shifted simplicial complexes are laplacian integral we show that the combinatorial laplace operators associated to the boundary maps in a shifted simplicial complex have all integer spectra we give a simple combinatorial interpretation for the spectra in terms of vertex degree sequences generalizing a theorem of merris for graphs we also conjecture a majorization inequality for the spectra of these laplace operators in an arbitrary simplicial complex with equality achieved if and only if the complex is shifted this generalizes a conjecture of grone and merris for graphs

relations between degrees conjugate degrees and graph energies abstract let g be a simple graph of order n with maximum degree and minimum degree let d d 1 d 2 d n and d d 1 d 2 d n be the sequences of degrees and conjugate degrees of g we define i 1 n d i and i 1 n d i and prove that l e l i e where lel and ie are respectively the laplacian energy like invariant and the incidence energy of g moreover we prove that 2 n for a certain class of graphs finally we compare the energy of g and and present an upper bound for the laplacian energy in terms of degree sequence

maximum laplacian energy among threshold graphs we impose some restrictions on the spectra of a threshold graph allowing us to compute its laplacian energy we then show that the pineapple with clique number 1 2n3 has largest laplacian energy among all pineapples with n vertices and among all the graphs satisfying those conditions we also find large families of threshold graphs that satisfy those restrictions and exhibit pairs of such graphs with the same laplacian energy and different laplacian spectra we show by computation that the above pineapple has maximum laplacian energy among all connected threshold graphs for all n 35

minimax entropy principle and its application to texture modeling this article proposes a general theory and methodology called the minimax entropy principle for building statistical models for images or signals in a variety of applications this principle consists of two parts the first is the maximum entropy principle for feature binding or fusion for a given set of observed feature statistics a distribution can be built to bind these feature statistics together by maximizing the entropy over all distributions that reproduce them the second part is the minimum entropy principle for feature selection among all plausible sets of feature statistics we choose the set whose maximum entropy distribution has the minimum entropy computational and inferential issues in both parts are addressed in particular a feature pursuit procedure is proposed for approximately selecting the optimal set of features the minimax entropy principle is then corrected by considering the sample variation in the observed feature statistics and an information criterion for feature pursuit is derived the minimax entropy principle is applied to texture modeling where a novel markov random field mrf model called frame filter random field and minimax entropy is derived and encouraging results are obtained in experiments on a variety of texture images the relationship between our theory and the mechanisms of neural computation is also discussed

on spectral integral variations of mixed graphs in this paper we characterize the mixed graphs with exactly one laplacian eigenvalue moving up by an integer and other laplacian eigenvalues remaining invariant when an edge is added the results extend those of fan linear and multilinear algebra 50 2002 133 for general graphs and so linear and multilinear algebra 46 1999 193 for simple graphs

on the reduced signless laplacian spectrum of a degree maximal graph abstract for a simple graph g the signless laplacian of g is the matrix a g d g where a g is the adjacency matrix and d g is the diagonal matrix of vertex degrees of g the reduced signless laplacian of g is the matrix g b g where b g is the reduced adjacency matrix of g and g is the diagonal matrix whose diagonal entries are the common degrees for vertices belonging to the same neighborhood equivalence class of g a graph is said to be degree maximal if it is connected and its degree sequence is not majorized by the degree sequence of any other connected graph for a maximal graph we obtain a formula for the characteristic polynomial of its reduced signless laplacian and use the formula to derive a localization result for its reduced signless laplacian eigenvalues and to compare the signless laplacian spectral radii of two well known maximal graphs we also obtain a necessary condition for a maximal graph to have maximal signless laplacian spectral radius among all connected graphs with given numbers of vertices and edges

laplacian graph eigenvectors abstract if g is a graph its laplacian is the difference of the diagonal matrix of its vertex degrees and its adjacency matrix the main thrust of the present article is to prove several laplacian eigenvector principles which in certain cases can be used to deduce the effect on the spectrum of contracting adding or deleting edges and or of coalescing vertices one application is the construction of two isospectral graphs on 11 vertices having different degree sequences only one of which is bipartite and only one of which is decomposable

completely positive measures and feller semigroups on donne d abord une approche unifiee aux mesures completement positives qui jouent un role important dans la theorie des equations de volterra a travers le theoreme de bernstein puis on etudie la solution d une equation de transport liee par une mesure non negative qu elle definit a l equation qui caracterise les noyaux completement positifs on obtient une desorption complete des generateurs de semigroupes de feller induits par de telles mesures on donne une application aux equations de flux thermique lineaire dans des materiaux avec memoire

the laplacian energy of threshold graphs and majorization we study the laplacian energy of threshold graphs inspired by the recent results of vinagre del vecchio justo and trevisan 22 in particular we compute the degree sequences of threshold graphs that maximize or minimize the laplacian energy for a fixed number of vertices and edges the analysis involves combinatorial methods using ferrers diagrams and ideas from majorization theory some new inequalities for threshold degree sequences are obtained in this process in the review process a referee pointed out that recently and independently helmberg and trevisan 14 obtained very similar results and we discuss this connection

a theorem of the dore venni type for noncommuting operators a theorem of the dore venni type for the sum of two closed linear operators is proved where the operators are noncommuting but instead satisfy a certain commutator condition this result is then applied to obtain optimal regularity results for parabolic evolution equations u t l t u t f t and evolutionary integral equations u t t 0 a t s l s u s ds g t which are nonautonomous the domains of the involved operators l t may depend on t but l t 1 is required to satisfy a certain smoothness property the results are then applied to parabolic partial differential and integro differential equations

turing instability in reaction diffusion models on complex networks in this paper the turing instability in reaction diffusion models defined on complex networks is studied here we focus on three types of models which generate complex networks i e the erd os renyi the watts strogatz and the threshold network models from analysis of the laplacian matrices of graphs generated by these models we reveal that the stable unstable regions of a spa tially homogeneous solution completely differ depending on network structures in particular we approximately argue the existence of the stable unstable re gions in the cases of regular enhanced ring lattices which include regular circles and networks generated by the threshold network model when the number of vertices is large enough

controllability of the multi agent system modeled by the threshold graph with one repeated degree abstract the controllability issue of multi agent systems modeled by a special class of graphs is studied suppose the modeling graph is simple connected and driven by only one controller the author shows that the system is controllable if the graph has exactly two vertices with the same degree and either one of these two vertices is selected to receive the control input this result is extended to the case of the threshold graph that has only one repeated degree specifically it is shown that if the threshold graph has only one repeated degree and its multiplicity is m then m 1 is the minimum number of the controllers required to make the system controllable in addition the necessary and sufficient condition that characterizes the binary control vectors to ensure the controllability of the system is derived

laplacian integrality in p4 sparse and p4 extendible graphs abstract let g be a simple graph and l l g the laplacian matrix of g g is called l integral if all its laplacian eigenvalues are integer numbers it is known that every cograph a graph free of p4 is l integral the class of p4 sparse graphs and the class of p4 extendible graphs contain the cographs it seems natural to investigate if the graphs in these classes are still l integral in this paper we characterized the l integral graphs for both cases p4 sparse graphs and p4 extendible graphs

laplacian integral graphs in s a b abstract let g n m be the family of graphs with n vertices and m edges when n and m are previously given it is well known that there is a subset of g n m constituted by graphs g such that the vertex connectivity the edge connectivity and the minimum degree are all equal in this paper s a b classes of connected a b linear graphs with n vertices and m edges are described where m is given as a function of a b n 2 some of them have extremal graphs for which the equalities above are extended to algebraic connectivity these graphs are laplacian integral although they are not threshold graphs however we do build threshold graphs in s a b

degree maximal graphs are laplacian integral abstract an integer sequence d d 1 d 2 d n is graphic if there is a graph whose degree sequence is d a graph g is maximal if its degree sequence is majorized by no other graphic sequence the laplacian matrix of g is l g d g a g where d g is the diagonal matrix of vertex degrees and a g is the 0 1 adjacency matrix the article contains an explicit algorithmic construction of all maximal graphs from which it follows e g that apart from 0 the laplacian spectrum of a maximal graph is the conjugate of its degree sequence

on the sum of the laplacian eigenvalues of a tree given an n vertex graph g v e the laplacian spectrum of g is the set of eigenvalues of the laplacian matrix l d a where d and a denote the diagonal matrix of vertex degrees and the adjacency matrix of g respectively in this paper we study the laplacian spectrum of trees more precisely we find a new upper bound on the sum of the k largest laplacian eigenvalues of every n vertex tree where k 1 n this result is used to establish that the n vertex star has the highest laplacian energy over all n vertex trees which answers affirmatively to a question raised by radenkovic and gutman 10

improved results on brouwer s conjecture for sum of the laplacian eigenvalues of a graph abstract let g be a graph with n vertices and m edges and let s k g be the sum of the k largest laplacian eigenvalues of g it was conjectured by brouwer that s k g m k 1 2 holds for 1 k n in this paper we present several families of graphs for which brouwer s conjecture holds which improve some previously known results we also establish a new upper bound on s k g for split graphs which is tight for each k 1 2 n 1 and turns out to be better than that conjectured by brouwer

embedding gestalt laws in markov random fields the goal of this paper is to study a mathematical framework of 2d object shape modeling and learning for middle level vision problems such as image segmentation and perceptual organization for this purpose we pursue generic shape models which characterize the most common features of 2d object shapes in this paper shape models are learned from observed natural shapes based on a minimax entropy learning theory the learned shape models are gibbs distributions defined on markov random fields mrfs the neighborhood structures of these mrfs correspond to gestalt laws colinearity cocircularity proximity parallelism and symmetry thus both contour based and region based features are accounted for stochastic markov chain monte carlo mcmc algorithms are proposed for learning and model verification furthermore this paper provides a quantitative measure for the so called nonaccidental statistics and thus justifies some empirical observations of gestalt psychology by information theory our experiments also demonstrate that global shape properties can arise from interactions of local features

sums of regular self adjoint operators in hilbert c modules abstract we introduce a notion of weak anticommutativity for a pair s t of self adjoint regular operators in a hilbert c module e we prove that the sum s t of such pairs is self adjoint and regular on the intersection of their domains a similar result then holds for the sum s 2 t 2 of the squares we show that our definition is closely related to the connes skandalis positivity criterion in kk theory as such we weaken a sufficient condition of kucerovsky for representing the kasparov product our proofs indicate that our conditions are close to optimal

admissibility and controllability of diagonal volterra equations with scalar inputs this article studies volterra evolution equations from the point of view of control theory in the case that the generator of the underlying semigroup has a riesz basis of eigenvectors conditions for admissibility of the system s control operator are given in terms of the carleson embedding properties of certain discrete measures moreover exact and null controllability are expressed in terms of a new interpolation question for analytic functions providing a generalization of results known to hold for the standard cauchy problem the results are illustrated by examples involving heat conduction with memory

on a polynomial scalar perturbation of a schrodinger system in lp spaces abstract in the paper 10 the l p realization l p of the matrix schrodinger operator l u d i v q u v u was studied the generation of a semigroup in l p r d c m and characterization of the domain d l p has been established in this paper we perturb the operator l p by a scalar potential belonging to a class including all polynomials and show that still we have a strongly continuous semigroup on l p r d c m with domain embedded in w 2 p r d c m we also study the analyticity compactness positivity and ultracontractivity of the semigroup and prove gaussian kernel estimates further kernel estimates and asymptotic behaviour of eigenvalues of the matrix schrodinger operator are investigated

constructing a controllable graph under edge constraints abstract this paper is concerned with the problem of constructing a controllable graph subject to some practical edge constraints specifically suppose the total amount of vertices and the upper bounds on the graph diameter or on the vertex degree are given we consider the problem of exploring a class of feasible graphs that satisfy the constraints using the hybrid of a path graph and an antiregular graph we propose a simple and systematic method to generate a class of controllable graphs whose diameters or degrees cover the full possible ranges the method to select the control vector to ensure the controllability of the combined graph is also proposed numerical examples are provided to demonstrate our results

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

maximal graphs and graphs with maximal spectral radius abstract a maximal graph is a connected graph with degree sequence not majorized by the degree sequence of any other graph relationships between three different sequences of integers that describe maximal graphs are given recursive and explicit forms of the characteristic polynomial of the adjacency matrix of a maximal graph are derived a correspondence between maximal graphs and connected graphs with stepwise adjacency matrices shows that among all connected graphs with n vertices and e edges the graph with maximal spectral radius is a maximal graph such maximal graphs are identified for certain values of n and e

stochastic approximation algorithms for partition function estimation of gibbs random fields we present an analysis of previously proposed monte carlo algorithms for estimating the partition function of a gibbs random field we show that this problem reduces to estimating one or more expectations of suitable functionals of the gibbs states with respect to properly chosen gibbs distributions as expected the resulting estimators are consistent certain generalizations are also provided we study computational complexity with respect to grid size and show that monte carlo partition function estimation algorithms can be classified into two categories e type algorithms that are of exponential complexity and p type algorithms that are of polynomial complexity turing reducible to the problem of sampling from the gibbs distribution e type algorithms require estimating a single expectation whereas p type algorithms require estimating a number of expectations with respect to gibbs distributions which are chosen to be sufficiently close to each other in the latter case the required number of expectations is of polynomial order with respect to grid size we compare computational complexity by using both theoretical results and simulation experiments we determine the most efficient e type and p type algorithms and conclude that p type algorithms are more appropriate for partition function estimation we finally suggest a practical and efficient p type algorithm for this task

extremal laplacian energy of threshold graphs let g be a connected threshold graph of order n with m edges and trace t in this paper we give a lower bound on laplacian energy in terms of n m and t of g from this we determine the threshold graphs with the first four minimal laplacian energies moreover we obtain the threshold graphs with the largest and the second largest laplacian energies

locating the eigenvalues of trees abstract e give an o n method that computes for any tree t and interval how many eigenvalues of t lie within the interval our method is based on sylvester s law of inertia we use our algorithm to show that the nonzero eigenvalues of a caterpillar are simple it follows that caterpillars having b back nodes where b 2 1 are not integral we also show that among the regular caterpillars c b k formed by adjoining k legs to each of b back nodes all positive roots are in the interval k 1 k 2 and c b k is not integral if b 2

spectral threshold dominance brouwer s conjecture and maximality of laplacian energy abstract the laplacian energy of a graph is the sum of the distances of the eigenvalues of the laplacian matrix of the graph to the graph s average degree the maximum laplacian energy over all graphs on n nodes and m edges is conjectured to be attained for threshold graphs we prove the conjecture to hold for graphs with the property that for each k there is a threshold graph on the same number of nodes and edges whose sum of the k largest laplacian eigenvalues exceeds that of the k largest laplacian eigenvalues of the graph we call such graphs spectrally threshold dominated these graphs include split graphs and cographs and spectral threshold dominance is preserved by disjoint unions and taking complements we conjecture that all graphs are spectrally threshold dominated this conjecture turns out to be equivalent to brouwer s conjecture concerning a bound on the sum of the k largest laplacian eigenvalues

on graphs with equal algebraic and vertex connectivity let g be an undirected unweighted graph on n vertices let l be its laplacian matrix and let l l i j be the group inverse of l it is known that for z l 1 2 max1 i j n s 1n li s lj s the quantity 1 z l is a lower bound on the algebraic connectivity a g of g while the vertex connectivity of g v g is an upper bound on a g we characterize the graphs g for which v g a g and subsequently prove that if n v g 2 then v g a g holds if and only if 1 z l a g v g we close with an example showing that the equality 1 z l a g does not necessarily imply that 1 z l a g v g

further developments on brouwer s conjecture for the sum of laplacian eigenvalues of graphs abstract let g be a simple graph with order n and size m and having laplacian eigenvalues 1 2 n 1 n 0 and let s k g i 1 k i be the sum of k largest laplacian eigenvalues of g brouwer conjectured that s k g m k 1 2 for all k 1 2 n we obtain upper bounds for s k g in terms of the clique number the order n and integers p 0 r 1 s 1 s 2 2 associated to the structure of the graph g we discuss brouwer s conjecture for two large families of graphs the first family of graphs is obtained from a clique of size by identifying each of its vertices to a vertex of an arbitrary c cyclic graph and the second family is composed of the graphs in which the removal of the edges of the maximal complete bipartite subgraph gives a graph each of whose non trivial components is a c cyclic graph we show among these two large families of graphs the brouwer s conjecture holds for various subfamilies of graphs depending upon the value of c the order of the c cyclic graphs the clique number of the graph the order of the maximal complete bipartite subgraph and the number of the c cyclic components of the graph

h calculus for products of non commuting operators it is shown that the product of two sectorial operators a and b admits a bounded h calculus on a banach space x provided suitable commutator estimates and kalton weis type assumptions on a and b are satisfied

spectra of weighted generalized bethe trees joined at the root abstract a generalized bethe tree is a rooted tree in which vertices at the same distance from the root have the same degree let b i 1 i m be a set of trees such that for i 1 2 m 1 b i is a generalized bethe tree of k i levels 2 the vertices of b i at the level j have degree d i k i j 1 for j 1 2 k i and 3 the edges of b i joining the vertices at the level j with the vertices at the level j 1 have weight w i k i j for j 1 2 k i 1 let v b i 1 i m be the tree obtained from the union of the trees b i joined at their respective root vertices we give a complete characterization of the eigenvalues of the laplacian and adjacency matrices of v b i 1 i m moreover we derive results concerning their multiplicities in particular we characterize the spectral radii the algebraic conectivity and the second largest laplacian eigenvalue

examples of unbounded imaginary powers of operators two examples are given the first one consists of an operator of positive type in hilbert space without bounded imaginary powers the second one is concerned with the closedness of the sum of two closed operators in a hilbert space

indecomposable laplacian integral graphs abstract a graph that can be constructed from isolated vertices by the operations of union and complement is decomposable every decomposable graph is laplacian integral i e its laplacian spectrum consists entirely of integers an indecomposable graph is not decomposable the main purpose of this note is to demonstrate the existence of infinitely many indecomposable laplacian integral graphs

a fast algorithm of convex hull vertices selection for online classification reducing samples through convex hull vertices selection chvs within each class is an important and effective method for online classification problems since the classifier can be trained rapidly with the selected samples however the process of chvs is np hard in this paper we propose a fast algorithm to select the convex hull vertices based on the convex hull decomposition and the property of projection in the proposed algorithm the quadratic minimization problem of computing the distance between a point and a convex hull is converted into a linear equation problem with a low computational complexity when the data dimension is high an approximate instead of exact convex hull is allowed to be selected by setting an appropriate termination condition in order to delete more nonimportant samples in addition the impact of outliers is also considered and the proposed algorithm is improved by deleting the outliers in the initial procedure furthermore a dimension convention technique via the kernel trick is used to deal with nonlinearly separable problems an upper bound is theoretically proved for the difference between the support vector machines based on the approximate convex hull vertices selected and all the training samples experimental results on both synthetic and real data sets show the effectiveness and validity of the proposed algorithm

h infty calculus for the sum of non commuting operators a recent result of kalton and weis is extended to the case of non commuting operators employing the commutator condition of labbas and terreni or of da prato and grisvard under appropriate assumptions it is shown that the sum of two non commuting operators admits an h calculus the main results are then applied to a parabolic problem on a wedge domain

theorems on partitioned matrices revisited and their applications to graph spectra some old results about spectra of partitioned matrices due to goddard and schneider or haynsworth are re proved a new result is given for the spectrum of a block stochastic matrix with the property that each off diagonal block has equal entries and each diagonal block has equal diagonal entries and equal off diagonal entries the result is applied to the study of the spectra of the usual graph matrices by partitioning the vertex set of the graph according to the neighborhood equivalence relation the concept of a reduced graph matrix is introduced the question of when n 2 is the second largest signless laplacian eigenvalue of a connected graph of order n is treated a recent conjecture posed by tam fan and zhou on graphs that maximize the signless laplacian spectral radius over all not necessarily connected graphs with given numbers of vertices and edges is refuted the laplacian spectrum of a degree maximal graph is reconsidered

the critical group of a threshold graph the critical group of a connected graph is a finite abelian group whose order is the number of spanning trees in the graph the structure of this group is a subtle isomorphism invariant that has received much attention recently partly due to its relation to the graph laplacian and chip firing games however the group structure has been determined for relatively few classes of graphs based on computer evidence we conjecture the exact group structure for a well studied class of graphs having integer spectra the threshold graphs and prove this conjecture for the subclass which we call generic threshold graphs

connected graphs with maximal q index the one dominating vertex case abstract by the signless laplacian of a simple graph g we mean the matrix q g d g a g where a g d g denote respectively the adjacency matrix and the diagonal matrix of vertex degrees of g for every pair of positive integers n k it is proved that if 3 k n 3 then h n k the graph obtained from the star k 1 n 1 by joining a vertex of degree 1 to k 1 other vertices of degree 1 is the unique connected graph that maximizes the largest signless laplacian eigenvalue over all connected graphs with n vertices and n k edges

on the closedness of the sum of two closed operators o t t 1 where e g a is the infinitesimal generator of an analytic semigroup in a complex banach space x we find that in general it is false that for every fe lp 0 t x problem 1 has a solution uewi p o t x c lp o t a usually it is necessary to impose some further regularity conditions on f consider for instance the way in which problem 1 is studied in the paper 8 and compare th 3 7 and 3 14 which are applied in w 4 of the same paper to solve problem 1 we find that in general we have only strong solutions while in the hilbert space setting we have strict solutions this corresponds to the fact that in general the operator a b where b u u is only closable while in a hilbert space it is closed this remark suggests that the better result may depend on the nicer geometric properties of a hilbert space with respect to a general banach space and it is natural to ask which conditions should be imposed on the banach space to force the sum of two suitable closed opera tors to be closed the above considerations motivate the manifold aim of the present paper a to find conditions on a banach space x and on closed linear operators a and b acting in x which ensure that a b is closed b to apply the result of a to problem 1 it seems that the convenient property for the banach space x is convexity or otherwise stated the umd condition for information about these equiva lent conditions we refer to 4 in which it is also proved that if x is convex and l p oe then the hilbert transform is continuous from lp r x into lp r x on the other hand it is also known see 2 that if there exists pe 1 oe such that the hilbert transform is continuous from lp r x into itself

bayes classification of online arabic characters by gibbs modeling of class conditional densities this study investigates bayes classification of online arabic characters using histograms of tangent differences and gibbs modeling of the class conditional probability density functions the parameters of these gibbs density functions are estimated following the zhu et al constrained maximum entropy formalism originally introduced for image and shape synthesis we investigate two partition function estimation methods one uses the training sample and the other draws from a reference distribution the efficiency of the corresponding bayes decision methods and of a combination of these is shown in experiments using a database of 9 504 freely written samples by 22 writers comparisons to the nearest neighbor rule method and a kohonen neural network method are provided

graphs with maximal signless laplacian spectral radius abstract by the signless laplacian of a simple graph g we mean the matrix q g d g a g where a g d g denote respectively the adjacency matrix and the diagonal matrix of vertex degrees of g it is known that connected graphs g that maximize the signless laplacian spectral radius q g over all connected graphs with given numbers of vertices and edges are degree maximal for a maximal graph g with n vertices and r distinct vertex degrees r r 1 1 it is proved that q g q h for some maximal graph h with n 1 respectively n vertices and the same number of edges as g if either g has precisely two dominating vertices or there exists an integer i 2 i r 2 respectively if there exist positive integers i l with l 2 i r 2 such that i r 1 i n 1 respectively i r 1 i l r l 1 graphs that maximize q g over the class of graphs with m edges and m k vertices for k 0 1 2 3 are completely determined

existence uniqueness and regularity for a class of semilinear stochastic volterra equations with multiplicative noise abstract we consider a class of semilinear volterra type stochastic evolution equation driven by multiplicative gaussian noise the memory kernel not necessarily analytic is such that the deterministic linear equation exhibits a parabolic character under appropriate lipschitz type and linear growth assumptions on the nonlinear terms we show that the unique mild solution is mean p holder continuous with values in an appropriate sobolev space depending on the kernel and the data in particular we obtain pathwise space time sobolev holder regularity of the solution together with a maximal type bound on the spatial sobolev norm as one of the main technical tools we establish a smoothing property of the derivative of the deterministic evolution operator family

unoriented laplacian maximizing graphs are degree maximal abstract a connected graph is said to be unoriented laplacian maximizing if the spectral radius of its unoriented laplacian matrix attains the maximum among all connected graphs with the same number of vertices and the same number of edges a graph is said to be threshold maximal if its degree sequence is not majorized by the degree sequence of any other graph and in addition the graph is connected it is proved that an unoriented laplacian maximizing graph is maximal and also that there are precisely two unoriented laplacian maximizing graphs of a given order and with nullity 3 our treatment depends on the following known characterization a graph g is threshold maximal if and only if for every pair of vertices u v of g the sets n u v n v u where n u denotes the neighbor set of u in g are comparable with respect to the inclusion relation and in addition the graph is connected a conjecture about graphs that maximize the unoriented laplacian matrix among all graphs with the same number of vertices and the same number of edges is also posed

filters random fields and maximum entropy frame towards a unified theory for texture modeling this article presents a statistical theory for texture modeling this theory combines filtering theory and markov random field modeling through the maximum entropy principle and interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of view our theory characterizes the ensemble of images i with the same texture appearance by a probability distribution f i on a random field and the objective of texture modeling is to make inference about f i given a set of observed texture examples in our theory texture modeling consists of two steps 1 a set of filters is selected from a general filter bank to capture features of the texture these filters are applied to observed texture images and the histograms of the filtered images are extracted these histograms are estimates of the marginal distributions of f i this step is called feature extraction 2 the maximum entropy principle is employed to derive a distribution p i which is restricted to have the same marginal distributions as those in 1 this p i is considered as an estimate of f i this step is called feature fusion a stepwise algorithm is proposed to choose filters from a general filter bank the resulting model called frame filters random fields and maximum entropy is a markov random field mrf model but with a much enriched vocabulary and hence much stronger descriptive ability than the previous mrf models used for texture modeling gibbs sampler is adopted to synthesize texture images by drawing typical samples from p i thus the model is verified by seeing whether the synthesized texture images have similar visual appearances to the texture images being modeled experiments on a variety of 1d and 2d textures are described to illustrate our theory and to show the performance of our algorithms these experiments demonstrate that many textures which are previously considered as from different categories can be modeled and synthesized in a common framework

strong order of convergence of a fully discrete approximation of a linear stochastic volterra type evolution equation in this paper we investigate a discrete approximation in time and in space of a hilbert space valued stochastic process u t t 0 t satisfying a stochastic linear evolution equation with a positive type memory term driven by an additive gaussian noise the equation can be written in an abstract form as du t 0 b t s au s ds dt dw t 0 t u 0 u0 h where w is a q wiener process on h l d and where the main example of b we consider is given by b t t 1 0 0 such that a has finite trace and that q is bounded from h into d a for some real with 1 1 the discretization is achieved via an implicit euler scheme and a laplace transform convolution quadrature in time parameter t t n and a standard continuous finite element method in space parameter h let un h be the discrete solution at t n t we show that e un h u t 1 2 o h t for any 1 1 2 and 1 1 m kovacs department of mathematics and statistics university of otago po box 56 dunedin 9054 new zealand e mail mkovacs maths otago ac nz j printems laboratoire d analyse et de mathematiques appliquees cnrs umr 8050 61 avenue du general de gaulle universite paris est 94010 creteil france e mail printems u pec fr 2 mihaly kovacs jacques printems

global properties of generalized ornstein uhlenbeck operators on lp rn rn with more than linearly growing coefficients we show that the realization ap of the elliptic operator au div q u f u vu in lp rn rn p 1 generates a strongly continuous semigroup and we determine its domain d ap u w2 p rn rn f u vu lp rn rn if 1 p the diffusion coefficients q qij are uniformly elliptic and bounded together with their first order derivatives the drift coefficients f can grow as x log x and v can grow logarithmically our approach relies on the monniaux pruss theorem on the sum of noncommuting operators we also prove lp lq estimates and under somewhat stronger assumptions we establish pointwise gradient estimates and smoothing of the semigroup in the spaces w p rn rn 0 1 where 1 p

h calculus for the stokes operator on lq spaces it is proved that the stokes operator on a bounded domain an exterior domain or a perturbed half space admits a bounded h calculus on lq if q 1

solvability and maximal regularity of parabolic evolution equations with coefficients continuous in time abstract we establish maximal regularity of type lp for a parabolic evolution equation u t a t u t f t with a c 0 t l d a 0 x and construct the corresponding evolution family on the underlying banach space x our proofs are based on the operator sum method and the use of evolution semigroups the results are applied to parabolic partial differential equations with continuous coefficients

constructably laplacian integral graphs a graph is laplacian integral if the spectrum of its laplacian matrix consists entirely of integers we consider the class of constructably laplacian integral graphs those graphs that be constructed from an empty graph by adding a sequence of edges in such a way that each time a new edge is added the resulting graph is laplacian integral we characterize the constructably laplacian integral graphs in terms of certain forbidden vertex induced subgraphs and consider the number of nonisomorphic laplacian integral graphs that can be constructed by adding a suitable edge to a constructably laplacian integral graph we also discuss the eigenvalues of constructably laplacian integral graphs and identify families of isospectral nonisomorphic graphs within the class