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Graphical representations of Ising and Potts models
Graphical representations Ising and Potts models
2010/11/18
We study graphical representations for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz a...
Representations of multidimensional linear process bridges
multidimensional linear process bridges math
2010/11/8
We derive bridges from general multidimensional linear non time-homogeneous processes using only the transition densities of the original process giving their integral representations (in terms of a s...
The number of Goldbach representations of an integer
Goldbach representations of an integer math
2010/11/19
We prove the following result: Let $N \geq 2$ and assume the Riemann Hypothesis (RH) holds. Then \[ \sum_{n=1}^{N} R(n) =\frac{N^{2}}{2} -2 \sum_{\rho} \frac{N^{\rho + 1}}{\rho (\rho + 1)} + O(N \log...
Modular branching rules for projective representations of symmetric groups and lowering operators for the supergroup Q(n)
projective representations symmetric groups lowering operators the supergroup Q(n)
2010/11/9
There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which...
Holomorphic Realization of Unitary Representations of Banach--Lie Groups
Holomorphic Realization Unitary Representations Banach--Lie Groups
2010/11/11
In this paper we explore the method of holomorphic induction for unitary representations of Banach--Lie groups. First we show that the classification of complex bundle structures on homogeneous Banac...
Representations of monomial algebras have poly-exponential complexities
monomial algebras poly-exponential complexities
2010/11/22
We use directed graphs called "syzygy quivers" to study the asymptotic growth rates of the dimensions of the syzygies of representations of finite dimensional algebras. For any finitely generated rep...
Free energy computations by minimization of Kullback-Leibler divergence: an efficient adaptive biasing potential method for sparse representations
Free energy Kullback-Leibler divergence
2010/11/17
The present paper proposes an adaptive biasing potential for the computation of free energy landscapes. It is motivated by statistical learning arguments and unifies the tasks of biasing the molecula...
Trianguline representations are a certain kind of p-adic representations of Gal(Qp^alg/Qp) like the crystalline, semistable and de Rham representations of Fontaine. Their definition involves the theo...
Neural Phase Oscillator Representations of Behavioral Stimulus-Response Models
Neural Phase Oscillator Representations Behavioral Stimulus Response Models
2010/11/15
The activity of a collection of neurons can be represented by weakly-coupled non-linear phase oscillators satisfying Kuramoto's equations. In this article, we build such neural-oscillator models, part...
An effective isomorphy criterion for mod $\ell$ Galois representations
effective isomorphy criterion mod $\ell$ Galois representations
2010/12/15
In this paper, we consider mod ℓ Galois representations of Q. In particular, we obtain an effective criterion to distinguish two semisimple 2-dimensional, odd mod ℓ Galois representations ...
Quasi-probability representations of quantum theory with applications to quantum information science
Quasi-probability representations quantum theory applications quantum information science
2010/11/5
This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability rep...
Approximate Representations and Approximate Homomorphisms
Approximate Representations Approximate Homomorphisms
2010/10/27
Approximate algebraic structures play a defining role in arithmetic combinatorics and have
found remarkable applications to basic questions in number theory and pseudorandomness.
Here we study appro...
Approximate Representations and Approximate Homomorphisms
Approximate Representations Approximate Homomorphisms
2010/12/15
Approximate algebraic structures play a defining role in arithmetic combinatorics and have
found remarkable applications to basic questions in number theory and pseudorandomness.
Discrete primitive-stable representations with large rank surplus
Primitive stable Whitehead graph Representations
2010/12/15
We construct a sequence of primitive-stable representations of free groups into PSL2(C) whose ranks go to in nity, but whose images are discrete with quotient manifolds that converge geometrically to ...
Tensor products of representations up to homotopy
Tensor products of representations homotopy
2010/12/14
We study the construction of tensor products of representations up to homotopy, which
are the A∞ version of ordinary representations. We provide formulas for the construction
of tensor products of r...