voevodsky s mixed motives versus kontsevich s noncommutative mixed motives abstract we prove that the quotient of voevodsky s category of geometric mixed motives dm gm by the endofunctor q 1 2 embeds fully faithfully into kontsevich s category of noncommutative mixed motives kmm we show moreover that this embedding is compatible with the one between chow motives and noncommutative chow motives along the way we relate kmm with morel voevodsky s stable a 1 homotopy category recover the twisted algebraic k theory of kahn levine from kmm and extend elmendorf mandell s foundational work on multicategories to a broader setting

models of social networks based on social distance attachment we propose a class of models of social network formation based on a mathematical abstraction of the concept of social distance social distance attachment is represented by the tendency of peers to establish acquaintances via a decreasing function of the relative distance in a representative social space we derive analytical results corroborated by extensive numerical simulations showing that the model reproduces the main statistical characteristics of real social networks large clustering coefficient positive degree correlations and the emergence of a hierarchy of communities the model is confronted with the social network formed by people that shares confidential information using the pretty good privacy pgp encryption algorithm the so called web of trust of pgp

model categories of diagram spectra working in the category mathcal t of based spaces we give the basic theory of diagram spaces and diagram spectra these are functors mathcal d longrightarrow mathcal t for a suitable small topological category mathcal d when mathcal d is symmetric monoidal there is a smash product that gives the category of mathcal d spaces a symmetric monoidal structure examples include begin enumerate item prespectra as defined classically item symmetric spectra as defined by jeff smith item orthogonal spectra a coordinate free analogue of symmetric spectra with symmetric groups replaced by orthogonal groups in the domain category item gamma spaces as defined by graeme segal item mathcal w spaces an analogue of gamma spaces with finite sets replaced by finite cw complexes in the domain category end enumerate we construct and compare model structures on these categories with the caveat that gamma spaces are always connective these categories and their simplicial analogues are quillen equivalent and their associated homotopy categories are equivalent to the classical stable homotopy category monoids in these categories are strict ring spectra often the subcategories of ring spectra module spectra over a ring spectrum and commutative ring spectra are also model categories when this holds the respective categories of ring and module spectra are quillen equivalent and thus have equivalent homotopy categories this allows interchangeable use of these categories in applications 2000 mathematics subject classification primary 55p42 secondary 18a25 18e30 55u35

algebraic cycles and higher k theory here g x is the grothendieck group of coherent sheaves on x 13 gr refers to the graded group defined by the y filtration on g x cf kratzer 14 soult 20 and ch x is the chow group of codimension i algebraic cycles defined by fulton 9 the left hand isomorphism is a formal consequence of the existence of a i structure on g x while the existence of r is the central theme of the b f m rr theorem the main purpose of this paper is to define a theory of higher chow groups ch x n n 2 0 so as to obtain isomorphisms

rings modules and algebras in infinite loop space theory we give a new construction of the algebraic k theory of small permutative categories that preserves multiplicative structure and therefore allows us to give a unified treatment of rings modules and algebras in both the input and output this requires us to define multiplicative structure on the category of small permutative categories the framework we use is the concept of multicategory elsewhere also called colored operad a generalization of symmetric monoidal category that precisely captures the multiplicative structure we have present at all stages of the construction our method ends up in the hovey shipley smith category of symmetric spectra with an intermediate stop at a category of functors out of a particular wreath product

locating invariant tori for a family of two dimensional hamiltonian mappings departamento de estatistica matemat apl e computaoinstituto de geociencias e ciencias exatas unesp univ estadual paulista av 24a 1515bela vista cep 13506 900 rio claro sp

advanced modularity specialized label propagation algorithm for detecting communities in networks abstract a modularity specialized label propagation algorithm lpam for detecting network communities was recently proposed this promising algorithm offers some desirable qualities however lpam favors community divisions where all communities are similar in total degree and thus it is prone to get stuck in poor local maxima in the modularity space to escape local maxima we employ a multistep greedy agglomerative algorithm msg that can merge multiple pairs of communities at a time combining lpam and msg we propose an advanced modularity specialized label propagation algorithm lpam experiments show that lpam successfully detects communities with higher modularity values than ever reported in two commonly used real world networks moreover lpam offers a fair compromise between accuracy and speed

additive invariants of toric and twisted projective homogeneous varieties via noncommutative motives abstract i panin proved in the nineties that the algebraic k theory of twisted projective homogeneous varieties can be expressed in terms of central simple algebras later merkurjev and panin described the algebraic k theory of toric varieties as a direct summand of the algebraic k theory of separable algebras in this article making use of the recent theory of noncommutative motives we extend panin and merkurjev panin s computations from algebraic k theory to every additive invariant as a first application we fully compute the cyclic homology and all its variants of twisted projective homogeneous varieties as a second application we show that the noncommutative motive of a twisted projective homogeneous variety is trivial if and only if the brauer classes of the associated central simple algebras are trivial along the way we construct a fully faithful functor from merkurjev panin s motivic category to kontsevich s category of noncommutative chow motives which is of independent interest

finding community structure in networks using the eigenvectors of matrices we consider the problem of detecting communities or modules in networks groups of vertices with a higher than average density of edges connecting them previous work indicates that a robust approach to this problem is the maximization of the benefit function known as modularity over possible divisions of a network here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix which plays a role in community detection similar to that played by the graph laplacian in graph partitioning calculations this result leads us to a number of possible algorithms for detecting community structure as well as several other results including a spectral measure of bipartite structure in networks and a centrality measure that identifies vertices that occupy central positions within the communities to which they belong the algorithms and measures proposed are illustrated with applications to a variety of real world complex networks

critical exponents for a transition from integrability to non integrability via localization of invariant tori in the hamiltonian system critical exponents that describe a transition from integrability to nonintegrability in a two dimensional nonlinear and area preserving map are obtained via localization of the first invariant spanning curve invariant tori in the phase space in a general class of systems the position of the first invariant tori is estimated by reducing the mapping of the system to the standard mapping where a transition takes place from local to global chaos the phase space of the mapping shows a large chaotic sea surrounding periodic islands and limited by a set of invariant tori whose position of the first of them depends on the control parameters the formalism leads us to obtain analytically critical exponents that describe the behaviour of the average variable action along the chaotic sea the result is compared to several models in the literature confirming the approach is of large interest the formalism used is general and the procedure can be extended to many other different systems

finding critical exponents for two dimensional hamiltonian maps two dimensional nonlinear area preserving mappings have been considered in the study of dynamical systems for many years applications of this formalism can be used in study of channel flows waveguide transport properties fermi acceleration and also for the study of magnetic field lines in toroidal plasma devices with reversed shear such as tokamaks1 10 generally such kind of mappings have one or more control parameters they can control the intensity of the nonlinearity controlling also a transition from integrability to nonintegrability the phase space of these mappings exhibit quite often mixed forms one can observe a large chaotic sea that eventually surrounds kolmogorov arnold moser islands and is limited by a set of invariant tori the size of the chaotic sea is strongly influenced by the control parameters since they play the rule of controlling the intensity of the nonlinearity in this paper we address specifically a transition from integrability to nonintegrability present in a special class of two dimensional nonlinear area preserving mappings we look at average properties along the chaotic sea and therefore we find critical exponents that describe the behavior of average quantities of the chaotic sea such quantities are described in terms of scaling arguments leading to a generic and robust description of a scaling observed for the chaotic sea the critical exponents are obtained for several values of the control parameters the knowledge of such exponents allow us to define and compare classes of universality for the two dimensional hamiltonian mappings the paper is organized as follows in sec ii we present the model and discuss the variables and control parameters used some properties of the phase space are also discussed including a characterization of fixed points the chaotic component of the phase space is characterized by lyapunov exponents in sec iii we obtain and describe the critical exponents that define classes of universality a merger of all the curves of the average quantity is obtained finally in the sec iv we present our concluding remarks ii definition of the problem and the mapping in this section we present and discuss some dynamical properties for a set of two dimensional hamiltonian mappings we assume that there is a two dimensional integrable system that is slightly perturbed the hamiltonian function that in principle describes the system is written as 11

higher homotopy excision and blakers massey theorems for structured ring spectra abstract working in the context of symmetric spectra we prove higher homotopy excision and higher blakers massey theorems and their duals for algebras and left modules over operads in the category of modules over a commutative ring spectrum e g structured ring spectra

the grothendieck construction for model categories the grothendieck construction is a classical correspondence between diagrams of categories and cocartesian fibrations over the indexing category in this paper we consider the analogous correspondence in the setting of model categories as a main result we establish an equivalence between suitable diagrams of model categories indexed by m and a new notion of model fibrations over m when m is a model category our construction endows the grothendieck construction with a model structure which gives a presentation of lurie s categorical grothendieck construction and enjoys several good formal properties we apply our construction to various examples yielding model structures on strict and weak group actions and on modules over algebra objects in suitable monoidal model categories

negative k theory of derived categories we define negative k groups for exact categories and for derived categories in the framework of frobenius pairs generalizing definitions of bass karoubi carter pedersen weibel and thomason we prove localization and vanishing theorems for these groups devissage for noetherian abelian categories additivity and resolution hold we show that the first negative k group of an abelian category vanishes and that in general negative k groups of a noetherian abelian category vanish our methods yield an explicit non connective delooping of the k theory of exact categories and chain complexes generalizing constructions of wagoner and pedersen weibel extending a theorem of auslander and sherman we discuss the k theory homotopy fiber of e e and its implications for negative k groups in the appendix we replace waldhausen s cylinder functor by a slightly weaker form of non functorial factorization which is still sufficient to prove his approximation and fibration theorems

column generation algorithms for exact modularity maximization in networks finding modules or clusters in networks currently attracts much attention in several domains the most studied criterion for doing so due to newman and girvan phys rev e 69 026113 2004 is modularity maximization many heuristics have been proposed for maximizing modularity and yield rapidly near optimal solution or sometimes optimal ones but without a guarantee of optimality there are few exact algorithms prominent among which is a paper by xu et al eur phys j b 60 231 2007 modularity maximization can also be expressed as a clique partitioning problem and the row generation algorithm of grotschel and wakabayashi math program 45 59 1989 applied we propose to extend both of these algorithms using the powerful column generation methods for linear and non linear integer programming performance of the four resulting algorithms is compared on problems from the literature instances with up to 512 entities are solved exactly moreover the computing time of previously solved problems are reduced substantially

chaotic properties of a time modulated barrier some chaotic properties of a classical particle interacting with a time modulated barrier are studied the dynamics of this problem is obtained by use of a two dimensional nonlinear area preserving map the chaotic low energy region is characterized in terms of lyapunov exponents the time that the particle stays trapped in the well is such that the distributions of successive reflections and of the corresponding successive reflection times obey power laws with the same exponent using time series analysis we show that the chaotic sea exhibits an interesting scaling property over a large range of control parameters our results indicate that the particle experiences unlimited energy growth when the barrier behaves randomly

modularity and community detection in bipartite networks the modularity of a network quantifies the extent relative to a null model network to which vertices cluster into community groups we define a null model appropriate for bipartite networks and use it to define a bipartite modularity the bipartite modularity is presented in terms of a modularity matrix b some key properties of the eigenspectrum of b are identified and used to describe an algorithm for identifying modules in bipartite networks the algorithm is based on the idea that the modules in the two parts of the network are dependent with each part mutually being used to induce the vertices for the other part into the modules we apply the algorithm to real world network data showing that the algorithm successfully identifies the modular structure of bipartite networks

the gysin triangle via localization and a 1 homotopy invariance the first author was partially supported by the nsf career award 1350472 and by the portuguese foundation for science and technology grant pest oe mat ui0297 2014

scaling properties of a simplified bouncer model and of chirikov s standard map scaling properties of chirikov s standard map are investigated by studying the average value of i2 where i is the action variable for initial conditions in a the stability island and b the chaotic component scaling behavior appears in three regimes defined by the value of the control parameter k i the integrable to non integrable transition k 0 and k kc kc 0 9716 ii the transition from limited to unlimited growth of i2 k kc iii the regime of strong nonlinearity k kc our scaling results are also applicable to pustylnikov s bouncer model since it is globally equivalent to the standard map we also describe the scaling properties of a stochastic version of the standard map which exhibits unlimited growth of i2 even for small values of k

algebras and modules in monoidal model categories in recent years the theory of structured ring spectra formerly known as a infty and e infty ring spectra has been simplified by the discovery of categories of spectra with strictly associative and commutative smash products now a ring spectrum can simply be defined as a monoid with respect to the smash product in one of these new categories of spectra in this paper we provide a general method for constructing model category structures for categories of ring algebra and module spectra this provides the necessary input for obtaining model categories of symmetric ring spectra functors with smash product gamma rings and diagram ring spectra algebraic examples to which our methods apply include the stable module category over the group algebra of a finite group and unbounded chain complexes over a differential graded algebra 1991 mathematics subject classification primary 55u35 secondary 18d10

modules over motivic cohomology abstract for fields of characteristic zero we show that the homotopy category of modules over the motivic ring spectrum representing motivic cohomology is equivalent to voevodsky s big category of motives the proof makes use of some highly structured models for motivic stable homotopy theory motivic spanier whitehead duality the homotopy theories of motivic functors and of motivic spaces with transfers as introduced from ground up in this paper working with rational coefficients we extend the equivalence for fields of characteristic zero to all perfect fields by employing the techniques of alterations and homotopy purity in motivic homotopy theory

a rescaling of the phase space for hamiltonian map in this work we study a rescale of the phase space in a family of two dimensional nonlinear hamiltonian mapping the mapping considered is parametrised by kepler map and mappings with diverging angles in the limit of vanishing action are recovered the transition from local to global chaos is used the chaotic sea is scaling invariant universality classes are defined a rescale of the phase space for a family of two dimensional nonlinear hamiltonian mappings was made by using the location of the first invariant kolmogorov arnold moser kam curve average properties of the phase space are shown to be scaling invariant and with different scaling times specific values of the control parameters are used to recover the kepler map and the mapping that describes a particle in a wave packet for the relativistic motion the phase space observed shows a large chaotic sea surrounding periodic islands and limited by a set of invariant kam curves whose position of the first of them depends on the control parameters the transition from local to global chaos is used to estimate the position of the first invariant kam curve leading us to confirm that the chaotic sea is scaling invariant the different scaling times are shown to be dependent on the initial conditions the universality classes for the kepler map and mappings with diverging angles in the limit of vanishing action are defined

uniqueness of enhancement for triangulated categories the paper contains general results on the uniqueness of a dg enhancement for trian gulated categories as a consequence we obtain such uniqueness for the unbounded categories of quasi coherent sheaves for the triangulated categories of perfect complexes and for the bounded de rived categories of coherent sheaves on quasi projective schemes if a scheme is projective then we also prove a strong uniqueness for the triangulated category of perfect complexes and for the bounded de rived categories of coherent sheaves these results directly imply that fully faithful functors from the bounded derived categories of coherent sheaves and the triangulated categories of perfect complexes on projective schemes can be represented by objects on the product

a cutting plane algorithm for a clustering problem in this paper we consider a clustering problem that arises in qualitative data analysis this problem can be transformed to a combinatorial optimization problem the clique partitioning problem we have studied the latter problem from a polyhedral point of view and determined large classes of facets of the associated polytope these theoretical results are utilized in this paper we describe a cutting plane algorithm that is based on the simplex method and uses exact and heuristic separation routines for some of the classes of facets mentioned before we discuss some details of the implementation of our code and present our computational results we mention applications from e g zoology economics and the political sciences

comment on evolutionary method for finding communities in bipartite networks in a recent paper zhan zhang guan and zhou phys rev e 83 066120 2011 presented a modified adaptive genetic algorithm maga tailored to the discovery of maximum modularity partitions of the node set into communities in unipartite bipartite and directed networks the authors claim that detection of communities in unipartite networks or in directed networks can be transformed into the same task in bipartite networks actually some tests show that it is not the case for the proposed transformations and why experimental results of maga for modularity maximization of untransformed unipartite or bipartite networks are also discussed