We introduce the notion of a cosheaf on a fan Σ and define the Z2 Hodge spaces Hpq(Σ), which are the homology groups Hp(∧E ) of the qth exterior power of the cosheaf E on Σ. Geometrically, for σ ∈ Σ the stalk Eσ of the cosheaf E is the compact real torus in the real orbit Oσ(R) of the real toric variety XΣ(R). The Z2 Hodge spaces Hpq(Σ) are indexed by pairs p, q with 0 ≤ q ≤ p ≤ d, where d = di...

We present a game-theoretic model of the polymorphic λ-calculus, system F , as a fibred category. Every morphism σ of the model defines an η-expanded, β-normal form σ̂ of system F whose interpretation is σ. Thus the model gives a precise, non-syntactic account of the calculus.

All compact AC(σ) operators have a representation analogous to that for compact normal operators. As a partial converse we obtain conditions which allow one to construct a large number of such operators. Using the results in the paper, we answer a number of questions about the decomposition of a compact AC(σ) into real and imaginary parts.

We continue our recent work on finite-sample, i.e., non-asymptotic, inference with two-step, monotone incomplete data from Nd(μ,Σ), a multivariate normal population with mean μ and covariance matrix Σ. Under the assumption that Σ is block-diagonal when partitioned according to the two-step pattern, we derive the distributions of the diagonal blocks of b Σ and of the estimated regression matrix,...

The conditional Gauss–Hermite filter (CGHF) utilizes a decomposition of the filter density p(y1, y2) into the product of the conditional density p(y1|y2) with p(y2) where the state vector y is partitioned into (y1, y2). In contrast to the usual Gauss–Hermite filter (GHF) it is assumed that the product terms can be approximated by Gaussians. Due to the nonlinear dependence of φ(y1|y2) from y2, q...

Hammett constants (σ) can be important factor to understanding substitution and position effects on benzoic acid. This report describes a computational study of ∆G◦ and σ for six substituted benzoic acid (X= F,Cl ,OH ,NH2 ,CN,NO2 )and phenylacetic acid substituted (X=OH ,NH2 ) at para and meta positions ingas and aqueousphases by DFT method and comparesit to available experimental and theoretic...

We study the spreading of single-site excitations in one-dimensional disordered Klein-Gordon chains with tunable nonlinearity |u(l)|(σ)u(l) for different values of σ. We perform extensive numerical simulations where wave packets are evolved (a) without and (b) with dephasing in normal-mode space. Subdiffusive spreading is observed with the second moment of wave packets growing as t(α). The depe...