Robots with Lights: Overcoming Obstructed Visibility Without Colliding

Robots with lights is a model of autonomous mobile computational entities operating in the plane in Look-Compute-Move cycles: each agent has an externally visible light which can assume colors from a fixed set; the lights are persistent (i.e., the color is not erased at the end of a cycle), but otherwise the agents are oblivious. The investigation of computability in this model, initially suggested by Peleg, is under way, and several results have been recently established. In these investigations, however, an agent is assumed to be capable to see through another agent. In this paper we start the study of computing when visibility is obstructable, and investigate the most basic problem for this setting, Complete Visibility: The agents must reach within finite time a configuration where they can all see each other and terminate. We do not make any assumption on a-priori knowledge of the number of agents, on rigidity of movements nor on chirality. The local coordinate system of an agent may change at each activation. Also, by definition of lights, an agent can communicate and remember only a constant number of bits in each cycle. In spite of these weak conditions, we prove that Complete Visibility is always solvable, even in the asynchronous setting, without collisions and using a small constant number of colors. The proof is constructive. We also show how to extend our protocol for Complete Visibility so that, with the same number of colors, the agents solve the (non-uniform) Circle Formation problem with obstructed visibility

Gegenbauer-solvable quantum chain model

In an innovative inverse-problem construction the measured, experimental energies $E_1$, $E_2$, ...$E_N$ of a quantum bound-state system are assumed fitted by an N-plet of zeros of a classical orthogonal polynomial $f_N(E)$. We reconstruct the underlying Hamiltonian $H$ (in the most elementary nearest-neighbor-interaction form) and the underlying Hilbert space ${\cal H}$ of states (the rich menu of non-equivalent inner products is offered). The Gegenbauer's ultraspherical polynomials $f_n(x)=C_n^\alpha(x)$ are chosen for the detailed illustration of technicalities.Comment: 29 pp., 1 fi

The locally covariant Dirac field

We describe the free Dirac field in a four dimensional spacetime as a locally covariant quantum field theory in the sense of Brunetti, Fredenhagen and Verch, using a representation independent construction. The freedom in the geometric constructions involved can be encoded in terms of the cohomology of the category of spin spacetimes. If we restrict ourselves to the observable algebra the cohomological obstructions vanish and the theory is unique. We establish some basic properties of the theory and discuss the class of Hadamard states, filling some technical gaps in the literature. Finally we show that the relative Cauchy evolution yields commutators with the stress-energy-momentum tensor, as in the scalar field case.Comment: 36 pages; v2 minor changes, typos corrected, updated references and acknowledgement

Measurement of circulating filarial antigen levels in human blood with a point-of-care test strip and a portable spectrodensitometer

The Alere Filariasis Test Strip (FTS) is a qualitative, point-of-care diagnostic tool that detects Wuchereria bancrofti circulating filarial antigen (CFA) in human blood, serum, or plasma. The Global Program to Eliminate Lymphatic Filariasis employs the FTS for mapping filariasis-endemic areas and assessing the success of elimination efforts. The objective of this study was to explore the relationship between the intensity of positive test lines obtained by FTS with CFA levels as determined by enzyme-linked immunosorbent assay (ELISA) with blood and plasma samples from 188 individuals who live in a filariasis-endemic area. The intensity of the FTS test line was assessed visually to provide a semiquantitative score (visual Filariasis Test Strip [vFTS]), and line intensity was measured with a portable spectrodensitometer (quantitative Filariasis Test Strip [gFTS]). These results were compared with antigen levels measured by ELISA in plasma from the same subjects. qFTS measurements were highly correlated with vFTS scores (p = 0.94; P < 0.001) and with plasma CFA levels (p = 0.91; P < 0.001). Thus, qFTS assessment is a convenient method for quantifying W bancrofti CFA levels in human blood, which are correlated with adult worm burdens. This tool may be useful for assessing the impact of treatment on adult filarial worms in individuals and communities

Some remarks on quasi-Hermitian operators

A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze the structure generated by unbounded metric operators in a Hilbert space. Following our previous work, we introduce several generalizations of the notion of similarity between operators. Then we explore systematically the various types of quasi-Hermitian operators, bounded or not. Finally we discuss their application in the so-called pseudo-Hermitian quantum mechanics.Comment: 18page

Hydrogen trapping by VC precipitates and structural defects in a high strength Fe-Mn-C steel studied by small-angle neutron scattering

The trapping of hydrogen by VC precipitates and structural defects in high strength Fe-Mn-C steel was studied by small angle neutron scattering. No interaction between H and V in solid solution has been detected but a significant interaction between H and structural defects introduced by plastic deformation has been measured. This last effect was reversible upon outgassing of the H. Moreover a significant interaction between H and VC precipitates has been measured; 5 ppm wt. of H could be trapped in the precipitates. This is consistent with the homogeneous trapping of H within the precipitates rather than at the precipitate/matrix interface

Numerical and experimental study of an air-soil heat exchanger for cooling habitat in Sahelian zone: case of Ouagadougou

The use of air-soil heat exchangers for the cooling home has developed considerably in recent years. In this work, we have leaded the numerical study of an air-soil heat exchanger by using a nodal approach. We have also presented our experimental prototype implemented in Ouagadougou. This study has allowed determining the evolution of air temperature along the exchanger and also validating our numerical results with those of the literature and the experiment

On Invariant Notions of Segre Varieties in Binary Projective Spaces

Invariant notions of a class of Segre varieties \Segrem(2) of PG(2^m - 1, 2) that are direct products of $m$ copies of PG(1, 2), $m$ being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that contains \Segrem(2) and is invariant under its projective stabiliser group \Stab{m}{2}. By embedding PG(2^m - 1, 2) into \PG(2^m - 1, 4), a basis of the latter space is constructed that is invariant under \Stab{m}{2} as well. Such a basis can be split into two subsets whose spans are either real or complex-conjugate subspaces according as $m$ is even or odd. In the latter case, these spans can, in addition, be viewed as indicator sets of a \Stab{m}{2}-invariant geometric spread of lines of PG(2^m - 1, 2). This spread is also related with a \Stab{m}{2}-invariant non-singular Hermitian variety. The case $m=3$ is examined in detail to illustrate the theory. Here, the lines of the invariant spread are found to fall into four distinct orbits under \Stab{3}{2}, while the points of PG(7, 2) form five orbits.Comment: 18 pages, 1 figure; v2 - version accepted in Designs, Codes and Cryptograph

Asymmetric XXZ chain at the antiferromagnetic transition: Spectra and partition functions

The Bethe ansatz equation is solved to obtain analytically the leading finite-size correction of the spectra of the asymmetric XXZ chain and the accompanying isotropic 6-vertex model near the antiferromagnetic phase boundary at zero vertical field. The energy gaps scale with size $N$ as $N^{-1/2}$ and its amplitudes are obtained in terms of level-dependent scaling functions. Exactly on the phase boundary, the amplitudes are proportional to a sum of square-root of integers and an anomaly term. By summing over all low-lying levels, the partition functions are obtained explicitly. Similar analysis is performed also at the phase boundary of zero horizontal field in which case the energy gaps scale as $N^{-2}$. The partition functions for this case are found to be that of a nonrelativistic free fermion system. From symmetry of the lattice model under $\pi /2$ rotation, several identities between the partition functions are found. The $N^{-1/2}$ scaling at zero vertical field is interpreted as a feature arising from viewing the Pokrovsky-Talapov transition with the space and time coordinates interchanged.Comment: Minor corrections only. 18 pages in RevTex, 2 PS figure