open 3 manifolds whose fundamental groups have infinite center and a torus theorem for 3 orbifolds our main result is a characterization of open seifert fibered 3 manifolds in terms of the fundamental group and large scale geometric properties of a triangulation as an application we extend the seifert fiber space theorem and the torus theorem to a class of 3 orbifolds

optimal codes for minimax criterion on error detection nonlinear quadratic codes that are optimal for the minimax error detection are presented characteristic functions for these codes are asymptotically bent for a given block size n and the number of codewords mod c mod these codes minimize max q e e not 0 where q e is the conditional error masking probability given the error pattern e the codewords are blocks of n symbols from gf q encoding and decoding procedures for the codes are described

on a class of totally unimodular matrices we examine the class of totally unimodular matrices that contain no odd cycles which we call restricted totally unimodular rtum we show that a matrix is rtum if and only if it can be decomposed in a very simple way into the incidence matrices or their transposes of bipartite graphs or directed graphs and give a linear time algorithm to perform this task based on this decomposition we show that the 0 1 integer programming problem with an rtum matrix of constraints has the same time complexity as the b matching and the max flow problems

structural properties and recognition of restricted and strongly unimodular matrices a 0 1 matrix a is restricted unimodular if every matrix obtained from a by setting to zero any subset of its entries is totally unimodular restricted unimodular matrices are also known as matrices without odd cycles they have been studied by commoner and recently yannakakis has given a polynomial algorithm to recognize when a matrix belongs to this class a matrix a is strongly unimodular if any matrix obtained from a by setting at most one of its entries to zero is totally unimodular crama et al have shown that 0 1 matrix a is strongly unimodular if and only if any basis of a 1 is triangular wherei is an identity matrix of suitable dimensions in this paper we give a very simple algorithm to test whether a matrix is restricted unimodular and we show that all strongly unimodular matrices can be obtained by composing restricted unimodular matrices with a simple operation

enlargeability and index theory let m be a closed enlargeable spin manifold we show nontriviality of the universal index obstruction in the k theory of the maximal c algebra of the fundamental group of m our proof is independent of the injectivity of the baum connes assembly map for 1 m and relies on the construction of a certain infinite dimensional flat vector bundle out of a sequence of finite dimensional vector bundles on m whose curvatures tend to zero besides the well known fact that m does not carry a metric with positive scalar curvature our results imply that the classifying map m b 1 m sends the fundamental class of m to a nontrivial homology class in h b 1 m q this answers a question of burghelea 1983

vector sets for exhaustive testing of logic circuits l d universal sets are useful for exhaustively testing logic circuits with a large number of functional components designed so that every functional component depends on at most d inputs randomized and deterministic constructions of l d universal test sets are presented and lower and upper bounds on the optimal sizes of such sets are proven it is also proven that the design of an optimal exhaustive test set for an arbitrary logic circuit is an np complete problem

a combinatorial approach to x tolerant compaction circuits test response compaction for integrated circuits ics with scan based design for testability dft support in the presence of unknown logic values xs is investigated from a combinatorial viewpoint the theoretical foundations of x codes employed in an x tolerant compaction technique called x compact are examined through the formulation of a combinatorial model of x compact novel design techniques are developed for x codes to detect a specified maximum number of errors in the presence of a specified maximum number of unknown logic values while requiring only small fan out the special class of x codes that results leads to an avoidance problem for configurations in combinatorial designs general design methods and nonconstructive existence theorems to estimate the compaction ratio of an optimal x compactor are also derived

balance 0 1 matrices bicoloring and total dual integrality a 0 1 matrixa is balanced if in every submatrix with two nonzero entries per row and column the sum of the entries is a multiple of four this definition was introduced by truemper 1978 and generalizes the notion of a balanced 0 1 matrix introduced by berge 1970 in this paper we extend a bicoloring theorem of berge 1970 and total dual integrality results of fulkerson hoffman and oppenheim 1974 to balanced 0 1 matrices

design of test sequences for vlsi self testing using lfsr consider a shift register sr of length n and a collection of designated subsets of 0 1 n 1 the problem is how to add feedback to the sr such that the resulting linear feedback shift register lfsr exercises almost exhaustively each of the designated subsets and is of small period several previously known results for maximum length lfsr are extended to more general lfsr and in particular a previously known algorithm is simplified and extended applications to the problems of vlsi self testing are discussed and illustrated

design of universal test sequences for vlsi a test sequence is called s t universal if it exercises every function depending on t or fewer inputs on a very large scale integration vlsi chip with s inputs randomized and deterministic procedures are deseribed for the design of s t universal sequences and for the signature analysis of the test outputs

embedded minimal surfaces exotic spheres and manifolds with positive ricci curvature let n be a three dimensional riemannian manifold let e be a closed embedded surface in n then it is a question of basic interest to see whether one can deform in its isotopy class to some canonical embedded surface from the point of view of geometry a natural canonical surface will be the extremal surface of some functional defined on the space of embedded surfaces the simplest functional is the area functional the extremal surface of the area functional is called the minimal surface such minimal surfaces were used extensively by meeks yau my21 in studying group actions on three dimensional manifolds in my2 the theory of minimal surfaces was used to simplify and strengthen the classical dehn s lemma loop theorem and the sphere theorem in the setting there one minimizes area among all immersed surfaces and proves that the extremal object is embedded in this paper we minimize area among all embedded surfaces isotopic to a fixed embedded surface in the category of these surfaces we prove a general existence theorem theorem 1 a particular consequence of this theorem is that for irreducible manifolds an embedded incompressible surface is isotopic to an embedded incompressible surface with minimal area we also prove that there exists an embedded sphere of least area enclosing a fake cell provided the complementary volume is not a standard ball and provided there exists no embedded one sided rp2 by making use of the last result and a cutting and pasting argument we are able to settle a well known problem in the theory of three dimensional manifolds we prove that the covering space of any irreducible orientable three dimensional manifold is irreducible it is possible to exploit our existence theorem to study

recursive pseudoexhaustive test pattern generation a recursive technique for generating exhaustive patterns is presented the method is optimal i e in one experiment it covers exhaustively every block of k adjacent inputs in the first 2 sup k vectors implementation methods based on characteristic functions of test vectors are provided they include a parallel pattern generator employing an exclusive or array and two serial generators that can be easily adopted in a scan based built in self test environment

pseudoexhaustive test pattern generator with enhanced fault coverage a method of pseudoexhaustive test pattern generation is proposed that is suitable above all for circuits using random access scan two linear feedback shift registers are used to generate scan addresses and test patterns to be scanned into these addresses it is shown that the method gives better results than random testing

bounds on the linear span of bent sequences recently olsen scholtz and welch presented families of binary sequences called bent function sequences which can be generated through nonlinear operations on m sequences these families of sequences possess asymptotically optimum correlation properties and large equivalent linear span els upper and lower bounds to the els of bent function sequences are derived the upper bound improves upon key s upper bound and the lower bound obtained through construction and exceeds left stackrel n 2 n 4 right cdot 2 n 4 where n is the length of the shift register generating the m sequence an interesting general result contained in the derivation is the exhibition of a class of nonlinear sequences whose els is guaranteed to be large

virtual betti numbers of mapping tori of 3 manifolds given a reducible 3 manifold m with an aspherical summand in its prime decomposition and a homeomorphism f m rightarrow m we construct a map of degree one from a finite cover of m rtimes f s 1 to a mapping torus of a certain aspherical 3 manifold we deduce that m rtimes f s 1 has virtually infinite first betti number except when all aspherical summands of m are virtual t 2 bundles this verifies all cases of a conjecture of t j li and y ni that any mapping torus of a reducible 3 manifold m not covered by s 2 times s 1 has virtually infinite first betti number except when m is virtually n t 2 rtimes s 1 ms 2 times s 1 li ni s conjecture was recently confirmed by ni with a group theoretic result namely by showing that there exists a pi 1 surjection from a finite cover of any mapping torus of a reducible 3 manifold to a certain mapping torus of m s 2 times s 1 and using the fact that free by cyclic groups are large when the free group is generated by more than one element

homology of finite k area we use gromov s k area to define homology groups for compact smooth manifolds in fact this theory collects obstructions to the enlargeability of the manifold and its nontrivial submanifolds moreover using the k area homology we can rephrase some classic results about positive scalar curvature we also show that the functor of k area homology determines the functor of singular homology on the category of compact smooth manifolds

multiple seed tpg structures linear feedback shift registers lfsrs are popular mechanisms for built in test pattern generation tpg they are normally used with a primitive characteristic polynomial because in that case only one initialization state seed is required we show that if the characteristic polynomial is nonprimitive irreducible the required seeds can still be efficiently generated we establish a formula that shows how the seeds of any nonprimitive irreducible polynomial relate to each other this leads to an efficient hardware implementation with small hardware overhead irrespective of the number of seeds and enhances the choices available for the design of appropriate tpg structures in the case of pseudoexhaustive tpg that were previously limited to primitive characteristic polynomials only

properties of balanced and perfect matrices in this paper we define wheel matrices and characterize some properties of matrices that are perfect but not balanced a consequence of our results is that if a matrixa is perfect then we can construct a polynomial number of submatricesai a n ofa such thata is balanced if and only if all the submatricesa1 a n ofa are perfect this implies that if the problem of testing perfection is polynomially solvable then so is the problem of testing balancedness

the existence of maps of nonzero degree between aspherical 3 manifolds for any two closed orientable surfaces there is a map of nonzero degree from one to another this result is based on the fact that the orientable closed surface are classified completely there is no such a classification in dimension 3 in this paper all closed aspherical 3 manifolds are divided into eight classes a complete answer of the existences of nonzero degree maps between 3 manifolds in the different classes is obtained in a reasonable sense the existence of nonzero degree maps between 3 manifolds in the same class are also discussed there are several results of independent interest it is noted that the existence of a map of nonzero degree between two 3 manifolds is a very restrictive condition posed on those two 3 manifolds which is much different from the case of dimension 2 the shape of our work is certainly influenced by thurston however both the statements and the proofs of our theorems do not involve the thurston s geometries we understand that if we state the results in the category of haken manifolds and thurston s geometrical manifolds and invoke the g r o m o v norm of hyperbol ic 3 manifold see chap 6 of r t l and chap 4 of gro the proof of some result in the paper can be simplified we present our work in the way below for two reasons a we prefer to prove all results in a uniform elementary way in the sense of using only the fundamental groups and the incompressible surfaces of 3 manifolds b since the thurston s most famous conjecture that every atoroidal closed irreducible 3 manifold has a hyperbolic structure is still open we get the results in a theoretically wider category there are 5 sections after the introduction all manifolds and maps under consideration are piece wise linear there is nothing lost under this assumption see chap 1 of hi in the first four sections of these five all 3 manifolds are orientable and irreducible section 1 states the theorems proved in the paper section 2 provides results which are used to prove the theorems section 3 and sect 4 are the proofs of the theorems various examples are given in sect 4

testing balancedness and perfection of linear matrices a 0 1 matrix is linear if it does not contain a 2 2 submatrix of all ones in this paper we give polynomial algorithms to test whether a linear matrix is balanced or perfect the algorithms are based on decomposition results previously obtained by the authors

odd cycles and matrices with integrality properties a cycle of a bipartite graphg v v e is odd if its length is 2 mod 4 even otherwise an odd cyclec is node minimal if there is no odd cyclec of cardinality less than that ofc such that one of the following holds c v c v orc v c v

recognizing balanceable matrices a 0 1 matrix is balanced if it does not contain a square submatrix with exactly two nonzero entries per row and per column in which the sum of all entries is 2 modulo 4 a 0 1 matrix is balanceable if its nonzero entries can be signed 1 so that the resulting matrix is balanced a signing algorithm due to camion shows that the problems of recognizing balanced 0 1 matrices and balanceable 0 1 matrices are equivalent conforti cornuejols kapoor and vuskovic gave an algorithm to test if a 0 1 matrix is balanced truemper has characterized balanceable 0 1 matrices in terms of forbidden submatrices in this paper we give an algorithm that explicitly finds one of these forbidden submatrices or shows that none exists

structural properties and decomposition of linear balanced matrices claude berge defines a 0 1 matrix a to be linear ifa does not contain a 2 2 submatrix of all ones a 0 1 matrixa is balanced ifa does not contain a square submatrix of odd order with two ones per row and column

the simplicial volume of mapping tori of 3 manifolds we prove that any mapping torus of a closed 3 manifold has zero simplicial volume when the fiber is a prime 3 manifold classification results can be applied to show vanishing of the simplicial volume however the case of reducible fibers is by far more subtle we thus analyse the possible self homeomorphisms of reducible 3 manifolds and use this analysis to produce an explicit representative of the fundamental class of the corresponding mapping tori to this end we introduce a new technique for understanding self homeomorphisms of connected sums in arbitrary dimensions on the level of classifying spaces and for computing the simplicial volume in particular we extend our computations to mapping tori of certain connected sums in higher dimensions our main result completes the picture for the vanishing of the simplicial volume of fiber bundles in dimension four moreover we deduce that dimension four together with the trivial case of dimension two are the only dimensions where all mapping tori have vanishing simplicial volume as a group theoretic consequence we derive an alternative proof of the fact that the fundamental group g of a mapping torus of a 3 manifold m is gromov hyperbolic if and only if m is virtually a connected sum s 2 times s 1 and g does not contain mathbb z 2

positive scalar curvature and 10 8 type inequalities on 4 manifolds with periodic ends we show 10 8 type inequalities for some end periodic 4 manifolds which have positive scalar curvature metrics on the ends as an application we construct a new family of closed 4 manifolds which do not admit positive scalar curvature metrics

least area incompressible surfaces in 3 manifolds let m be a riemannian manifold and let f be a closed surface a map f f m is called least area if the area of f is less than the area of any homotopic map from f to m note that least area maps are always minimal surfaces but that in general minimal surfaces are not least area as they represent only local stationary points for the area function the existence of least area immersions in a homotopy class of maps has been established when the homotopy class satisfies certain injectivity conditions on the fundamental group 18 17 in this paper we shall consider the possible singularities of such immersions our results show that the general philosophy is that least area surfaces intersect least meaning that the intersections and self intersections of least area immersions are as small as their homotopy classes allow when measured correctly one should note that evidence supporting this view had been found by meeks yau in their embedding theorems for minimal disks and 2 spheres 13 143 our main result asserts that if a least area immersion is homotopic to an embedding then it has no self intersections which clearly exemplifies the above philosophy the precise result is the following

exhaustive generation of bit patterns with applications to vlsi self testing one has a shift register of length n and a collection of designated subsets of 0 1 n 1 the problem is to devise a method for feeding a string of bits into the shift register in such an order that for each designated subset s k1 kr if one keeps track of the bit patterns appearing at the corresponding positions k1 krof the shift register all 2r possible bit patterns will ultimately appear at those positions a simple and efficient solution to this problem derived from the connections between polynomials over finite fields and linear feedback shift registers is presented applications of this solution to the problem of vlsi self testing are discussed and illustrated

on three manifolds dominated by circle bundles we determine which three manifolds are dominated by products the result is that a closed oriented connected three manifold is dominated by a product if and only if it is finitely covered either by a product or by a connected sum of copies of s2 s1 this characterization can also be formulated in terms of thurston geometries or in terms of purely algebraic properties of the fundamental group we also determine which three manifolds are dominated by non trivial circle bundles and which three manifold groups are presentable by products