On the Definition of Fluctuating Temperature

The Maxwell distribution is derived from the F-distribution in the limit where one of the degrees of freedom of the ² variates tends to infinity. The estimator of the temperature is consistent, and, hence coincides with the temperature of the heat reservoir in the asymptotic limit; it is also unbiased and efficient. Consequently, there is a contradiction between indentifying the Lagrange multiplier in the variational formalism that Tsallis and co-workers use to maximize his nonadditive entropy with respect to escort expectation values in order to derive the Student t- and r-distributions and the physical meaning of these variables. Only in the asymptotic limit when these distributions become the ²-distributions of MBG statistics can the Lagrange multiplier be interpreted as the inverse temperature. Hence, there is no generalization of the ²-distributions that can be made which involves interpreting the Lagrange multiplier as the inverse temperature. The frequency interpretation of the fluctuating temperature is contrasted with the Bayesian approach that treats a parameter to be estimated as a random variable which is equipped with a probability distribution.     

Redesign of a Systems Engineering Language: Formalisation of χ

This paper describes the redesign of a systems engineering language called . This is an engineering language designed to specify and analyse industrial systems. The main objective of this redesign was to enable mathematical reasoning about specifications. We discuss the original language, the requirements and design decisions, and the resulting syntax and semantics of the new version of , called . In particular, we elaborate on semantical aspects of s time model.     

Thiele Rational Interpolation for the Numerical Computation of the Reversible Randles–Sevcik Function in Electrochemistry

This paper uses Thiele rational interpolation to derive a simple method for computing the Randles–Sevcik function ^1/2(x), with relative error at most 1.9 × 10^–5 for – < x < . We develop a piecewise approximation method for the numerical computation of ^1/2(x) on the union (–, –10) [–10, 10] (10, ). This approximation is particularly convenient to employ in electrochemical applications where four significant digits of accuracy are usually sufficient. Although this paper is primarily concerned with the approximation of the Randles–Sevcik function, some examples are included that illustrate how Thiele rational interpolation can be employed to generate useful approximations to other functions of interest in scientific work.     

Constructing sets of functions which have a givenF-cardinality

The termF-cardinality of (=F-card()) is introduced whereF: ^{n n} is a partial function and is a set of partial functionsf: ^{n n} . TheF-cardinality yields a lower bound for the worst-case complexity of computingF if only functionsf can be evaluated by the underlying abstract automaton without conditional jumps. This complexity bound isindependent from the oracles available for the abstract machine. Thus it is shown that any automaton which can only apply the four basic arithmetic operations needs (n logn) worst-case time to sortn numbers; this result is even true if conditional jumps witharbitrary conditions are possible. The main result of this paper is the following: Given a total functionF: ^{n n} and a natural numberk, it is almost always possible to construct a set such that itsF-cardinality has the valuek; in addition, can be required to be closed under composition of functionsf,g . Moreover, ifF is continuous, then consists of continuous functions.     

Prequential and Cross-Validated Regression Estimation

Prequential model selection and delete-one cross-validation are data-driven methodologies for choosing between rival models on the basis of their predictive abilities. For a given set of observations, the predictive ability of a model is measured by the model's accumulated prediction error and by the model's average-out-of-sample prediction error, respectively, for prequential model selection and for cross-validation. In this paper, given i.i.d. observations, we propose nonparametric regression estimators—based on neural networks—that select the number of hidden units (or neurons) using either prequential model selection or delete-one cross-validation. As our main contributions: (i) we establish rates of convergence for the integrated mean-squared errors in estimating the regression function using off-line or batch versions of the proposed estimators and (ii) we establish rates of convergence for the time-averaged expected prediction errors in using on-line versions of the proposed estimators. We also present computer simulations (i) empirically validating the proposed estimators and (ii) empirically comparing the proposed estimators with certain novel prequential and cross-validated mixture regression estimators.     

The informed neuron: Issues in the use of information theory in the behavioral sciences

The concept of information is virtually ubiquitous in contemporary cognitive science. It is claimed to be processed (in cognitivist theories of perception and comprehension), stored (in cognitivist theories of memory and recognition), and otherwise manipulated and transformed by the human central nervous system. Fred Dretske's extensive philosophical defense of a theory of informational content (semantic information) based upon the Shannon-Weaver formal theory of information is subjected to critical scrutiny. A major difficulty is identified in Dretske's equivocations in the use of the concept of a signal bearing informational content. Gibson's alternative conception of information (construed as analog by Dretske), while avoiding many of the problems located in the conventional use of signal, raises different but equally serious questions. It is proposed that, taken literally, the human CNS does not extract or process information at all; rather, whatever information is construed as locatable in the CNS is information only for an observer-theorist and only for certain purposes.Blood courses through our veins, andinformation through our central nervous system.— A Neuropsychology Textbook.     

The University of Texas at Arlington Autonomous Aerial Vehicle—An overview

This paper reports on the status of The University of Texas at Arlington student effort to design, build and fly an Autonomous Aerial Vehicle. Both the 1991 entry into the First International Aerial Robotics Competition as well as refinements being made for 1992 are described. Significant technical highlights include a real-time vision system for target objective tracking, a real-time ultrasonic locator system for position sensing, a novel mechanism for gradually moving from human to computer control, and a hierarchical control structure implemented on a 32-bit microcontroller. Detailed discussion about the design of multivariable automatic controls for stability augmentation is included. Position and attitude control loops are optimized according to a combined ₂ and criteria. We present a modification of a recently published procedure for recovering a desired open-loop transfer function shape within the framework of the mixed ₂/ problem. This work has led to a new result that frees a design parameter related to imposing the constraint. The additional freedom can be used to improve upon the performance and robustness characteristics of the system.     

Deterministic sequential functions

The simple rational partial functions accepted by generalized sequential machines are shown to coincide with the compositions _P ^–1 , where _P consists of the prefix codings. The rational functions accepted by generalized sequential machines are proved to coincide with the compositions _P ^–1 , where is the family of endmarkers and is the family of removals of endmarkers. (The compositions are read from left to right). We also show that _P ^–1 is the family of the subsequential functions.This work was partially supported by the Esprit Basic Research Action Working Group No. 3166 ASMICS, the CNRS and the Academy of Finland     

The Claremont Shakespeare Authorship Clinic: How Severe Are the Problems?

Ward Elliott (from 1987) and Robert Valenza (from 1989) set out to the find the true Shakespeare from among 37 anti-Stratfordian Claimants. As directors of the Claremont Shakespeare Authorship Clinic, Elliott and Valenza developed novel attributional tests, from which they concluded that most Claimants are not-Shakespeare. From 1990-4, Elliott and Valenza developed tests purporting further to reject much of the Shakespeare canon as not-Shakespeare (1996a). Foster (1996b) details extensive and persistent flaws in the Clinic's work: data were collected haphazardly; canonical and comparative text-samples were chronologically mismatched; procedural controls for genre, stanzaic structure, and date were lacking. Elliott and Valenza counter by estimating maximum erosion of the Clinic's findings to include five of our 54 tests, which can amount, at most, to half of one percent (1998). This essay provides a brief history, showing why the Clinic foundered. Examining several of the Clinic's representative tests, I evaluate claims that Elliott and Valenza continue to make for their methodology. A final section addresses doubts about accuracy, validity and replicability that have dogged the Clinic's work from the outset.     

Hierarchy theorems for two-way finite state transducers

Summary For a family of languages , CAL() is defined as the family of images of under nondeterministic two-way finite state transducers, while FINITE · VISIT() is the closure of under deterministic two-way finite state transducers; CAL⁰()= and for n0, CAL ⁿ⁺¹()=CAL ⁿ (CAL()). For any semiAFL , if FINITE · VISIT() CAL(), then CAL ⁿ () forms a proper hierarchy and for every n0, FINITE · VISIT(CALⁿ()) CAL ⁿ⁺¹() FINITE · VISIT(CAL ⁿ⁺¹()). If is a SLIP semiAFL or a weakly k-iterative full semiAFL or a semiAFL contained in any full bounded AFL, then FINITE · VISIT() CAL() and in the last two cases, FINITE · VISIT(). If is a substitution closed full principal semiAFL and FINITE · VISIT(), then FINITE · VISIT() CAL(). If is a substitution closed full principal semiAFL generated by a language without an infinite regular set and ₁ is a full semiAFL, then is contained in CAL^m(₁) if and only if it is contained in ₁. Among the applications of these results are the following. For the following families , CAL ⁿ () forms a proper hierarchy: =INDEXED, =ETOL, and any semiAFL contained in CF. The family CF is incomparable with CAL ^m (NESA) where NESA is the family of one-way nonerasing stack languages and INDEXED is incomparable with CAL ^m (STACK) where STACK is the family of one-way stack languages.This work was supported in part by the National Science Foundation under Grants No. DCR74-15091 and MCS-78-04725     

The dynamic clusters method in nonhierarchical clustering

Given a finite setE R ⁿ, the problem is to find clusters (or subsets of similar points inE) and at the same time to find the most typical elements of this set. An original mathematical formulation is given to the problem. The proposed algorithm operates on groups of points, called samplings (samplings may be called multiple centers or cores); these samplings adapt and evolve into interesting clusters. Compared with other clustering algorithms, this algorithm requires less machine time and storage. We provide some propositions about nonprobabilistic convergence and a sufficient condition which ensures the decrease of the criterion. Some computational experiments are presented.     

A new polynomial-time algorithm for the maximum weighted (χ(G) — 1)-coloring problem in comparability graphs

For a weighted graph G = (V, E), the maximum weightedk-coloring problem is to color a set of vertices of maximum weight usingk colors. In this paper we are interested in solving this problem in comparability graphs. For these graphs, as shown by Cameron, the problem can be translated into a dual transportation problem. Let (G) denote the chromatic number of a comparability graphG. We prove that whenk is equal to (G) — 1, the problem can be solved more efficiently by finding a maximum weighted stable set in a bipartite graph. Maximum matching algorithms can be used in the unweighted case.This work was supported by an NSERC International Fellowship to the University of Montréal, and by NSERC #OGP0105384.     

Analysis of an Industrial System

Studying industrial systems by simulation enables the designer to study their dynamic behaviour and to determine characteristics of the system. Unfortunately, simulation also has some disadvantages. These can be overcome by using formal methods. Formal methods allow a thorough analysis of the possible behaviours of a system, parameterised system analysis and a modular approach to the analysis of systems. We present a case study in which a model of an industrial system is studied in a formal way. For this purpose, the model is first specified and simulated using the CSP-based executable specification language . The model is translated into a model in the process algebra CRL. This enables us to give a correctness proof of the parameterised model and to study the model in isolation.     

On the Complexity of Function Learning

The majority of results in computational learning theory are concerned with concept learning, i.e. with the special case of function learning for classes of functions with range {0, 1}. Much less is known about the theory of learning functions with a larger range such as or . In particular relatively few results exist about the general structure of common models for function learning, and there are only very few nontrivial function classes for which positive learning results have been exhibited in any of these models.We introduce in this paper the notion of a binary branching adversary tree for function learning, which allows us to give a somewhat surprising equivalent characterization of the optimal learning cost for learning a class of real-valued functions (in terms of a max-min definition which does not involve any learning model).Another general structural result of this paper relates the cost for learning a union of function classes to the learning costs for the individual function classes.Furthermore, we exhibit an efficient learning algorithm for learning convex piecewise linear functions from ^d into . Previously, the class of linear functions from ^d into was the only class of functions with multidimensional domain that was known to be learnable within the rigorous framework of a formal model for online learning.Finally we give a sufficient condition for an arbitrary class of functions from into that allows us to learn the class of all functions that can be written as the pointwise maximum ofk functions from . This allows us to exhibit a number of further nontrivial classes of functions from into for which there exist efficient learning algorithms.     

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.     

Optimal shape design for contact problems

A new optimization problem of controlling the contact pressurep is presented. We seek the minimum of the maximum contact pressurep _max under the following conditions: (a) the contact pressure should satisfy the inequalityp 0 as well as the controlling condition = v(x) p _max –p(x) 0, wherev(x) is the controller function; (b) the gapd between two bodies should be positive or zerod 0 after deformation; (c) at any possible contact point the conditionpd = 0 should be satisfied and the body that is capable of rigid body motion should be in equilibrium.If the gapd = d(p, h) is a linear function of both the pressurep and the contour changeh, then the optimization problem is a linear programming problem of restricted basis exchange. Three algorithms are presented for the solution of this problem. Finally, numerical examples will demonstrate the controlling technique for the shape optimization problem of a roller bearing.     

Relativized polynomial hierarchies extending two levels

The existence of relativized polynomial hierarchies extending exactly two levels is shown. More precisely, oraclesX andY are constructed such thatNP(X) ₂ ^{P, X} = ₂ ^{P, X} and ₂ ^{P, Y} ₂ ^{P, Y} = ₂ ^{P, Y} . These results answer a question posed by Baker, Gill, and Solovay ([1]) and generalize their constructions of relativized polynomial hierarchies extending 0 resp. 1 level; i.e.,P(A) = NP(A) resp.P(B) NP(B) = coNP(B) for recursive oraclesA andB.     

Translating VHDL into functional symbolic finite-state models

In this paper we present a method to translate VHDL into symbolic finite-state models. Our method can handle those aspects of VHDL which have a finite representation obtaining the semantics defined in the IEEE statndard. We describe an intermediate representation based on finite automata and its translation into a BDD-based reperesentation. Our model interfaces VHDL with a BDD-based functional symbolic model checker.The work of these authors is supported by ESPRIT project 6128 FORMAT.The work of this author is supported by the Volkswagenstiftung project Informatiksysteme.