Non Parametric Distributed Inference in Sensor Networks Using Box Particles Messages

This paper deals with the problem of inference in distributed systems where the probability model is stored in a distributed fashion. Graphical models provide powerful tools for modeling this kind of problems. Inspired by the box particle filter which combines interval analysis with particle filtering to solve temporal inference problems, this paper introduces a belief propagation-like message-passing algorithm that uses bounded error methods to solve the inference problem defined on an arbitrary graphical model. We show the theoretic derivation of the novel algorithm and we test its performance on the problem of calibration in wireless sensor networks. That is the positioning of a number of randomly deployed sensors, according to some reference defined by a set of anchor nodes for which the positions are known a priori. The new algorithm, while achieving a better or similar performance, offers impressive reduction of the information circulating in the network and the needed computation times.     

500 GHz mode-hop-free idler tuning range with a frequency-stabilized singly resonant optical parametric oscillator

A 1064 nm pumped continuous-wave, mid-IR (3-4 μm), signal-wave resonant optical parametric oscillator is frequency stabilized at the kilohertz jitter level to the transmission peak of an external high-finesse Fabry-Perot cavity. Owing to the high stability of the resonator length against acoustical perturbation, fine pump tuning of the idler wave around 3.3 μm results in an unprecedented mode-hop-free continuous scan over 500 GHz (17 cm?1).     

A closer look at "social" boundary genes reveals knowledge to gene expression profiles

As social network analysis is gaining popularity in modeling real world problems, the task of applying the social network model concepts and notions to biological data is still one of the most attractive research problems to be addressed. According, our work described in this paper focuses on a particular set of genes that reside on the community boundaries in gene co-expression networks. Stemmed from community mining problem in social networks, peripheries of communities (i.e., boundaries) can be used to aid certain biological analysis. The proposed method consists of three parts: 1) Finding communities of gene co-expression networks through clustering. 2) Analyzing stability of community structures by Monte Carlo method. 3) Designing of dynamic adoption of boundaries using geometric convexity. We validated our findings using breast cancer gene expression data from various studies. Our approach contributes to the new branch of applying social network mechanisms in biological data analysis, leading to new data mining strategies implied by witnessing social behaviors in gene expression analysis.     

The Cauchy–Riemann equations in the unit ball of l^{2}

We study the local exactness of the \(\overline{\partial }\) operator in the Hilbert space \(l^2\) for a particular class of \((0,1)\) -forms \(\omega \) of the type \(\omega (z) = \sum _i z_i\omega ^i(z) d\overline{z}_i\) , \(z = (z_i)\) in \(l^2\) . We suppose each function \(\omega ^i\) of class \(C^\infty \) in the closed unit ball of \(l^2\) , of the form \(\omega ^i(z) = \sum _k \omega ^i_k\left( z^k\right) \) , where \(\mathbf N = \bigcup I_k\) is a partition of \(\mathbf N\) , \((\) card \(I_k < +\infty )\) and \(z^k\) is the projection of \(z\) on \(\mathbf C^{I_k}\) . We establish sufficient conditions for exactness of \(\omega \) related to the expansion in Fourier series of the functions \(\omega ^i_k\) .     

A full analysis of a new second order finite volume approximation based on a low-order scheme using general admissible spatial meshes for the unsteady one dimensional heat equation

The present work is an extension of our previous works ,  and  which dealt with first order (both in time and space) and second order time accurate (second order in time and first order in space) implicit finite volume schemes for parabolic equations. We aim in this work (and some forthcoming studies) at getting higher order (both in time and space) finite volume approximations for the exact solution of parabolic equations using the class of spatial generic meshes introduced recently in [13]. We focus in the present contribution on the one dimensional heat equation and its implicit finite volume scheme described in [3]. The implicit finite volume scheme approximating the one dimensional heat equation we consider (hereafter referred to as the basic finite volume scheme) yields linear systems to be solved successively. The matrices involved in these linear systems are tridiagonal. The finite volume approximate solution is of order h+k$h+k$, where h (resp. k  ) is the mesh size of the spatial (resp. time) discretization. We construct a new finite volume approximation of order (h+k)²${(h+k)}^2$ in several discrete norms which allows us to get approximations of order two for the exact solution and its first derivatives. This new high-order approximation can be computed using the same linear systems involved in the basic finite volume scheme while the right hand sides are corrected. The construction of these right hand sides includes the approximations of the second, third, and fourth spatial derivatives of the exact solution. The computation of the approximation of these high-order derivatives can be performed using the same matrices stated above with another two tridiagonal matrices. The manner by which this new high-order approximation is constructed can be repeated to compute successively finite volume approximations of arbitrary order using the same matrices stated above. These high-order approximations can be obtained on any one dimensional admissible finite volume mesh in the sense of [12] without any restrictive condition on the spatial mesh. A full analysis for the stated theoretical results as well as some numerical examples supporting the theory is presented. The results obtained in the present study are based essentially on two facts. The first fact is the use of the results provided in [3] which state the convergence order of the finite volume approximate solution in several norms. The second fact is the comparison between the stated new higher order approximations and suitable auxiliary finite volume approximations.     

A theoretical analysis of a new second order finite volume approximation based on a low-order scheme using general admissible spatial meshes for the one dimensional wave equation

This paper details our note [6] and it is an extension of our previous works  and  which dealt with first order (both in time and space) and second order time accurate (second order in time and first order in space) implicit finite volume schemes for second order hyperbolic equations with Dirichlet boundary conditions on general nonconforming multidimensional spatial meshes introduced recently in [14]. We aim in this work (and some forthcoming studies) to get higher order (both in time and space) finite volume approximations for the exact solution of hyperbolic equations using the class of spatial generic meshes introduced recently in [14] on low order schemes from which the matrices used to compute the discrete solutions are sparse. We focus in the present contribution on the one dimensional wave equation and on one of its implicit finite volume schemes described in [4]. The implicit finite volume scheme approximating the one dimensional wave equation we consider (hereafter referred to as the basic finite volume scheme) yields linear systems to be solved successively. The matrices involved in these linear systems are tridiagonal, symmetric and definite positive. The finite volume approximate solution of the basic finite volume scheme is of order h+k$h+k$, where h (resp. k  ) is the mesh size of the spatial (resp. time) discretization. We construct a new finite volume approximation of order (h+k)²${(h+k)}^2$ in several discrete norms which allow us to get approximations of order two for the exact solution and its first derivatives. This new high-order approximation can be computed using linear systems whose matrices are the same ones used to compute the discrete solution of the basic finite volume scheme while the right hand sides are corrected. The construction of these right hand sides includes the approximation of some high order spatial derivatives of the exact solution. The computation of the approximation of these high order spatial derivatives can be performed using the same matrices stated above with another two tridiagonal matrices. The manner by which this new high-order approximation is constructed can be repeated to compute successively finite volume approximations of arbitrary order using the same matrices stated above. These high-order approximations can be obtained on any one dimensional admissible finite volume mesh in the sense of [13] without any condition. To reach the above results, a theoretical framework is developed and some numerical examples supporting the theory are presented. Some of the tools of this framework are new and interesting and they are stated in the one space dimension but they can be extended to several space dimensions. In particular a new and useful a prior estimate for a suitable discrete problem is developed and proved. The proof of this a prior estimate result is based essentially on the decomposition of the solution of the discrete problem into the solutions of two suitable discrete problems. A new technique is used in order to get a convenient finite volume approximation whose discrete time derivatives of order up to order two are also converging towards the solution of the wave equation and their corresponding time derivatives.     

Synthese Originale de 5-Aryl (ou 5-benzyl)-2[(1-Diethoxyphosphonyl)methyl]-1,3,4-oxadiazoles par Action du Phosphonomethylhydrazide sur les Imidates N-Acyles

The phosphonomethylhydrazide 2a reacts with N-acylated imidates 3a–d to give the corresponding 5-aryl (or 5-benzyl)-2-[(1-diethoxyphosphonyl)methyl]-1,3,4-oxadiazoles 4a–d after the elimination of ethanamide 5. Compounds 2a–e are prepared by the action of triethyl phosphonoacetate 1 with hydrazine and its derivatives. The structures of 1,3,4-oxadiazoles 4a–d and hydrazides 2a–e have been unequivocally confirmed by means of IR, ¹ H, ¹³ C, ³¹ P NMR and mass spectrometry.     

The Stereoselective Synthesis of Conjugated Allylsilanes

2-trimethylsilylethylidenetriphenylphosphorane (5) (Seyferth–Wittig reagent) reacts stereoselectively with the carbonyl compounds 6a–f to give the conjugated allylsilanes 7a–f, each as a mixture of E-and Z-isomers. The stereoselectivity of reactions of E-cinnamaldehyde (6c) with 5 has been investigated at different temperatures. A successful E-stereoselective synthesis of 7c was achieved by reacting 5 with E-cinnamaldehyde (6c) under the conditions of a Wittig–Schlosser modification reaction. Structures of the allylsilanes 7a–f were deduced by compatible analytical and spectroscopic (IR, ¹H NMR, ¹³C NMR, and GC/MS) measurements. An assignment of the E:Z ratios of 7a–f is based on their ¹H NMR spectral data.     

Organophosphorus Chemistry,Part 37: Synthesis and Insecticidal Activities of Some Phosphonate Adducts Derived from 6-(Aryliminomethyl)-furobenzopyran-5-ones

Dialkyl phosphites attack 6-(Aryliminomethyl)furobenzopyran-5-ones at the imine-carbon atom to give new phosphonate 1:1 adducts. The obtained compounds regenerate the starting materials upon thermolysis under reduced pressure. Structures of the new products were attested by compatible analytical and spectroscopic measurements. Insecticidal activity tests assured that some new compounds show marked potency against adults of Aphis gossypii (Glover), which infests cotton crops.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.     

Preparation,Thermolysis, and Photolysis of Some New Thiophosphoramidates Derived from 3-Methyl-2-Benzothiazolinone Hydrazone

3-Methyl-2-benzothiazolinone hydrazone (1) reacts with dialkyl phosphorothiochloridates 2a,b in the presence of a base, to give the respective dialkylthiophosphorylated hydrazones 3a,b. Upon thermolysis, compound 3b yields bi(3-methylbenzothiazole-2-iminyl) (4). Exposure of 3b to sunlight in methanol results in the formation of 3-methyl-2-benzothiazolinone (5). When the same experiment was carried on the starting hydrazone 1, bis(3-methyl- benzothiazole-2-iminyl)diazine (6) was formed. Elemental analyses and spectroscopic details are presented for the new compounds.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.