We define ambient isotopy invariants of oriented knots and links using the counting invariants of framed links defined by finite racks. These invariants reduce to the usual quandle counting invariant when the rack in question is a quandle. We are able to further enhance these counting invariants with 2-cocycles from the coloring rack’s second rack cohomology satisfying a new degeneracy conditio...

The recent surge of interest in reasoning about probabilistic graphical models has led to the development of various techniques for probabilistic reasoning. Of these, techniques based on weighted model counting are particularly interesting since they can potentially leverage recent advances in unweighted model counting and in propositional satisfiability solving. In this paper, we present a new...

Many fundamental multi-processor coordination problems can be expressed as counting problems: processes must cooperate to assign successive values from a given range, such as addresses in memory or destinations on an interconnection network. Conventional solutions to these problems perform poorly because of synchronization bottlenecks and high memory contention. Motivated by observations on the...

Full counting statistics is a fundamentally new concept in quantum transport. After a review of basic statistics theory, we introduce the powerful Green’s function approach to full counting statistics. To illustrate the concept we consider a number of examples. For generic two-terminal contacts we show how counting statistics elucidates the common (and different) features of transport between n...

This paper introduces a new instantaneous frequency computation approach -Counting Instantaneous Frequency for a general class of signals called simple waves. The classsimple wave contains a wide range of continuous signals for which the concept instantaneous frequency has a perfect physical sense. The concept of -Counting Instantaneous Frequency also applies to all the discrete data. For all t...

We prove that counting copies of any graph F in another graph G can be achieved using basic matrix operations on the adjacency matrix of G. Moreover, the resulting algorithm is competitive for medium-sized F : our algorithm recovers the best known complexity for rooted 6-clique counting and improves on the best known for 9-cycle counting. Underpinning our proofs is the new result that, for a ge...

We hypothesize that the correct power counting for charmonia is in the parameter ΛQCD/mc, but is not based purely on dimensional analysis (as is HQET). This power counting leads to predictions which differ from those resulting from the usual velocity power counting rules of NRQCD. In particular, we show that while ΛQCD/mc power counting preserves the empirically verified predictions of spin sym...

Model counting is a fundamental problem which has been influential in many applications, from artificial intelligence to formal verification. Due the intrinsic hardness of model counting, approximate techniques have developed solve real-world instances counting. This paper designs new anytime approach called PartialKC for The idea form partial knowledge compilation provide an unbiased estimate ...