localic sup lattices and tropological systems the approach to process semantics using quantales and modules is topologized by considering tropological systems whose sets of states are replaced by locales and which satisfy a suitable stability axiom a corresponding notion of localic sup lattice algebra for the lower powerlocale monad is described and it is shown that there are contravariant functors from sup lattices to localic sup lattices and for each quantale q from left q modules to localic right q modules a proof technique for third completeness due to abramsky and vickers is reset constructively and an example of application to failures semantics is given

ideal structure of uniform roe algebras of coarse spaces abstract let c u x e be the uniform roe algebra of a coarse space x e with uniformly locally finite coarse structure by a controlled truncation technique we show that the controlled propagation operators in an ideal i of c u x e are exactly the controlled truncations of elements in i it follows that the lattice of the ideals of the uniform roe algebra c u x e in which controlled propagation operators are dense the lattice of the invariant open subsets in the unit space of the groupoid g x introduced by skandalis tu and yu the lattice of the ideals of the coarse structure e and the lattice of the ideals of the coarse space x are mutually isomorphic these lattices also give rise to a type of classification for the ideals of c u x e

sheaves on involutive quantales we show that sheaves on grothendieck quantales which are the quantales that correspond to grothendieck toposes may be defined in several equivalent ways the main topic of this paper is the characterization of internal posets and suplattices in the topos of sheaves on a grothendieck quantale q in terms of categories enriched in a suitable quantaloid and by means of q modules we thereby extend the existing results concerning locales

heuristic approach to the strong coupling regime of the kardar parisi zhang equation we propose a heuristic approach of treating the strong coupling regime of the kardar parisi zhang kpz equation the method which suggests that mathrm d mathrm uc 4 is the upper critical dimension of the kpz equation enables one to use the ensuremath varepsilon expansion below d 4 substrate dimensions to compute the critical exponents in the strong coupling regime we compute the dynamic exponent z and the roughness exponent ensuremath chi to the first order in ensuremath varepsilon 4 d as z 2 4 d 5 and ensuremath chi 4 d 5

crossed products extensions of lp bounds for amenable actions abstract we will extend earlier transference results due to neuwirth and ricard from the context of noncommutative l p spaces associated with amenable groups to that of noncommutative l p spaces associated with crossed products of amenable actions namely if m g c is a completely bounded fourier multiplier on l p then it extends to the crossed product with similar bounds provided that the action is amenable and trace preserving furthermore our construction also allows to extend g equivariant completely bounded operators acting on the space part to the crossed product provided that the generalized folner sets of the action satisfy certain accretivity property as a corollary we obtain stability results for maximal l p bounds over crossed products we derive using that stability results an application to the boundedness of smooth multipliers in the l p spaces of group algebras

extremely large scale simulation of a kardar parisi zhang model using graphics cards the octahedron model introduced recently has been implemented onto graphics cards which permits extremely large scale simulations via binary lattice gases and bit coded algorithms we confirm scaling behavior belonging to the two dimensional kardar parisi zhang universality class and find a surface growth exponent 0 2415 15 on 2 17 2 17 systems ruling out 1 4 suggested by field theory the maximum speedup with respect to a single cpu is 240 the steady state has been analyzed by finite size scaling and a growth exponent 0 393 4 is found correction to scaling exponent are computed and the power spectrum density of the steady state is determined we calculate the universal scaling functions and cumulants and show that the limit distribution can be obtained by the sizes considered we provide numerical fitting for the small and large tail behavior of the steady state scaling function of the interface width

critical exponents of the kpz equation via multi surface coding numerical simulations we study the kpz equation in d 2 3 and 4 spatial dimensions by using a restricted solid on solid discretization of the surface we measure the critical exponents very precisely and we show that the rational guess is not appropriate and that d 4 is not the upper critical dimension we are also able to determine very precisely the exponent of the sub leading scaling corrections that turns out to be close to unity in all cases we introduce and use a multi surface coding technique that allows a gain of the order of 30 fold over usual numerical simulations

pseudogroups and their etale groupoids abstract a pseudogroup is a complete infinitely distributive inverse monoid such inverse monoids bear the same relationship to classical pseudogroups of transformations as frames do to topological spaces the goal of this paper is to develop the theory of pseudogroups motivated by applications to group theory c algebras and aperiodic tilings our starting point is an adjunction between a category of pseudogroups and a category of etale groupoids from which we are able to set up a duality between spatial pseudogroups and sober etale groupoids as a corollary to this duality we deduce a non commutative version of stone duality involving what we call boolean inverse semigroups and boolean etale groupoids as well as a generalization of this duality to distributive inverse semigroups non commutative stone duality has important applications in the theory of c algebras it is the basis for the construction of cuntz and cuntz krieger algebras and in the case of the cuntz algebras it can also be used to construct the thompson groups we then define coverages on inverse semigroups and the resulting presentations of pseudogroups as applications we show that paterson s universal groupoid is an example of a booleanization and reconcile exel s recent work on the theory of tight maps with the work of the second author

a quasi local characterisation of lp roe algebras abstract very recently spakula and tikuisis provide a new characterisation of uniform roe algebras via quasi locality when the underlying metric spaces have straight finite decomposition complexity in this paper we improve their method to deal with the l p version of uniform roe algebras for any p 1 due to the lack of reflexivity on l 1 spaces some extra work is required for the case of p 1

surface pattern formation and scaling described by conserved lattice gases we extend our 2 1 dimensional discrete growth model odor et al phys rev e 79 021125 2009 with conserved local exchange dynamics of octahedra describing surface diffusion a roughening process was realized by uphill diffusion and curvature dependence by mapping the slopes onto particles two dimensional nonequilibrium binary lattice model emerges in which the smoothing or roughening surface diffusion can be described by attracting or repelling motion of oriented dimers the binary representation allows simulations on very large size and time scales we provide numerical evidence for mullins herring or molecular beam epitaxy class scaling of the surface width the competition of inverse mullins herring diffusion with a smoothing deposition which corresponds to a kardar parisi zhang kpz process generates different patterns dots or ripples we analyze numerically the scaling and wavelength growth behavior in these models in particular we confirm by large size simulations that the kpz type of scaling is stable against the addition of this surface diffusion hence this is the asymptotic behavior of the kuramoto sivashinsky equation as conjectured by field theory in two dimensions but has been debated numerically if very strong normal surface diffusion is added to a kpz process we observe smooth surfaces with logarithmic growth which can describe the mean field behavior of the strong coupling kpz class we show that ripple coarsening occurs if parallel surface currents are present otherwise logarithmic behavior emerges

regular representation of groupoid c algebras and applications to inverse semigroups the analogue of the left regular representation of a locally compact groupoid is constructed in the hausdoras well as in the non hausdorcase a necessary and su cient condition for a locally compact groupoid with a cocycle to be morita equi valent to a group action is obtained as an application the c algebras of a class of inverse semigroups is shown to be morita equivalent to crossed products of groups by abelian c

directed d mer diffusion describing the kardar parisi zhang type surface growth we show that d 1 dimensional surface growth models can be mapped onto driven lattice gases of d mers the continuous surface growth corresponds to one dimensional drift of d mers perpendicular to the d ensuremath 1 dimensional plane spanned by the d mers this facilitates efficient bit coded algorithms with generalized kawasaki dynamics of spins our simulations in d 2 3 4 5 dimensions provide scaling exponent estimates on much larger system sizes and simulations times published so far where the effective growth exponent exhibits an increase we provide evidence for the agreement with field theoretical predictions of the kardar parisi zhang universality class and numerical results we show that the 2 1 dimensional exponents conciliate with the values suggested by l assig within error margin for the largest system sizes studied here but we cannot support his predictions for 3 1 d numerically

property a and affine buildings abstract yu s property a is a non equivariant generalisation of amenability introduced in his study of the coarse baum connes conjecture in this paper we show that all affine buildings of type a 2 b 2 and g 2 have property a together with results of guentner higson and weinberger this completes a programme to show that all affine building have property a in passing we use our technique to obtain a new proof for groups acting on a n buildings

quantales and fell bundles abstract we study fell bundles on groupoids from the viewpoint of quantale theory given any saturated upper semicontinuous fell bundle e g on an etale groupoid g with g 0 locally compact hausdorff equipped with a suitable completion c algebra a of its convolution algebra we obtain a map of involutive quantales p max a g where max a consists of the closed linear subspaces of a and g is the topology of g we study various properties of p which mimick to various degrees those of open maps of topological spaces these are closely related to properties of g and a such as g being hausdorff principal or topological principal or being a line bundle under suitable conditions which include g being hausdorff but without requiring saturation of the fell bundle a is an algebra of sections of the bundle if and only if it is the reduced c algebra c r g e we also prove that max a is stably gelfand this implies the existence of a pseudogroup i b and of an etale groupoid b associated canonically to any sub c algebra b a we study a correspondence between fell bundles and sub c algebras based on these constructions and compare it to the construction of weyl groupoids from cartan subalgebras

geometry of the mapping class groups i boundary amenability we construct a geometric model for the mapping class group mathcal m mathcal c mathcal g of a non exceptional oriented surface s of genus g with k punctures and use it to show that the action of mathcal m mathcal c mathcal g on the compact metrizable hausdorff space of complete geodesic laminations for s is topologically amenable as a consequence the novikov higher signature conjecture holds for every subgroup of mathcal m mathcal c mathcal g

etale groupoids and their quantales abstract we establish close and previously unknown relations between quantales and groupoids in particular to each etale groupoid either localic or topological there is associated a unital involutive quantale we obtain a bijective correspondence between localic etale groupoids and their quantales which are given a rather simple characterization and here are called inverse quantal frames we show that the category of inverse quantal frames is equivalent to the category of complete and infinitely distributive inverse monoids and as a consequence we obtain a non functorial correspondence between these and localic etale groupoids that generalizes more classical results concerning inverse semigroups and topological etale groupoids this generalization is entirely algebraic and it is valid in an arbitrary topos as a consequence of these results we see that a localic groupoid is etale if and only if its sublocale of units is open and its multiplication map is semiopen and an analogue of this holds for topological groupoids in practice we are provided with new tools for constructing localic and topological etale groupoids as well as inverse semigroups for instance via presentations of quantales by generators and relations the characterization of inverse quantal frames is to a large extent based on a new quantale operation here called a support whose properties are thoroughly investigated and which may be of independent interest

universality in two dimensional kardar parisi zhang growth we analyze simulation results of a model proposed for etching of a crystalline solid and results of other discrete models in the 2 1 dimensional kardar parisi zhang kpz class in the steady states the moments w n of orders n 2 3 4 of the height distribution are estimated results for the etching model the ballistic deposition model and the temperature dependent body centered restricted solid on solid model suggest the universality of the absolute value of the skewness s ensuremath equiv w 3 w 2 3 2 and of the value of the kurtosis q ensuremath equiv w 4 w 2 2 ensuremath 3 the sign of the skewness is the same as of the parameter ensuremath lambda of the kpz equation which represents the process in the continuum limit the best numerical estimates obtained from the etching model are s 0 26 ifmmode pm else textpm fi 0 01 and q 0 134 ifmmode pm else textpm fi 0 015 for this model the roughness exponent ensuremath alpha 0 383 ifmmode pm else textpm fi 0 008 is obtained accounting for a constant correction term intrinsic width in the scaling of the squared interface width this value is slightly below previous estimates of extensive simulations and rules out the proposal of the exact value ensuremath alpha 2 5 the conclusion is supported by results for the ballistic deposition model independent estimates of the dynamical exponent and of the growth exponent are 1 605l zl 1 64 and ensuremath beta 0 229 ifmmode pm else textpm fi 0 005 respectively which are consistent with the relations ensuremath alpha z 2 and z ensuremath alpha ensuremath beta

width distributions and the upper critical dimension of kardar parisi zhang interfaces simulations of restricted solid on solid growth models are used to build the width distributions of d 2 5 dimensional kardar parisi zhang kpz interfaces we find that the universal scaling function associated with the steady state width distribution changes smoothly as d is increased thus strongly suggesting that d 4 is not an upper critical dimension for the kpz equation the dimensional trends observed in the scaling functions indicate that the upper critical dimension is at infinity

on the k theory of groups with finite asymptotic dimension it is proved that the assembly maps in algebraic kand l theory with respect to the family of finite subgroups is injective for groups with finite asymptotic dimension that admit a finite model for e the result also applies to certain groups that admit only a finite dimensional model for e in particular it applies to discrete subgroups of virtually connected lie groups

scaling cumulant ratios and height distribution of ballistic deposition in 3 1 and 4 1 dimensions we investigate the origin of the scaling corrections in ballistic deposition models in high dimensions using the method proposed by alves et al phys rev e 90 052405 2014 in d 2 1 dimensions where the intrinsic width associated with the fluctuations of the height increments during the deposition processes is explicitly taken into account in the present work we show that this concept holds for d 3 1 and 4 1 dimensions we have found that growth and roughness exponents and dimensionless cumulant ratios are in agreement with other models presenting small finite time corrections to the scaling that in principle belong to the kardar parisi zhang kpz universality class in both d 3 1 and 4 1 our results constitute further evidence that the upper critical dimension of the kpz class if it exists is larger than 4

the many groupoids of a stably gelfand quantale abstract we study the projections of an arbitrary stably gelfand quantale q and show that each projection determines a pseudogroup s q and a corresponding localic etale groupoid g together with a map of involutive quantales p q l s o g as an application we obtain a simplified axiomatization of inverse quantal frames quantales of etale groupoids whereby such a quantale is shown to be the same as a unital stably gelfand quantal frame q whose partial units cover q

growth exponents of the etching model in high dimensions in this work we generalize the etching model mello et al 2001 phys rev e 63 041113 t o d 1 dimensions the dynamic exponents of this model are compatible with those of the kardar parisi zhang universality class we investigate the roughness dynamics with surfaces up to d 6 we show that the data from all substrate lengths and for all dimensions can be collapsed into one common curve we determine the dynamic exponents as a function of the dimension moreover our results suggest that d 4 is not an upper critical dimension for the etching model and that it fulfills the galilean invariance

dynamic asymptotic dimension relation to dynamics topology coarse geometry and c algebras we introduce dynamic asymptotic dimension a notion of dimension for actions of discrete groups on locally compact spaces and more generally for locally compact etale groupoids we study our notion for minimal actions of the integer group its relation with conditions used by bartels luck and reich in the context of controlled topology and its connections with gromov s theory of asymptotic dimension we also show that dynamic asymptotic dimension gives bounds on the nuclear dimension of winter and zacharias for c algebras associated to dynamical systems dynamic asymptotic dimension also has implications for k theory and manifold topology these will be drawn out in subsequent work

two loop renormalization group analysis of the burgers kardar parisi zhang equation a systematic analysis of the burgers kardar parisi zhang equation in d 1 dimensions by dynamic renormalization group theory is described the fixed points and exponents are calculated to two loop order we use the dimensional regularization scheme carefully keeping the full d dependence originating from the angular parts of the loop integrals for dimensions less than mathit d mathit c 2 we find a strong coupling fixed point which diverges at d 2 indicating that there is nonperturbative strong coupling behavior for all d ensuremath ge 2 at d 1 our method yields the identical fixed point as in the one loop approximation and the two loop contributions to the scaling functions are nonsingular for dg2 dimensions there is no finite strong coupling fixed point in the framework of a 2 ensuremath epsilon expansion we find the dynamic exponent corresponding to the unstable fixed point which described the nonequilibrium roughening transition to be z 2 o mathrm ensuremath epsilon 3 in agreement with a recent scaling argument by doty and kosterlitz phys rev lett 69 1979 1992 similarly our result for the correlation length exponent at the transition is 1 ensuremath nu ensuremath epsilon o mathrm ensuremath epsilon 3 for the smooth phase some aspects of the crossover from gaussian to critical behavior are discussed

twisted actions and regular fell bundles over inverse semigroups we introduce a new notion of twisted actions of inverse semigroups and show that they correspond b ectively to certain regular fell bundles over inverse semigroups yielding in this way a structure classication of such bun dles these include as special cases all the stable fell bundles our denition of twisted actions properly generalizes a pre vious one intro duced by sieben and corresponds to busby smith twisted actions in the group case as an application we describe twisted etale groupoid c algebras in terms of crossed products by twisted actions of inverse semigroups and show that sieben s twisted actions essentially correspond to twisted etale groupoids with topologically trivial twists

upper critical dimension of the kardar parisi zhang equation a recent mapping of the interface roughening problem to directed polymers by lassig and kinzelbech has shown that the upper critical dimension of the kardar parisi zhang equation is less than or equal to four by combining the mode coupling technique with a small roughening exponent expansion we show that the upper critical dimension is four the validity of this conclusion is obviously limited by the applicability of the mode coupling technique to the strong coupling regime

multisurface coding simulations of the restricted solid on solid model in four dimensions we study the restricted solid on solid model for surface growth in spatial dimension d 4 by means of a multisurface coding technique that allows us to analyze samples of size up to 256 4 in the steady state regime for such large systems we are able to achieve a controlled asymptotic regime where the typical scale of the fluctuations are larger than the lattice spacing used in the simulations a careful finite size scaling analysis of the critical exponents clearly indicate that d 4 is not the upper critical dimension of the model

stochastic model in the kardar parisi zhang universality class with minimal finite size effects we introduce a solid on solid lattice model for growth with conditional evaporation a measure of finite size effects is obtained by observing the time invariance of distribution of local height fluctuations the model parameters are chosen so that the change in the distribution in time is minimum on a one dimensional substrate the results obtained from the model for the roughness exponent from three different methods are same as predicted for the kardar parisi zhang equation one of the unique features of the model is that as obtained from the structure factor s k t for the one dimensional substrate growth exactly matches the predicted value of 0 5 within statistical errors the model can be defined in any dimensions we have obtained results for this model on two and three dimensional substrates

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

the novikov conjecture for groups with finite asymptotic dimension recall that the asymptotic dimension is a coarse geometric analogue of the covering dimension in topology page 28 14 more precisely the asymptotic dimension for a metric space is the smallest integer n such that for any r 0 there exists a uniformly bounded cover c ui iei of the metric space for which the r multiplicity of c is at most n 1 i e no ball of radius r in the metric space intersects more than n 1 members of c 14 the class of finitely generated discrete groups with finite asymptotic dimension is hereditary in the sense that if a finitely generated group has finite asymptotic dimension as metric space with a word length metric then its finitely generated subgroups also have finite asymptotic dimension as metric spaces with word length metrics cf section 6 this together with a result of gromov in 14 implies that finitely generated subgroups of gromov s hyperbolic groups have finite asymptotic dimension currently no example of a finitely generated group with infinite asymptotic dimension and finite classifying space is known it should also be noted that two different definitions of asymptotic dimension