Beyond their security guarantees under well-studied assumptions, algebraic pseudo-random functions are motivated by their compatibility with efficient zero-knowledge proof systems, which is useful in a number of privacy applications like digital cash. We consider the problem of proving the correct evaluation of lattice-based PRFs based on the Learning-With-Rounding (LWR) problem introduced by B...

This survey is intended as a brief introduction to the theory of hyperbolic buildings and their lattices. Hyperbolic buildings are negatively curved geometric objects which also have a rich algebraic and combinatorial structure, and the study of these buildings and the lattices in their automorphism groups involves a fascinating mixture of techniques from many different areas of mathematics. Ro...

Nuclear reactions in a lattice are described using an extension of the resonating group method to include the lattice explicitly. Phonon exchange during fusion and dissociation reactions is predicted Second-order site-other-site reactions are predicted under conditions where the reactions at each site exchange phonons with a common phonon mode. The null reaction in which a dd-fusion at one site...

We prove a von Neumann type ergodic theorem for averages of unitary operators arising from the Furstenberg-Poisson boundary representation (the quasi-regular representation) of any lattice in a non-compact connected semisimple Lie group with finite center.

The quasi-classical ∂̄-dressing method is used to derive compact generating equations for dispersionless hierarchies. Dispersionless Kadomtsev-Petviashvili (KP) and two-dimensional Toda lattice (2DTL) hierarchies are considered as illustrative examples.

We establish the theoretical feasibility of direct analog simulation of the compact U(1) lattice gauge theories in optical lattices with dipolar bosons. We discuss the realizability of the topological Coulomb phase in extended Bose-Hubbard models in several optical lattice geometries. We predict the testable signatures of this emergent phase in noise correlation measurements, thus suggesting th...

Let G be a noncompact real algebraic group and Γ < G a lattice. One purpose of this paper is to show that there is an smooth, volume preserving, mixing action of G or Γ on a compact manifold which admits a smooth deformation. We also describe some other, rather special, deformations when G = SO(1, n) and provide a simple proof that any action of a compact Lie group is locally rigid.

The paper presents the Position Specific Posterior Lattice, a novel lossy representation of automatic speech recognition lattices that naturally lends itself to efficient indexing and subsequent relevance ranking of spoken documents. Albeit lossy, the PSPL lattice is much more compact than the ASR 3-gram lattice from which it is computed, at virtually no degradation in word-error-rate performan...

Given a lattice Λ in a locally compact abelian group G and a measurable subset Ω with finite and positive measure, then the set of characters associated to the dual lattice form a frame for L2(Ω) if and only if the distinct translates by Λ of Ω have almost empty intersections. Some consequences of this results are the wellknown Fuglede theorem for lattices, as well as a simple characterization ...

In this paper we give a natural ordering relation between distances based on 3D-neighbourhood sequences. We prove that this ordering induces a complete compact distributive lattice over the set of 3D-neighbourhood sequences.