fault tolerant hamiltonian laceability of balanced hypercubes the balanced hypercube as a new variant of hypercube has many desirable properties such as strong connectivity high regularity and symmetry the particular property of the balanced hypercube is that each processor has a backup processor sharing the same neighborhood a hamiltonian bipartite graph g v 0 v 1 e is said to be hamiltonian laceable if there is a hamiltonian path between any two vertices x v 0 and y v 1 it has been proved that the balanced hypercube bh n is hamiltonian laceable for all n 1 in this paper we have proved that after at most 2 n 2 faulty edges occur bh n remains hamiltonian laceable for all n 2 this result is optimal with respect to the number of faulty edges can be tolerated in bh n

matching preclusion for n dimensional torus networks abstract the matching preclusion number of a graph is the minimum number of edges whose deletion results in the remaining graph that has neither perfect matchings nor almost perfect matchings wang et al 13 proved that a class of n dimensional tours networks with even order are super matched later cheng et al 8 further showed that all n dimensional tours networks with even order are super matched in this paper we prove that all n dimensional torus networks with odd order are super matched if n 3 two dimensional torus networks with odd order is maximally matched except for c 3 c 3 our results are complementary to those of wang et al 13 and cheng et al 8

the t k diagnosability of star graph networks the t k diagnosis is a diagnostic strategy at system level that can significantly enhance the system s self diagnosing capability it can detect up to t faulty processors or nodes units which might include at most k misdiagnosed processors where k is typically a small number somani and peleg 1996 claimed that an n dimensional star graph denoted s n a well studied interconnection model for multiprocessor systems is k 1 n 3k 2 k diagnosable recently chen and liu 2012 found counterexamples for the diagnosability obtained in without further pursuing the cause of the flawed result in this paper we provide a new complete proof that an mbi n dimensional star graph is actually k 1 n 3k 1 k diagnosable where 1 leq k leq 3 and investigate the reason that caused the flawed result in based on our newly obtained fault tolerance properties we will also outline an o n log n diagnostic algorithm n n is the number of nodes in s n to locate all up to k 1 n 3k 1 faulty processors among which at most k 1 leq k leq 3 fault free processors might be wrongly diagnosed as faulty

diagnosability of star graphs with missing edges in this paper we study the system diagnosis on an n dimensional star under the comparison model following the concept of local diagnosability 3 the strong local diagnosability property 7 is discussed this property describes the equivalence of the local diagnosability of a node and its degree we prove that an n dimensional star has this property and it keeps this strong property even if there exist n 3 missing edges in it

hyper hamiltonian laceability on edge fault star graph the star graph possess many nice topological properties edge fault tolerance is an important issue for a network since the edges in the network may fail sometimes in this paper we show that the n dimensional star graph is n 3 edge fault tolerant hamiltonian laceable n 3 edge fault tolerant strongly hamiltonian laceable and n 4 edge fault tolerant hyper hamiltonian laceable all these results are optimal in a sense described in this paper

routing properties of supercubes abstract usually each vertex of the s 1 dimensional hypercube is labeled with a unique integer k with 0 k 2 s 1 1 the supercube s n of n nodes with 2 s n 2 s 1 is constructed by merging nodes u and u 2 s with n u 2 s 1 1 in the s 1 dimensional hypercube into a single node labeled as u 2 s and leaving other nodes in the s 1 dimensional hypercube unchanged in this paper we give the exact distance between any two nodes of supercube and present a new shortest path routing algorithm on s n then we show how to construct s n disjoint paths between any two nodes of the supercube where s n is the connectivity of s n finally we compute the wide diameter and the fault diameter of s n we show that both the wide diameter and the fault diameter are equal to s 2 if n 2 s 1 2 i 1 0 i s 1 and s 1 otherwise

two disjoint cycle cover bipancyclicity of balanced hypercubes abstract a bipartite graph g is two disjoint cycle cover r1 r2 bipancyclic if for any even integer l satisfying r1 l r2 there exist two vertex disjoint cycles c1 and c2 in g such that v c 1 l and v c 2 v g l where v g denotes the number of vertices in g in this paper we study the two disjoint cycle cover bipancyclicity of the n dimensional balanced hypercube bhn which is a hypercube variant network and is superior to hypercube due to having a smaller diameter as a consequence we show that bhn is two disjoint cycle cover 4 2 2 n 1 bipancyclic for n 2

strong matching preclusion for n dimensional torus networks the strong matching preclusion number of a graph is the minimum number of edges and or vertices whose deletion results in the remaining graph that has neither perfect matchings nor almost perfect matchings in 14 wang et al proved that c k c k is super strongly matched where k 3 is odd in this paper we show that c k 1 c k 2 c k n is super strongly matched where n 3 is an integer and k i 3 is an odd integer for each i 1 n our studies generalize the results of wang et al 14

strong matching preclusion of n k star graphs the strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings this is an extension of the matching preclusion problem that was introduced by park and ihm the generalized n k star graph was introduced to address scaling issues of the star graph and it has many desirable properties in this paper the goal is to find the strong matching preclusion number of n k star graphs and to categorize all optimal strong matching preclusion sets of these graphs since bipartite graphs generally have low strong matching preclusion numbers we assume that k n 2

recursive circulants and their embeddings among hypercubes we propose an interconnection structure for multicomputer networks called recursive circulant recursive circulant g n d is defined to be a circulant graph with n nodes and jumps of powers of d g n d is node symmetric and has some strong hamiltonian properties g n d has a recursive structure when n cdm 1 c d we develop a shortest path routing algorithm in g cdm d and analyze various network metrics of g cdm d such as connectivity diameter mean internode distance and visit ratio g 2m 4 whose degree is m compares favorably to the hypercube qm g 2m 4 has the maximum possible connectivity and its diameter is 3m 1 4 recursive circulants have interesting relationship with hypercubes in terms of embedding we present expansion one embeddings among recursive circulants and hypercubes and analyze the costs associated with each embedding the earlier version of this paper appeared in park and chwa proc internat symp parallel architectures algorithms and networks ispan 94 kanazawa japan december 1994 pp 73 80

matching preclusion number in product graphs abstract the matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has no perfect matchings or almost perfect matchings for many interconnection networks the matching preclusion number is equal to the minimum degree of a vertex in the network and the sets of edges attaining the minimum are precisely those incident to a single vertex of minimum degree we say such networks are super matched in this paper we derive upper and lower bounds for the matching preclusion number for networks constructed using a variety of binary graph operations and give sufficient conditions for such networks to be super matched

the first suslin homology sheaf of a split simply connected semisimple algebraic group abstract let k be a perfect field and g be a k split simply connected semisimple algebraic group denote k 2 m the second unramified milnor k theory sheaf in the nisnevich topology we prove in this article that the first suslin singular homology sheaf h 1 nis g of the variety g is isomorphic to the direct sum k 2 m d where d is the number of irreducible components of the root system of g

strong matching preclusion number of graphs abstract the matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings the strong matching preclusion number or simply smp number s m p g of a graph g is the minimum number of vertices and or edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings this is an extension of the matching preclusion problem and has been introduced by park and ihm in this paper we first study the smp number of some special graph classes and give some sharp upper and lower bounds of smp number next graphs with large and small smp number are characterized respectively in the end we investigate the nordhaus gaddum type relations on smp number

strong matching preclusion for k composition networks abstract let g 1 v 1 e 1 g 2 v 2 e 2 g k v k e k be k graphs and let f 1 v 1 v 2 f 2 v 2 v 3 f k 1 v k 1 v k f k v k v 1 be k bijections the k composition networks g induced by g 1 g 2 g k is the graph with v g t 1 k v g t and e g t 1 k e g t a t f t a t a t v g t and 1 t k many interconnection networks such as n dimensional torus networks recursive circulant graphs and cayley graphs on abelian groups generated by minimal generating sets are special k composition networks the strong matching preclusion number of a graph is the minimum number of edges and or vertices whose deletion results in the remaining graph has neither perfect matchings nor almost perfect matchings in this paper we study the strong matching preclusion number and strong matching preclusion sets for k composition networks with odd order our results generalize the main conclusion in 12

bipanconnectivity of balanced hypercubes the balanced hypercube proposed by wu and huang is a variant of the hypercube network in this paper paths of various lengths are embedded into balanced hypercubes a bipartite graph g is bipanconnected if for two arbitrary nodes x and y of g with distance d x y there exists a path of length l between x and y for every integer l with d x y l v g 1 and l d x y 0 mod 2 we prove that the n dimensional balanced hypercube bh n is bipanconnected for all n 1 this result is stronger than that obtained by xu et al which shows that the balanced hypercube is edge bipancyclic and hamiltonian laceable

edge pancyclicity and hamiltonian laceability of the balanced hypercubes abstract the balanced hypercube bh n is a variant of the hypercube q n huang and wu proved that bh n has better properties than q n with the same number of links and processors in particularly they showed that there exists a cycle of length 2 l in bh n for all l 2 l 2 n in this paper we improve this result by showing that bh n is edge pancyclic which means that for arbitrary edge e there exists a cycle of even length from 4 to 2 2 n containing e in bh n we also show that the balanced hypercubes are hamiltonian laceable

many to many disjoint path covers in the presence of faulty elements a many to many k disjoint path cover k dpc of a graph g is a set of k disjoint paths joining k sources and k sinks in which each vertex of g is covered by a path it is called a paired many to many disjoint path cover when each source should be joined to a specific sink and it is called an unpaired many to many disjoint path cover when each source can be joined to an arbitrary sink in this paper we discuss about paired and unpaired many to many disjoint path covers including their relationships application to strong hamiltonicity and necessary conditions and then we give a construction scheme for paired many to many disjoint path covers in the graph h0 oplus h1 obtained from connecting two graphs h0 and h1 with v h0 v h1 by v h1 pairwise nonadjacent edges joining vertices in h0 and vertices in h1 where h0 g0 oplus g1 and h1 g2 oplus g3 for some graphs gj using the construction we show that every m dimensional restricted hl graph and recursive circulant g 2m 4 with f or less faulty elements have a paired k dpc for any f and k ges 2 with f 2k les m

linearly many faults in cayley graphs generated by transposition trees abstract we prove that when linearly many vertices are deleted in a cayley graph generated by a transposition tree the resulting graph has a large connected component containing almost all remaining vertices

the balanced hypercube a cube based system for fault tolerant applications in this paper we present an interconnection structure called the balanced hypercube which is a variation of the standard hypercube with desirable properties of strong connectivity regularity and symmetry the proposed structure is a special type of load balanced graph designed to tolerate processor failure in balanced hypercubes each processor has a backup matching processor that shares the same set of neighboring nodes therefore tasks that run on a faulty processor can be reactivated in the backup processor to provide efficient system reconfiguration other properties of balanced hypercubes are examined it is also shown that odd dimensional balanced hypercubes have smaller diameters than that of standard hypercubes as an application of balanced hypercubes we show a fault tolerant embedding of rings in balanced hypercubes

birational invariants and 1 connectedness we study the a singular chain complex and zeroth a homology sheaf of smooth algebraic varieties over a field k these objects provide quadratic analogs of the motive and zeroth suslin homology sheaf of a smooth scheme in a sense we will explain we show that if k has characteristic 0 the zeroth a homology resp suslin homology sheaf is a birational invariant of smooth proper varieties both are a homotopy invariant we relate these sheaves to various types of unramified invariants in particular unramified cohomology we then show how the techniques in voevodsky s proof of the milnor conjecture and the voevodsky rost proof of its generalization the bloch kato conjecture can be used to study these sheaves using this last set of ideas we provide a construction of unirational non rational varieties where non rationality is detected by non triviality of a degree n unramified etale cohomology group with torsion coefficients yet cannot be detected by lower degree invariants

on conditional diagnosability of the folded hypercubes the n dimensional folded hypercube fq n a variation of the hypercube proposed by ahmed et al a el amawy s latifi properties and performance of folded hypercubes ieee transactions on parallel and distributed systems 2 3 1991 31 42 is an n 1 regular n 1 connected graph conditional diagnosability a new measure of diagnosability introduced by lai et al pao lien lai jimmy j m tan chien ping chuang lih hsing hsu conditional diagnosability measures for large multiprocessor systems ieee transactions on computers 54 2 2005 165 175 can better measure the diagnosability of regular interconnection networks this paper determines that under pmc model the conditional diagnosability of fq n t c fq n is 4n 3 when n 5 or n 8 t c fq 3 3 t c fq 4 7

strong matching preclusion for augmented cubes the strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings the concept was introduced by park and son in this paper we study the strong matching preclusion problem for the augmented cube graphs as a result we find smp aqn and classify all optimal solutions

theoretical comparison of fourier and wavelet encoding in magnetic resonance imaging a theoretical comparison of the wavelet and fourier encoding methods is made with respect to resolution sensitivity to artifact and signal to noise ratios snr s a general mathematical description is developed in which magnetic resonance mr image encoding is represented by a projection of the function representing the mr signal density onto an approximation subspace of the finite energy functions characteristics of the subspace are used to define a generalized point spread function for space variant systems using the formal model of mr image encoding it is shown that wavelet encoding approaches the resolution limit defined by fourier encoding artifact is treated according to whether or not the source of the variation in the measured data is stationary nonstationary imperfections perturb the projection operation and result in encoding method dependent effects which can be modeled by a distortion matrix suitable for treating shift variant systems a framework is developed in which to derive expressions for snr s applicable to a general class of mr encoding methods

strong matching preclusion for non bipartite torus networks the strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in the remaining graph that has neither perfect matchings nor almost perfect matchings the torus network is one of the most popular interconnection network topologies for massively parallel computing systems because of its desirable properties it is known that bipartite torus networks have low strong matching preclusion numbers hu et al 13 proved that non bipartite torus networks with an odd number of vertices have good strong matching preclusion properties to complete the study of strong matching preclusion problem for non bipartite torus networks in this paper we establish the strong matching preclusion number and classify all optimal strong matching preclusion sets for the n dimensional non bipartite torus network with an even number of vertices where n 3

fault diagnosability of arrangement graphs the growing size of the multiprocessor system increases its vulnerability to component failures it is crucial to locate and to replace the faulty processors to maintain a system s high reliability the fault diagnosis is the process of identifying faulty processors in a system through testing in this paper we show that the largest connected component of the survival graph contains almost all of the remaining vertices in the n k arrangement graph a n k when the number of moved faulty vertices is up to twice or three times the traditional connectivity using this fault resiliency we establish the conditional diagnosability of a n k under the comparison model and prove that the conditional diagnosability of a n k is 3k 2 n k 3 for k 4 n k 2 and the conditional diagnosability of a n n 1 is 3n 7 for n 5

principal component filter banks for optimal multiresolution analysis an important issue in multiresolution analysis is that of optimal basis selection an optimal p band perfect reconstruction filter bank prfb is derived in this paper which minimizes the approximation error in the mean square sense between the original signal and its low resolution version the resulting prfb decomposes the input signal into uncorrelated low resolution principal components with decreasing variance optimality issues are further analyzed in the special case of stationary and cyclostationary processes by exploiting the connection between discrete time filter banks and continuous wavelets an optimal multiresolution decomposition of l sub 2 r is obtained analogous results are also derived for deterministic signals some illustrative examples and simulations are presented

hamiltonian cycle embedding for fault tolerance in balanced hypercubes abstract the balanced hypercube bh n defined by wu and huang is a variant of the hypercube network yang proposed that fault tolerance of balanced hypercube bh n is an important issue in parallel computing which needs further study yang 2010 24 in this paper we prove that there exists a fault free hamiltonian path between any two adjacent vertices in bh n with 2 n 2 faulty edges as a corollary we derive that for any fault free edge e there exists a fault free hamiltonian cycle containing e in bh n with 2 n 2 faulty edges which is optimal in the sense of the number of faulty edges

fault tolerant strong menger edge connectivity and 3 extra edge connectivity of balanced hypercubes abstract a connected graph g is called strongly menger edge connected if for any two distinct vertices x y of g there are min deg g x deg g y edge disjoint paths between x and y the g g 0 extra edge connectivity of the connected graph g denoted by g g is the minimal cardinality of a set of edges of g if exists whose deletion disconnects g and each remaining component contains more than g vertices in this paper we show that the n dimensional balanced hypercube b h n which is a variant of hypercube q n is still strongly menger edge connected even when there are 2 n 4 faulty vertices resp 2 n 2 faulty edges for n 2 moreover under the restricted condition that each vertex has at least two fault free edges we show that b h n is still strongly menger edge connected even when there are 6 n 8 faulty edges for n 2 these results are all optimal with respect to the maximum number of tolerated edge faults furthermore we showed that the 3 extra edge connectivity of b h n is 8 n 8 for n 2

conditional matching preclusion for the arrangement graphs the matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings for many interconnection networks the optimal sets are precisely those induced by a single vertex recently the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex it is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost perfect matchings in this paper we find this number and classify all optimal sets for the arrangement graphs one of the most popular interconnection networks

super rk vertex connectedness abstract for a graph g v e a subset f v g is called an rk vertex cut of g if g f is disconnected and each vertex u v g f has at least k neighbours in g f the rk vertex connectivity of g denoted by k g is the cardinality of a minimum rk vertex cut of g in this paper we further study the rk vertex connectivity by introducing the concept called super rk vertex connectedness the graph g is called super rk vertex connectedness if for every minimum rk vertex cut s g s contains a component which is isomorphic to a certain graph h where h is related to the graph g and integer k for the cayley graphs generated by wheel graphs h is isomorphic to k2 when k 1 and h is isomorphic to c4 when k 2 in this paper we show that the cayley graphs generated by wheel graphs are super r1 vertex connectedness and super r2 vertex connectedness our studies generalize the main result in 8

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed

orienting cayley graphs generated by transposition trees day and tripathi k day a tripathi unidirectional star graphs inform process lett 45 1993 123 129 proposed an assignment of directions on the star graphs and derived attractive properties for the resulting directed graphs cheng and lipman e cheng m j lipman on the day tripathi orientation of the star graphs connectivity inform process lett 73 2000 5 10 e cheng m j lipman connectivity properties of unidirectional star graphs congr numer 150 2001 33 42 studied the connectivity properties of these unidirectional star graphs the class of star graphs is a special case of cayley graphs generated by transposition trees in this paper we give directions on these graphs and study the connectivity properties of the resulting unidirectional graphs

on reliability of the folded hypercubes in terms of the extra edge connectivity for a graph g and a non negative integer g the g extra edge connectivity of g is the minimum cardinality of a set of edges in g if it exists whose deletion disconnects g and each remaining component will have at least g vertices the extra edge connectivity is an important parameters for the reliability evaluation of interconnection networks in this paper we explore g extra edge connectivity g fq n of the folded hypercube fq n for g n denote g by i 0 s 2 t i where t 0 log 2 g and t i log 2 g r 0 i 1 2 t r we show that g fq n g n 1 i 0 s t i 2 t i i 0 s 2 i 2 t i for n 6 this result generalizes the previous results by zhu et al 2007 for 3 fq n and by hsieh and tsai in press for 4 fq n and so on

the 2 good neighbor diagnosability of cayley graphs generated by transposition trees under the pmc model and mm model diagnosability is an important metric for measuring the reliability of multiprocessor systems in 2012 peng et al proposed a new measure for fault diagnosis of the system which is called g good neighbor diagnosability that restrains every fault free node containing at least g fault free neighbors as a favorable topology structure of interconnection networks the cayley graph c n generated by the transposition tree n has many good properties in this paper we give that the 2 good neighbor diagnosability of c n under the pmc model and mm model is g n 2 1 where n 4 and g is the girth of c n

strongly menger edge connectedness and strongly menger vertex connectedness of regular networks abstract let f be a conditional faulty edge set of a graph g here the condition imposed on f is g f r for some fixed integer r the graph g is called f strongly menger edge connected of order r if each pair of distinct vertices u and v are connected by min deg g f u deg g f v edge disjoint paths in g f where deg g f u and deg g f v are the degrees of u and v in g f respectively a graph g is t strongly menger edge connected of order r if g is f strongly menger edge connected of order r for every f e g with f t one can consider the vertex version in an analogous way there are a number of papers with results for r 2 for several popular classes of interconnection network in this paper we develop a unified approach by considering various sufficient conditions of a regular graph to be f strongly menger edge connected of order r and the corresponding vertex version as corollaries several results on fundamental classes of interconnection networks are presented including new results as well as strengthening of existing results such as the one given by qiao and yang 2017 20

restricted connectivity for three families of interconnection networks vertex connectivity and edge connectivity are two important parameters in interconnection networks even though they reflect the fault tolerance correctly they undervalue the resilience of large networks by the concept of conditional connectivity and super connectivity the concept of restricted vertex connectivity and restricted edge connectivity of graphs was proposed by esfahanian a h esfahanian generalized measures of fault tolerance with application to n cube networks ieee transactions on computers 38 1989 1586 1591 such measures take the resilience of large networks into consideration in this paper we propose three families of interconnection networks and discuss their restricted vertex connectivity and restricted edge connectivity in particular the hypercubes twisted cubes crossed cubes mobius cubes star graphs pancake graphs recursive circulant graphs and k ary n cubes are special cases of these families

strong matching preclusion for torus networks the torus network is one of the most popular interconnection network topologies for massively parallel computing systems strong matching preclusion that additionally permits more destructive vertex faults in a graph is a more extensive form of the original matching preclusion that assumes only edge faults in this paper we establish the strong matching preclusion number and all minimum strong matching preclusion sets for bipartite torus networks and 2 dimensional nonbipartite torus networks

on the brauer group of a semisimple algebraic group let k be a field with algebraic closure g a semisimple algebraic k group and a maximal torus with character group denote the abstract weight lattice of the roots system of g and by and the n torsion subgroup of the brauer group of k and g respectively we prove that if chark does not divide n and n is prime to the order of then the natural homomorphism is an isomorphism

degree three unramified cohomology of adjoint semisimple groups we compute degree 3 unramified cohomology of adjoint semisimple group new classes of non rational adjoint semisimple groups are found

on the conditional diagnosability of matching composition networks the conditional diagnosability of interconnection networks has been studied by using a number of ad hoc methods recently gathering various ad hoc methods developed in the last decade a unified approach was developed and this approach was used to find the conditional diagnosability of many interconnection networks in this paper we study the conditional diagnosability of matching composition networks including those that are not triangle free

smooth varieties up to a 1 homotopy and algebraic h cobordisms abstract we start to study the problem of classifying smooth proper varieties over a field k from the standpoint of a 1 homotopy theory motivated by the topological theory of surgery we discuss the problem of classifying up to isomorphism all smooth proper varieties having a specified a 1 homotopy type arithmetic considerations involving the sheaf of a 1 connected components lead us to introduce several different notions of connectedness in a 1 homotopy theory we provide concrete links between these notions connectedness of points by chains of affine lines and various rationality properties of algebraic varieties e g rational connectedness we introduce the notion of an a 1 h cobordism an algebro geometric analog of the topological notion of h cobordism and use it as a tool to produce non trivial a 1 weak equivalences of smooth proper varieties also we give explicit computations of refined a 1 homotopy invariants such as the a 1 fundamental sheaf of groups for some a 1 connected varieties we observe that the a 1 fundamental sheaf of groups plays a central yet mysterious role in the structure of a 1 h cobordisms as a consequence of these observations we completely solve the classification problem for rational smooth proper surfaces over an algebraically closed field while there exist arbitrary dimensional moduli of such surfaces there are only countably many a 1 homotopy types each uniquely determined by the isomorphism class of its a 1 fundamental sheaf of groups

conditional matching preclusion for hypercube like interconnection networks the conditional matching preclusion number of a graph with n vertices is the minimum number of edges whose deletion results in a graph without an isolated vertex that does not have a perfect matching if n is even or an almost perfect matching if n is odd we develop some general properties on conditional matching preclusion and then analyze the conditional matching preclusion numbers for some hl graphs hypercube like interconnection networks

a doubly adaptive approach to dynamic mri sequence estimation dynamic magnetic resonance imaging mri refers to the acquisition of a sequence of mri images to monitor temporal changes in tissue structure we present a method for the estimation of dynamic mri sequences based on two complimentary strategies an adaptive framework for the estimation of the mri images themselves and an adaptive method to tailor the mri system excitations for each data acquisition we refer to this method as the doubly adaptive temporal update method datum for dynamic mri analysis of the adaptive image estimate framework shows that calculating the optimal system excitations for each new image requires complete knowledge of the next image in the sequence since this is not realizable we introduce a linear predictor to aid in determining appropriate excitations simulated examples using real mri data are included to illustrate that the doubly adaptive strategy can provide estimates with lower steady state error than previously proposed methods and also the ability to recover from dramatic changes in the image sequence

edge fault tolerant edge bipancyclicity of balanced hypercubes abstract the balanced hypercube bh n is a variant of hypercube q n hao et al 2014 showed that there exists a fault free hamiltonian path between any two adjacent vertices in bh n with 2 n 2 faulty edges cheng et al 2015 proved that bh n is 6 edge bipancyclic after 2 n 3 faulty edges occur for all n 2 in this paper we improve these two results by demonstrating that bh n is 6 edge bipancyclic even when there exist 2 n 2 faulty edges for all n 2 our result is optimal with respect to the maximum number of tolerated edge faults

linearly many faults in cayley graphs generated by transposition triangle free unicyclic graphs abstract we consider a kind of cayley graphs including the modified bubble sort graphs m b n the cayley graphs generated by lollipop graphs h n n 1 and the other cayley graphs generated by unicyclic triangle free graphs we get that if we delete linearly many vertices in cayley graphs generated by transposition unicyclic triangle free graphs then the resulting graphs has a large connected component that comprises of nearly all residual vertices

hamiltonian paths passing through prescribed edges in balanced hypercubes abstract the balanced hypercube was proposed as a novel interconnection network for large scale parallel systems it is known that the balanced hypercube is edge bipancyclic given a set of edges p with p n 1 and two vertices x and y in different bipartite sets we show that there exists a hamiltonian path from x to y passing through p in b h n if and only if p is a linear forest and neither x nor y is an internal vertex of p and x and y are not end vertices of a component of p simultaneously consequently the balanced hypercube contains a hamiltonian cycle passing through a set p of at most n prescribed edges if and only if p is a linear forest moreover our result improves some known results

efficient design of orthonormal wavelet bases for signal representation the efficient representation of a signal as a linear combination of elementary atoms or building blocks is central to much signal processing theory and many applications wavelets provide a powerful flexible and efficiently implementable class of such atoms in this paper we develop an efficient method for selecting an orthonormal wavelet that is matched to a given signal in the sense that the squared error between the signal and some finite resolution wavelet representation of it is minimized since the squared error is not an explicit function of the design parameters some form of approximation of this objective is required if conventional optimization techniques are to be used previous approximations have resulted in nonconvex optimization problems which require delicate management of local minima in this paper we employ an approximation that results in a design problem that can be transformed into a convex optimization problem and efficiently solved constraints on the smoothness of the wavelet can be efficiently incorporated into the design we show that the error incurred in our approximation is bounded by a function that decays to zero as the number of vanishing moments of the wavelet grows in our examples we demonstrate that our method provides wavelet bases that yield substantially better performance than members of standard wavelet families and are competitive with those designed by more intricate nonconvex optimization methods

a kind of conditional connectivity of cayley graphs generated by unicyclic graphs abstract for a graph g v e a subset f v g is called an r k vertex cut of g if g f is disconnected and each vertex u v g f has at least k neighbors in g f the r k vertex connectivity of g denoted by k g is the cardinality of the minimum r k vertex cut of g which is a refined measure for the fault tolerance of network g in this paper we study 2 for cayley graphs generated by unicyclic graphs let sym n be the symmetric group on 1 2 n and t be a set of transpositions of sym n let g t be the graph on vertex set 1 2 n and edge set ij ij t if g t is a unicyclic graph then simply denote the cayley graph cay sym n t by ug n in particular if g t is a cycle then ug n is the well known modified bubble sort graph mb n we prove in this paper that if m is the length of the unique cycle in g t then 2 ug n 4 n 10 if 3 m n 4 n 8 if 4 m n

a kind of conditional vertex connectivity of cayley graphs generated by 2 trees let g be a graph then t v g is called an r k vertex cut if g t is disconnected and each vertex in v g t has at least k neighbors in g t the size of a smallest r k vertex cut is the r k vertex connectivity of g and is denoted by k k g in this paper we determine the numbers k 1 and k 2 for cayley graphs generated by 2 trees including the popular alternating group graphs

a kind of conditional connectivity of cayley graphs generated by wheel graphs for a connected graph g v e a subset fv is called an rk vertex cut of g if gf is disconnected and each vertex in vf has at least k neighbors in gf the cardinality of the minimum rk vertex cut is the rk vertex connectivity of g and is denoted by k g the conditional connectivity is a measure to explore the structure of networks beyond the vertex connectivity let sym n be the symmetric group on 1 2 n and t be a set of transpositions of sym n denote by g t the graph with vertex set 1 2 n and edge set ij ij t if g t is a wheel graph then simply denote the cayley graph cay sym n t by wgn in this paper we determine the values of 1 and 2 for cayley graphs generated by wheel graphs and prove that 1 wgn 4n6 and 2 wgn 8n18

matching preclusion for balanced hypercubes matching preclusion is a measure of robustness in the event of edge failure in interconnection networks the matching preclusion number of a graph g is the minimum number of edges whose deletion leaves the resulting graph without a perfect matching or an almost perfect matching and the conditional matching preclusion number of g is the minimum number of edges whose deletion leaves the resulting graph with no isolated vertices and without a perfect matching or an almost perfect matching in this paper we consider balanced hypercubes we obtain that an n dimension balanced hypercube bh n has the matching preclusion number 2n and mainly prove that for the balanced hypercube bh n each matching preclusion set of cardinality 2n is trivial and the conditional matching preclusion number of balanced hypercube is 4n 2 whenever n 2

the diagnosability of the matching composition network under the comparison diagnosis model the classical problem of diagnosability is discussed widely and the diagnosability of many well known networks has been explored we consider the diagnosability of a family of networks called the matching composition network mcn a perfect matching connects two components the diagnosability of mcn under the comparison model is shown to be one larger than that of the component provided some connectivity constraints are satisfied applying our result the diagnosability of the hypercube qn the crossed cube cq sub n the twisted cube tq sub n and the mobius cube mq sub n can all proven to be n for n spl ges 4 in particular we show that the diagnosability of the four dimensional hypercube q sub 4 is 4 which is not previously known

conditional matching preclusion sets abstract the matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings for many interconnection networks the optimal sets are precisely those induced by a single vertex in this paper we look for obstruction sets beyond these sets we introduce the conditional matching preclusion number of a graph it is the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost perfect matchings we find this number and classify all optimal sets for several basic classes of graphs

strong matching preclusion the matching preclusion problem introduced by brigham et al r c brigham f harary e c violin and j yellen perfect matching preclusion congressus numerantium 174 2005 185 192 studies how to effectively make a graph have neither perfect matchings nor almost perfect matchings by deleting as small a number of edges as possible extending this concept we consider a more general matching preclusion problem called the strong matching preclusion in which deletion of vertices is additionally permitted we establish the strong matching preclusion number and all possible minimum strong matching preclusion sets for various classes of graphs

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

the conditional fault diagnosability of n k star graphs abstract the growing size of the multiprocessor system increases its vulnerability to component failures it is crucial to locate and replace the faulty processors to maintain a system s high reliability the fault diagnosis is the process of identifying faulty processors in a system through testing this paper shows that the largest connected component of the survival graph contains almost all the remaining vertices when a lot of faulty vertices occur in the n k star graph s n k n 5 k 3 n k 2 based on this fault resiliency it establishes the conditional fault diagnosability of s n k under the comparison model

linearly many faults in dual cube like networks the dual cubes were introduced as a better interconnection network than the hypercubes for large scale distributed memory multiprocessors in this paper we introduce a generalization of these networks called dual cube like networks which preserve the basic structure of dual cubes and retain many of its topological properties we investigate structural properties of these networks beyond simple measures such as connectivity we prove that if up to kn k k 1 2 vertices are deleted from a dual cube like n regular network then the resulting graph will either be connected or will have a large component and small components having at most k 1 vertices in total and this result is sharp for k n as an application we derive additional results such as the cyclic vertex connectivity and the restricted vertex connectivity of these networks

various cycles embedding in faulty balanced hypercubes consider the balanced hypercube bh n with f e 2 n 3 faulty edges prove that every edge of bh n f e lies on fault free cycles of even lengths from 6 to 22n prove that the lower limit of the length 6 is sharp quite a lot of interconnection networks are served as the underlying topologies of large scale multiprocessor systems the hypercube is one of the most popular interconnection networks in this paper we consider the balanced hypercube which is a variant of the hypercube huang and wu showed that the balanced hypercube has better properties than hypercube with the same number of links and processors let f e be the set of faulty edges in an n dimensional balanced hypercube bh n where n 2 in this paper we consider bh n with f e 2 n 3 faulty edges and prove that every fault free edge lies on a fault free cycle of every even length from 6 to 2 2 n in bh n f e furthermore we prove that the lower limit of the length 6 is sharp by giving a counter example

a note on generalized matching preclusion in bipartite graphs abstract for a graph with an even number of vertices the matching preclusion number is the minimum number of edges whose deletion results in a graph with no perfect matchings the conditional matching preclusion number introduced as an extension of the matching preclusion number has the additional requirement that the resulting graph have no isolated vertices in bipartite graphs the edge sets that achieve these minimum numbers can be construed in terms of obstruction sets of vertices from this perspective the generalized matching preclusion problem was developed the matching preclusion number of order a is the minimum number of edges whose deletion results in a graph with no perfect matchings and no obstruction sets with fewer than a vertices in this paper we extend known sufficient conditions regarding the matching preclusion and conditional matching preclusion numbers orders 1 and 2 respectively to give sufficient conditions for the matching preclusion problem of order a for any positive integer a

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

matching preclusion number of graphs abstract the matching preclusion number of a graph g denoted by mp g is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings in this paper we first give some sharp upper and lower bounds of matching preclusion number next graphs with large and small matching preclusion number are characterized respectively in the end we investigate some extremal problems and the nordhaus gaddum type relations on matching preclusion number

conditional connectivity of star graph networks under embedding restriction the n dimensional star graph s n is one of the most attractive interconnection networks of large scale multiprocessor systems the k embedding restricted edge connectivity h k s n z k s n of s n is defined to be the cardinality of a minimum subset of edges nodes if any whose deletion disconnects s n and each node of the remaining components lies in an undamaged k dimensional substar s k in this paper we investigate the k embedding restricted edge connectivity of s n and determine the values of h k s n and z k s n for some k s

on the genus of star graphs the star graph has recently been suggested as an alternative to the hypercube the star graph has a rich structure and symmetry properties as well as desirable fault tolerant characteristics the star graph s maximum vertex degree and diameter viewed as functions of network size grow less rapidly than the corresponding measures in a hypercube we investigate the genus of the star graph and compare it with the genus of the hypercube

matching preclusion and conditional matching preclusion problems for the folded petersen cube the matching preclusion number of an even graph is the minimum number of edges whose deletion results in a graph that has no perfect matchings for many interconnection networks the optimal sets are precisely those induced by a single vertex recently the conditional matching preclusion number of an even graph was introduced to look for obstruction sets beyond those induced by a single vertex it is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices and no perfect matchings in this paper we study this problem for the folded petersen cube fpq n k via some matching preclusion and conditional matching preclusion results of the cartesian products of graphs

on informational completeness of covariant localization observables and wigner coefficients an orthogonality theorem is obtained for square integrable representations on homogeneous spaces of a locally compact group from this a series of lemmas is derived showing the informational completeness of natural covariant localization operators as well as of the generalized wigner distributions matrix elements of the group some of these results give explicit reconstruction formulas for the quantum state from its expectation values against these families of operators the results are applied to special phase space representations of the heisenberg affine and galilei groups

super connectivity and super edge connectivity for some interconnection networks let g v e be a k regular graph with connectivity k and edge connectivity l g is maximum connected if k k and g is maximum edge connected if l k moreover g is super connected if it is a complete graph or it is maximum connected and every minimum vertex cut is x v x e for some vertex email protected v and g is super edge connected if it is maximum edge connected and every minimum edge disconnecting set is v x v x e for some vertex email protected v in this paper we present three schemes for constructing graphs that are super connected and super edge connected applying these construction schemes we can easily discuss the super connected property and the super edge connected property of hypercubes twisted cubes crossed cubes mobius cubes split stars and recursive circulant graphs

two applications of wavelet transforms in magnetic resonance imaging the authors describe two different applications of wavelet transforms in magnetic resonance imaging mri in each case the use of wavelets offers tangible benefits over the traditional fourier transform based imaging these stem from the simultaneous time and frequency localization properties of the wavelets the first application utilizes the localization properties of wavelets to acquire single t sub 2 weighted images in times which are short relative to current methods an interesting combinatorial scheduling problem arises from the multiscale structure inherent in the formulation of this procedure its solution is sketched and applied to the imaging process the second example is a technique for potentially instant imaging image acquisition is modeled as an inverse wavelet transform of the spin density in the region in question signal acquisition takes place in as few as one or two echoes after the excitation by rf pulses designed to excite a moving band of spins in a slice these sweeping rf pulses excite strips of spins which rephase at different times during acquisition they replace phase encoding gradients no fast pulsed gradients are required

fault tolerance and diagnosability of burnt pancake networks under the comparison model processor fault diagnosis plays an important role in measuring the reliability of a multiprocessor system and the diagnosabilities of many well known multiprocessor systems have been investigated the conditional diagnosability has been widely accepted as a new measure of diagnosability by assuming an additional condition that any faulty set can t contain all the neighbors of any node in a multiprocessor system in this paper we explore algebraic and combinatorial properties of burnt pancake networks and investigate the structural vulnerability as well as super and extra connectivities furthermore we show that the classic diagnosability and the conditional diagnosability of n dimensional burnt pancake network bp n n 4 are n and 3 n 4 respectively algebraic and combinatorial properties of burnt pancake networks are established the structural vulnerability as well as super and extra connectivities are explored the classic and conditional diagnosabilities under the comparison model are derived

reliability evaluation of bc networks in terms of the extra vertex and edge connectivity reliability evaluation of interconnection network is important to the design and maintenance of multiprocessor systems the extra connectivity and the extra edge connectivity are two important parameters for the reliability evaluation of interconnection networks the mbi n dimensional bijective connection network in brief bc network includes several well known network models such as hypercubes mobius cubes crossed cubes and twisted cubes in this paper we explore the extra connectivity and the extra edge connectivity of bc networks and discuss the structure of bc networks with many faults we obtain a sharp lower bound of g extra edge connectivity of an mbi n dimensional bc network for n geq 4 and 1 leq g leq 2 n over 2 we also obtain a sharp lower bound of g extra connectivity of an n dimensional bc network for n geq 4 and 1 leq g leq 2 n which improves the result in reliability evaluation of bc networks ieee trans computers doi 10 1109 tc 2012 106 for 1 leq g leq n 3 furthermore we give a remark about exploring the g extra edge connectivity of bc networks for the more general mbi g and we also characterize the structure of bc networks with many faulty nodes or links as an application we obtain several results on the mbi g extra edge connectivity and the structure of faulty networks on hypercubes mobius cubes crossed cubes and twisted cubes

painless nonorthogonal expansions in a hilbert space h discrete families of vectors hj with the property that f j hj f hj for every f in h are considered this expansion formula is obviously true if the family is an orthonormal basis of h but also can hold in situations where the hj are not mutually orthogonal and are overcomplete the two classes of examples studied here are i appropriate sets of weyl heisenberg coherent states based on certain non gaussian fiducial vectors and ii analogous families of affine coherent states it is believed that such quasiorthogonal expansions will be a useful tool in many areas of theoretical physics and applied mathematics

feature preserving mri denoising a nonparametric empirical bayes approach this paper presents a novel method for bayesian denoising of magnetic resonance mr images that bootstraps itself by inferring the prior i e the uncorrupted image statistics from the corrupted input data and the knowledge of the rician noise model the proposed method relies on principles from empirical bayes eb estimation it models the prior in a nonparametric markov random field mrf framework and estimates this prior by optimizing an information theoretic metric using the expectation maximization algorithm the generality and power of nonparametric modeling coupled with the eb approach for prior estimation avoids imposing ill fitting prior models for denoising the results demonstrate that unlike typical denoising methods the proposed method preserves most of the important features in brain mr images furthermore this paper presents a novel bayesian inference algorithm on mrfs namely iterated conditional entropy reduction icer this paper also extends the application of the proposed method for denoising diffusion weighted mr images validation results and quantitative comparisons with the state of the art in mr image denoising clearly depict the advantages of the proposed method