the topology on the primitive ideal space of transformation group c algebras and c c r transformation group c algebras if g 8 is a second countable transformation group and the stability groups are amenable then c g 8 is c c r if and only if the orbits are closed and the stability groups are c c r in addition partial results relating closed orbits to c c r algebras are obtained in the nonseparable case in several cases the topology of the primitive ideal space is calculated explicitly in particular if the stability groups are all contained in a fixed abelian subgroup h then the topology is computed in terms of h and the orbit structure provided c g 8 and c h 8 are eh regular these conditions are automatically met if g is abelian and g 8 is second countable

initial trace of solutions of some quasilinear parabolic equations with absorption we study the existence of an initial trace of nonnegative solutions of the problem tu u p 2 u uq 0in qt 0 t we prove that the initial trace is an outer regular borel measure which may not be locally bounded for some values of the parameters p and q we study also the corresponding cauchy problems with a given generalized borel measure as initial data

active learning of multiple source multiple destination topologies we consider the problem of inferring the topology of a network with m sources and n receivers an m by n network by sending probes between the sources and receivers prior work has shown that this problem can be decomposed into two parts first infer smaller subnetwork components 1 by n s or 2 by 2 s and then merge them to identify the m by n topology we focus on the second part which had previously received less attention in the literature we assume that a 1 by n topology is given and that all 2 by 2 components can be queried and learned using end to end probes the problem is which 2 by 2 s to query and how to merge them with the given 1 by n so as to exactly identify the 2 by n topology and optimize a number of performance metrics including the number of queries which directly translates into measurement bandwidth time complexity and memory usage we provide a lower bound n 2 on the number of 2 by 2 s required by any active learning algorithm and propose two greedy algorithms the first algorithm follows the framework of multiple hypothesis testing in particular generalized binary search gbs the second algorithm is called the receiver elimination algorithm rea and follows a bottom up approach it requires exactly n 1 steps which is much less than all 2n possible 2 by 2 s simulation results demonstrate that both algorithms correctly identify the 2 by n topology and are near optimal but rea is more efficient in practice

network delay tomography the substantial overhead of performing internal network monitoring motivates techniques for inferring spatially localized information about performance using only end to end measurements in this paper we present a novel methodology for inferring the queuing delay distributions across internal links in the network based solely on unicast end to end measurements the major contributions are 1 we formulate a measurement procedure for estimation and localization of delay distribution based on end to end packet pairs 2 we develop a simple way to compute maximum likelihood estimates mles using the expectation maximization em algorithm 3 we develop a new estimation methodology based on recently proposed nonparametric wavelet based density estimation method and 4 we optimize the computational complexity of the em algorithm by developing a new fast fourier transform implementation realistic network simulations are carried out using network level simulator ns 2 to demonstrate the accuracy of the estimation procedure

on transformation group algebras with continuous trace in this paper we answer some questions posed by dana williams in 19 concerning the problem under which conditions the transformation group c algebra c g q of a locally compact transformation group g li has continuous trace one consequence will be for compact g that c g q2 has continuous trace if and only if the stabilizer map is continuous we also give a complete solution to the problem if g is discrete

inducing primitive ideals we study conditions on a c dynamical system a g under which induction of primitive ideals resp irreducible representations from stabilizers for the action of g on the primitive ideal space prim a give primitive ideals resp irreducible representations of the crossed product a g the results build on earlier results of sauvageot 17 and others and will correct a possibly overly optimistic statement of the first author in 5 in an appendix the first author takes the opportunity to fill a gap in the proof of another result in 5

the periodic logistic equation with spatial and temporal degeneracies in this article we study the degenerate periodic logistic equation with homogeneous neumann boundary conditions tu u au b x t u in 0 u 0 on 0 u x 0 u0 x 6 0 in where r n 2 is a bounded domain with smooth boundary a and p 1 are constants the function b c r 0 1 is t periodic in t nonnegative and vanishes i e has a degeneracy in some subdomain of r we examine the effects of various natural spatial and temporal degeneracies of b x t on the long time dynamical behavior of the positive solutions our analysis leads to a new eigenvalue problem for periodic parabolic operators over a varying cylinder and certain parabolic boundary blow up problems not known before the investigation in this paper shows that the temporal degeneracy causes a fundamental change of the dynamical behavior of the equation only when spatial degeneracy also exists but in sharp contrast whether or not temporal degeneracy appears in the equation the spatial degeneracy always induces fundamental changes of the behavior of the equation though such changes differ significantly according to whether or not there is temporal degeneracy

on a class of semilinear fractional elliptic equations involving outside dirac data abstract the purpose of this article is to give a complete study of the weak solutions of the fractional elliptic equation 0 1 u u p 0 in b 1 e n u 0 in r n b 1 e n where p 0 with 0 1 denotes the fractional laplacian operator in the principle value sense b 1 e n is the unit ball centered at e n 0 0 1 in r n with n 2 and 0 is the dirac mass concentrated at the origin we prove that problem eq 0 1 admits a unique weak solution when p 1 2 n moreover if in addition p n 2 n 2 the weak solution vanishes as 1 we also show that problem eq 0 1 does not have any weak solution when p 0 1 2 n these results are very surprising since they are in total contradiction with the classical setting i e u u p 0 in b 1 e n u 0 in r n b 1 e n for which it has been proved that there are no solutions for p n 1 n 1

semilinear fractional elliptic equations involving measures abstract we study the existence of weak solutions to e u g u in a bounded regular domain in r n n 2 which vanish in r n where denotes the fractional laplacian with 0 1 is a radon measure and g is a nondecreasing function satisfying some extra hypotheses when g satisfies a subcritical integrability condition we prove the existence and uniqueness of weak solution for problem e for any measure in the case where is a dirac measure we characterize the asymptotic behavior of the solution when g r r k 1 r with k supercritical we show that a condition of absolute continuity of the measure with respect to some bessel capacity is a necessary and sufficient condition in order e to be solved

positive solutions for superlinear elliptic equations the existence of a positive radial solution for superlinear elliptic boundary value problem in an exterior domain is proved by the use of cone expansion fixed point theorem

on the existence of bounded positive solutions for a class of singular bvps abstract we investigate the existence and properties of solutions to a second order singular ode we base ourselves on the variational approach which enables the approximation of solutions and gives a measure of a duality gap between primal and dual functional for minimizing sequences

network tomography based on additive metrics network tomography studies the inference of network structure and dynamics based on indirect measurements when direct measurements are unavailable or difficult to collect in this paper we design and analyze routing tree topology and link performance inference algorithms for communication networks using tools from phylogenetic inference in evolutionary biology we develop polynomial time distance based inference algorithms and derive sufficient conditions for the correctness of the algorithms we show that the algorithms are consistent and robust in particular the algorithms achieve the optimal l radius 1 2 for binary trees and 1 4 for general trees when a threshold neighbor selection criterion is used

hierarchical inference of unicast network topologies based on end to end measurements in this paper we address the problem of topology discovery in unicast logical tree networks using end to end measurements without any cooperation from the internal routers topology estimation can be formulated as hierarchical clustering of the leaf nodes based on pairwise correlations as similarity metrics unlike previous work that first assumes the network topology is a binary tree and then tries to generalize to a nonbinary tree we provide a framework that directly deals with general logical tree topologies a hierarchical algorithm to estimate the topology is developed in a recursive manner by finding the best partitions of the leaf nodes level by level our simulations show that the algorithm is more robust than binary tree based methods

boundary singularities of solutions to elliptic viscous hamilton jacobi equations abstract we study the boundary value problem with measures for e1 u g u 0 in a bounded domain in r n satisfying e2 u on and prove that if g l 1 1 t 2 n 1 n d t is nondecreasing e1 e2 can be solved with any positive bounded measure when g r r q with q 1 we prove that any positive function satisfying e1 admits a boundary trace which is an outer regular borel measure not necessarily bounded when g r r q with 1 q q c n 1 n we prove the existence of a positive solution with a general outer regular borel measure as boundary trace and characterize the boundary isolated singularities of positive solutions when g r r q with q c q 2 we prove that a necessary condition for solvability is that must be absolutely continuous with respect to the bessel capacity c 2 q q q we also characterize boundary removable sets for moderate and sigma moderate solutions

a diffusive logistic equation with a free boundary and sign changing coefficient in time periodic environment abstract this paper concerns a diffusive logistic equation with a free boundary and sign changing intrinsic growth rate in heterogeneous time periodic environment in which the variable intrinsic growth rate may be very negative in a suitable large region see conditions h1 h2 4 3 such a model can be used to describe the spreading of a new or invasive species with the free boundary representing the expanding front in the case of higher space dimensions with radial symmetry and when the intrinsic growth rate has a positive lower bound this problem has been studied by du guo peng 11 they established a spreading vanishing dichotomy the sharp criteria for spreading and vanishing and estimate of the asymptotic spreading speed in the present paper we show that the above results are retained for our problem

negatively curved manifolds elliptic operators and the martin boundary consider a riemannian manifold m of dimension n 2 and assume that m is complete simply connected and that its sectional curvatures are bounded between two negative constants in a recent paper 7 m anderson and r schoen have proved that the martin boundary of m with respect to the laplace beltrami operator a is naturally homeomorphic to soo m the sphere at infinity of m here we shall first establish a similar result for a wide class of elliptic operators on m giving at the same time a new proof of the theorem of anderson and schoen our proof relies heavily on several concepts of potential theory but on the other hand avoids the quite difficult calculations of 7 and perhaps makes the result more understandable roughly speaking we show that if y is a second order elliptic operator defined over m and has a uniformly nice behaviour on each ball of radius 1 in m then dq m the y martin boundary of m is s m provided that the following condition holds there is a positive y ci superharmonic function on m for some positive if instead we only assume the existence of the green function for y a minimal requirement when studying the y martin boundary then d m may be very different from so m even for a rotation invariant operator y on the unit ball of rn equipped

crossed products by actions which are locally unitary on the stabilisers let a g be a c dynamical system with g abelian and hausdorff we investigate the ideal structure of the crossed product a g under the hypothesis that the stabiliser subgroups for the action of g on vary continuously we discuss a new notion of locally trivial g space for such actions and dually actions which are locally unitarily implemented on the stabiliser groups our main result asserts that when is locally unitary in this sense and is a locally trivial g space a g is a locally trivial space

reduced limits for nonlinear equations with measures we consider equations e delta u g u mu in smooth bounded domains omega subset of r n where g is a continuous nondecreasing function and mu is a finite measure in omega given a bounded sequence of measures mu k assume that for each k 1 there exists a solution u k of e with datum mu k and zero boundary data we show that if u k u to in l 1 omega then u is a solution of e relative to some finite measure mu we call mu the reduced limit of mu k this reduced limit has the remarkable property that it does not depend on the boundary data but only on mu k and on g for power nonlinearities g t vertical bar t vertical bar q 1 t for all t is an element of r we show that if mu k is nonnegative and bounded in w 2 w q omega then mu and mu are absolutely continuous with respect to each other we then produce an example where mu not equal mu c 2009 elsevier inc all rights reserved

semilinear fractional elliptic equations with gradient nonlinearity involving measures we study the existence of solutions to the fractional elliptic equation e1 delta alpha u epsilon g nabla u nu in a bounded regular domain omega of r n n ge2 subject to the condition e2 u 0 in omega c where epsilon 1 or 1 delta alpha denotes the fractional laplacian with alpha in 1 2 1 nu is a radon measure and g r mapsto r is a continuous function we prove the existence of weak solutions for problem e1 e2 when g is subcritical furthermore the asymptotic behavior and uniqueness of solutions are described when nu is dirac mass g s s p p geq 1 and epsilon 1

on the equation δu eu 1 0 with measures as boundary data if is a bounded domain in mathbb r n we study conditions on a radon measure on for solving the equation u e u 1 0 in with u on the conditions are expressed in terms of orlicz capacities

the orbit spaces of groupoids whose c algebras are ccr abstract let g be a second countable locally compact hausdorff groupoid with a continuous haar system we show that if the groupoid c algebra of g is ccr then the orbits of g are closed and the stabilizers of g are ccr in particular we remove the assumption of amenability in a theorem of clark

a class of boundary traces for solutions of the equation lu ψ u our subject is the class u of all positive solutions of a semilinear equation lu u in e where l is a second order elliptic differential operator e is a domain in rd and belongs to a convex class of c1 functions which contains functions u u with 1 a special role is played by a class u0 of solutions which we call moderate a solution u is moderate if there exists h u such that lh 0 in e we say that u u is moderate if u is the limit of an increasing sequence of moderate solutions in e b dynkin s e kuznetsov fine topology and fine trace on the boundary associated with a class of quasilinear differential equations comm pure appl math 51 1998 897 936 all moderate solutions were classified by using their fine boundary traces 2 in m marcus l veron the precise boundary trace of positive solutions of the equation u uq in the supercritical case in perspectives in nonlinear partial differential equations in honor of haim brezis contemp math amer math soc providence ri 2007 arxiv org math 0610102 marcus and veron introduced a different characteristic called the precise trace for solutions of the equation u u with 1 in a bounded c2 domain in the present paper we develop a general scheme covering both approaches and we prove the equivalence in a certain sense of the fine and precise traces an implication of this equivalence is a wiener type criterion for vanishing of the poisson kernel of the equation lu x a x u x

semilinear parabolic equations diffusions and superdiffusions the semilinear equationu l0u u wherel0is a second order elliptic differential operator without zero order term and 1 1 related problems are treated with the help of diffusion processes this approach is useful even in the linear theory for instance the first boundary value problem for equationu lu fcan be investigated for a class of domains described in probabilistic terms which is substantially larger than the class considered in the literature on pdes

minimax bounds for active learning this paper analyzes the potential advantages and theoretical challenges of active learning algorithms active learning involves sequential sampling procedures that use information gleaned from previous samples in order to focus the sampling and accelerate the learning process relative to passive learning algorithms which are based on nonadaptive usually random samples there are a number of empirical and theoretical results suggesting that in certain situations active learning can be significantly more effective than passive learning however the fact that active learning algorithms are feedback systems makes their theoretical analysis very challenging this paper aims to shed light on achievable limits in active learning using minimax analysis techniques we study the achievable rates of classification error convergence for broad classes of distributions characterized by decision boundary regularity and noise conditions the results clearly indicate the conditions under which one can expect significant gains through active learning furthermore we show that the learning rates derived are tight for boundary fragment classes in d dimensional feature spaces when the feature marginal density is bounded from above and below

the ideal property the projection property continuous fields and crossed products abstract let a be the c algebra associated to an arbitrary continuous field of c algebras we give a necessary and sufficient condition for a to have the ideal property and if moreover a is separable we give a necessary and sufficient condition for a to have the projection property some applications of these results are given we also prove that many crossed products of commutative c algebras by discrete amenable groups have the projection property generalizing some of our previous results

solvability of parabolic variational hemivariational inequalities involving space fractional laplacian abstract the paper is devoted to investigate a new kind of variational hemivariational inequality of parabolic type driven by a generalized space fractional laplace operator and two multivalued terms which are expressed by the clarke generalized gradient and convex subgradient respectively an existence theorem of weak solutions to the problem is established by applying a surjectivity theorem for the sum of operators combined with results from nonsmooth analysis

the boundary trace and generalized boundary value problem for semilinear elliptic equations with coercive absorption in the first part of the paper we establish the existence of a boundary trace for positive solutions of the equation u g x u 0 in a smooth domain n for a general class of positive nonlinearities this class includes every space independent monotone increasing g which satisfies the keller osserman condition as well as degenerate nonlinearities g q of the form g q x u d x u q 1u with 2 and q 1 the boundary trace is given by a positive regular borel measure which may blow up on compact sets in the second part we concentrate on the family of nonlinearities g q determine the critical value of the exponent q for fixed 2 and discuss a positive solutions with an isolated singularity for subcritical nonlinearities and b the boundary value problem for u g q x u 0 with boundary data given by a positive regular borel measure possibly unbounded we show that in the subcritical case the problem possesses a unique solution for every such measure 2003 wiley periodicals inc

existence localization and multiplicity results for positive radial solutions of semilinear elliptic systems existence localization and multiplicity results of positive solutions to a system of singular second order differential equations are established by means of the vector version of krasnoselskii s cone fixed point theorem the results are then applied for positive radial solutions to semilinear elliptic systems

a dixmier douady theorem for fell algebras abstract we generalise the dixmier douady classification of continuous trace c algebras to fell algebras to do so we show that c diagonals in fell algebras are precisely abelian subalgebras with the extension property and use this to prove that every fell algebra is morita equivalent to one containing a diagonal subalgebra we then use the machinery of twisted groupoid c algebras and equivariant sheaf cohomology to define an analogue of the dixmier douady invariant for fell algebras and to prove our classification theorem

unicast based inference of network link delay distributions with finite mixture models providers of high quality of service over telecommunication networks require accurate methods for remote measurement of link level performance recent research in network tomography has demonstrated that it is possible to estimate internal link characteristics e g link delays and packet losses using unicast probing schemes in which probes are exchanged between several pairs of sites in the network we present a new method for estimation of internal link delay distributions using the end to end packet pair delay statistics gathered by back to back packet pair unicast probes our method is based on a variant of the penalized maximum likelihood expectation maximization pml em algorithm applied to an additive finite mixture model for the link delay probability density functions the mixture model incorporates a combination of discrete and continuous components and we use a minimum message length mml penalty for selection of model order we present results of matlab and ns 2 simulations to illustrate the promise of our network tomography algorithm for light cross traffic scenarios

multicast topology inference from measured end to end loss the use of multicast inference on end to end measurement has been proposed as a means to infer network internal characteristics such as packet link loss rate and delay we propose three types of algorithm that use loss measurements to infer the underlying multicast topology i a grouping estimator that exploits the monotonicity of loss rates with increasing path length ii a maximum likelihood estimator mle and iii a bayesian estimator we establish their consistency compare their complexity and accuracy and analyze the modes of failure and their asymptotic probabilities

boundary layer and spike layer solutions for a bistable elliptic problem with generalized boundary conditions abstract we show that for large 0 the generalized boundary value problem u u u a x 1 u in u where 1 x behaves like the special case 1 in particular we show the existence of solutions with sharp boundary layers and interior spikes and determine the location of the spikes

strength of convergence in the orbit space of a transformation group abstract let g x be a second countable transformation group with g acting freely on x it is shown that measure theoretic accumulation of the action and topological strength of convergence in the orbit space x g provide equivalent ways of quantifying the extent of nonproperness of the action these notions are linked via the representation theory of the transformation group c algebra c 0 x g

pointwise unitary automorphism groups abstract let a g be a separable c dynamical system in which g is abelian and a has continuous trace the action is said to pointwise unitary if for each in a there is a covariant representation u of the system a g it is shown that for pointwise unitary actions the spectrum a g of the crossed product is a locally compact hausdorff space and the restriction map res which takes u in a g to maps a g onto a furthermore res induces a homeomorphism of a g g onto a these results lead to a characterization of crossed products a g with continuous trace when a has continuous trace and g acts freely on a this happens precisely when the action of g on a is also proper this extends green s characterization of free and proper transformation groups finally it is shown that the results have applications to the problem of determining the dual topology on a locally compact group

on the existence of weak solutions of semilinear elliptic equations and systems with hardy potentials abstract let r n n 3 be a bounded c 2 domain and x dist x put l 2 with 0 in this paper we provide various necessary and sufficient conditions for the existence of weak solutions to l u u p in u on where 0 p 0 and are measures on and respectively we then establish existence results for the system l u v p in l v u p in u v on where 1 p 0 p 0 and are measures on and are measures on we also deal with elliptic systems where the nonlinearities are more general

stochastic boundary values and boundary singularities for solutions of the equationlu uα abstract we investigate positive solutions of a nonlinear equationlu u wherelis a second order elliptic differential operator in a riemannian manifoldeand 1 2 we establish a 1 1 correspondence between the set u of positive solutions and a class z of functionals ofxwhich we call linear boundary functionals they depend only on the behavior ofxnear the martin boundarye the class z is a closed convex cone andu u is a subadditive function ofz z special roles belong to moderate solutions corresponding tozwith finite mathematical expectations and to a family of solutions determined by the range ofx a new formula is deduced connectingu zandl diffusions conditioned to hit the boundarye at a given pointy a concept of a singular boundary point foruis introduced in terms of the conditioned diffusion

learning latent tree graphical models we study the problem of learning a latent tree graphical model where samples are available only from a subset of variables we propose two consistent and computationally efficient algorithms for learning minimal latent trees that is trees without any redundant hidden nodes unlike many existing methods the observed nodes or variables are not constrained to be leaf nodes our algorithms can be applied to both discrete and gaussian random variables and our learned models are such that all the observed and latent variables have the same domain state space our first algorithm recursive grouping builds the latent tree recursively by identifying sibling groups using so called information distances one of the main contributions of this work is our second algorithm which we refer to as clgrouping clgrouping starts with a pre processing procedure in which a tree over the observed variables is constructed this global step groups the observed nodes that are likely to be close to each other in the true latent tree thereby guiding subsequent recursive grouping or equivalent procedures such as neighbor joining on much smaller subsets of variables this results in more accurate and efficient learning of latent trees we also present regularized versions of our algorithms that learn latent tree approximations of arbitrary distributions we compare the proposed algorithms to other methods by performing extensive numerical experiments on various latent tree graphical models such as hidden markov models and star graphs in addition we demonstrate the applicability of our methods on real world data sets by modeling the dependency structure of monthly stock returns in the s p index and of the words in the 20 newsgroups data set

transformation group c algebras with continuous trace we obtain several results characterizing when transformation group c algebras have continuous trace these results can be stated most succinctly when g l is second countable and the stability groups are contained in a fixed abelian subgroup in this case c g q has continuous trace if and only if the stability groups vary continuously on r and compact subsets of q are wandering in an appropriate sense in general we must assume that the stability groups vary continuously and if g j is not second countable that the natural maps of g s onto g x are homeomorphisms for each x then c g 0 has continuous trace if and only if compact subsets of 0 are wandering and an additionai c algebra constructed from the stability groups and 0 has continuous trace

solutions of nonlinear differential equations on a riemannian manifold and their trace on the martin boundary let l be a second order elliptic differential operator on a riemannian manifold e with no zero order terms we say that a function h is l harmonic if lh 0 every positive l harmonic function has a unique representation

reduced measures on the boundary we study the existence of solutions of the nonlinear problem delta u g u 0 in omega u mu on partial derivative omega where mu is a and g r r is a nondecreasing continuous function with g t 0 for all t 0 problem 0 1 admits a solution for every mu epsilon l 1 partial derivative omega but this need not be the case when p is a general bounded measure we introduce a concept of reduced measure mu in the spirit of brezis et al ann math stud to appear this is the closest measure to mu for which 0 1 admits a solution

the ideal structure of the hecke c algebra of bost and connes we compute explicitly the primitive ideal space of the bost connes hecke c algebra by embedding it as a full corner in a transformation group c algebra and applying a general theorem of williams this requires the computation of the quasi orbit space for the action of q on the space mathcal a f of finite adeles we then carry out a similar computation for the action of q on the space mathcal a mathcal a f times mathbb r of full adeles

large solutions for yamabe and similar problems on domains in riemannian manifolds we present a unifled approach to study large positive solutions i e u x 1 as x of the equation u hu i k u if in an arbitrary domain we assume u is convex and grows su ciently fast as u 1 equations of this type arise in geometry yamabe problem two dimensional curvature equation probability superdifiusion we prove that both existence and uniqueness are local properties of points of the boundary i e they depend only on properties of in arbitrary small neighborhood of each boundary point we also flnd several new necessary and su cient conditions for existence and uniqueness of large solutions including an existence theorem on domains with fractal boundaries

trace on the boundary for solutions of nonlinear differential equations let l be a second order elliptic differential operator in rd with no zero order terms and let e be a bounded domain in rd with smooth boundary e we say that a function h is l harmonic if lh 0 in e every positive l harmonic function has a unique representation h x j x y i dy e where k is the poisson kernel for l and z is a finite measure on e we call z the trace of h on me our objective is to investigate positive solutions of a nonlinear equation lu u in e for 1 2 we associate with every solution u a pair if i where f is a closed subset of e and zis a radon measure on 0 e f we call f zi the trace of u on me f is empty if and only if u is dominated by an l harmonic function we call such solutions moderate a moderate solution is determined uniquely by its trace in general many solutions can have the same trace we establish necessary and sufficient conditions for a pair f z to be a trace and we give a probabilistic formula for the maximal solution with a given trace

strength of convergence in non free transformation groups let g x be a transformation group where the group g does not necessarily act freely on the space x we investigate the extent to which the action of g may fail to be proper stability subgroups are used to define new notions of strength of convergence in the orbit space and of measure accumulation along orbits by using the representation theory of the associated crossed product c algebra we show that these notions are equivalent under certain conditions

exact singular behavior of positive solutions to nonlinear elliptic equations with a hardy potential abstract in this paper we study the singular behavior at x 0 of positive solutions to the equation u x 2 u x u p x 0 where r n n 3 is a bounded domain with 0 and p 1 2 are given constants for the case n 2 2 4 the singular behavior of all the positive solutions is completely classified in the recent paper 5 here we determine the exact singular behavior of all the positive solutions for the remaining case n 2 2 4 in sharp contrast to the case n 2 2 4 where several converging blow up rates of u x are possible as x 0 we show that when n 2 2 4 every positive solution u x blows up in the same fashion lim x 0 x 2 p 1 u x 2 p 1 2 p 1 2 n 1 p 1

blowup in diffusion equations a survey this paper deals with quasilinear reaction diffusion equations for which a solution local in time exists if the solution ceases to exist for some finite time we say that it blows up in contrast to linear equations blowup can occur even if the data are smooth and well defined for all times depending on the equation either the solution or some of its derivatives become singular we shall concentrate on those cases where the solution becomes unbounded in finite time this can occur in quasilinear equations if the heat source is strong enough there exist many theoretical studies on the question on the occurrence of blowup in this paper we shall recount some of the most interesting criteria and most important methods for analyzing blowup the asymptotic behavior of solutions near their singularities is only completely understood in the special case where the source is a power a better knowledge would be useful also for their numerical treatment thus not surprisingly the numerical analysis of this type of problems is still at a rather early stage the goal of this paper is to collect some of the known results and algorithms and to direct the attention to some open problems

continuous trace groupoid c algebras iii suppose that g is a second countable locally compact groupoid with a haar system and with abelian isotropy we show that the groupoid c algebra c g has continuous trace if and only if there is a haar system for the isotropy groupoid a and the action of the quotient groupoid g a is proper on the unit space of g

the geometry of generalized binary search this paper investigates the problem of determining a binary valued function through a sequence of strategically selected queries the focus is an algorithm called generalized binary search gbs gbs is a well known greedy algorithm for determining a binary valued function through a sequence of strategically selected queries at each step a query is selected that most evenly splits the hypotheses under consideration into two disjoint subsets a natural generalization of the idea underlying classic binary search this paper develops novel incoherence and geometric conditions under which gbs achieves the information theoretically optimal query complexity i e given a collection of n hypotheses gbs terminates with the correct function after no more than a constant times logn queries furthermore a noise tolerant version of gbs is developed that also achieves the optimal query complexity these results are applied to learning halfspaces a problem arising routinely in image processing and machine learning

network tomography identifiability and fourier domain estimation the statistical problem for network tomography is to infer the distribution of x with mutually independent components from a measurement model y ax where a is a given binary matrix representing the routing topology of a network under consideration the challenge is that the dimension of x is much larger than that of y and thus the problem is often ill posed this paper studies some statistical aspects of network tomography we first develop a unifying theory on the identifiability of the distribution of x we then focus on an important instance of network tomography network delay tomography where the problem is to infer internal link delay distributions using end to end delay measurements we propose a novel mixture model for link delays and develop a fast algorithm for estimation based on the general method of moments through extensive model simulations and real internet trace driven simulation the proposed approach is shown to be favorable to previous methods using simple discretization for inferring link delays in a heterogeneous network

semilinear elliptic equations with subcritical absorption in lipschitz domains abstract let be a bounded lipschitz domain in r n consider the equation u g x u 0 g c r and g x positive and increasing on r x we say that g is subcritical at y if has a solution u k y with boundary trace k y k 0 for a large family of functions g we establish existence and stability results for boundary value problems for with data given by measures concentrated on the set of subcritical points in addition we describe the precise asymptotic behavior of u k y at y some related results have been obtained in marcus and veron 2011 when g t t q in the case that g satisfies the keller osserman condition we prove if u is a positive solution with strong singularity at y i e u is not dominated by a harmonic function then u lim k u k y finally we extend estimates related to the keller osserman condition that are well known in the case of c 2 domains when g is independent of the space variable to lipschitz domains and a large class of functions g including cases where g x t 0 or g x t as x

deformation quantization of heisenberg manifolds form a smooth manifold equipped with a poisson bracket we formulate ac algebra framework for deformation quantization including the possibility of invariance under a lie group of diffeomorphisms preserving the poisson bracket we then show that the much studied non commutative tori give examples of such deformation quantizations invariant under the usual action of ordinary tori going beyond this the main results of the paper provide a construction of invariant deformation quantizations for those poisson brackets on heisenberg manifolds which are invariant under the action of the heisenberg lie group and for various generalizations suggested by this class of examples interesting examples are obtained of simplec algebras on which the heisenberg group acts ergodically

semilinear elliptic equations admitting similarity transformations in this paper we study the equation u 2 h u 0 in a smooth bounded domain where x dist x 0 and h is a nondecreasing function which satisfies keller osserman condition we introduce a condition on h which implies that the equation is subcritical i e the corresponding boundary value problem is well posed with respect to data given by finite measures under additional assumptions on h we show that this condition is necessary as well as sufficient we also discuss b v problems with data given by positive unbounded measures our results extend results of 13 treating equations of the form u uq 0 with q 1 2

maximum pseudo likelihood estimation in network tomography network monitoring and diagnosis are key to improving network performance the difficulties of performance monitoring lie in today s fast growing internet accompanied by increasingly heterogeneous and unregulated structures moreover these tasks become even harder since one cannot rely on the collaboration of individual routers and servers to measure network traffic directly even though the aggregative nature of possible network measurements gives rise to inverse problems existing methods for solving inverse problems are usually computationally intractable or statistically inefficient a pseudo likelihood approach is proposed to solve a group of network tomography problems the basic idea of pseudo likelihood is to form simple subproblems and ignore the dependences among the subproblems to form a product likelihood of the subproblems as a result this approach keeps a good balance between the computational complexity and the statistical efficiency of the parameter estimation some statistical properties of the pseudo likelihood estimator such as consistency and asymptotic normality are established a pseudo expectation maximization em algorithm is developed to maximize the pseudo log likelihood function two examples with simulated or real data are used to illustrate the pseudo likelihood proposal 1 inference of the internal link delay distributions through multicast end to end measurements 2 origin destination matrix estimation through link traffic counts

ideals in some continuous nonselfadjoint crossed product algebras abstract let y t be a locally compact dynamical system where the t denotes a continuous one parameter semigroup of maps on y when each t is a homeomorphism a nonselfadjoint crossed product algebra is defined as the subalgebra of the c crossed product c 0 y r supported on t 0 when each t is only continuous the crossed product c 0 y r can still be defined the ideal structure of such an algebra is determined in the case where the semigroup action is the suspension of a discrete free action on a smaller space x a generalization of effros hahn is given whereby one may find a meet irreducible ideal over any arc closure in y the meet irreducible ideals form a topological space in the hull kernel topology and there is a one to one correspondence between closed sets in this space and closed ideals in the algebra a subset of this space is homeomorphic to the space of finite arcs in the subarc topology the irrational flow algebra is considered as a special case