Universal stabilization of a class of nonlinear systems with homogeneous vector fields

Under relative-degree-one and minimum-phase assumptions, it is well known that the class of finite-dimensional, linear, single-input (u), single-output (y) systems (A,b,c) is universally stabilized by the feedback strategy u = Λ(λ)y, λ = y², where Λ is a function of Nussbaum type (the terminology “universal stabilization” being used in the sense of rendering /s(0/s) a global attractor for each member of the underlying class whilst assuring boundedness of the function λ(·)). A natural generalization of this result to a class ^k of nonlinear control systems (a,b,c), with positively homogeneous (of degree k 1) drift vector field a, is described. Specifically, under the relative-degree-one (cb ≠ 0) and minimum-phase hypotheses (the latter being interpreted as that of asymptotic stability of the equilibrium of the “zero dynamics”), it is shown that the strategy u = Λ(λ)/vby/vb^k−1y, assures ^k-universal stabilization. More generally, the strategy u = Λ(λ)exp(/vby/vb)y, assures -universal stabilization, where = _{k 1} ^k.     

Collecting Statistics over Runtime Executions

By collecting statistics over runtime executions of a program we can answer complex queries, such as “what is the average number of packet retransmissions” in a communication protocol, or “how often does process P₁ enter the critical section while process P₂ waits” in a mutual exclusion algorithm. We present an extension to linear-time temporal logic that combines the temporal specification with the collection of statistical data. By translating formulas of this language to alternating automata we obtain a simple and efficient query evaluation algorithm. We illustrate our approach with examples and experimental results.     

Languages Defined with Modular Counting Quantifiers

We prove that a regular language defined by a boolean combination of generalized Σ₁-sentences built using modular counting quantifiers can be defined by a boolean combination of Σ₁-sentences in which only regular numerical predicates appear. The same statement, with “Σ₁” replaced by “first-order,” is equivalent to the conjecture that the nonuniform circuit complexity class ACC is strictly contained in NC¹. The argument introduces some new techniques, based on a combination of semigroup theory and Ramsey theory, which may shed some light on the general case.     

One-way functions and circuit complexity

A finite function f is a mapping of {0, 1}ⁿ into {0, 1}^m{#}, where “#” is a symbol to be thought of as “undefined.” A family of finite functions is said to be one-way (in a circuit complexity sense) if it can be computed with polynomial-size circuits, but every family of inverses of these functions cannot. In this paper we show that, provided functions that are not one-to-one are allowed, one-way functions exist if and only if the satisfiability problem SAT does not have polynomial-size circuits. A family of functions f_i(x) can be checked if some family of polynomial-size circuits with inputs x and y can determine if f_i(x) = y. A family of functions f_i(x) can be evaluated if some family of polynomial-size circuits with input x can compute f_i(x). Can all families of total functions that can be checked also be evaluated? We show that this is true if and only if the nonuniform versions of the complexity classes P and UP co-UP are equal. A family of functions f_i is one-way for constant depth circuits if f_i can be computed with unbounded famin circuits of polynomial size and constant depth, but every family of inverses f_i⁻¹ cannot. We give two provably one-way functions (in fact permutaions) for constant-depth circuits. The second example has the stronger property that no bit of its inverse can be computed in polynomial size and constant depth.     

Detecting innovative topics based on user-interest ontology

In this paper, we detect “innovative topics”, those that are new and hopefully interesting to the user. We try to expand user interests significantly by letting the user browse those topics.We first generate user-interest ontologies that allow user profiles to be constructed as a hierarchy of classes where a user interest weight is assigned to each class and instance. Next, we measure the similarity between user interests by using interest weights on their user-interest ontologies and generate user group G_U that has high similarity to user u. The innovative topics for u are then detected by determining a suitable size of G_U and analyzing the ontologies in G_U.     

Expressing Priorities and External Probabilities in Process Algebra via Mixed Open/Closed Systems

Defining operational semantics for a process algebra is often based either on labeled transition systems that account for interaction with a context or on the so-called reduction semantics: we assume to have a representation of the whole system and we compute unlabeled reduction transitions (leading to a distribution over states in the probabilistic case). In this paper we consider mixed models with states where the system is still open (towards interaction with a context) and states where the system is already closed. The idea is that (open) parts of a system “P” can be closed via an operator “P↑G” that turns already synchronized actions whose “handle” is specified inside “G” into prioritized reduction transitions (and, therefore, states performing them into closed states). We show that we can use the operator “P↑G” to express multi-level priorities and external probabilistic choices (by assigning weights to handles inside G), and that, by considering reduction transitions as the only unobservable τ transitions, the proposed technique is compatible, for process algebra with general recursion, with both standard (probabilistic) observational congruence and a notion of equivalence which aggregates reduction transitions in a (much more aggregating) trace based manner. We also observe that the trace-based aggregated transition system can be obtained directly in operational semantics and we present the “aggregating” semantics. Finally, we discuss how the open/closed approach can be used to also express discrete and continuous (exponential probabilistic) time and we show that, in such timed contexts, the trace-based equivalence can aggregate more with respect to traditional lumping based equivalences over Markov Chains.     

The prism machine: An alternative to the pyramid

The prism machine is a stack of n cellular arrays, each of size 2ⁿ × 2ⁿ. Cell (i, j) on level k is connected to cells (i, j), (i + 2^k, j), and (i, j + 2^k) on level k + 1, 1 ≤ k < n, where the sums are modulo 2ⁿ. Such a machine can perform various operations (e.g., “Gaussian” convolutions or least-squares polynomial fits) on image neighborhoods of power-of-2 sizes in every position in O(n) time, unlike a pyramid machine which can do this only in sampled positions. It can also compute the discrete Fourier transform in O(n) time. It consists of n · 4ⁿ cells, while a pyramid consists of fewer than 4ⁿ⁺¹/3 cells; but in practice n would be at most 10, so that a prism would be at most about seven times as large as a pyramid.     

Two alternative ways for solving the coordination problem in multilevel optimization

The paper describes two new techniques for formulating the coupling between levels in multilevel optimization by linear decomposition, proposed as improvements over the original formulation, now several years old, that relied on explicit equality constraints which were shown by application experience as occasionally causing numerical difficulties. The two new techniques account for the coupling without using explicit equality constraints, thus avoiding the above difficulties and also reducing the computational cost of the procedure. The old and new formulations are presented in detail, illustrated by an example of a structural optimization. A generic version of the improved algorithm is also developed for applications to multidisciplinary systems not limited to structures.The symbolsU andL withX, Y, Z, e.g.XU, XL, denote upper and lower bounds on these variables; other symbols are defined where first used.Notation (vectors indicated by bold-face, or by {}) A vector of cross-sectional areas,A _i - C _i cumulative constraint of thei-th beam - D _i vector defined by (22) - g vector of constraintsg _k for a beam, e.g. stress limits, and local buckling,k = 1 NGB, partitioned in subsets of lengthsNGB _i, each subset corresponding to thei-th beam - G vector of constraintsG _k for the assembled structure, e.g. displacement limits,k = 1 NGA - I vector of cross-sectional moments of inertia,I _i,i = 1 NGB _i - KS(f _i) the Kreisselmeier-Steinhauser function of the set of functionsf _i,i = 1NF, defined by (5) and (5a) - L _i length of thei-th beam - NE number of beams in a framework - N _i vector of the end forces for thei-th beam - NP _i length of vectorP _i - NN _i length of vectorN _i - NSS number of subsystems - NX length of vectorX - P _i vector of parameters in optimization of thei-th beam, comprising elementsP _q,q = 1 NP _i - P _qi q-th element of vectorP _i - SA system analysis - SI input vector of lengthNSI intoSA - SO output vector of lengthNSO fromSA - SSA _i i-th subsystem black box analysis - SSC vector of geometrical variables determining the structure overall shape - SSI _i input vector of lengthNSSI _i intoSSA _i - SSO _i output vector of lengthNSSO _i fromSSA _i - TOL tolerance parameter set by user - U vector of displacements - W weight, equivalent to volume in a homogeneous structure - X vector of design variables at the system level (assembled structure) in optimization by decomposition - Y _i vector of design variables in thei-th beam optimization problem - Z vector of design variables in optimization without decomposition - user-defined coefficient in the KS function, e.g. (5)     

Dynamic learning from multiple examples for semantic object segmentation and search

We present a novel “dynamic learning” approach for an intelligent image database system to automatically improve object segmentation and labeling without user intervention, as new examples become available, for object-based indexing. The proposed approach is an extension of our earlier work on “learning by example,” which addressed labeling of similar objects in a set of database images based on a single example. The proposed dynamic learning procedure utilizes multiple example object templates to improve the accuracy of existing object segmentations and labels. Multiple example templates may be images of the same object from different viewing angles, or images of related objects. This paper also introduces a new shape similarity metric called normalized area of symmetric differences (NASD), which has desired properties for use in the proposed “dynamic learning” scheme, and is more robust against boundary noise that results from automatic image segmentation. Performance of the dynamic learning procedures has been demonstrated by experimental results.     

Toward a theory of Pollard's rho method

Pollard's “rho” method for integer factorization iterates a simple polynomial map and produces a nontrivial divisor of n when two such iterates agree modulo this divisor. Experience and heuristic arguments suggest that a prime divisor p should be detected in steps, but this has never been proved. Indeed, nothing seems to be have been rigorously proved about the probability of success that would improve the obvious lower bound of 1/p. This paper shows that for fixed k, this probability is at least (₂^k)/p + O(p^−3/2) as p → ∞. This leads to an Ω(log²p)/p estimate of the success probability.     

A logic for reasoning about probabilities

We consider a language for reasoning about probability which allows us to make statements such as “the probability of E₁ is less than ” and “the probability of E₁ is at least twice the probability of E₂,” where E₁ and E₂ are arbitrary events. We consider the case where all events are measurable (i.e., represent measurable sets) and the more general case, which is also of interest in practice, where they may not be measurable. The measurable case is essentially a formalization of (the propositional fragment of) Nilsson's probabilistic logic. As we show elsewhere, the general (nonmeasurable) case corresponds precisely to replacing probability measures by Dempster-Shafer belief functions. In both cases, we provide a complete axiomatization and show that the problem of deciding satisfiability is NP-complete, no worse than that of propositional logic. As a tool for proving our complete axiomatizations, we give a complete axiomatization for reasoning about Boolean combinations of linear inequalities, which is of independent interest. This proof and others make crucial use of results from the theory of linear programming. We then extend the language to allow reasoning about conditional probability and show that the resulting logic is decidable and completely axiomatizable, by making use of the theory of real closed fields.     

A simple algorithm for the unique characterization of convex polygons

A simple method for specifying the shape and orientation of a convex polygon is described. The method utilizes eigenvalues and eigenvectors of a “moment of inertia” or mass matrix computed from the nodal coordinates of the polygon. The “shape” is characterized then by the parameter ( , where ξ₁ and ξ₂ are the eigenvalues (ξ₁ ξ₂), and the orientation by the axial direction of the first eigenvector. FORTRAN subroutines are provided for this algorithm.     

Optimal strategies against a liar

We consider the following scenario: There are two individuals, say Q (Questioner) and R (Responder), involved in a search game. Player R chooses a number, say x, from the set S={1,…,M}. Player Q has to find out x by asking questions of type: “which one of the sets A₁,A₂,…,A_q, does x belong to?”, where the sets A₁,…,A_q constitute a partition of S. Player R answers “i” to indicate that the number x belongs to A_i. We are interested in the least number of questions player Q has to ask in order to be always able to correctly guess the number x, provided that R can lie at most e times. The case e=0 obviously reduces to the classical q-ary search, and the necessary number of questions is [log_qM]. The case q=2 and e1 has been widely studied, and it is generally referred to as Ulam's game. In this paper we consider the general case of arbitrary q2. Under the assumption that player R is allowed to lie at most twice throughout the game, we determine the minimum number of questions Q needs to ask in order to successfully search for x in a set of cardinality M=qⁱ, for any i1. As a corollary, we obtain a counterexample to a recently proposed conjecture of Aigner, for the case of an arbitrary number of lies. We also exactly solve the problem when player R is allowed to lie a fixed but otherwise arbitrary number of times e, and M=qⁱ, with i not too large with respect to q. For the general case of arbitrary M, we give fairly tight upper and lower bounds on the number of the necessary questions.     

Comparison of Selected Features for Target Detection in Synthetic Aperture Radar Imagery

Cooke, Tristrom, Redding, Nicholas J., Schroeder, Jim, and Zhang, Jingxin, Comparison of Selected Features for Target Detection in Synthetic Aperture Radar Imagery, Digital Signal Processing10 (2000), 286–296.Several methods are available that capture the statistics of radar imagery. The best features, in the sense of man-made target discrimination, are expected to be different for different types of natural background and for different objects of interest such as vehicles. We demonstrate that discrimination of natural background and man-made objects using low resolution synthetic aperture radar imagery is possible using singular value decomposition; several other simple features are also used to augment the feature vector. We use a subset of eigenvectors as features for target discrimination. The optimal set of features used to classify a region as “background clutter only” or “target region” is automatically chosen by a standard suboptimal feature selection algorithm.     

Multidimensional visualisation for process historical data analysis: a comparative study with multivariate statistical process control

This paper describes a comparative study of a multidimensional visualisation technique and multivariate statistical process control (MSPC) for process historical data analysis. The visualisation technique uses parallel coordinates which visualise multidimensional data using two dimensional presentations and allow identification of clusters and outliers, therefore, can be used to detect abnormal events. The study is based on a database covering 527 days of operation of an industrial wastewater treatment plant. It was found that both the visualisation technique and MSPC based on T² chart captured the same 17 days as “clearly abnormal” and another eight days as “likely abnormal”. Pattern recognition using K-means clustering was also applied to the same data in literature and was found to have identified 14 out of the 17 “clearly abnormal” days.     

On the Construction of Classes of Suffix Trees for Square Matrices: Algorithms and Applications

We provide a uniform framework for the study of index data structures for a two-dimensional matrixTEXT[1:n, 1:n] whose entries are drawn from an ordered alphabetΣ. An index forTEXTcan be informally seen as the two-dimensional analog of the suffix tree for a string. It allows on-line searches and statistics to be performed onTEXTby representing compactly theΘ(n³) square submatrices ofTEXTin optimalO(n²) space. We identify 4ⁿ⁻¹families of indices forTEXT, each containing ∏ⁿ_i=1 (2i−1)! isomorphic data structures. We also develop techniques leading to a single algorithm that efficiently builds any index in any family inO(n² log n) time andO(n²) space. Such an algorithm improves in various respects the algorithms for the construction of the PAT tree and the Lsuffix tree. The framework and the algorithm easily generalize tod>2 dimensions. Moreover, as part of our algorithm, we provide new algorithmic tools that yield a space-efficient implementation of the “naming scheme” of R. Karpet al.(in“Proceedings, Fourth Symposium on Theory of Computing,” pp. 125–136) for strings and matrices.     

Completeness of Continuation Models for λμ-Calculus

We show that a certain simple call-by-name continuation semantics of Parigot's λ_μ-calculus is complete. More precisely, for every λ_μ-theory we construct a cartesian closed category such that the ensuing continuation-style interpretation of λ_μ, which maps terms to functions sending abstract continuations to responses, is full and faithful. Thus, any λ_μ-category in the sense of L. Ong (1996, in “Proceedings of LICS '96,” IEEE Press, New York) is isomorphic to a continuation model (Y. Lafont, B. Reus, and T. Streicher, “Continuous Semantics or Expressing Implication by Negation,” Technical Report 93-21, University of Munich) derived from a cartesian-closed category of continuations. We also extend this result to a later call-by-value version of λ_μ developed by C.-H. L. Ong and C. A. Stewart (1997, in “Proceedings of ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, Paris, January 1997,” Assoc. Comput. Mach. Press, New York).     

A new test against an umbrella alternative and the associated simultaneous confidence intervals

For the usual balanced one-way fixed effects analysis of variance (ANOVA) model, a new test of the null hypothesis H₀: μ₁==μ_k against the umbrella alternative H_h:μ₁≤≤μ_h≥≥μ_k with at least one strict inequality is proposed. More usefully, this new test can be easily inverted to produce a set of one-sided simultaneous confidence intervals (SCIs) for all the ordered pairwise differences μ_j−μ_i for 1≤i<j≤h and h≤j<i≤k, and therefore enables the experimenter to infer which μ_i's are different when H₀ is rejected. A table of critical values is provided to allow immediate and simple implementation of this new inference procedure.     

Lower Bounds for Dynamic Algebraic Problems

We consider dynamic evaluation of algebraic functions (matrix multiplication, determinant, convolution, Fourier transform, etc.) in the model of Reif and Tate; i.e., if f(x₁,…, x_n)=(y₁, …, y_m) is an algebraic problem, we consider serving online requests of the form “change input x_i to value v” or “what is the value of output y_i?” We present techniques for showing lower bounds on the worst case time complexity per operation for such problems. The first gives lower bounds in a wide range of rather powerful models (for instance, history dependent algebraic computation trees over any infinite subset of a field, the integer RAM, and the generalized real RAM model of Ben-Amram and Galil). Using this technique, we show optimal Ω(n) bounds for dynamic matrix–vector product, dynamic matrix multiplication, and dynamic discriminant and an Ω( ) lower bound for dynamic polynomial multiplication (convolution), providing a good match with Reif and Tate's O( ) upper bound. We also show linear lower bounds for dynamic determinant, matrix adjoint, and matrix inverse and an Ω( ) lower bound for the elementary symmetric functions. The second technique is the communication complexity technique of Miltersen, Nisan, Safra, and Wigderson which we apply to the setting of dynamic algebraic problems, obtaining similar lower bounds in the word RAM model. The third technique gives lower bounds in the weaker straight line program model. Using this technique, we show an Ω((log n)²/log log n) lower bound for dynamic discrete Fourier transform. Technical ingredients of our techniques are the incompressibility technique of Ben-Amram and Galil and the lower bound for depth-two superconcentrators of Radhakrishnan and Ta-Shma. The incompressibility technique is extended to arithmetic computation in arbitrary fields.