application of the karhunen loeve procedure for the characterization of human faces the use of natural symmetries mirror images in a well defined family of patterns human faces is discussed within the framework of the karhunen loeve expansion this results in an extension of the data and imposes even and odd symmetry on the eigenfunctions of the covariance matrix without increasing the complexity of the calculation the resulting approximation of faces projected from outside of the data set onto this optimal basis is improved on average

the phase transition of the directed polymer on disordered hierarchical lattices the directed polymer on disordered hierarchical lattices is studied using an exact renormalization scheme the phase transition is studied and a hyperscaling relation is derived the fixed distributions of the renormalized energies are obtained numerically the specific heat and associated exponents are computed from the fixed distributions

polymers with a bimodal disorder distribution and directed percolation the ground state scaling properties of directed paths on a 1 1 dimensional lattice are reanalysed to each bond energy 0 or 1 is randomly assigned with probability p or 1 p respectively at variance with previous claims the result strongly suggests that only one universality class exists for 0 p 1 except for the directed percolation threshold

a method for still image interpretation relying on a multi algorithms fusion scheme application to human face characterization abstract we propose a method for analysing still images relying on fusion of information obtained from several complementary processing channels each processing path works in three steps a first stage manipulating raw data segments the image into aggregates it is followed by a characterization stage that integrates information conveyed by aggregates the terminal interpretation stage instanciates fuzzy rules these rules constitute a loose model of objects present in the image they semantically qualify aggregates once the interpretation has resumed on each separate channel results of the different methods are collated on a fuzzy rule basis providing the final semantic identification of aggregates this approach provides an interesting alternative for managing complementarity of several algorithms by introducing knowledge on each algorithm and on its intrinsic properties the method is illustrated through an example of human face constituents characterization from black and white identity photographs we give a thorough description of the method and provide quantitative results these results show that a substantial improvement of recognition capabilities 50 is obtained by fusing results of separate algorithms

anomalous roughening in three dimensional polynucleation growth abstract the surface properties of the three dimensional polynucleation growth model were studied at the kinetic roughening transition the dependence of the surface width w on time t and linear size l of the substrate is determined by anomalous roughening w x log l tf t l z where tf is a scaling function for the exponents x 2 8 0 2 and z 1 79 0 05 were found the latter being related to directed percolation

polymers on disordered hierarchical lattices a nonlinear combination of random variables the problem of directed polymers on disordered hierarchical and hypercubic lattices is considered for the hierarchical lattices the problem can be reduced to the study of the stable laws for combining random variables in a nonlinear way we present the results of numerical simulations of two hierarchical lattices finding evidence of a phase transition in one case for a limiting case we extend the perturbation theory developed by derrida and griffiths to nonzero temperature and to higher order and use this approach to calculate thermal and geometrical properties overlaps of the model in this limit we obtain an interpolation formula allowing one to obtain the noninteger moments of the partition function from the integer moments we obtain bounds for the transition temperature for hierarchical and hypercubic lattices and some similarities between the problem on the two different types of lattice are discussed

diffusion of directed polymers in a random environment we consider a system of random walks or directed polymers interacting weakly with an environment which is random in space and time in spatial dimensionsd 2 we establish that the behavior is diffusive with probability one the diffusion constant is not renormalized by the interaction

some characterizations of the weil representations of the symplectic and unitary groups abstract let g be a finite symplectic or unitary group we characterize the weil representations of g via their restriction to a standard subgroup then we complete the determination of complex representations of g with specific minimal polynomials of certain elements by showing that they coincide with the weil representations

hall higman type theorems for semisimple elements of finite classical groups minimum polynomials of semisimple elements of prime power order p a of finite classical groups in nontrivial irreducible cross characteristic representations are studied in particular an analogue of the hall higman theorem is established which shows that the degree of such a polynomial is at least p a 1 p 1 with a few explicit exceptions

directed random walks on directed percolation clusters 0 63 this probability distribution is independent of the cluster s length t up to d values comparable to the cluster s width t n the results are shown to be consistent with a tree description of the directed percolation clusters pacs number s 61 66 dk 64 60 cn 71 20 be the subject of random walks on percolation clusters known as the ant in the labyrinth problem 1 has drawn quite intensive attention in the physical literature 2 however in spite of the numerous efforts no simple connection was found between the static and dynamical exponents of percolation though the alexander orbach conjecture 3 comes close to this goal in this article it is shown that such a simple connection does exist in the special case of directed random walks on directed percolation clusters in the directed percolation model 4 there is a predefined direction in which the percolation clusters can grow in the directed random walk considered in the present study walks are also performed only in the same predefined direction balents and kardar 5 have already studied random walks on directed percolation clusters but while their main concern was the variability of distances between different clusters the main concern of the present article is the variability of distances within each cluster in order to study this issue numerical results were obtained for directed random walks performed along twodimensional directed percolation clusters grown at the critical probability pc these numerical results indicated that the distance d of the directed random walkers from their most probable end point is determined by a probability distribution p d d 2 11w n where w 0 50 and n 0 63 this probability distribution is independent of the cluster s length t up to d values comparable to the cluster s width t n the known values of these two exponents are shown to be consistent with a tree description of the directed percolation clusters the article starts with a description of the model and the way the numerical data were gathered the second part presents the numerical results which have similar characteristics to previous results 6 obtained for the directed polymer model 7 8 this similarity is investigated further in the final part of the article the connection between the directed percolation model and the directed polymer model was studied in a number of articles 9 13 and the present study points to some similarity between entropy in the directed percolation model and energy in the directed polymer model on an arbitrary lattice structure a directed percolation cluster can be defined as the set of lattice points sites which are connected to some origin while the connecting paths are oriented in a predefined direction thus all of them are of

nonuniversality and analytical continuation in moments of directed polymers on hierarchical lattices we prove the moments of the directed polymer partition function gz using an exact position space renormalization group scheme on a hierarchical lattice after sufficient iteration the characteristic functionf n ln gzn of the probability z converges to a stable limitf n for smalln the limiting behavior is independent of the initial distribution while for largen f n is completely determined by it and is thus nonuniversal there is a smooth crossover between the two regimes for small effective dimensions and the nonlinear behavior of the small moments can be used to extract information on the universal scaling properties of the distribution for large effective dimensions there is a sharp transition between the two regimes and analytical continuation from integer moments ton 0 is not possible replica arguments can account for most features of the observed results

on the connection between directed percolation and directed polymers we consider the scaling behaviour of the directed paths of minimum energy on a lattice to each bond of which energy 0 or 1 is randomly assigned in 1 1 dimensions it is shown by numerical transfer matrix calculations that in all the regions below the directed percolation threshold these paths still scale with the directed percolation exponent at the same time degeneracy of these paths at and below the threshold is found to be very different the problem of stability of the directed percolation ground state and the case when the energy on each bond can take randomly q 2 different values are also considered

low dimensional representations of special unitary groups abstract we prove gap results for the low dimensional representation of unitary groups in nondefining characteristics more precisely we give a lower bound for the third smallest degree of a nontrivial absolutely irreducible representation of the groups mentioned above which is almost in the order of magnitude of the square of the two smallest such representations as a corollary we obtain the uniqueness of weil representations in all cross characteristics for the unitary groups our approach uses some results on ordinary representations which can be proved using deligne lusztig theory and which might be of independent interest as well as information on decomposition matrices

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

branching interfaces with infinitely strong couplings a hierarchical froth model of the interface of a random q state potts ferromagnet in 2d is studied by recursive methods a fraction p of the nearest neighbour bonds is made inaccessible to domain walls by infinitely strong ferromagnetic couplings energetic and geometric scaling properties of the interface are controlled by zero temperature fixed distributions for the directed percolation threshold the interface behaves as for p 0 and scaling supports random ising q 2 critical behaviour for all q s at three regimes are obtained for different rates of ferro versus antiferromagnetic couplings with rates above a threshold value the interface is linear fractal dimension and its energy fluctuations scale with length as with when the threshold is reached the interface branches at all scales and is fractal with thus at dilution modifies both low temperature interfacial properties and critical scaling below threshold the interface becomes a probe of the backbone geometry backbone fractal dimension which even controls energy fluctuations numerical determinations of directed percolation exponents on diamond hierarchical lattice are also presented

statistical mechanics of random paths on disordered lattices the dependence of the universality class on the statistical weight of unrestricted random paths is explicitly shown both for deterministic and statistical fractals such as the incipient infinite percolation cluster equally weighted paths ideal chain and kinetically generated paths random walks belong in general to different universality classes for deterministic fractals exact renormalization group techniques are used asymptotic behaviors for the end to end distance ranging from power to logarithmic localization laws are observed for the ideal chain in all these cases random walks in the presence of nonperfect traps are shown to be in the same universality class of the ideal chain logarithmic behavior is reflected insingular renormalization group recursions for the disordered case numerical transfer matrix techniques are exploited on percolation clusters in two and three dimensions the two point correlation function scales with critical exponents not obeying standard scaling relations the distribution of the number of chains and the number of chains returning to the starting point are found to be well approximated by a log normal distribution the logmoment of the number of chains is found to have an essential type of singularity consistent with the log normal distribution a non self averaging behavior is argued to occur on the basis of the results

directed paths on percolation clusters we consider a variant of the problem of directed polymers on a disordered lattice in which the disorder is geometrical in nature in particular we allow a finite probability for each bond to be absent from the lattice we show through the use of numerical and scaling arguments on both euclidean and hierarchical lattices that the model has two distinct scaling behaviors depending upon whether the concentration of bonds on the lattice is at or above the directed percolation threshold we are particularly interested in the exponents and defined by f t and x t describing the free energy and transverse fluctuations respectively above the percolation threshold the scaling behavior is governed by the standard random energy exponents 1 3 and 2 3 in 1 1 dimensions at the percolation threshold we predict and verify numerically in 1 1 dimensions the exponents 1 2 and v v where v and v are the directed percolation exponents in addition we predict the absence of a free phase in any dimension at the percolation threshold

minimal path on the hierarchical diamond lattice we consider the minimal paths on a hierarchical diamond lattice where bonds are assigned a random weight depending on the initial distribution of weights we find all possible asymptotic scaling properties the different cases found are the small disorder case the analog of levy s distributions with a power law decay at and finally a limit of large disorder which can be identified as a percolation problem the asymptotic shape of the stable distributions of weights of the minimal path are obtained as well as their scaling properties as a side result we obtain the asymptotic form of the distribution of effective percolation thresholds for finite size hierarchical lattices

directed polymers with killing the problem of directed polymers in a random medium is generalized to include a killing probability the model is then studied using results of the theory of extreme statistics these reveal that in a region of parameters the thermodynamics of polymers with killing in finite dimensions is similar to that of the mean field solution of directed polymers on a cayley tree the implication of these results for the behaviour of directed polymers in high dimensions is also discussed

eigenvalues of unipotent elements in cross characteristic representations of finite classical groups abstract let h be a finite classical group g be a unipotent element of h of order s and be an irreducible representation of h with dim 1 over an algebraically closed field of characteristic coprime to s we show that almost always all the s roots of unity occur as eigenvalues of g and classify all the triples h g for which this does not hold in particular we list the triples for which 1 is not an eigenvalue of g we also give estimates of the asymptotic behavior of eigenvalue multiplicities when the rank of h grows and s is fixed

cross characteristic representations of even characteristic symplectic groups we classify the small irreducible representations of sp 2n q with q even in odd characteristic this improves even the known results for complex representations the smallest representation for this group is much larger than in the case when q is odd this makes the problem much more difficult