Polya properties in sequence spaces

Let V be a finite dimensional affine subspace of l₁=l₁ N and suppose thath∈l₁/V. For 1<p<∞, leth ^p be the best l_p-approximation toh from V andh ^∞ be the strict best l^∞-approximation toh from V. We show thath ^p converges toh ^∞ at rate no worse than 1/p. A condition is given which is sufficient to guarantee that exists. This research was partially supported by a grant from the Office of the Vice Chancellor for Academic Affairs, Indiana University-Purdue University at Fort Wayne.     

Prediction in Orlicz spaces

In this paper, we investigate the prediction (or best approximation) operator from a uniformly convex real Orlicz space to a subset of -lattice measurable functions. In particular, a counterexample to the monotoncity property, which holds in L_p spaces, is given. Also, a sufficient condition for monotonicity to hold is given. Finally, nested -lattices, as occur in isotonic regression, are considered.This author supported by a grant from the Indiana University-Purdue University at Fort Wayne Research and Instructional Development Support Program     

Scan Statistics on Enron Graphs

We introduce a theory of scan statistics on graphs and apply the ideas to the problem of anomaly detection in a time series of Enron email graphs. Previous presentation: Workshop on Link Analysis, Counterterrorism and Security at the SIAM International Conference on Data Mining, Newport Beach, CA, April 23, 2005. Carey E. Priebe received the B.S. degree in mathematics from Purdue University in 1984, the M.S. degree in computer science from San Diego State University in 1988, and the Ph.D. degree in information technology (computational statistics) from George Mason University in 1993. From 1985 to 1994 he worked as a mathematician and scientist in the US Navy research and development laboratory system. Since 1994 he has been a professor in the Department of Applied Mathematics and Statistics, Whiting School of Engineering, Johns Hopkins University, Baltimore, Maryland. At Johns Hopkins, he holds joint appointments in the Department of Computer Science and the Center for Imaging Science. He is a past President of the Interface Foundation of North America—Computing Science & Statistics, a past Chair of the Section on Statistical Computing of the American Statistical Association, and on the editorial boards of Journal of Computational and Graphical Statistics, Computational Statistics and Data Analysis, and Computational Statistics. His research interests are in computational statistics, kernel and mixture estimates, statistical pattern recognition, statistical image analysis, and statistical inference for high-dimensional and graph data. He was elected Fellow of the American Statistical Association in 2002. John M. Conroy received a B.S. in Mathematics from Saint Joseph's University in 1980 and a Ph.D. in Applied Mathematics from the University of Maryland in 1986. Since then he has been a research staff member for the IDA Center for Computing Sciences in Bowie, MD. His research interest is applications of numerical linear algebra. He is a member of the Society for Industrial and Applied Mathematics, Institute of Electrical and Electronics Engineers (IEEE), and the Association for Computational Linguistics. David J. Marchette received a B.A. in 1980, and an M.A. in mathematics in 1982, from the University of California at San Diego. He received a Ph.D. in Computational Sciences and Informatics in 1996 from George Mason University under the direction of Ed Wegman. From 1985–1994 he worked at the Naval Ocean Systems Center in San Diego doing research on pattern recognition and computational statistics. In 1994 he moved to the Naval Surface Warfare Center in Dahlgren Virginia where he does research in computational statistics and pattern recognition, primarily applied to image processing, text processing, automatic target recognition and computer security. Dr. Marchette is a Fellow of the American Statistical Society. Youngser Park received the B.E. degree in electrical engineering from Inha University in Korea in 1985, the M.S. degree in computer science from The George Washington University in 1991, and had pursued a doctoral degree there. From 1998 to 2000 he worked at the Johns Hopkins Medical Institutes as a senior research engineer. Since 2003 he is working as a research analyst in the Center for Imaging Science at the Johns Hopkins University. His research interests are clustering algorithm, pattern classification, and data mining.     

Uniformity,Bipolarization and Pluriformity Captured as Generic Stylized Behavior with an Agent-Based Simulation Model of Attitude Change

This paper focuses at the dynamics of attitude change in large groups. A multi-agent computer simulation has been developed as a tool to study hypothesis we take to study these dynamics. A major extension in comparison to earlier models is that Social Judgment Theory is being formalized to incorporate processes of assimilation and contrast in persuasion processes. Results demonstrate that the attitude structure of agents determines the occurrence of assimilation and contrast effects, which in turn cause a group of agents to reach consensus, to bipolarize, or to develop a number of subgroups sharing the same position. Subsequent experiments demonstrate the robustness of these effects for a different formalization of the social network, and the susceptibility for population size.This paper won the best paper award at NAACSOS 2004, Pittsburgh PA. NAACSOS is the main conference of the North American Association for Computational Social and Organizational Science.Wander Jager received his Ph.D. degree in Social Sciences in 2000 from the University of Groningen, the Netherlands. Dr. Jager is currently Associate Professor at the University of Groningen. His current application domain concerns marketing, innovation diffusion and social simulation. Dr. Jager has authored or co-authored various papers on market dynamics, diffusion processes, resource use and sustainable consumption.Frédéric Amblard received his Ph.D. degree in Multi-Agent Simulation in 2003 from Blaise Pascal University, Clermont-Ferrand, France. Dr. Amblard is currently Associate Professor at the University of Social Sciences in Toulouse and researcher associated to the CNRS-IRIT, Institute of Research in Computer Sciences in Toulouse. His current application domain now concerns Agent-Based Social Simulation. Dr. Amblard has authored or coauthored various research papers either in computer sciences, in physics or in sociology.A preceding version of this paper has been presented to the 2004 Conference of the North American Association for Computational Social and Organization Science, Pittsburgh, USA and received the best paper award from this conference.     

Diffusion dynamics in small-world networks with heterogeneous consumers

Diffusions of new products and technologies through social networks can be formalized as spreading of infectious diseases. However, while epidemiological models describe infection in terms of transmissibility, we propose a diffusion model that explicitly includes consumer decision-making affected by social influences and word-of-mouth processes. In our agent-based model consumers’ probability of adoption depends on the external marketing effort and on the internal influence that each consumer perceives in his/her personal networks. Maintaining a given marketing effort and assuming its effect on the probability of adoption as linear, we can study how social processes affect diffusion dynamics and how the speed of the diffusion depends on the network structure and on consumer heterogeneity. First, we show that the speed of diffusion changes with the degree of randomness in the network. In markets with high social influence and in which consumers have a sufficiently large local network, the speed is low in regular networks, it increases in small-world networks and, contrarily to what epidemic models suggest, it becomes very low again in random networks. Second, we show that heterogeneity helps the diffusion. Ceteris paribus and varying the degree of heterogeneity in the population of agents simulation results show that the more heterogeneous the population, the faster the speed of the diffusion. These results can contribute to the development of marketing strategies for the launch and the dissemination of new products and technologies, especially in turbulent and fashionable markets. This paper won the best student paper award at the North American Association for Computational Social and Organizational Science (NAACSOS) Conference 2005, University of Notre Dame, South Bend, Indiana, USA. Preceding versions of this paper have been presented to the Conference of the North American Association for Computational Social and Organizational Science (NAACSOS), 2005, University of Notre Dame, South Bend, USA and to the Conference of the European Social Simulation Association (ESSA), 2005, Koblenz, Germany. Sebastiano Alessio Delre received his Master Degree in Communication Science at the University of Salerno. After one year collaboration at the Institute of Science and Technologies of Cognition (ISTC, Rome, Italy), now he is a PhD student at the faculty of economics, University of Groningen, the Netherlands. His work focus on how different network structures affect market dynamics. His current application domain concerns Agent-Based Simulation Models for social and economic phenomena like innovation diffusion, fashions and turbulent market. Wander Jager is an associate professor of marketing at the University of Groningen. He studied social psychology and obtained his PhD in the behavioral and social sciences, based on a dissertation about the computer modeling of consumer behaviors in situations of common resource use. His present research is about consumer decision making, innovation diffusion, market dynamics, crowd behavior, stock-market dynamics and opinion dynamics. In his work he combines methods of computer simulation and empirical surveys. He is involved in the management committee of the European Social Simulation Association (ESSA). Marco Janssen is an assistant professor in the School of Human Evolution and Social Change and in the Department of Computer Science and Engineering at Arizona State University. He got his degrees in Operations Research and Applied Mathematics. During the last 15 years, he uses computational tools to study social phenomena, especially human-environmental interactions. His present research focuses on diffusion dynamics, institutional innovation and robustness of social-ecological systems. He combined computational studies with laboratory and field experiments, case study analysis and archeological data. He is an associate editor-in-chief of the journal Ecology and Society.     

Application of relaxed solutions to minimum sensitivity optimal control

Relaxed variational techniques are applied to a minimum sensitivity control problem. Sensitivity of a trajectory is minimized to perturbations in initial conditions. Rather than using the optimal control that does indeed exist and that satisfies the final conditions exactly, a suboptimal control is used that transfers the system from the given initial state to an arbitrary small neighborhood of the given final state, and that results in a considerably better performance than the optimal solution. The suboptimal control is constructed using the optimal controls of the relaxed problem.This paper is based upon the Ph.D. dissertation by the author at Purdue University, Lafayette, Indiana. The author wishes to thank Professor Violet B. Haas, School of Electrical Engineering, Purdue University, for introducing him to relaxed variational problems and for many very helpful suggestions through the course of this work.     

Discrete and Lexicographic Helly-Type Theorems

Helly’s theorem says that if every d+1 elements of a given finite set of convex objects in ℝ ^d have a common point, then there is a point common to all of the objects in the set. We define three new types of Helly theorems: discrete Helly theorems—where the common point should belong to an a-priori given set, lexicographic Helly theorems—where the common point should not be lexicographically greater than a given point, and lexicographic-discrete Helly theorems. We study the relations between the different types of the Helly theorems. We obtain several new discrete and lexicographic Helly numbers. An extended abstract containing parts of this work appeared in the proceedings of the Forty-Fifth Annual Symposium on Foundations of Computer Science (FOCS) 2004. This work is part of the author’s Ph.D. thesis, prepared in the school of mathematical sciences at Tel Aviv University, under the supervision of Professor Arie Tamir.     

Padé approximations to the logarithm II: Identities, recurrences, and symbolic computation

Combinatorial identities that were needed in [25] are proved, mostly with C. Schneider’s computer algebra package Sigma. The form of the Padé approximation of the logarithm of arbitrary order is stated as a conjecture. 2000 Mathematics Subject Classification Primary—41A21, 05A19, 33F10 Supported by NRF-grant 2047226. Supported by NRF-grant 2053748. Supported by the Austrian Academy of Sciences, by the John Knopfmacher Research Centre for Applicable Analysis and Number Theory, and by the SFB-grant F1305 and the grant P16613-N12 of the Austrian FWF. Supported by NRF-grant 2053756.     

Padé approximations to the logarithm III: Alternative methods and additional results

We use C. Schneider’s summation software Sigma and a method due to Andrews-Newton-Zeilberger to reprove results from [5] and [24] as well as to prove new related material. 2000 Mathematics Subject Classification Primary—41A21, 05A19, 33F10 K. Driver: Supported by NRF-Grant 2047226. H. Prodinger: Supported by NRF-Grant 2053748. C. Schneider: Supported by the Austrian Academy of Sciences, by the John Knopfmacher Research Centre for Applicable Analysis and Number Theory, and by the SFB-grant F1305 and the grant P16613-N12 of the Austrian FWF. J. A. C. Weideman: Supported by NRF-Grant FA2005032300018.     

A Note on the Singular Limit of the Exact Controllability of Dissipative Wave Equations

Abstract In this note we analyze the exact controllability of singularly perturbed damped wave equations under more general geometric control condition than that of [1]. We show that the null controllability of the heat equation can be obtained as a singular limit of the exact controllability of such sorts of wave equations. The work of Yuping Tang was carried out when she visited the “School of Mathematics, Sichuan University”. The work of Xu Zhang was partially supported by NSF of China under Grant 19901024     

Qualitative criteria of admissibility for enforced agreements

It is desirable that artificial agents can help each other when they cannot achieve their goals, or when they profit from social exchanges. In this work we study coalition formation processes supported by enforced agreements and we define two qualitative criteria, the do-ut-des property and the composition property, that establish when a coalition is admissible to be formed. The do-ut-des property is based on a balance between the advantages and the burdens of an agent, when it agrees an enforced agreements. The composition property is a refinement of the do-ut-des property that takes into account also the costs and the risks deriving from the coalition formation process. Two relevant aspects distinguish our approach from the solution criteria developed in cooperative game theory. First, the do-ut-des property and the composition property are not based on an explicit utility function associated to the goals of an agent, and hance they can be used also in that cases in which the importance that agents give to their own goals is unknown. Second, a coalition has all the necessary information to establish if it satisfies the do-ut-des property or the composition property, therefore these two properties can be used in the case not all the space of possible coalitions is known. Luigi Sauro graduated in Physics at the University “Federico II” of Naples in 2001. From February 2002 to July 2002 he was collaborator at the SRA division of the IRST Institute (Trento). He got is Ph.D. in Computer Science from University of Torino in February 2006. Currently he is member of the Natural Language Processing and Agents Group, directed by prof. Leonardo Lesmo. His research interests include social reasoning, coalition formation and coordination in multiagent systems.     

Axioms of determinacy and biorthogonal systems

If allΠ _n ¹ games are determined, every non-norm-separable subspaceX ofl ^∞(N) which is W* —Σ _n ^+1/1 contains a biorthogonal system of cardinality 2^ℵ ₀. In Levy’s model of Set Theory, the same is true of every non-norm-separable subspace ofl ^∞(N) which is definable from reals and ordinals. Under any of the above assumptions,X has a quotient space which does not linearly embed into 1^∞(N).     

Social Network Discovery by Mining Spatio-Temporal Events

Knowing patterns of relationship in a social network is very useful for law enforcement agencies to investigate collaborations among criminals, for businesses to exploit relationships to sell products, or for individuals who wish to network with others. After all, it is not just what you know, but also whom you know, that matters. However, finding out who is related to whom on a large scale is a complex problem. Asking every single individual would be impractical, given the huge number of individuals and the changing dynamics of relationships. Recent advancement in technology has allowed more data about activities of individuals to be collected. Such data may be mined to reveal associations between these individuals. Specifically, we focus on data having space and time elements, such as logs of people's movement over various locations or of their Internet activities at various cyber locations. Reasoning that individuals who are frequently found together are likely to be associated with each other, we mine from the data instances where several actors co-occur in space and time, presumably due to an underlying interaction. We call these spatio-temporal co-occurrences events, which we use to establish relationships between pairs of individuals. In this paper, we propose a model for constructing a social network from events, and provide an algorithm that mines these events from the data. Experiments on a real-life data tracking people's accesses to cyber locations have also yielded encouraging results. Hady W. Lauw is a graduate student at the School of Computer Engineering, Nanyang Technological University, Singapore. His research interests include spatio-temporal data mining, social network discovery, and link analyisis. He has a BEng in computer engineering from Nanyang Technological University. Ee-Peng Lim is an Associate Professor with the School of Computer Engineering, Nanyang Technological University, Singapore. He received his PhD from the University of Minnesota, Minneapolis in 1994 and B.Sc. in Computer Science from National University of Singapore. Ee-Peng's research interests include information integration, data/text/web mining, digital libraries, and wireless intelligence. He is currently an Associate Editor of the ACM Transactions on Information Systems (TOIS), International Journal of Digital Libraries (IJDL) and International Journal of Data Warehousing and Mining (IJDWM). He was the Program Co-Chair of the ACM/IEEE Joint Conference on Digital Libraries (JCDL 2004), and Conference/Program Co-Chairs of International Conference on Asian Digital Libraries (ICADL 2004). He has also served in the program committee of numerous international conferences. Dr Lim is a Senior Member of IEEE and a Member of ACM. HweeHwa Pang received the B.Sc.—with first class honors—and M.S. degrees from the National University of Singapore in 1989 and 1991, respectively, and the PhD degree from the University of Wisconsin at Madison in 1994, all in Computer Science. He is currently an Associate Professor at the Singapore Management University. His research interests include database management systems, data security and quality, operating systems, and multimedia servers. He has many years of hands-on experience in system implementation and project management. He has also participated in transferring some of his research results to industry. Teck-Tim Tan is an IT Manager (Operations) at the Centre for IT Services, Nanyang Technological University (NTU), Singapore. He administers and oversees NTU's campus-wide wireless LAN infrastructure which facilitates access to the University's vast IT resources and services practically anywhere on campus.     

Local approximation properties of certain class of linear positive operators via <Emphasis Type="Italic">I</Emphasis>—convergence

In this study, we obtain a local approximation theorems for a certain family of positive linear operators via I—convergence by using the first and the second modulus of continuities and the elements of Lipschitz class functions. We also give an example to show that the classical Korovkin Theory does not work but the theory works in I—convergence sense.      

A note on slant submanifolds of nearly trans-Sasakian manifolds

The geometry of slant submanifolds of a nearly trans-Sasakian manifold is studied when the tensor field Q is parallel. It is proved that Q is not parallel on the submanifold unless it is anti-invariant and thus the result of [CABRERIZO, J. L.—CARRIAZO, A.—FERNANDEZ, L. M.—FERNANDEZ, M.: Slant submanifolds in Sasakian manifolds, Glasg. Math. J. 42 (2000), 125–138] and [GUPTA, R. S.—KHURSHEED HAIDER, S. M.—SHARFUDIN, A.: Slant submanifolds of a trans-Sasakian manifold, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 47 (2004), 45–57] are generalized.     

Integrating modeling,algorithm design,and computational implementation to solve a large-scale nonlinear mixed integer programming problem

This paper describes the formulation of a nonlinear mixed integer programming model for a large-scale product development and distribution problem and the design and computational implementation of a special purpose algorithm to solve the model. The results described demonstrate that integrating the art of modeling with the sciences of solution methodology and computer implementation provides a powerful approach for attacking difficult problems. The efforts described here were successful because they capitalized on the wealth of existing modeling technology and algorithm technology, the availability of efficient and reliable optimization, matrix generation and graphics software, and the speed of large-scale computer hardware. The model permitted the combined use of decomposition, general linear programming and network optimization within a branch and bound algorithm to overcome mathematical complexity. The computer system reliably found solutions with considerably better objective function values 30 to 50 times faster than had been achieved using general purpose optimization software alone. Throughout twenty months of daily use, the system was credited with providing insights and suggesting strategies that led to very large dollar savings. This research was supported in part by the Office of Naval Research Contract N00014-78-C-0222, by the Center for Business Decision Analysis*, by the University of Texas at Austin, and by the David Bruton, Jr., Centennial Chair in Business Decision Support Systems. Reproduction in whole or in part is permitted for any purpose of the U.S. Government. Center for Business Decision Analysis, Graduate School of Business — GSB 3.126, University of Texas, Austin, Texas 78712, USA.     

Generalized dirichlet problem in nonlinear potential theory

The operator extending the classical solution of the Dirichlet problem for the quasilinear elliptic equation divA (x,▽u)=0 akin to thep-Laplace equation is shown to be unique providedA obeys a specific order principle. The Keldych lemma is also generalized to this nonlinear setting. Part of this research was performed in 1988–1989 while a visitor at Indiana University, Bloomington, Indiana.     

A reciprocity theorem for certain q-series found in Ramanujan’s lost notebook

Three proofs are given for a reciprocity theorem for a certain q-series found in Ramanujan’s lost notebook. The first proof uses Ramanujan’s ₁ψ₁ summation theorem, the second employs an identity of N. J. Fine, and the third is combinatorial. Next, we show that the reciprocity theorem leads to a two variable generalization of the quintuple product identity. The paper concludes with an application to sums of three squares. Dedicated to Richard Askey on the occasion of his 70th birthday. 2000 Mathematics Subject Classification Primary—33D15 B. C. Berndt: Research partially supported by grant MDA904-00-1-0015 from the National Security Agency. A. J. Yee: Research partially supported by a grant from The Number Theory Foundation.     

My agents love to conform: Norms and emotion in the micro-macro link

This contribution investigates the function of emotion in relation to norms, both in natural and artificial societies. We illustrate that unintentional behavior can be normative and socially functional at the same time, thereby highlighting the role of emotion. Conceiving of norms as mental objects we then examine the role of emotion in maintaining and enforcing such propositional attitudes. The findings are subsequently related to social structural dynamics and questions concerning micro-macro linkage, in natural societies as well as in artificial systems. Finally, we outline the possibilities of an application to the socionic multi-agent architecture SONAR. Christian von Scheve graduated in Sociology with minors in Psychology, Economics, and Political Science at the University of Hamburg, where he also worked as a research assistant at the Institute of Sociology. Currently, he is a 3rd year PhD student at the University of Hamburg. He was a Fellow of the Research Group “Emotions as Bio-Cultural Processes” at the Center for Interdisciplinary Research (ZiF) at Bielefeld University. In his doctoral thesis he develops an interdisciplinary approach to emotion and social structural dynamics, integrating emotion theories from the neurosciences, psychology, and the social sciences. He has published on the role of emotion in large-scale social systems, human-computer interaction, and multi-agent systems. He is co-editor of a forthcoming volume on emotion regulation. Daniel Moldt received his BSc in Computer Science/Software Engineering from the University of Birmingham (England) in 1984, graduated in Informatics at the University of Hamburg, with a minor in Economics in 1990. He received his PhD in Informatics from the University of Hamburg in 1996, where he has been a researcher and lecturer at the Department of Informatics since 1990. Daniel Moldt is also the head of the Laboratory for Agent-Oriented Systems (LAOS) of the theoretical foundations group at the Department of Informatics. His research interests focus on theoretical foundations, software engineering and distributed systems with an emphasis on agent technology, Petri nets, specification languages, intra- and inter-organizational application development, Socionics and emotion in informatics. Julia Fix is currently a PhD student at the Theoretical Foundations of Computer Science Group, Department for Informatics at the University of Hamburg. She studied Informatics and Psychology at the University of Hamburg, with an emphasis on theoretical foundations of multi-agent systems and wrote her diploma theses about emotional agent systems. Her current research interests focus on conceptual challenges and theoretical foundations of modelling emotions in multi-agent systems, emotion-based norm enforcement and maintenance, and Socionics. A further research focus are Petri nets, in particular the use of Petri-net modelling formalisms for representing different aspects of emotion in agent systems. Rolf von Lüde is a professor of Sociology at the University of Hamburg with a focus in teaching and research in Sociology of Organizations, Work and Industry since 1996. He graduated in Economics, Sociology, and Psychology, and received his doctorate in Economics and the venia legendi in Sociology from the University of Dortmund. His current research focuses on labor conditions, the organization of production, social change and the educational system, the organizational structures of university, Socionics as a new approach to distributed artificial intelligence in cooperation with computer scientists, new public management, and emotions and social structures. Rolf von Lüde is currently Head of Department of Social Sciences and Vice Dean of the School of Business, Economics and Social Sciences, University of Hamburg.