a fixed point formula and harish chandra s character formula the main result in this paper is a fixed point formula for equivariant indices of elliptic differential operators for proper actions by connected semisimple lie groups on possibly noncompact manifolds with compact quotients for compact groups and manifolds this reduces to the atiyah segal singer fixed point formula other special cases include an index theorem by connes and moscovici for homogeneous spaces and an earlier index theorem by the second author both in cases where the group acting is connected and semisimple as an application of this fixed point formula we give a new proof of harish chandra s character formula for discrete series representations

geometric quantization and families of inner products abstract we formulate a quantization commutes with reduction principle in the setting where the lie group g the symplectic manifold it acts on and the orbit space of the action may all be noncompact it is assumed that the action is proper and the zero set of a deformation vector field associated to the momentum map and an equivariant family of inner products on the lie algebra g of g is g cocompact the central result establishes an asymptotic version of this quantization commutes with reduction principle using an equivariant family of inner products on g instead of a single one makes it possible to handle both noncompact groups and manifolds by extending tian and zhang s witten deformation approach to the noncompact case

distribution based behavioral distance for nondeterministic fuzzy transition systems modal logics and behavioral equivalences play an important role in the specification and verification of concurrent systems in this paper we first present a new notion of bisimulation for nondeterministic fuzzy transition systems which is distribution based and coarser than state based bisimulation appeared in the literature then we define a distribution based bisimilarity metric as the least fixed point of a suitable monotonic function on a complete lattice which is a behavioral distance and is a more robust way of formalizing behavioral similarity between states than bisimulations we also propose an on the fly algorithm for computing the bisimilarity metric moreover we present a fuzzy modal logic and provide a sound and complete characterization of the bisimilarity metric interestingly this characterization holds for a class of fuzzy modal logics in addition we show the nonexpansiveness of a typical parallel composition operator with respect to the bisimilarity metric which makes compositional verification possible

note on free lunches and cross validation the no free lunch theorems wolpert macready 1995 have sparked heated debate in the computational learning community a recent communication zhu rohwer 1996 attempts to demonstrate the inefficiency of cross validation on a simple problem we elaborate on this result by considering a broader class of cross validation when used more strictly cross validation can yield the expected results on simple examples

a geometric realisation of tempered representations restricted to maximal compact subgroups let g be a connected linear real reductive lie group with compact centre let k g be maximal compact for a tempered representation pi of g we realise the restriction pi k as the k equivariant index of a dirac operator on a homogeneous space of the form g h for a cartan subgroup h g the result in fact applies to every standard representation such a space can be identified with a coadjoint orbit of g so that we obtain an explicit version of kirillov s orbit method for pi k in a companion paper we use this realisation of pi k to give a geometric expression for the multiplicities of the k types of pi in the spirit of the quantisation commutes with reduction principle this generalises work by paradan for the discrete series to arbitrary tempered representations

quantisation commutes with reduction at discrete series representations of semisimple groups abstract using the analytic assembly map that appears in the baum connes conjecture in noncommutative geometry we generalise the guillemin sternberg conjecture that quantisation commutes with reduction to discrete series representations of semisimple groups g with maximal compact subgroups k acting cocompactly on symplectic manifolds we prove this generalised statement in cases where the image of the momentum map in question lies in the set of strongly elliptic elements g se the set of elements of g with compact stabilisers this assumption on the image of the momentum map is equivalent to the assumption that m g k n for a compact hamiltonian k manifold n the proof comes down to a reduction to the compact case this reduction is based on a quantisation commutes with induction principle and involves a notion of induction of hamiltonian group actions this principle in turn is based on a version of the naturality of the assembly map for the inclusion k g

t norm based logics with an independent involutive negation in this paper we investigate the addition of arbitrary independent involutive negations to t norm based logics we deal with several extensions of mtl and establish general completeness results indeed we will show that given any t norm based logic satisfying some basic properties its extension by means of an involutive negation preserves algebraic and finite strong standard completeness we will deal with both propositional and predicate logics

k theorie bivariante pour les algebres de banach et conjecture de baum connes je suis parvenu dans ma these a construire une k theorie bivariante pour les algebres de banach cela m a permis de demontrer la conjecture de baum connes pour les groupes de lie semi simples et les groupes reductifs p adiques ainsi que pour les sous groupes discrets de type fini de sl 3 f avec f une extension finie de q p et pour les sous groupes discrets cocompacts de sp n 1 sl 3 r et sl 3 c j ai aussi demontre une conjecture analogue a la conjecture de baum connes pour les algebres l 1 et plus generalement toutes les bonnes completions des sous groupes fermes des groupes de lie semi simples et des groupes reductifs p adiques

logistic evolutionary product unit neural networks innovation capacity of poor guatemalan households a new logistic regression algorithm based on evolutionary product unit pu neural networks is used in this paper to determine the assets that influence the decision of poor households with respect to the cultivation of non traditional crops ntc in the guatemalan highlands in order to evaluate high order covariate interactions pus were considered to be independent variables in product unit neural networks punn analysing two different models either including the initial covariates logistic regression by the product unit and initial covariate model or not logistic regression by the product unit model our results were compared with those obtained using a standard logistic regression model and allow us to interpret the most relevant household assets and their complex interactions when adopting ntc in order to aid in the design of rural policies

on the rigidity theorems of witten in this paper we prove the rigidity theorems predicted by witten in 1986 about the index of certain elliptic operators on manifolds with an s1 action w witten s insight was the culmination of an interesting interchange of ideas between him and hopkins landweber ochanine and stong for the detailed history we refer the reader to la the present account is essentially a reinterpretation of the second author s taubes t original proof of the theorem the senior author s contribution was solely to notice that the rather densely written arguments of the original manuscript could be formulated in terms of the well known fixed point formulae of equivariant index theory and equivariant cohomology in this context the final proof then appears in direct lineage of the atiyah hirzebruch theorem concerning the vanishing of the a genus of spin manifolds admitting a circle action a h and of the even older idea of lusztig concerning circle actions in the complex case there remains however the beautiful physics inspired novelty of connecting these techniques with elliptic function theory

on the upper estimate of the heat kernel of a complete riemannian manifold let m be a complete non compact riemannian manifold whose sectional curvature is bounded between two constants k and k then one expects that the heat diffusion in such a manifold behaves like the heat diffusion in euclidean space the purpose of this paper is to give a justification of such a statement in 5 j cheeger and the third author found a lower estimate of the heat kernel by comparing it with the heat kernel of the space form whose curvature is the lower bound of the curvature of the manifold this lower estimate is sharp if we insist the dependence should be on the lower bound of the ricci curvature alone it remains to give an upper estimate of the heat kernel one does not however expect to have a comparison theorem for the upper bound because it is more sensitive to the geometry of the manifold in fact the heat kernel of the upper hialf space and the heat kernel of the complete hyperbolic manifold with finite volume have quite different behavior this is reflected by the fact that the laplacian has no discrete spectrum in the first case while infinite number of discrete eigenvalues may exist in the latter case what we will prove here is that in any case the heat kernel has to decay in a manner similar to the euclidean heat kernel thus we will prove that for any constant c 4 there exists c1 depending on c t the bound of the curvature of m and x so that for all t e 0 t

product units a computationally powerful and biologically plausible extension to backpropagation networks we introduce a new form of computational unit for feedforward learning networks of the backpropagation type instead of calculating a weighted sum this unit calculates a weighted product where each input is raised to a power determined by a variable weight such a unit can learn an arbitrary polynomial term which would then feed into higher level standard summing units we show how learning operates with product units provide examples to show their efficiency for various types of problems and argue that they naturally extend the family of theoretical feedforward net structures there is a plausible neurobiological interpretation for one interesting configuration of product and summing units

spin structures and proper group actions abstract we generalise atiyah and hirzebruch s vanishing theorem for actions by compact groups on compact spin manifolds to possibly noncompact groups acting properly and cocompactly on possibly noncompact spin manifolds as corollaries we obtain some vanishing results for an a type genus

dirac cohomology unitary representations and a proof of a conjecture of vogan u radu je dokazana slutnja d vogana koja odredjuje infinitesimalni karakter ireducibilnog g k modula koji ima diracovu kohomologiju razlicitu od nula infinitesimalni karakter je dan kao rho translat najvece tezine k tipa u diracovoj kohomologiji diracova kohomologija se definira kao ker d im d cap ker d gdje d oznacava diracov operator na zadanom g k modulu tenzoriranom sa spin modulom

l2 index and the selberg trace formula abstract a method is developed for computing the l 2 index of a locally symmetric elliptic differential operator d acting on a locally symmetric manifold m g k with g semisimple of real rank one and of finite co volume based on applying the selberg trace formula to the difference of the two heat kernels associated to d the applications include an extension of the osborne warner multiplicity formula to certain non integrable discrete series derived from the l 2 spinor formula and showing the existence in some cases of non invariant l 2 cohomology classes in the middle dimension via the l 2 signature formula

logical characterizations of simulation and bisimulation for fuzzy transition systems simulations and bisimulations are known to be useful for abstracting and comparing formal systems and they have recently been introduced into fuzzy systems in this study we provide sound and complete logical characterizations for simulation and bisimulation which are defined over fuzzy labeled transition systems via two variants of the hennessy milner logic the logic for characterizing fuzzy simulation has neither negation nor disjunction which is very different from the well known logical characterizations of probabilistic simulations although the completeness proofs of our characterization results are inspired by relevant research in probabilistic concurrency theory the logic for characterizing fuzzy bisimulation also deviates from that for probabilistic bisimulations

additive logistic regression a statistical view of boosting boosting is one of the most important recent developments in classification methodology boosting works by sequentially applying a classification algorithm to reweighted versions of the training data and then taking a weighted majority vote of the sequence of classifiers thus produced for many classification algorithms this simple strategy results in dramatic improvements in performance we show that this seemingly mysterious phenomenon can be understood in terms of well known statistical principles namely additive modeling and maximum likelihood for the two class problem boosting can be viewed as an approximation to additive modeling on the logistic scale using maximum bernoulli likelihood as a criterion we develop more direct approximations and show that they exhibit nearly identical results to boosting direct multiclass generalizations based on multinomial likelihood are derived that exhibit performance comparable to other recently proposed multiclass generalizations of boosting in most situations and far superior in some we suggest a minor modification to boosting that can reduce computation often by factors of 10 to 50 finally we apply these insights to produce an alternative formulation of boosting decision trees this approach based on best first truncated tree induction often leads to better performance and can provide interpretable descriptions of the aggregate decision rule it is also much faster computationally making it more suitable to large scale data mining applications

on bias plus variance this article presents several additive corrections to the conventional quadratic loss bias plus variance formula one of these corrections is appropriate when both the target is not fixed as in bayesian analysis and training sets are averaged over as in the conventional bias plus variance formula another additive correction casts conventional fixed trainingset bayesian analysis directly in terms of bias plus variance another correction is appropriate for measuring full generalization error over a test set rather than as with conventional bias plus variance error at a single point yet another correction can help explain the recent counterintuitive bias variance decomposition of friedman for zero one loss after presenting these corrections this article discusses some other loss function specific aspects of supervised learning in particular there is a discussion of the fact that if the loss function is a metric e g zero one loss then there is bound on the change in generalization error acco

nondeterministic fuzzy automata to handle fuzzy uncertainty in system modeling nondeterministic finite automata have been generalized into fuzzy automata after a reexamination of the notions of fuzzy automata in the literature we ascertain that the fundamental property nondeterminism in nondeterministic finite automata has not been well embodied in the generalization in order to reflect nondeterminism in fuzzy automata we introduce nondeterministic fuzzy automata with or without e moves and fuzzy languages recognized by them like nondeterministic finite automata nondeterministic fuzzy automata provide a mathematical representation of nondeterministic dynamic fuzzy systems moreover we show that deterministic fuzzy automata nondeterministic fuzzy automata and nondeterministic fuzzy automata with e moves are all equivalent in the sense that they recognize the same class of fuzzy languages which is an extension of the well known equivalence among finite automata nondeterministic finite automata and nondeterministic finite automata with e moves

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

quantitative computation tree logic model checking based on generalized possibility measures we study generalized possibilistic computation tree logic gpoctl model checking in this paper which is an extension of possibilistic computation logic model checking introduced by li et al 2014 the system is modeled by generalized possibilistic kripke structures and the verifying property is specified by a gpoctl formula based on generalized possibility measures and generalized necessity measures the method of gpoctl model checking is discussed and the corresponding algorithm and its complexity are shown in detail furthermore the comparison between possibilistic computation tree logic and gpoctl is given finally a thermostat example is given to illustrate the gpoctl model checking method

income prediction in the agrarian sector using product unit neural networks abstract european union financial subsidies in the agrarian sector are directly related to maintaining a sustainable farm income so its determination using for example the farm gross margin is a basic element in agrarian programs for sustainable development using this tool it is possible the identification of the agrarian structures that need financial support and to what extent it is needed however the process of farm gross margin determination is complicated and expensive because it is necessary to find the value of all the inputs consumed and outputs produced considering the circumstances mentioned the objectives of this research were to 1 select a representative and reduced set of easy to collect descriptive variables to estimate the gross margin of a group of olive tree farms in andalusia 2 investigate if artificial neural network models ann with two different types of basis functions sigmoidal and product units could effectively predict the gross margin of olive tree farms 3 compare the effectiveness of multiple linear quadratic and robust regression models versus ann and 4 validate the best mathematical model obtained for gross margin prediction by analysing realistic farm and farmer scenarios results from ann models specially the product unit ones have provided the most accurate gross margin predictions

model checking of linear time properties based on possibility measure using possibility measure we study model checking of linear time properties in possibilistic kripke structures first the notion of possibilistic kripke structures and the related possibility measure are introduced and then model checking of reachability and repeated reachability linear time properties in finite possibilistic kripke structures are studied standard safety properties and regular properties in possibilistic kripke structures are introduced the verification of regular safety properties and regular properties using finite automata are thoroughly studied it has been shown that the verification of regular safety properties and regular properties in a finite possibilistic kripke structure can be transformed into the verification of reachability properties and repeated reachability properties in the product possibilistic kripke structure that is introduced in this paper several examples are given to illustrate the methods that are presented in this paper

bisimulations for fuzzy transition systems there has been a long history of using fuzzy language equivalence to compare the behavior of fuzzy systems however the comparison at this level is too coarse recently a finer behavioral measure i e bisimulation has been introduced to fuzzy finite automata however the results obtained are applicable only to finite state systems in this paper we consider bisimulation for general fuzzy systems which may be infinite state or infinite event by modeling them as fuzzy transition systems ftss to help understand and check bisimulation we characterize it in three ways by enumerating whole transitions comparing individual transitions and using a monotonic function in addition we address composition operations subsystems quotients and homomorphisms of ftss and discuss their properties connected with bisimulation the results presented here are useful to compare the behavior of general fuzzy systems in particular this makes it possible to relate an infinite fuzzy system to a finite one which is easier to analyze with the same behavior

bisimulation through probabilistic testing abstract we propose a language for testing concurrent processes and examine its strength in terms of the processes that are distinguished by a test by using probabilistic transition systems as the underlying semantic model we show how a testing algorithm can distinguish with a probability arbitrarily close to one between processes that are not bisimulation equivalent we also show a similar result in a slightly stronger form for a new process relation called 2 3 bisimulation which lies strictly between that of simulation and bisimulation finally the ultimately strength of the testing language is shown to identify a new process relation called probabilistic bisimulation which is strictly stronger than bisimulation

the l 2 index theorem for homogeneous spaces of lie groups the l2 index theorem for covering spaces of atiyah 3 and singer 20 asserts that given a discrete group f acting smoothly and freely on a manifold m with compact quotient m f m and an elliptic differential operator d on m which is f invariant and thus descends to an elliptic differential operator d on the compact manifold m then the p index indrd dimrkerd dimrkerd of d coincides with the ordinary index ind d dim ker d dim ker d of d here ker d is the space of l2 solutions of du 0 and dim r denotes the dimension function corresponding to the trace on the commutant of f acting on the hilbert space of l2 sections over m naturally associated to p the importance of this theorem lies in the fact that indd 0 implies the existence of nontrivial l2 solutions for the equation du 0 and as such it was used in a crucial way by atiyah and schmid 5 to construct explicit realizations of the discrete series representations for semisimple lie groups indeed if g is a lie group which possesses a discrete torsion free cocompact subgroup f and h is a compact subgroup of g then the l2 index theorem applied to the covering space m g h of m f g h combined with the index formula of atiyah singer 6 yields existence results for l2 solutions of g invariant elliptic equations on the homogeneous space g h it is relevant to note that with d denoting this time a g invariant elliptic differential operator on g h the ratio between the f index of d and the covolume of f gives a number independent of f this real number indg d can be in fact intrinsically defined as the difference of the two formal degrees corresponding to the representations of g on ker d and ker d respectively and hence makes sense for any unimodular lie group g even when it has no discrete cocompact subgroups which outside the semisimple case is the generic

algebraic laws for nondeterminism and concurrency since a nondeterministic and concurrent program may in general communicate repeatedly with its environment its meaning cannot be presented naturally as an input output function as is often done in the denotational approach to semantics in this paper an alternative is put forth first a definition is given of what it is for two programs or program parts to be equivalent for all observers then two program parts are said to be observation congruent if they are in all program contexts equivalent the behavior of a program part that is its meaning is defined to be its observation congruence class the paper demonstrates for a sequence of simple languages expressing finite terminating behaviors that in each case observation congruence can be axiomatized algebraically moreover with the addition of recursion and another simple extension the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties

logical characterizations of regular equivalence in weighted social networks abstract social network analysis is a methodology used extensively in social science classical social networks can only represent the qualitative relationships between actors but weighted social networks can describe the degrees of connection between actors in a classical social network regular equivalence is used to capture the similarity between actors based on their links to other actors specifically two actors are deemed regularly equivalent if they are equally related to equivalent others the definition of regular equivalence has been extended to weighted social networks in two ways the first definition called regular similarity considers regular equivalence as an equivalence relation that commutes with the underlying graph edges while the second definition called generalized regular equivalence is based on the notion of role assignment or coloring a role assignment resp coloring is a mapping from the set of actors to a set of roles resp colors the mapping is regular if actors assigned to the same role have the same roles in their neighborhoods recently it was shown that social positions based on regular equivalence can be syntactically expressed as well formed formulas in a kind of modal logic thus actors occupying the same social position based on regular equivalence will satisfy the same set of modal formulas in this paper we present analogous results for regular similarity and generalized regular equivalence based on many valued modal logics

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

supervisory control of fuzzy discrete event systems for simulation equivalence the supervisory control theory of fuzzy discrete event systems fdess for fuzzy language equivalence has been developed however in a way language equivalence has limited expressiveness therefore if the given specification can not be expressed by language equivalence then the control for language equivalence does not work in this paper we further establish the supervisory control theory of fdess for fuzzy simulation equivalence whose expressiveness is stronger than that of fuzzy language equivalence first we formalize the notions of fuzzy simulation and fuzzy simulation equivalence between two fdess then we present a method for deciding whether there is a fuzzy simulation or not in addition we also show several basic properties of fuzzy simulation relations afterward we put forward the notion of fuzzy simulation based controllability and in particular show that it serves as a necessary and sufficient condition for the existence of the fuzzy supervisors of fdess moreover we study the range control problem of fdess some examples are given to illustrate the main results obtained

logistic regression using covariates obtained by product unit neural network models we propose a logistic regression method based on the hybridation of a linear model and product unit neural network models for binary classification in a first step we use an evolutionary algorithm to determine the basic structure of the product unit model and afterwards we apply logistic regression in the new space of the derived features this hybrid model has been applied to seven benchmark data sets and a new microbiological problem the hybrid model outperforms the linear part and the nonlinear part obtaining a good compromise between them and they perform well compared to several other learning classification techniques we obtain a binary classifier with very promising results in terms of classification accuracy and the complexity of the classifier