On Coherent Conditional Probabilities and Disintegrations

Existence of coherent extensions of coherent conditional probabilities is one of the major merits of de Finetti's theory of probability. However, coherent extensions which meet some special property, like -additivity or disintegrability, can fail to exist. An example is given where a coherent and -additive conditional probability cannot be extended preserving both -additivity and coherence. Motivated by such example, conditions are provided in order that a coherent and -additive conditional probability admits a coherent and -additive extension. Moreover, conditions are given for the existence of disintegrations, possibly -additive, of a probability along a partition.     

Probabilistic analysis of the application of the cross ratio to model based vision: Misclassification

The cross ratio of four colinear points is of fundamental importance in model based vision, because it is the simplest numerical property of an object that is invariant under projection to an image. It provides a basis for algorithms to recognise objects from images without first estimating the position and orientation of the camera.A quantitative analysis of the effectiveness of the cross ratio in model based vision is made. A given imageI of four colinear points is classified by making comparisons between the measured cross ratio of the four image points and the cross ratios stored in the model database. The imageI is accepted as a projection of an objectO with cross ratio if |–|ntu, wheren is the standard deviation of the image noise,t is a threshold andu=. The performance of the cross ratio is described quantitatively by the probability of rejectionR, the probability of false alarmF and the probability of misclassificationp (), defined for two model cross ratios , . The trade off between these different probabilities is determined byt.It is assumed that in the absence of an object the image points have identical Gaussian distributions, and that in the presence of an object the image points have the appropriate conditional densities. The measurements of the image points are subject to small random Gaussian perturbations. Under these assumptions the trade offs betweenR,F andp () are given to a good approximation byR=2(1–(t)),F=r _F t, t|–|^–1, where is the relative noise level, is cumulative distribution function for the normal distribution,r _F is constant, ande is a function of only. The trade off betweenR andF is obtained in Maybank (1994). In this paper the trade off betweenR andp () is obtained.It is conjectured that the general form of the above trade offs betweenR,F andp () is the same for a range of invariants useful in model based vision. The conjecture prompts the following definition: an invariant which has trade offs betweenR,F,p () of the above form is said to benon-degenerate for model based vision.The consequences of the trade off betweenR andp () are examined. In particular, it is shown that for a fixed overall probability of misclassification there is a maximum possible model cross ratio _m , and there is a maximum possible numberN of models. Approximate expressions for _m andN are obtained. They indicate that in practice a model database containing only cross ratio values can have a size of order at most ten, for a physically plausible level of image noise, and for a probability of misclassification of the order 0.1.     

Low-Rank Approximation of Integral Operators by Interpolation

A central component of the analysis of panel clustering techniques for the approximation of integral operators is the so-called -admissibility condition min {diam(),diam()} 2dist(,) that ensures that the kernel function is approximated only on those parts of the domain that are far from the singularity. Typical techniques based on a Taylor expansion of the kernel function require a subdomain to be far enough from the singularity such that the parameter has to be smaller than a given constant depending on properties of the kernel function. In this paper, we demonstrate that any is sufficient if interpolation instead of Taylor expansionisused for the kernel approximation, which paves the way for grey-box panel clustering algorithms.     

Sampling from binomial and poisson distributions: A method with bounded computation times

An accurate acceptance-rejection algorithm is devised and tested. The procedure requires an average of less than 3 uniform deviates whenever the standard deviation of the distribution is at least 4, and this number decreases monotonically to 2.63 as . Variable parameters are permitted, and no subroutines for sampling from other statistical distributions are needed.This research was supported by the Austrian Research Council (Fonds zur Förderung der wissenschaftlichen Forschung).     

Multiscale Connected Operators

Among the major developments in Mathematical Morphology in the last two decades are the interrelated subjects of connectivity classes and connected operators. Braga-Neto and Goutsias have proposed an extension of the theory of connectivity classes to a multiscale setting, whereby one can assign connectivity to an object observed at different scales. In this paper, we study connected operators in the context of multiscale connectivity. We propose the notion of a -connected operator, that is, an operator connected at scale . We devote some attention to the study of binary -grain operators. In particular, we show that families of -grain openings and -grain closings, indexed by the connectivity scale parameter, are granulometries and anti-granulometries, respectively. We demonstrate the use of multiscale connected operators with image analysis applications. The first is the scale-space representation of grayscale images using multiscale levelings, where the role of scale is played by the connectivity scale. Then we discuss the application of multiscale connected openings in granulometric analysis, where both size and connectivity information are summarized. Finally, we describe an application of multiscale connected operators to an automatic target recognition problem.Ulisses Braga-Neto received the Baccalaureate degree in Electrical Engineering from the Universidade Federal de Pernambuco (UFPE), Brazil, in 1992, the Masters degree in Electrical Engineering from the Universidade Estadual de Campinas, Brazil, in 1994, the M.S.E. degree in Electrical and Computer Engineering and the M.S.E. degree in Mathematical Sciences, both from The Johns Hopkins University, in 1998, and the Ph.D. degree in Electrical and Computer Engineering, from The Johns Hopkins University, in 2001. He was a Post-Doctoral Fellow at the University of Texas MD Anderson Cancer Center and a Visiting Scholar at Texas A&M University, from 2002 to 2004. He is currently an Associate Researcher at the Aggeu Magalhães Research Center of the Osvaldo Cruz Foundation, Brazilian Ministry of Health. His research interests include Bioinformatics, Pattern Recognition, Image Analysis, and Mathematical Morphology.     

Formalizing Strong Normalization Proofs of Explicit Substitution Calculi in ALF

The past decade has given rise to a number of explicit substitution calculi. An important question of explicit substitution calculi is that of the termination of the underlying calculus of substitution. Proofs of termination of substitutions fall in two categories: those that are easy because a decreasing measure can be established and those that are difficult because such a decreasing measure is not easy to establish. This paper considers two styles of explicit substitution: and s, for which different termination proof methods apply. The termination of s is guaranteed by a decreasing weight, while a decreasing weight for showing the termination of has not yet been found. These termination methods for and s are formalized in the proof checker ALF. During our process of formally checking the termination of and s we comment on what is needed to make a proof formally checkable.     

Simple adaptive stabilization of output feedback stabilizable distributed parameter systems

We show that the simple universal adaptive control lawu(t)=N(k(t))y(t)=|y(t)| ², withN(k)=(logk) cos((logk)) and 3+<1, stabilizes all detectable and stabilizable infinite dimensional systems of Pritchard-Salamon type which are externally stabilized by somescalar output feedback. The same controller is also shown to stabilize time varying systems satisfying the same type of output feedback stabilizability.     

Technical Update: Least-Squares Temporal Difference Learning

TD./ is a popular family of algorithms for approximate policy evaluation in large MDPs. TD./ works by incrementally updating the value function after each observed transition. It has two major drawbacks: it may make inefficient use of data, and it requires the user to manually tune a stepsize schedule for good performance. For the case of linear value function approximations and = 0, the Least-Squares TD (LSTD) algorithm of Bradtke and Barto (1996, Machine learning, 22:1–3, 33–57) eliminates all stepsize parameters and improves data efficiency.This paper updates Bradtke and Barto's work in three significant ways. First, it presents a simpler derivation of the LSTD algorithm. Second, it generalizes from = 0 to arbitrary values of ; at the extreme of = 1, the resulting new algorithm is shown to be a practical, incremental formulation of supervised linear regression. Third, it presents a novel and intuitive interpretation of LSTD as a model-based reinforcement learning technique.     

Coordinating Multiple Agents via Reinforcement Learning

In this paper, we attempt to use reinforcement learning techniques to solve agent coordination problems in task-oriented environments. The Fuzzy Subjective Task Structure model (FSTS) is presented to model the general agent coordination. We show that an agent coordination problem modeled in FSTS is a Decision-Theoretic Planning (DTP) problem, to which reinforcement learning can be applied. Two learning algorithms, coarse-grained and fine-grained, are proposed to address agents coordination behavior at two different levels. The coarse-grained algorithm operates at one level and tackle hard system constraints, and the fine-grained at another level and for soft constraints. We argue that it is important to explicitly model and explore coordination-specific (particularly system constraints) information, which underpins the two algorithms and attributes to the effectiveness of the algorithms. The algorithms are formally proved to converge and experimentally shown to be effective.     

Implementing the ‘Fool's model’ of combinatory logic

This paper studies Fool's models of combinatory logic, and relates them to Hindley's D-completeness problem. A fool's model is a family of sets of formulas, closed under condensed detachment. Alternatively, it is a model ofCL in naive set theory. We examine Resolution; and the P-W problem. A sequel shows T is D-complete; also, its extensions. We close with an implementation FMO of these ideas.     

Duality in Quantum Information Geometry

Let H be a separable Hilbert space. We consider the manifold M consisting of density operators on H such that ^p is of trace class for some p (0, 1). We say M is nearby if there exists C > 1 such that C ^–1C. We show that the space of nearby points to can be furnished with the two flat connections known as the (±)-affine structures, which are dual relative to the BKM metric. We furnish M with a norm making it into a Banach manifold.     

Complexity classes and theories of finite models

LetL ^* be accepted in timef(n) by a nondeterministic Turing machine. Then there is a monadic existential second-order sentence in the language of + such that for everyx^*,xL if and only if a certain structureU _x ^f of cardinalityf(|x|) satisfies . It follows that ifL is accepted in nondeterministic timen ^d, d a natural number, then there is a sentence whose relational symbols ared-ary or less, whose finite spectrum isL. This research was partially supported by NSF Grants MCS78-01832 and MCS-8002695.     

A sublinear algorithm for approximate keyword searching

Given a relatively short query stringW of lengthP, a long subject stringA of lengthN, and a thresholdD, theapproximate keyword search problem is to find all substrings ofA that align withW with not more than D insertions, deletions, and mismatches. In typical applications, such as searching a DNA sequence database, the size of the databaseA is much larger than that of the queryW, e.g.,N is on the order of millions or billions andP is a hundred to a thousand. In this paper we present an algorithm that given a precomputedindex of the databaseA, finds rare matches in time that issublinear inN, i.e.,N ^c for somec<1. The sequenceA must be overa. finite alphabet . More precisely, our algorithm requires 0(DN ^pow() logN) expected-time where =D/P is the maximum number of differences as a percentage of query length, and pow() is an increasing and concave function that is 0 when =0. Thus the algorithm is superior to current O(DN) algorithms when is small enough to guarantee that pow() < 1. As seen in the paper, this is true for a wide range of , e.g., . up to 33% for DNA sequences (¦¦=4) and 56% for proteins sequences (¦¦=20). In preliminary practical experiments, the approach gives a 50-to 500-fold improvement over previous algorithms for prolems of interest in molecular biology.This work was supported in part by the National Institutes of Health under Grant R01 LM04960-01 and the Aspen Center for Physics.     

Least Squares Policy Evaluation Algorithms with Linear Function Approximation

We consider policy evaluation algorithms within the context of infinite-horizon dynamic programming problems with discounted cost. We focus on discrete-time dynamic systems with a large number of states, and we discuss two methods, which use simulation, temporal differences, and linear cost function approximation. The first method is a new gradient-like algorithm involving least-squares subproblems and a diminishing stepsize, which is based on the -policy iteration method of Bertsekas and Ioffe. The second method is the LSTD() algorithm recently proposed by Boyan, which for =0 coincides with the linear least-squares temporal-difference algorithm of Bradtke and Barto. At present, there is only a convergence result by Bradtke and Barto for the LSTD(0) algorithm. Here, we strengthen this result by showing the convergence of LSTD(), with probability 1, for every [0, 1].     

Context-free text grammars

A text is a triple=(, ₁, ₂) such that is a labeling function, and ₁ and ₂ are linear orders on the domain of ; hence may be seen as a word (, ₁) together with an additional linear order ₂ on the domain of . The order ₂ is used to give to the word (, ₁) itsindividual hierarchical representation (syntactic structure) which may be a tree but it may be also more general than a tree. In this paper we introducecontext-free grammars for texts and investigate their basic properties. Since each text has its own individual structure, the role of such a grammar should be that of a definition of a pattern common to all individual texts. This leads to the notion of ashapely context-free text grammar also investigated in this paper.     

Shape optimization of elasto-plastic bodies under plane strains: Sensitivity analysis and numerical implementation

Optimal shape design problems for an elastic body made from physically nonlinear material are presented. Sensitivity analysis is done by differentiating the discrete equations of equilibrium. Numerical examples are included.Notation U ^ad set of admissible continuous design parameters - U _h ^ad set of admissible discrete design parameters - function fromU _h ^ad defining shape of body - _h function fromU _h ^ad defining approximated shape of body - vector of nodal values of _h - { _n} sequence of functions tending to - () domain defined by - K bulk modulus - shear modulus - penalty parameter for contact condition - V() space of virtual displacements in() - V _h(_h) finite element approximation ofV() - J cost functional - J _h discretized cost functional - J algebraic form ofJ _h - (u) stress tensor - e(u) strain tensor - K stiffness matrix - f force vector - b(q) term arising from nonlinear boundary conditions - q vector of nodal degrees of freedom - p vector of adjoint state variables - J Jacobian of isoparametric mapping - |J| determinant ofJ - N vector of shape function values on parent element - L matrix of shape function derivatives on parent element - G matrix of Cartesian derivatives of shape functions - X matrix of nodal coordinates of element - D matrix of elastic coefficients - B strain-displacement matrix - _P part of boundary where tractions are prescribed - _u part of boundary where displacements are prescribed - variable part of boundary - strain invariant     

Hierarchies of polynomially solvable satisfiability problems

In this paper, we introduce general techniques for extending classes of polynomially solvable SAT instances. We generalize the approach of Gallo and Scutellà, who defined the hierarchy { _i }, where _l corresponds to the Generalized Horn class. We propose a family of polynomial hierarchies, where a polynomial hierarchy { _i } is a sequence of polynomially solvable classes that cover the whole set of CNF formulas, and such that _{i i+1} fori0. Following a different approach, based on a new decomposition technique, we define the class of Split-Horn formulas, which is an extension of _l. We discuss and compare the basic properties of the proposed classes; polynomial time algorithms for recognition and solution are provided.     

Organisational development issues and the implementation of the Clean Technology paradigm in industry

Environmental protection activities in industry have rapidly increased in number over the last years. Additionally, surveys of environmental activities have identified a change in the kind or in the approaches used to environmental problem solving. A new paradigm Clean Technology has been developed which gradually seems to replace the Clean-up Technology paradigm and the older Dilute and Disperse paradigm. The new Clean Technology paradigm brings with it not only a new way of looking at environmental protection, but also a range of rules guiding the application of technology and the design of technological systems. This paper presents a few case studies highlighting and evaluating Clean Technology activities.     

Is Solar System Stable? A Remark

It is not yet known (1997) whether the Solar system is stable or not. Common belief is that the Solar system is stable if and only if it is not a resonant system, i.e., whenever its orbital frequencies i satisfy an inequality | nii| for i|ni| N; a similar inequality is true for randomly chosen frequencies. In this paper, we show that the Solar system does not have such resonances, and therefore (if the above-mentioned belief is correct), it is stable.     

Exact Linear Thermodynamic Evolution Equations from the Robertson Formalism

A linear evolution equation for a thermodynamic variable F, odd under time-reversal, is obtained from the exact equation derived by Robertson from the Liouville equation for the information-theoretic phase-space distribution. One obtains an exact expression for , the relaxation time for F. For very short , is time-independent for t > if C(t) F{exp(-i t)}Fo, the equilibrium time correlation, decays exponentially for t > . is the Liouville operator. So long as C(t) is such that decays rapidly to a steady-state value, the t limit of agrees with the fluctuation-dissipation theorem in applications to fluid transport.