stability analysis of markovian jump stochastic bam neural networks with impulse control and mixed time delays this paper discusses the issue of stability analysis for a class of impulsive stochastic bidirectional associative memory neural networks with both markovian jump parameters and mixed time delays the jumping parameters are modeled as a continuous time discrete state markov chain based on a novel lyapunov krasovskii functional the generalized ito s formula mathematical induction and stochastic analysis theory a linear matrix inequality approach is developed to derive some novel sufficient conditions that guarantee the exponential stability in the mean square of the equilibrium point at the same time we also investigate the robustly exponential stability in the mean square of the corresponding system with unknown parameters it should be mentioned that our stability results are delay dependent which depend on not only the upper bounds of time delays but also their lower bounds moreover the derivatives of time delays are not necessarily zero or smaller than one since several free matrices are introduced in our results consequently the results obtained in this paper are not only less conservative but also generalize and improve many earlier results finally two numerical examples and their simulations are provided to show the effectiveness of the theoretical results

remarques sur l apparition de singularites dans les ecoulements euleriens compressible we recall some basic facts about the breakdown of smoothness in general hyperbolic systems and then we prove that the breakdown of smoothness in an euclidean flow comes from an accumulation of vorticity divergence or compression

controlling correlations in latin hypercube samples abstract monte carlo integration is competitive for high dimensional integrands latin hypercube sampling is a stratification technique that reduces the variance of the integral previous work has shown that the additive part of the integrand is integrated with error op n 1 2 under latin hypercube sampling with n integrand evaluations a bilinear part of the integrand is more accurately estimated if the sample correlations among input variables are negligible other authors have proposed an algorithm for controlling these correlations we show that their method reduces the correlations by roughly a factor of 3 for 10 n 500 we propose a method that based on simulations appears to produce correlations of order op n 3 2 an analysis of the algorithm indicates that it cannot be expected to do better than n 3 2

adaptive probability based latin hypercube designs adaptive sampling is an effective method developed mainly for regular regions however experimental regions in irregular shapes are commonly observed in practice motivated by a data center thermal management study a new class of adaptive designs is proposed to accommodate a specific type of irregular region because the adaptive procedure introduces biases into conventional estimators several design unbiased estimators are given for estimating the population mean efficient and easy to compute unbiased estimators are also introduced the proposed method is applied to obtain an adaptive sensor placement plan to monitor and study the thermal distribution in a data center all of the supplemental materials used in this work are available online

generalization bounds of erm based learning processes for continuous time markov chains many existing results on statistical learning theory are based on the assumption that samples are independently and identically distributed i i d however the assumption of i i d samples is not suitable for practical application to problems in which samples are time dependent in this paper we are mainly concerned with the empirical risk minimization erm based learning process for time dependent samples drawn from a continuous time markov chain this learning process covers many kinds of practical applications e g the prediction for a time series and the estimation of channel state information thus it is significant to study its theoretical properties including the generalization bound the asymptotic convergence and the rate of convergence it is noteworthy that since samples are time dependent in this learning process the concerns of this paper cannot at least straightforwardly be addressed by existing methods developed under the sample i i d assumption we first develop a deviation inequality for a sequence of time dependent samples drawn from a continuous time markov chain and present a symmetrization inequality for such a sequence by using the resultant deviation inequality and symmetrization inequality we then obtain the generalization bounds of the erm based learning process for time dependent samples drawn from a continuous time markov chain finally based on the resultant generalization bounds we analyze the asymptotic convergence and the rate of convergence of the learning process

a blow up criterion of strong solutions to a viscous liquid gas two phase flow model with vacuum in 3d abstract in this paper we get a blow up criterion for the strong solutions to the 3d viscous liquid gas two phase flow model with vacuum more precisely we prove that the bound of l t 1 l x norm of the deformation tensor of velocity gradient controls the possible breakdown of the strong solutions

constrained maximin designs for computer experiments finding a design scheme for expensive computer experiments in arbitrary design regions is often a difficult task a well known criterion that is often used for computer experiments is the minimal euclidean distance between any pair of design sites which should be maximal in this article we describe methods to create such a constrained maximin simulation scheme we give some numerical results for both theoretical and practical examples

local regularity criteria of the 3d navier stokes and related equations abstract in this paper we are concerned with the local regularity of suitable weak solutions to the 3d navier stokes equations and its generalized case with fractional power of the laplacian 3 4 1 in the first part we derive some regularity criteria in terms of the deformation tensor d u for the classical navier stokes equations in the second part for the fractional case we obtain some regularity conditions for suitable weak solutions including the velocity u the gradient of the velocity u the rotation tensor u and the deformation tensor d u this generalizes the results obtained by gustafson et al 2007

the level based stratified sampling plan abstract if the probability distribution of the input variables to a system described by a computer code is known the distribution function of the output variable can be obtained by computer simulations with a complicated program each simulation can take very long time it thus is necessary to choose the combinations of the input parameters carefully to get as much information as possible with a small number of computer runs different methods true random sampling stratified sampling latin hypercube sampling and updated latin hypercube sampling for choosing the input parameters are described in the literature as a criteria for a good sampling plan unbiased estimates and low mean squared error are used by computer experiments it has been shown that the sampling plans based on latin hypercubes often have the smallest variance of the estimated output variable in this article it is shown that a stratified sampling plan with strata defined by the surfaces in the sampling space where the output var

the three dimensional euler equations where do we stand the three dimensional euler equations have stood for a quarter of a millenium as a challenge to mathematicians and physicists while much has been discovered the nature of solutions is still largely a mystery this paper surveys some of the issues such as singularity formation that have cost so much effort in the last 25 years in this light we review the beale kato majda theorem and its consequences and then list some of the results of numerical experiments that have been attempted a different line of endeavour focuses on work concerning the pressure hessian and how it may be used and modelled the euler equations are finally discussed in terms of their membership of a class of general lagrangian evolution equations using hamilton s quaternions these are reformulated in an elegant manner to describe the motion and rotation of fluid particles c 2007 elsevier b v all rights reserved

singularities of euler flow not out of the blue does three dimensional incompressible euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time this blowup problem is still open after briefly reviewing what is known and pointing out some of the difficulties we propose to tackle this issue for the class of flows having analytic initial data for which hypothetical real singularities are preceded by singularities at complex locations we present some results concerning the nature of complex space singularities in two dimensions and propose a new strategy for the numerical investigation of blowup

capacity of reproducing kernel spaces in learning theory the capacity of reproducing kernel hilbert spaces rkhs plays an essential role in the analysis of learning theory covering numbers and packing numbers of balls of these reproducing kernel spaces are important measurements of this capacity we first present lower bound estimates for the packing numbers by means of nodal functions then we show that if a mercer kernel is c sup s for some s 0 being not an even integer the rkhs associated with this kernel can be embedded into c sup s 2 this gives upper bound estimates for the covering number concerning sobolev smooth kernels examples and applications to v sub spl gamma dimension and tikhonov 1977 regularization are presented to illustrate the upper and lower bound estimates

blow up criterion for the compressible magnetohydrodynamic equations with vacuum abstract in this paper the 3 d compressible magnetohydrodynamic mhd equations with initial vacuum or infinite electric conductivity is considered we prove that the l norms of the deformation tensor d u and the absolute temperature control the possible blow up see 18 23 of strong solutions especially for the non resistive mhd system when the magnetic diffusion vanishes this conclusion means that if a solution of the compressible mhd equations is initially regular and loses its regularity at some later time then the formation of singularity must be caused by losing the bound of d u or as the critical time approaches the viscosity coefficients are only restricted by the physical conditions our criterion see 1 17 is similar to 17 for 3 d incompressible euler equations and to 12 for 3 d compressible isentropic navier stokes equations

3d euler equations and ideal mhd mapped to regular systems probing the finite time blowup hypothesis abstract we prove by an explicit construction that solutions to incompressible 3d euler equations defined in the periodic cube 0 l 3 can be mapped bijectively to a new system of equations whose solutions are globally regular we establish that the usual beale kato majda criterion for finite time singularity or blowup of a solution to the 3d euler system is equivalent to a condition on the corresponding regular solution of the new system in the hypothetical case of euler finite time singularity we provide an explicit formula for the blowup time in terms of the regular solution of the new system the new system is amenable to being integrated numerically using similar methods as in euler equations we propose a method to simulate numerically the new regular system and describe how to use this to draw robust and reliable conclusions on the finite time singularity problem of euler equations based on the conservation of quantities directly related to energy and circulation the method of mapping to a regular system can be extended to any fluid equation that admits a beale kato majda type of theorem e g 3d navier stokes 2d and 3d magnetohydrodynamics and 1d inviscid burgers we discuss briefly the case of 2d ideal magnetohydrodynamics in order to illustrate the usefulness of the mapping we provide a thorough comparison of the analytical solution versus the numerical solution in the case of 1d inviscid burgers equation

blowup criterion for viscous baratropic flows with vacuum states we prove that the maximum norm of the deformation tensor of velocity gradients controls the possible breakdown of smooth strong solutions for the 3 dimensional 3d barotropic compressible navier stokes equations more precisely if a solution of the 3d barotropic compressible navier stokes equations is initially regular and loses its regularity at some later time then the loss of regularity implies the growth without bound of the deformation tensor as the critical time approaches our result is the same as ponce s criterion for 3 dimensional incompressible euler equations ponce in commun math phys 98 349 353 1985 in addition initial vacuum states are allowed in our cases

probability based latin hypercube designs for slid rectangular regions existing space filling designs are based on the assumption that the experimental region is rectangular while in practice this assumption can be violated motivated by a data centre thermal management study a class of probability based latin hypercube designs is proposed to accommodate a specific type of irregular region a heuristic algorithm is proposed to search efficiently for optimal designs unbiased estimators are proposed their variances are given and their performances are compared empirically the proposed method is applied to obtain an optimal sensor placement plan to monitor and study the thermal distribution in a data centre

limiting case of the sobolev inequality in bmo with application to the euler equations we shall prove a logarithmic sobolev inequality by means of the bmo norm in the critical exponents as an application we shall establish a blow up criterion of solutions to the euler equations

a multi fluid compressible system as the limit of weak solutions of the isentropic compressible navier stokes equations this paper mainly concerns the mathematical justification of a viscous compressible multi fluid model linked to the baer nunziato model used by engineers see for instance ishii thermo fluid dynamic theory of two phase flow eyrolles paris 1975 under a stratification assumption more precisely we show that some approximate finite energy weak solutions of the isentropic compressible navier stokes equations converge on a short time interval to the strong solution of this viscous compressible multi fluid model provided the initial density sequence is uniformly bounded with corresponding young measures which are linear convex combinations of m dirac measures to the authors knowledge this provides in the multidimensional in space case a first positive answer to an open question see hillairet j math fluid mech 9 343 376 2007 with a stratification assumption the proof is based on the weak solutions constructed by desjardins commun partial differ equ 22 5 6 977 1008 1997 and on the existence and uniqueness of a local strong solution for the multi fluid model established by hillairet assuming initial density to be far from vacuum in a first step adapting the ideas from hoff and santos arch ration mech anal 188 509 543 2008 we prove that the sequence of weak solutions built by desjardins has extra regularity linked to the divergence of the velocity without any relation assumption between and coupled with the uniform bound of the density property this allows us to use appropriate defect measures and their nice properties introduced and proved by hillairet aspects interactifs de la m ecanique des fluides phd thesis ens lyon 2005 in order to prove that the young measure associated to the weak limit is the convex combination of m dirac measures finally under a non degeneracy assumption of this combination stratification assumption this provides a multi fluid system using a weak strong uniqueness argument we prove that this convex combination is the one corresponding to the strong solution of the multi fluid model built by hillairet if initial data are equal we will briefly discuss this assumption to complete the paper we also present a blow up criterion for this multi fluid system following huang et al in serrin type criterion for the three dimensional viscous compressible flows arxiv 2010

discretized vapnik chervonenkis dimension for analyzing complexity of real function classes in this paper we introduce the discretized vapnik chervonenkis vc dimension for studying the complexity of a real function class and then analyze properties of real function classes and neural networks we first prove that a countable traversal set is enough to achieve the vc dimension for a real function class whereas its classical definition states that the traversal set is the output range of the function class based on this result we propose the discretized vc dimension defined by using a countable traversal set consisting of rational numbers in the range of a real function class by using the discretized vc dimension we show that if a real function class has a finite vc dimension only a finite traversal set is needed to achieve the vc dimension we then point out that the real function classes which have the infinite vc dimension can be grouped into two categories type a and type b subsequently based on the obtained results we discuss the relationship between the vc dimension of an indicator output network and that of the real output network when both networks have the same structure except for the output activation functions finally we present the risk bound based on the discretized vc dimension for a real function class that has infinite vc dimension and is of type a we prove that with such a function class the empirical risk minimization erm principle for the function class is still consistent with overwhelming probability this is a development of the existing knowledge that the erm learning is consistent if and only if the function class has a finite vc dimension

reporting bias and sampling errors in a survey of a rare population using multiplicity counting rules abstract this article examines a methodology to improve the efficiency of surveys to locate and estimate characteristics of rare populations two multiplicity counting rules are compared with a conventional rule in terms of reporting errors sample variances and survey yields the analysis is based on data from two survey field experiments with diagnosed cancer patients and a subsample of their siblings or children who reside outside their households the article concludes with a brief discussion of the circumstances in which a multiplicity counting rule is the preferred methodology and those in which other approaches should be pursued

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

towards a sufficient criterion for collapse in 3d euler equations abstract a sufficient integral criterion for a blow up solution of the hopf equations the euler equations with zero pressure is found this criterion shows that a certain positive integral quantity blows up in a finite time under specific initial conditions blow up of this quantity means that solution of the hopf equation in 3d cannot be continued in the sobolev space h 2 r 3 for infinite time

sharper criteria for the wave collapse abstract sharper criteria for three dimensional wave collapse described by the nonlinear schrodinger equation nlse are derived the collapse threshold corresponds to the ground state soliton which is known to be unstable thus for nonprefocusing distributions this represents the separatrix between collapsing and noncollapsing sectors numerical results support the theoretical results generalizations of the criteria for the nlse with arbitrary power nonlinearity are also presented

training based mimo channel estimation a study of estimator tradeoffs and optimal training signals in this paper we study the performance of multiple input multiple output channel estimation methods using training sequences we consider the popular linear least squares ls and minimum mean square error mmse approaches and propose new scaled ls sls and relaxed mmse techniques which require less knowledge of the channel second order statistics and or have better performance than the conventional ls and mmse channel estimators the optimal choice of training signals is investigated for the aforementioned techniques in the case of multiple ls channel estimates the best linear unbiased estimation blue scheme for their linear combining is developed and studied

learnability and the vapnik chervonenkis dimension valiant s learnability model is extended to learning classes of concepts defined by regions in euclidean space e n the methods in this paper lead to a unified treatment of some of valiant s results along with previous results on distribution free convergence of certain pattern recognition algorithms it is shown that the essential condition for distribution free learnability is finiteness of the vapnik chervonenkis dimension a simple combinatorial parameter of the class of concepts to be learned using this parameter the complexity and closure properties of learnable classes are analyzed and the necessary and sufficient conditions are provided for feasible learnability

generalization performance of regularized ranking with multiscale kernels the regularized kernel method for the ranking problem has attracted increasing attentions in machine learning the previous regularized ranking algorithms are usually based on reproducing kernel hilbert spaces with a single kernel in this paper we go beyond this framework by investigating the generalization performance of the regularized ranking with multiscale kernels a novel ranking algorithm with multiscale kernels is proposed and its representer theorem is proved we establish the upper bound of the generalization error in terms of the complexity of hypothesis spaces it shows that the multiscale ranking algorithm can achieve satisfactory learning rates under mild conditions experiments demonstrate the effectiveness of the proposed method for drug discovery and recommendation tasks

regularity and singularity in solutions of the three dimensional navier stokes equations higher moments of the vorticity field m t in the form of l 2 m norms graphic 1 are used to explore the regularity problem for solutions of the three dimensional incompressible navier stokes equations on the domain graphic 2 it is found that the set of quantities formula 3 provide a natural scaling in the problem resulting in a bounded set of time averages d m t on a finite interval of time 0 t the behaviour of d m 1 d m is studied on what are called good and bad intervals of 0 t which are interspersed with junction points neutral i for large but finite values of m with large initial data m 0 o gr 4 it is found that there is an upper bound formula 4 which is punctured by infinitesimal gaps or windows in the vertical walls between the good bad intervals through which solutions may escape while this result is consistent with that of leray leray 1934 acta math 63 193 248 doi 10 1007 bf02547354 5 and scheffer scheffer 1976 pacific j math 66 535 552 this estimate for m corresponds to a length scale well below the validity of the navier stokes equations 1 embed inline graphic 1 gif 2 embed inline graphic 2 gif 3 embed graphic 1 gif 4 embed graphic 2 gif 5 http dx doi org doi 10 1007 bf02547354

blow up criterion for the 3d compressible non isentropic navier stokes equations without thermal conductivity abstract in this paper we prove a blow up criterion in terms of the density and the pressure p for the strong solutions with vacuum to cauchy problem of the 3d compressible non isentropic navier stokes equations without thermal conductivity more precisely we show that the strong solution exists globally if the norm p l 0 t r 3 is bounded from above

evolutions of the momentum density deformation tensor and the nonlocal term of the camassa holm equation abstract methods originally developed to study the finite time blow up problem of the regular solutions of the three dimensional incompressible euler equations are used to investigate the regular solutions of the camassa holm equation we obtain results on the relative behaviors of the momentum density the deformation tensor and the nonlocal term along the trajectories in terms of these behaviors we get new types of asymptotic properties of global solutions blow up criterion and blow up time estimate for local solutions more precisely certain ratios of the quantities are shown to be vaguely monotonic along the trajectories of global solutions finite time blow up of the accumulated momentum density is necessary and sufficient for the finite time blow up of the solution an upper estimate of the blow up time and a blow up criterion are given in terms of the initial short time trajectorial behaviors of the deformation tensor and the nonlocal term

numerical simulations of possible finite time singularities in the incompressible euler equations comparison of numerical methods abstract the numerical simulation of the 3d incompressible euler equations is analyzed with respect to different integration methods the numerical schemes we considered include spectral methods with different strategies for dealiasing and two variants of finite difference methods based on this comparison a kida pelz like initial condition is integrated using adaptive mesh refinement and estimates on the necessary numerical resolution are given this estimate is based on analyzing the scaling behavior similar to the procedure in critical phenomena and present simulations are put into perspective

rates of convergence for empirical processes of stationary mixing sequences classical empirical process theory for vapnik cervonenkis classes deals mainly with sequences of independent variables this paper extends the theory to stationary sequences of dependent variables it establishes rates of convergence for mixing and mixing empirical processes indexed by classes of functions the method of proof depends on a coupling of the dependent sequence with sequences of independent blocks to which the classical theory can be applied a uniform o ns 1 s rate of convergence over v c classes is established for sequences whose mixing coefficients decay slightly faster than o n s

ricci curvature of markov chains on metric spaces abstract we define the coarse ricci curvature of metric spaces in terms of how much small balls are closer in wasserstein transportation distance than their centers are this definition naturally extends to any markov chain on a metric space for a riemannian manifold this gives back after scaling the value of ricci curvature of a tangent vector examples of positively curved spaces for this definition include the discrete cube and discrete versions of the ornstein uhlenbeck process moreover this generalization is consistent with the bakry emery ricci curvature for brownian motion with a drift on a riemannian manifold positive ricci curvature is shown to imply a spectral gap a levy gromov like gaussian concentration theorem and a kind of modified logarithmic sobolev inequality the bounds obtained are sharp in a variety of examples

blow up criterions of strong solutions to 3d compressible navier stokes equations with vacuum abstract in the paper we establish a blow up criterion in terms of the integrability of the density for strong solutions to the cauchy problem of compressible isentropic navier stokes equations in r 3 with vacuum under the assumptions on the coefficients of viscosity 29 3 this extends the corresponding results in huang et al 2011 sun et al 2011 20 36 where a blow up criterion in terms of the upper bound of the density was obtained under the condition 7 as a byproduct the restriction 7 in fan et al 2010 sun et al 2011 12 37 is relaxed to 29 3 for the full compressible navier stokes equations by giving a new proof of lemma 3 1 besides we get a blow up criterion in terms of the upper bound of the density and the temperature for strong solutions to the cauchy problem of the full compressible navier stokes equations in r 3 the appearance of vacuum could be allowed this extends the corresponding results in sun et al 2011 37 where a blow up criterion in terms of the upper bound of 1 was obtained without vacuum the effective viscous flux plays a very important role in the proofs

learning with coefficient based regularized regression on markov resampling big data research has become a globally hot topic in recent years one of the core problems in big data learning is how to extract effective information from the huge data in this paper we propose a markov resampling algorithm to draw useful samples for handling coefficient based regularized regression cbrr problem the proposed markov resampling algorithm is a selective sampling method which can automatically select uniformly ergodic markov chain u e m c samples according to transition probabilities based on u e m c samples we analyze the theoretical performance of cbrr algorithm and generalize the existing results on independent and identically distributed observations to be specific when the kernel is infinitely differentiable the learning rate depending on the sample size m can be arbitrarily close to mathcal o m 1 under a mild regularity condition on the regression function the good generalization ability of the proposed method is validated by experiments on simulated and real data sets

remarks on a paper by j t beale t kato and a majda we prove that the maximum norm of the deformation tensor controls the possible breakdown of smooth solutions for the 3 dimensional euler equations more precisely the loss of regularity in a local smooth solution of the euler equations implies the growth without bound of the deformation tensor as the critical time approaches equivalently if the deformation tensor remains bounded the existence of a smooth solution is guaranteed

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

the critical sobolev inequalities in besov spaces and regularity criterion to some semi linear evolution equations we show the critical sobolev inequalities in the besov spaces with the logarithmic form such as brezis gallouet wainger and beale kato majda as an application of those inequalities the regularity problem under the critical condition to the navier stokes equations the euler equations in mathbb r n and the gradient flow to the harmonic map to the sphere are discussed namely the serrin ohyama type regularity criteria are improved in the terms of the besov spaces

adaptive cluster sampling abstract in many real world sampling situations researchers would like to be able to adaptively increase sampling effort in the vicinity of observed values that are high or otherwise interesting this article describes sampling designs in which whenever an observed value of a selected unit satisfies a condition of interest additional units are added to the sample from the neighborhood of that unit if any of these additional units satisfies the condition still more units may be added sampling designs such as these in which the selection procedure is allowed to depend on observed values of the variable of interest are in contrast to conventional designs in which the entire selection of units to be included in the sample may be determined prior to making any observations because the adaptive selection procedure introduces biases into conventional estimators several estimators are given that are design unbiased for the population mean with the adaptive cluster designs of this article that is the

svm multiregression for nonlinear channel estimation in multiple input multiple output systems this paper addresses the problem of multiple input multiple output mimo frequency nonselective channel estimation we develop a new method for multiple variable regression estimation based on support vector machines svms a state of the art technique within the machine learning community for regression estimation we show how this new method which we call m svr can be efficiently applied the proposed regression method is evaluated in a mimo system under a channel estimation scenario showing its benefits in comparison to previous proposals when nonlinearities are present in either the transmitter or the receiver sides of the mimo system

logarithmically improved bkm s criterion for the 3d nematic liquid crystal flows abstract this paper proves a logarithmically improved beale kato majda s criterion for the 3d nematic liquid crystal flows which says that if 0 t u t b m o ln e u t b m o d t then the solution u d is smooth up to the time t t

intermittency and regularity issues in 3d navier stokes turbulence two related open problems in the theory of 3d navier stokes turbulence are discussed in this paper the first is the phenomenon of intermittency in the dissipation field dissipation range intermittency was first discovered experimentally by batchelor and townsend over fifty years ago it is characterized by spatio temporal binary behaviour in which long quiescent periods in the velocity signal are interrupted by short active events during which there are violent fluctuations away from the average the second and related problem is whether solutions of the 3d navier stokes equations develop finite time singularities during these events this paper shows that leray s weak solutions of the three dimensional incompressible navier stokes equations can have a binary character in time the time axis is split into good and bad intervals on the good intervals solutions are bounded and regular whereas singularities are still possible within the bad intervals an estimate for the width of the latter is very small and decreases with increasing reynolds number it also decreases relative to the lengths of the good intervals as the reynolds number increases within these bad intervals lower bounds on the local energy dissipation rate and other quantities such as u t and u t are very large resulting in strong dynamics at sub kolmogorov scales intersections of bad intervals for n 1 are related to the potentially singular set in time it is also proved that the navier stokes equations are conditionally regular provided in a given bad interval the energy has a lower bound that is decaying exponentially in time

improved unbiased estimators in adaptive cluster sampling summary the usual design unbiased estimators in adaptive cluster sampling are easy to compute but are not functions of the minimal sufficient statistic and hence can be improved improved unbiased estimators obtained by conditioning on sufficient statistics not necessarily minimal are described first estimators that are as easy to compute as the usual design unbiased estimators are given estimators obtained by conditioning on the minimal sufficient statistic which are more difficult to compute are also discussed estimators are compared in examples

remarks on the breakdown of smooth solutions for the 3 d euler equations the authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3 d euler equations in other words if a solution of the euler equations is initially smooth and loses its regularity at some later time then the maximum vorticity necessarily grows without bound as the critical time approaches equivalently if the vorticity remains bounded a smooth solution persists

local rademacher complexities we propose new bounds on the error of learning algorithms in terms of a data dependent notion of complexity the estimates we establish give optimal rates and are based on a local and empirical version of rademacher averages in the sense that the rademacher averages are computed from the data on a subset of functions with small empirical error we present some applications to classification and prediction with convex function classes and with kernel classes in particular

strong solutions of the compressible nematic liquid crystal flow abstract we study strong solutions of the simplified ericksen leslie system modeling compressible nematic liquid crystal flows in a domain r 3 we first prove the local existence of a unique strong solution provided that the initial data 0 u 0 d 0 are sufficiently regular and satisfy a natural compatibility condition the initial density function 0 may vanish on an open subset i e an initial vacuum may exist we then prove a criterion for possible breakdown of such a local strong solution at finite time in terms of blow up of the quantities l t l x and d l t 3 l x

impact of antenna correlation on the capacity of multiantenna channels this paper applies random matrix theory to obtain analytical characterizations of the capacity of correlated multiantenna channels the analysis is not restricted to the popular separable correlation model but rather it embraces a more general representation that subsumes most of the channel models that have been treated in the literature for arbitrary signal to noise ratios snr the characterization is conducted in the regime of large numbers of antennas for the low and high snr regions in turn we uncover compact capacity expansions that are valid for arbitrary numbers of antennas and that shed insight on how antenna correlation impacts the tradeoffs among power bandwidth and rate

stratified adaptive cluster sampling summary stratified adaptive cluster sampling refers to designs in which following an initial stratified sample additional units are added to the sample from the neighbourhood of any selected unit with an observed value that satisfies a condition of interest if any of the added units in turn satisfies the condition still more units are added to the sample estimation of the population mean or total with the stratified adaptive cluster designs is complicated by the possibility that a selection in one stratum may result in the addition of units from other strata to the sample so that observations in separate strata are not independent since conventional estimators such as the stratified sample mean are biased with the adaptive designs of this paper several types of estimators are developed which are unbiased for the population mean or total with stratified adaptive cluster sampling