shape preserving local histogram modification a novel approach for shape preserving contrast enhancement is presented in this paper contrast enhancement is achieved by means of a local histogram equalization algorithm which preserves the level sets of the image this basic property is violated by common local schemes thereby introducing spurious objects and modifying the image information the scheme is based on equalizing the histogram in all the connected components of the image which are defined based both on the grey values and spatial relations between pixels in the image and following mathematical morphology constitute the basic objects in the scene we give examples for both grey value and color images

a new bartholdi zeta function of a digraph we introduce a new type of the bartholdi zeta function of a digraph d and give a determinant expression of it furthermore we define a new type of the bartholdi l function of d and give a determinant expression of it as a corollary we obtain a decomposition formula for a new type of the bartholdi zeta function of a group covering of d by new bartholdi l functions of d

spectra of sparse non hermitian random matrices an analytical solution we present the exact analytical expression for the spectrum of a sparse non hermitian random matrix ensemble generalizing two standard results in random matrix theory this analytical expression constitutes a non hermitian version of the kesten mckay measure as well as a sparse realization of girko s elliptic law our exact result opens new perspectives in the study of several physical problems modelled on sparse random graphs which are locally treelike in this context we show analytically that the convergence rate of a transport process on a very sparse graph depends in a nonmonotonic way upon the degree of symmetry of the graph edges

the coefficients of the reduced bartholdi zeta function abstract in this paper we establish a new zeta function based on the bartholdi zeta function for an undirected graph g called the reduced bartholdi zeta function we study the relation between its coefficients and the structure of the graph and demonstrate that the coefficients count the star subgraphs in the symmetric digraph d g moreover we investigate the properties of semi principle minors extracted from the adjacency matrix of the oriented line graph of g we also present a general formula for calculating all the coefficients of the reduced bartholdi zeta function

quantum chaos on discrete graphs adapting a method developed for the study of quantum chaos on quantum metric graphs kottos and smilansky 1997 phys rev lett 79 4794 kottos and smilansky 1999 ann phys ny 274 76 spectral functions and trace formulae for discrete laplacians on graphs are derived this is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph and obtaining functions which belong to the class of functions proposed originally by ihara 1966 j mat soc japan 18 219 and expanded by subsequent authors stark and terras 1996 adv math 121 124 kotani and sunada 2000 j math sci univ tokyo 7 7 finally a model of classical dynamics on the discrete graph is proposed it is analogous to the corresponding classical dynamics derived for quantum graphs kottos and smilansky 1997 phys rev lett 79 4794 kottos and smilansky 1999 ann phys ny 274 76

a nonlinear image contrast sharpening approach based on munsell s scale contrast is a measure of the variation in intensity or gray value in a specified region of an image the region can be most or all of the image giving rise to a global concept of contrast the region might on the other hand be a small window in which case the concept of contrast is a locally defined expression in this work we introduce a nonlinear local contrast enhancement method this method utilizes the munsell value scale which is based upon human visual perception use of the munsell value scale allows for the partitioning of the gray scale into ten discrete subintervals subsequent local processing occurs within each of these subintervals inside each subinterval this method constructs a contrast enhancement function that is a smooth approximation to the threshold step function and which maps a given subinterval into itself this function then thresholds the gray values in a subinterval in a smooth manner about a locally computed quantity called the mean edge gray value by enhancing the contrast in this way the original shades of gray are preserved that is the groupings of the gray values by subinterval are preserved as a result no gray value distortion is introduced into the image

eigenvectors of the discrete laplacian on regular graphs a statistical approach in an attempt to characterize the structure of eigenvectors of random regular graphs we investigate the correlations between the components of the eigenvectors associated with different vertices in addition we provide numerical observations suggesting that the eigenvectors follow a gaussian distribution following this assumption we reconstruct some properties of the nodal structure which were observed in numerical simulations but were not explained so far dakel et al 2007 approx random pp 436 48

the isospectral fruits of representation theory quantum graphs and drums we present a method which enables one to construct isospectral objects such as quantum graphs and drums one aspect of the method is based on representation theory arguments which are shown and proved the complementary part concerns techniques of assembly which are both stated generally and demonstrated for this purpose quantum graphs are grist to the mill we develop the intuition that stands behind the construction as well as the practical skills of producing isospectral objects we discuss the theoretical implications which include sunada s theorem of isospectrality sunada 1985 ann math 121 169 arising as a particular case of this method a gallery of new isospectral examples is presented and some known examples are shown to result from our theory

zeta functions of discrete groups acting on trees abstract this paper generalizes bass work on zeta functions for uniform tree lattices using the theory of von neumann algebras machinery is developed to define the zeta function of a discrete group of automorphisms of a bounded degree tree the main theorems relate the zeta function to determinants of operators defined on edges or vertices of the tree a zeta function associated to a non uniform tree lattice with appropriate hilbert representation is defined zeta functions are defined for infinite graphs with a cocompact or finite covolume group action

the quaternionic second weighted zeta function of a graph and the study determinant abstract we establish a generalization of the second weighted zeta function of a graph to the case of quaternions for an arc weighted graph whose weights are quaternions we define the second weighted zeta function by using the study determinant that is a quaternionic determinant for quaternionic matrices defined by study this definition is regarded as a quaternionic analogue of the determinant expression of hashimoto type for the ihara zeta function of a graph we derive the study determinant expression of bass type and the euler product for the quaternionic second weighted zeta function

trace formulae and spectral statistics for discrete laplacians on regular graphs i following the derivation of the trace formulas in the first paper in this series we establish here a connection between the spectral statistics of random regular graphs and the predictions of random matrix theory rmt this follows from the known poisson distribution of cycle counts in regular graphs in the limit that the cycle periods are kept constant and the number of vertices increases indefinitely the result is analogous to the so called diagonal approximation in quantum chaos we also show that by assuming that the spectral correlations are given by rmt to all orders we can compute the leading deviations from the poisson distribution for cycle counts we provide numerical evidence which supports this conjecture

unitary stochastic matrix ensembles and spectral statistics we propose to study unitary matrix ensembles defined in terms of unitary stochastic transition matrices associated with markov processes on graphs we argue that the spectral statistics of such an ensemble after ensemble averaging depends crucially on the spectral gap between the leading and subleading eigenvalue of the underlying transition matrix it is conjectured that unitary stochastic ensembles follow one of the three standard ensembles of random matrix theory in the limit of infinite matrix size n if the spectral gap of the corresponding transition matrices closes slower than 1 n the hypothesis is tested by considering several model systems ranging from binary graphs to uniformly and non uniformly connected star graphs and diffusive networks in arbitrary dimensions

a general framework for quadratic volterra filters for edge enhancement an inherent problem in most image enhancement schemes is the amplification of noise which due to weber s law is mostly visible in the darker portions of an image using a special class of quadratic volterra filters we can adapt the enhancement process in a computationally efficient way to the local image brightness because these filters are approximately equivalent to the product of a local mean estimator and a highpass filter we analyze and derive this subclass of quadratic volterra filters by investigating the 1 d case first and then we generalize the results to two dimensions an important property of these filters is that they map sinusoidal inputs to constant outputs which allows us to develop a new filter characterization that is more intuitive for our application than the 4 d frequency response this description finally leads to a novel least squares design methodology image enhancement results using our volterra filters are superior to those obtained with standard linear filters which we demonstrate both quantitatively and qualitatively

exterior interior duality for discrete graphs the exterior interior duality expresses a deep connection between the laplace spectrum in bounded and connected domains in and the scattering matrices in the exterior of the domains here this link is extended to the study of the spectrum of the discrete laplacian on finite graphs for this purpose two methods are devised for associating scattering matrices to the graphs the exterior interior duality is derived for both methods

numerical diffusion in the fct algorithm revisited numerical diffusion in a flux corrected transport fct algorithm embedded in a navier stokes solver tiny3d has been analytically and numerically studied for flows where density variations can be neglected it is found that numerical diffusion can be analytically expressed in a form similar to that of viscous diffusion the effective total viscosity can be written as an effective viscosity which is the sum of the physical and numerical viscosities a low mach number laminar boundary layer flow is used to test the analytical model of numerical diffusion a series of simulations in which the amount of numerical diffusion is varied show results consistent with predictions of boundary layer theory when the effective total viscosity is used the minimum required numerical viscosity to meet the linear stability condition and the lower and upper limits of the cell reynolds number are also derived

effective viscosity in the simulation of spatially evolving shear flows with monotonic fct models abstract the global numerical diffusion of a model for the low mach number simulation of free mixing layers is investigated the numerical model solves the inviscid time dependent conservation equations for mass momentum and energy for ideal gases the equations are solved using an explicit flux corrected transport fct algorithm directional timestep splitting techniques on structured grids and appropriate inflow and outflow boundary conditions effective measurement of the numerical diffusion of the model in uniform grids is performed by comparison of the laminar spread of the simulated mixing layers with that predicted by boundary layer theory the results show that the residual numerical diffusion of the fct model can emulate physical viscosity for laminar shear flows at moderately high reynolds numbers the global numerical diffusion is not very sensitive to changes in free stream velocity ratio and can be reduced in a predictable way by refining the grid spacing

zeta functions of digraphs abstract we define a zeta function of a digraph and an l function of a symmetric digraph and give determinant expressions of them furthermore we give a decomposition formula for the zeta function of a g cyclic cover of a symmetric digraph for any finite group and g

large eddy simulation of high reynolds number free and wall bounded flows the ability to simulate complex unsteady flows is limited by the current state of the art of subgrid scale sgs modeling which invariably relies on the use of smagorinsky type isotropic eddy viscosity models turbulent flows of practical importance involve inherently three dimensional unsteady features often subjected to strong inhomogeneous effects and rapid deformation which cannot be captured by isotropic models although some available improved sgs models can outperform the isotropic eddy viscosity models their practical use is typically limited because of their complexity development of more sophisticated sgs models is actively pursued and it is desirable to also investigate alternative nonconventional approaches in ordinary large eddy simulation les approaches models are introduced for closure of the low pass filtered navier strokes equations nse a promising les approach is the monotonically integrated les miles which involves solving the unfiltered nse using high resolution monotone algorithms in this approach implicit sgs models provided by intrinsic nonlinear high frequeacy filters built into the convection discretization are coupled naturally to the resolvable scales of the flow formal properties of the effective sgs modeling using miles are documented using databases of simulated free and wall bounded inhomogeneous flows including isotropic decaying turbulence transitional jets and channel flows mathematical and physical aspects of implicit sgs modeling through the use of nonlinear flux limiters are addressed using a formalism based on the modified les equations

an estimate for the average spectral measure of random band matrices for a class of random band matrices of band width w we prove regularity of the average spectral measure at scales w 0 99 and find its asymptotics at these scales

some weighted bartholdi zeta function of a digraph related to the weighted bond scattering matrix of a graph we define some weighted bartholdi zeta function of a digraph d and give a determinant expression for it we present a decomposition formula for the weighted zeta function of a group covering of d furthermore we define an l function of d and give a determinant expression for it as a corollary we express the weighted bartholdi zeta function of a group covering of d by means of its l functions

the autocorrelation function for spectral determinants of quantum graphs this paper considers the spectral determinant of quantum graph families with chaotic classical limit the secular coefficients of the spectral determinant are found to follow distributions with zero mean and variance approaching a constant in the limit of large network size for graphs without symmetries this constant is in general different from the random matrix result and depends on the classical limit a closed expression for this system dependent constant is given here explicitly in terms of the spectrum of an underlying markov process related results for graphs with time reversal symmetry are given

universal spectral statistics in quantum graphs we prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations as predicted by random matrix theory the stability of these correlations with regard to nonuniversal corrections is analyzed in terms of the linear operator governing the classical dynamics on the graph

spectral gap of doubly stochastic matrices generated from equidistributed unitary matrices to a unitary matrix u we associate a doubly stochastic matrix m by taking the squared modulus of each element of u to study the connection between onset of quantum chaos on graphs and ergodicity of the underlying markov chain specified by m we study the limiting distribution of the spectral gap of m when u is taken from the circular unitary ensemble and the dimension n of u is taken to infinity we prove that the limiting distribution is degenerate the gap tends to its maximal value 1 the shape of the gap distribution for finite n is also discussed

kirchhoff s rule for quantum wires we formulate and discuss one particle quantum scattering theory on an arbitrary finite graph with n open ends and where we define the hamiltonian to be minus the laplace operator with general boundary conditions at the vertices this results in a scattering theory with n channels the corresponding on shell s matrix formed by the reflection and transmission amplitudes for incoming plane waves of energy e 0 is given explicitly in terms of the boundary conditions and the lengths of the internal lines it is shown to be unitary which may be viewed as the quantum version of kirchhoff s law we exhibit covariance and symmetry properties it is symmetric if the boundary conditions are real also there is a duality transformation on the set of boundary conditions and the lengths of the internal lines such that the low energy behaviour of one theory gives the high energy behaviour of the transformed theory finally we provide a composition rule by which the on shell s matrix of a graph is factorizable in terms of the s matrices of its subgraphs all proofs use only known facts from the theory of self adjoint extensions standard linear algebra complex function theory and elementary arguments from the theory of hermitian symplectic forms

adaptive contrast enhancement and de enhancement abstract two different interpolative schemes for adaptive contrast enhancement have been presented for speeding up the contrast enhancement algorithm proposed by beghdadi and negrate to reduce the enhancement of noise in relatively flat regions present in the image an adaptive power variation technique is used in which the degree of contrast enhancement is varied depending on the severity of brightness change in a region a contrast transformation function is proposed which can be used for adaptive enhancement as well as de enhancement of images

the spectral edge of some random band matrices we study the asymptotic distribution of the eigenvalues of random hermitian periodic band matrices focusing on the spectral edges the eigenvalues close to the edges converge in distribution to the airy point process if and only if the band is sufficiently wide w n 5 6 otherwise a different limiting distribution appears

zeta functions of finite graphs and coverings iii abstract a graph theoretical analog of brauer siegel theory for zeta functions of number fields is developed using the theory of artin l functions for galois coverings of graphs from parts i and ii in the process we discuss possible versions of the riemann hypothesis for the ihara zeta function of an irregular graph

on the exponential generating function for non backtracking walks we derive an explicit formula for the exponential generating function associated with non backtracking walks around a graph we study both undirected and directed graphs our results allow us to derive computable expressions for non backtracking versions of network centrality measures based on the matrix exponential we find that eliminating backtracking walks in this context does not significantly increase the computational expense we show how the new measures may be interpreted in terms of standard exponential centrality computation on a certain multilayer network insights from this block matrix interpretation also allow us to characterize centrality measures arising from general matrix functions rigorous analysis on the star graph illustrates the effect of non backtracking and shows that unwanted localization effects can be eliminated when we restrict to non backtracking walks we also investigate the localization issue on synthetic networks

flux corrected transport algorithms for an adaptively refined cartesian mesh the flux corrected transport algorithm was implemented on an adaptively refined cartesian mesh the error at a mesh refinement boundary investigated using fourier analysis showed low accuracy when a wave moves from a coarse to a fine mesh this was improved by using a linear interpolation between neighbor cells for evaluating convective fluxes for extension to multidimensions the flux corrected transport limiter was modified to take into account information from all the cells facing a mesh refinement boundary a series of computations show that the present method simulates a shock wave passing through a mesh refinement boundary without causing any unphysical waves methods for estimating the gain of adaptive mesh refinement based on available computer memory or computational time are discussed