For many computer vision applications labeled/segmented data is needed. Manually assigning labels or segmenting images is a time consuming and tedious task and becomes infeasible for a huge amount of data (e.g., when analyzing a video stream). Thus, this paper proposes a new approach to minimize the manual labeling/segmentation effort for learning an object detector by automatically extracting training data directly from a video sequence. Therefore, a robust background model, a tracker and an on-line learning method are combined. The main idea is to track an object through a video sequence and to directly use the obtained image patches, showing the object from different views, to incrementally update an existing model which in turn can be used for detection. As the tracker is initialized automatically by change detection, no user interaction is needed! Thus, an unknown object can be learned without having any prior information. To show the benefit of the proposed approach the framework is demonstrated on several typical objects that can be found on a desktop. 1

In this paper we briefly introduce a Wide Spectrum Language and its transformation theory and describe a recent success of the theory: a general recursion removal theorem. Recursion removal often forms an important step in the systematic development of an algorithm from a formal specification. We use semantic-preserving transformations to carry out such developments and the theorem proves the correctness of many different classes of recursion removal. This theorem includes as special cases the two techniques discussed by Knuth [13] and Bird [7]. We describe some applications of the theorem to cascade recursion, binary cascade recursion, Gray codes, and an inverse engineering problem.

Summary. Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and

Specification Approach As is common in programming, it is possible in ALF to work with abstract sets and operations rather than with their actual inductive and recursive definitions. Thus, we may specify abstract structures and operations, which consist of a collection of propositions implicitly characterizing a number of sets and operations on them (such a specification is usually given by a set of equations). When writing the proof, we used this approach in order to work in a modular style, and so, independently from the exact definitions of some sets and propositions. The usual definition of tuples, for instance, is given by requiring (a family of) sets T(n) for n ffl N, having the following operations: nil ffl T(0), cons: N \Theta T(n) ! T(succ(n)), for all n ffl N, hd: T(succ(n)) ! N, for all n ffl N, tl: T(succ(n)) ! T(n), for all n ffl N, such that the following equalities hold: hd(cons(a; t))= a, for all a ffl N, t ffl T(n) (n ffl N), tl(cons(a; t))= t, for all a ffl N, t f...

. After a brief flirtation with logicism in 1917--1920, David Hilbert proposed his own program in the foundations of mathematics in 1920 and developed it, in concert with collaborators such as Paul Bernays and Wilhelm Ackermann, throughout the 1920s. The two technical pillars of the project were the development of axiomatic systems for ever stronger and more comprehensive areas of mathematics and finitistic proofs of consistency of these systems. Early advances in these areas were made by Hilbert (and Bernays) in a series of lecture courses at the University of Gttingen between 1917 and 1923, and notably in Ackermann 's dissertation of 1924. The main innovation was the invention of the e-calculus, on which Hilbert's axiom systems were based, and the development of the e-substitution method as a basis for consistency proofs. The paper traces the development of the "simultaneous development of logic and mathematics" through the e-notation and provides an analysis of Ackermann's consisten...

Project, and my advisor Shuki Bruck for supporting me during my studies. I would also like to thank Shuki for being a good advisor and collaborator. I am grateful not only to Shuki but to all the people I have worked with, including Erik Winfree and David Soloveichik, in collaboration with whom the material in section 3.4.2 was produced. My family has supported my adventure of being a student, especially my wife Éva, my children András, Adam, and Emma, my mother Sarah, and my grandfather Howard, and to them I am very grateful. iv Relations are everywhere. In particular, we think and reason in terms of mathematical and English sentences that state relations. However, we teach our students much more about how to manipulate functions than about how to manipulate relations. Consider functions. We know how to combine functions to make new functions, how to evaluate functions efficiently, and how to think about compositions of functions. Especially in the area of boolean functions, we have become experts in the theory and art of designing combinations of functions to yield what we want, and this expertise has led to techniques that enable

Abstract. When reservations are made to for instance a train, it is an on-line problem to accept or reject, i.e., decide if a person can be fitted in given all earlier reservations. However, determining a seating arrangement, implying that it is safe to accept, is an off-line problem with the earlier reservations and the current one as input. We develop optimal algorithms to handle problems of this nature.

This paper uses Ackerman's function as a testbed to illustrate the operation of various program transformations which take recursive procedures to equivalent iterative forms. The transformations are taken from the author's DPhil thesis [19]. In this paper we illustrate that they can be successfully applied to even the most convoluted recursion. For many programs a recursive function is the most natural and clear specification while an iterative (or tail-recursive) form is the most efficient implementation. This paper illustrates how an efficient iterative program can be developed and verified by starting with a simple recursive program and using proven transformations to remove the recursion. The resulting iterative program will be correct by construction, so the problem of a direct verification of the iterative algorithm is avoided. This process can also throw light on the nature of the recursive specification. Several interesting properties of Ackermann's function and the iterative algorithms are derived in the course of this development.

This paper develops a database query language called Transducer Datalog motivated by the needs of a new and emerging class of database applications. In these applications, such as text databases and genome databases, the storage and manipulation of long character sequences is a crucial feature. The issues involved in managing this kind of data are not addressed by traditional database systems, either in theory or in practice. To address these issues, we recently introduced a new machine model called a generalized sequence transducer. These generalized transducers extend ordinary transducers by allowing them to invoke other transducers as "subroutines." This paper establishes the computational properties of Transducer Datalog, a query language based on this new machine model. In the process, we develop a hierarchy of time-complexity classes based on the Ackermann function. The lower levels of this hierarchy correspond to well-known complexity classes, such as polynomial time...

INTRODUCTION Les sujets abord6s dans cette thbse concernent essentiellement les fonctions de Hilbert-Samuel d'idaux de K[X,..., X]. Plus prcisment, nous tudions des escaliers (appels aussi "order ideals of monomials" en anglais), qui sont des objets plus fins que les fonctions de Hilbert-Samuel, et sont oMenus en introduisant un ordre sur les mon6mes. Cette idle remonte k F. S. Macaulay, eta t employee par H. Hironaka ("bases standard") dans son ceuvre sur la rsolution de singularit,s. Mais c'est B. Buchberger qui l'a popularisle dans les milieux informatiques en introduisant un algorithme de calcul de "bases de GrSbner" fond sur la rsolution des conflits provenant des paires critiques (aussi appeles syzygies). Dans ce travail nous considrons principalement deux types d'escaliers: les escaliers gnriques d'un c6t (oh nous avons obtenu des thorbmes de structure), et, k l'oppos pour ainsi dire, les escaliers compresses (utiliss pour donner des bornes sur la longueur de chanes