Quasi-symmetric 2-(64,24,46) designs derived from AG(3,4)

This paper completes the enumeration of quasi-symmetric 2-$(64,24,46)$ designs supported by the dual code $C^{\perp }$ of the binary linear code $C$ spanned by the lines of $AG(3,4)$, initiated in Rodrigues and Tonchev (2015). It is shown that $C^{\perp }$ supports exactly 30,264 nonisomorphic quasi-symmetric 2-$(64,24,46)$ designs. The automorphism groups of the related strongly regular graphs are computed.     

p-Hub approach for the optimal park-and-ride facility location problem

Park and Ride facilities (P&R) are car parks at which users can transfer to public transportation to reach their final destination. We propose a mixed linear programming formulation to determine the location of a fixed number of P&R facilities so that their usage is maximized. The facilities are modeled as hubs. Commuters can use one of the P&R facilities or choose to travel by car to their destinations, and their behavior follows a logit model. We apply a p-hub approach considering that users incur in a known generalized cost of using each P&R facility as input for the logit model. For small instances of the problem, we propose a novel linearization of the logit model, which allows transforming the binary nonlinear programming problem into a mixed linear programming formulation. A modification of the Heuristic Concentration Integer (HCI) procedure is applied to solve larger instances of the problem. Numerical experiments are performed, including a case in Queens, NY. Further research is proposed.     

Semi-integer derivatives of the Airy functions and related properties of the Korteweg-de Vries-type equations

Fractional integrals and derivatives of Airy functions (Riesz potentials) are considered. For half integrals D ^−1/2 Ai(x) and D ^−1/2 Gi(x) explicit representations are found in terms of the products of Airy functions. Here Ai(x) and Gi(x) are the Airy function of the first kind and the Scorer function, respectively. Based on that representations are obtained for all semi-integer derivatives of Ai(x) and Gi(x). Applications to Korteweg–de Vries type equations are provided.      

Scientific contributions of Leo Khachiyan (a short overview)

On April 29, 2005, Leo Khachiyan passed away with tragic suddenness in the middle of his scientific career. He became famous for his polynomial time algorithm for linear programming (LP)[L. Khachiyan, A polynomial algorithm in linear programming, Soviet Math. Doklady 20 (1) (1979) 191-194; L. Khachiyan, Polynomial algorithms for linear programming, USSR Comp. Math. and Math. Phys. 20 (2) (1980) 51-68]. However, he contributed fundamentally to several other areas, as well. In this introductory paper, we would like to recall briefly his main contributions, and provide a complete (up to our best knowledge) list of his publications.     

On the Painlevé Property of Isomonodromic Deformations of Fuchsian Systems

We give a review of the modern theory of isomonodromic deformations of Fuchsian systems discussing both classical and modern results, such as a general form of the isomonodromic deformations of Fuchsian systems, their differences from the classical Schlesinger deformations, the Fuchsian system moduli space structure and the geometric meaning of new degrees of freedom appeared in a non-Schlesinger case. Using this we illustrate some general relations between such concepts as integrability, isomonodromy and Painlevé property. The work is supported by N.Sh.-6849.2006.1 and RFBR 07-01-00526 grants.     

Signature codes for noisy multiple access adder channel

We prove new lower bounds on the rate of codes for noisy multiple access adder channel and discuss its application to the well-known coin weighing problem in the case when some measurements are incorrect.     

Optimal signaling with cheap talk and money burning

We study Sender-optimal signaling equilibria with cheap talk and money-burning. Under general assumptions, the Sender never uses money-burning to reveal all states, but always wants to garble information for at least some states. With quadratic preferences and any log-concave density of the states, optimal communication is garbled for all states: money-burning, if used at all, is used to adjust pooling intervals. This is illustrated by studying in depth the well-known uniform-quadratic case. We also show how the presence of a cost of being “caught unprepared” that gives rise to a small change in a common assumption on the Receiver’s utility function makes full revelation through money-burning Sender-optimal.     

Random and algebraic permutations’ statistics

An algebraic permutation $\hat{A}\in S(N=n^{m})$ is the permutation of the N points of the finite torus ? _n ^m , realized by a linear operator A∈SL(m,? _n ). The statistical properties of algebraic permutations are quite different from those of random permutations of N points. For instance, the period length T(A) grows superexponentially with N for some (random) permutations A of N elements, whereas $T(\hat{A})$ is bounded by a power of N for algebraic permutations  $\hat{A}$ . The paper also contains a strange mean asymptotics formula for the number of points of the finite projective line P¹(? _n ) in terms of the zeta function.     

On Edgeworth expansions for dependency-neighborhoods chain structures and Stein's method

Let W be the sum of dependent random variables, and h(x) be a function. This paper provides an Edgeworth expansion of an arbitrary ``length' for %E{h(W)} in terms of certain characteristics of dependency, and of the smoothness of h and/or the distribution of W. The core of the class of dependency structures for which these characteristics are meaningful is the local dependency, but in fact, the class is essentially wider. The remainder is estimated in terms of Lyapunov's ratios. The proof is based on a Stein's method.Supported in part by NSF grant DMS-98-03623Supported in part by the Russian Foundation of Basic Research, grant # 00-01-00194, and by NSF grant DMS-98-03623Mathematics Subject Classification (2000):Primary 62E20; Secondary 60E05