The new partitional approach to (literally) interpreting quantum mechanics

This paper presents a new `partitional' approach to understanding or interpreting standard quantum mechanics (QM). The thesis is that the mathematics (not the physics) of QM is the Hilbert space version of the math of partitions on a set and, conversely, the math of partitions is a skeletonized set level version of the math of QM. Since at the set level, partitions are the mathematical tool to represent distinctions and indistinctions (or definiteness and indefiniteness), this approach shows how to interpret the key non-classical QM notion of superposition in terms of (objective) indefiniteness between definite alternatives (as opposed to seeing it as the sum of `waves'). Hence this partitional approach substantiates what might be called the Objective Indefiniteness Interpretation or what Abner Shimony called the Literal Interpretation of QM

Theoretical Studies in Unawareness and Discovery Process

中央大学博士(経済学)【学位授与の要件】中央大学学位規則第4条第1項 【論文審査委員主査】瀧澤　弘和(中央大学経済学部教授) 【論文審査委員副査】浅田　統一郎(中央大学経済学部教授),谷口　洋志(中央大学経済学部教授),石川　竜一郎(早稲田大学国際学術院教授)application/pdfdoctoral thesi

On the combinatorics of plethysm

AbstractWe construct three (large, reduced) incidence algebras whose semigroups of multiplicative functions, under convolution, are anti-isomorphic, respectively, to the semigroups of what we call partitional, permutational and exponential formal power series without constant term, in infinitely many variables x = (x1, x2,…), under plethysm. We compute the Möbius function in each case. These three incidence algebras are the linear duals of incidence bialgebras arising, respectively, from the classes of transversals of partitions (with an order that we define), partitions compatible with permutations (with the usual refinement order), and linear transversals of linear partitions (with the order induced by that on transversals). We define notions of morphisms between partitions, permutations and linear partitions, respectively, whose kernels are defined to be, in each case, transversals, compatible partitions and linear transversals. We introduce, in each case, a pair of sequences of polynomials in x of binomial type, counting morphisms and monomorphisms, and obtain expressions for their connection constants, by summation and Möbius inversion over the corresponding posets of kernels

Anomaly Detection in Streaming Sensor Data

In this chapter we consider a cell phone network as a set of automatically deployed sensors that records movement and interaction patterns of the population. We discuss methods for detecting anomalies in the streaming data produced by the cell phone network. We motivate this discussion by describing the Wireless Phone Based Emergency Response (WIPER) system, a proof-of-concept decision support system for emergency response managers. We also discuss some of the scientific work enabled by this type of sensor data and the related privacy issues. We describe scientific studies that use the cell phone data set and steps we have taken to ensure the security of the data. We describe the overall decision support system and discuss three methods of anomaly detection that we have applied to the data.Comment: 35 pages. Book chapter to appear in "Intelligent Techniques for Warehousing and Mining Sensor Network Data" (IGI Global), edited by A. Cuzzocre

On morphological hierarchical representations for image processing and spatial data clustering

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satis ed. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing

Consensus clustering with differential evolution

summary:Consensus clustering algorithms are used to improve properties of traditional clustering methods, especially their accuracy and robustness. In this article, we introduce our approach that is based on a refinement of the set of initial partitions and uses differential evolution algorithm in order to find the most valid solution. Properties of the algorithm are demonstrated on four benchmark datasets

Learning and Discovery

We formulate a dynamic framework for an individual decision-maker within which discovery of previously unconsidered propositions is possible. Using a standard game-theoretic representation of the state space as a tree structure generated by the actions of agents (including acts of nature), we show how unawareness of propositions can be represented by a coarsening of the state space. Furthermore we develop a semantics rich enough to describe the individual's awareness that currently undiscovered propositions may be discovered in the future. Introducing probability concepts, we derive a representation of ambiguity in terms of multiple priors, reflecting implicit beliefs about undiscovered proposition, and derive conditions for the special case in which standard Bayesian learning may be applied to a subset of unambiguous propositions. Finally, we consider exploration strategies appropriate to the context of discovery, comparing and contrasting them with learning strategies appropriate to the context of justification, and sketch applications to scientific research and entrepreneurship.

Data clustering using a model granular magnet

We present a new approach to clustering, based on the physical properties of an inhomogeneous ferromagnet. No assumption is made regarding the underlying distribution of the data. We assign a Potts spin to each data point and introduce an interaction between neighboring points, whose strength is a decreasing function of the distance between the neighbors. This magnetic system exhibits three phases. At very low temperatures it is completely ordered; all spins are aligned. At very high temperatures the system does not exhibit any ordering and in an intermediate regime clusters of relatively strongly coupled spins become ordered, whereas different clusters remain uncorrelated. This intermediate phase is identified by a jump in the order parameters. The spin-spin correlation function is used to partition the spins and the corresponding data points into clusters. We demonstrate on three synthetic and three real data sets how the method works. Detailed comparison to the performance of other techniques clearly indicates the relative success of our method.Comment: 46 pages, postscript, 15 ps figures include

An Investigation of Clustering Algorithms in the Identification of Similar Web Pages

In this paper we investigate the effect of using clustering algorithms in the reverse engineering field to identify pages that are similar either at the structural level or at the content level. To this end, we have used two instances of a general process that only differ for the measure used to compare web pages. In particular, two web pages at the structural level and at the content level are compared by using the Levenshtein edit distances and Latent Semantic Indexing, respectively. The static pages of two web applications and one static web site have been used to compare the results achieved by using the considered clustering algorithms both at the structural and content level. On these applications we generally achieved comparable results. However, the investigation has also suggested some heuristics to quickly identify the best partition of web pages into clusters among the possible partitions both at the structural and at the content level