extracting randomness via repeated condensing extractors as defined by nisan and zuckerman are procedures that use a small number of truly random bits called the seed to extract many almost truly random bits from arbitrary distributions as long as distributions have sufficient min entropy a natural weakening of an extractor is a condenser whose output distribution has a higher entropy rate than the input distribution without losing much of the initial entropy an extractor can be viewed as an ultimate condenser because it outputs a distribution with the maximal entropy rate in this paper we construct explicit condensers with short seed length the condenser constructions combine variants of or more efficient versions of ideas from several works including the block extraction scheme of n nisan and d zuckerman j comput system sci 52 1996 pp 43 52 the observation made in a srinivasan and d zuckerman siam j comput 28 1999 pp 1433 1459 n nisan and a ta shma j comput system sci 58 1999 pp 148 173 that a failure of the block extraction scheme is also useful the recursive win win case analysis of r impagliazzo r shaltiel and a wigderson near optimal conversion of hardness into pseudo randomness in proceedings of the 40th annual ieee symposium on foundations of computer science ieee los alamitos ca 1999 pp 181 190 r impagliazzo r shaltiel and a wigderson extractors and pseudo random generators with optimal seed length in proceedings of the 32nd annual acm symposium on theory of computing acm new york 2000 pp 1 10 and the error correction of random sources used in l trevisan j acm 48 2001 pp 860 879 as a by product via repeated iterating of condensers we obtain new extractor constructions the new extractors give significant qualitative improvements over previous ones for sources of arbitrary min entropy they are nearly optimal simultaneously in the two main parameters of seed length and output length specifically our extractors can make any one of these two parameters optimal up to a constant factor only at a polylogarithmic loss in the other previous constructions require polynomial loss in both cases for general sources we also give a simple reduction converting standard extractors which are good for an average seed into strong ones which are good for most seeds with essentially the same parameters with this reduction all the above improvements apply to strong extractors as well

applications of the complex interpolation method to a von neumann algebra non commutative lp spaces non commutative lp spaces 1 p associated with a von neumann algebra are considered the paper consists of two parts in part i by making use of the complex interpolation method non commutative lp spaces are defined as interpolation spaces between the von neumann algebra in question and its predual also all expected properties such as duality and uniform convexity are proved in the frame of interpolaton theory and relative modular theory in part ii these lp spaces are compared with haagerup s lp spaces based on this comparison a non commutative analogue of the classical stein weiss interpolation theorem is obtained

ergodic actions of group extensions on von neumann algebras on considere des actions automorphes sur des algebres de von neumann d un groupe localement compact e donne comme une extension topologique o a e g o ou a est abelien compact et second denombrable on cherche a decrire et a classer des actions ergodiques de e quand g est fini

deterministic extractors for bit fixing sources and exposure resilient cryptography we give an efficient deterministic algorithm that extracts omega n 2 gamma almost random bits from sources where n frac 1 2 gamma of the n bits are uniformly random and the rest are fixed in advance this improves upon previous constructions which required that at least n 2 of the bits be random in order to extract many bits our construction also has applications in exposure resilient cryptography giving explicit adaptive exposure resilient functions and in turn adaptive all or nothing transforms for sources where instead of bits the values are chosen from d for d 2 we give an algorithm that extracts a constant fraction of the randomness we also give bounds on extracting randomness for sources where the fixed bits can depend on the random bits

compact lie group action with the continuous rokhlin property abstract in this paper we study the continuous rokhlin property of c dynamical systems using techniques of equivariant kk theory and quantum group theory in particular we determine the kk equivalence class and give a classification of kirchberg g algebras when the g is a compact lie group with the hodgkin condition

linear algebraic methods in communication complexity abstract the notion of communication complexity seeks to capture the amount of communication between different parties that is required to find the output of a boolean function when each party is provided with only part of the input different variants of the model governing the rules of this communication lead to different connections with problems in combinatorial linear algebra in particular problems arise in this context that concern the rank of a 0 1 matrix and the minimum rank of a matrix meeting a given combinatorial description this paper surveys these connections

pointwise inner automorphisms of injective factors abstract it is shown that for the injective factor of type iii 1 with separable predual an automorphism is pointwise inner if and only if it is the composition of an inner and a modular automorphism

ergodic actions of compact groups on operator algebras i general theory we introduce some general machinery for studying ergodic actions of compact groups on operator algebras the most important tool being that of the multiplicity map this theory is used subsequently in 42 to prove that a von neumann algebra on which su 2 acts ergodically is necessarily of type i

towards a theory of classification abstract the well known difficulties arising in a classification which is not set theoretically trivial involving what is sometimes called a non smooth quotient have been overcome in a striking way in the theory of operator algebras by the use of what might be called a classification functor the very existence of which is already a surprise here the notion of such a functor is developed abstractly and a number of examples are considered including those which have arisen for various classes of operator algebras

analysis of triangle quality measures several of the more commonly used triangle quality measures are analyzed and compared proofs are provided to verify that they do exhibit the expected extremal properties the asymptotic behavior of these measures is investigated and a number of useful results are derived it is shown that some of the quality measures are equivalent in the sense of displaying the same extremal and asymptotic behavior and that it is therefore possible to achieve a concise classification of triangle quality measures

extracting computational entropy and learning noisy linear functions we study the task of deterministically extracting randomness from sources containing computational entropy the sources we consider have the form of a conditional distribution f x x for some function f and some distribution x and we say that such a source has computational min entropy k if any circuit of size 2k can only predict f x correctly with probability at most 2 k given input x sampled from x we first show that it is impossible to have a seedless extractor to extract from one single source of this kind then we show that it becomes possible if we are allowed a seed which is weakly random instead of perfectly random but contains some statistical min entropy or even a seed which is not random at all but contains some computational min entropy this can be seen as a step toward extending the study of multisource extractors from the traditional statistical setting to a computational setting we reduce the task of constructing such extractors to a problem in computational learning theory learning linear functions under arbitrary distribution with adversarial noise and we provide a learning algorithm for this problem in fact this problem is a well recognized one in computational learning theory and variants of this problem have been studied intensively before thus in addition to its application to extractors our learning algorithm also has independent interest of its own and it can be considered as the main technical contribution of this paper

classification of minimal actions of a compact kac algebra with amenable dual on injective factors of type iii abstract we classify a certain class of minimal actions of a compact kac algebra with amenable dual on injective factors of type iii the structural analysis of type iii factors and the canonical extension of endomorphisms introduced by izumi are our main technical tools

deterministic extractors for bit fixing sources by obtaining an independent seed an n k bit fixing source is a distribution x over 0 1 n such that there is a subset of k variables in x 1 ldots x n which are uniformly distributed and independent of each other and the remaining n k variables are fixed a deterministic bit fixing source extractor is a function e 0 1 n rightarrow 0 1 m which on an arbitrary n k bit fixing source outputs m bits that are statistically close to uniform recently kamp and zuckerman proceedings of the 44th annual ieee symposium on foundations of computer science 2003 pp 92 101 gave a construction of a deterministic bit fixing source extractor that extracts omega k 2 n bits and requires k sqrt n in this paper we give constructions of deterministic bit fixing source extractors that extract 1 o 1 k bits whenever k log n c for some universal constant c 0 thus our constructions extract almost all the randomness from bit fixing sources and work even when k is small for k gg sqrt n the extracted bits have statistical distance 2 n omega 1 from uniform and for k le sqrt n the extracted bits have statistical distance k omega 1 from uniform our technique gives a general method to transform deterministic bit fixing source extractors that extract few bits into extractors which extract almost all the bits

amplifying the randomness of weak sources correlated with devices the problem of device independent randomness amplification against no signaling adversaries has so far been studied under the assumption that the weak source of randomness is uncorrelated with the quantum devices used in the amplification procedure in this paper we relax this assumption and reconsider the original protocol of colbeck and renner using a santha vazirani sv source to do so we introduce an sv like condition for devices namely that any string of sv source bits remains weakly random conditioned upon any other bit string from the same sv source and the outputs obtained when this further string is input into the devices assuming this condition we show that a quantum device using a singlet state to violate the chained bell inequalities leads to full randomness in the asymptotic scenario of a large number of settings for a restricted set of sv sources with 0 leq varepsilon we also study a device independent protocol that allows for correlations between the sequence of boxes used in the protocol and the sv source bits used to choose the particular box from whose output the randomness is obtained assuming the sv like condition for devices we show that the honest parties can achieve amplification of the weak source for the parameter range 0 leq varepsilon against a class of attacks given as a mixture of product box sequences made of extremal no signaling boxes with additional symmetry conditions composable security proof against this class of attacks is provided

the characteristic square of a factor and the cocycle conjugacy of discrete group actions on factors this paper has three main purposes rst to associate to any separable factor m a canonical commuting exact square of groups called the characteristic square ofm secondly to formulate at least in a preliminary way a methodology for approaching non smooth classi cation problems in analysis and thirdly to use this approach in conjunction with the characteristic square to complete the cocycle conjugacy classi cation of actions of discrete amenable groups on injective factors of type iii1 this result and previous works on the cocyle conjugacy classi cation problem combine to produce a cocycle conjugacy classi cation theorem which applies simultaneously to all countable amenable groups and all injective separable factors and in which the characteristic square and our new methodology play a crucial role the cocycle conjugacy classi cation problem has by now a long and distinguished history beginning with connes ground breaking outer conjugacy classi cation of single automorphisms of the approximately nite dimensional or afd factor r0 of type ii1 c3 in the intervening 20 years enormous progress has been made the rst step was taken by v jones j who identi ed the true nature of the cocycle conjugacy invariants and completed the classi cation of actions of nite groups on r0 ocneanu o re ned this work and introduced new analytic techniques enabling him to extend the classi cation to countable amenable groups acting on the semi nite afd factor r0 1 and to some actions on afd factors of type iii also sutherland and takesaki using groupoid and duality techniques originating in jt extended the classi cation results to invent math 132 331 380 1998

on the security of pseudorandomized information theoretically secure schemes in this paper we discuss a naive method of randomness reduction for cryptographic schemes which replaces the required perfect randomness with output distribution of a computationally secure pseudorandom generator prg we propose novel ideas and techniques for evaluating the indistinguishability between the random and pseudorandom cases even against an adversary with computationally unbounded attack algorithm hence the prg based randomness reduction can be effective even for information theoretically secure cryptographic schemes especially when the amount of information received by the adversary is small in comparison to a preceding result of dubrov and ishai stoc 2006 our result removes the requirement of generalized notion of nb prgs and is effective for more general kinds of protocols we give some numerical examples to show the effectiveness of our result in practical situations and we also propose a further idea for improving the effect of the prg based randomness reduction

quantum entanglement and the communication complexity of the inner product function we consider the communication complexity of the binary inner product function in a variation of the two party scenario where the parties have an a priori supply of particles in an entangled quantum state we prove linear lower bounds for both exact protocols as well as for protocols that determine the answer with bounded error probability our proofs employ a novel kind of quantum reduction from a quantum information theory problem to the problem of computing the inner product the communication required for the former problem can then be bounded by an application of holevo s theorem we also give a specific example of a probabilistic scenario where entanglement reduces the communication complexity of the inner product function by one bit

classification of minimal actions of a compact kac algebra with amenable dual we show the uniqueness of minimal actions of a compact kac algebra with amenable dual on the afd factor of type ii1 this particularly implies the uniqueness of minimal actions of a compact group our main tools are a rohlin type theorem the 2 cohomology vanishing theorem and the evans kishimoto type intertwining argument

a product theorem in free groups if a is a nite subset of a free group with at least two noncommuting elements thenja a aj jaj 2 logjaj o 1 more generally the same conclusion holds in an arbitrary virtually free group unless a generates a virtually cyclic subgroup the central part of the proof of this result is carried on by estimating the number of collisions in multiple products a1 ak we include a few simple observations showing that in this statistical context

compact abelian group actions on injective factors we classify compact abelian group actions on injective type iii factors up to conjugacy which completes the final step of classification of compact abelian group actions on injective factors

ultraproducts of von neumann algebras abstract we study several notions of ultraproducts of von neumann algebras from a unified viewpoint in particular we show that for a sigma finite von neumann algebra m the ultraproduct m introduced by ocneanu is a corner of the ultraproduct m introduced by groh and raynaud using this connection we show that the ultraproduct action of the modular automorphism group of a normal faithful state of m on the ocneanu ultraproduct is the modular automorphism group of the ultrapower state t t applying these results we obtain several properties of the ocneanu ultraproduct of type iii factors which are not present in the tracial ultraproducts for instance it turns out that the ultrapower m of a type iii0 factor is never a factor moreover we settle in the affirmative a recent problem by ueda about the connection between the relative commutant of m in m and connes asymptotic centralizer algebra m

improving the hadamard extractor in this paper we construct a strong randomness extractor with two independent bit input distributions with min entropies b x b y b x b y the probability of any particular output is upper bounded by 2 b x and 2 b y respectively for b x b y 1 our extractor produces one bit which is by the factor of 2 closer to the uniform distribution when compared to the hadamard extractor what is more this distance drops to zero if at least one of the min entropies raises to this is in sharp contrast to the hadamard extractor which fails to produce even a single unbiased bit even if one of the input distributions is uniform we also extend our construction to produce k bits of output with a bias that is by the factor of 3 2 smaller than that of the corresponding hadamard extractor and retains the ability to produce unbiased bits if one of the input distributions is uniform the strongness property of the extractor is maintained in both cases however in the multi bit scenario the bias is increased by the factor of 3 2

communication lower bounds using directional derivatives we study the set disjointness problem in the most powerful model of bounded error communication the k party randomized number on the forehead model we show that set disjointness requires n 2kk bits of communication where n is the size of the universe our lower bound generalizes to quantum communication where it is essentially optimal proving this bound was a longstanding open problem even in restricted settings such as one way classical protocols with k 4 parties wigderson 1997 the proof contributes a novel technique for lower bounds on multiparty communication based on directional derivatives of protocols over the reals

entropy waves the zig zag graph product and new constant degree expanders the main contribution of this work is a new type of graph product which we call the zig zag product taking a product of a large graph with a small graph the resulting graph inherits roughly its size from the large one its degree from the small one and its expansion properties from both iteration yields simple explicit constructions of constant degree expanders of arbitrary size starting from one constant size expander crucial to our intuition and simple analysis of the properties of this graph product is the view of expanders as functions which act as entropy wave propagators they transform probability distributions in which entropy is concentrated in one area to distributions where that concentration is dissipated in these terms the graph product affords the constructive interference of two such waves

universal meshes a method for triangulating planar curved domains immersed in nonconforming meshes summary we introduce a new method to triangulate planar curved domains that transforms a specific collection of triangles in a background mesh to conform to the boundary in the process no new vertices are introduced and connectivities of triangles are left unaltered the method relies on a novel way of parameterizing an immersed boundary over a collection of nearby edges with its closest point projection to guarantee its robustness we require that the domain be c2 regular the background mesh be sufficiently refined near the boundary and that specific angles in triangles near the boundary be strictly acute the method can render both straight edged and curvilinear triangulations for the immersed domain the latter includes curved triangles that conform exactly to the immersed boundary and ones constructed with isoparametric mappings to interpolate the boundary at select points high order finite elements constructed over these curved triangles achieve optimal accuracy which has customarily proven difficult in numerical schemes that adopt nonconforming meshes aside from serving as a quick and simple tool for meshing planar curved domains with complex shapes the method provides significant advantages for simulating problems with moving boundaries and in numerical schemes that require iterating over the geometry of domains with no conformity requirements the same background mesh can be adopted to triangulate a large family of domains immersed in it including ones realized over several updates during the coarse of simulating problems with moving boundaries we term such a background mesh as a universal mesh for the family of domains it can be used to triangulate universal meshes hence facilitate a framework for finite element calculations over evolving domains while using only fixed background meshes furthermore because the evolving geometry can be approximated with any desired order numerical solutions can be computed with high order accuracy we present demonstrative examples using universal meshes to simulate the interaction of rigid bodies with stokesian fluids copyright 2014 john wiley sons ltd

unbalanced expanders and randomness extractors from parvaresh vardy codes we give an improved explicit construction of highly unbalanced bipartite expander graphs with expansion arbitrarily close to the degree which is polylogarithmic in the number of vertices both the degree and the number of right hand vertices are polynomially close to optimal whereas the previous constructions of ta shma et al 2007 required at least one of these to be quasipolynomial in the optimal our expanders have a short and self contained description and analysis based on the ideas underlying the recent list decodable error correcting codes of parvaresh and vardy 2005 our expanders can be interpreted as near optimal randomness condensers that reduce the task of extracting randomness from sources of arbitrary min entropy rate to extracting randomness from sources of min entropy rate arbitrarily close to 1 which is a much easier task using this connection we obtain a new self contained construction of randomness extractors that is optimal up to constant factors while being much simpler than the previous construction of lu et al 2003 and improving upon it when the error parameter is small e g 1 poly n

extracting kolmogorov complexity with applications to dimension zero one laws we apply results on extracting randomness from independent sources to extract kolmogorov complexity for any a e 0 given a string x with k x a x we show how to use a constant number of advice bits to efficiently compute another string y y w x with k y 1 e y this result holds for both unbounded and space bounded kolmogorov complexity we use the extraction procedure for space bounded complexity to establish zero one laws for the strong dimensions of complexity classes within espace the unbounded extraction procedure yields a zero one law for the constructive strong dimensions of turing degrees

approximation of boolean functions by combinatorial rectangles this paper deals with the number of monochromatic combinatorial rectangles required to approximate a boolean function on a constant fraction of all inputs where each rectangle may use its own partition of the input variables the main result of the paper is that the number of rectangles required for the approximation of boolean functions in this model is very sensitive to the allowed error there is an explicitly defined sequence of boolean functions fn on n variables such that fn has rectangle approximations with a constant number of rectangles and one sided error 13 o 1 or two sided error 14 o 1 but on the other hand fn requires exponentially many rectangles if the error bounds are decreased by an arbitrarily small constant as applications of this result the following separation results for read once branching programs are obtained the functions from the main result require only linear size for nondeterministic read once branching programs and randomized read once branching programs with two sided error 13 o 1 while randomized read once branching programs with constant two sided error smaller than 13 and unambiguous nondeterministic read once branching programs require exponential size

noncommutative lp structure encodes exactly jordan structure abstract we prove that for all 1 p p 2 the l p spaces associated to two von neumann algebras m n are isometrically isomorphic if and only if m and n are jordan isomorphic this follows from a noncommutative l p banach stone theorem a specific decomposition for surjective isometries of noncommutative l p spaces

compact abelian prime actions on von neumann algebras we classify the compact abelian actions on semifinite injective von neumann algebras with factor fixed point algebra the method uses that the nonzero eigenspaces of such an action contain unitaries which give rise to a classifying invariant

equivariant kirchberg phillips type absorption for amenable group actions we show an equivariant kirchberg phillips type absorption theorem for pointwise outer actions of discrete amenable groups on kirchberg algebras with respect to natural model actions on the cuntz algebras mathcal o infty and mathcal o 2 this generalizes results known for finite groups and poly mathbb z groups the model actions are shown to be determined up to strong cocycle conjugacy by natural abstract properties which are verified for some examples of actions arising from tensorial shifts we also show the following homotopy rigidity result which may be understood as a precursor to a general kirchberg phillips type classification theory if two outer actions of an amenable group on a unital kirchberg algebra are equivariantly homotopy equivalent then they are conjugate this marks the first c dynamical classification result up to cocycle conjugacy that is applicable to actions of all amenable groups

ergodic actions of compact groups on operator algebras iii classification for su 2 we prove that the only ergodic actions ofsu 2 are on type i von neumann algebras using the theory developed in 8

extractors for a constant number of polynomially small min entropy independent sources we consider the problem of randomness extraction from independent sources we construct an extractor that can extract from a constant number of independent sources of length n each of which have min entropy n gamma for an arbitrarily small constant gamma 0 our extractor is obtained by composing seeded extractors in simple ways we introduce a new technique to condense independent somewhere random sources which looks like a useful way to manipulate independent sources our techniques are different from those used in recent work b barak r impagliazzo and a wigderson siam j comput 36 2006 pp 1095 1118 b barak g kindler r shaltiel b sudakov and a wigderson simulating independence new constructions of condensers ramsey graphs dispersers and extractors in proceedings of the 37th annual acm symposium on theory of computing acm new york 2005 pp 1 10 r raz extractors with weak random seeds in proceedings of the 37th annual acm symposium on theory of computing acm new york 2005 pp 11 20 j bourgain int j number theory 1 2005 pp 1 32 for this problem in the sense that they do not rely on any results from arithmetic combinatorics using an extractor of bourgain s int j number theory 1 2005 pp 1 32 as a black box we obtain a new extractor for two independent block sources with few blocks even when the min entropy is as small as operatorname polylog n we also show how to modify the 2 source disperser for linear min entropy of barak et al simulating independence new constructions of condensers ramsey graphs dispersers and extractors in proceedings of the 37th annual acm symposium on theory of computing acm new york 2005 pp 1 10 and the three source extractor of raz extractors with weak random seeds in proceedings of the 37th annual acm symposium on theory of computing acm new york 2005 pp 11 20 to get dispersers extractors with exponentially small error and linear output length where previously both were constant

improved average case lower bounds for de morgan formula size matching worst case lower bound we give an explicit function h 0 1 n to 0 1 such that every de morgan formula of size n 3 o 1 r 2 agrees with h on at most a fraction of frac 1 2 2 omega r of the inputs our technical contributions include a theorem that shows that the expected shrinkage result of h aastad siam j comput 27 1998 pp 48 64 actually holds with very high probability where the restrictions are chosen from a certain distribution that takes into account the structure of the formula using ideas of impagliazzo meka and zuckerman proceedings of focs 2012 pp 111 119

equivalence of normal states on von neumann algebras and the flow of weights abstract let m be a von neumann algebra two positive normal functionals on m are called equivalent if is in the norm closure of the orbit of under the action of inner automorphisms our main result is an isometric characterization of the quotient space m we construct a natural isometry a g4 of m into the set of positive normal functionals on the smooth flow of weights of m where the smooth flow of weights is realized as the center z n of the crossed product n m r for some faithful normal semifinite weight on m as an application we obtain that an automorphism on a factor m with separable predual acts trivially on m if and only if acts trivially on the smooth flow of weights i e the connes takesaki modulus mod of vanishes we also obtain a new proof of the diameter formula diam s n m 2 1 1 for the quotient of the state space of a factor of type iii 0 1

unbiased bits from sources of weak randomness and probabilistic communication complexity a new model for weak random physical sources is presented the new model strictly generalizes previous models e g the santha and vazirani model 27 the sources considered output strings according to probability distributions in which no single string is too probable the new model provides a fruitful viewpoint on problems studied previously such as extracting almost perfect bits from sources of weak randomness the question of possibility as well as the question of efficiency of such extraction schemes are addressed probabilistic communication complexity it is shown that most functions have linear communication complexity in a very strong probabilistic sense robustness of bpp with respect to sources of weak randomness generalizing a result of vazirani and vazirani 32 33

lower bounds for one way probabilistic communication complexity and their application to space complexity abstract we prove three different types of complexity lower bounds for the one way unbounded error and bounded error error probabilistic communication protocols for boolean functions the lower bounds are proved in terms of the deterministic communication complexity of functions and in terms of the notion probabilistic communication characteristic that we define we present boolean functions with the different probabilistic communication characteristics which demonstrates that each of these lower bounds can be more precise than the others depending on the probabilistic communication characteristics of a function our lower bounds are good enough for proving that proper hierarchy for one way probabilistic communication complexity classes depends on a measure of bounded error as the application of lower bounds for probabilistic communication complexity we prove two different types of complexity lower bounds for the one way bounded error error probabilistic space complexity our lower bounds are good enough for proving proper hierarchies for different one way probabilistic space communication complexity classes inside space n namely for bounded error probabilistic computation and for errors of probabilistic computation

finite group actions on c algebras with the rohlin property i basic properties of finite group actions with the rohlin property on unital c algebras are investigated a characterization of finite group actions with the rohlin property on the cuntz algebra 02 is given in terms of central sequences which may be considered as an equivariant version of e kirchberg and n c phillips s characterization of 02 a large class of symmetries on 02 are classified in terms of the fixed point algebras for conjugacy and the crossed products for cocycle conjugacy model actions of symmetries of 02 are constructed for given k theoretical invariants

post challenge leakage in public key encryption when an adversary can measure the physical memory storing the decryption key decryption functionality often comes in handy halevi and lin tcc 11 studied after the fact or post challenge leakage in public key encryption pke in which an adversary can make leakage queries from a split state after seeing the challenge ciphertext but left security against chosen ciphertext attacks cca as a future work in this paper we follow their work and formulate the definition of entropic leakage resilient cca secure pke which we show can be realized by the naor yung double encryption paradigm stoc 90 we then leverage it to get a cca secure key encapsulation mechanism in the presence of post challenge leakage in the same model of bounded memory leakage from a split state finally we prove that the hybrid encryption framework is still applicable by presenting a construction of cca secure pke in the presence of post challenge leakage as additional results we extend these concepts to the identity based setting where many identity based secret keys can be leaked after the adversary got the challenge and give a construction of identity based encryption in the presence of post challenge leakage in the split state model which can be instantiated by the identity based hash proof systems of alwen et al eurocrypt 10 and chow et al ccs 10

invertible extractors and wiretap protocols a wiretap protocol is a pair of randomized encoding and decoding functions such that knowledge of a bounded fraction of the encoding of a message reveals essentially no information about the message while knowledge of the entire encoding reveals the message using the decoder in this paper the notion of efficiently invertible extractors is studied and it is shown that a wiretap protocol can be constructed from such an extractor then invertible extractors for symbol fixing affine and general sources are constructed and used to create wiretap protocols with asymptotically optimal trade offs between their rate ratio of the length of the message versus its encoding and resilience ratio of the observed positions of the encoding and the length of the encoding the results are further applied to create wiretap protocols for challenging communication problems such as active intruders who change portions of the encoding network coding and intruders observing arbitrary boolean functions of the encoding

mesh smoothing using a posteriori error estimates we develop a simple mesh smoothing algorithm for adaptively improving finite element triangulations the algorithm makes use of a posteriori error estimates which are now widely used in finite element calculations in this paper we derive the method present some numerical illustrations and give a brief analysis of the issue of uniqueness

the non commutative flow of weights on a von neumann algebra abstract the flow of weights of connes and takesaki is a canonical functor from the category of separable factors to the category of ergodic flows the non commutative flow of weights is another canonical functor from the category of separable factors to the category of covariant systems of semi finite von neumann algebras equipped with trace scaling one parameter automorphism groups with conjugations as morphisms the constructions of these two functors are very similar the flow of weights functor is obtained by looking at all semi finite normal weights on a factor with the murray von neumann equivalence relation the non commutative flow of weights functor is obtained by relating an arbitrary pair of faithful semi finite normal weights by the connes cocycle not only does this construction put a period to the search for a canonical construction of the core of a factor of type iii but it also allows us to put the characteristic square of a factor obtained by katayama sutherland and takesaki in a new perspective the power of this new approach is seen in an ultimate solution to a long standing question of extending the extended modular automorphism of a dominant weight to an arbitrary weight which has been left open ever since the introduction of extended modular automorphisms by connes and takesaki over 20 years ago the construction of the functor ties together the theory of l p spaces of haagerup kosaki hilsum terp and izumi to the structure theory of a factor of type iii in fact the non commutative flow of weights is obtained by the analytic continuation of l p spaces to a pure imaginary value of p

hnn extensions of von neumann algebras abstract reduced hnn extensions of von neumann algebras as well as c algebras will be introduced and their modular theory factoriality and ultraproducts will be discussed in several concrete settings detailed analysis on them will be also carried out

the sign rank of ac 0 the sign rank of a matrix a a ij with pm1 entries is the least rank of a real matrix b b ij with a ij b ij 0 for all i j we obtain the first exponential lower bound on the sign rank of a function in mathsf ac 0 namely let f x y bigwedge i 1 dots m bigvee j 1 dots m 2 x ij wedge y ij we show that the matrix f x y x y has sign rank exp omega m this in particular implies that sigma 2 cc not subseteq mathsf upp cc which solves a longstanding open problem in communication complexity posed by babai frankl and simon proceedings of the 27th symposium on foundations of computer science focs 1986 pp 337 347 our result additionally implies a lower bound in learning theory specifically let phi 1 dots phi r 0 1 n to mathbb r be functions such that every dnf formula f 0 1 n to 1 1 of polynomial size has the representation f equiv mathrm sgn a 1 phi 1 dots a r phi r for some reals a 1 dots a r we prove that then r geqslant exp omega n 1 3 which essentially matches an upper bound of exp tilde o n 1 3 due to klivans and servedio j comput system sci 68 2004 pp 303 318 finally our work yields the first exponential lower bound on the size of threshold of majority circuits computing a function in mathsf ac 0 this substantially generalizes and strengthens the results of krause and pudlak theoret comput sci 174 1997 pp 137 156

simulating independence new constructions of condensers ramsey graphs dispersers and extractors we present new explicit constructions of deterministic randomness extractors dispersers and related objects we say that a distribution x on binary strings of length n is a source if x assigns probability at most 2 n to any string of length n for every 0 we construct the following poly n time computable functions 2 source disperser d 0 1 n 2 0 1 such that for any two independent sources x1 x2 we have that the support of d x1 x2 is 0 1 bipartite ramsey graph let ne2n a corollary is that the function d is a 2 coloring of the edges of kn n the complete bipartite graph over two sets of n vertices such that any induced subgraph of size n by n is not monochromatic 3 source extractor e 0 1 n 3 0 1 such that for any three independent sources x1 x2 x3 we have that e x1 x2 x3 is o 1 close to being an unbiased random bit no previous explicit construction was known for either of these for any a component in these results is a new construction of condensers that may be of independent interest this is a function c 0 1 n 0 1 n c d where c and d are constants that depend only on such that for every source x one of the output blocks of c x is exponentially close to a 0 9 source this result was obtained independently by ran raz the constructions are quite involved and use as building blocks other new and known objects a recurring theme in these constructions is that objects that were designed to work with independent inputs sometimes perform well enough with correlated high entropy inputs the construction of the disperser is based on a new technique which we call the challenge response mechanism that in some sense allows identifying high entropy regions in a given pair of sources using only one sample from the two sources

the structure of the automorphism group of an injective factor and the cocycle conjugacy of discrete abelian group actions we complete classification of discrete abelian or finite group actions on injective type iii1 factors up to cocycle conjugacy we also give a proof for connes characterization of the ker mod and cnt m for an injective factor m of type iii 0 introduction the purpose of this paper is to give a proof of connes announcement on approximately inner automorphisms and centrally trivial automorphisms of an injective 1980 mathematics subject classification 1985 revision 46l40

les espaces lp d une algebre de von neumann definies par la derivee spatiale abstract this work answers a question raised by a connes on the spatial theory of von neumann algebras preprint inst hautes etudes sci france and generalizes for a general von neumann algebra the theory of non commutative integration of j dixmier bull soc math france 81 1953 and i segal ann of math 57 1973

an efficient reduction from two source to nonmalleable extractors achieving near logarithmic min entropy the breakthrough result of chattopadhyay and zuckerman explicit two source extractors and resilient functions in proceedings of the 48th annual acm sigact symposium on theory of computing stoc

a new general derandomization method we show that quick hitting set generators can replace quick pseudorandom generators to derandomize any probabilistic two sided error algorithms up to now quick hitting set generators have been known as the general and uniform derandomization method for probabilistic one sided error algorithms while quick pseudorandom generators as the generators as the general and uniform method to derandomize probabilistic two sided error algorithms our method is based on a deterministic algorithm that given a boolean circuit c and given access to a hitting set generator constructs a discrepancy set for c the main novelty is that the discrepancy set depends on c so the new derandomization method is not uniform i e not oblivious the algorithm works in time exponential in k p n where k is the price of the hitting set generator and p is a polynomial function in the size of c we thus prove that if a logarithmic price quick hitting set generator exists then bpp p

explicit or dispersers with polylogarithmic degree an n m t or disperser is a bipartite multigraph g v w e with v n and w m having the following expansion property any subset of v having at least t vertices has a neighbor set of size at least m 2 for any pair of constants x 1 x 0 any sufficiently large n and for any t 2 log n m 2 log n we give an explicit elementary construction of an n m t or disperser such that the out degree of any vertex in v is at most polylogarithmic in n using this with known applications of or dispersers yields several results first our construction implies that the complexity class strong rp defined by sipser equals rp second for any fixed e 0 we give the first polynomial time simulation of rp algorithms using the output of any e minimally random source for any integral r 0 such a source accepts a single request for an r bit string and generates the string according to a distribution that assigns probability at most 2 r e to any string it is minimally random in the sense that any weaker source is insufficient to do a black box polynomial time simulation of rp algorithms

algebraic mesh quality metrics quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics the theory based on the jacobian and related matrices provides a means of constructing classifying and evaluating mesh quality metrics the jacobian matrix is factored into geometrically meaningful parts a nodally invariant jacobian matrix can be defined for simplicial elements using a weight matrix derived from the jacobian matrix of an ideal reference element scale and orientation invariant algebraic mesh quality metrics are defined the singular value decomposition is used to study relationships between metrics equivalence of the element condition number and mean ratio metrics is proved the condition number is shown to measure the distance of an element to the set of degenerate elements algebraic measures for skew length ratio shape volume and orientation are defined abstractly with specific examples given two combined metrics shape volume and shape volume orientation are algebraically defined and examples of such metrics are given algebraic mesh quality metrics are extended to nonsimplicial elements a series of numerical tests verifies the theoretical properties of the metrics defined

pointwise inner automorphisms of von neumann algebras an automorphism of a von neumann algebra m is called pointwise inner if for all m there is a unitary u m such that u u we analyse such automorphisms in particular we show that if m is a factor of type iii 0 1 with separable predual then an automorphism is pointwise inner if and only if there are an inner automorphism and an extended modular automorphism gsc in the sense of connes and takesaki such that gsc

extracting randomness using few independent sources in this work we give the first deterministic extractors from a constant number of weak sources whose entropy rate is less than 1 2 specifically for every delta 0 we give an explicit construction for extracting randomness from a constant depending polynomially on 1 delta number of distributions over bits n each having min entropy delta n these extractors output n bits that are 2 n close to uniform this construction uses several results from additive number theory and in particular a recent result of bourgain et al we also consider the related problem of constructing randomness dispersers for any constant output length m our dispersers use a constant number of identical distributions each with requires min entropy omega log n and outputs every possible m bit string with positive probability the main tool we use is a variant of the stepping up lemma of erdods and hajnal used in establishing a lower bound on the ramsey number for hypergraphs

fuzzy extractors how to generate strong keys from biometrics and other noisy data we provide formal definitions and efficient secure techniques for turning noisy information into keys usable for any cryptographic application and in particular reliably and securely authenticating biometric data our techniques apply not just to biometric information but to any keying material that unlike traditional cryptographic keys is 1 not reproducible precisely and 2 not distributed uniformly we propose two primitives a fuzzy extractor reliably extracts nearly uniform randomness r from its input the extraction is error tolerant in the sense that r will be the same even if the input changes as long as it remains reasonably close to the original thus r can be used as a key in a cryptographic application a secure sketch produces public information about its input w that does not reveal w and yet allows exact recovery of w given another value that is close to w thus it can be used to reliably reproduce error prone biometric inputs without incurring the security risk inherent in storing them we define the primitives to be both formally secure and versatile generalizing much prior work in addition we provide nearly optimal constructions of both primitives for various measures of closeness of input data such as hamming distance edit distance and set difference

deterministic extractors for independent symbol sources in this paper we consider the task of deterministically extracting randomness from sources consisting of a sequence of n independent symbols from 0 1 d the only randomness guarantee on such a source is that the whole source has min entropy k we give an explicit deterministic extractor which extract logk loglog 1 e bits with error e for any n d k bbn and e 0 1 for sources with a larger min entropy we can extract even more randomness when k n1 2 for any constant 0 1 2 we can extract m k o d log 1 e bits with any error e 2 n when k logcn for some constant c 0 we can extract m k 1 e o 1 bits with any error e k 1 our results generalize those of kamp and zuckerman and gabizon which only work for bit fixing sources with d 1 and each bit of the source being either fixed or perfectly random moreover we show the existence of a nonexplicit deterministic extractor which can extract m k o log 1 e bits whenever k d log n e finally we show that even to extract from bit fixing sources any extractor seeded or not must suffer an entropy loss k m log 1 e this generalizes a lower bound of radhakrishnan and ta shma on extracting from general sources

a pseudorandom generator from any one way function pseudorandom generators are fundamental to many theoretical and applied aspects of computing we show how to construct a pseudorandom generator from any one way function since it is easy to construct a one way function from a pseudorandom generator this result shows that there is a pseudorandom generator if and only if there is a one way function

upper and lower bounds on the power of advice proving superpolylogarithmic lower bounds for dynamic data structures has remained an open problem despite years of research p trascu proposed an exciting approach for breaking this barrier via a two player communication model in which one player gets private advice at the beginning of the protocol he gave reductions from the problem of solving an asymmetric version of set disjointness in his model to a diverse collection of natural dynamic data structure problems in the cell probe model he also conjectured that for any hard problem in the standard two party communication model the asymmetric version of the problem is hard in his model provided not too much advice is given in this paper we prove several surprising results about his model we show that there exist boolean functions requiring linear randomized communication complexity in the two party model for which the asymmetric versions in his model have deterministic protocols with exponentially smaller complexity for set disjointness which

amenability of hopf von neumann algebras and kac algebras abstract let m be a hopf von neumann algebra the operator predualm ofmis a completely contractive banach algebra with multiplicationm m m m we call m operator amenableif the completely contractive banach algebram isoperator amenable i e for every operatorm bimodulev every completely bounded derivation fromm into the dualm bimodulev is inner there is a weaker notion of amenability introduced by d voiculescu we say that a hopf von neumann algebra m isvoiculescu amenableif there exists a left invariant mean onm we show that if a hopf von neumann algebra m is operator amenable then it is voiculescu amenable for kac algebras there is astrong voiculescu amenability we show that for discrete kac algebras these amenabilities are all equivalent in fact if we letk m be a discrete kac algebra and letk m be its compact dual kac algebra then the following are equivalent 1 kis operator amenable 2 kis voiculescu amenable 3 the von neumann algebramis hyperfinite 4 kis strong voiculescu amenable 5 kis operator amenable 6 m has a bounded approximate identity

extraction of optimally unbiased bits from a biased source we explore the problem of transforming n independent and identically biased 1 1 valued random variables x sub 1 x sub n into a single 1 1 random variable f x sub 1 x sub n so that this result is as unbiased as possible in general no function f produces a completely unbiased result we perform the first study of the relationship between the bias b of these x sub i and the rate at which f x sub 1 x sub n can converge to an unbiased 1 1 random variable as n spl rarr spl infin a 1 1 random variable has bias b if e x sub i b fixing a bias b we explore the rate at which the output bias e f x sub 1 x sub n can tend to zero for a function f 1 1 spl rarr 1 1 this is accomplished by classifying the behavior of the natural normalized quantity spl xi b spl delta inf sub f lim sub n spl rarr spl infin n spl radic e f x sub 1 x sub n this infimum taken over all such f we show that for rational b spl xi b 1 s where 1 b 2 r s r and s relatively prime developing the theory of uniform distribution of sequences to suit our problem we then explore the case where b is irrational we prove a new metrical theorem concerning multidimensional diophantine approximation type from which we show that for lebesgue almost all biases b spl xi b 0 finally we show that algebraic biases exhibit curious boundary behavior falling into two classes class 1 those algebraics b for which spl xi b 0 and furthermore c sub 1 spl les spl xi b spl les c sub 2 where c sub 1 and c sub 2 are positive constants depending only on b s algebraic characteristics class 2 those algebraics b for which there exist n 0 and f 1 1 sup n spl rarr 1 1 so that e f x sub 1 x sub n 0 notice that this classification excludes the possibility that n spl radic e f x sub 1 x sub n limits to zero for algebraics for rational and algebraic biases we also study the computational problem by restricting f to be a polynomial time computable function finally we discuss natural extensions where output distributions other than the uniform distribution on 1 1 are sought

full factors bicentralizer flow and approximately inner automorphisms we show that a factor m is full if and only if the c algebra generated by its left and right regular representations contains the compact operators we prove that the bicentralizer flow of a type mathrm iii 1 factor is always ergodic as a consequence for any type mathrm iii 1 factor m and any lambda in 0 1 there exists an irreducible afd type mathrm iii lambda subfactor with expectation in m moreover any type mathrm iii 1 factor m which satisfies m cong m mathbin overline otimes r lambda for some lambda in 0 1 has trivial bicentralizer finally we give a counter example to the characterization of approximately inner automorphisms conjectured by connes and we prove a weaker version of this conjecture in particular we obtain a new proof of kawahigashi sutherland takesaki s result that every automorphism of the afd type mathrm iii 1 factor is approximately inner

two source dispersers for polylogarithmic entropy and improved ramsey graphs in his 1947 paper that inaugurated the probabilistic method erdos proved the existence of 2 o 1 log n ramsey graphs on n vertices matching erdos s result with a constructive proof is cons

on the shape of tetrahedra from bisection we present a procedure for bisecting a tetrahedron t successively into an infinite sequence of tetrahedral meshes j 0 91 g2 which has the following properties 1 each mesh sfn is conforming 2 there are a finite number of classes of similar tetrahedra in all the 3n n 0 3 for any tetrahedron t7 in s7n jj t cl1 t where ti is a tetrahedron shape measure and cl is a constant 4 3 j c2 1 2 ni3j t where d t denotes the diameter of tetrahedron t1 and c2 is a constant estimates of cl and c2 are provided properties 2 and 3 extend similar results of stynes and adler and of rosenberg and stenger respectively for the 2 d case the diameter bound in property 4 is better than one given by kearfott

2 source dispersers for n o 1 entropy and ramsey graphs beating the frankl wilson construction the main result of this paper is an explicit disperser for two independent sources on n bits each of min entropy k 2 1 0 for some small absolute constant 0 0 put differently setting n 2 and k 2 we construct an explicit n n boolean matrix for which no k k sub matrix is monochromatic viewed as the adjacency matrix of a bipartite graph this gives an explicit construction of a bipartite k ramsey graph of 2n vertices this improves the previous the previous bound of k o n of barak kindler shaltiel sudakov and wigderson bks05 as a corollary we get a construction of a 2 log1 0 n non bipartite ramsey graph of 2 vertices significantly improving the previous bound of 2o n due to frankl and wilson fw81 we also give a construction of a new independent sources extractor that can extract from a constant number of sources of polynomially small min entropy with exponentially small error this improves independent sources extractor of rao rao06 which only achieved polynomially small error our dispersers combine ideas and constructions from several previous works in the area together with some new ideas in particular we rely on the extractors of raz raz05 and bourgain bou05 as well as an improved version of the extractor of rao rao06 a key ingredient that allows us to beat the barrier of k n is a new and more complicated variant of the challenge response mechanism of barak et al bks05 that allows us to locate the min entropy concentrations in a source of low min entropy

strongly self absorbing c dynamical systems iii abstract in this paper we accomplish two objectives firstly we extend and improve some results in the theory of semi strongly self absorbing c dynamical systems which was introduced and studied in previous work in particular this concerns the theory when restricted to the case where all the semi strongly self absorbing actions are assumed to be unitarily regular which is a mild technical condition the central result in the first part is a strengthened version of the equivariant mcduff type theorem where equivariant tensorial absorption can be achieved with respect to so called very strong cocycle conjugacy secondly we establish completely new results within the theory this mainly concerns how equivariantly z stable absorption can be reduced to equivariantly uhf stable absorption with respect to a given semi strongly self absorbing action combining these abstract results with known uniqueness theorems due to matui and izumi matui we obtain the following main result if g is a torsion free abelian group and d is one of the known strongly self absorbing c algebras then strongly outer g actions on d are unique up to very strong cocycle conjugacy this is new even for z 3 actions on the jiang su algebra

average and randomized communication complexity the communication complexity of a two variable function f x y is the number of information bits two communicators need to exchange to compute f when initially each knows only one of the variables there are several communication complexity measures corresponding to whether 1 the worst case or average number of bits is considered 2 computation errors are allowed and 3 randomization is allowed tight bounds are provided for the typical behavior of all bounded error communication complexity measures of boolean functions in the present work the authors formally define the deterministic model they describe randomized protocols and compare them to deterministic ones they both survey previous work and describe original results

space lower bounds for online pattern matching we present space lower bounds for online pattern matching under a number of different distance measures given a pattern of length m and a text that arrives one character at a time the online pattern matching problem is to report the distance between the pattern and a sliding window of the text as soon as the new character arrives we require that the correct answer is given at each position with constant probability we give w m bit space lower bounds for l 1 l 2 l hamming edit and swap distances as well as for any algorithm that computes the cross correlation convolution we then show a dichotomy between distance functions that have wildcard like properties and those that do not in the former case which includes as an example pattern matching with character classes we give w m bit space lower bounds for other distance functions we show that there exist space bounds of w logm and o log 2m bits finally we discuss space lower bounds for non binary inputs and show how in some cases they can be improved