comments on hastings additivity counterexamples hastings 12 recently provided a proof of the existence of channels which violate the additivity conjecture for minimal output entropy in this paper we present an expanded version of hastings proof in addition to a careful elucidation of the details of the proof we also present bounds for the minimal dimensions needed to obtain a counterexample

resolution of singularities of threefolds in positive characteristic ii abstract together with vincent cossart olivier piltant resolution of singularities of threefolds in positive characteristic i reduction to local uniformization on artin schreier and purely inseparable coverings j algebra 320 3 2008 1051 1082 this article gives a complete proof of desingularization of quasiprojective varieties of dimensional 3 on fields which are differentially finite over perfect fields

inseparable local uniformization abstract it is known since the works of zariski in the early 40s that desingularization of varieties along valuations called local uniformization of valuations can be considered as the local part of the desingularization problem it is still an open problem if local uniformization exists in positive characteristic and dimension larger than three in this paper we prove that zariski local uniformization of algebraic varieties is always possible after a purely inseparable extension of the field of rational functions and therefore any valuation can be uniformized by a purely inseparable alteration

effect algebras with state operator state operators on convex effect algebras in particular effect algebras of unital jc algebras jw algebras and convex mv algebras are studied and their relations with conditional expectations in algebraic sense as well as in the sense of probability on mv algebras are shown

existence of states on quantum structures orthomodular lattices occurred as generalized event structures in the models of probability for quantum mechanics here we contribute to the question of existence of states probability measures on orthomodular lattices we prove that known techniques do not allow to find examples with less than 19 blocks maximal boolean subalgebras this bound is achieved by the example by mayet r mayet personal communication 1993 although we do not finally exclude the existence of other techniques breaking this bound existence of smaller examples is highly unexpected

partial correlations in multipartite quantum systems abstract quantum correlations are more general than entanglement a problem on how to characterize and quantify quantum correlations has attracted substantial attention quantum correlations in bipartite systems have been researched extensively in this paper partial correlations in a multipartite quantum system a 1 a 2 a n are discussed in detail in order to reveal correlations of a given state with respect to some subsystems for a nonempty subset of the index set 1 2 n classical correlations cc quantum correlations qc partially classical correlations pcc and genuinely quantum correlations gqc are introduced in a multipartite system subsequently characterizations of cc are obtained secondly a measure function g of partial correlations of a state is defined and called the quantum discord it is proved that g is nonnegative independent of the choice of basis and invariant under local unitary transformations it is also proved that a state is cc if and only if g 0 and then it is qc if and only if g 0 moreover some relationships among partial correlations with respect to different are discussed in light of the measure function finally an illustrative example with 6 qubit ghz state is given

polar decomposition in e rings an e ring is a generalization of the ring of bounded linear operators on a hilbert space together with the subset consisting of all effect operators on that space associated with an e ring is a partially ordered abelian group called its directed group that generalizes the additive group of bounded hermitian operators on the hilbert space we prove that every element of the directed group of an e ring has a polar decomposition if and only if every element has a carrier projection and is split by a projection into a positive and a negative part

well posedness for the continuity equation for vector fields with suitable modulus of continuity abstract we prove well posedness of linear scalar conservation laws using only assumptions on the growth and the modulus of continuity of the velocity field but not on its divergence as an application we obtain uniqueness of solutions in the atomic hardy space h 1 for the scalar conservation law induced by a class of vector fields whose divergence is an unbounded bmo function

general formulas for capacity of classical quantum channels the capacity of a classical quantum channel or in other words the classical capacity of a quantum channel is considered in the most general setting where no structural assumptions such as the stationary memoryless property are made on a channel a capacity formula as well as a characterization of the strong converse property is given just in parallel with the corresponding classical results of verdu han 1994 which are based on the so called information spectrum method the general results are applied to the stationary memoryless case with or without cost constraint on inputs whereby a deep relation between the channel coding theory and the hypothesis testing for two quantum states is elucidated

boolean algebras r generated by mv effect algebras we prove that every mv effect algebra m is as an effect algebra a homomorphic image of its r generated boolean algebra we characterize central elements of m in terms of the constructed homomorphism

pasting of lattice ordered effect algebras in this study we present techniques for constructing a lattice ordered effect algebra using a given family of mv effect algebras first we introduce the greechie diagrams of the pastings of a family of mv effect algebras as application of the greechie diagrams we provide some sufficient conditions for pasting a lattice ordered effect algebra using a family of mv effect algebras especially we illustrate a kind of technique of how to obtain a lattice ordered effect algebra by substituting the atoms of an orthomodular lattice with the lattice ordered effect algebras finally we prove a version of the loop lemma for mv effect algebras pasting

singularities in positive characteristic stratification and simplification of the singular locus abstract we introduce an upper semi continuous function that stratifies the highest multiplicity locus of a hypersurface in arbitrary characteristic the blow up along the maximum stratum defined by this function leads to a form of simplification of the singularities known as the reduction to the monomial case

results on residual renyi entropy of order statistics and record values this paper explores properties of the residual renyi entropy of some ordered random variables the residual renyi entropy of the kth order statistic from a continuous distribution function is represented in terms of the residual renyi entropy of the kth order statistic from uniform distribution the monotone behavior of the residual renyi entropy of order statistic under various conditions is discussed analogues results for the residual renyi entropy of record values are also given

properties of a hierarchical network based on the star graph this paper introduces a new class of interconnection networks named star pyramid an n level star pyramid is formed by piling up star graphs of dimensions 1 to n in a hierarchy connecting any node in each i dimensional star 1

observables on quantum structures an observable on a quantum structure is any s homomorphism of quantum structures from the borel s algebra into the quantum structure we show that our partial information on an observable known only for all intervals of the form t is sufficient to derive the whole information about the observable defined on quantum structures like s mv algebras s lattice effect algebras boolean s algebras monotone s complete effect algebras with the riesz decomposition property the effect algebra of effect operators of a hilbert space and systems of functions effect tribes

transport equation extension of classical results for div b bmo we investigate the transport equation ut b u 0 our result improves the criteria on uniqueness of weak solutions replacing the classical condition divb l by divb bmo

isomorphism theorems on generalized effect algebras based on atoms a well known fact is that every generalized effect algebra can be uniquely extended to an effect algebra in which it becomes a sub generalized effect algebra and simultaneously a proper order ideal the set theoretic complement of which is its dual poset we show that two non isomorphic generalized effect algebras even finite ones may have isomorphic effect algebraic extensions for archimedean atomic lattice effect algebras we prove isomorphism theorem based on atoms as an application we obtain necessary and sufficient conditions for isomorphism of two prelattice archimedean atomic generalized effect algebras with common or isomorphic effect algebraic extensions

the polya information divergence extensions of sanov s theorem and the conditional limit theorem colt are established for a multicolor polya eggenberger pe urn sampling scheme giving the polya information divergence and a polya extension to the maximum relative entropy maxent method polya maxent includes the standard maxent as well as its variants used in bose einstein fermi dirac and intermediate acharya swamy statistics as special cases in the pe setting standard maxent is in general asymptotically inconsistent

free boundaries in optimal transport and monge ampere obstacle problems given compactly supported 0 f g 2 l 1 r n the problem of trans porting a fraction m min kfkl1 kgkl1 of the mass of f onto g as cheaply as possible is considered where cost per unit mass transported is given by a cost function c typically quadratic c x y x y 2 2 this question is shown to be equivalent to a double obstacle problem for the monge ampere equation for which sucient conditions are given to guarantee uniqueness of the solution such as f vanishing on sptg in the quadratic case the part of f to be transported increases monotonically with m and if sptf and sptg are separated by a hyperplane h then this part will separated from the balance of f by a semiconcave lipschitz graph over the hyperplane if f f and g g are bounded away from zero and infinity on separated strictly convex domains r n for the quadratic cost this graph is shown to be a c 1 loc hypersurface in whose normal coincides with the direction transported the optimal map between f and g is shown to be holder continuous up to this free bound ary and to those parts of the fixed boundary which map to locally convex parts of the path connected target region

markov property in quantum logic a possible way of the markov property introduction within the framework of the orthomodular quantum logic which is commonly used as the calculus model for quantum mechanics is presented in this paper the presented work follows the logical line rather than any physical interpretation in the framework of quantum mechanics the basic algebraic structure which is used as a model for noncompatible random events is an orthomodular lattice on the orthomodular lattice a dynamical structure is introduced coupled with mappings which have similar properties as s n maps on the orthomodular lattice this construction leads to the definition of an l process with the markov property on the orthomodular lattice

flows for non smooth vector fields with subexponentially integrable divergence abstract in this paper we study flows associated to sobolev vector fields with subexponentially integrable divergence our approach is based on the transport equation following diperna lions 17 a key ingredient is to use a quantitative estimate of solutions to the cauchy problem of transport equation to obtain the regularity of density functions

geometrical analysis of physically allowed quantum cloning transformations for quantum cryptography the security of quantum key distribution qkd relies on the no cloning theorem which allows no to copy perfectly a quantum system an eavesdropping activity on the quantum channel perturbs the state of the quantum states which results in noise at the receiver the physical layer detection of the eavesdropping activity of the quantum channel requires tomography which is intractable in experiment an adequate and equivalent answer for the problem can be proposed through the logical layer we propose an efficient algorithmical tool to study the eavesdropping activity on the quantum channel and characterize the properties of a quantum cloning based attack for dv and cvqkd protocols the physically allowed quantum cloning transformations on a quantum system can be described in terms of information geometry we propose a computational geometrical method to analyze the cloning activity on the quantum channel and to characterize the noise properties the security analysis studies the dv discrete variable and cv continuous variable qkd schemes through the four state bb84 and six state dvqkd protocols and the two way cvqkd protocol the proposed geometrical method provides a useful tool to analyze the most powerful attacks against quantum cryptography and the effects of the physically allowed quantum cloning transformations

characteristic polyhedra of singularities without completion in hironaka j math kyoto univ 7 3 251 293 1967 defines characteristic polyhedra of a singularity embedded in spec r where r is a regular local ring unfortunately to build these polyhedra he must pick up coordinates in the completion widehat r in this article we show that in the hypersurface case whenever r is a g ring by using a different algorithm than hironaka s it is not necessary to extend r to compute the polyhedra

fractal properties of mv algebra pastings abstract we implement the fractal construction process to the mv algebra pastings pasted mv algebras generate special types of difference posets d posets we compute the dimension of new fractal d posets and show that the fractal structures discussed in this paper have a non integer fractal dimension furthermore we observe an interesting agreement between the fractal dimension of the classical linear fractals cantor sets koch curves and the dimension of fractal d posets cantor fractal d posets and koch fractal d posets

additivity of the classical capacity of entanglement breaking quantum channels we show that for the tensor product of an entanglement breaking quantum channel with an arbitrary quantum channel both the minimum entropy of an output of the channel and the holevo schumacher westmoreland capacity are additive in addition for the tensor product of two arbitrary quantum channels we give a bound involving entanglement of formation for the amount of subadditivity for minimum entropy output or superadditivity for classical capacity that can occur

distillation of secret key and entanglement from quantum states we study and solve the problem of distilling a secret key from quantum states representing correlation between two parties alice and bob and an eavesdropper eve via oneway public discussion we

pseudocomplemented lattice effect algebras and existence of states we prove that in every pseudocomplemented atomic lattice effect algebra the subset of all pseudocomplements is a boolean algebra including the set of sharp elements as a subalgebra as an application we show families of effect algebras for which the existence of a pseudocomplementation implies the existence of states these states can be obtained by smearing of states existing on the boolean algebra of sharp elements

the pasting constructions of lattice ordered effect algebras the aim of this paper is to present some ways of constructing a lattice ordered effect algebra from the given family of mv algebras the loop lemma of lattice ordered effect algebras is proved then the definitions of greechie diagrams of effect algebras are given all these results have generalized those of orthomodular lattices as applications of loop lemma and greechie diagrams some lattice ordered effect algebras without states are presented

flows associated with irregular r d vector fields abstract this work consists on the study of flows associated with non smooth r d vector fields namely concerning existence and uniqueness for almost every initial condition it is also proved that the flows avoid some special compact sets

algorithmic superactivation of asymptotic quantum capacity of zero capacity quantum channels the superactivation of zero capacity quantum channels makes it possible to use two zero capacity quantum channels with a positive joint capacity for their output currently we have no theoretical background to describe all possible combinations of superactive zero capacity channels hence there may be many other possible combinations in practice to discover such superactive zero capacity channel pairs we must analyze an extremely large set of possible quantum states channel models and channel probabilities there is still no extremely efficient algorithmic tool for this purpose this paper shows an efficient algorithmical method of finding such combinations our method can be a very valuable tool for improving the results of fault tolerant quantum computation and possible communication techniques over very noisy quantum channels

strong ill posedness of the incompressible euler equation in borderline sobolev spaces for the d dimensional incompressible euler equation the standard energy method gives local wellposedness for initial velocity in sobolev space h s mathbb r d s s c d 2 1 the borderline case s s c was a folklore open problem in this paper we consider the physical dimension d 2 and show that if we perturb any given smooth initial data in h s c norm then the corresponding solution can have infinite h s c norm instantaneously at t 0 in a companion paper 1 we settle the 3d and more general cases the constructed solutions are unique and even c infty smooth in some cases to prove these results we introduce a new strategy large lagrangian deformation induces critical norm inflation as an application we also settle several closely related open problems

continuous lattice effect algebras admitting order continuous states we prove that a necessary and sufficient condition for the existence of a faithful o continuous state on a complete modular atomic effect algebra e is the separability of e moreover we generalize the famous kaplansky theorem about order continuity of complemented complete modular lattices onto complete modular atomic effect algebras some other statements about the algebraic structure of modular effect algebras are shown we prove that every chain and every block in an irreducible complete modular atomic effect algebra is finite moreover every complete atomic modular effect algebra is compactly generated by finite elements

a transitivity analysis of bipartite rankings in pairwise multi class classification many multi class classification algorithms in statistics and machine learning typically combine several binary classifiers in order to construct an overall classifier in the popular pairwise ensemble one classifier is built for each pair of classes resulting in pairwise bipartite rankings in contrast ordinal regression algorithms consider a single ranking function for several ordered classes it is known in the literature that pairwise ensembles can be useful for ordinal regression however can single ranking models make a contribution to multi class classification the answer to this question should be affirmative as supported by theoretical results presented in this article we conduct a formal analysis of the consistency of pairwise bipartite rankings by uncovering the conditions under which they can be equivalently expressed in terms of a single ranking similar to the utility representability of pairwise preference relations it turns out that transitivity plays a crucial role in the characterization of the ranking representability of pairwise bipartite rankings to this end we introduce the new concepts of strict ranking representability a restrictive condition that can be verified easily and auc ranking representability a practically more useful condition that is more difficult to verify however the link between pairwise bipartite rankings and dice games allows us to formulate necessary transitivity conditions for auc ranking representability a sufficient condition on the other hand is obtained by introducing a new type of transitivity that can be verified by solving an integer quadratic program

canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant this article contains an elementary constructive proof of resolution of singularities in characteristic zero our proof applies in particular to schemes of finite type and to analytic spaces so we recover the great theorems of hironaka we introduce a discrete local invariant rm inv x a whose maximum locus determines a smooth centre of blowing up leading to desingularization to define rm inv x we need only to work with a category of local ringed spaces x x cal o x satisfying certain natural conditions if a in x then rm inv x a depends only on widehat cal o x a more generally rm inv x is defined inductively after any sequence of blowings up whose centres have only normal crossings with respect to the exceptional divisors and lie in the constant loci of rm inv x cdot the paper is self contained and includes detailed examples one of our goals is that the reader understand the desingularization theorem rather than simply know it is true

techniques for the study of singularities with applications to resolution of 2 dimensional schemes we give an overview of invariants of algebraic singularities over perfect fields we then show how they lead to a synthetic proof of embedded resolution of singularities of 2 dimensional schemes

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

resolution of singularities for 3 folds in positive characteristic a concise complete proof of resolution of singularities of 3 folds in positive characteristic 5 is given abhyankar first proved this theorem in 1966

on minimum fisher information distributions with restricted support and fixed variance fisher information is of key importance in estimation theory it also serves in inference problems as well as in the interpretation of many physical processes the mean squared estimation error for the location parameter of a distribution is bounded by the inverse of the fisher information associated with this distribution in this paper we look for minimum fisher information distributions with a restricted support more precisely we study the problem of minimizing the fisher information in the set of distributions with fixed variance defined on a bounded subset s of r or on the positive real line we show that the solutions of the underlying differential equation can be expressed in terms of whittaker functions then in the two considered cases we derive the explicit expressions of the solutions and investigate their behavior we also characterize the behavior of the minimum fisher information as a function of the imposed variance

simple hironaka resolution in characteristic zero building upon work of villamayor and bierstone milman we give a proof of the canonical hironaka principalization and desingularization the idea of homogenized ideals introduced in the paper gives a priori the canonicity of algorithm and radically simplifies the proof

geometries of quantum states the quantum analog of the fisher information metric of a probability simplex is searched and several riemannian metrics on the set of positive definite density matrices are studied some of them appeared in the literature in connection with cramer rao type inequalities or the generalization of the berry phase to mixed states they are shown to be stochastically monotone here all stochastically monotone riemannian metrics are characterized by means of operator monotone functions and it is proven that there exist a maximal and a minimal among them a class of metrics can be extended to pure states and a constant multiple of the fubini study metric appears in the extension

resolution of singularities of arithmetical threefolds ii abstract we prove grothendieck s conjecture on resolution of singularities for quasi excellent schemes x of dimension three and of arbitrary characteristic this applies in particular to x spec a a a reduced complete noetherian local ring of dimension three and to algebraic or arithmetical varieties of dimension three similarly if f is a number field a complete discretely valued field or more generally the quotient field of any excellent dedekind domain o any regular projective surface x f has a proper and flat model x over o which is everywhere regular

a history of graph entropy measures this survey seeks to describe methods for measuring the entropy of graphs and to demonstrate the wide applicability of entropy measures setting the scene with a review of classical measures for determining the structural information content of graphs we discuss graph entropy measures which play an important role in a variety of problem areas including biology chemistry and sociology in addition we examine relationships between selected entropy measures illustrating differences quantitatively with concrete examples

geometric transformations of multidimensional color images based on nass we present quantum algorithms to realize geometric transformations two point swappings symmetric flips local flips orthogonal rotations and translations based on an n qubit normal arbitrary superposition state nass these transformations are implemented using quantum circuits consisting of basic quantum gates which are constructed with polynomial numbers of single qubit and two qubit gates complexity analysis shows that the global operators symmetric flips local flips orthogonal rotations can be implemented with o n gates the proposed geometric transformations are used to facilitate applications of quantum images with low complexity

enhancing the security of quantum communication by hiding the message in a superposition a new method to hide specific quantum states in a superposition will be proposed the proposed method is used to hide an encrypted message in a superposition the process of hiding and unhiding the target quantum states is fast by using a single iteration of the amplitude amplification operators this makes the message 100 safe by direct measurement from an eavesdropper no entanglement sharing is required among the communicating parties

graph approach to quantum systems using a graph approach to quantum systems we show that descriptions of 3 dim kochen specker ks setups as well as descriptions of 3 dim spin systems by means of greechie diagrams a kind of lattice that we find in the literature are wrong correct lattices generated by mckay megill pavicic mmp hypergraphs and hilbert subspace equations are given to enable future exhaustive generation of 3 dim ks setups by means of our recently found stripping technique bipartite graph generation is used to provide us with lattices with equal numbers of elements and blocks orthogonal triples of elements up to 41 of them we obtain several new results on such lattices and hypergraphs in particular on properties such as superposition and orthoraguesian equations

almost etale resolution of foliations in the general this article addresses the nature of and relation between canonical and log canonical singularities of foliations by curves the case of equivariance under a finite group action has several peculiarities amongst which are examples from dimension 3 onward where no birational modification can be both gorenstein and log canonical the article in the specific i e a functorial resolution algorithm for foliated 3 folds in the 2 category of deligne mumford champs is thus not only optimal but natural

every place admits local uniformization in a finite extension of the function field we prove that every place p of an algebraic function field f k of arbitrary characteristic admits local uniformization in a finite extension f of f we show that f f can be chosen to be galois after a finite purely inseparable extension of the ground field k instead of being galois the extension can also be chosen such that the induced extension fp fp of the residue fields is purely inseparable and the value group of f only gets divided by the residue characteristic if f lies in the completion of an abhyankar place then no extension of f is needed our proofs are based solely on valuation theoretical theorems which are of particular importance in positive characteristic they are also applicable when working over a subring r k and yield similar results if r is regular and of dimension smaller than 3

resolution of singularities of real analytic vector fields in dimension three let be an analytic vector field defined in a real analytic manifold of dimension three we prove that all the singularities of can be made elementary by a finite number of blowing ups in the ambient space

the transport equation in the scaling invariant besov or essen janson peng xiao space abstract this paper addresses a well posedness of the weak solution to the transport equation describing how a scalar quantity is transported in a space with an initial data in the scaling invariant besov or essen janson peng xiao space via the boundedness of the left and right compositions acting on each space

renyi entropy rate for gaussian processes in this paper we introduce the definition of the conditional renyi entropy for continuous random variables and show that the so called chain rule holds then we use this rule to obtain another relation for getting the rate of renyi entropy using this relation and properties of the renyi entropy we obtain the renyi entropy rate for stationary gaussian processes finally we show that the bound for the renyi entropy rate is simply the shannon entropy rate and that the renyi entropy rate reduces to the shannon entropy rate as a 1

resolution of singularities of threefolds in positive characteristic i reduction to local uniformization on artin schreier and purely inseparable coverings abstract in dimension 3 the desingularization problem is reduced to local uniformization on artin schreier and purely inseparable coverings of regular space

the variety of modular basic algebras generated by mv chains and horizontal sums of three element chain basic algebras basic algebras or lattices with section antitone involutions turned out to be appropriate structures when axiomatizing both many valued and quantum logics see e g 11 the aim of the present paper is to describe the variety of basic algebras generated by mv chains and horizontal sums of three element chain basic algebras