aggregating local image descriptors into compact codes this paper addresses the problem of large scale image search three constraints have to be taken into account search accuracy efficiency and memory usage we first present and evaluate different ways of aggregating local image descriptors into a vector and show that the fisher kernel achieves better performance than the reference bag of visual words approach for any given vector dimension we then jointly optimize dimensionality reduction and indexing in order to obtain a precise vector comparison as well as a compact representation the evaluation shows that the image representation can be reduced to a few dozen bytes while preserving high accuracy searching a 100 million image data set takes about 250 ms on one processor core

an axiomatization of the algebra of petri net concatenable processes the concatenable processes of a petri net n can be characterized abstractly as the arrows of a symmetric monoidal category view the mathml source n however this is only a partial axiomatization since it is based on a concrete ad hoc chosen category of symmetries symn in this paper we give a completely abstract characterization of the category of concatenable processes of n thus yielding an axiomatic theory of the noninterleaving behaviour of petri nets

the non sequential behaviour of petri nets the idea of representing non sequential processes as partially ordered sets occurrence nets is applied to place transition nets petri nets based on the well known notion of process for condition event systems for occurrence nets some theorems relating k density cut finiteness and discreteness are proved with these theorems the result that a place transition net is bounded if and only if its processes are k dense is obtained

determinism event structure isomorphism step sequence equivalence abstract a concurrent system s is called determinism if for all states s of s we have that whenever s can evolve from state s into states s and s by doing an action a it must be the case that s equals s it is well known that for deterministic concurrent systems most of the interleaved equivalences bisimulation failure trace equivalence coincide in this paper we prove in the setting of event structures that also most of the non interleaved equivalences coincide with each other on this domain in the last section of the paper we show that as a consequence of our result the causal structure of a deterministic concurrent system can be unravelled by observers who are capable of observing the beginning and termination of events

sequential and concurrent behaviour in petri net theory abstract two ways of describing the behaviour of concurrent systems have widely been suggested arbitrary interleaving and partial orders sometimes the latter has been claimed superior because concurrency is represented in a true way on the other hand some authors have claimed that the former is sufficient for all practical purposes petri net theory offers a framework in which both kinds of semantics can be defined formally and hence compared with each other occurence sequences correspond to interleaved behaviour while the notion of a process is used to capture partial order semantics this paper aims at obtaining formal results about the relationship between various classes of processes and occurence sequences in net theory we shall compare an axiomatic approach to the definition of processes with an inductive approach which relates processes to occurence sequences and generalisations thereof we shall show that in general axiomatic process semantics is more powerful than inductive semantics using occurence sequences however we shall also show that the latter can be generalised or the former be restricted to yield various equivalence results the structure of the relation between sequences and processes will also be explored exhibiting two meaningful relations one on the sequences and one on the processes which correspond to each other bijectively we shall apply and simplify the theory to the practically important case of nets which are of finite synchronisation and 1 safe

an extension of kleene s and ochman ski s theorems to infinite traces abstract as was noted by mazurkiewicz traces constitute a convenient tool for describing finite behaviour of concurrent systems extending in a natural way mazurkiewicz s original definition infinite traces have recently been introduced enabling one to deal with infinite behaviour of nonterminating concurrent systems in this paper we examine the basic families of recognizable sets and of rational sets of infinite traces the seminal kleene characterization of recognizable subsets of the free monoid and its subsequent extensions to infinite words due to buchi and to finite traces due to ochmanski are the cornerstones of the corresponding theories the main result of our paper is an extension of these characterizations to the domain of infinite traces using recognizing and weakly recognizing morphisms as well as a generalization of the schutzenberger product of monoids we prove various closure properties of recognizable trace languages moreover we establish normal form representations for recognizable and rational sets of infinite traces

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

a causal semantics for time petri nets the objective of this work is to give time petri nets a partial order semantics akin to the nonsequential processes of untimed net systems to this end a time process of a time petri net is defined as a traditionally constructed causal process with a valid timing a timing is a labelling that attaches occurrence times to the events of the process that must satisfy specific validness criteria the main result of the paper is the bijective correspondence between firing schedules the classical interleaving semantics of time petri nets and linearizations of time processes the result shows that time processes correctly represent the behavior of the system using the definition of validness an efficient algorithm for checking validness of given timings is derived also a sufficient condition is given for when the invalidity of timings for a process can be inferred from its initial subprocess to compute e g the maximum time separation between two events in a time process an alternative characterization of validness is developed this definition is used to derive an algorithm for constructing the set of all valid timings for a process the set of valid timings is presented as sets of alternative linear constraints which can be used in optimization problems it is shown that the existence of a valid timing for a given process can be decided in np time

configuration structures event structures and petri nets in this paper the correspondence between safe petri nets and event structures due to nielsen plotkin and winskel is extended to arbitrary nets without self loops under the collective token interpretation to this end we propose a more general form of event structure matching the expressive power of such nets these new event structures and nets are connected by relating both notions with configuration structures which can be regarded as representations of either event structures or nets that capture their behaviour in terms of action occurrences and the causal relationships between them but abstract from any auxiliary structure a configuration structure can also be considered logically as a class of propositional models or equivalently as a propositional theory in disjunctive normal from converting this theory to conjunctive normal form is the key idea in the translation of such a structure into a net for a variety of classes of event structures we characterise the associated classes of configuration structures in terms of their closure properties as well as in terms of the axiomatisability of the associated propositional theories by formulae of simple prescribed forms and in terms of structural properties of the associated petri nets

petri nets are moniods abstract petri nets are widely used to model concurrent systems however their composition and abstraction mechanisms are inadequate we solve this problem in a satisfactory way we start by remarking that place transition petri nets can be viewed as ordinary directed graphs equipped with two algebraic operations corresponding to parallell and sequential composition of transitions a distributive law between the two operations captures a basic fact about concurrency new morphisms are defined mapping single atomic transitions into whole computations thus relating system descriptions at different levels of abstraction categories equipped with products and coproducts corresponding to parallel and nondeterministic compositions are introduced for petri nets with and without initial markings petri net duality is expressed as a duality functor and several new invariants are introduced a tensor product is defined on nets and their category is proved to be symmetric monoidal closed this construction is generalized to a large class of algebraic theories on graphs these results provide a formal basis for expressing the semantics of concurrent languages in terms of petri nets they also provide a new understanding of concurrency in terms of algebraic structures over graphs and categories that should apply to other models besides petri nets and thus contribute to the conceptual unification of concurrency

strengths and weaknesses of quantum computing recently a great deal of attention has been focused on quantum computation following a sequence of results bernstein and vazirani in proc 25th annual acm symposium theory comput 1993 pp 11 20 siam j comput 26 1997 pp 1277 1339 simon in proc 35th annual ieee symposium foundations comput sci 1994 pp 116 123 siam j comput 26 1997 pp 1340 1349 shor in proc 35th annual ieee symposium foundations comput sci 1994 pp 124 134 suggesting that quantum computers are more powerful than classical probabilistic computers following shor s result that factoring and the extraction of discrete logarithms are both solvable in quantum polynomial time it is natural to ask whether all of np can be efficiently solved in quantum polynomial time in this paper we address this question by proving that relative to an oracle chosen uniformly at random with probability 1 the class np cannot be solved on a quantum turing machine qtm in time o 2 n 2 we also show that relative to a permutation oracle chosen uniformly at random with probability 1 the class np cap conp cannot be solved on a qtm in time o 2 n 3 the former bound is tight since recent work of grover in it proc 28 th annual acm symposium theory comput 1996 shows how to accept the class np relative to any oracle on a quantum computer in time o 2 n 2

generalized om bisimulation history preserving bisimilarity and maximality preserving bisimilarity take full account of the interplay between causality and branching and they are congruences w r t action refinement for suitable classes of petri nets but even for finite safe petri nets they are based on possibly infinite transition systems and it is not obvious how to decide them om bisimulation gives a characterization of history preserving bisimulation for safe nets without internal moves and it allows a decidability result in this paper we generalize om bisimulation and this decidability result to safe nets with internal moves and also treat the case of maximality preserving bisimulation

complexity results for 1 safe nets we study the complexity of several standard problems for 1 safe petri nets and some of its subclasses we prove that reachability liveness and deadlock are all pspace complete for 1 safe nets we also prove that deadlock is np complete for free choice nets and for 1 safe free choice nets finally we prove that for arbitrary petri nets deadlock is equivalent to reachability and liveness

unfolding semantics of graph transformation several attempts have been made of extending to graph grammars the unfolding semantics originally developed by winskel for safe petri nets but only partial results were obtained in this paper we fully extend winskel s approach to single pushout grammars providing them with a categorical concurrent semantics expressed as a coreflection between the category of semi weighted graph grammars and the category of prime algebraic domains which factorises through the category of occurrence grammars and the category of asymmetric event structures for general possibly nonsemi weighted single pushout grammars we define an analogous functorial concurrent semantics which however is not characterised as an adjunction similar results can be obtained for double pushout graph grammars under the assumptions that nodes are never deleted

zero safe nets comparing the collective and individual token approaches abstract the main feature of zero safe nets is a primitive notion of transition synchronization to this aim besides ordinary places called stable places zero safe nets are equipped with zero places which in an observable marking cannot contain any token this yields the notion of transaction a basic atomic computation which may use zero tokens as triggers but defines an evolution between observable markings only the abstract counterpart of a generic zero safe net b consists of an ordinary p t net whose places are the stable places of b and whose transitions represent the transactions of b the two nets offer the refined and the abstract models of the same system respectively where the former can be much smaller than the latter because of the transition synchronization mechanism depending on the chosen approach collective vs individual token philosophy two notions of transaction may be defined each leading to different operational and abstract models their comparison is fully discussed on the basis of a multicasting system example in the second part of the paper we make use of category theory to analyze and motivate our framework more precisely the two operational semantics of zero safe nets are characterized as adjunctions and the derivation of abstract p t nets as coreflections

comparing logics for rewriting the large diffusion of concurrent and distributed systems has spawned in recent years a variety of new formalisms equipped with features for supporting an easy specification of such systems the aim of our paper is to analyze three proposals namely rewriting logic action calculi and tile logic chosen among those formalisms designed for the description of rule based systems for each of these logics we first try to understand their foundations then we briefly sketch some applications the overall goal of our work is to find out a common layout where these logics can be recast thus allowing for a comparison and an evaluation of their specific features

on the power of ambainis lower bounds the polynomial method and the ambainis lower bound or alb for short method are two main quantum lower bound techniques while recently ambainis showed that the polynomial method is not tight the present paper aims at studying the power and limitation of alb s we first use known alb s to derive n1 5 lower bounds for bipartiteness bipartiteness matching and graph matching in which the lower bound for bipartiteness improves the previous n one we then show that all the three known ambainis lower bounds have a limitation n min c0 f c1 f where c0 f and c1 f are the 0 and 1 certificate complexities respectively this implies that for many problems such as triangle k clique bipartiteness and bipartite graph matching which draw wide interest and whose quantum query complexities are still open the best known lower bounds cannot be further improved by using ambainis techniques another consequence is that all the ambainis lower bounds are not tight for total functions this upper bound for alb s can be further improved to min c0 f c1 f n ci f where ci f is the size of max intersection of a 0 and a 1 certificate set again this implies that alb s cannot improve the best known lower bound for some specific problems such as and or tree whose precise quantum query complexity is still open finally we generalize the three known alb s and give a new alb style lower bound method which may be easier to use for some problems

dimension reduction by local principal component analysis reducing or eliminating statistical redundancy between the components of high dimensional vector data enables a lower dimensional representation without significant loss of information recognizing the limitations of principal component analysis pca researchers in the statistics and neural network communities have developed nonlinear extensions of pca this article develops a local linear approach to dimension reduction that provides accurate representations and is fast to compute we exercise the algorithms on speech and image data and compare performance with pca and with neural network implementations of nonlinear pca we find that both nonlinear techniques can provide more accurate representations than pca and show that the local linear techniques outperform neural network implementations

a coalgebraic presentation of structured transition systems this paper relates labelled transition systems and coalgebras with the motivation of comparingand combiningtheir complementary contributions to the theory of concurrent systems the well known mismatch between these two notions concerningthe morphisms is resolved by extendingthe coalg ebraic framework by lax cohomomorphisms enriching both labelled transition systems and coalgebras with algebraic structure for an algebraic speci cation the correspondence is lost again this motivates the introduction of lax coalgebras where the coalgebra structure is given by a lax homomorphism the resulting category of lax coalgebras and lax cohomomorphisms for a suitable endofunctor is shown to be isomorphic to the category of structured transition systems where both states and transitions form algebras the framework is also presented on a more abstract categorical level using monads and comonads extendingthe bialgebraic approach introduced by turi and plotkin c 2001 elsevier science b v all rights reserved

the box algebra petri nets process expressions the paper describes a petri net as well as a structural operational semantics for an algebra of process expressions it specifically addresses this problem for the box algebra a model of concurrent computation which combines petri nets and standard process algebras the main result is that it is possible to obtain a framework where process expressions can be given two entirely consistent kinds of semantics one based on petri nets the other on sos rules this consistency can also be extended to a partial order semantics

quantum query complexity of minor closed graph properties we study the quantum query complexity of minor closed graph properties which include such problems as determining whether an n vertex graph is planar is a forest or does not contain a path of a given length we show that most minor closed properties those that cannot be characterized by a finite set of forbidden subgraphs have quantum query complexity theta n 3 2 to establish this we prove an adversary lower bound using a detailed analysis of the structure of minor closed properties with respect to forbidden topological minors and forbidden subgraphs on the other hand we show that minor closed properties and more generally sparse graph properties that can be characterized by finitely many forbidden subgraphs can be solved strictly faster in o n 3 2 queries our algorithms are a novel application of the quantum walk search framework and give improved upper bounds for several subgraph finding problems

an event structure semantics for general petri nets abstract in this paper we address the following question what type of event structures are suitable for representing the behaviour of general petri nets as a partial answer to this question we define a new class of event structures called local event structures and identify a subclass called ul event structures we propose that ul event structures are appropriate for capturing the behaviour of general petri nets our answer is a partial one in that in the proposed event structure semantics auto concurrency is filtered out from the behaviour of petri nets it turns out that this limited event structure semantics for petri nets is nevertheless a non trivial and conservative extension of the prime event structure semantics of 1 safe petri nets provided in nielsen et al 1981 we also show that the strong relationship between prime event structures and 1 safe petri nets established in a categorical framework in winskel 1987 can be extended to the present setting provided we restrict our attention to the subclass of petri nets whose behaviours do not exhibit any auto concurrency finally we show that winskel s general and stable event structures can be smoothly related to local event structures and that similarly prime event structures can be related to ul event structures

product quantization for nearest neighbor search this paper introduces a product quantization based approach for approximate nearest neighbor search the idea is to decompose the space into a cartesian product of low dimensional subspaces and to quantize each subspace separately a vector is represented by a short code composed of its subspace quantization indices the euclidean distance between two vectors can be efficiently estimated from their codes an asymmetric version increases precision as it computes the approximate distance between a vector and a code experimental results show that our approach searches for nearest neighbors efficiently in particular in combination with an inverted file system results for sift and gist image descriptors show excellent search accuracy outperforming three state of the art approaches the scalability of our approach is validated on a data set of two billion vectors

quantum query complexity of some graph problems quantum algorithms for graph problems are considered both in the adjacency matrix model and in an adjacency list like array model we give almost tight lower and upper bounds for the bounded error quantum query complexity of connectivity strong connectivity minimum spanning tree and single source shortest paths for example we show that the query complexity of minimum spanning tree is in theta n 3 2 in the matrix model and in theta sqrt nm in the array model while the complexity of connectivity is also in theta n 3 2 in the matrix model but in theta n in the array model the upper bounds utilize search procedures for finding minima of functions under various conditions

maximality preserving bisimulation abstract a new bisimulation notion is introduced for the specification of concurrent systems which resists to a large class of action refinements even in the presence of invisible actions the work is presented in the context of labelled p t nets but it may be transported to other popular frameworks like prime event structures process graphs etc

functional behavior of nondeterministic and concurrent programs the functions behavior of a deterministic program segment is a function f d d where d is some set of states for the computation this notion of functional behavior can be extended to nondeterministic and concurrent programs using techniques from linear algebra in particular the functional behavior of a nondeterministic program segment is a linear transformation f a a where a is a free semiring module other notions from linear algebra carry over into this setting for example weakest preconditions and predicate transformers correspond to well studied concepts in linear algebra using multilinear algebra programs with tuples of inputs and outputs can be handled for nondeterministic concurrent programs the functional behavior is a linear transformation f a a where a is a free semiring algebra in this case f may also be an algebra morphism which indicates that the program involves no interprocess communication finally a model of syntax for programs is studied whose semantics is given using linear algebra it is shown that in this model free interpretations essentially herbrand universes do not generally exist

an algebraic description of system behaviours abstract the paper is an attempt of characterizing algebraically the sets of processes generated by systems a characterization is given for discrete systems which are equivalent to the condition event systems in the sense of petri the stress is put on the existing concurrency of processes main feature of the approach is that processes are regarded as primitives which need not to be defined only relationships between processes are described and this is done in terms of two partial operations of composing processes sequentially and in parallel natural axioms are imposed on these operations such that the resulting structure of processes of a system can be represented as a partial algebra of labelled partially ordered sets of a sort with suitable compositions in particular from the axiomatic characterization of behaviour a process concept and other related concepts can be derived

a trace semantics for petri nets a generalization of the notion of trace is proposed this enables us to associate with each petri net a single behavioural object namely a poset of generalized traces a characterization is given of the trace languages defined by petri nets we show that the general event structures of winskel and the stable event structures can also be characterized in terms of our trace languages one consequence is that in this framework stable event structures general event structures and petri nets constitute a strictly ascending chain in terms of expressive power

a framework for the verification of infinite state graph transformation systems we propose a technique for the analysis of infinite state graph transformation systems based on the construction of finite structures approximating their behaviour following a classical approach one can construct a chain of finite under approximations k truncations of the winskel style unfolding of a graph grammar more interestingly also a chain of finite over approximations k coverings of the unfolding can be constructed the fact that k truncations and k coverings approximate the unfolding with arbitrary accuracy is formalised by showing that both chains converge in a categorical sense to the full unfolding we discuss how the finite over and under approximations can be used to check properties of systems modelled by graph transformation systems illustrating this with some small examples we also describe the augur tool which provides a partial implementation of the proposed constructions and has been used for the verification of larger case studies

petr nets algebras morphisms and compositionality abstract it is shown how a category of petri nets can be viewed as a subcategory of two sorted algebras over multisets this casts petri nets in a familiar framework and provides a useful idea of morphism on nets different from the conventional definition the morphisms here respect the behaviour of nets the categorical constructions which result provide a useful way to synthesise nets and reason about nets in terms of their components for example various forms of parallel composition of petri nets arise naturally from the product in the category this abstract setting makes plain a useful functor from the category of petri nets to a category of spaces of invariants and provides insight into the generalisations of the basic definition of petri nets for instance the coloured and higher level nets of kurt jensen arise through a simple modification of the sorts of the algebras underlying nets further it provides a smooth formal relation with other models of concurrency such as milner s calculus of communicating systems ccs and hoare s communicating sequential processes csp though this is only indicated in this paper

improving bag of features for large scale image search this article improves recent methods for large scale image search we first analyze the bag of features approach in the framework of approximate nearest neighbor search this leads us to derive a more precise representation based on hamming embedding he and weak geometric consistency constraints wgc he provides binary signatures that refine the matching based on visual words wgc filters matching descriptors that are not consistent in terms of angle and scale he and wgc are integrated within an inverted file and are efficiently exploited for all images in the dataset we then introduce a graph structured quantizer which significantly speeds up the assignment of the descriptors to visual words a comparison with the state of the art shows the interest of our approach when high accuracy is needed experiments performed on three reference datasets and a dataset of one million of images show a significant improvement due to the binary signature and the weak geometric consistency constraints as well as their efficiency estimation of the full geometric transformation i e a re ranking step on a short list of images is shown to be complementary to our weak geometric consistency constraints our approach is shown to outperform the state of the art on the three datasets

operational and denotational semantics for the box algebra this paper describes general theory underpinning the operational semantics and the denotational petri net semantics of the box algebra including recursion for the operational semantics inductive rules for process expressions are given for the net semantics a general mechanism of refinement and relabelling is introduced using which the connectives of the algebra are defined the paper also describes a denotational approach to the petri net semantics of recursive expressions a domain of nets is identified such that the solution of a given recursive equation can be found by fixpoint approximation from some suitable starting point the consistency of the two semantics is demonstrated the theory is generic for a wide class of algebraic operators and synchronisation schemes

probabilistic principal component analysis principal component analysis pca is a ubiquitous technique for data analysis and processing but one which is not based upon a probability model in this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum likelihood estimation of parameters in a latent variable model closely related to factor analysis we consider the properties of the associated likelihood function giving an em algorithm for estimating the principal subspace iteratively and discuss the advantages conveyed by the definition of a probability density function for pca

conditional rewriting logic as a unified model of concurrency abstract rewriting with conditional rewrite rules modulo a set e of structural axioms provides a general framework for unifying a wide variety of models of concurrency concurrent rewriting coincides with logical deduction in conditional rewriting logic a logic of actions whose models are concurrent systems this logic is sound and complete and has initial models in addition to general models interpreted as concurrent systems which provide a more operational style of semantics more restricted semantics with an incresingly denotational flavor such as preorder poset cpo and standard algebraic models appear as special cases of the model theory this permits dealing with operational and denotational issues within the same model theory and logic a programming language called maude whose modules are rewriting logic theories is defined and given denotational and operational semantics maude provides a simple unification of concurrent programming with functional and object oriented programming and supports high level declarative programming of concurrent systems

relaxed models for rewriting logic we modify the definition of the models for rewrite theories by replacing the equality of functors defined by e equal terms with the equality via a natural isomorphism called natural symmetry the relaxation process can be adapted by relaxing all or only a part of the equations and by relaxing the state structure and implicitly the computation structure or just the computation structure we also consider the subclasses of c coherent models where c is a set of equations specifying a collection of commutative symmetry diagrams the result is a wide palette of model classes which offers more flexibility in modeling concurrent systems

process versus unfolding semantics for place transition petri nets in the last few years the semantics of petri nets has been investigated in several different ways apart from the classical token game one can model the behaviour of petri nets via non sequential processes via unfolding constructions which provide formal relationships between nets and domains and via algebraic models which view petri nets as essentially algebraic theories whose models are monoidal categories in this paper we show that these three points of view can be reconciled in our formal development a relevant role is played by cdecocc a category of occurrence nets appropriately decorated to take into account the history of tokens the structure of decorated occurrence nets at the same time provides natural unfoldings for place transition pt nets and suggests a new notion of processes the decorated processes which induce on petri nets the same semantics as that of unfolding in addition we prove that the decorated processes of a net can be axiomatized as the arrows of a symmetric monoidal category which therefore provides the aforesaid unification

normal forms for algebras of connections recent years have seen a growing interest towards algebraic structures that are able to express formalisms different from the standard tree like presentation of terms many of these approaches reveal a specific interest towards the application to the distributed and concurrent systems field but an exhaustive comparison between them is sometimes difficult because their presentations can be quite dissimilar this work is a first step towards a unified view focusing on the primitive ingredients of distributed spaces namely interfaces links and basic modules we introduce a general schema for describing a normal form presentation of many algebraic formalisms and show that those normal forms can be thought of as arrows of suitable monoidal categories

functorial models for petri nets we show that although the algebraic semantics of place transition petri nets under the collective token philosophy can be fully explained in terms of strictly symmetric monoidal categories the analogous construction under the individual token philosophy is not completely satisfactory because it lacks universality and also functoriality we introduce the notion of pre nets to overcome this obtaining a fully satisfactory categorical treatment where the operational semantics of nets yields an adjunction this allows us to present a uniform logical description of net behaviors under both the collective and the individual token philosophies in terms of theories and theory morphisms in partial membership equational logic moreover since the universal property of adjunctions guarantees that colimit constructions on nets are preserved in our algebraic models the resulting semantic framework has good compositional properties

planning as satisfiability parallel plans and algorithms for plan search we address two aspects of constructing plans efficiently by means of satisfiability testing efficient encoding of the problem of existence of plans of a given number t of time points in the propositional logic and strategies for finding plans given these formulae for different values of t for the first problem we consider three semantics for plans with parallel operator application in order to make the search for plans more efficient the standard semantics requires that parallel operators are independent and can therefore be executed in any order we consider a more relaxed definition of parallel plans which was first proposed by dimopoulos et al as well as a normal form for parallel plans that requires every operator to be executed as early as possible we formalize the semantics of parallel plans emerging in this setting and present translations of these semantics into the propositional logic the sizes of the translations are asymptotically optimal each of the semantics is constructed in such a way that there is a plan following the semantics exactly when there is a sequential plan and moreover the existence of a parallel plan implies the existence of a sequential plan with as many operators as in the parallel one for the second problem we consider strategies based on testing the satisfiability of several formulae representing plans of n time steps for several values of n concurrently by several processes we show that big efficiency gains can be obtained in comparison to the standard strategy of sequentially testing the satisfiability of formulae for an increasing number of time steps

on the geometry and algebra of networks with state in 1 an algebra of automata with interfaces span graph was introduced with main operation being communicating parallel composition a system is represented by an expression in this algebra a system so described has two aspects an informal network geometry arising from the algebraic expression and a space of states and transition given by its evaluation in span graph note that span graph yields purely compositional descriptions of systems in this paper we give an alternative globally non compositional view of the same systems in order to do this we make mathematically precise the network geometry in terms of monoidal graphs and assignment of state in terms of morphisms of monoidal graphs we call such globally described systems networks with state to relate networks with state and span graph systems we use the algebra of cospans of monoidal graphs as an illustration we give a new representation of a non compositionally described class of petri nets in the compositional setting of span graph we also present a tool for calculating with networks with state both algebras of spans and of cospans are symmetric monoidal categories with commutative separable algebra structures on the objects we include a short section following 2 in which we show that a simple modification of the algebra allows the description of networks in which the tangling of connectors may be represented yielding a connection with the theory of knots

mixture of subspaces image representation and compact coding for large scale image retrieval there are two major approaches to content based image retrieval using local image descriptors one is descriptor by descriptor matching and the other is based on comparison of global image representation that describes the set of local descriptors of each image in large scale problems the latter is preferred due to its smaller memory requirements however it tends to be inferior to the former in terms of retrieval accuracy to achieve both low memory cost and high accuracy we investigate an asymmetric approach in which the probability distribution of local descriptors is modeled for each individual database image while the local descriptors of a query are used as is we adopt a mixture model of probabilistic principal component analysis the model parameters constitute a global image representation to be stored in database then the likelihood function is employed to compute a matching score between each database image and a query we also propose an algorithm to encode our image representation into more compact codes experimental results demonstrate that our method can represent each database image in less than several hundred bytes achieving higher retrieval accuracy than the state of the art method using fisher vectors