We consider the complexity of computing Boolean functions by analog circuits of bounded fan-in, i.e., by circuits of gates computing real-valued functions, either exactly or as sign-representation. Sharp upper bounds are obtained for the complexity of the most difficult n-variable function over certain bases (sign-representation by arithmetic circuits and exact computation by piecewise linear c...

We consider the ǫ-regime of QCD in 3 dimensions. It is shown that the leading term of the effective partition function satisfies a set of Toda lattice equations, recursive in the number of flavors. Taking the replica limit of these Toda equations allows us to derive the microscopic spectral correlation functions for the QCD Dirac operator in 3 dimensions. For an even number of flavors we reprod...

We prove that if V n is a Chebyshev system on the circle and f(x) is a continuous function with at least n + 1 sign changes then there exists an orientation preserving diffeomorphism of S that takes f to a function L-orthogonal to V . We also prove that if f(x) is a function on the real projective line with at least four sign changes then there exists an orientation preserving diffeomorphism of...

We present a novel method to compute the overlap Dirac operator at zero and nonzero quark chemical potential. To approximate the sign function of large, sparse matrices, standard methods project the operator on a much smaller Krylov subspace, on which the matrix function is computed exactly. However, for large lattices this subspace can still be too large for an efficient calculation of the sig...

Pathogen recognition receptors (PRRs) function to maintain the balance between controlled responses to pathogens and uncontrolled innate immune activation leading to inflammation. In the context of commensal bacteria and the etiology of inflammatory bowel disease, although a role for the TLRs is known, there is a less defined function for C-type lectin receptors (CLRs). We demonstrate that mice...

We investigate QCD in the canonical ensemble with respect to the quark number. We reveal that the canonical description in which the quark number is fixed would be reduced to the grand canonical description under the thermodynamic limit. Since the grand canonical ensemble contains fluctuations of the quark number, the idea of the canonical ensemble is of no use for the purpose of defining order...

This paper describes an algorithm for solving large state-space MDPs (represented as factored MDPs) using search by successive refinement in the space of non-homogeneous partitions. Homogeneity is defined in terms of bisimulation and reward equivalence within blocks of a partition. Since homogeneous partitions that define equivalent reduced state-space MDPs can have a large number of blocks, we...

In single-index models the link or response function is not considered as fixed. The data determine the form of the unknown link function. In order to obtain a flexible form of the link function we specify the link function as an expansion in basis function and propose to estimate parameters as well as the link function by weak learners within a boosting framework. It is shown that the method i...

Lyapunov theory-based radial basis function neural network (RBFNN) is developed for traffic sign recognition in this paper to perform multiple inputs multiple outputs (MIMO) classification. Multidimensional input is inserted into RBF nodes and these nodes are linked with multiple weights. An iterative weight adaptation scheme is hence designed with regards to the Lyapunov stability theory to ob...