We present a novel framework for denoising signals from their compact representation in multiple domains. Each domain captures, uniquely, certain signal characteristics better than others. We define confidence sets around data in each domain and find sparse estimates that lie in the intersection of these sets, using a POCS algorithm. Simulations demonstrate the superior nature of the reconstruc...

The number of satisfying assignments of k-CNF formulas is computed using the inclusion-exclusion formula for sets of clauses. Recently, it was shown that the information on the sets of clauses of size ≤ log k + 2 already uniquely determines the number of satisfying assignments of k-CNF formulas [1]. The proof was, however, only existential and no explicit procedure was presented. In this paper,...

A set T ⊂ R at which interpolation from Π≤n(R ) (polynomials of degree ≤ n) is uniquely possible is a GCn-set if the associated Lagrange fundamental polynomials have only linear factors. For such GCn-sets T in the plane, Gasca and Maeztu conjectured the existence of a line containing n + 1 points from T. It is shown here that, already in R, there exist GC2-sets T without any hyperplanes contain...

Primates undoubtedly have impressive abilities in perceiving, recognizing, manipulating, and predicting other individuals, but only great apes seem to recognize the cognitive basis of manipulative and cooperative tactics or the concept of self. None of these abilities is unique to primates. We distinguish (1) a package of quantitative advantages in social sophistication, perhaps based on more e...

Existing algorithms for generating referential descriptions to sets of objects have serious deficits: while incremental approaches may produce ambiguous and redundant expressions, exhaustive searches are computationally expensive. Mediating between these extreme control regimes, we propose a best-first searching algorithm for uniquely identifying sets of objects. We incorporate linguistically m...

Abstract We introduce languages of higher-dimensional automata (HDAs) and develop some their properties. To this end, we define a new category precubical sets, uniquely naturally isomorphic to the standard one, notion event consistency. HDAs are then finite, labeled, event-consistent sets with distinguished subsets initial accepting cells. Their interval orders closed under subsumption; as majo...

A dominating set S of a graph is a metric-locating-dominating set if each vertex of the graph is uniquely distinguished by its distances from the elements of S, and the minimum cardinality of such a set is called the metric-locationdomination number. In this paper, we undertake a study that, in general graphs and specific families, relates metric-locating-dominating sets to other special sets: ...

Uniquely closable skeletons of lambda terms are Motzkin-trees that predetermine the unique closed lambda term that can be obtained by labeling their leaves with de Bruijn indices. Likewise, uniquely typable skeletons of closed lambda terms predetermine the unique simply-typed lambda term that can be obtained by labeling their leaves with de Bruijn indices. We derive, through a sequence of logic...