We study the group-valued and semigroup-valued conservation laws in cellular automata (CA). We provide examples to distinguish between semigroup-valued, group-valued and real-valued conservation laws. We prove that, even in one-dimensional case, it is undecidable if a CA has any non-trivial conservation law of each type. For a fixed range, each CA has a most general (group-valued or semigroup-v...

Many learning systems use the space of logic formulas as the search space of hypotheses. To build eecient systems, the set of rst order logic formulas can be reduced in many ways. Most systems restrict themselves to (subsets of) Horn clauses. In this paper we investigate the space of reduced rst order sentences, which has the same expressive power as an arbritrary rst order logic. Shapiro 6] ha...

Multi-level modeling aims to reduce redundancy in data models by defining properties at the right abstraction level and inheriting them to more specific levels. We revisit one of the earliest such approaches, Telos, and investigate what needs to be added to its axioms to get a true multi-level modeling language. Unlike previous approaches, we define levels not with numeric potencies but with hi...

We obtain the most general spherically symmetric M2-branes and type IIB strings, with R 1,2 × SO(8) and R 1,1 × SO(8) isometries, respectively. We find that there are 12 different classes of M2-branes, and we study their curvature properties. In particular, we obtain new smooth M2-brane wormholes that connect two asymptotic regions: one is flat and the other can be either flat or AdS 4 × S 7. W...

We consider a graph polynomial ξ(G;x, y, z) introduced by Ilia Averbouch, Benny Godlin, and Johann A. Makowsky (2008). This graph polynomial simultaneously generalizes the Tutte polynomial as well as a bivariate chromatic polynomial defined by Klaus Dohmen, André Pönitz, and Peter Tittmann (2003). We derive an identity which relates the graph polynomial ξ of a thickened graph (i.e. a graph with...

Consider the subband coder of figure 1, consisting of k = 0, 1, ..., M − 1 channels. Each channel has an analysis filter H k (z), a synthesis filter F k (z), down/up-sampling ratio m k , and a b k bit quantizer. The input is x[n], after passing through the analysis filters it becomes x k [n], and the subband signals are x k [n]. The subband coder is maximally decimated, M −1 k=0 m k = 1. (1) As...

In medical research logistic regression and Cox proportional hazards regression analysis, in which all the confounders are included as covariates, are often used to estimate an adjusted treatment effect in observational studies. In the last decade the method of propensity scores has been developed as an alternative adjustment method and many examples of applications can be found in the literatu...

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This article presents axioms for comparative conditional probability relations. The axioms presented here are more general than usual. Each comparative relation is a weak partial order on pairs of sentences (i.e. each relation is transitive and reflexive) but need not be a complete order relation. The axioms for these comparative relations are probabilistically sound for the broad class of cond...