Fuzzy Logic Control of Adaptive ARQ for Video Distribution over a Bluetooth Wireless Link

Bluetooth's default automatic repeat request (ARQ) scheme is not suited to video distribution resulting in missed display and decoded deadlines. Adaptive ARQ with active discard of expired packets from the send buffer is an alternative approach. However, even with the addition of cross-layer adaptation to picture-type packet importance, ARQ is not ideal in conditions of a deteriorating RF channel. The paper presents fuzzy logic control of ARQ, based on send buffer fullness and the head-of-line packet's deadline. The advantage of the fuzzy logic approach, which also scales its output according to picture type importance, is that the impact of delay can be directly introduced to the model, causing retransmissions to be reduced compared to all other schemes. The scheme considers both the delay constraints of the video stream and at the same time avoids send buffer overflow. Tests explore a variety of Bluetooth send buffer sizes and channel conditions. For adverse channel conditions and buffer size, the tests show an improvement of at least 4 dB in video quality compared to nonfuzzy schemes. The scheme can be applied to any codec with I-, P-, and (possibly) B-slices by inspection of packet headers without the need for encoder intervention.</jats:p

Power-Constrained Fuzzy Logic Control of Video Streaming over a Wireless Interconnect

Wireless communication of video, with Bluetooth as an example, represents a compromise between channel conditions, display and decode deadlines, and energy constraints. This paper proposes fuzzy logic control (FLC) of automatic repeat request (ARQ) as a way of reconciling these factors, with a 40% saving in power in the worst channel conditions from economizing on transmissions when channel errors occur. Whatever the channel conditions are, FLC is shown to outperform the default Bluetooth scheme and an alternative Bluetooth-adaptive ARQ scheme in terms of reduced packet loss and delay, as well as improved video quality

A numerical finite size scaling approach to many-body localization

We develop a numerical technique to study Anderson localization in interacting electronic systems. The ground state of the disordered system is calculated with quantum Monte-Carlo simulations while the localization properties are extracted from the ``Thouless conductance'' $g$, i.e. the curvature of the energy with respect to an Aharonov-Bohm flux. We apply our method to polarized electrons in a two dimensional system of size $L$. We recover the well known universal $\beta(g)=\rm{d}\log g/\rm{d}\log L$ one parameter scaling function without interaction. Upon switching on the interaction, we find that $\beta(g)$ is unchanged while the system flows toward the insulating limit. We conclude that polarized electrons in two dimensions stay in an insulating state in the presence of weak to moderate electron-electron correlations.Comment: 5 pages, 4 figure

Local Fractional Supersymmetry for Alternative Statistics

A group theory justification of one dimensional fractional supersymmetry is proposed using an analogue of a coset space, just like the one introduced in $1D$ supersymmetry. This theory is then gauged to obtain a local fractional supersymmetry {\it i.e.} a fractional supergravity which is then quantized {\it \`a la Dirac} to obtain an equation of motion for a particle which is in a representation of the braid group and should describe alternative statistics. A formulation invariant under general reparametrization is given, by means of a curved fractional superline.Comment: 15 pages, latex, no figur

Fractional Supersymmetry and Fth-Roots of Representations

A generalization of super-Lie algebras is presented. It is then shown that all known examples of fractional supersymmetry can be understood in this formulation. However, the incorporation of three dimensional fractional supersymmetry in this framework needs some care. The proposed solutions lead naturally to a formulation of a fractional supersymmetry starting from any representation D of any Lie algebra g. This involves taking the Fth-roots of D in an appropriate sense. A fractional supersymmetry in any space-time dimension is then possible. This formalism finally leads to an infinite dimensional extension of g, reducing to the centerless Virasoro algebra when g=sl(2,R).Comment: 23 pages, 1 figure, LaTex file with epsf.st

On a graded q-differential algebra

Given a unital associatve graded algebra we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-th power (N>1) of the differential of this graded q-differential algebra is equal to zero. We use our approach to construct the graded q-differential algebra in the case of a reduced quantum plane which can be endowed with a structure of a graded algebra. We consider the differential d satisfying d to power N equals zero as an analog of an exterior differential and study the first order differential calculus induced by this differential.Comment: 6 pages, submitted to the Proceedings of the "International Conference on High Energy and Mathematical Physics", Morocco, Marrakech, April 200

Quantization on Curves

Deformation quantization on varieties with singularities offers perspectives that are not found on manifolds. Essential deformations are classified by the Harrison component of Hochschild cohomology, that vanishes on smooth manifolds and reflects information about singularities. The Harrison 2-cochains are symmetric and are interpreted in terms of abelian $*$-products. This paper begins a study of abelian quantization on plane curves over \Crm, being algebraic varieties of the form R2/I where I is a polynomial in two variables; that is, abelian deformations of the coordinate algebra C[x,y]/(I). To understand the connection between the singularities of a variety and cohomology we determine the algebraic Hochschild (co-)homology and its Barr-Gerstenhaber-Schack decomposition. Homology is the same for all plane curves C[x,y]/(I), but the cohomology depends on the local algebra of the singularity of I at the origin.Comment: 21 pages, LaTex format. To appear in Letters Mathematical Physic