Beam shaping by spatial coherence modulation based on spatial coherence wavelets

A novel technique for designing specific shapes of power distributions is presented. It bases on the modulation of the spatial coherence of the optical field in amplitude and phase. The modulating functions are synthesized from the phase-space diagram of the field, provided by the marginal power spectrum. Numerical results for the phase modulation of the complex degree of spatial coherence are presented. This beam shaping technique is suitable in applications that require specific shapes and sizes.     

Chemotopological study of positron emitter radionuclides used in PET diagnostic imaging: physical, physico-chemical, dosimetric, quantum and nuclear properties

We carried out a chemotopological study of two groups of positron emitter radionuclides of current and potential use in positron emission tomography (PET) diagnostic imaging. The aim was to look for potential β⁺ radionuclides not yet in use for PET imaging, taking into account the similarities of these radionuclides with radionuclides already used in PET imaging. The similarity was studied through physical, physico-chemical, dosimetric, quantum and nuclear properties of the radionuclides. We applied cluster analysis (two similarity functions and three grouping methodologies) and generated six dendrograms. One dendrogram was selected in each group, which was used to build up a basis for a topology. From the calculation of topological properties of several subsets of interest, we propose β⁺ radionuclides ⁴⁷V, ⁴⁸V, ⁶³Zn, ⁷⁰As, ⁹⁰Nb, ¹⁰⁶Ag, ¹¹⁵Sb, ¹¹⁶Sb, ¹²⁰Sb, ¹³⁰Cs, ¹³⁴La and ¹⁴⁰Pr, as potential new radionuclides of use in PET imaging.     

Electrochemical Sensors Based on Stationary Electrodes and Immobilized DNA or Its Fragments and the Assessment of Their Analytical Potentials

Amperometric biosensors were developed on the basis of stationary mercury-film and glassy-carbon electrodes and DNA or its fragments, oligodeoxynucleotides (ODNs), immobilized in a nitrocellulose matrix. Taking into account the high affinity of Cu(II) and Fe(III) ions to denatured DNA ((19.1 ± 0.1) ×10⁵ and (1.4 ± 0.3) × 10⁵ L/mol, respectively), a procedure was proposed for the voltammetric determination of these ions in natural materials and blood serum at a level of n × 10⁻¹¹ M. This procedure involves analyte pre-concentration on a DNA-containing biosensor. An ODN-containing biosensor (DNA probe) was used in the study of DNA hybridization for the highly specific determination of its nucleotide sequence.__________Translated from Zhurnal Analiticheskoi Khimii, Vol. 60, No. 6, 2005, pp. 639–645.Original Russian Text Copyright © 2005 by Babkina, Palecek, Jelen, Fojta.Presented at the VI All-Russia Conference (with international participation) on Electrochemical Methods of Analysis (EMA-2004, Ufa, May 23–27, 2004).     

Spatial coherence in the high-frequency limit

Two expressions for the spatial coherence of acoustic signals scattered by a randomly rough pressure-release surface using composite-roughness theory are presented. One model is the conventional result, obtained by splitting the surface spectrum. The second model includes diffractive corrections which in principle remove the first model's dependence on choice of spectral cut-off wavenumber. We find that both models produce outcomes that do not differ significantly from one another, particularly for very high frequencies, for any reasonable choice of spectral wavenumber cut-off. Thus, for the purpose of coherence computations, the diffractive corrections are unnecessary in the high frequency/roughness regime. We show, as well, that in this regime the composite roughness models agree with Kirchhoff integral formulations for the coherence.     

Effects of network topology, transmission delays, and refractoriness on the response of coupled excitable systems to a stochastic stimulus

We study the effects of network topology on the response of networks of coupled discrete excitable systems to an external stochastic stimulus. We extend recent results that characterize the response in terms of spectral properties of the adjacency matrix by allowing distributions in the transmission delays and in the number of refractory states and by developing a nonperturbative approximation to the steady state network response. We confirm our theoretical results with numerical simulations. We find that the steady state response amplitude is inversely proportional to the duration of refractoriness, which reduces the maximum attainable dynamic range. We also find that transmission delays alter the time required to reach steady state. Importantly, neither delays nor refractoriness impact the general prediction that criticality and maximum dynamic range occur when the largest eigenvalue of the adjacency matrix is unity.     

Improved mixing condition on the grid for counting and sampling independent sets

The hard-core model has received much attention in the past couple of decades as a lattice gas model with hard constraints in statistical physics, a multicast model of calls in communication networks, and as a weighted independent set problem in combinatorics, probability and theoretical computer science. In this model, each independent set I in a graph G is weighted proportionally to λ^|I|, for a positive real parameter λ. For large λ, computing the partition function (namely, the normalizing constant which makes the weighting a probability distribution on a finite graph) on graphs of maximum degree Δ ≥ 3, is a well known computationally challenging problem. More concretely, let ${\lambda_c(\mathbb{T}_\Delta)}$ denote the critical value for the so-called uniqueness threshold of the hard-core model on the infinite Δ-regular tree; recent breakthrough results of Weitz (Proceedings of the 38th Annual ACM Symposium on Theory of Computing (STOC), pp. 140–149, 2006) and Sly (Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 287–296, 2010) have identified ${\lambda_c(\mathbb{T}_\Delta)}$ as a threshold where the hardness of estimating the above partition function undergoes a computational transition. We focus on the well-studied particular case of the square lattice ${\mathbb{Z}^2}$ , and provide a new lower bound for the uniqueness threshold, in particular taking it well above ${\lambda_c(\mathbb{T}_4)}$ . Our technique refines and builds on the tree of self-avoiding walks approach of Weitz, resulting in a new technical sufficient criterion (of wider applicability) for establishing strong spatial mixing (and hence uniqueness) for the hard-core model. Our new criterion achieves better bounds on strong spatial mixing when the graph has extra structure, improving upon what can be achieved by just using the maximum degree. Applying our technique to ${\mathbb{Z}^2}$ we prove that strong spatial mixing holds for all λ < 2.3882, improving upon the work of Weitz that held for λ < 27/16 = 1.6875. Our results imply a fully-polynomial deterministic approximation algorithm for estimating the partition function, as well as rapid mixing of the associated Glauber dynamics to sample from the hard-core distribution.     

A simple GAP-canceling algorithm for the generalized maximum flow problem

We give a simple primal algorithm for the generalized maximum flow problem that repeatedly finds and cancels generalized augmenting paths (GAPs). We use ideas of Wallacher (A generalization of the minimum-mean cycle selection rule in cycle canceling algorithms, 1991) to find GAPs that have a good trade-off between the gain of the GAP and the residual capacity of its arcs; our algorithm may be viewed as a special case of Wayne’s algorithm for the generalized minimum-cost circulation problem (Wayne in Math Oper Res 27:445–459, 2002). Most previous algorithms for the generalized maximum flow problem are dual-based; the few previous primal algorithms (including Wayne in Math Oper Res 27:445–459, 2002) require subroutines to test the feasibility of linear programs with two variables per inequality (TVPIs). We give an O(mn) time algorithm for finding negative-cost GAPs which can be used in place of the TVPI tester. This yields an algorithm with O(m log(mB/ε)) iterations of O(mn) time to compute an ε-optimal flow, or O(m ² log (mB)) iterations to compute an optimal flow, for an overall running time of O(m ³ nlog(mB)). The fastest known running time for this problem is , and is due to Radzik (Theor Comput Sci 312:75–97, 2004), building on earlier work of Goldfarb et al. (Math Oper Res 22:793–802, 1997). David P. Williamson is supported in part by an IBM Faculty Partnership Award and NSF grant CCF-0514628.