Linear recurrences and asymptotic behavior of exponential sums of symmetric boolean functions

In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer coefficients that exponential sums of symmetric Boolean functions satisfy. This improvement is tight. We also compute the asymptotic behavior of symmetric Boolean functions and provide a formula that allows us to determine if a symmetric boolean function is asymptotically not balanced. In particular, when the degree of the symmetric function is a power of two, then the exponential sum is much smaller than $2^n$.Comment: 18 pages, 3 figure

Gauge field theory approach to spin transport in a 2D electron gas

We discuss the Pauli Hamiltonian including the spin-orbit interaction within an U(1) x SU(2) gauge theory interpretation, where the gauge symmetry appears to be broken. This interpretation offers new insight into the problem of spin currents in the condensed matter environment, and can be extended to Rashba and Dresselhaus spin-orbit interactions. We present a few outcomes of the present formulation: i) it automatically leads to zero spin conductivity, in contrast to predictions of Gauge symmetric treatments, ii) a topological quantization condition leading to voltage quantization follows, and iii) spin interferometers can be conceived in which, starting from a arbitrary incoming unpolarized spinor, it is always possible to construct a perfect spin filtering condition.Comment: Invited contribution to Statphys conference, June 2009, Lviv (Ukraine

Equilibrium currents in a Corbino graphene ring

We address the description of a graphene Corbino disk in the context of a tight binding approach that includes both kinetic and Rashba spin-orbit coupling due to an external out-of-plane electric field. Persistent equilibrium currents are induced by an external magnetic field breaking time reversal symmetry. By direct diagonalization, we compute the spectrum and focus on the dispersion near the $K$ points at the Fermi level. The dispersion keenly reproduces that of a continuum model in spite of the complexity of the boundary conditions. We validate the assumptions of the continuum model in terms of predominant zig-zag boundaries conditions and weak sub-band coupling. The wave functions displaying the lowest transverse modes are obtained, showing the predominance of edge states with charge density at the zig-zag edges. The persistent charge currents, nevertheless, do not follow the traditional argument of current cancellation from levels below the Fermi level, and thus they depart in the tight-binding from those found in the continuum model.Comment: 8 pages, 6 figure

On a class of minimum contrast estimators for Gegenbauer random fields

The article introduces spatial long-range dependent models based on the fractional difference operators associated with the Gegenbauer polynomials. The results on consistency and asymptotic normality of a class of minimum contrast estimators of long-range dependence parameters of the models are obtained. A methodology to verify assumptions for consistency and asymptotic normality of minimum contrast estimators is developed. Numerical results are presented to confirm the theoretical findings.Comment: 23 pages, 8 figure

An Energy-conscious Transport Protocol for Multi-hop Wireless Networks

We present a transport protocol whose goal is to reduce power consumption without compromising delivery requirements of applications. To meet its goal of energy efficiency, our transport protocol (1) contains mechanisms to balance end-to-end vs. local retransmissions; (2) minimizes acknowledgment traffic using receiver regulated rate-based flow control combined with selected acknowledgements and in-network caching of packets; and (3) aggressively seeks to avoid any congestion-based packet loss. Within a recently developed ultra low-power multi-hop wireless network system, extensive simulations and experimental results demonstrate that our transport protocol meets its goal of preserving the energy efficiency of the underlying network.Defense Advanced Research Projects Agency (NBCHC050053

A Two-step Statistical Approach for Inferring Network Traffic Demands (Revises Technical Report BUCS-2003-003)

Accurate knowledge of traffic demands in a communication network enables or enhances a variety of traffic engineering and network management tasks of paramount importance for operational networks. Directly measuring a complete set of these demands is prohibitively expensive because of the huge amounts of data that must be collected and the performance impact that such measurements would impose on the regular behavior of the network. As a consequence, we must rely on statistical techniques to produce estimates of actual traffic demands from partial information. The performance of such techniques is however limited due to their reliance on limited information and the high amount of computations they incur, which limits their convergence behavior. In this paper we study a two-step approach for inferring network traffic demands. First we elaborate and evaluate a modeling approach for generating good starting points to be fed to iterative statistical inference techniques. We call these starting points informed priors since they are obtained using actual network information such as packet traces and SNMP link counts. Second we provide a very fast variant of the EM algorithm which extends its computation range, increasing its accuracy and decreasing its dependence on the quality of the starting point. Finally, we evaluate and compare alternative mechanisms for generating starting points and the convergence characteristics of our EM algorithm against a recently proposed Weighted Least Squares approach.National Science Foundation (ANI-0095988, EIA-0202067, ITR ANI-0205294