Projective Ring Line of an Arbitrary Single Qudit

As a continuation of our previous work (arXiv:0708.4333) an algebraic geometrical study of a single $d$-dimensional qudit is made, with $d$ being {\it any} positive integer. The study is based on an intricate relation between the symplectic module of the generalized Pauli group of the qudit and the fine structure of the projective line over the (modular) ring \bZ_{d}. Explicit formulae are given for both the number of generalized Pauli operators commuting with a given one and the number of points of the projective line containing the corresponding vector of \bZ^{2}_{d}. We find, remarkably, that a perp-set is not a set-theoretic union of the corresponding points of the associated projective line unless $d$ is a product of distinct primes. The operators are also seen to be structured into disjoint `layers' according to the degree of their representing vectors. A brief comparison with some multiple-qudit cases is made

Parameter estimation for generalized thurstone choice models

We consider the maximum likelihood parameter estimation problem for a generalized Thurstone choice model, where choices are from comparison sets of two or more items. We provide tight characterizations of the mean square error, as well as necessary and sufficient conditions for correct classification when each item belongs to one of two classes. These results provide insights into how the estimation accuracy depends on the choice of a generalized Thurstone choice model and the structure of comparison sets. We find that for a priori unbiased structures of comparisons, e.g., when comparison sets are drawn independently and uniformly at random, the number of observations needed to achieve a prescribed estimation accuracy depends on the choice of a generalized Thurstone choice model. For a broad set of generalized Thurstone choice models, which includes all popular instances used in practice, the estimation error is shown to be largely insensitive to the cardinality of comparison sets. On the other hand, we found that there exist generalized Thurstone choice models for which the estimation error decreases much faster with the cardinality of comparison sets

Generalized Elastic Model: thermal vs non-thermal initial conditions. Universal scaling, roughening, ageing and ergodicity

We study correlation properties of the generalized elastic model which accounts for the dynamics of polymers, membranes, surfaces and fluctuating interfaces, among others. We develop a theoretical framework which leads to the emergence of universal scaling laws for systems starting from thermal (equilibrium) or non-thermal (non-equilibrium) initial conditions. Our analysis incorporates and broadens previous results such as observables' double scaling regimes, (super)roughening and anomalous diffusion, and furnishes a new scaling behavior for correlation functions at small times (long distances). We discuss ageing and ergodic properties of the generalized elastic model in non-equilibrium conditions, providing a comparison with the situation occurring in continuous time random walk. Our analysis also allows to assess which observable is able to distinguish whether the system is in or far from equilibrium conditions in an experimental set-up

A Codebook Generation Algorithm for Document Image Compression

Pattern-matching-based document-compression systems (e.g. for faxing) rely on finding a small set of patterns that can be used to represent all of the ink in the document. Finding an optimal set of patterns is NP-hard; previous compression schemes have resorted to heuristics. This paper describes an extension of the cross-entropy approach, used previously for measuring pattern similarity, to this problem. This approach reduces the problem to a k-medians problem, for which the paper gives a new algorithm with a provably good performance guarantee. In comparison to previous heuristics (First Fit, with and without generalized Lloyd's/k-means postprocessing steps), the new algorithm generates a better codebook, resulting in an overall improvement in compression performance of almost 17%