experiments with implicit upwind methods for the euler equations abstract a number of implicit integration schemes for the one dimensional euler equations with conservative upwind spatial differencing are tested on a problem of steady discontinuous flow fastest convergence quadratic for the first order backward euler scheme is obtained with the upwind switching provided by van leer s differentiable split fluxes which easily linearize in time with roe s nondifferentiable split flux differences the iterations may get trapped in a limit cycle this also happens in a second order scheme with split fluxes if the matrix coefficients arising in the implicit time linearization are not properly centered in space the use of second order terms computed from split fluxes degrades the accuracy of the solution especially if these are subjected to a limiter for the sake of monotonicity preservation second order terms computed from the characteristic variables perform best

asymptotic behavior of conjunctive boolean networks over weakly connected digraphs a conjunctive boolean network cbn is a finite state dynamical system whose variables take values from a binary set and the value update rule for each variable is a boolean function consisting only of logic and operations we investigate the asymptotic behavior of cbns by computing their periodic orbits when the underlying digraph is strongly connected the periodic orbits of the associated cbn have been completely understood one to one corresponding to binary necklaces of a certain length given by the loop number of the graph we characterize in the paper the periodic orbits of cbns over arbitrary weakly connected digraphs we establish among other things a new method to investigate their asymptotic behavior specifically we introduce a graphical approach termed system reduction which turns the underlying digraph into a special weakly connected digraph whose strongly connected components are all cycles we show that the reduced system uniquely determines the asymptotic behavior of the original system moreover we provide a constructive method for computing the periodic orbit of the reduced system which the system will enter for a given but arbitrary initial condition

trees with minimal laplacian coefficients let g be a simple undirected graph with the characteristic polynomial of its laplacian matrix l g p g m email protected k 0 n 1 kc email protected n k it is well known that for trees the laplacian coefficient c n 2 is equal to the wiener index of g while c n 3 is equal to the modified hyper wiener index of the graph in this paper we characterize n vertex trees with given matching number m which simultaneously minimize all laplacian coefficients the extremal tree a n m is a spur obtained from the star graph s n m 1 with n m 1 vertices by attaching a pendant edge to each of certain m 1 non central vertices of s n m 1 in particular a n m minimizes the wiener index the modified hyper wiener index and the recently introduced incidence energy of trees defined as ie g email protected k 0 email protected k where m k are the eigenvalues of signless laplacian matrix q g d g a g we introduced a general r transformation which decreases all laplacian coefficients simultaneously in conclusion we illustrate on examples of wiener index and incidence energy that the opposite problem of simultaneously maximizing all laplacian coefficients has no solution

on the flexibility of agglomeration based physical space discontinuous galerkin discretizations in this work we show that the flexibility of the discontinuous galerkin dg discretization can be fruitfully exploited to implement numerical solution strategies based on the use of elements with very general shapes thanks to the freedom in defining the mesh topology we propose a new h adaptive technique based on agglomeration coarsening of a fine mesh the possibility to enhance the error distribution over the computational domain is investigated on a poisson problem with the goal of obtaining a mesh independent discretization the main building block of our dg method consists of defining discrete polynomial spaces directly on physical frame elements for this purpose we orthonormalize with respect to the l 2 product a set of monomials relocated in a specific element frame and we introduce an easy way to reduce the cost related to numerical integration on agglomerated meshes to complete the dg formulation for second order problems two extensions of the br2 scheme to arbitrary polyhedral grids including an estimate of the stabilization parameter ensuring the coercivity property are here proposed

hp version composite discontinuous galerkin methods for elliptic problems on complicated domains in this paper we introduce the hp version discontinuous galerkin composite finite element method for the discretization of second order elliptic partial differential equations this class of methods allows for the approximation of problems posed on computational domains which may contain a huge number of local geometrical features or microstructures while standard numerical methods can be devised for such problems the computational effort may be extremely high as the minimal number of elements needed to represent the underlying domain can be very large in contrast the minimal dimension of the underlying composite finite element space is independent of the number of geometric features the key idea in the construction of this latter class of methods is that the computational domain omega is no longer resolved by the mesh instead the finite element basis or shape functions are adapted to the geometric details present in omega in this paper we extend these ideas to the discontinuous galer

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

on the nullity of the line graph of unicyclic graph with depth one abstract a connected graph with a unique cycle is called a unicyclic graph a unicyclic graph with depth one may be thought of as being obtained from a cycle by appending n i pendent edges on each vertex v i in the cycle c t for some integer t 3 denoted by c n 1 n 2 n t in this paper we give a complete characterization on the nullity of the line graph g l c n 1 n 2 n t as follows let m i n i 0 then i g 2 if and only if m 0 and t 0 mod 4 ii g 1 if and only if m 1 and either 1 n i 0 1 for i 1 t the length of any zero chain of n 1 n 2 n t is even and t m 0 mod 4 or 2 t 0 mod 4 and one of n 1 n 3 n t 1 0 and n 2 n 4 n t 0 must hold iii g 0 otherwise

maximal sensitivity of boolean nested canalizing functions abstract boolean nested canalizing functions ncf have important applications in molecular regulatory networks engineering and computer science in the literature there are two sensitivities to measure the complexity of a boolean function one is average sensitivity the other one is maximal sensitivity we follow the tradition and omit the word maximal in other words in this paper sensitivity is always maximal sensitivity using the past work of the authors and their coauthors on a characterization of ncf we obtain the formula of the sensitivity of any ncf we find that the sensitivity of any ncf is between n 2 2 and n both lower and upper bounds are tight we prove that the block sensitivity hence the l block sensitivity is the same as the sensitivity for ncf it is well known that monotone boolean functions mbf also have this property we characterize all functions which are both monotone and nested canalizing mncf the closed formula of the cardinality of the set of mncfs is also provided

signless laplacians of finite graphs we survey properties of spectra of signless laplacians of graphs and discuss possibilities for developing a spectral theory of graphs based on this matrix for regular graphs the whole existing theory of spectra of the adjacency matrix and of the laplacian matrix transfers directly to the signless laplacian and so we consider arbitrary graphs with special emphasis on the non regular case the results which we survey old and new are of two types a results obtained by applying to the signless laplacian the same reasoning as for corresponding results concerning the adjacency matrix b results obtained indirectly via line graphs among other things we present eigenvalue bounds for several graph invariants an interpretation of the coefficients of the characteristic polynomial a theorem on powers of the signless laplacian and some remarks on star complements

nested canalyzing unate cascade and polynomial functions this paper focuses on the study of certain classes of boolean functions that have appeared in several different contexts nested canalyzing functions have been studied recently in the context of boolean network models of gene regulatory networks in the same context polynomial functions over finite fields have been used to develop network inference methods for gene regulatory networks finally unate cascade functions have been studied in the design of logic circuits and binary decision diagrams this paper shows that the class of nested canalyzing functions is equal to that of unate cascade functions furthermore it provides a description of nested canalyzing functions as a certain type of boolean polynomial function using the polynomial framework one can show that the class of nested canalyzing functions or equivalently the class of unate cascade functions forms an algebraic variety which makes their analysis amenable to the use of techniques from algebraic geometry and computational algebra as a corollary of the functional equivalence derived here a formula in the literature for the number of unate cascade functions provides such a formula for the number of nested canalyzing functions

a low dissipation dg method for the under resolved simulation of low mach number turbulent flows abstract in recent years the use of high order discontinuous galerkin dg methods for the under resolved direct numerical simulations udns of turbulent flows has received special attention the suitability of the approach for this kind of applications is related to the dissipation and dispersion proprieties of the scheme while the dispersion errors are small over a broad range of frequencies a relevant dissipation error mainly acts at the smallest under resolved scales resembling a high frequency filter nevertheless it was recognized flad and gassner 2017 mengaldo et al 2018 that the choice of the interface convective numerical flux strongly affects this dissipation behaviour and ultimately the success of the udns approach in this regard the excess of numerical dissipation caused by some upwind numerical convective fluxes must be avoided in particular when dealing with low speed flows since this behaviour is exacerbated approaching the incompressibility limit fixes for the excess of numerical dissipation of these schemes have been proposed by several authors in the context of different numerical methods see for example weiss and smith 1995 in this work a simple modification of the dissipation term of the low mach preconditioned roe scheme proposed by weiss and smith is considered the aim is to reduce further the amount of numerical dissipation with the intent of improving the results of udns a spatial dg discretization coupled with a linearly implicit rosenbrock type time integrator is here considered as a numerical framework perfectly suited for the assessment and comparison of different numerical flux functions results on canonical turbulent flow problems as the taylor green vortex and the flow in a straight sided channel are presented the improved accuracy of the proposed flux function is demonstrated the new low dissipation flux can be useful also in the context of standard lower order finite volume methods

convergence behavior and n roots of stack filters the convergence behavior of two types of stack filters is investigated both types are shown to possess the convergence property and to exhibit nontrivial behavior the first type of stack filter has the erosive property it erodes any input signal to a root after a sufficient number of passes the second type of stack filter has the dilative property it dilates any input signal to a root after a sufficient number of passes for each type of stack filter an algorithm is presented which can determine a filter that has any specific signal or set of signals as roots these two algorithms are efficient in that their execution time is a linear function of the length of the input signal the width of the filter window and the number of signals to be preserved since some stack filters have the phenomenon of oscillations when they filter some input signals successively a partial ordering is defined over the set of stack filters which makes it possible to determine upper and lower bounds for these oscillations

graphs with least eigenvalue 2 ten years on abstract the authors monograph spectral generalizations of line graphs was published in 2004 following the successful use of star complements to complete the classification of graphs with least eigenvalue 2 guided by citations of the book we survey progress in this area over the past decade some new observations are included

genetic networks with canalyzing boolean rules are always stable we determine stability and attractor properties of random boolean genetic network models with canalyzing rules for a variety of architectures for all power law exponential and flat in degree distributions we find that the networks are dynamically stable furthermore for architectures with few inputs per node the dynamics of the networks is close to critical in addition the fraction of genes that are active decreases with the number of inputs per node these results are based upon investigating ensembles of networks using analytical methods also for different in degree distributions the numbers of fixed points and cycles are calculated with results intuitively consistent with stability analysis fewer inputs per node implies more cycles and vice versa there are hints that genetic networks acquire broader degree distributions with evolution and hence our results indicate that for single cells the dynamics should become more stable with evolution however such an effect is very likely compensated for by multicellular dynamics because one expects less stability when interactions among cells are included we verify this by simulations of a simple model for interactions among cells

stack filters the median and other rank order operators possess two properties called the threshold decomposition and the stacking properties the first is a limited superposition property which leads to a new architecture for these filters the second is an ordering property which allows an efficient vlsi implementation of the threshold decomposition architecture motivated by the success of rank order filters in a wide variety of applications and by the ease with which they can now be implemented we consider in this paper a new class of filters called stack filters they share the threshold decomposition and stacking properties of rank order filters but are otherwise unconstrained they are shown to form a very large class of easily implemented nonlinear filters which includes the rank order operators as well as all compositions of morphological operators the convergence properties of these filters are investigated using techniques similar to those used to determine root signal behavior of median filters the results obtained include necessary conditions for a stack filter to preserve monotone regions or edges in signals the output distribution for these filters is also found all the stack filters of window width 3 are determined along with their convergence properties among these filters are found two which we have named asymmetric median filters they share all the properties of median filters except that they remove impulses of one sign only that is one removes only positive going edges the other removes only negative going edges while the median filter removes impulses of both signs this investigation of the properties of stack filters thus produces several new useful and easily implemented filters

on the laplacian coefficients of signed graphs abstract let g be a signed graph where g is its underlying graph and its sign function defined on edges of g a signed graph the subgraph of is its signed tu subgraph if the signed graph induced by the vertices of consists of trees and or unbalanced unicyclic signed graphs let l d g a be the laplacian of in this paper we express the coefficient of the laplacian characteristic polynomial of based on the signed tu subgraphs of and establish the relation between the laplacian characteristic polynomial of a signed graph with adjacency characteristic polynomials of its signed line graph and signed subdivision graph as an application we identify the signed unicyclic graphs having extremal coefficients of the laplacian characteristic polynomial

robust untangling of curvilinear meshes this paper presents a technique that allows to untangle high order curvilinear meshes the technique makes use of unconstrained optimization where element jacobians are constrained to lie in a prescribed range through moving log barriers the untangling procedure starts from a possibly invalid curvilinear mesh and moves mesh vertices with the objective of producing elements that all have bounded jacobians bounds on jacobians are computed using the results of johnen et al 2012 2013 1 2 the technique is applicable to any kind of polynomial element for surface volume hybrid or boundary layer meshes a series of examples demonstrate both the robustness and the efficiency of the technique the final example involving a time explicit computation shows that it is possible to control the stable time step of the computation for curvilinear meshes through an alternative element deformation measure

smoothed aggregation multigrid for the discontinuous galerkin method the aim of this paper is to investigate theoretically as well as experimentally an algebraic multilevel algorithm for the solution of the linear systems that arise from the discontinuous galerkin method the smoothed aggregation multigrid introduced by vanek for the conforming finite element method is applied to low order discretizations of convection diffusion equations for the elliptic model problem the algorithm is shown to be quasi optimal adjustments for the case of nonvanishing advection such as directionally implicit smoothing and a suitable splitting of the operator are discussed several numerical experiments are presented for two dimensional problems including a newton type linearization of the compressible navier stokes equations

a flexible inner outer preconditioned gmres algorithm a variant of the gmres algorithm is presented that allows changes in the preconditioning at every step there are many possible applications of the new algorithm some of which are briefly discussed in particular a result of the flexibility of the new variant is that any iterative method can be used as a preconditioner for example the standard gmres algorithm itself can be used as a preconditioner as can cgnr or cgne the conjugate gradient method applied to the normal equations however the more appealing utilization of the method is in conjunction with relaxation techniques possibly multilevel techniques the possibility of changing preconditioners may be exploited to develop efficient iterative methods and to enhance robustness a few numerical experiments are reported to illustrate this fact

the deformed consensus protocol this paper studies a generalization of the standard continuous time consensus protocol obtained by replacing the laplacian matrix of the communication graph with the so called deformed laplacian the deformed laplacian is a second degree matrix polynomial in the real variable s which reduces to the standard laplacian for s equal to unity the stability properties of the ensuing deformed consensus protocol are studied in terms of parameter s for some special families of undirected and directed graphs and for arbitrary graph topologies by leveraging the spectral theory of quadratic eigenvalue problems examples and simulation results are provided to illustrate our theoretical findings

a multilevel discontinuous galerkin method a variable v cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented an analysis under a mild regularity assumption shows that the preconditioner is uniform the interior penalty method is then combined with a discontinuous galerkin scheme to arrive at a discretization scheme for an advection diffusion problem for which an error estimate is proved a multigrid algorithm for this method is presented and numerical experiments indicating its robustness with respect to diffusion coefficient are reported

stratification and enumeration of boolean functions by canalizing depth abstract boolean network models have gained popularity in computational systems biology over the last dozen years many of these networks use canalizing boolean functions which has led to increased interest in the study of these functions the canalizing depth of a function describes how many canalizing variables can be recursively picked off until a non canalizing function remains in this paper we show how every boolean function has a unique algebraic form involving extended monomial layers and a well defined core polynomial this generalizes recent work on the algebraic structure of nested canalizing functions and it yields a stratification of all boolean functions by their canalizing depth as a result we obtain closed formulas for the number of n variable boolean functions with depth k which simultaneously generalizes enumeration formulas for canalizing and nested canalizing functions

multigrid algorithms for hp discontinuous galerkin discretizations of elliptic problems we present w cycle h p and hp multigrid algorithms for the solution of the linear system of equations arising from a wide class of hp version discontinuous galerkin discretizations of elliptic problems starting from a classical framework in geometric multigrid analysis we define a smoothing and an approximation property which are used to prove uniform convergence of the w cycle scheme with respect to the discretization parameters and the number of levels provided the number of smoothing steps is chosen of order p 2 mu where p is the polynomial approximation degree and mu 0 1 a discussion on the effects of employing inherited or noninherited sublevel solvers is also presented numerical experiments confirm the theoretical results

difference equation for tracking perturbations in systems of boolean nested canalyzing functions this paper studies the spread of perturbations through networks composed of boolean functions with special canalyzing properties canalyzing functions have the property that at least for one value of one of the inputs the output is fixed irrespective of the values of the other inputs in this paper the focus is on partially nested canalyzing functions in which multiple but not all inputs have this property in a cascading fashion they naturally describe many relationships in real networks for example in a gene regulatory network the statement if gene a is expressed then gene b is not expressed regardless of the states of other genes implies that a is canalyzing on the other hand the additional statement if gene a is not expressed and gene c is expressed then gene b is automatically expressed otherwise gene b s state is determined by some other type of rule implies that gene b is expressed by a partially nested canalyzing function with more than two variables but with two canalyzing variables in this paper a difference equation model of the probability that a network node s value is affected by an initial perturbation over time is developed analyzed and validated numerically it is shown that the effect of a perturbation decreases towards zero over time if the boolean functions are canalyzing in sufficiently many variables the maximum dynamical impact of a perturbation is shown to be comparable to the average impact for a wide range of values of the average sensitivity of the network percolation limits are also explored these are parameter values which generate a transition of the expected perturbation effect to zero as other parameters are varied so that the initial perturbation does not scale up with the parameters once the percolation limits are reached

the number of multistate nested canalyzing functions abstract identifying features of molecular regulatory networks is an important problem in systems biology it has been shown that the combinatorial logic of such networks can be captured in many cases by special functions called nested canalyzing in the context of discrete dynamic network models it was also shown that the dynamics of networks constructed from such functions has very special properties that are consistent with what is known about molecular networks and that simplify analysis it is important to know how restrictive this class of functions is for instance for the purpose of network reverse engineering this paper contains a formula for the number of such functions and a comparison to the class of all functions in particular it is shown that as the number of variables becomes large the ratio of the number of nested canalyzing functions to the number of all functions converges to zero this shows that the class of nested canalyzing functions is indeed very restrictive the principal tool used for this investigation is a description of these functions as polynomials and a parametrization of the class of all such polynomials in terms of relations on their coefficients this parametrization can also be used for the purpose of network reverse engineering using only nested canalyzing functions

an artificial compressibility flux for the discontinuous galerkin solution of the incompressible navier stokes equations discontinuous galerkin dg methods have proved to be well suited for the construction of robust high order numerical schemes on unstructured and possibly nonconforming grids for a variety of problems their application to the incompressible navier stokes ins equations has also been recently considered although the subject is far from being fully explored in this work we propose a new approach for the dg numerical solution of the ins equations written in conservation form the inviscid numerical fluxes both in the continuity and in the momentum equation are computed using the values of velocity and pressure provided by the exact solution of the riemann problem associated with a local artificial compressibility perturbation of the equations unlike in most of the existing methods artificial compressibility is here introduced only at the interface flux level therefore resulting in a consistent discretization of the ins equations irrespectively of the amount of artificial compressibility introduced the discretization of the viscous term follows the well established dg scheme named br2 the performance and the accuracy of the method are demonstrated by computing the kovasznay flow and the two dimensional lid driven cavity flow for a wide range of reynolds numbers and for various degrees of polynomial approximation

perturbations of discrete elliptic operators abstract given v a finite set a self adjoint operator k on c v is called elliptic if it is positive semi definite and its lowest eigenvalue is simple therefore there exists a unique up to sign unitary function c v satisfying k and then k is named elliptic clearly a elliptic operator is singular iff 0 examples of elliptic operators are the so called schrodinger operators on finite connected networks as well as the signless laplacian of connected bipartite networks a elliptic operator k defines an automorphism on whose inverse is called orthogonal green operator of k we aim here at studying the effect of a perturbation of k on its orthogonal green operator the perturbation here considered is performed by adding a self adjoint and positive semi definite operator to k as particular cases we consider the effect of changing the conductances on semi definite schodinger operators on finite connected networks and on the signless laplacian of connected bipartite networks the expression obtained for the perturbed network is explicitly given in terms of the orthogonal green function of the original network

on q integral graphs with edge degrees at most six abstract q integral graphs are graphs whose signless laplacians have only integral eigenvalues the edge degree of an edge is the number of edges adjacent to the edge in 2008 s k simic and z stanic studied connected q integral graphs with edge degrees at most five in this paper we study connected q integral graphs with edge degrees at most six

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 signless laplacian coefficients and incidence energy of bicyclic graphs abstract let q g x det x i q g i 1 n 1 i i x n i be the characteristic polynomial of the signless laplacian matrix of a graph g of order n this paper investigates how the signless laplacian coefficients i e coefficients of q g x change after some graph transformations these results are used to prove that the set b n of all bicyclic graphs of order n has exactly two minimal elements with respect to the partial ordering of their coefficients furthermore we present a sharp lower bound for the incidence energy of bicyclic graphs of order n and characterize all extremal graphs

multigrid algorithms for symmetric discontinuous galerkin methods on graded meshes we study a class of symmetric discontinuous galerkin methods on graded meshes optimal order error estimates are derived in both the energy norm and the l 2 norm and we establish the uniform convergence of v cycle f cycle and w cycle multigrid algorithms for the resulting discrete problems numerical results that confirm the theoretical results are also presented

the influence of canalization on the robustness of boolean networks abstract time and state discrete dynamical systems are frequently used to model molecular networks this paper provides a collection of mathematical and computational tools for the study of robustness in boolean network models the focus is on networks governed by k canalizing functions a recently introduced class of boolean functions that contains the well studied class of nested canalizing functions the variable activities and sensitivity of a function quantify the impact of input changes on the function output this paper generalizes the latter concept to c sensitivity and provides formulas for the activities and c sensitivity of general k canalizing functions as well as canalizing functions with more precisely defined structure a popular measure for the robustness of a network the derrida value can be expressed as a weighted sum of the c sensitivities of the governing canalizing functions and can also be calculated for a stochastic extension of boolean networks these findings provide a computationally efficient way to obtain derrida values of boolean networks deterministic or stochastic that does not involve simulation

characterizing threshold graphs with k main signless laplacian eigenvalues abstract we show that the number k of main signless laplacian eigenvalues of a threshold graph on n 3 vertices is bounded by n 2 and we characterize for any integer 1 k n 2 all such graphs with exactly k main signless laplacian eigenvalues moreover we also determine the number of threshold graphs on n vertices with k main signless laplacian eigenvalues

the number and probability of canalizing functions canalizing functions have important applications in physics and biology for example they represent a mechanism capable of stabilizing chaotic behavior in boolean network models of discrete dynamical systems when comparing the class of canalizing functions to other classes of functions with respect to their evolutionary plausibility as emergent control rules in genetic regulatory systems it is informative to know the number of canalizing functions with a given number of input variables this is also important in the context of using the class of canalizing functions as a constraint during the inference of genetic networks from gene expression data to this end we derive an exact formula for the number of canalizing boolean functions of n variables we also derive a formula for the probability that a random boolean function is canalizing for any given bias p of taking the value 1 in addition we consider the number and probability of boolean functions that are canalizing for exactly k variables finally we provide an algorithm for randomly generating canalizing functions with a given bias p and any number of variables which is needed for monte carlo simulations of boolean networks

canalizing boolean functions maximize mutual information information processing in biologically motivated boolean networks is of interest in recent information theoretic research one measure to quantify this ability is the well known mutual information using fourier analysis we show that canalizing functions maximize mutual information between a single input variable and the outcome of a function with fixed expectation a similar result can be obtained for the mutual information between a set of input variables and the output further if the expectation of the function is not fixed we obtain that the mutual information is maximized by a function only dependent on this single variable i e the dictatorship function we prove our findings for boolean functions with uniformly distributed as well as product distributed input variables

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 forcing functions in kauffman s random boolean networks the phase transition between frozen and chaotic behavior in kauffman s cellular automata on a nearest neighbor square lattice does not agree with the percolation threshold of the forcing functions

which graphs are determined by their spectrum for almost all graphs the answer to the question in the title is still unknown here we survey the cases for which the answer is known not only the adjacency matrix but also other types of matrices such as the laplacian matrix are considered

permanental roots and the star degree of a graph abstract for undirected graphs without loops or multiple edges we define the star degree of a graph and prove that it is equal to the multiplicity of the root 1 of per xi b where b d a considering bipartite graphs we prove that per xi b per xi l where l d a and consequently that the star degree of a bipartite graph can also be characterized by the multiplicity of the root 1 of per xi l

signless laplacian spectral radius and hamiltonicity we give tight conditions on the signless laplacian spectral radius of a graph for the existence of hamiltonian paths and cycles

h multigrid agglomeration based solution strategies for discontinuous galerkin discretizations of incompressible flow problems abstract in this work we exploit agglomeration based h multigrid preconditioners to speed up the iterative solution of discontinuous galerkin discretizations of the stokes and navier stokes equations as a distinctive feature h coarsened mesh sequences are generated by recursive agglomeration of a fine grid admitting arbitrarily unstructured grids of complex domains and agglomeration based discontinuous galerkin discretizations are employed to deal with agglomerated elements of coarse levels both the expense of building coarse grid operators and the performance of the resulting multigrid iteration are investigated for the sake of efficiency coarse grid operators are inherited through element by element l 2 projections avoiding the cost of numerical integration over agglomerated elements specific care is devoted to the projection of viscous terms discretized by means of the br2 dg method we demonstrate that enforcing the correct amount of stabilization on coarse grids levels is mandatory for achieving uniform convergence with respect to the number of levels the numerical solution of steady and unsteady linear and non linear problems is considered tackling challenging 2d test cases and 3d real life computations on parallel architectures significant execution time gains are documented

a high order discontinuous galerkin method for the unsteady incompressible navier stokes equations we present a high order discontinuous galerkin discretization of the unsteady incompressible navier stokes equations in convection dominated flows using triangular and tetrahedral meshes the scheme is based on a semi explicit temporal discretization with explicit treatment of the nonlinear term and implicit treatment of the stokes operator the nonlinear term is discretized in divergence form by using the local lax friedrichs fluxes thus local conservativity is inherent spatial discretization of the stokes operator has employed both equal order p k p k and mixed order p k p k 1 velocity and pressure approximations a second order approximate algebraic splitting is used to decouple the velocity and pressure calculations leading to an algebraic helmholtz equation for each component of the velocity and a consistent poisson equation for the pressure the consistent poisson operator is replaced by an equivalent in stability and convergence operator namely that arising from the interior penalty discretization of the standard poisson operator with appropriate boundary conditions this yields a simpler and more efficient method characterized by a compact stencil size we show the temporal and spatial behavior of the method by solving some popular benchmarking tests for an unsteady stokes problem second order temporal convergence is obtained while for the taylor vortex test problem on both semi structured and fully unstructured triangular meshes spectral convergence with respect to the polynomial degree k is obtained by studying the orr sommerfeld stability problem we demonstrate that the p k p k method yields a stable solution while the p k p k 1 formulation leads to unphysical instability the good performance of the method is further shown by simulating vortex shedding in flow past a square cylinder we conclude that the proposed discontinuous galerkin method with the p k p k formulation is an efficient scheme for accurate and stable solution of the unsteady navier stokes equations in convection dominated flows

average path length of binary decision diagrams the traditional problem in binary decision diagrams bdds has been to minimize the number of nodes since this reduces the memory needed to store the bdd recently a new problem has emerged minimizing the average path length apl apl is a measure of the time needed to evaluate the function by applying a sequence of variable values it is of special significance when bdds are used in simulation and design verification a main result of this paper is that the apl for benchmark functions is typically much smaller than for random functions that is for the set of all functions we show that the average apl is close to the maximum path length whereas benchmark functions show a remarkably small apl surprisingly however typical functions do not achieve the absolute maximum apl we show that the parity functions are unique in having that distinction we show that the apl of a bdd can vary considerably with variable ordering we derive the apl for various functions including the and or threshold achilles heel and certain arithmetic functions we show that the unate cascade functions uniquely achieve the absolute minimum apl

limit cycle structure for dynamic bi threshold systems in this paper we determine the limit cycle structures of synchronous and sequential finite dynamical systems governed by dynamic bi threshold functions over non uniform networks so far work in this area has been concerned with static threshold values and our results generalize these in particular this includes the celebrated result by goles and olivos on synchronous neural networks 1981 5 the work by kuhlman et al 2012 12 on static bi threshold systems and the work by chang et al 2014 2 on dynamic standard threshold systems in our work the state of each vertex v includes the usual binary state x v 0 1 the dynamic up thresholds k v and down thresholds k v whose values change only upon a transition of x v we show that the projection of the periodic orbits onto the boolean x dynamics have maximal size 2 under the synchronous update method regardless of how the up and down thresholds evolve the proof is a careful extension of the technique originally developed in the proof by goles and olivos 1981 5 and which was later modified by kuhlman et al 2012 12 to cover bi threshold systems we also derive sufficient conditions on the evolution of the up and down thresholds that ensures that the sequential systems only have fixed points as limit sets the results should be relevant for modeling and analyzing a large range of social and biological systems where agent adaptation occurs and needs to be accounted for

spectra of copies of a generalized bethe tree attached to any graph abstract a generalized bethe tree is a rooted unweighted tree in which vertices at the same level have the same degree let g be any connected graph let g b be the graph obtained from g by attaching a generalized bethe tree b by its root to each vertex of g we characterize completely the eigenvalues of the signless laplacian laplacian and adjacency matrices of the graph g b including results on the eigenvalue multiplicities finally for the laplacian and signless laplacian matrices we recall a procedure to compute a tight upper bound on the algebraic connectivity of g b as well as on the smallest eigenvalue of the signless laplacian matrix of g b whenever g is a non bipartite graph

boolean nested canalizing functions a comprehensive analysis abstract boolean network models of molecular regulatory networks have been used successfully in computational systems biology the boolean functions that appear in published models tend to have special properties in particular the property of being nested canalizing a concept inspired by the concept of canalization in evolutionary biology it has been shown that networks comprised of nested canalizing functions have dynamic properties that make them suitable for modeling molecular regulatory networks namely a small number of large attractors as well as relatively short limit cycles this paper contains a detailed analysis of this class of functions based on a novel normal form as polynomial functions over the boolean field the concept of layer is introduced that stratifies variables into different classes depending on their level of dominance using this layer concept a closed form formula is derived for the number of nested canalizing functions with a given number of variables additional metrics considered include hamming weight the activity number of any variable and the average sensitivity of the function it is also shown that the average sensitivity of any nested canalizing function is between 0 and 2 this provides a rationale for why nested canalizing functions are stable since a random boolean function in n variables has average sensitivity n 2 the paper also contains experimental evidence that the layer number is an important factor in network stability

mixed hp dgfem for incompressible flows we consider several mixed discontinuous galerkin approximations of the stokes problem and propose an abstract framework for their analysis using this framework we derive a priori error estimates for hp approximations on tensor product meshes we also prove a new stability estimate for the discrete divergence bilinear form