We provide a number of new construction techniques for cubical complexes and cubical polytopes, and thus for cubifications (hexahedral mesh generation). As an application we obtain an instance of a cubical 4-polytope that has a non-orientable dual manifold (a Klein bottle). This confirms an existence conjecture of Hetyei (1995). More systematically, we prove that every normal crossing codimensi...

This paper studies a class of probabilistic models on graphs, where edge variables depend on incident node variables through a fixed probability kernel. The class includes planted constraint satisfaction problems (CSPs), as well as more general structures motivated by coding and community clustering problems. It is shown that under mild assumptions on the kernel, the conditional entropy of the ...

This paper studies a class of probabilistic models on graphs, where edge variables depend on incident node variables through a fixed probability kernel. The class includes planted constraint satisfaction problems (CSPs), as well as more general structures motivated by coding and community clustering problems. It is shown that under mild assumptions on the kernel and for sparse random graphs, th...

Recently, perfect matching in bounded planar cutwidth bipartite graphs (BGGM) was shown to be in ACC by Hansen et al. [8]. They also conjectured that the problem is in AC. In this paper, we disprove their conjecture by showing that the problem is not in AC[p] for every prime p. Our results show that the previous upper bound is almost tight. Our techniques involve giving a reduction from Parity ...

We prove that the Fourier dimension of any Boolean function with Fourier sparsity s is at most O ( s ) . Our proof method yields an improved bound of Õ( √ s) assuming a conjecture of Tsang et. al. [TWXZ13], that for every Boolean function of sparsity s there is an affine subspace of F2 of co-dimension O(poly log s) restricted to which the function is constant. This conjectured bound is tight up...

We examine empirically the conjecture that limits to speculation in the foreign exchange market may induce nonlinearities in the spot-forward relationship and in the process driving the deviations from the uncovered interest rate parity (UIP) condition. Our empirical results provide strong evidence of important nonlinearities which are consistent with a model of deviations from UIP with two ext...

We report on the observation of α decay from a state in 10B at 11.48 MeV. The only observed decay branch is to the first T = 1 state in 6Li at 3.56 MeV. The apparent absence of an α-decay branch to the (T = 0) ground state in 6Li suggests that the 11.48-MeV state should be assigned isospin T = 1. The spin and parity of the 11.48-MeV state could not be directly determined from the present study ...

Let q be a nonzero rational number. We investigate for which q there are in nitely many sets consisting of ve nonzero rational numbers such that the product of any two of them plus q is a square of a rational number. We show that there are in nitely many square-free such q and on assuming the Parity Conjecture for the twists of an explicitly given elliptic curve we derive that the density of su...

Recent results of Zlobin and Cresson-Fischler-Rivoal allow one to decompose any suitable p-uple series of hypergeometric type into a linear combination (over the rationals) of multiple zeta values of depth at most p; in some cases, only the multiple zeta values with 2's and 3's are involved (as in Hoffman's conjecture). In this text, we study the depth p part of this linear combination, namely ...