The correspondences proposed previously between higher spin gauge theories and free singleton field theories were recently extended into a more complete picture by Klebanov and Polyakov in the case of the minimal bosonic theory inD = 4 to include the strongly coupled fixed point of the 3d O(N) vector model. Here we propose an N = 1 supersymmetric version of this picture. We also elaborate on th...

this note introduces a new general conjecture correlating the dimensionality dt of an infinitelattice with n nodes to the asymptotic value of its wiener index w(n). in the limit of large nthe general asymptotic behavior w(n)≈ns is proposed, where the exponent s and dt are relatedby the conjectured formula s=2+1/dt allowing a new definition of dimensionality dw=(s-2)-1.being related to the topol...

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...

We conjecture that neutrino physics might correspond to the spontaneous magnetisation phase of an Ising-like spin model interaction coupled to neutrino chirality which operates at scales close to the Planck mass. We argue that this scenario leads to a simple extension of the Standard Model with no additional parameters that dynamically generates parity violation and spontaneous symmetry breakin...

Hypercubes are known to be able to simulate other structures such as grids and binary trees. It has been shown that an arbitrary binary tree can be embedded into a hypercube with constant expansion and constant dilation. This paper presents a simple linear-time heuristic which embeds an arbitrary binary tree into a hypercube with expansion 1 and average dilation no more than 2. We also give som...

We survey a number of powerful recent results concerning diophantine and asymptotic properties of (ordinary) characters of symmetric groups. Apart from their intrinsic interest, these results are motivated by a connection with subgroup growth theory and the theory of random walks. As applications, we present an estimate for the subgroup growth of an arbitrary Fuchsian group, as well as a finite...

A Lagrangian description of a maximally supersymmetric conformal field theory in three dimensions was constructed recently by Bagger and Lambert (BL). The BL theory has SO(4) gauge symmetry and contains scalar and spinor fields that transform as 4-vectors. We verify that this theory has OSp(8|4) superconformal symmetry and that it is parity conserving despite the fact that it contains a Chern–S...

Physical Unclonable Functions (PUFs) are a promising new cryptographic primitive that leverage manufacturing variation to create unclonable secrets in embedded systems. In this case, the secret is no longer stored permanently in digital form, but rather as the physical properties of the manufactured chip. Further, the recent proposal of "Public Model Physical Unclonable Functions" (PPUFs) does ...

We determine the generating function counting the asymptotic number of (minimal) codewords of low weight for standard parallel concatenated (turbo) code ensembles. We then show that the number of minimal codewords of weight up to some fixed constant follows in the limit of large block lengths a Poisson distribution. In analogy to the standard random graph model, we conjecture that this statemen...

Given an elliptic curve E defined over Q, we are motivated by the 2-part of the Birch and Swinnerton-Dyer formula to study the relation between the 2-Selmer rank of E and the 2-Selmer rank of an abelian variety A obtained by Ribet’s level raising theorem. For certain imaginary quadratic fields K satisfying the Heegner hypothesis, we prove that the 2-Selmer ranks of E and A over K have different...