Aperiodic tilings and entropy

In this paper we present a construction of Kari-Culik aperiodic tile set - the smallest known until now. With the help of this construction, we prove that this tileset has positive entropy. We also explain why this result was not expected

Jets and Jet Multiplicities in High Energy Photon-Nucleon Inetraction:

We discuss the theory of jet events in high-energy photon-proton interactions using a model which gives a good description of the data available on total inelastic $\gamma p$ cross sections up to $\sqrt{s}$=210 GeV. We show how to calculate the jet cross sections and jet multiplicities and give predictions for these quantities for energies appropriate for experiments at the HERA $ep$ collider and for very high energy cosmic ray observations.Comment: 12 pages + 4 figs, MAD/TH/92-8, submitted to Phys. Rev. D(Rapid Communications), figs. available on request from [email protected]

On the Representation Theory of Orthofermions and Orthosupersymmetric Realization of Parasupersymmetry and Fractional Supersymmetry

We construct a canonical irreducible representation for the orthofermion algebra of arbitrary order, and show that every representation decomposes into irreducible representations that are isomorphic to either the canonical representation or the trivial representation. We use these results to show that every orthosupersymmetric system of order $p$ has a parasupersymmetry of order $p$ and a fractional supersymmetry of order $p+1$.Comment: 13 pages, to appear in J. Phys. A: Math. Ge

Quasiperiodicity and non-computability in tilings

We study tilings of the plane that combine strong properties of different nature: combinatorial and algorithmic. We prove existence of a tile set that accepts only quasiperiodic and non-recursive tilings. Our construction is based on the fixed point construction; we improve this general technique and make it enforce the property of local regularity of tilings needed for quasiperiodicity. We prove also a stronger result: any effectively closed set can be recursively transformed into a tile set so that the Turing degrees of the resulted tilings consists exactly of the upper cone based on the Turing degrees of the later.Comment: v3: the version accepted to MFCS 201

Fixed Point and Aperiodic Tilings

An aperiodic tile set was first constructed by R.Berger while proving the undecidability of the domino problem. It turned out that aperiodic tile sets appear in many topics ranging from logic (the Entscheidungsproblem) to physics (quasicrystals) We present a new construction of an aperiodic tile set that is based on Kleene's fixed-point construction instead of geometric arguments. This construction is similar to J. von Neumann self-reproducing automata; similar ideas were also used by P. Gacs in the context of error-correcting computations. The flexibility of this construction allows us to construct a "robust" aperiodic tile set that does not have periodic (or close to periodic) tilings even if we allow some (sparse enough) tiling errors. This property was not known for any of the existing aperiodic tile sets.Comment: v5: technical revision (positions of figures are shifted

Impaired Hyperemic Response to Exercise Post Stroke

Individuals with chronic stroke have reduced perfusion of the paretic lower limb at rest; however, the hyperemic response to graded muscle contractions in this patient population has not been examined. This study quantified blood flow to the paretic and non-paretic lower limbs of subjects with chronic stroke after submaximal contractions of the knee extensor muscles and correlated those measures with limb function and activity. Ten subjects with chronic stroke and ten controls had blood flow through the superficial femoral artery quantified with ultrasonography before and immediately after 10 second contractions of the knee extensor muscles at 20, 40, 60, and 80% of the maximal voluntary contraction (MVC) of the test limb. Blood flow to the paretic and non-paretic limb of stroke subjects was significantly reduced at all load levels compared to control subjects even after normalization to lean muscle mass. Of variables measured, increased blood flow after an 80% MVC was the single best predictor of paretic limb strength, the symmetry of strength between the paretic and non-paretic limbs, coordination of the paretic limb, and physical activity. The impaired hemodynamic response to high intensity contractions was a better predictor of lower limb function than resting perfusion measures. Stroke-dependent weakness and atrophy of the paretic limb do not explain the reduced hyperemic response to muscle contraction alone as the response is similarly reduced in the non-paretic limb when compared to controls. These data may suggest a role for perfusion therapies to optimize rehabilitation post stroke

5-State Rotation-Symmetric Number-Conserving Cellular Automata are not Strongly Universal

We study two-dimensional rotation-symmetric number-conserving cellular automata working on the von Neumann neighborhood (RNCA). It is known that such automata with 4 states or less are trivial, so we investigate the possible rules with 5 states. We give a full characterization of these automata and show that they cannot be strongly Turing universal. However, we give example of constructions that allow to embed some boolean circuit elements in a 5-states RNCA

A Simple n-Dimensional Intrinsically Universal Quantum Cellular Automaton

We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of the intrinsically universal QCA. Several steps of the intrinsically universal QCA then correspond to one step of the simulated QCA. The simulation preserves the topology in the sense that each cell of the simulated QCA is encoded as a group of adjacent cells in the universal QCA.Comment: 13 pages, 7 figures. In Proceedings of the 4th International Conference on Language and Automata Theory and Applications (LATA 2010), Lecture Notes in Computer Science (LNCS). Journal version: arXiv:0907.382

A New Approach to Nuclear Collisions at RHIC Energies

We present a new parton model approach for nuclear collisions at RHIC energies (and beyond). It is a selfconsistent treatment, using the same formalism for calculating cross sections like the total and the inelastic one and, on the other hand, particle production. Actually, the latter one is based on an expression for the total cross section, expanded in terms of cut Feynman diagrams. Dominant diagrams are assumed to be composed of parton ladders between any pair of nucleons, with ordered virtualities from both ends of the ladder.Comment: 8 pages, 3 figures (proceedings Quark Matter 99