the classification of differential structures on quantum 2 spheres exterior algebras of differential forms on quantum 2 spheress qc 2 q 1 1 0 c 0 c 0 forq 1 are classified in the definition of exterior algebras we assume the invariance w r t the action of the quantumsu 2 group and dimensionality conditions which imply that we deal with two dimensional manifolds the exterior algebras exist only forc 0 and are unique in that case the corresponding generalized directional derivatives are provided

gibbs sampling methods for stick breaking priors a rich and flexible class of random probability measures which we call stick breaking priors can be constructed using a sequence of independent beta random variables examples of random measures that have this characterization include the dirichlet process its two parameter extension the two parameter poisson dirichlet process finite dimensional dirichlet priors and beta two parameter processes the rich nature of stick breaking priors offers bayesians a useful class of priors for nonparametric problems while the similar construction used in each prior can be exploited to develop a general computational procedure for fitting them in this article we present two general types of gibbs samplers that can be used to fit posteriors of bayesian hierarchical models based on stick breaking priors the first type of gibbs sampler referred to as a polya urn gibbs sampler is a generalized version of a widely used gibbs sampling method currently employed for dirichlet process computing this method applies t

an analogue of weyl s law for quantized irreducible generalized flag manifolds we prove an analogue of weyl s law for quantized irreducible generalized flag manifolds this is formulated in terms of a zeta function which similarly to the classical setting satisfies the following two properties as a functional on the quantized algebra it is proportional to the haar state and its first singularity coincides with the classical dimension the relevant formulas are given for the more general case of compact quantum groups

doubly nonparametric sparse nonnegative matrix factorization based on dependent indian buffet processes sparse nonnegative matrix factorization snmf aims to factorize a data matrix into two optimized nonnegative sparse factor matrices which could benefit many tasks such as document word co clustering however the traditional snmf typically assumes the number of latent factors i e dimensionality of the factor matrices to be fixed this assumption makes it inflexible in practice in this paper we propose a doubly sparse nonparametric nmf framework to mitigate this issue by using dependent indian buffet processes dibp we apply a correlation function for the generation of two stick weights associated with each column pair of factor matrices while still maintaining their respective marginal distribution specified by ibp as a consequence the generation of two factor matrices will be columnwise correlated under this framework two classes of correlation function are proposed 1 using bivariate beta distribution and 2 using copula function compared with the single ibp based nmf this paper jointly makes two factor matrices nonparametric and sparse which could be applied to broader scenarios such as co clustering this paper is seen to be much more flexible than gaussian process based and hierarchial beta process based dibps in terms of allowing the two corresponding binary matrix columns to have greater variations in their nonzero entries our experiments on synthetic data show the merits of this paper compared with the state of the art models in respect of factorization efficiency sparsity and flexibility experiments on real world data sets demonstrate the efficiency of this paper in document word co clustering tasks

transgression and the chern character of finite dimensional k cycles it is shown that the jlo entire cocycle of a finitely summable unbounded fredholm module can be retracted to a periodic cocycle moreover the retracted cocycle admits a zero temperature limit which provides the extension of the transgressed cocycle of cm1 from the invertible case to the general case

modeling studies and efficient numerical methods for proton exchange membrane fuel cell abstract in this paper a three dimensional 3d nonisothermal multiphysics two phase steady state transport model and its efficient numerical methods are systematically studied for a full proton exchange membrane fuel cell pemfc in the sense of efficiency and accuracy the conservation equations of mass momentum species charge and energy are fully addressed in view of nonisothermality and multiphase characteristics in addition from an accurate numerical discretization s point of view we present some new formulations for species equations by investigating the interactions among the species in a framework of the combined finite element upwind finite volume method some efficient numerical methods are developed in terms of kirchhoff transformation for the sake of a fast and convergent numerical simulation the 3d simulations demonstrate that the convergent solutions can be attained within 80 nonlinear iterations in contrast to the oscillating and nonconvergent iterations conducted by commercial flow solvers or in house code with standard finite element volume methods numerical convergence tests are carried out to verify the efficiency and accuracy of our numerical algorithms and techniques

a necessary and sufficient condition for finite speed of propagation in the theory of doubly nonlinear degenerate parabolic equations a degenerate parabolic partial differential equation with a time derivative and first and second order derivatives with respect to one spatial variable is studied the coefficients in the equation depend nonlinearly on both the unknown and the first spatial derivative of a function of the unknown the equation is said to display finite speed of propagation if a non negative weak solution which has bounded support with respect to the spatial variable at some initial time also possesses this property at later times a criterion on the coefficients in the equation which is both necessary and sufficient for the occurrence of this phenomenon is established according to whether or not the criterion holds weak travelling wave solutions or weak travelling wave strict subsolutions of the equation are constructed and used to prove the main theorem via a comparison principle applications to special cases are provided

nonparametric bayes estimators based on beta processes in models for life history data the article studies the problem of finding bayes estimators for cumulative hazard rates and related quantities w r t prior distributions that correspond to cumulative hazard rate processes with nonnegative independent increments a particular class of prior processes termed beta processes is introduced and is shown to constitute a conjugate class an important bonus of the approach based on cumulative hazards is that more complicated models for life history data than the simple life table situation can be treated for example time inhomogeneous markov chains we find posterior distributions and derive bayes estimators in such models and present a semiparametric bayesian analysis of the cox regression model

infinite factorial unbounded state hidden markov model there are many scenarios in artificial intelligence signal processing or medicine in which a temporal sequence consists of several unknown overlapping independent causes and we are interested in accurately recovering those canonical causes factorial hidden markov models fhmms present the versatility to provide a good fit to these scenarios however in some scenarios the number of causes or the number of states of the fhmm cannot be known or limited a priori in this paper we propose an infinite factorial unbounded state hidden markov model ifuhmm in which the number of parallel hidden markovmodels hmms and states in each hmm are potentially unbounded we rely on a bayesian nonparametric bnp prior over integer valued matrices in which the columns represent the markov chains the rows the time indexes and the integers the state for each chain and time instant first we extend the existent infinite factorial binary state hmm to allow for any number of states then we modify this model to allow for an unbounded number of states and derive an mcmc based inference algorithm that properly deals with the trade off between the unbounded number of states and chains we illustrate the performance of our proposed models in the power disaggregation problem

stochastic blockmodels for directed graphs abstract holland and leinhardt 1981 proposed the p 1 model for the analysis of binary directed graph data in network studies such a model provides information about the attractiveness and expansiveness of the individual nodes in the network as well as the tendency of a pair of nodes to reciprocate relational ties when the nodes are a priori partitioned into subgroups based on attributes such as race and sex the density of ties from one subgroup to another can differ considerably from that relating another pair of subgroups thus creating a situation called blocking in social networks the p 1 model completely ignores this extra piece of information and is therefore unable to explain the block structure blockmodels that are simple extensions of the p 1 model are proposed specifically for such data an iterative scaling algorithm is presented for fitting the model parameters by maximum likelihood the methodology is illustrated in detail on two empirical examples

discrete sparse coding sparse coding algorithms with continuous latent variables have been the subject of a large number of studies however discrete latent spaces for sparse coding have been largely ignored in this work we study sparse coding with latents described by discrete instead of continuous prior distributions we consider the general case in which the latents while being sparse can take on any value of a finite set of possible values and in which we learn the prior probability of any value from data this approach can be applied to any data generated by discrete causes and it can be applied as an approximation of continuous causes as the prior probabilities are learned the approach then allows for estimating the prior shape without assuming specific functional forms to efficiently train the parameters of our probabilistic generative model we apply a truncated expectation maximization approach expectation truncation that we modify to work with a general discrete prior we evaluate the performance of the alg

estimation and prediction for stochastic blockstructures a statistical approach to a posteriori blockmodeling for digraphs and valued digraphs is proposed the probability model assumes that the vertices of the digraph are partitioned into several unobserved latent classes and that the probability distribution of the relation between two vertices depends only on the classes to which they belong a bayesian estimator based on gibbs sampling is proposed the basic model is not identified because class labels are arbitrary the resulting identifiability problems are solved by restricting inference to the posterior distributions of invariant functions of the parameters and the vertex class membership in addition models are considered where class labels are identified by prior distributions for the class membership of some of the vertices the model is illustrated by an example from the social networks literature kapferer s tailor shop

a semiparametric bayesian model for randomised block designs summary a model is proposed for a bayesian semiparametric analysis of randomised block experiments the model is a hierarchical model in which a dirichlet process is inserted at the middle stage for the distribution of the block effects this model allows an arbitrary distribution of block effects and it results in effective estimates of treatment contrasts block effects and the distribution of block effects an effective computational strategy is presented for describing the posterior distribution

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

a unifying review of linear gaussian models factor analysis principal component analysis mixtures of gaussian clusters vector quantization kalman filter models and hidden markov models can all be unified as variations of unsupervised learning under a single basic generative model this is achieved by collecting together disparate observations and derivations made by many previous authors and introducing a new way of linking discrete and continuous state models using a simple nonlinearity through the use of other nonlinearities we show how independent component analysis is also a variation of the same basic generative model we show that factor analysis and mixtures of gaussians can be implemented in autoencoder neural networks and learned using squared error plus the same regularization term we introduce a new model for static data known as sensible principal component analysis as well as a novel concept of spatially adaptive observation noise we also review some of the literature involving global and local mixtures of the basic models and provide pseudocode for inference and learning for all the basic models

solving the nonlinear richards equation model with adaptive domain decomposition modeling the transport processes in a vadose zone plays an important role in predicting the reactions of soil biotopes to anthropogenic activity e g modeling contaminant transport the effect of the soil water regime on changes in soil structure and composition etc water flow is governed by the richards equation while the constitutive laws are typically supplied by the van genuchten model which can be understood as a pore size distribution function certain materials with dominantly uniform pore sizes e g coarse grained materials can exhibit ranges of constitutive function values within several orders of magnitude possibly beyond the length of real numbers that computers can handle thus a numerical approximation of the richards equation often requires the solution of systems of equations that cannot be solved on computer arithmetics an appropriate domain decomposition into subdomains that cover only a limited range of constitutive function values and that will change adaptively reflecting the time progress of the model will enable an effective and reliable solution of this problem parts of this problem have already been treated in our work kuraz et al 2014 this paper focuses on improving the performance of a nonlinear solver by locating the areas with abrupt changes in the solution

a local index formula for the quantum sphere for the dirac operator d on the standard quantum sphere we obtain an asymptotic expansion of the suq 2 equivariant entire cyclic cocycle corresponding to open image in new window when evaluated on the element open image in new window the constant term of this expansion is a twisted cyclic cocycle which up to a scalar coincides with the volume form and computes the quantum as well as the classical fredholm indices

continuity of solutions of a singular parabolic equation which is of parabolic divergence form since 3 0 a e however it is the solution u of 0 1 which will be continuous while the solution u of 0 2 need not be in certain physical applications u corresponds to temperature while u is the enthalpy the difficulty in the analysis of this equation written in the form 0 2 stems from the fact that c need not be bounded or bounded away from zero thus the equation may be of degenerate or singular parabolic type as particular cases of the equations covered by our results we mention the three model problems

hierarchical dirichlet processes we consider problems involving groups of data where each observation within a group is a draw from a mixture model and where it is desirable to share mixture components between groups we assume that the number of mixture components is unknown a priori and is to be inferred from the data in this setting it is natural to consider sets of dirichlet processes one for each group where the well known clustering property of the dirichlet process provides a nonparametric prior for the number of mixture components within each group given our desire to tie the mixture models in the various groups we consider a hierarchical model specifically one in which the base measure for the child dirichlet processes is itself distributed according to a dirichlet process such a base measure being discrete the child dirichlet processes necessarily share atoms thus as desired the mixture models in the different groups necessarily share mixture components we discuss representations of hierarchical dirichlet processes

higher integrability for solutions to parabolic problems with irregular obstacles and nonstandard growth abstract the aim of this paper is to derive the self improving property of integrability for the spatial gradient of solutions to degenerate parabolic obstacle problem with irregular obstacles and p x t nonstandard growth more precisely we prove that the spatial gradient of the solution is integrable to a larger power than the natural one determined by the structural assumptions on the involved differential operator

asymptotic behaviour of solutions to parabolic elliptic variational inequalities in a real hilbert space h where j is a given interval in r 0 co j is the subdifferential of a convex function 4 on h and b is a maximal monotone operator in h the abstract setting reflects the form of a class of parabolic elliptic boundary value problems with time dependent obstacles such problems arise in particular as mathematical models of various processes in electrochemical technology and some flows with saturations in porous media time dependent obstacles may represent geometric controls moving control actions in these problems in particular such controls may be comprehended in variable boundary conditions prescribed over time dependent parts of the boundary of domain or in source terms distributed over time dependent subdomains the former refers to control of flows via variable water table in reservoirs the latter characterizes control of electrochemical process via mechanically driven motion of a toolpiece cathode the most typical control objective consists there in stabilizing the state of the process at a given spatial distribution for example constant water head and desired shape of anode this motivates our interest in the asymptotic behavior of solutions to the corresponding boundary value problems as t a to the knowledge of the authors this question has so far not been studied in literature as it has been shown in kenmochi pawlow 16 171 the class of considered time dependent problems admits a representation in the form of evolution equation e b in 16 171 the corresponding results on existence uniqueness and stability of solutions have been established in the present paper we study the asymptotic properties of solutions to e c b as t 00 provided some hypotheses are imposed on the family t e r and the limit 4 of as t a for the solution u u of e d b on r we prove that

evolution monge kantorovich equation abstract the paper deals with monge kantorovich equation mk for short in an open bounded domain with dirichlet boundary condition we study existence and uniqueness of a solution to the associated evolution problem emk for short and we prove the convergence to a solution of mk when time goes to a solution is a couple u where u is the potential and is the transportation flux we study the problem for a given radon measure source term and we show how to use the numerical method of dumont and igbida 2009 22 to provide numerical approximation of the solution of mk

propagation profile of support for evolution p laplacian with convection in half space abstract consider the cauchy dirichlet problem in half space for a one dimensional evolution p laplacian with convection for p 2 and pay attention to the interface t sup x u x t 0 it is well known that lim t t in the absence of the convection while the inclusion of the first order term may change the property of finite or infinite speed of propagation in this paper it will be shown that the nonlinear convection plays a very important role to the evolution of t for the convection with promoting diffusion the fast propagation phenomenon occurs i e u x t 0 whenever t 0 if the convection is strong enough otherwise t remains finite and non localized while under the convection with counteracting diffusion if the convection is strong enough localization even shrinking and extinction appears otherwise t keeps non localized in addition it is found that the time related boundary data are significant also to the behavior of solutions the decay or incremental rates of the boundary data affect not only the contraction or expansion of the supports but also the propagation speed of the interface

bayesian group factor analysis with structured sparsity latent factor models are the canonical statistical tool for exploratory analyses of low dimensional linear structure for a matrix of p features across n samples we develop a structured bayesian group factor analysis model that extends the factor model to multiple coupled observation matrices in the case of two observations this reduces to a bayesian model of canonical correlation analysis here we carefully define a structured bayesian prior that encourages both element wise and column wise shrinkage and leads to desirable behavior on high dimensional data in particular our model puts a structured prior on the joint factor loading matrix regularizing at three levels which enables element wise sparsity and unsupervised recovery of latent factors corresponding to structured variance across arbitrary subsets of the observations in addition our structured prior allows for both dense and sparse latent factors so that covariation among either all features or only a subset of features can be recovered we use fast parameter expanded expectation maximization for parameter estimation in this model we validate our method on simulated data with substantial structure we show results of our method applied to three high dimensional data sets comparing results against a number of state of the art approaches these results illustrate useful properties of our model including i recovering sparse signal in the presence of dense effects ii the ability to scale naturally to large numbers of observations iii flexible observation and factor specific regularization to recover factors with a wide variety of sparsity levels and percentage of variance explained and iv tractable inference that scales to modern genomic and text data sizes

bayesian density estimation and inference using mixtures abstract we describe and illustrate bayesian inference in models for density estimation using mixtures of dirichlet processes these models provide natural settings for density estimation and are exemplified by special cases where data are modeled as a sample from mixtures of normal distributions efficient simulation methods are used to approximate various prior posterior and predictive distributions this allows for direct inference on a variety of practical issues including problems of local versus global smoothing uncertainty about density estimates assessment of modality and the inference on the numbers of components also convergence results are established for a general class of normal mixture models

the characterization of reaction convection diffusion processes by travelling waves it has long been known that the heat equation displays infinite speed of propagation this is to say that if the initial data are nonnegative and have nonempty compact support the solution of an initial value problem is positive everywhere after any infinitesimal time however since the nineteen fifties it has also been known that certain nonlinear diffusion equations of degenerate parabolic type do not display this phenomenon for these equations the generalized solution of an initial value problem with compactly supported initial data will have bounded support with respect to the spatial variable at all times in this paper the necessary and sufficient criterion for finite speed of propagation for the general nonlinear reaction convection diffusion equation formula is determined the assumptions on the coefficientsa bandcare such that the classification unifies and generalizes previously known results the technique employed is comparision of an arbitrary solution of the equation with suitably constructed travelling wave solutions and subsolutions basically the central conclusion is that the equation exhibits finite speed of propagation if and only if it admits a travelling wave solution with bounded support concurrently the search for a travelling wave solution with bounded support can be reduced to the study of a singular nonlinear integral equation whose solution must satisfy a certain constraint

an invariant for homogeneous spaces of compact quantum groups abstract the central notion in connes formulation of noncommutative geometry is that of a spectral triple given a homogeneous space of a compact quantum group restricting our attention to all spectral triples that are well behaved with respect to the group action we construct a certain dimensional invariant in particular taking the quantum group itself as the homogeneous space this gives an invariant for a compact quantum group computations of this invariant in several cases including all type a quantum groups are given

hyperbolic phenomena in a strongly degenerate parabolic equation we consider the equation u t u u x x where 0 and where is a strictly increasing function with lim s we solve the associated cauchy problem for an increasing initial function and discuss to what extent the solution behaves qualitatively like solutions of the first order conservation law u t u x equations of this type arise for example in the theory of phase transitions where the corresponding free energy functional has a linear growth rate with respect to the gradient

the indian buffet process an introduction and review the indian buffet process is a stochastic process defining a probability distribution over equivalence classes of sparse binary matrices with a finite number of rows and an unbounded number of columns this distribution is suitable for use as a prior in probabilistic models that represent objects using a potentially infinite array of features or that involve bipartite graphs in which the size of at least one class of nodes is unknown we give a detailed derivation of this distribution and illustrate its use as a prior in an infinite latent feature model we then review recent applications of the indian buffet process in machine learning discuss its extensions and summarize its connections to other stochastic processes

uniqueness of renormalized solutions of degenerate elliptic parabolic problems we consider a general class of degenerate elliptic paraboic problems associated with the equation b v t div a v dv f using kruzhkov s method of doubling variables both in space and time we prove uniqueness and a comparison principle in l 1 for renormalized solutions

a class based link prediction using distance dependent chinese restaurant process one of the important tasks in relational data analysis is link prediction which has been successfully applied on many applications such as bioinformatics information retrieval etc the link prediction is defined as predicting the existence or absence of edges between nodes of a network in this paper we propose a novel method for link prediction based on distance dependent chinese restaurant process ddcrp model which enables us to utilize the information of the topological structure of the network such as shortest path and connectivity of the nodes we also propose a new gibbs sampling algorithm for computing the posterior distribution of the hidden variables based on the training data experimental results on three real world datasets show the superiority of the proposed method over other probabilistic models for link prediction problem

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

uniqueness of the bounded solution to a strongly degenerate parabolic problem abstract this paper concerns the uniqueness of the bounded solution to a strongly degenerate parabolic problem the equation considered may have two kinds of strong degeneracies and there is no restriction on the relation between the two degeneracies by using holmgren s approach we prove that the bounded solution of the associated initial boundary value problem is unique under some essentially necessary condition on the growth of the convection

dynamic infinite mixed membership stochastic blockmodel directional and pairwise measurements are often used to model interactions in a social network setting the mixed membership stochastic blockmodel mmsb was a seminal work in this area and its ability has been extended however models such as mmsb face particular challenges in modeling dynamic networks for example with the unknown number of communities accordingly this paper proposes a dynamic infinite mixed membership stochastic blockmodel a generalized framework that extends the existing work to potentially infinite communities inside a network in dynamic settings i e networks are observed over time additional model parameters are introduced to reflect the degree of persistence among one s memberships at consecutive time stamps under this framework two specific models namely mixture time variant and mixture time invariant models are proposed to depict two different time correlation structures two effective posterior sampling strategies and their results are presented respectively using synthetic and real world data

a numerical approach to degenerate parabolic equations in this work we propose a numerical approach to solve some kind of degenerate parabolic equations the underlying idea is based on the maximum principle more precisely we locally perturb the initial and boundary data instead of the nonlinear diffusion coefficients so that the resulting problem is not degenerate the efficiency of this method is shown analytically as well as numerically the numerical experiments show that this new approach is comparable with the existing ones

propagation property for anisotropic nonlinear diffusion equation with convection abstract we consider propagation property for anisotropic diffusion equation with convection in 2 dimension t u m x 1 x 1 u p 1 1 x 1 u x 2 x 2 u p 2 1 x 2 u u 1 x 1 u 0 where p 1 p 2 m 0 among the results we show that perturbation for the nonnegative solutions propagates with infinite speed in x 1 direction and with finite speed in x 2 direction if 0 m p 2 we also show that the anisotropic propagation may appear when the convection term is weak backward or even missing if 0 p 1 m p 2 p 1 1

projective module description of the q monopole the dirac q monopole connection is used to compute projector matrices of quantum hopf line bundles for arbitrary winding number the chern connes pairing of cyclic cohomology and k theory is computed for the winding number 1 the non triviality of this pairing is used to conclude that the quantum principal hopf fibration is non cleft among general results we provide a left right symmetric characterization of the canonical strong connections on quantum principal homogeneous spaces with an injective antipode we also provide for arbitrary strong connections on algebraic quantum principal bundles hopf galois extensions their associated covariant derivatives on projective modules

twisted cyclic theory equivariant kk theory and kms states given a c algebra a with a kms weight for a circle action we construct and compute a secondary invariant on the equivariant k theory of the mapping cone of a t a both in terms of equivariant kk theory and in terms of a seminite spectral ow this in particular puts the previously considered examples of cuntz algebras 9 and suq 2 13 in a general framework as a new example we consider the araki woods iii representations of the fermion algebra

flow of oil and water in a porous medium abstract the flow of two immiscible and incompressible fluids in a porous medium is described by a system of quasilinear degenerate partial differential equations in this paper the existence of a weak solution by regularization is shown

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing

the dirac operator on compact quantum groups for the q deformation gq 0 q 1 of any simply connected simple compact lie group g we construct an equivariant spectral triple which is an isospectral deformation of that defined by the dirac operator d on g our quantum dirac operator dq is a unitary twist of d considered as an element of ug cl g the commutator of dq with a regular function on gq consists of two parts one is a twist of a classical commutator and so is automatically bounded the second is expressed in terms of the commutator of the associator with an extension of d we show that in the case of the drinfeld associator the latter commutator is also bounded

a network model characterized by a latent attribute structure with competition the quest for a model that is able to explain describe analyze and simulate real world complex networks is of uttermost practical as well as theoretical interest in fact networks can be a natural way to represent many phenomena often they arise from a complex interweaving of some features of the nodes for example in a co authorship network a link stems more easily between authors with similar interests similarly in a genetic regulatory network links are affected by the different biological functions of the regulators in this paper we introduce and study a novel network model that is based on a latent attribute structure this model inspired by a generalization of the indian buffet process is simple and contains a small number of parameters with a clear and intuitive role each node is characterized by a number of features and the probability of the existence of an edge between two nodes depends on the features they share the number of possible features is not fixed a priori and can grow indefinitely moreover a random fitness parameter is introduced for each node in order to determine its ability to transmit its own features to other nodes this behavior is added on top of a process of indian buffet type because of the fitness property a node s connectivity does not depend on its age alone so that also young but fit nodes are able to compete and succeed in propagating their features and acquiring links we also show how considering the resulting bipartite node attribute network it is possible to gain some insight about which nodes were originally the most fit our model for this bipartite network depends on few parameters that are characterized by their straightforward interpretation and by the availability of proper estimators even if the parameters are easy to interpret and tune the model is general enough to represent complex phenomena e g homophily heterophily or any interplay between features we provide some theoretical as well as experimental results regarding the power law behavior of the model and the proposed tools for the estimation of the parameters we also show through a number of experiments how the proposed model naturally captures most local and global properties e g degree distributions connectivity and distance distributions real networks exhibit