A Statistical Mechanical Load Balancer for the Web

The maximum entropy principle from statistical mechanics states that a closed system attains an equilibrium distribution that maximizes its entropy. We first show that for graphs with fixed number of edges one can define a stochastic edge dynamic that can serve as an effective thermalization scheme, and hence, the underlying graphs are expected to attain their maximum-entropy states, which turn out to be Erdos-Renyi (ER) random graphs. We next show that (i) a rate-equation based analysis of node degree distribution does indeed confirm the maximum-entropy principle, and (ii) the edge dynamic can be effectively implemented using short random walks on the underlying graphs, leading to a local algorithm for the generation of ER random graphs. The resulting statistical mechanical system can be adapted to provide a distributed and local (i.e., without any centralized monitoring) mechanism for load balancing, which can have a significant impact in increasing the efficiency and utilization of both the Internet (e.g., efficient web mirroring), and large-scale computing infrastructure (e.g., cluster and grid computing).Comment: 11 Pages, 5 Postscript figures; added references, expanded on protocol discussio

CdZnTe strip detectors as sub-millimeter resolution imaging gamma radiation spectrometers

We report γ-ray detection performance measurements and computer simulations of a sub-millimeter pitch CdZnTe strip detector. The detector is a prototype for γ-ray measurements in the range of 20-600 keV. The prototype is a 1.5 mm thick, 64×64 orthogonal stripe CdZnTe detector of 0.375 mm pitch in both dimensions, with approximately one square inch of sensitive area. Using discrete laboratory electronics to process signals from an 8×8 stripe region of the prototype we measured good spectroscopic uniformity and sub-pitch (~0.2 mm) spatial resolution in both x and y dimensions. We present below measurements of the spatial uniformity, relative timing and pulse height of the anode and cathode signals. We simulated the photon interactions and signal generation in the strip detector and the test electronics and we compare these results with the data. The data indicate that cathode signal-as well as the anode signal-arises more strongly from the conduction electrons rather than the holes

Performance of CdZnTe strip detectors as sub-millimeter resolution imaging gamma radiation spectrometers

We report & gamma;-ray detection performance measurements and computer simulations of a sub-millimeter pitch CdZnTe strip detector. The detector is a prototype for & gamma;-ray astronomy measurements in the range of 20-200 keV. The prototype is a 1.5 mm thick, 64×64 orthogonal stripeCdZnTe detector of 0.375 mm pitch in both dimensions, with approximately one square inch of sensitive area. Using discrete laboratory electronics to process signals from an 8×8 stripe region of the prototype we measured good spectroscopic uniformity and sub-pitch (~0.2 mm) spatial resolution in both x and y dimensions. We present below measurements of the spatial uniformity, relative timing and pulse height of the anode and cathode signals, and the photon detection efficiency. We also present a technique for determining the location of the event in the third dimension (depth). We simulated the photon interactions and signal generation in the strip detector and the test electronics and we compare these results with the data. The data indicate that the cathode signal-as well as the anode signal-arises more strongly from the conduction electrons rather than the holes

A SIMULATION STUDY ON THE RELATIONSHIP BETWEEN THE ABUNDANCE AND SPATIAL DISTRIBUTION OF INSECTS AND SELECTED SAMPLING SCHEMES

During the development of a Bayesian approach to estimate insect population abundance, it was necessary to compare not only the reliability of Bayesian estimates, but to also compare these estimates to those obtained by traditional methods employed by entomologists. To facilitate these comparisons it was necessary to use simulated fields apportioned into quadrats where conditions representative of insect abundance and dispersion are modeled. Thus, a simulation model was developed using SAS to derive example insect populations from which samples could be drawn. The negative binomial distribution was used to simulate the proportion of infested plants (p) with various degrees of clustering (k) for specified quadrat sizes. Another component varies sample parameters which represent the total number of plants sampled per field, the number of plants sampled per quadrat, and thus the number of quadrats sampled per field

MUBs inequivalence and affine planes

There are fairly large families of unitarily inequivalent complete sets of N+1 mutually unbiased bases (MUBs) in C^N for various prime powers N. The number of such sets is not bounded above by any polynomial as a function of N. While it is standard that there is a superficial similarity between complete sets of MUBs and finite affine planes, there is an intimate relationship between these large families and affine planes. This note briefly summarizes "old" results that do not appear to be well-known concerning known families of complete sets of MUBs and their associated planes.Comment: This is the version of this paper appearing in J. Mathematical Physics 53, 032204 (2012) except for format changes due to the journal's style policie

Balloon-borne coded aperture telescope for arc-minute angular resolution at hard x-ray energies

We are working on the development of a new balloon-borne telescope, MARGIE (minute-of-arc resolution gamma ray imaging experiment). It will be a coded aperture telescope designed to image hard x-rays (in various configurations) over the 20 - 600 keV range with an angular resolution approaching one arc minute. MARGIE will use one (or both) of two different detection plane technologies, each of which is capable of providing event locations with sub-mm accuracies. One such technology involves the use of cadmium zinc telluride (CZT) strip detectors. We have successfully completed a series of laboratory measurements using a prototype CZT detector with 375 micron pitch. Spatial location accuracies of better than 375 microns have been demonstrated. A second type of detection plane would be based on CsI microfiber arrays coupled to a large area silicon CCD readout array. This approach would provide spatial resolutions comparable to that of the CZT prototype. In one possible configuration, the coded mask would be 0.5 mm thick tungsten, with 0.5 mm pixels at a distance of 1.5 m from the central detector giving an angular resolution of 1 arc-minute and a fully coded field of view of 12 degrees. We review the capabilities of the MARGIE telescope and report on the status of our development efforts and our plans for a first balloon flight

On the connection between mutually unbiased bases and orthogonal Latin squares

We offer a piece of evidence that the problems of finding the number of mutually unbiased bases (MUB) and mutually orthogonal Latin squares (MOLS) might not be equivalent. We study a particular procedure which has been shown to relate the two problems and generates complete sets of MUBs in power-of-prime dimensions and three MUBs in dimension six. For these cases, every square from an augmented set of MOLS has a corresponding MUB. We show that this no longer holds for certain composite dimensions.Comment: 6 pages, submitted to Proceedings of CEWQO 200

Pharmacology of DB844, an orally active aza analogue of pafuramidine, in a monkey model of second stage human African trypanosomiasis

Novel drugs to treat human African trypanosomiasis (HAT) are still urgently needed despite the recent addition of nifurtimox-eflornithine combination therapy (NECT) to WHO Model Lists of Essential Medicines against second stage HAT, where parasites have invaded the central nervous system (CNS). The pharmacology of a potential orally available lead compound, N-methoxy-6-{5-[4-(N-methoxyamidino) phenyl]-furan-2-yl}-nicotinamidine (DB844), was evaluated in a vervet monkey model of second stage HAT, following promising results in mice. DB844 was administered orally to vervet monkeys, beginning 28 days post infection (DPI) with Trypanosoma brucei rhodesiense KETRI 2537. DB844 was absorbed and converted to the active metabolite 6-[5-(4-phenylamidinophenyl)-furanyl-2-yl]-nicotinamide (DB820), exhibiting plasma C(max) values of 430 and 190 nM for DB844 and DB820, respectively, after the 14th dose at 6 mg/kg qd. A 100-fold reduction in blood trypanosome counts was observed within 24 h of the third dose and, at the end of treatment evaluation performed four days post the last drug dose, trypanosomes were not detected in the blood or cerebrospinal fluid of any monkey. However, some animals relapsed during the 300 days of post treatment monitoring, resulting in a cure rate of 3/8 (37.5%) and 3/7 (42.9%) for the 5 mg/kg×10 days and the 6 mg/kg×14 days dose regimens respectively. These DB844 efficacy data were an improvement compared with pentamidine and pafuramidine both of which were previously shown to be non-curative in this model of CNS stage HAT. These data show that synthesis of novel diamidines with improved activity against CNS-stage HAT was possible

The Lie Algebraic Significance of Symmetric Informationally Complete Measurements

Examples of symmetric informationally complete positive operator valued measures (SIC-POVMs) have been constructed in every dimension less than or equal to 67. However, it remains an open question whether they exist in all finite dimensions. A SIC-POVM is usually thought of as a highly symmetric structure in quantum state space. However, its elements can equally well be regarded as a basis for the Lie algebra gl(d,C). In this paper we examine the resulting structure constants, which are calculated from the traces of the triple products of the SIC-POVM elements and which, it turns out, characterize the SIC-POVM up to unitary equivalence. We show that the structure constants have numerous remarkable properties. In particular we show that the existence of a SIC-POVM in dimension d is equivalent to the existence of a certain structure in the adjoint representation of gl(d,C). We hope that transforming the problem in this way, from a question about quantum state space to a question about Lie algebras, may help to make the existence problem tractable.Comment: 56 page

Consequences of local gauge symmetry in empirical tight-binding theory

A method for incorporating electromagnetic fields into empirical tight-binding theory is derived from the principle of local gauge symmetry. Gauge invariance is shown to be incompatible with empirical tight-binding theory unless a representation exists in which the coordinate operator is diagonal. The present approach takes this basis as fundamental and uses group theory to construct symmetrized linear combinations of discrete coordinate eigenkets. This produces orthogonal atomic-like "orbitals" that may be used as a tight-binding basis. The coordinate matrix in the latter basis includes intra-atomic matrix elements between different orbitals on the same atom. Lattice gauge theory is then used to define discrete electromagnetic fields and their interaction with electrons. Local gauge symmetry is shown to impose strong restrictions limiting the range of the Hamiltonian in the coordinate basis. The theory is applied to the semiconductors Ge and Si, for which it is shown that a basis of 15 orbitals per atom provides a satisfactory description of the valence bands and the lowest conduction bands. Calculations of the dielectric function demonstrate that this model yields an accurate joint density of states, but underestimates the oscillator strength by about 20% in comparison to a nonlocal empirical pseudopotential calculation.Comment: 23 pages, 7 figures, RevTeX4; submitted to Phys. Rev.