consistency and convergence rates of one class svms and related algorithms we determine the asymptotic behaviour of the function computed by support vector machines svm and related algorithms that minimize a regularized empirical convex loss function in the reproducing kernel hilbert space of the gaussian rbf kernel in the situation where the number of examples tends to infinity the bandwidth of the gaussian kernel tends to 0 and the regularization parameter is held fixed non asymptotic convergence bounds to this limit in the l2 sense are provided together with upper bounds on the classification error that is shown to converge to the bayes risk therefore proving the bayes consistency of a variety of methods although the regularization term does not vanish these results are particularly relevant to the one class svm for which the regularization can not vanish by construction and which is shown for the first time to be a consistent density level set estimator

parametrization of all strictly causal stabilizing controllers within the framework of the factorization approach we present parametrizations of all strictly causal stabilizing controllers

feedback stabilization over commutative rings the matrix case this paper provides a solution of the feedback stabilization problem over commutative rings for matrix transfer functions stabilizability of a transfer matrix is realised as local stabilizability over the entire spectrum of the ring for stabilizable plants certain modules generated by its fractions and that of the stabilizing controller are shown to be projective compliments of each other in the case of rings with irreducible spectrum this geometric relationship shows that the plant is stabilizable if and only if the above modules of the plant are projective of ranks equal to the number of inputs and the outputs if the maxspectrum of the ring is noetherian and of zero krull dimension then this result shows that the stabilizable plants have doubly coprime fractions over unique factorization domains the above stabilizability condition is interpreted in terms of matrices formed by the fractions of the plant certain invariants of these matrices known as elementary factors are defined and it is shown that the plant is stabilizable if and only if these elementary factors generate the whole ring this condition thus provides a generalization of the coprime factorizability as a condition for stabilizabilty a formula for the class of all stabilizing controllers is then developed that generalizes the previous well known formula in factorization theory for multidimensional transfer functions these results provide concrete conditions for stabilizabilty finally it is shown that the class of polynomial rings over principal ideal domains is an additional class of rings over which stabilizable plants always have doubly coprime fractions

generalization error bounds in semi supervised classification under the cluster assumption we consider semi supervised classification when part of the available data is unlabeled these unlabeled data can be useful for the classification problem when we make an assumption relating the behavior of the regression function to that of the marginal distribution seeger 2000 proposed the well known cluster assumption as a reasonable one we propose a mathematical formulation of this assumption and a method based on density level sets estimation that takes advantage of it to achieve fast rates of convergence both in the number of unlabeled examples and the number of labeled examples

stochastic approximations of constrained discounted markov decision processes abstract we consider a discrete time constrained markov decision process under the discounted cost optimality criterion the state and action spaces are assumed to be borel spaces while the cost and constraint functions might be unbounded we are interested in approximating numerically the optimal discounted constrained cost to this end we suppose that the transition kernel of the markov decision process is absolutely continuous with respect to some probability measure then by solving the linear programming formulation of a constrained control problem related to the empirical probability measure n of we obtain the corresponding approximation of the optimal constrained cost we derive a concentration inequality which gives bounds on the probability that the estimation error is larger than some given constant this bound is shown to decrease exponentially in n our theoretical results are illustrated with a numerical application based on a stochastic version of the beverton holt population model

semi cancellable fractions in system theory in this paper we propose to define the transfer function of a system in a new way namely as a semi cancellable fraction scf i e a fraction in which unstable pole zero cancellations are not allowed within this new framework it is possible to be rigorous and coherent in dealing with the stabilizability of a system from an input output viewpoint not focusing on the stabilizability of infinite dimensional input output systems

topological uniqueness of the nash equilibrium for selfish routing with atomic users we consider the problem of selfish routing in a congested network shared by several users where each user wishes to minimize the cost of its own flow users are atomic in the sense that each has a nonnegligible amount of flow demand and flows may be split over different routes the total cost for each user is the sum of its link costs which in turn may depend on the user s own flow as well as the total flow on that link our main interest here is network topologies that ensure uniqueness of the nash equilibrium for any set of users and link cost functions that satisfy some mild convexity conditions we characterize the class of two terminal network topologies for which this uniqueness property holds and show that it coincides with the class of nearly parallel networks that was recently shown by milchtaich milchtaich i 2005 topological conditions for uniqueness of equilibrium in networks math oper res 30 225 244 to ensure uniqueness in nonatomic or wardrop routing games we further show that uniqueness of the link flows holds under somewhat weaker convexity conditions which apply to the mixed nash wardrop equilibrium problem we finally propose a generalized continuum game formulation of the routing problem that allows for a unified treatment of atomic and nonatomic users

solving linear systems via pfaffians abstract an explicit solution is given for the system of linear equations e e t where are alternating matrices of pfaffian 1 which at most differ in their first row and column and e is of the form i 2 2 r e 1 i x i if v v w r r 1 with v w 1 v w then a sequence of cohn transforms with respect to the fixed w which takes v w to v w is prescribed

constrained traffic equilibrium in routing we study noncooperative routing in which each user is faced with a multicriterion optimization problem formulated as the minimization of one criterion subject to constraints on others we address the questions of existence and uniqueness of equilibrium we show that equilibria indeed exist but uniqueness may be destroyed due to the multicriteria nature of the problem we obtain uniqueness in some weaker sense under appropriate conditions we show that the link utilizations are uniquely determined at equilibrium we further study the normalized constrained equilibrium and apply it to pricing

a plug in approach to neyman pearson classification the neyman pearson np paradigm in binary classification treats type i and type ii errors with different priorities it seeks classifiers that minimize type ii error subject to a type i error constraint under a user specified level in this paper plug in classifiers are developed under the np paradigm based on the fundamental neyman pearson lemma we propose two related plug in classifiers which amount to thresholding respectively the class conditional density ratio and the regression function these two classifiers handle different sampling schemes this work focuses on theoretical properties of the proposed classifiers in particular we derive oracle inequalities that can be viewed as finite sample versions of risk bounds np classification can be used to address anomaly detection problems where asymmetry in errors is an intrinsic property as opposed to a common practice in anomaly detection that consists of thresholding normal class density our approach does not assume a specific form for anomaly distributions such consideration is particularly necessary when the anomaly class density is far from uniformly distributed

controller parameterization of anantharam s example we consider the controller parameterization of anantharam s example 1985 it is shown that the parameterization is achieved by using only one parameter even though the plant does not have a coprime factorization

constrained games the impact of the attitude to adversary s constraints we consider properties of constrained games where the strategy set available to a player depends on the choice of strategies made by other players we show that the utilities of each player associated with that player s own performance and constraints are not sufficient to model a constrained game and to define equilibria for the latter one also needs to model how a player values the fact that other players meet their constraints we study three different approaches to other players constraints and show that they exhibit completely different equilibrium behaviors further we study a general class of stochastic games with partial information and focus on the case where the players are indifferent to whether the constraints of other players hold

any discrimination rule can have an arbitrarily bad probability of error for finite sample size consider the basic discrimination problem based on a sample of size n drawn from the distribution of x y on the borel sets of rdx 0 1 if 0 thus any attempt to find a nontrivial distribution free upper bound for rn will fail and any results on the rate of convergence of rn to r must use assumptions about the distribution of x y

semi supervised novelty detection a common setting for novelty detection assumes that labeled examples from the nominal class are available but that labeled examples of novelties are unavailable the standard inductive approach is to declare novelties where the nominal density is low which reduces the problem to density level set estimation in this paper we consider the setting where an unlabeled and possibly contaminated sample is also available at learning time we argue that novelty detection in this semi supervised setting is naturally solved by a general reduction to a binary classification problem in particular a detector with a desired false positive rate can be achieved through a reduction to neyman pearson classification unlike the inductive approach semi supervised novelty detection ssnd yields detectors that are optimal e g statistically consistent regardless of the distribution on novelties therefore in novelty detection unlabeled data have a substantial impact on the theoretical properties of the decision rule we validate the practical utility of ssnd with an extensive experimental study we also show that ssnd provides distribution free learning theoretic solutions to two well known problems in hypothesis testing first our results provide a general solution to the general two sample problem that is the problem of determining whether two random samples arise from the same distribution second a specialization of ssnd coincides with the standard p value approach to multiple testing under the so called random effects model unlike standard rejection regions based on thresholded p values the general ssnd framework allows for adaptation to arbitrary alternative distributions in multiple dimensions

empirical bayes analysis of a microarray experiment microarrays are a novel technology that facilitates the simultaneous measurement of thousands of gene expression levels a typical microarray experiment can produce millions of data points raising serious problems of data reduction and simultaneous inference we consider one such experiment in which oligonucleotide arrays were employed to assess the genetic effects of ionizing radiation on seven thousand human genes a simple nonparametric empirical bayes model is introduced which is used to guide the efficient reduction of the data to a single summary statistic per gene and also to make simultaneous inferences concerning which genes were affected by the radiation although our focus is on one specific experiment the proposed methods can be applied quite generally the empirical bayes inferences are closely related to the frequentist false discovery rate fdr criterion

algebraic geometric aspects of feedback stabilization this paper develops a theory of feedback stabilization for siso transfer functions over a general integral domain which extends the well known coprime factorization approach to stabilization necessary and sufficient conditions for stabilizability of a transfer function in this general setting are obtained these conditions are then refined in the special cases of unique factorization domains ufds noetherian rings and rings of fractions it is shown that these conditions can be naturally interpreted geometrically in terms of the prime spectrum of the ring this interpretation provides a natural generalization to the classical notions of the poles and zeros of a plant the set of transfer functions is topologized so as to restrict to the graph topology of vidyasagar ieee trans automatic control ac 29 1984 pp 403 418 when the ring is a bezout domain it is shown that stability of a feedback system is robust in this topology when the ring is a ufd this theory is then applied to the problem of sta

a convex characterization of multidimensional linear systems subject to sqi constraints this technical note proposes a convex characterization of the set of all stable closed loop linear systems that are obtained from a given plant which may be multidimensional by interconnecting it in feedback with controllers that satisfy a certain pre selected constraint we take an approach that is particularly useful when a doubly coprime factorization of the plant is difficult to obtain and a stable stabilizing controller may not exist the plant is not strongly stabilizable or when one may be difficult to find most related work requires one of these we adopt the so called coordinate free approach which unlike youla s parametrization does not rely on a doubly coprime factorization of the plant we show that if constraints which satisfy a condition called strong quadratic invariance sqi are imposed on the controllers then the set of all stable closed loop multidimensional linear systems has a convex representation and norm optimal control problems can be cast in convex form although the sqi condition is in general slightly stronger than quadratic invariance qi which was developed in related work they are equivalent for common classes of problems arising in decentralized control

on the performance of fdr control constraints and a partial solution the false discovery rate fdr paradigm aims to attain certain control on type i errors with relatively high power for multiple hypothesis testing the benjamini hochberg bh procedure is a wellknown fdr controlling procedure under a random effects model we show that in general unlike the fdr the positive fdr pfdr of the bh procedure cannot be controlled at an arbitrarily low level due to the limited evidence provided by the observations to separate false and true nulls this results in a criticality phenomenon which is characterized by a transition of the procedure s power from being positive to asymptotically 0 without any reduction in the pfdr once the target fdr control level is below a positive critical value to address the constraints on the power and pfdr control imposed by the criticality phenomenon we propose a procedure which applies bh type procedures at multiple locations in the domain of p values both analysis and simulations show that the proposed procedure can attain substantially improved power and pfdr control

stability and stabilization of multidimensional input output systems in this paper we discuss stability and stabilization of continuous and discrete multidimensional input output io behaviors of dimension r which are described by linear systems of complex partial differential resp difference equations with constant coefficients where the signals are taken from various function spaces in particular from those of polynomial exponential functions stability is defined with respect to a disjoint decomposition of the r dimensional complex space into a stable and an unstable region with the standard stable region in the one dimensional continuous case being the set of complex numbers with negative real part a rational function is called stable if it has no poles in the unstable region an io behavior is called stable if the characteristic variety of its autonomous part has no points in the unstable region this is equivalent to the stability of its transfer matrix and an additional condition the system is called stabilizable if there is a compensator io system such that the output feedback system is well posed and stable we characterize stability and stabilizability and construct all stabilizing compensators of a stabilizable io system parametrization the theorems and proofs are new but essentially inspired and influenced by and related to the stabilization theorems concerning multidimensional io maps as developed for instance by bose guiver shankar sule xu lin ying zerz and quadrat and of course the seminal papers of vidyasagar youla and others in the one dimensional case in contrast to the existing literature the theorems and proofs of this paper do not need or employ the so called fractional representation approach i e various matrix fraction descriptions of the transfer matrix thus avoiding the often lengthy matrix computations and seeming to be of interest even for one dimensional systems at least to the author an important mathematical tool new in systems theory is gabriel s localization theory which only in the case of ideal convex shankar sule unstable regions coincides with the usual one algorithmic tests for stability stabilizability and ideal convexity and the algorithmic construction of stabilizing compensators are addressed but still encounter many difficulties see in particular the open problems listed by xu e

novelty detection using level set methods this paper presents a level set boundary description lsbd approach for novelty detection that treats the nonlinear boundary directly in the input space the proposed approach consists of level set function lsf construction boundary evolution and termination of the training process it employs kernel density estimation to construct the lsf of the initial boundary for the training data set then a sign of the lsf based algorithm is proposed to evolve the boundary and make it fit more tightly in the data distribution the training process terminates when an expected fraction of rejected normal data is reached the evolution process utilizes the signs of the lsf values at all training data points to decide whether to expand or shrink the boundary extensive experiments are conducted on benchmark data sets to evaluate the proposed lsbd method and compare it against four representative novelty detection methods the experimental results demonstrate that the novelty detector modeled with the proposed lsbd can effectively detect anomalies

frustration tuning and perfect phase synchronization in the kuramoto sakaguchi model we present an analysis of conditions under which the dynamics of a frustrated kuramoto or kuramoto sakaguchi model on sparse networks can be tuned to enhance synchronization using numerical optimization techniques linear stability and dimensional reduction analysis a simple tuning scheme for setting node specific frustration parameters as functions of native frequencies and degrees is developed finite size scaling analysis reveals that even partial application of the tuning rule can significantly reduce the critical coupling for the onset of synchronization in the second part of the paper a codynamics is proposed which allows a dynamic tuning of frustration parameters simultaneously with the ordinary kuramoto dynamics we find that such codynamics enhance synchronization when operating on slow time scales and impede synchronization when operating on fast time scales relative to the kuramoto dynamics

feedback stabilization over commutative rings further study of the coordinate free approach this paper is concerned with the coordinate free approach to control systems the coordinate free approach is a factorization approach but does not require the coprime factorizations of the plant we present two criteria for feedback stabilizability for multi input multi output mimo systems in which transfer functions belong to the total rings of fractions of commutative rings both of them are generalizations of sule s results in siam j control optim 32 1994 pp 1675 1695 the first criterion is expressed in terms of modules generated from a causal plant and does not require the plant to be strictly causal it shows that if the plant is stabilizable the modules are projective the other criterion is expressed in terms of ideals called generalized elementary factors this gives the stabilizability of a causal plant in terms of the coprimeness of the generalized elementary factors as an example a discrete finite time delay system is considered

fisher information and criticality in the kuramoto model of nonidentical oscillators we use the fisher information to provide a lens on the transition to synchronization of the kuramoto model of nonidentical frequencies on a variety of undirected graphs we numerically solve the equations of motion for a n 400 complete graph and n 1000 small world scale free uniform random and random regular graphs for large but finite graphs of small average diameter the fisher information f as a function of coupling shows a peak closely coinciding with the critical point as determined by kuramoto s order parameter or synchronization measure r however for graphs of larger average diameter the position of the peak in f differs from the critical point determined by estimates of r on the one hand this is a finite size effect even at n 1000 however we show across a range of topologies that the fisher information peak points to a transition for smaller graphs that indicates structural changes in the numbers of locally phase synchronized clusters often directly from metastable to stable frequency synchronization solving explicitly for a two cluster ansatz subject to gaussian noise shows that the fisher infomation peaks at such a transition we discuss the implications for fisher information as an indicator for edge of chaos phenomena in finite coupled oscillator systems

on a generalization of the youla kucera parametrization part i the fractional ideal approach to siso systems abstract in this paper we show how to use the theory of fractional ideals in order to study the fractional representation approach to analysis and synthesis problems for siso systems within this mathematical framework we give necessary and sufficient conditions so that a plant is internally strongly bistably stabilizable or admits a weak coprime factorization moreover we show how to generalize the youla kucera parametrization of the stabilizing controllers to any stabilizable plant which does not necessarily admit a coprime factorization this parametrization is generally affine in two free parameters

elementary proof of controller parametrization without coprime factorizability recently a controller parametrization method without coprime factorizability was presented by mori in this note we present this method using elementary matrix operations unlike in the earlier paper good knowledge of commutative algebra and module theory is not required

synchronisation of networked kuramoto oscillators under stable levy noise abstract we study the kuramoto model on several classes of network topologies examining the dynamics under the influence of levy noise such noise exhibits heavier tails than gaussian and allows us to understand how shocks influence the individual oscillator and collective system behaviour skewed stable levy noise equivalent to fractional diffusion perturbations are considered we perform numerical simulations for erd s renyi er and barabasi albert ba scale free networks of size n 1000 while varying the levy index for the noise we find that synchrony now assumes a surprising variety of forms not seen for gaussian type noise and changing with a noise generated drift a smooth dependence of the point of cross over of er and ba networks in the degree of synchronisation and a severe loss of synchronisation at low values of we also show that this robustness of the ba network across most values of can also be understood as a consequence of the laplacian of the graph working within the fractional fokker planck equation of the linearised system close to synchrony with both eigenvalues and eigenvectors alternately contributing in different regimes of

oracle and adaptive compound decision rules for false discovery rate control we develop a compound decision theory framework for multiple testing problems and derive an oracle rule based on the z values that minimizes the false nondiscovery rate fnr subject to a constraint on the false discovery rate fdr we show that many commonly used multiple testing procedures which are p value based are inefficient and propose an adaptive procedure based on the z values the z value based adaptive procedure asymptotically attains the performance of the z value oracle procedure and is more efficient than the conventional p value based methods we investigate the numerical performance of the adaptive procedure using both simulated and real data in particular we demonstrate our method in an analysis of the microarray data from a human immunodeficiency virus study that involves testing a large number of hypotheses simultaneously

synchronization of two interacting populations of oscillators we analyze synchronization between two interacting populations of different phase oscillators for the important case of asymmetric coupling functions we find a much richer dynamical behavior compared to that of symmetrically coupled populations of identical oscillators it includes three types of bistabilities higher order entrainment and the existence of states with unusual stability properties all possible routes to synchronization of the populations are presented and some stability boundaries are obtained analytically the impact of these findings for neuroscience is discussed

a stochastic process approach to false discovery control this paper extends the theory of false discovery rates fdr pioneered by benjamini and hochberg j roy statist soc ser b 57 1995 289 300 we develop a framework in which the false discovery proportion fdp the number of false rejections divided by the number of rejections is treated as a stochastic process after obtaining the limiting distribution of the process we demonstrate the validity of a class of procedures for controlling the false discovery rate the expected fdp we construct a confidence envelope for the whole fdp process from these envelopes we derive confidence thresholds for controlling the quantiles of the distribution of the fdp as well as controlling the number of false discoveries we also investigate methods for estimating the p value distribution

a neyman pearson approach to statistical learning the neyman pearson np approach to hypothesis testing is useful in situations where different types of error have different consequences or a priori probabilities are unknown for any spl alpha 0 the np lemma specifies the most powerful test of size spl alpha but assumes the distributions for each hypothesis are known or in some cases the likelihood ratio is monotonic in an unknown parameter this paper investigates an extension of np theory to situations in which one has no knowledge of the underlying distributions except for a collection of independent and identically distributed i i d training examples from each hypothesis building on a fundamental lemma of cannon et al we demonstrate that several concepts from statistical learning theory have counterparts in the np context specifically we consider constrained versions of empirical risk minimization np erm and structural risk minimization np srm and prove performance guarantees for both general conditions are given under which np srm leads to strong universal consistency we also apply np srm to dyadic decision trees to derive rates of convergence finally we present explicit algorithms to implement np srm for histograms and dyadic decision trees

from incoherence to synchronicity in the network kuramoto model we study the synchronization properties of the kuramoto model of coupled phase oscillators on a general network here we distinguish the ability of such a system to self synchronize from the stability of this behavior while self synchronization is a consequence of genuine nonperturbative dynamics the stability in dynamical systems is usually accessible by fluctuations about a fixed point here taken to be the phase synchronized solution we examine this problem in terms of modes of the graph laplacian by which the absolute lyapunov stability of the phase synchronized fixed point is readily demonstrated departures from stability are seen to arise at the next order in fluctuations where depending on a truncation in the number of time dependent laplacian modes the dynamical equations can be reduced to forms resembling those for species population models the logistic and the lotka volterra equations methods from these systems are exploited to analytically derive new critical couplings signaling deviation from classical stability we thereby analytically explain the existence of an intermediate regime of behavior between incoherence and synchronization where system wide periodic behaviors are exhibited and stable unstable and hyperbolic fixed points can be identified we discuss these results in light of numerical solutions of the equations of motion for various networks

frequency response estimation for normalized coprime factors this paper investigates estimating the frequency response of the normalized coprime factors of a possibly unstable transfer function from closed loop frequency domain experimental data a stochastic framework has been adopted the dual youla kucera parametrization approach in closed loop system identification has been developed to guarantee the normality of the estimated frequency response a parametrization of all the normalized coprime factors has been established for transfer functions internally stabilizable by a known controller based on this parametrization interpolation conditions have been derived for the measurement errors being consistent with the stabilizing controller and experimental data an analytic expression has been obtained for the maximum likelihood estimate of the frequency response the effectiveness of the suggested method is confirmed through numerical simulations

an introduction to kernel based learning algorithms this paper provides an introduction to support vector machines kernel fisher discriminant analysis and kernel principal component analysis as examples for successful kernel based learning methods we first give a short background about vapnik chervonenkis theory and kernel feature spaces and then proceed to kernel based learning in supervised and unsupervised scenarios including practical and algorithmic considerations we illustrate the usefulness of kernel algorithms by discussing applications such as optical character recognition and dna analysis

estimating the support of a high dimensional distribution suppose you are given some data set drawn from an underlying probability distribution p and you want to estimate a simple subset s of input space such that the probability that a test point drawn from p lies outside of s equals some a priori specified value between 0 and 1 we propose a method to approach this problem by trying to estimate a function f that is positive on s and negative on the complement the functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data it is regularized by controlling the length of the weight vector in an associated feature space the expansion coefficients are found by solving a quadratic programming problem which we do by carrying out sequential optimization over pairs of input patterns we also provide a theoretical analysis of the statistical performance of our algorithm the algorithm is a natural extension of the support vector algorithm to the case of unlabeled data

games with coupled propagated constraints in optical networks with multi link topologies we consider games in optical networks in the class of m player games with coupled utilities and constraints nash equilibria of such games can be computed based on recent extension of duality to a game theoretical framework this work extends previous results on games with coupled constraints in optical links to multi link topologies coupled constraints in optical networks are propagated along links which introduces additional complexities for analysis specifically convexity of the propagated constraints is no longer automatically ensured we show that convexity is satisfied for single sink multi link topologies the general case of multi links with arbitrary sources and sinks is dealt with by a partitioned game with stages we exploit the single sink structure of each stage and the ladder nested form of the game and we discuss iterative computation of equilibria based on a three level hierarchical algorithm and prove its convergence under certain conditions

a classification framework for anomaly detection one way to describe anomalies is by saying that anomalies are not concentrated this leads to the problem of finding level sets for the data generating density we interpret this learning problem as a binary classification problem and compare the corresponding classification risk with the standard performance measure for the density level problem in particular it turns out that the empirical classification risk can serve as an empirical performance measure for the anomaly detection problem this allows us to compare different anomaly detection algorithms empirically i e with the help of a test set furthermore by the above interpretation we can give a strong justification for the well known heuristic of artificially sampling labeled samples provided that the sampling plan is well chosen in particular this enables us to propose a support vector machine svm for anomaly detection for which we can easily establish universal consistency finally we report some experiments which compare our svm to other commonly used methods including the standard one class svm

gaussian noise and the two network frustrated kuramoto model abstract we examine analytically and numerically a variant of the stochastic kuramoto model for phase oscillators coupled on a general network two populations of phased oscillators are considered labelled blue and red each with their respective networks internal and external couplings natural frequencies and frustration parameters in the dynamical interactions of the phases we disentangle the different ways that additive gaussian noise may influence the dynamics by applying it separately on zero modes or normal modes corresponding to a laplacian decomposition for the sub graphs for blue and red under the linearisation ansatz that the oscillators of each respective network remain relatively phase synchronised centroids or clusters we are able to obtain simple closed form expressions using the fokker planck approach for the dynamics of the average angle of the two centroids in some cases this leads to subtle effects of metastability that we may analytically describe using the theory of ratchet potentials these considerations are extended to a regime where one of the populations has fragmented in two the analytic expressions we derive largely predict the dynamics of the non linear system seen in numerical simulation in particular we find that noise acting on a more tightly coupled population allows for improved synchronisation of the other population where deterministically it is fragmented

the positive false discovery rate a bayesian interpretation and the q value multiple hypothesis testing is concerned with controlling the rate of false positives when testing several hypotheses simultaneously one multiple hypothesis testing error measure is the false discovery rate fdr which is loosely defined to be the expected proportion of false positives among all significant hypotheses the fdr is especially appropriate for exploratory analyses in which one is interested in finding several significant results among many tests in this work we introduce a modified version of the fdr called the positive false discovery rate pfdr we discuss the advantages and disadvantages of the pfdr and investigate its statistical properties when assuming the test statistics follow a mixture distribution we show that the pfdr can be written as a bayesian posterior probability and can be connected to classification theory these properties remain asymptotically true under fairly general conditions even under certain forms of dependence also a new quantity called the q value is introduced and investigated which is a natural bayesian posterior p value or rather the pfdr analogue of the p value 1 introduction when testing a single hypothesis one is usually concerned with controlling the false positive rate while maximizing the probability of detecting an effect when one really exists in statistical terms we maximize the power conditional on the type i error rate being at or below some level the field of multiple hypothesis testing tries to extend this basic paradigm to the situation where several hypotheses are tested simultaneously one must define an appropriate compound error measure according to the rate of false positives one is willing to encounter then a procedure is developed that allows one to control the error rate at a desired level while maintaining the power of each test as much as possible the most commonly controlled quantity when testing multiple hypotheses is the family wise error rate fwer which is the probability of yielding one or more false positives out of all hypotheses tested the most familiar example of this is the bonferroni method if there are m hypothesis tests each test is controlled so that the probability of a false positive is less than or equal to m for some chosen value of it then follows that the overall fwer is less than or equal to m any

fixed points and stability in the two network frustrated kuramoto model we examine a modification of the kuramoto model for phase oscillators coupled on a network here two populations of oscillators are considered each with different network topologies internal and cross network couplings and frequencies additionally frustration parameters for the interactions of the cross network phases are introduced this may be regarded as a model of competing populations internal to any one network phase synchronisation is a target state while externally one or both populations seek to frequency synchronise to a phase in relation to the competitor we conduct fixed point analyses for two regimes one where internal phase synchronisation occurs for each population with the potential for instability in the phase of one population in relation to the other the second where one part of a population remains fixed in phase in relation to the other population but where instability may occur within the first population leading to fragmentation we compare analytic results to numerical solutions for the system at various critical thresholds

there is no non zero stable fixed point for dense networks in the homogeneous kuramoto model this paper is concerned with the existence of multiple stable fixed point solutions of the homogeneous kuramoto model we develop a necessary condition for the existence of stable fixed points for the general network kuramoto model this condition is applied to show that for sufficiently dense n node networks with node degrees at least 0 9395 n 1 the homogeneous equal frequencies model has only one stable fixed point solution over the full space of phase angles in the range to this is the zero fixed point solution defined by all phase angle differences being zero this result together with existing research proves a conjecture of verwoerd and mason 2007 proc of the american control conf pp 4613 8 that for the complete network and the homogeneous model the zero fixed point has a basin of attraction consisting of the entire space minus a set of measure zero the necessary conditions are also tested to see how close to sufficiency they might be by applying them to a class of regular degree networks studied by wiley et al 2006 chaos 16 015103

on stabilization and the existence of coprime factorizations let k be an integral domain and f its quotient field we show there are plants over f which have no stable coprime factorizations but can be stabilized in a stable closed loop this answers a question posed by vidyasagar schneider and francis

on false discovery rate thresholding for classification under sparsity we study the properties of false discovery rate fdr thresholding viewed as a classification procedure the 0 class null is assumed to have a known density while the 1 class alternative is obtained from the 0 class either by translation or by scaling furthermore the 1 class is assumed to have a small number of elements w r t the 0 class sparsity we focus on densities of the subbotin family including gaussian and laplace models nonasymptotic oracle inequalities are derived for the excess risk of fdr thresholding these inequalities lead to explicit rates of convergence of the excess risk to zero as the number m of items to be classified tends to infinity and in a regime where the power of the bayes rule is away from 0 and 1 moreover these theoretical investigations suggest an explicit choice for the target level alpha m of fdr thresholding as a function of m our oracle inequalities show theoretically that the resulting fdr thresholding adapts to the unknown sparsity regime contained in the data this property is illustrated with numerical experiments

the fractional representation approach to synthesis problems an algebraic analysis viewpoint part i weakly doubly coprime factorizations in this paper we show how to reformulate the fractional representation approach to analysis and synthesis problems within an algebraic analysis framework in terms of modules we give necessary and sufficient conditions so that a system admits weakly left right doubly coprime factorizations moreover we explicitly characterize the integral domains a such that every plant defined by means of a transfer matrix whose entries belong to the quotient field of a admits weakly doubly coprime factorizations finally we show that this algebraic analysis approach allows us to recover on the one hand the approach developed in m c smith ieee trans automat control 34 1989 pp 1005 1007 and on the other hand the ones developed in k mori and k abe siam j control optim 39 2001 pp 1952 1973 v r sule siam j control optim 32 1994 pp 1675 1695 and 36 1998 pp 2194 2195 m vidyasagar h schneider and b a francis ieee trans automat control 27 1982 pp 880 894 m vidyasagar control system synthesis a factorization approach mit press cambridge ma 1985

parameterization of stabilizing controllers with either right or left coprime factorization a parameterization method of stabilizing controllers that requires only one of right left coprime factorizations is presented as an illustrative model we will consider the multidimensional system with structural stability for which it is not yet known in general whether or not a doubly coprime factorization always exists a parameterization of stabilizing controllers for the model is presented