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In previous articles, we formalized the problem of optimal allocation strategies for a (perfect) vaccine in an infinite-dimensional metapopulation model. The aim of the current paper is to illustrate this theoretical framework with multiple examples where one can derive the analytic expression of the optimal strategies. We discuss in particular the following points: whether or not it is possible to vaccinate optimally when the vaccine doses are given one at a time (greedy vaccination strategies); the effect of assortativity (that is, the tendency to have more contacts with similar individuals) on the shape of optimal vaccination strategies; the particular case where everybody has the same number of neighbors. [ABSTRACT FROM AUTHOR]

Arterial spin labeling magnetic resonance imaging is highly suited to the exploration of brain perfusion in neonates and has the potential to provide relevant complementary information to neuroimaging studies, with insights into neurodevelopmental outcomes. Applying this technique within the first days of life is challenging and requires specific technical adaptations. The literature on this topic is scarce and heterogeneous, especially on 1.5-T scanners, limiting widespread clinical adoption. This paper aims to describe a simple approach for arterial spin labeling in neonates, with key considerations for radiologists. [ABSTRACT FROM AUTHOR]

In this article, we introduce an infinite-dimensional deterministic metapopulation SIS model which takes into account the heterogeneity of the infections and the social network among a large population. We study the long-time behavior of the dynamic. We identify the basic reproduction number R 0 which determines whether there exists a stable endemic steady state (super-critical case: R 0 > 1) or if the only equilibrium is disease-free (critical and sub-critical case: R 0 ≤ 1). As an application of this general study, we prove that the so-called "leaky" and "all-or-nothing" vaccination mechanism have the same effect on R 0. This framework is also very natural and intuitive to model lockdown policies and study their impact. [ABSTRACT FROM AUTHOR]

We give an invariance principle for very general additive functionals of conditioned Bienaymé-Galton-Watson trees in the global regime when the offspring distribution lies in the domain of attraction of a stable distribution, the limit being an additive functional of a stable Lévy tree. This includes the case when the offspring distribution has finite variance (the Lévy tree being then the Brownian tree). We also describe, using an integral test, a phase transition for toll functions depending on the size and height. [ABSTRACT FROM AUTHOR]

We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant population at some fixed time and prove that, up to a deterministic time-change, it is distributed as a continuous-time Galton–Watson process with immigration. We obtain similar results for a critical stable branching mechanism when only looking at immigrants arriving in some fixed time-interval. For a general sub-critical branching mechanism, we consider the number of individuals that give descendants in the extant population. The associated processes (forward or backward in time) are pure-death or pure-birth Markov processes, for which we compute the transition rates. [ABSTRACT FROM AUTHOR]

• The asymptotic distribution of the projector associated with the SCM is given for arbitrary distributions of the useful signal and noise with finite fourth-order moments. • The asymptotic distribution of the DOA estimate given by the MUSIC algorithm is proved for both nonparametric non-Gaussian noise and parametric CES noise models. Theoretical evaluation of the loss of performance is given for heavy-tailed distributions of the noise which is significant for weak SNR and closely spaced sources. • For CES distributed observations, the asymptotic distribution of the projector associated with any M -estimate of the covariance matrix is given. This allows us to prove that this loss of performance can be alleviated. • These theoretical results are confirmed by some simulations performed with either a complex circular Student t -distribution or a complex generalized Gaussian distribution of the noise or the observations model. This paper addresses the theoretical analysis of the robustness of subspace-based algorithms with respect to non-Gaussian noise distributions using perturbation expansions. Its purpose is twofold. It aims, first, to derive the asymptotic distribution of the estimated projector matrix obtained from the sample covariance matrix (SCM) for arbitrary distributions of the useful signal and the noise. It proves that this distribution depends only of the second-order statistics of the useful signal, but also on the second and fourth-order statistics of the noise. Second, it derives the asymptotic distribution of the estimated projector matrix obtained from any M -estimate of the covariance matrix for both real (RES) and complex elliptical symmetric (CES) distributed observations. Applied to the MUSIC algorithm for direction-of-arrival (DOA) estimation, these theoretical results allow us to theoretically evaluate the performance loss of this algorithm for heavy-tailed noise distributions when it is based on the SCM, which is significant for weak signal-to-noise ratio (SNR) or closely spaced sources. These results also make it possible to prove that this performance loss can be alleviated by replacing the SCM by an M -estimate of the covariance for CES distributed observations, which has been observed until now only by numerical experiments. [ABSTRACT FROM AUTHOR]

Linear beamformers are optimal, in a mean square (MS) sense, when the signal of interest (SOI) and observations are jointly Gaussian and circular. Otherwise, linear beamformers become suboptimal. When the SOI and observations are zero-mean, jointly Gaussian and noncircular, optimal beamformers become widely linear (WL). They become nonlinear with a structure depending on the unknown joint probability distribution of the SOI and observations when the latter are jointly nonGaussian, assumption which is very common in radiocommunications. In this context, the paper aims at introducing, for small-scale systems, third-order Volterra minimum variance distortionless response (MVDR) beamformers, for the reception of an SOI, whose waveform is unknown but whose steering vector is known, corrupted by nonGaussian and potentially noncircular interference, omnipresent in practical situations. Properties, performance, complexity, and adaptive implementation of these beamformers in the presence of nonGaussian and potentially noncircular interference are analyzed in this paper. These new beamformers are shown to always improve, in the steady state, the performance of Capon beamformer for nonGaussian/circular interference, whereas some of them improve the performance of the WL MVDR beamformer for nonGaussian/noncircular interference. These new beamformers open new perspectives for spectrum monitoring of nonGaussian signals and for radiocommunication networks using such signals. [ABSTRACT FROM AUTHOR]

We consider the Brownian tree introduced by Aldous and the associated Q-process which consists in an infinite spine on which are grafted independent Brownian trees. We present a reversal procedure on these trees that consists in looking at the tree downward from its top: the branching points becoming leaves and leaves becoming branching points. We prove that the distribution of this tree is invariant under this reversal procedure, which provides a better understanding of previous results from Bi and Delmas (2016). [ABSTRACT FROM AUTHOR]

• An extension of the matrix Slepian-Bangs formula to elliptical symmetric distributions under the assumption that the arbitrary density generator depends on unknown parameters is given. • This new matrix Slepian-Bangs formula involves a common structure to the existing one with a simple corrective coefficient. • Closed-form expressions of this coefficient are given for Student's t and generalized Gaussian distributions and are each compared according to different knowledge of the density generator. • This allows us to conclude that for an arbitrary parameterization, the Cramér-Rao bound may be very sensitive to the knowledge of the density generator for super-Gaussian distributions contrary to sub-Gaussian distributions. This paper mainly deals with an extension of the matrix Slepian-Bangs (SB) formula to elliptical symmetric (ES) distributions under the assumption that the arbitrary density generator depends on unknown parameters, aiming to rigorously quantify and understand the impact of this assumption on ES distributed parametric estimation models. This matrix SB formula is derived in a unified way within the framework of real (RES) and circular (C-CES) or noncircular (NC-CES) complex elliptically symmetric distributions, and then compared to the matrix SB formula obtained with fully known or completely unknown density generators. This new matrix SB formula involves a common structure to the existing one with a simple corrective coefficient. Closed-form expressions of this coefficient are given for Student's t and generalized Gaussian distributions and are each compared according to different knowledge of the density generator. This allows us to conclude that for an arbitrary parameterization, the Cramér-Rao bound (CRB) may be very sensitive to the knowledge of the density generator for super-Gaussian distributions contrary to sub-Gaussian distributions. Finally, we prove that for the parametrization with an unknown scale factor, the CRB for the estimation of the other parameters of the scatter matrix does not depend on the type of knowledge of the density generator. This latter result remains true for the specific noisy linear mixture data model where the parameter of interest is characterized by the range space of the mixing matrix. [ABSTRACT FROM AUTHOR]

This paper focuses on the Cramér Rao bound (CRB) of the azimuth, elevation and range with planar arrays for narrowband near-field source localization, using the exact expression of the time delay. Specifically, the aim of this paper is twofold. First, we derive explicit non-matrix closed-form expressions of approximations of these three CRBs. Second, we use these expressions to optimize near-field source localization. For deriving these expressions, we introduce conditions on the array geometry that allow us to decouple the azimuth, elevation and range parameters to a certain order in λ / r (in which λ and r denote the wavelength and the range, respectively). A particular attention is given to the popular array configurations which are the concentric uniform circular-based arrays, cross and square-based centro-symmetric arrays which satisfy these conditions. In order to control directions of arrivals (DOA) ambiguity, we propose a new criterion, which allows us to design non-uniform square [resp., cross]-based centro-symmetric array configurations with improved near-field range estimation capabilities without deteriorating the DOA precisions w.r.t. uniform square [resp., cross]-based arrays. Finally, we specify the accuracy of our proposed approximated CRBs׳expressions and isotropy׳s conditions w.r.t. the range and the number of sensors. [ABSTRACT FROM AUTHOR]

The problem of directional sensor placement and orientation is considered when statistical information about the source direction of arrival is available. We focus on two-sensor arrays and form a cost function based on the Cramer?Rao bound that depends on the probability distribution of the coplanar source direction. Proper positioning and orientation of the sensors enable the two-sensor array to have an accuracy comparable to that of a three- or four-sensor uniform circular array. [ABSTRACT FROM PUBLISHER]

We prove the existence of the total length process for the genealogical tree of a population model with random size given by quadratic stationary continuous-state branching processes. We also give, for the one-dimensional marginal, its Laplace transform as well as the fluctuation of the corresponding convergence. This result is to be compared with the one obtained by Pfaffelhuber and Wakolbinger for a constant size population associated to the Kingman coalescent. We also give a time reversal property of the number of ancestors process at all times, and a description of the so-called lineage tree in this model. [ABSTRACT FROM AUTHOR]

A correction is presented to the article "A practical guide to optimize arterial spin labeling in neonates at 1.5 Tesla: what the radiologist needs to know" published in previous issue.

• General closed-form expressions of the deterministic Cramér Rao bound (DCRB), semiparametric DCRB, stochastic Cramér Rao bound (SCRB) and semiparametric SCRB for direction of arrival (DOA) estimation are given in complex elliptically symmetric (CES) data models. • Simple exact and asymptotic (for small DOA separation) interpretable closed-form expressions are presented for the DCRB and SCRB of the DOA for two equi-powered correlated known, arbitrary, circular or rectilinear sources in CES data models. • The dependence of these bounds on the magnitude and phase of the correlation is examined. • Using asymptotic expressions of DCRBs and SCRBs, interpretable closed-form expressions of Statistical Resolution Limit (SRL) based on Smith's criterion are derived in different scenarios. • Comments to explain how different parameters impact the derived SRLs and how also the SRLs derived from the SCRBs are much less optimistic than those that have so far been deduced only from the DCRB under the assumption of known sources are discussed. This paper analyzes the deterministic (DCRB) and the stochastic (SCRB) Cramér-Rao bound on direction-of-arrival (DOA) estimation for two equi-powered correlated complex circular or rectilinear sources affected by complex circular white noise in different complex elliptically symmetric (CES) data models. Beginning by decomposing these CRBs, into factors depending on signal and noise parameters, and on geometric parameters of the array, some new interpretable closed-form expressions are derived in particular scenarios. These expressions provide useful insight into the behavior of these CRB's dependence on the correlation factor. Approximate closed-form expressions of these CRBs for small DOA separation are also derived. These results lead to new formulas for statistical resolution limit (SRL) based on the Smith criterion at which an unbiased DOA estimation algorithm can resolve two closely-spaced circular or rectilinear sources. These SCRB-derived formulas are much less optimistic than those which have so far been deduced only from the DCRB under the assumption of known sources. [ABSTRACT FROM AUTHOR]

Recently, there has been an increased awareness that simplistic adaptation of performance analysis developed for random real-valued signals and parameters to the complex case may be inadequate or may lead to intractable calculations. Unfortunately, many fundamental statistical tools for handling complex-valued parameter estimators are missing or scattered in the open literature. In this paper, we survey some known results and provide a rigorous and unified framework to study the statistical performance of complex-valued parameter estimators with a particular attention paid to properness (i.e., second order circularity), specifically referring to the second-order statistical properties. In particular, some new properties relative to the properness of the estimates, asymptotically minimum variance bound and Whittle formulas are presented. A new look at the role of nuisance parameters is given, proving and illustrating that the noncircular Gaussian distributions do not necessarily improve the Cramer–Rao bound (CRB) with respect to the circular case. Efficiency of subspace-based complex-valued parameter estimators that are presented with a special emphasis is put on noisy linear mixture. [ABSTRACT FROM AUTHOR]

We consider copulas with a given diagonal section and compute the explicit density of the unique optimal copula which maximizes the entropy. In this sense, this copula is the least informative among the copulas with a given diagonal section. We give an explicit criterion on the diagonal section for the existence of the optimal copula and give a closed formula for its entropy. We also provide examples for some diagonal sections of usual bivariate copulas and illustrate the differences between these copulas and the associated maximum entropy copula with the same diagonal section. [ABSTRACT FROM AUTHOR]

We study the pruning process developed by Abraham and Delmas (2012) on the discrete Galton–Watson sub-trees of the Lévy tree which are obtained by considering the minimal sub-tree connecting the root and leaves chosen uniformly at rate λ , see Duquesne and Le Gall (2002). The tree-valued process, as λ increases, has been studied by Duquesne and Winkel (2007). Notice that we have a tree-valued process indexed by two parameters: the pruning parameter θ and the intensity λ . Our main results are: construction and marginals of the pruning process, representation of the pruning process (forward in time that is as θ increases) and description of the growing process (backward in time that is as θ decreases) and distribution of the ascension time (or explosion time of the backward process) as well as the tree at the ascension time. A by-product of our result is that the super-critical Lévy trees independently introduced by Abraham and Delmas (2012) and Duquesne and Winkel (2007) coincide. This work is also related to the pruning of discrete Galton–Watson trees studied by Abraham, Delmas and He (2012). [ABSTRACT FROM AUTHOR]

Representation of coalescent processes using pruning of trees has been used by Goldschmidt and Martin for the Bolthausen-Sznitman coalescent and by Abraham and Delmas for the β(3/2, 1/2)-coalescent. By considering a pruning procedure on stable Galton-Watson tree with n labeled leaves, we give a representation of the discrete β(1+α, 1-α)-coalescent, with α ∈ [1/2, 1) starting from the trivial partition of the n first integers. The construction can also be made directly on the stable continuum Lévy tree, with parameter 1/α, simultaneously for all n. This representation allows to use results on the asymptotic number of coalescence events to get the asymptotic number of cuts in stable Galton-Watson tree (with infinite variance for the offspring distribution) needed to isolate the root. Using convergence of the stable Galton-Watson tree conditioned to have infinitely many leaves, one can get the asymptotic distribution of blocks in the last coalescence event in the β(1 + α, 1 - α)-coalescent. [ABSTRACT FROM AUTHOR]

We give an explicit construction of the increasing tree-valued process introduced by Abraham and Delmas using a random point process of trees and a grafting procedure. This random point process will be used in companion papers to study record processes on Lévy trees. We use the Poissonian structure of the jumps of the increasing tree-valued process to describe its behavior at the first time the tree grows higher than a given height, using a spinal decomposition of the tree, similar to the classical Bismut and Williams decompositions. We also give the joint distribution of this exit time and the ascension time which corresponds to the first infinite jump of the tree-valued process. [ABSTRACT FROM AUTHOR]

This paper is devoted to the Cramer Rao bound (CRB) on the angle and range of a narrow-band near-field source localized by means of an arbitrary linear array using the exact expression of the time delay parameter. First, we prove that the conditional and unconditional CRBs are proportional for an arbitrary parametrization of the steering vector (that may include, but is not limited to, the source DOA, range or polarization). Then, a Taylor expansion of the CRB is conducted to obtain accurate nonmatrix closed-form expressions of the CRB on angle and range. In contrast to the existing expressions, our expressions are simple, interpretable and more general because the sensors are only constrained to be placed along some axis. Our analysis leads to the characterization and design of a class of centro-symmetric linear arrays with improved near-field angle and range estimation capabilities. [ABSTRACT FROM PUBLISHER]

Abstract: Widely Linear (WL) Minimum Mean Square Error (MMSE) estimation has received a great interest these last 20 years for second order (SO) noncircular signals. In the context of radio communications networks, it has been shown in particular that WL MMSE receivers allow to implement Single Antenna Interference Cancellation (SAIC) of one rectilinear interference, such as Binary Phase Shift Keying (BPSK) or Amplitude Shift Keying (ASK) interference, or of quasi-rectilinear interference, such as Minimum Shift keying (MSK), Gaussian MSK (GMSK) or Offset Quadrature Amplitude Modulation (OQAM) interference, hence their great interest for Global System for Mobile Communications (GSM) cellular networks in particular. However, one may wonder whether WL MMSE receivers remain attractive for SO noncircular nonrectilinear interferences, not so scarce in practice. The purpose of this paper is mainly to answer to this important question by giving, in a self-contained and unified way, some new insights into the behavior, properties and performance of the WL MMSE beamformer in the presence of arbitrary noncircular signals and interference which are not necessarily rectilinear. It is shown in particular that, surprisingly, WL MMSE receivers lose their practical interest for strong interferences which are not rectilinear. This breakthrough thus generates a new open problem for the choice between linear and WL MMSE receiver corresponding to the detection of rectilinearity (and/or quasi-rectilinearity), instead of noncircularity, in a given noisy observation. Although this question is out of the scope of this paper, we finally propose preliminary tools based on blind source separation methods to solve this problem. [Copyright &y& Elsevier]

We perform a pruning procedure on a Lévy tree and instead of throwing away the removed sub-tree, we regraft it on a given branch (not related to the Lévy tree). We prove that the tree constructed by regrafting is distributed as the original Lévy tree, generalizing a result of Addario-Berry, Broutin and Holmgren where only Aldous’s tree is considered. As a consequence, we obtain that the “average pruning time” of a leaf is distributed as the height of a leaf picked at random in the Lévy tree. [ABSTRACT FROM AUTHOR]

• This paper derives interpretable unified closed-form expressions for the threshold ASNR along the Cox and the Sharman and Durrani criteria associated with the conventional MUSIC and NC MUSIC algorithms in the context of arbitrary circular or rectilinear distributed correlated sources and circular CES distributed noise. • Using these expressions, we investigate the impact of the non-Gaussianity of the noise, as well as of the phase and magnitude of the correlation of the sources. • In particular, we prove for the first time that the phase of the correlation, which is the non-circularity phase separation for rectilinear sources, may have a strong impact on the resolution and a zero phase may lead to overly optimistic resolution. • We quantify the resolution benefit provided when the SCM is replaced by M - estimates of the covariance matrix for CES observations. The concept of threshold array signal-to-noise ratio (ASNR) which is defined as the minimal SNR at which specific high-resolution algorithms are able to resolve two closely spaced far-field sources, allows to quantify and to compare sensors array performance in localizing remote targets. This paper generalizes and extends the expressions of the threshold ASNR given in the literature for the conventional and non-circular (NC) MUSIC direction-of-arrival (DOA) estimation algorithms in the context of uncorrelated stochastic circular or rectilinear Gaussian sources and circular complex Gaussian (C-CG) noise, in a more general stochastic framework. We assume that the sources are correlated with an arbitrary distribution, which is inherent in a context of multipath or smart jammers, and that the noise is circular complex elliptically symmetric (C-CES) distributed, which can model impulsive noise with heavy-tailed distributions. The C-CES and NC-CES distributed observations are also considered to quantify the gain in resolution provided when the sample covariance matrix (SCM) of the observations is replaced by M -estimates of this matrix. Asymptotic approaches and perturbation analysis have been performed to derive closed-form expressions of the mean null spectra of the two considered MUSIC algorithms for both observation models, which allow us to derive, for the first time, general unified explicit analytical expressions of the threshold ASNR along the Cox and the Sharman and Durrani criteria. These expressions allow us to quantify the impact of the non-Gaussianity of noise and observations, as well as of the phase and magnitude of the correlation on the resolution threshold, and to quantify the benefit provided when the SCM is replaced by M -estimates of this covariance matrix for CES observations. Finally, numerical illustrations are included to support our theoretical analysis. [ABSTRACT FROM AUTHOR]

We consider the problem of sensor placement for estimating the direction of arrival of a narrow-band source randomly located in the far-field of a planar antenna array. Performance is evaluated by means of the expectation of the conditional Cramer Rao bound, normalized to that of the uniform circular array. Two cost functions are obtained, relative to azimuth and elevation, respectively. They depend on the array geometry as well as the distribution of the source azimuth. A class of uniform antenna arrays is investigated. It is adapted to the particular probabilistic distribution of the azimuth, while ensuring protection against array ambiguities. Using an exhaustive search procedure, we either seek the same reduction of both cost functions, or rather focus on one in particular. In the first approach, we achieve a reduction of almost 36% of both, regardless of the source azimuth distribution. In the second approach, we can obtain larger reductions for the targeted parameter. In both cases, optimal arrays are close to the V shape, for which performance analysis is conducted and closed-form expressions are obtained. [ABSTRACT FROM PUBLISHER]

We present a new pruning procedure on discrete trees by adding marks on the nodes of trees. This procedure allows us lo construct and study a tree-valued Markov process {G/(u)} by pruning Galton-Watson trees and an analogous process {G*(u)} by pruning a critical or subcritical Galton-Watson tree conditioned to be infinite. Under a mild condition on offspring distributions, we show dial the process {G(u)} run until its ascension time has a representation in terms of {G*(u)} A similar result was obtained by Aldous and Pitman (Ann. Inst. H. Poincare Probab. Statist. 34 (1998) 637-686) in the special case of Poisson offspring distributions where they considered uniform pruning of Galton-Watson trees by adding marks on the edges of treese. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the problem of testing impropriety (i.e., second-order noncircularity) of a sequence of complex-valued random variables (RVs) based on the generalized likelihood ratio test (GLRT) for Gaussian distributions is considered. Asymptotic (w.r.t. the data length) distributions of the GLR are given under the hypothesis that RVs are proper or improper, and under the true, not necessarily Gaussian distribution of the RVs. The considered RVs are independent but not necessarily identically distributed: assumption which has never been considered until now. This enables us to deal with the practical important situations of noncircular RVs disturbed by residual frequency offsets and additive circular noise. The receiver operating characteristic (ROC) of this test is derived as byproduct, an issue previously overlooked. Finally illustrative examples are presented in order to strengthen the obtained theoretical results. [Copyright &y& Elsevier]

Abstract: A performance analysis of likelihood ratio test (LRT)-based and generalized likelihood ratio test (GLRT)-based array receivers for the detection of a known real-valued signal corrupted by a potentially noncircular interference is considered in this paper. The distribution of the decision statistics associated with the LRT and GLRT is studied. This allows us to give exact closed-form expressions of the probability of detection (P D) and false alarm (P FA) for two LRT-based receivers. Then, asymptotic (with respect to the data length) closed-form expressions are given for P D and P FA for four GLRT-based receivers. Finally, in order to strengthen the obtained results, some illustrative examples are presented. [Copyright &y& Elsevier]

This correspondence presents an asymptotic analysis of the eigenvalue decomposition (EVD) of the sample covariance matrix associated with independent identically distributed (i.i.d.) non necessarily circular and Gaussian data that extends the well known analysis presented in the literature for circular and Gaussian data. Closed-form expressions of the asymptotic bias and variance of the sample eigenvalues and eigenvectors are given. As an application of these extended expressions, the statistical performance analysis of the widely used minimum description length (MDL) criterion applied to the detection of the number of noncircular or/and non-Gaussian sources impinging on an array of sensors is considered with a particular attention paid to uncorrelated rectilinear sources. [ABSTRACT FROM PUBLISHER]

Abstract: We consider the bifurcating Markov chain model introduced by Guyon to detect cellular aging from cell lineage. To take into account the possibility for a cell to die, we use an underlying super-critical binary Galton–Watson process to describe the evolution of the cell lineage. We give in this more general framework a weak law of large number, an invariance principle and thus fluctuation results for the average over all individuals in a given generation, or up to a given generation. We also prove that the fluctuations over each generation are independent. Then we present the natural modifications of the tests given by Guyon in cellular aging detection within the particular case of the auto-regressive model. [ABSTRACT FROM AUTHOR]

Abstract: In this correspondence we mainly consider the asymptotic distribution of the estimator of circularity coefficients of scalar and multidimensional complex random variables. A particular attention is paid to rectilinear RV. After deriving new properties of the circularity coefficients, the maximum likelihood estimate of the circularity coefficients in the Gaussian case and asymptotic distribution of this estimate for arbitrary distributions are given. Finally, an illustrative example is presented in order to strengthen the obtained theoretical results. [Copyright &y& Elsevier]

Abstract: In many detection applications, the main performance criterion is the signal to interference plus noise ratio (SINR). After linear filtering, the optimal SINR corresponds to the maximum value of a Rayleigh quotient, which can be interpreted as the largest generalized eigenvalue of two covariance matrices. Using an extension of Szegö''s theorem for the generalized eigenvalues of Hermitian block Toeplitz matrices, an expression of the theoretical asymptotic optimal SINR w.r.t. the number of taps is derived for arbitrary arrays with a limited but arbitrary number of sensors and arbitrary spectra. This bound is interpreted as an optimal zero-bandwidth spatial SINR in some sense. Finally, the speed of convergence of the optimal wideband SINR for a limited number of taps is analyzed for several interference scenarios. [Copyright &y& Elsevier]

A custom-designed laboratory prototype of a four-stage Stirling-type pulse tube cryocooler was recently developed by Lockheed Martin for niobium integrated circuits (ICs) operating close to 4 K. Basic system performance has been verified by integration with a Nb IC test chip, with cells that include a high-speed rapid single flux quantum (RSFQ) binary counter. For 650 W total compressor power, extended stable operation of the counter at T = 4.5 K was demonstrated with a clock frequency up to 46 GHz, with 25 mW of excess cooling capacity on the coldest stage. The thermodynamic, electromagnetic, and mechanical performance are promising for the development of an improved compact cryocooler for practical superconducting electronic applications in fields such as wireless communications. [ABSTRACT FROM AUTHOR]

We report on High Temperature Superconductor (HTS) DC current leads developed for the specific purpose of delivering small currents (<100 mA) to cryocooled electronic devices operating at 4 K, with significantly reduced heat leak. Multi-stage cryocoolers can provide a suitable platform for niobium-based superconducting electronics at 4 K; the necessary multiple parallel biasing of the circuitry can result in total currents of several amps, which can produce substantial thermal loading of the cryocooler when conventional resistive leads are used. Our approach has been to adapt the comparatively mature technology of high-current second-generation (2G) YBCO-coated conductor tape to low current needs by splitting the tape into electrically isolated narrow lines by ion milling. Performance issues discussed are: obtained critical currents, thermal conductance of the composite conductors, line-to-line electrical isolation, resistance of the joints and robustness. Operation as a current lead between the first and second stage of a Gifford-McMahon cryocooler is reported. [ABSTRACT FROM AUTHOR]

Abstract: We consider an initial Eve-population and a population of neutral mutants, such that the total population dies out in finite time. We describe the evolution of the Eve-population and the total population with continuous state branching processes, and the neutral mutation procedure can be seen as an immigration process with intensity proportional to the size of the population. First we establish a Williams’ decomposition of the genealogy of the total population given by a continuum random tree, according to the ancestral lineage of the last individual alive. This allows us to give a closed formula for the probability of simultaneous extinction of the Eve-population and the total population. [Copyright &y& Elsevier]

We consider an initial population whose size evolves according to a continuous state branching process. Then we add to this process an immigration (with the same branching mechanism as the initial population), in such a way that the immigration rate is proportional to the whole population size. We prove this continuous state branching process with immigration proportional to its own size is itself a continuous state branching process. By considering the immigration as the apparition of a new type, this construction is a natural way to model neutral mutation. It also provides in some sense a dual construction of the particular pruning at nodes of continuous state branching process introduced by the authors in a previous paper. For a critical or sub-critical quadratic branching mechanism, it is possible to explicitly compute some quantities of interest. For example, we compute the Laplace transform of the size of the initial population conditionally on the non-extinction of the whole population with immigration. We also derive the probability of simultaneous extinction of the initial population and the whole population with immigration. [ABSTRACT FROM AUTHOR]

In many detection and estimation problems associated with processing of second-order stationary random processes, the observation data are the sum of two zero-mean second-order stationary processes: the process of interest and the noise process. In particular, the main performance criterion is the signal-to-noise ratio (SNR). After linear filtering, the optimal SNR corresponds to the maximal value of a Rayleigh quotient which can be interpreted as the largest generalized eigenvalue of the covariance matrices associated with the signal and noise processes, which are block multilevel Toeplitz structured for m-dimensional vector-valued second-order stationary p-dimensional random processes xi1, i2,…, ip ϵ.ℝm. In this paper, an extension of Szego's theorem to the generalized eigenvalues of Hermitian block multilevel Toeplitz matrices is given, providing information about the asymptotic distribution of those generalized eigenvalues and in particular of the optimal SNR after linear filtering. A simple proof of this theorem, under the hypothesis of absolutely summable elements is given. The proof is based on the notion of multilevel asymptotic equivalence between block multilevel matrix sequences derived from the celebrated Gray approach. Finally, a short example in wideband space-time beamforming is given to illustrate this theorem. [ABSTRACT FROM AUTHOR]

Finite impulse responses (FIR) of single-input single-output (SISO) channels can be blindly identified from second-order statistics of transformed data, for instance when the channel is excited by binary phase shift keying (BPSK), minimum shift keying (MSK), or quadrature phase shift keying (QPSK) inputs. Identifiability conditions are derived by considering that noncircularity induces diversity. Theoretical performance issues are addressed to evaluate the robustness of standard subspace-based estimators with respect to these identifiability conditions. Then benchmarks such as asymptotically minimum variance (AMV) bounds based on various statistics are presented. Some illustrative examples are eventually given where Monte Carlo experiments are compared to theoretical performances. These comparisons allow to quantify limits to the use of the alphabet diversities for the identification of FIR SISO channels, and to demonstrate the robustness of algorithms based on high-order statistics. [ABSTRACT FROM AUTHOR]

This paper addresses the resolution of the conventional and noncircular MUSIC algorithms for arbitrary circular and noncircular second-order distributions of two uncorrelated closely spaced transmitters observed by an arbitrary array. An explicit closed-form expression of the mean null spectrum of the conventional and noncircular MUSIC algorithms is derived using an analysis based on perturbations of the noise projector instead of those of the eigenvectors. Based on these results, theoretical and approximate interpretable closed-form expressions of the threshold array signal-to-noise ratios (ASNR) at which these two algorithms are able to resolve two closely spaced transmitters along the Cox and the Sharman and Durrani criteria are given. It is proved that the threshold ASNRs given by the conventional MUSIC algorithm do not depend on the distribution of the sources including their noncircularity, in contrast to the noncircular MUSIC algorithm for which they are very sensitive to the noncircularity phase separation of the sources. This threshold ASNR given by the noncircular MUSIC algorithm is proven to be comfortably lower than that given by the conventional MUSIC algorithm except for weak phase separations of the sources for which the resolving powers of these two algorithms are very close. Finally, these results are analyzed through several illustrations and Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

This paper addresses the robustness of adaptive narrowband beamforming with respect to bandwidth based on the loss of performance in terms of signal-to-interference-plus-noise ratio (SINR). The criterion used by Zatman to define a narrowband environment, i.e., the ratio between the jammer plus noise covariance matrix and the noise eigenvalue, is studied from the point of view of a loss of SINR after narrowband beamforming under non narrowband conditions. Using theoretical results about the eigenvalues and eigenvectors of covariance matrices for signals closely spaced in frequency by Lee, it is shown that Zatman's criterion can be interpreted as an upper bound on the SINR loss which is nearly reached under certain conditions that are specified. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses subspace-based direction of arrival (DOA) estimation and its purpose is to complement previously available theoretical results generally obtained for specific algorithms. We focus on asymptotically (in the number of measurements) minimum variance (AMV) estimators based on estimates of orthogonal projectors obtained from singular value decompositions of sample covariance matrices in the general context of noncircular complex signals. After extending the standard AMV bound to statistics whose first covariance matrix of its asymptotic distribution is singular and deriving explicit expressions of this first covariance matrix associated with several projection-based statistics, we give closed-form expressions of AMV bounds based on estimates of different orthogonal projectors. This enable us to prove that these AMV bounds attain the stochastic Cramer–Rao bound (CRB) in the case of circular or noncircular Gaussian signals. [Copyright &y& Elsevier]

This paper is devoted to a statistical performance analysis of blind estimation of bit error rates (BER5) of a bank of detectors, using empirical estimation algorithms that have appeared in the literature (by Dixit et al.). In particular, we prove that these blind estimators asymptotically (in the number of observed bits) achieve the accuracy obtained with perfect knowledge of the transmitted bits. We propose a maximum-likelihood solution which follows from the standard expectation-maximization (EM) algorithm, considered to be a reference algorithm. Finally, the optimal fusion rule is revisited and our theoretical results are compared to Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Abstract: We consider the height process of a Lévy process with no negative jumps, and its associated continuous tree representation. Using tools developed by Duquesne and Le Gall, we construct a fragmentation process at height, which generalizes the fragmentation at height of stable trees given by Miermont. In this more general framework, we recover that the dislocation measures are the same as the dislocation measures of the fragmentation at nodes introduced by Abraham and Delmas, up to a factor equal to the fragment size. We also compute the asymptotics for the number of small fragments. [Copyright &y& Elsevier]

Abstract: This paper addresses asymptotically minimum variance (AMV) of parameter estimators within the class of algorithms based on second-order statistics for estimating parameter of strict-sense stationary complex circular processes. As an application, the estimation of the frequencies of cisoids for mixed spectra time series containing a sum of cisoids and an MA process is considered. [Copyright &y& Elsevier]

This paper examines the asymptotic performance of MUSIC-like algorithms for estimating directions of arrival (DOA) of narrowband complex noncircular sources. Using closed-form expressions of the covariance of the asymptotic distribution of different projection matrices, it provides a unifying framework for investigating the asymptotic performance of arbitrary subspace- based algorithms valid for Gaussian or non-Gaussian and complex circular or noncircular sources. We also derive different robustness properties from the asymptotic covariance of the estimated DOA given by such algorithms. These results are successively applied to four algorithms: to two attractive MUSIC-like algorithms previously introduced in the literature, to an extension of these algorithms, and to an optimally weighted MUSIC algorithm proposed in this paper. Numerical examples illustrate the performance of the studied algorithms compared to the asymptotically minimum variance (AMY) algorithms introduced as benchmarks. [ABSTRACT FROM AUTHOR]

This paper focuses on the stochastic Cramer-Rao bound (C RB) of direction of arrival (DOA) estimates for binary phase-shift keying (BPSK) and quaternary phase-shift keying (QPSK) modulated signals corrupted by additive circular complex Gaussian noise. Explicit expressions of the CRB for the DOA parameter alone in the case of a single signal waveform are given. These CRBs are compared, on the one hand, with those obtained with different a priori knowledge and, on the other hand, with CRBs under the noncircular and circular complex Gaussian distribution and with different deterministic CRBs. It is shown in particular that the CRBs under the noncircular [respectively,. circular] complex Gaussian distribution are tight upper bounds on the CRBs under the BPSK [respectively, QPSK] distribution at very low and very high signal-to-noise ratios (SNRs) only. Finally, these results and comparisons are extended to the case of two independent BPSK or QPSK distributed sources where an explicit expression of the CRB for the DOA parameters alone is given for large SNR. [ABSTRACT FROM AUTHOR]

This paper focuses on the stochastic Cramer-Rao bound (CRB) on direction of arrival (DOA) estimation accuracy for noncircular Gaussian sources in the general case of an arbitrary unknown Gaussian noise field parameterized by a vector of unknowns. Explicit closed-form expressions of the stochastic CRB for DOA parameters alone are obtained directly from the Slepian-Bangs formula for general noncircular complex Gaussian distributions. As a special case, the CRB under the nonuniform white noise assumption is derived. Our expressions can be viewed as extensions of the well-known results by Stoica and Nehorai, Ottersten et al., Weiss and Friedlander, Pesavento and Gershman, and Gershman et al. Some properties of these CRBs are proved and finally, these bounds are numerically compared with the conventional CRBs under the circular complex Gaussian distribution for different unknown noise field models. [ABSTRACT FROM AUTHOR]

Abstract: Let D be a bounded domain in with smooth boundary ∂D. We give a probabilistic representation formula for the non-negative solution of the mixed Dirichlet non-linear Neumann boundary value problem (DNP) where is a non-trivial partition of ∂D, φ is a non-negative, bounded and continuous function defined on , and denotes the outward normal derivative on the boundary of D. To solve the DNP, we consider a catalytic super-Brownian motion with underlying motion a Brownian motion reflected on ∂D, killed when it reaches and catalysed by the set , i.e. the branching rate is given by the local time of the paths on . Then we prove that the log-Laplace transform of φ integrated with respect to the exit measure of the catalytic process on , is a non-negative weak solution of the DNP. In a second part we show that we still have a probabilistic representation formula if the Dirichlet condition on is replaced by a Neumann condition. [Copyright &y& Elsevier]