A second-order random walk on a graph or network is where transition probabilities depend not only the present node but also previous one. notable example non-backtracking walk, walker allowed to revisit in one step. Second-order walks can model physical diffusion phenomena more realistic way than traditional and have been very successfully used various mining machine learning settings. However...

High temperature series for the magnetic susceptibility, χ, of random anisotropy axis models in the limit of infinite anisotropy are presented, for two choices of the number of spin components, m. For m=2, we find T c =1.78 J on the simple cubic lattice, and on the face‐centered cubic lattice we find T c =4.29 J. There is no divergence of χ at finite temperature for m=3 on either lattice. For t...

In this paper, we study the high-order phase transition in random r-uniform hypergraphs. For a positive integer n and a real p ∈ [0, 1], let H := H(n, p) be the random r-uniform hypergraph on the vertex set [n], where each r-set is an edge with probability p independently. For 1 ≤ s ≤ r − 1 and two s-sets S and S, we say S is connected to S if there is a sequence of alternating s-sets and edges...

Recent experiments have found that polyisocyanates composed of a mixture of opposite enantiomers follow a chiral “majority rule:” the chiral order of the copolymer, measured by optical activity, is dominated by whichever enantiomer is in the majority. We explain this majority rule theoretically by mapping the random copolymer onto the random-field Ising model. Using this model, we predict the c...

In an online problem, information is revealed incrementally and decisions have to be made before the full information is known. This occurs in various applications like, for example, resource allocation or online ad assignment. To analyze the performance of algorithms for online problems, it is classically assumed that there is a malicious adversary who always provides the worst-possible input....

This paper describes am-ary exponentiation algorithm where the radix-m digits of an exponent can be treated in a somewhat random order without using any more group operations than a standard rightto-left m-ary exponentiation. This paper demonstrates that the random order countermeasure, commonly used to protect implementations of secret key cryptographic algorithms, can be applied to public key...

Contention resolution schemes have proven to be an incredibly powerful concept which allows to tackle a broad class of problems. The framework has been initially designed to handle submodular optimization under various types of constraints, that is, intersections of exchange systems (including matroids), knapsacks, and unsplittable flows on trees. Later on, it turned out that this framework per...