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Mathematics by Experiment: Plausible Reasoning in the 21st Century, extended second edition, A K
 2008. EXPERIMENTATION AND COMPUTATION 19
, 2008
"... If mathematics describes an objective world just like physics, there is no reason why inductive methods should not be applied in mathematics just the same as in physics. (Kurt Gödel, 1951) Paper Revised 09–09–04 This paper is an extended version of a presentation made at ICME10, related work is elab ..."
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Cited by 47 (19 self)
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If mathematics describes an objective world just like physics, there is no reason why inductive methods should not be applied in mathematics just the same as in physics. (Kurt Gödel, 1951) Paper Revised 09–09–04 This paper is an extended version of a presentation made at ICME10, related work is elaborated in references [1–7]. 1 I shall generally explore experimental and heuristic mathematics and give (mostly) accessible, primarily visual and symbolic, examples. The emergence of powerful mathematical computing environments like Maple and Matlab, the growing
A Class of Geometric Lattices Based on Finite Groups
, 1972
"... For any finite group G and positive integer n a finite geometric 1attice Q (G) of rank n, the lattice of partial Gpartitions, is constructed. n ..."
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Cited by 46 (0 self)
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For any finite group G and positive integer n a finite geometric 1attice Q (G) of rank n, the lattice of partial Gpartitions, is constructed. n
Universal compression of memoryless sources over unknown alphabets
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2004
"... It has long been known that the compression redundancy of independent and identically distributed (i.i.d.) strings increases to infinity as the alphabet size grows. It is also apparent that any string can be described by separately conveying its symbols, and its pattern—the order in which the symbol ..."
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Cited by 35 (10 self)
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It has long been known that the compression redundancy of independent and identically distributed (i.i.d.) strings increases to infinity as the alphabet size grows. It is also apparent that any string can be described by separately conveying its symbols, and its pattern—the order in which the symbols appear. Concentrating on the latter, we show that the patterns of i.i.d. strings over all, including infinite and even unknown, alphabets, can be compressed with diminishing redundancy, both in block and sequentially, and that the compression can be performed in linear time. To establish these results, we show that the number of patterns is the Bell number, that the number of patterns with a given number of symbols is the Stirling number of the second kind, and that the redundancy of patterns can be bounded using results of Hardy and Ramanujan on the number of integer partitions. The results also imply an asymptotically optimal solution for the GoodTuring probabilityestimation problem.
Some Probabilistic Aspects Of Set Partitions
 American Mathematical Monthly
, 1996
"... this paper, section (1.2) offers an elementary combinatorial proof of Dobinski's formula which seems simpler than other proofs in the literature (Rota [35], Berge [5], p. 44, Comtet [9], p. 211). This argument involves identities whose probabilistic interpretations are brought out later in the ..."
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Cited by 24 (2 self)
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this paper, section (1.2) offers an elementary combinatorial proof of Dobinski's formula which seems simpler than other proofs in the literature (Rota [35], Berge [5], p. 44, Comtet [9], p. 211). This argument involves identities whose probabilistic interpretations are brought out later in the paper. 1.1 Notation
Data Morphing: An Adaptive, CacheConscious Storage Technique
 In Proc. VLDB, 2003
, 2003
"... The number of processor cache misses has a critical impact on the performance of DBMSs running on servers with large mainmemory configurations. ..."
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Cited by 22 (1 self)
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The number of processor cache misses has a critical impact on the performance of DBMSs running on servers with large mainmemory configurations.
Umbral nature of the Poisson random variables
 In Algebraic combinatorics and computer science
, 2001
"... Abstract. Extending the rigorous presentation of the “classical umbral calculus” [28], the socalled partition polynomials are interpreted with the aim to point out the umbral nature of the Poisson random variables. Among the new umbrae introduced, the main tool is the partition umbra that leads als ..."
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Cited by 16 (9 self)
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Abstract. Extending the rigorous presentation of the “classical umbral calculus” [28], the socalled partition polynomials are interpreted with the aim to point out the umbral nature of the Poisson random variables. Among the new umbrae introduced, the main tool is the partition umbra that leads also to a simple expression of the functional composition of the exponential power series. Moreover a new short proof of the Lagrange inversion formula is given. 1
Simultaneous team assignment and behavior recognition from spatiotemporal agent traces
 In Proceedings of TwentyFirst National Conference on Artificial Intelligence (AAAI06
, 2006
"... This paper addresses the problem of activity recognition for physicallyembodied agent teams. We define team activity recognition as the process of identifying team behaviors from traces of agent positions over time; for many physical domains, military or athletic, coordinated team behaviors create ..."
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Cited by 15 (5 self)
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This paper addresses the problem of activity recognition for physicallyembodied agent teams. We define team activity recognition as the process of identifying team behaviors from traces of agent positions over time; for many physical domains, military or athletic, coordinated team behaviors create distinctive spatiotemporal patterns that can be used to identify lowlevel action sequences. This paper focuses on the novel problem of recovering agenttoteam assignments for complex team tasks where team composition, the mapping of agents into teams, changes over time. Without a priori knowledge of current team assignments, the behavior recognition problem is challenging since behaviors are characterized by the aggregate motion of the entire team and cannot generally be determined by observing the movements of a single agent in isolation. To handle this problem, we introduce a new algorithm, Simultaneous Team Assignment and Behavior Recognition (STABR), that generates behavior annotations from spatiotemporal agent traces. The proposed approach is able to perform accurate team behavior recognition without an exhaustive search over the combinatorial space of potential team assignments, as demonstrated on several scenarios of simulated military maneuvers.
On the Combinatorics of Cumulants
, 2000
"... this paper, we shall employ the full freedom of Umbral Calculus to study cumulants. Umbral Calculus leads to various formulae for the cumulant sequence, each of which reveals one portion of the secret encoded in cumulants. Through these formulae, cumulants are connected to familiar combinatorial obj ..."
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Cited by 12 (2 self)
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this paper, we shall employ the full freedom of Umbral Calculus to study cumulants. Umbral Calculus leads to various formulae for the cumulant sequence, each of which reveals one portion of the secret encoded in cumulants. Through these formulae, cumulants are connected to familiar combinatorial objects such as binomial sequences and symmetric functions. In return, the study of cumulants has stimulated new extension of the existing theory of Umbral Calculus. For instance, for the first time in this paper, we discuss umbral derivatives (or the star algebra)
Efficient learning of action schemas and webservice descriptions
, 2008
"... This work addresses the problem of efficiently learning action schemas using a bounded number of samples (interactions with the environment). We consider schemas in two languages — traditional STRIPS, and a new language STRIPS+WS that extends STRIPS to allow for the creation of new objects when an a ..."
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Cited by 12 (3 self)
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This work addresses the problem of efficiently learning action schemas using a bounded number of samples (interactions with the environment). We consider schemas in two languages — traditional STRIPS, and a new language STRIPS+WS that extends STRIPS to allow for the creation of new objects when an action is executed. This modification allows STRIPS+WS to model web services and can be used to describe webservice composition (planning) problems. We show that general STRIPS operators cannot be efficiently learned through raw experience, though restricting the size of action preconditions yields a positive result. We then show that efficient learning is possible without this restriction if an agent has access to a “teacher” that can provide solution traces on demand. We adapt this learning algorithm to efficiently learn webservice descriptions in STRIPS+WS. 1