In this work we find the isomonodromic (Jimbo-Miwa) tau-function corresponding to Frobenius manifold structures on Hurwitz spaces. We discuss several applications of this result. First, we get an explicit expression for the G-function (solution of Getzler’s equation) of the Hurwitz Frobenius manifolds. Second, in terms of this tau-function we compute the genus one correction to the free energy ...

In this article we prove that quasi-multiplicative (with respect to the usual length function) mappings on the permutation group Sn (or, more generally, on arbitrary amenable Coxeter groups), determined by self-adjoint contractions fulfilling the braid or Yang-Baxter relations, are completely positive. We point out the connection of this result with the construction of a Fock representation of ...

A class of graphs is Kruskalian if Kruskal’s theorem on a well-quasi-ordering of finite trees provides a finite characterization in terms of forbidden induced subgraphs. Let k be a natural number. A graph is a k-cograph if its vertices can be colored with colors from the set {1, . . . ,k} such that for every nontrivial subset of vertices W there exists a partition {W1,W2} of W into nonempty sub...

We study the initial value problem for the quasi-geostrophic type equations ∂θ ∂t + u · ∇θ + (−∆)θ = 0, on R × (0,∞), θ(x, 0) = θ0(x), x ∈ R n , where λ(0 ≤ λ ≤ 1) is a fixed parameter and u = (uj) is divergence free and determined from θ through the Riesz transform uj = ±Rπ(j)θ, with π(j) a permutation of 1, 2, · · · , n. The initial data θ0 is taken in the Sobolev space L̇r,p with negative ind...

This paper is devoted to dealing with global attitude synchronization problems for networked rigid bodies subjected directed topologies and arbitrary initial orientations. To avoid the asynchronous pitfall where only vector parts of reach agreement on some identical value but scalar do not, multiplicative quaternion errors are incorporated develop protocols absolute measurements. It shown that ...

In this paper a new permutation generator is proposed. Each subsequent permutation is generated in a cellular permutation network by reversing a suffix/prefix of the preceding permutation. The sequence of suffix/prefix sizes is computed by a complex parallel counter in O(1) time per generated object. Suffix/prefix reversing operations are performed at the same time when the permutation is actua...

The technique of in-situ associative permuting is introduced which is an association of in-situ permuting and in-situ inverting. It is suitable for associatively permutable permutations of {1, 2, . . . , n} where the elements that will be inverted are negative and stored in order relative to each other according to their absolute values. Let K[1 . . . n] be an array of n integer keys each in th...

In this paper , an LDPC decoder fully compliant to the G.hn standard is presented. The decoder implements one kind of Layered Decoding Algorithm – turbo decoding massage passing (TDMP) algorithm for Quasi-Cyclic LDPC codes. A simple early termination strategy is presented to significantly increase the throughput and reduce the power consumption. Partially parallel architecture with an overlappe...

A quasi-cyclic (QC) low-density parity-check (LDPC) code can be viewed as the protograph code with circulant permutation matrices. In this paper, we find all the subgraph patterns of protographs of QC LDPC codes having inevitable cycles of length 2i, i = 6, 7, 8, 9, 10, i.e., the cycles existing regardless of the shift values of circulants. It is also derived that if the girth of the protograph...

A procedure is developed to test the null hypothesis of conditional homoskedasticity in the context of GARCH models. The approach is based on the quasi-likelihood function, leaving the true distribution of model disturbances completely unspecified. The presence of possible nuisance parameters in the testing problem is dealt with by using a pivotal bound and Monte Carlo resampling techniques to ...