this grant successfully developed a method for determining an optimal stateage dependent replacement policy for a semiMarkov shock model. Comparisons between the method developed here and the standard policy iteration approach show a significant improvement in computer speed and memory requirements. (Author)
Topics: DTIC Archive, Feldman,Richard M, TEXAS A AND M UNIV COLLEGE STATION DEPT OF INDUSTRIAL ENGINEERING,...
Networks of queues occur frequently in diverse applications. In particular, they are widely used in studies of computer and communication system performance as models for the interactions among system resources. This monograph deals with mathematical and statistical methods for discrete event simulation of networks of queues. The emphasis is on methods for the estimation of general characteristics of 'passage times' in closed networks. Informally, a passage time is the time for a job to...
Topics: DTIC Archive, Iglehart,Donald L, STANFORD UNIV CA DEPT OF OPERATIONS RESEARCH, *QUEUEING THEORY,...
The results of the reliability and availability analyses of the individual S and Xband travelingwave maser (TWM) assemblies and their operational configurations in the 70meter antennas of NASA's Deep Space Network (DSN) are described. For the period 1990 through 1991, the TWM availability parameters for the Telemetry Data System are: mean time between failures (MTBF), 930 hr; mean time to restore services (MTTRS), 1.4 hr; and the average availability, 99.85 percent. In previously published...
Topics: NASA Technical Reports Server (NTRS), AVAILABILITY, FAILURE ANALYSIS, PERFORMANCE PREDICTION,...
We describe an approach for exploiting structure in Markov Decision Processes with continuous state variables. At each step of the dynamic programming, the state space is dynamically partitioned into regions where the value function is the same throughout the region. We first describe the algorithm for piecewise constant representations. We then extend it to piecewise linear representations, using techniques from POMDPs to represent and reason about linear surfaces efficiently. We show that for...
Topics: NASA Technical Reports Server (NTRS), DYNAMIC PROGRAMMING, MARKOV PROCESSES, DECISION THEORY,...
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Häggström, Olle
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ix, 114 p. : 24 cm
Topics: Markov processes, Algorithms
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International Symposium on SemiMarkov Processes and Their Applications (1984 : Brussels, Belgium)
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Topics: Markov processes  Congresses, Renewal theory  Congresses
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Barbu, Vlad Stefan
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xiii, 224 p. : 24 cm
Topics: Markov processes, Reliability (Engineering)  Mathematical models, DNA  Analysis  Mathematical...
A firstorder stochastic difference equation with random coefficients is shown to have a solution which makes the marginal distribution of the stationary sequence generated by the equation a convex mixture of two exponential distributions. This Markovian process should be broadly applicable in stochastic modelling in operations analysis. Moreover it can be extended quite simply to a mixed exponential process with mixed pthorder autoregressive and qthorder moving average correlation structure....
Topics: DTIC Archive, Lawrance,A J, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *DIFFERENCE EQUATIONS, *TIME...
In models of reliability growth in stages, it is usual to assume that system parameters improve monotonically from stage to stage, following some postulated law of growth. This paper explores a Bayesian model where such improvement only occurs on the average, e.g., a case when the parameters are assumed to be stochastically ordered. It is shown that the problem can be recast into a hierarchical form in which there are strictlyordered hyperparameters which index the admissible family of ordered...
Topics: DTIC Archive, Jewell,William S, CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER, *STOCHASTIC...
The problem of partitioning a timeseries into segments is considered. The segments fall into classes, which may correspond to phases of a cycle (recession, recovery, expansion in the business cycle) or to portions of a signal obtained by scanning (background/ clutter, target, background/clutter again, another target, etc.), or normal tissue, tumor, normal tissue in medical applications. A probability distribution is associated with each class of segment. Parametric families of distributions...
Topics: DTIC Archive, Sclove,Stanley L, ILLINOIS UNIV AT CHICAGO CIRCLE, *Images, *Time series analysis,...
Given a time inhomogeneous Markov transition semigroup P(s/t) (x,dy) and an entrance rule m = (m sub t) satisfying m sub s P(s/t) or = m sub t, Kuznetsov constructed a measure o sub m on path space so that the coordinate maps are Markovian with semigroup P (s/t) and so that the process is born according to the entrance rule m. Kuznetosov's approach was a Kolmogorov type construction. The authors give a new approach based on standard Markov process theory and a new analytic proof of the...
Topics: DTIC Archive, Getoor,R K, FLORIDA UNIV GAINESVILLE DEPT OF MATHEMATICS, *OPERATORS(MATHEMATICS),...
We characterize the sets of positive states and null states for nonsingular Markov processes and, more generally, for positive contractions in L sub 1. The set P of positive states is an invariant set and carries all finite invariant measures which are absolutely continuous with respect to a given measure mu, the initial distribution.
Topics: DTIC Archive, Krengel,Ulrich, UNIVERSITY OF CALIFORNIA, BERKELEY BERKELEY United States, markov...
Let x sub t (t = 1,2,..) be a stationary Gaussian Markov process of order one with E(x sub t) = mu and Cov(x sub t, x sub t + k) = rho to the k power. We derive a prediction interval for x sub 2n + 1 based on the preceding 2n observations x sub 1, x sub 2,...,x sub 2n. (Author)
Topics: DTIC Archive, Jayachandran,Toke, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *LINEAR REGRESSION...
Statistical cost control decisions may be based on two competing decision models. The Markovian Control model controls a process by investigating the process whenever the reported cost exceeds a fixed critical limit. The Bayesian Control model controls a process by using the reported cost to update the probability of the process being incontrol and investigate the process whenever such posterior probability is less than a fixed critical value. This paper compares the relative effectiveness of...
Topics: DTIC Archive, Song,Soo sup, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *DECISION MAKING, *COST...
A variety of stochastic models in reliability were studied. Approximations in renewal theory and continuous time Markov chains were obtained by analyzing the relevant stochastic process at a gamma distributed rather than a fixed time. Some statistical problems related to software reliability were considered. Keywords: Reliability, Simulation, Continuous time markov chains, Renewal processes, Stochastic models.
Topics: DTIC Archive, Ross, Sheldon M, CALIFORNIA UNIV BERKELEY DEPT OF INDUSTRIAL ENGINEERING AND...
Computer network security is a very serious concern in many commercial, industrial, and military environments. This paper proposes a new computer network security approach defined by self organized agent swarms (SOMAS) which provides a novel computer network security management framework based upon desired overall system behaviors. The SOMAS structure evolves based upon the partially observable Markov decision process (POMDP) formal model and the more complex InteractivePOMDP and...
Topics: DTIC Archive, AIR FORCE INST OF TECH WRIGHTPATTERSON AFB OH SCHOOL OF ENGINEERING AND MANAGEMENT,...
This is the second of three technical reports describing a methodology for projecting the future availability of Air Force personnel and analyzing the potential impacts of personnel policy changes. Developed within the Air Force Human Resources Laboratory's Project 1959, 'Advanced System for the Human Resources Support of Weapon System Development,' the methodology will provide the Air Force with an increased capability for considering the human resources requirements of weapon systems in terms...
Topics: DTIC Archive, Goclowski,John C, DYNAMICS RESEARCH CORP WILMINGTON MASS, *PERSONNEL MANAGEMENT, *AIR...
The paper presents an analysis of the phased array radar allocation demands, when tracking highly maneuverable antiship missiles (ASM) using a collocated radar/IRST sensor combination. The motion of the ASM is modelled using the quantized acceleration levels. The principal aim of this analysis is to determine an upper bound on the average radar update time. This bound follows from a CramerRao type error bound for the estimation of linear jump Markov dynamic systems [1]. Given a dynamic motion...
Topics: DTIC Archive, DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION MELBOURNE (AUSTRALIA), *PHASED ARRAYS,...
We present a heuristicbased propagation algorithm for solving restricted Markov decision processes (MDPs). Our approach, which combines ideas from deterministic search and recent dynamic programming methods, focuses computation towards promising areas of the state space. It is thus able to significantly reduce the amount of processing required in producing a solution. We present a number of results comparing our approach to existing algorithms on a robotic path planning domain.
Topics: DTIC Archive, CARNEGIEMELLON UNIV PITTSBURGH PA ROBOTICS INST, *MARKOV PROCESSES, *DYNAMIC...
In this project we perform theoretical studies of 3dimensional cosmic ray propagation in magnetic field configurations of the Galaxy with an extended halo. We employ our newly developed Markov stochastic process methods to solve the diffusive cosmic ray transport equation. We seek to understand observations of cosmic ray spectra, composition under the constraints of the observations of diffuse gamma ray and radio emission from the Galaxy. The model parameters are directly are related to...
Topics: NASA Technical Reports Server (NTRS), COSMIC RAYS, INTERSTELLAR MAGNETIC FIELDS, GALACTIC HALOS,...
This is the fifth in a series of reports concerned with developing probability models for the analysis of raodom urinalysis programs. A Markov daily testing model was developed. The distributions of the time to detection and the number of tests to detection were derived as a function of the daily testing rate and the conditional probability of testing positive. Deterrence functions are defined and examples are given. When the testing rate has no deterrent effect on drug use, the average time to...
Topics: DTIC Archive, Boyle, James P., NAVY PERSONNEL RESEARCH AND DEVELOPMENT CENTER SAN DIEGO CA, *DRUGS,...
A methodology for evaluating the military payoffs of adding various advanced equipments to the baseline SSN716 was developed. This report addresses an effort directed at improving and extending the SSN evaluation models dealing with two areas of SSN performance including: (1) SSN effectiveness in an area clearance mission, (2) SSN effectiveness in multiple engagement scenarios. Area clearance is characterized by the existence of a specific geographic ocean area which must be cleared of enemy...
Topics: DTIC Archive, SUMMIT RESEARCH CORP GAITHERSBURG MD, *ATTACK SUBMARINES, *NAVAL OPERATIONS,...
Ground vehicle classification is performed using hidden Markov modelling of cepstral coefficients. The hidden Markov model (HMM) is used to represent audio signals. These signals are obtained as the vehicles travel past audio sensor arrays. Well known HMM training algorithms are applied to train models from training data. The trained models are used in two classification rules: the MAP rule, and a listbased rule due to Forney. Under some general assumptions, these approaches can be regarded as...
Topics: DTIC Archive, Roberts, William J, ATLANTIC COAST TECHNOLOGIES INC SILVER SPRING MD,...
The performance of the Concert Multiprocessor is investigated using probabilistic models. Analysis proceeds by decomposing Concert along its natural hierarchies into a Multibus subsystem and a Ringbus subsystem. Each subsystem is modeled in isolation ignoring the interactions between subsystems. A series of Multibus models is developed based on a very simple processor model and some simplifying assumptions. These models are analyzed using Markov chains and queueing theory. Ways to relax some of...
Topics: DTIC Archive, Osborne,Randy B, MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR COMPUTER SCIENCE,...
Recently the MultiLevel algorithm was introduced as a general purpose solver for the solution of steady state Markov chains. In this paper we consider the performance of the MultiLevel algorithm for solving Nearly Completely Decomposable (NCD) Markov chains, for which specialpurpose interactive aggregation/disaggregation algorithms such as the KouryMcAllister Stewart (KMS) method have been developed that can exploit the decomposability of the Markov chain. We present experimental results...
Topics: DTIC Archive, Leutenegger, Scott T, INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING...
We propose a method for choosing the number of colors., or true gray levels, in an image. This is motivated by medical and satellite image segmentation, and may also be useful for color and gray scale image quantization, the display and storage of computergenerated holograms, and the use of cooccurrence matrices for assessing texture in images. Our underlying probability model is a hidden Markov random field. Each number of colors considered is viewed as corresponding to a statistical model...
Topics: DTIC Archive, Stanford, Derek C, WASHINGTON UNIV SEATTLE DEPT OF STATISTICS, *COLORS, *IMAGES,...
"NPS5582034."
Topics: Markov processes, Iterative methods (Mathematics), Decision making, Algorithms
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vi, 373 p. : 25 cm
Topics: Probabilities  Congresses, Quantum theory  Congresses, Stochastic processes  Congresses,...
The purpose of this thesis is to firstly analyze the determinants on the survival of United States Marine Corps Officers, and secondly, to develop the methodology to optimize the accessions of prior and nonprior enlisted officers. Using data from the Marine Corps Officer Accession Career file (MCCOAC), the Cox Proportional Hazards Model is used to estimate the effects of officer characteristics on their survival as a commissioned officer in the USMC. A Markov model for career transition is...
Topics: Markov processes, Recruiting and enlistment, Quality of life, Attrition, Accession, Commissioning...
We consider the problem of classifying an unknown probability distribution based on a sequence of random samples drawn according to this distribution. Specifically, if A is a subset of the space of all probability measures M1(sigma) over some compact Polish space E, we want to decide whether or not the unknown distribution belongs to A or its complement. We propose an algorithm which leads a.s. to a correct decision for any A satisfying certain structural assumptions. A refined decision...
Topics: DTIC Archive, Zeitouni, Ofer, PRINCETON UNIV NJ DEPT OF ELECTRICAL ENGINEERING, *PROBABILITY...
In this paper we report on the various techniques that we implemented in order to improve the basic speech recognition performance of the BYBLOS system. Some of these methods are new, while others are not. We present methods that improved performance as well as those that did not. The methods include Linear Discriminant Analysis, Supervised Vector Quantization, Shared Mixture VQ. Deleted Estimation of Context Weights, MMI Estimation Using NBest Alternatives, CrossWord Triphone Models. While...
Topics: DTIC Archive, Austin, Steve, BBN SYSTEMS AND TECHNOLOGIES CORP CAMBRIDGE MA, *SPEECH RECOGNITION,...
The project has produced new computational models and algorithms for coordination, prediction and planning in situations involving multiple decision makers that operate over an extended period of time in either collaborative or adversarial domains. This includes the development of the decentralized partiallyobservable Markov decision process (DECPOMDP) model, memorybounded algorithm for solving finitehorizon DECPOMDPs, sparse representations of agent strategies using finitestate...
Topics: DTIC Archive, Zilberstein, Shlomo, MASSACHUSETTS UNIV AMHERST, *DECISION MAKING, *ALGORITHMS,...
We consider the restless multiarmed bandit (RMAB) problem with unknown dynamics. In this problem, at each time, a player chooses K out of N (N K) arms to play. The state of each arm determines the reward when the arm is played and transits according to Markovian rules no matter the arm is engaged or passive. The Markovian dynamics of the arms are unknown to the player. The objective is to maximize the longterm reward by designing an optimal arm selection policy. The performance of a policy is...
Topics: DTIC Archive, CALIFORNIA UNIV DAVIS DEPT OF ELECTRICAL AND COMPUTER ENGINEERING, *MARKOV PROCESSES,...
This research is in response to a request by the Marine Aviation Detachment at Naval Air Station Patuxent River, MD. Currently, no manpower planning tools exist for force shaping of the Marine Corps Acquisition Community. This thesis creates a force shaping and forecasting tool for Marine Corps manpower planners. The tool assists planners in forecasting inventory levels across rank and Military Occupational Specialty combinations and in determining the most robust force structure for the...
Topics: DTIC Archive, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *ACQUISITION, *MARINE CORPS PLANNING, *MARKOV...
We propose a family of efficient algorithms for learning the parameters of a Bayesian network from incomplete data. Our approach is based on recent theoretical analyses of missing data problems, which utilize a graphical representation called the missingness graph. In the case of MCAR and MAR data, this graph need not be explicit, and yet we can still obtain closed form asymptotically consistent parameter estimates without the need for inference. When this missingness graph is explicated (based...
Topics: DTIC Archive, CALIFORNIA UNIV LOS ANGELES DEPT OF COMPUTER SCIENCE, *BAYES THEOREM, *LEARNING...
A mathematical model, using semi Markov Processes, is suggested for the career paths of military officers. The model consists of a rectangular array of nodes with rows representing activity types and columns representing successive tours. Thus each billet of an officer is described by an activity type and a tour number. The duration of such a billet, called a tourlength, is considered fixed, given the activity type and the tour number. Transitions from activities in one tour to activities in...
Topics: DTIC Archive, Milch, Paul R, NAVAL POSTGRADUATE SCHOOL MONTEREY CA, *OFFICER PERSONNEL, *NAVAL...
As humans, we develop the ability to identify people by their voice at an early age. Getting computers to perform the same task has proven to be an interesting problem. Speaker recognition involves two applications, speaker identification and speaker verification. Both applications are examined in this effort. Two methods are employed to perform speaker recognition. The first is an enhancement of hidden Markov models. Rather than alter some part of the model itself, a singlelayer perceptron is...
Topics: DTIC Archive, Zeek, Erik J, AIR FORCE INST OF TECH WRIGHTPATTERSON AFB OH, *MARKOV PROCESSES,...
This research focused on the problem of providing military commanders with realtime, optimal control of military airtoground operations for a 24hour segment of a Joint Air Operations (JAO) campaign. In particular, we focused on developing control algorithms that anticipate possible airtoground mission modifications due to uncertain future events, thereby generating missions that can be readily adapted in the presence of contingencies. The primary benefit of this technology is agile and...
Topics: DTIC Archive, Logan, David, ALPHATECH INC BURLINGTON MA, *MILITARY OPERATIONS, *ADAPTIVE CONTROL...