soliton like phenomena in one dimensional cross diffusion systems a predator prey pursuit and evasion example abstract we have studied properties of non linear waves in a mathematical model of a predator prey system with pursuit and evasion we demonstrate a new type of propagating wave in this system the mechanism of propagation of these waves essentially depends on the taxis represented by non linear cross diffusion terms in the mathematical formulation we have shown that the dependence of the velocity of wave propagation on the taxis has two distinct forms parabolic and linear transition from one form to the other correlates with changes in the shape of the wave profile dependence of the propagation velocity on diffusion in this system differs from the square root dependence typical of reaction diffusion waves we also demonstrate that for systems with negative and positive taxis for example pursuit and evasion there typically exists a large region in the parameter space where the waves demonstrate quasi soliton interaction colliding waves can penetrate through each other and waves can also reflect from impermeable boundaries

complete multipartite graphs are determined by their distance spectra abstract in this paper we prove that the complete multipartite graphs are determined by their distance spectra which confirms the conjecture proposed by lin hong wang and shu 2013 7 although it is well known that the complete multipartite graphs cannot be determined by their adjacency spectra

the graphs with the least distance eigenvalue at least 1 172 let g be a connected graph with order n and d g be the distance matrix of g suppose that 1 d g n d g are the distance spectra of g in this paper we characterize the graphs with n d g 1 172 1 1 1 2 where is the smallest root of x3 x2 3x 1 0 and 1 172 1 1 2 furthermore we show that the graphs with n 1 172 are determined by their d spectrum

note on the energy of regular graphs abstract for a simple graph g the energy e g is defined as the sum of the absolute values of all the eigenvalues of its adjacency matrix a g let n m respectively be the number of vertices and edges of g one well known inequality is that e g 1 n 1 2 m 1 where 1 is the spectral radius if g is k regular we have e g k k n 1 n k denote e 0 k k n 1 n k balakrishnan r balakrishnan the energy of a graph linear algebra appl 387 2004 287 295 proved that for each 0 there exist infinitely many n for each of which there exists a k regular graph g of order n with k n 1 and e g e 0 and proposed an open problem that given a positive integer n 3 and 0 does there exist a k regular graph g of order n such that e g e 0 1 in this paper we show that for each 0 there exist infinitely many such n that e g e 0 1 moreover we construct another class of simpler graphs which also supports the first assertion that e g e 0

adaptive linear filtering using interior point optimization techniques we propose a novel approach for the linear adaptive filtering problem using techniques from interior point optimization the main idea is to formulate a feasibility problem at each iteration and obtain as an estimate a filter near the center of the feasible region it is shown under some mild conditions that this algorithm generates a sequence of filters converging to the optimum linear filter at the rate o 1 n where n is the number of data samples furthermore we show that the algorithm can be made recursive with a per sample complexity of o m sup 2 3 where m is the filter length the potential of the algorithm for practical applications is demonstrated via numerical simulations where the new algorithm is shown to have superior transient behavior and improved robustness to the source signal statistics when compared to the recursive least squares rls method

adaptive blind channel estimation by least squares smoothing a least squares smoothing lss approach is presented for the blind estimation of single input multiple output simo finite impulse response systems by exploiting the isomorphic relation between the input and output subspaces this geometrical approach identifies the channel from a specially formed least squares smoothing error of the channel output lss has the finite sample convergence property i e in the absence of noise the channel is estimated perfectly with only a finite number of data samples referred to as the adaptive least squares smoothing a lss algorithm the adaptive implementation has a high convergence rate and low computation cost with no matrix operations a lss is order recursive and is implemented in part using a lattice filter it has the advantage that when the channel order varies channel estimates can be obtained without structural change of the implementation for uncorrelated input sequence the proposed algorithm performs direct deconvolution as a by product

unicyclic graphs with maximal energy abstract let 1 2 n be the eigenvalues of a graph g of order n the energy of g is defined as e g 1 2 n let p n 6 6 be the graph obtained from two copies of c 6 joined by a path p n 10 b n be the class of all bipartite bicyclic graphs that are not the graph obtained from two cycles c a and c b a b 10 and a b 2 mod 4 joined by an edge in this paper we show that p n 6 6 is the graph with maximal energy in b n which gives a partial solution to gutman s conjecture in gutman and vidovic 2001 i gutman d vidovic quest for molecular graphs with maximal energy a computer experiment j chem inf sci 41 2001 1002 1005

on graphs whose energy exceeds the number of vertices abstract let g be a graph on n vertices and let 1 2 n be the eigenvalues of a 0 1 adjacency matrix of g the energy of g is e i 1 n i we characterize several classes of graphs for which e n

on graphs with at least three distance eigenvalues less than 1 abstract let g be a connected graph with order n and d g be the distance matrix of g suppose that 1 d 2 d n d are the d eigenvalue of g in this paper we show that n 1 d g 1 if n 4 and n 2 d g 1 if n 7 we also characterize all connected graphs with n 1 d g 1 moreover it is shown that these graphs are determined by their distance spectra

interior point least squares estimation transient convergence analysis and application to mmse decision feedback equalization in many communication systems training sequences are used to help the receiver identify and or equalize the channel the amount of training data required depends on the convergence properties of the adaptive filtering algorithms used for equalization in this paper we propose the use of a new adaptive filtering method called interior point least squares ipls for adaptive equalization first we show that ipls converges exponentially fast in the transient phase then we use the ipls algorithm to update the weight vector for a minimum mean square error decision feedback equalizer mmse dfe in a cdma downlink scenario numerical simulations show that when training sequences are short ipls consistently outperforms rls in terms of system bit error rate and packet error rate as the training sequence gets longer ipls matches the performance of the rls algorithm

classification of coupled systems with two component nonlinear diffusion equations by the invariant subspace method the invariant subspace method is developed to perform classification of systems with two component nonlinear diffusion equations which was carried out with respect to the invariant subspaces defined by linear ordinary differential equations as a result the corresponding exact solutions generated by invariant subspaces to the resulting systems are obtained in most cases two components of these exact solutions belong to different scalar subspaces behaviour to several exact solutions of the systems is described

wavy fronts and speed bifurcation in excitable systems with cross diffusion a bifurcation of excitation fronts induced by cross diffusion in two component bistable reaction diffusion systems of activator inhibitor type is discovered this bifurcation is similar to the nonequilibrium ising bloch bifurcation a different type of fronts whose spatial profiles are characterized by oscillating tails are associated with this bifurcation these fronts are described using exact analytical solutions of piecewise linear reaction diffusion equations

sharp bounds on the distance spectral radius and the distance energy of graphs the d eigenvalues 1 2 p of a graph g are the eigenvalues of its distance matrix d and form the d spectrum of g denoted by specd g the greatest d eigenvalue is called the d spectral radius of g denoted by 1 the d energy ed g of the graph g is the sum of the absolute values of its d eigenvalues in this paper we obtain some lower bounds for 1 and characterize those graphs for which these bounds are best possible we also obtain an upperbound for ed g and determine those maximal d energy graphs

some sufficient conditions on k connected graphs abstract a connected graph g is said to be k connected if it has more than k vertices and remains connected whenever fewer than k vertices are removed feng et al 2017 presented sufficient conditions based on spectral radius for a graph to be k connected k edge connected k hamiltonian k edge hamiltonian deficient and k path coverable in this paper we present some further sufficient conditions for a graph to be k connected in terms of signless laplacian spectral radius distance spectral radius distance signless laplacian spectral radius of g and wiener index harary index of its complement

on the distance spectra of threshold graphs abstract a graph is called a threshold graph if it does not contain induced c 4 p 4 or 2 k 2 such graphs have numerous applications in computer science and psychology and they also have nice spectral properties in this paper we consider the distance matrix of a connected threshold graph we show that there are no distance eigenvalues of threshold graphs lying in the interval 2 1 and all the eigenvalues other than 2 or 1 are simple besides we determine all threshold graphs with distinct distance eigenvalues

sharp upper bounds on the distance spectral radius of a graph let m mij be a nonnegative irreducible n n matrix with diagonal entries 0 the largest eigenvalue of m is called the spectral radius of the matrix m denoted by m in this paper we give two sharp upper bounds of the spectral radius of matrix m as corollaries we give two sharp upper bounds of the distance matrix of a graph

maximizing wiener index for trees with given vertex weight and degree sequences abstract the wiener index is maximized over the set of trees with the given vertex weight and degree sequences this model covers the traditional unweighed wiener index the terminal wiener index and the vertex distance index it is shown that there exists an optimal caterpillar if weights of internal vertices increase in their degrees then an optimal caterpillar exists with weights of internal vertices on its backbone monotonously increasing from some central point to the ends of the backbone and the same is true for pendent vertices a tight upper bound of the wiener index value is proposed and an efficient greedy heuristics is developed that approximates well the optimal index value finally a branch and bound algorithm is built and tested for the exact solution of this np complete problem

strongly regular graphs with maximal energy the energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix koolen and moulton have proved that the energy of a graph on n vertices is at most n 1 n 2 and that equality holds if and only if the graph is strongly regular with parameters n n n 2 n 2 n 4 n 2 n 4 such graphs are equivalent to a certain type of hadamard matrices here we survey constructions of these hadamard matrices and the related strongly regular graphs

on the energy of some circulant graphs we give an explicit construction of circulant graphs of very high energy this construction is based on gauss sums we also show the littlewood conjecture can be used to establish new result for a certain class of circulant graphs

mmse interference suppression for direct sequence spread spectrum cdma we consider interference suppression for direct sequence spread spectrum code division multiple access cdma systems using the minimum mean squared error mmse performance criterion the conventional matched filter receiver suffers from the near far problem and requires strict power control typically involving feedback from receiver to transmitter for acceptable performance multiuser detection schemes previously proposed mitigate the near far problem but are complex and require explicit knowledge or estimates of the interference parameters in this paper we present and analyze several new mmse interference suppression schemes which have the advantage of being near far resistant to varying degrees depending on their complexity and can be implemented adaptively when interference parameters are unknown and or time varying numerical results are provided that show that these schemes offer significant performance gains relative to the matched filter receiver we conclude that mmse detectors can alleviate the need for stringent power control in cdma systems and may be a practical alternative to the matched filter receiver

sharp upper bounds on the distance energies of a graph abstract in this paper for a simple undirected connected graph sharp upper bounds on the distance energy distance laplacian energy and distance signless laplacian energy are obtained the graphs attaining the corresponding upper bound are characterized

some results on the distance and distance signless laplacian spectral radius of graphs and digraphs let d g denote the distance spectral radius of a graph g and g denote the distance signless laplacian spectral radius of a digraph g let g n k d be the set of all k connected graphs of order n with diameter d in this paper we first determine the unique graph with minimum distance spectral radius in g n k d we then give sharp upper and lower bounds for the distance signless laplacian spectral radius of strongly connected digraphs we also characterize the digraphs having the maximal and minimal distance signless laplacian spectral radii among all strongly connected digraphs furthermore we determine the extremal digraph with the minimal distance signless laplacian spectral radius with given dichromatic number

solitary waves in excitable systems with cross diffusion we consider a fitzhughnagumo system of equations where the traditional diffusion terms are replaced with linear cross diffusion of components this system describes solitary waves that have unusual

study of the transient phase of the forgetting factor rls we investigate the convergence properties of the forgetting factor rls algorithm in a stationary data environment using the settling time as our performance measure we show that the algorithm exhibits a variable performance that depends on the particular combination of the initialization and noise level specifically when the observation noise level is low high snr rls when initialized with a matrix of small norm it has an exceptionally fast convergence convergence speed decreases as we increase the norm of the initialization matrix in a medium snr environment the optimum convergence speed of the algorithm is reduced as compared with the previous case however rls becomes more insensitive to initialization finally in a low snr environment we show that it is preferable to initialize the algorithm with a matrix of large norm

the distance eigenvalues of the complements of unicyclic graphs abstract in this paper we determine the unique graph among complements of unicyclic graphs which maximizes the distance spectral radius we also characterize the unique graph among complements of unicyclic graphs of diameter three which maximizes the least distance eigenvalues

on the distance spectrum of graphs abstract let g be a connected graph and d g be the distance matrix of g suppose that 1 d 2 d n d are the d eigenvalues of g in this paper we characterize all connected graphs with n d 2 furthermore we characterize all connected graphs of diameter 2 with exactly three d eigenvalues when 1 d is not an integer we also conjecture that the complete k partite graph is determined by its d spectrum

effects of cross diffusion on turing bifurcations in two species reaction transport systems we study the turing bifurcation in general two species reaction transport systems where particle dispersal is governed by diffusion including cross diffusion by performing a linear stability analysis we find conditions for the turing instability and compare the results with the standard turing conditions we apply our results to two model systems the lengyel epstein model and the brusselator and find strong effects of cross diffusion on the turing bifurcation

mmse decision feedback equalizers and coding i equalization results the minimum mean squared error decision feedback equalizer mmse dfe has properties that suggest that it is a canonical equalization structure for systems that combine equalization with coded modulation the structure and performance of the mmse dfe are succinctly derived using linear estimation theoretic principles in this first part of this two part paper the front end of the mmse dfe called the mean square whitened matched filter ms wmf is preferable in some ways to a matched filter or a whitened matched filter as a canonical receiver front end in a coded system the feedback filter of the mmse dfe may be implemented in the transmitter using precoding the mmse dfe can perform significantly better than a zero forcing decision feedback equalizer particularly at moderate to low snr s and on severe isi channels the mmse dfe is biased the optimum unbiased mmse dfe is the mmse dfe with the bias removed removing bias improves error probability but reduces the snr to snr sub mmse dfe u snr sub mmse dfe 1 it is shown that this snr relationship is a particular case of a very general result and that snr sub mmse dfe u gives a more realistic estimate of snr the results are extended to partial response equalization and to equalization with correlated inputs in an appendix

mmse decision feedback equalizers finite length results this paper extends a number of results on the infinite length minimum mean square error decision feedback equalizer mmse dfe reported by cioffi dudevoir eyuboglu and forney see ieee trans commun 1995 to the finite length case cholesky factorization and displacement structure theory are demonstrated to be two powerful analytical tools for analyzing the finite length mmse dfe our objective throughout the paper is to establish finite length analogs of the well known infinite length mmse dfe results similarities and differences between the two cases are examined and delineated finally convergence of our derived finite length results to their well established infinite length counterparts is shown

on the least distance eigenvalue of a graph abstract denote by d g d i j n n the distance matrix of a connected graph g with n vertices where d i j is equal to the distance between vertices v i and v j in g the least eigenvalue of d g is called the least distance eigenvalue of g denoted by n in this paper we determine all the graphs with n 2 383 0

the energy of graphs and matrices abstract given a complex m n matrix a we index its singular values as 1 a 2 a and call the value e a 1 a 2 a the energy of a thereby extending the concept of graph energy introduced by gutman let 2 m n a be an m n nonnegative matrix with maximum entry and a 1 n extending previous results of koolen and moulton for graphs we prove that e a a 1 m n m 1 a 2 2 a 1 2 m n n m m 2 furthermore if a is any nonconstant matrix then e a 1 a a 2 2 1 2 a 2 a finally we note that wigner s semicircle law implies that e g 4 3 o 1 n 3 2 for almost all graphs g

the inertia and energy of the distance matrix of a connected graph abstract let g be a connected graph and d g be the distance matrix of g suppose that 1 d 2 d n d are the d eigenvalues of g in this paper we show that the distance matrix of a clique tree is non singular moreover we also prove that the distance matrix of a clique tree has exactly one positive d eigenvalue in addition we determine the extremal graphs with maximum and minimum distance energy among all clique trees

on the distance spectral radius of bipartite graphs abstract in this paper we determine the unique graph with minimum distance spectral radius among all connected bipartite graphs of order n with a given matching number moreover we characterize the graphs with minimal distance spectral radius in the class of all connected bipartite graphs with a given vertex connectivity

front propagation and segregation in a reaction diffusion model with cross diffusion abstract a study of front propagation and segregation in a system of reaction diffusion equations with cross diffusion is presented the reaction models predator prey dynamics involving two fields the diffusive part is nonlinear in the sense that the diffusion coefficient instead of being a constant as in the well studied case depends on one of the fields a key element of the model is a cross diffusion term according to which the flux of one of the fields is driven by gradients of the other field the original motivation of the model was the study of the turbulence shear flow interaction in plasmas the model also bears some similarities with models used in the study of spatial segregation of interacting biological species the system has three nontrivial fixed points and a study of traveling fronts solutions joining these states is presented depending on the stability properties of the fixed points the fronts are uniform or have spatial structure in the latter case a cross diffusion driven pattern forming k 0 instability leads to segregation in the wake of the front the segregated state consists of layered structures a ginzburg landau amplitude equation is used to describe the dynamics near marginal stability

on the distance and distance laplacian eigenvalues of graphs abstract let g v e be a simple graph with vertex set v g v 1 v 2 v n and edge set e g let d g be the distance matrix of g for a given nonnegative integer k when n is sufficiently large with respect to k we show that n k d 1 thereby solving a problem proposed by lin et al 2014 8 the distance laplacian spectral radius of a connected graph g is the spectral radius of the distance laplacian matrix of g defined as d l g tr g d g where tr g is the diagonal matrix of vertex transmissions of g aouchiche and hansen 2014 3 conjectured that m 1 d l n 2 when g k n and the equality holds if and only if either g k 1 n 1 or g k n 2 n 2 in this paper we confirm the conjecture

segregation and pursuit waves in activator inhibitor systems we investigate the effects of cross diffusion on propagating waves in an activator inhibitor system the model consists of a piecewise linear approximation of fitzhugh nagumo kinetics and a cross diffusion term for either the activator or the inhibitor we obtain exact analytic solutions for traveling fronts and solitary pulses and discuss the corresponding speed diagrams a detailed comparison with the corresponding rinzel keller model for the usually studied case of self diffusion is performed

on the distance spectral radius of some graphs abstract for a connected graph the distance spectral radius is the largest eigenvalue of its distance matrix in this paper we determine the unique graph with minimum distance spectral radius among all connected graphs of order n with a given diameter moreover we determine the unique graph with maximum distance spectral radius among the catacondensed hexagonal systems with h hexagons

applications of convex optimization in signal processing and digital communication in the last two decades the mathematical programming community has witnessed some spectacular advances in interior point methods and robust optimization these advances have recently started to significantly impact various fields of applied sciences and engineering where computational efficiency is essential this paper focuses on two such fields digital signal processing and communication in the past the widely used optimization methods in both fields had been the gradient descent or least squares methods both of which are known to suffer from the usual headaches of stepsize selection algorithm initialization and local minima with the recent advances in conic and robust optimization the opportunity is ripe to use the newly developed interior point optimization techniques and highly efficient software tools to help advance the fields of signal processing and digital communication this paper surveys recent successes of applying interior point and robust optimization to solve some core problems in these two fields the successful applications considered in this paper include adaptive filtering robust beamforming design and analysis of multi user communication system channel equalization decoding and detection throughout our emphasis is on how to exploit the hidden convexity convex reformulation of semi infinite constraints analysis of convergence complexity and performance as well as efficient practical implementation

singular perturbation theory of traveling waves in excitable media a review abstract waves of chemical or electrical activity traveling through space have been observed in several contexts chemical reaction mixtures in non convecting liquid phase cell suspensions nerve axons and neuromuscular tissues typically wave supporting preparations are excitable that is they respond and sensitivity to perturbations are rapidly damped out but suprathreshold disturbances trigger an abrupt and substantial response the abruptness of the response can be exploited by the methods of singular perturbation theory to obtain a mathematical description of wave propagation in spatially distributed excitable media singular perturbation analysis of propagating waves in one spatial dimension is straightforward and uncontentious but the analysis of propagating waves in one spatial dimension is straightforward and several fundamentally different ways we compare and contrast the approaches taken by greenberg zykov fife krinskii and his collaborators and ourselves with particular emphasis on the case of rotating spiral waves our intention is to bring some order to the important but difficult theory of propagating waves in two dimensional excitable media in conclusion we discuss briefly some possible extensions of the singular perturbation approach to propagating wave surfaces in three dimensional space