link prediction based on local information considering preferential attachment abstract link prediction in complex networks has attracted much attention in many fields in this paper a common neighbors plus preferential attachment index is presented to estimate the likelihood of the existence of a link between two nodes based on local information of the nearest neighbors numerical experiments on six real networks demonstrated the high effectiveness and efficiency of the new index compared with five well known and widely accepted indices the common neighbors resource allocation index preferential attachment index local path index and katz index the new index provides competitively accurate prediction with local path index and katz index while has less computational complexity and is more accurate than the other two indices

context free complexity of finite languages abstract in this paper the investigation of the theory of grammatical complexity as started by bucher 1981 and bucher culik ii maurer and wotschke 1981 is continued the basic question we are concerned with is the following given some finite language l what is the smallest number of context free productions needed to generate l the so called context free complexity of l we strengthen some of the results given by bucher et al 1981 the main result being a necessary condition for certain sequences of finite languages to be of sublinear complexity

a reciprocity map and the two variable p adic l function for primes p 5 we propose a conjecture that relates the values of cup products in the galois cohomology of the maximal unramied outside p extension of a cyclotomic eld on cyclotomic p units to the values of p adic l functions of cuspidal eigenforms that satisfy mod p congruences with eisenstein series passing up the cyclotomic and hida towers we construct an isomorphism of certain spaces that allows us to compare the value of a reciprocity map on a particular norm compatible system of p units to what is essentially the two variable p adic l function of mazur and kitagawa

pseudo modularity and iwasawa theory we prove assuming greenberg s conjecture that the ordinary eigencurve is gorenstein at an intersection point between the eisenstein family and the cuspidal locus as a corollary we obtain new results on sharifi s conjecture this result is achieved by constructing a universal ordinary pseudodeformation ring and proving an r t result

a really simple approximation of smallest grammar in this paper we present a really simple linear time algorithm constructing a context free grammar of size 4 g log 3 2 n g for the input string where n is the size of the input string and g the size of the optimal grammar generating this string the algorithm works for arbitrary size alphabets but the running time is linear assuming that the alphabet of the input string can be identified with numbers from 1 n c for some constant c algorithms with such an approximation guarantee and running time are known however all of them were non trivial and their analyses were involved the here presented algorithm computes the lz77 factorisation and transforms it in phases to a grammar in each phase it maintains an lz77 like factorisation of the word with at most factors as well as additional o letters where was the size of the original lz77 factorisation in one phase in a greedy way by a left to right sweep and a help of the factorisation we choose a set of pairs of consecutive letters to be replaced with new symbols i e nonterminals of the constructed grammar we choose at least 2 3 of the letters in the word and there are o many different pairs among them hence there are o log n phases each of them introduces o nonterminals to a grammar a more precise analysis yields a bound 4 log n as g this yields the desired bound g 4 g log n g

percolation theory and fragmentation measures in social networks abstract we study the statistical properties of a recently proposed social networks measure of fragmentation f after removal of a fraction q of nodes or links from the network the measure f is defined as the ratio of the number of pairs of nodes that are not connected in the fragmented network to the total number of pairs in the original fully connected network we compare this measure with the one traditionally used in percolation theory p the fraction of nodes in the largest cluster relative to the total number of nodes using both analytical and numerical methods we study erd s renyi er and scale free sf networks under various node removal strategies we find that for a network obtained after removal of a fraction q of nodes above criticality p 1 f 1 2 for fixed p and close to criticality we show that 1 f better reflects the actual fragmentation for a given p 1 f has a broad distribution and thus one can improve significantly the fragmentation of the network we also study and compare the fragmentation measure f and the percolation measure p for a real national social network of workplaces linked by the households of the employees and find similar results

the smallest grammar problem this paper addresses the smallest grammar problem what is the smallest context free grammar that generates exactly one given string spl sigma this is a natural question about a fundamental object connected to many fields such as data compression kolmogorov complexity pattern identification and addition chains due to the problem s inherent complexity our objective is to find an approximation algorithm which finds a small grammar for the input string we focus attention on the approximation ratio of the algorithm and implicitly the worst case behavior to establish provable performance guarantees and to address shortcomings in the classical measure of redundancy in the literature our first results are concern the hardness of approximating the smallest grammar problem most notably we show that every efficient algorithm for the smallest grammar problem has approximation ratio at least 8569 8568 unless p np we then bound approximation ratios for several of the best known grammar based compression algorithms including lz78 b isection sequential longest match greedy and re pair among these the best upper bound we show is o n sup 1 2 we finish by presenting two novel algorithms with exponentially better ratios of o log sup 3 n and o log n m sup where m sup is the size of the smallest grammar for that input the latter algorithm highlights a connection between grammar based compression and lz77

diagonal cycles and euler systems ii the birch and swinnerton dyer conjecture for hasse weil artin l functions this article establishes new cases of the birch and swinnerton dyer conjecture in analytic rank 0 for elliptic curves over mathbb q viewed over the fields cut out by certain self dual artin representations of dimension at most 4 when the associated l function vanishes to even order ge 2 at its central point two canonical classes in the corresponding selmer group are constructed and shown to be linearly independent assuming the non vanishing of a garrett hida p adic l function at a point lying outside its range of classical interpolation the key tool for both results is the study of certain p adic families of global galois cohomology classes arising from gross kudla schoen diagonal cycles in a tower of triple products of modular curves

decidability and complexity of simultaneous rigid e unification with one variable and related results we show that simultaneous rigid e unification or sreu for short is decidable and in fact exptime complete in the case of one variable this result implies that the for all there exists for all f

spin glass model for the c dismantling problem c dismantling cd problem aims at finding the minimum vertex set d of a graph g v e after removing which the remaining graph will break into connected components with the size not larger than c in this paper we introduce a spin glass model with c 1 integer value states into the cd problem and then study the properties of this spin glass model by the belief propagation bp equations under the replica symmetry ansatz we give the lower bound rho c of the relative size of d with finite c on regular random graphs and erdos renyi random graphs we find rho c will decrease gradually with growing c and it converges to rho infty as c to infty the cd problem is called dismantling problem when c is a small finite fraction of v therefore rho infty is also the lower bound of the dismantling problem when v to infty to reduce the computation complexity of the bp equations taking the knowledge of the probability of a random selected vertex belonging to a remaining connected component with the size a the original bp equations can be simplified to one with only three states when c to infty the simplified bp equations are very similar to the bp equations of the feedback vertex set spin glass model h j zhou eur phys j b 86 455 2013 at last we develop two practical belief propagation guide decimation algorithms based on the original bp equations cd bpd and the simplified bp equations scd bpd to solve the cd problem on a certain graph our bpd algorithms and two other state of art heuristic algorithms are applied on various random graphs and some real world networks computation results show that the cd bpd is the best in all tested algorithms in the case of small c but considering the performance and computation consumption we recommend using scd bpd for the network with small clustering coefficient when c is large

connection methods in linear logic and proof nets construction linear logic ll is the logical foundation of some type theoretic languages and also of environments for specification and theorem proving in this paper we analyse the relationships between the proof net notion of ll and the connection notion used for efficient proof search in different logics aiming at using proof nets as a tool for automated deduction in linear logic we define a connection based characterization of provability in multiplicative linear logic mll we show that an algorithm for proof net construction can be seen as a proof search connection method this central result is illustrated with a specific algorithm that is able to construct for a provable mll sequent a set of connections a proof net and a sequent proof from these results we expect to extend to other ll fragments we analyse what happens with the additive connectives of ll by tackling the additive fragment in a similar way

variation of heegner points in hida families given a weight two modular form f with associated p adic galois representation v f for certain quadratic imaginary fields k one can construct canonical classes in the galois cohomology of v f by taking the kummer images of heegner points on the modular abelian variety attached to f we show that these classes can be interpolated as f varies in a hida family and construct an euler system of big heegner points for hida s universal ordinary deformation of v f we show that the specialization of this big euler system to any form in the hida family is nontrivial extending results of cornut and vatsal from modular forms of weight two and trivial character to all ordinary modular forms and propose a horizontal nonvanishing conjecture for these cohomology classes the horizontal nonvanishing conjecture implies via the theory of euler systems a conjecture of greenberg on the generic ranks of selmer groups in hida families

coauthorship networks and patterns of scientific collaboration by using data from three bibliographic databases in biology physics and mathematics respectively networks are constructed in which the nodes are scientists and two scientists are connected if they have coauthored a paper we use these networks to answer a broad variety of questions about collaboration patterns such as the numbers of papers authors write how many people they write them with what the typical distance between scientists is through the network and how patterns of collaboration vary between subjects and over time we also summarize a number of recent results by other authors on coauthorship patterns

mixing patterns in networks we study assortative mixing in networks the tendency for vertices in networks to be connected to other vertices that are like or unlike them in some way we consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age as a special example of the latter we consider mixing according to vertex degree i e according to the number of connections vertices have to other vertices do gregarious people tend to associate with other gregarious people we propose a number of measures of assortative mixing appropriate to the various mixing types and apply them to a variety of real world networks showing that assortative mixing is a pervasive phenomenon found in many networks we also propose several models of assortatively mixed networks both analytic ones based on generating function methods and numerical ones based on monte carlo graph generation techniques we use these models to probe the properties of networks as their level of assortativity is varied in the particular case of mixing by degree we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices

correlations in complex networks under attack for any initially correlated network after any kind of attack where either nodes or edges are removed we obtain general expressions for the degree degree probability matrix and degree distribution we show that the proposed analytical approach predicts the correct topological changes after the attack by comparing the evolution of the assortativity coefficient for different attack strategies and intensities in theory and simulations we find that it is possible to turn an initially assortative network into a disassortative one and vice versa by fine tuning removal of either nodes or edges for an initially uncorrelated network on the other hand we discover that only a targeted edge removal attack can induce such correlations

linearity and regularity with negation normal form proving completeness of nc resolution under a linear restriction has been elusive it is proved here for formulas in negation normal form the proof uses a generalization of the anderson bledsoe excess literal argument which was developed for resolution that result is extended to nc resolution with partial replacement a simple proof of the completeness of regular connected tableaux for formulas in conjunctive normal form is also presented these techniques are then used to establish the completeness of regular connected tableaux for formulas in negation normal form

bridges in complex networks a bridge in a graph is an edge whose removal disconnects the graph and increases the number of connected components we calculate the fraction of bridges in a wide range of real world networks and their randomized counterparts we find that real networks typically have more bridges than their completely randomized counterparts but they have a fraction of bridges that is very similar to their degree preserving randomizations we define an edge centrality measure called bridgeness to quantify the importance of a bridge in damaging a network we find that certain real networks have a very large average and variance of bridgeness compared to their degree preserving randomizations and other real networks finally we offer an analytical framework to calculate the bridge fraction and the average and variance of bridgeness for uncorrelated random networks with arbitrary degree distributions

graph partitioning induced phase transitions we study the percolation properties of graph partitioning on random regular graphs with n vertices of degree k optimal graph partitioning is directly related to optimal attack and immunization of complex networks we find that for any partitioning process even if nonoptimal that partitions the graph into essentially equal sized connected components clusters the system undergoes a percolation phase

optimization of random searches on defective lattice networks we study the general problem of how to search efficiently for targets randomly located on defective lattice networks i e regular lattices which have some fraction of its nodes randomly removed we consider large but finite triangular lattices and assume for the search dynamics that the walker chooses steps lengths lj from the power law distribution p lj approximately lj mu with the exponent mu regulating the strategy of the search process at each step lj the searcher moves in straight lines and constantly looks within a detection radius of vision rv for the targets along the way if there is contact with a defect the movement stops and a new step length is chosen hence the presence of defects decreases the efficiency of the overall process we study numerically how three different aspects of the lattice influence the optimization of the search efficiency i the type of boundary conditions ii the concentration of targets and defects and iii the category or class of search destructive nondestructive or regenerative motivated by the results we develop a type of mean field model for the problem and obtain an analytical approximation for the search efficiency function finally we discuss in the context of searches how defective lattices compare with perfect lattices and with continuous environments

attack vulnerability of complex networks we study the response of complex networks subject to attacks on vertices and edges several existing complex network models as well as real world networks of scientific collaborations and internet traffic are numerically investigated and the network performance is quantitatively measured by the average inverse geodesic length and the size of the largest connected subgraph for each case of attacks on vertices and edges four different attacking strategies are used removals by the descending order of the degree and the betweenness centrality calculated for either the initial network or the current network during the removal procedure it is found that the removals by the recalculated degrees and betweenness centralities are often more harmful than the attack strategies based on the initial network suggesting that the network structure changes as important vertices or edges are removed furthermore the correlation between the betweenness centrality and the degree in complex networks is studied

minimal cover automata for finite languages abstract a cover automaton a of a finite language l is a finite deterministic automaton dfa that accepts all words in l and possibly other words that are longer than any word in l a minimal deterministic finite cover automaton dfca of a finite language l usually has a smaller size than a minimal dfa that accept l thus cover automata can be used to reduce the size of the representations of finite languages in practice in this paper we describe an efficient algorithm that for a given dfa accepting a finite language constructs a minimal deterministic finite cover automaton of the language we also give algorithms for the boolean operations on deterministic cover automata i e on the finite languages they represent

predicting percolation thresholds in networks we consider different methods which do not rely on numerical simulations of the percolation process to approximate percolation thresholds in networks we perform a systematic analysis on synthetic graphs and a collection of 109 real networks to quantify their effectiveness and reliability as prediction tools our study reveals that the inverse of the largest eigenvalue of the nonbacktracking matrix of the graph often provides a tight lower bound for true percolation threshold however in more than 40 of the cases this indicator is less predictive than the naive expectation value based solely on the moments of the degree distribution we find that the performance of all indicators becomes worse as the value of the true percolation threshold grows thus none of them represents a good proxy for the robustness of extremely fragile networks

robustness of network controllability in cascading failure controllability of networks widely existing in real life systems have been a critical and attractive research subject for both network science and control systems communities research in network controllability has mostly focused on the effects of the network structure on its controllability and some studies have begun to investigate the controllability robustness of complex networks cascading failure is common phenomenon in many infrastructure networks which largely affect normal operation of networks and sometimes even lead to collapse resulting in considerable economic losses the robustness of network controllability against the cascading failure is studied by a linear load capacity model with a breakdown probability in this paper the controllability of canonical model networks under different node attack strategies is investigated random failure and malicious attack it is shown by numerical simulations that the tolerant parameter of load capacity model has an important role in the emergence of cascading failure independent to the types of network the networks with moderate average degree are more vulnerable to the cascading failure while these with high average degree are very robust in particular betweenness attack strategy is more harmful to the network controllability than degree attack one especially for the scale free networks

a decidable fragment of predicate calculus abstract we describe a decision procedure for what we call direct predicate calculus this fragment of predicate logic coincides with those formulas that can be proved in the gentzen sequent calculus with the rule of contraction eliminated it arose by thinking about what kinds of inferences should be considered obvious and in that sense characterizes fragments of logic by the tools available for proving results rather than by syntactic properties of formulas

enhancing robustness and immunization in geographical networks we find that different geographical structures of networks lead to varied percolation thresholds although these networks may have similar abstract topological structures thus strategies for enhancing robustness and immunization of a geographical network are proposed using the generating function formalism we obtain an explicit form of the percolation threshold q c for networks containing arbitrary order cycles for three cycles the dependence of q c on the clustering coefficients is ascertained the analysis substantiates the validity of the strategies with analytical evidence

efficiency of scale free networks error and attack tolerance the concept of network efficiency recently proposed to characterize the properties of small world networks is here used to study the effects of errors and attacks on scale free networks two different kinds of scale free networks i e networks with power law p k are considered 1 scale free networks with no local clustering produced by the barabasi albert model and 2 scale free networks with high clustering properties as in the model by klemm and eguiluz and their properties are compared to the properties of random graphs exponential graphs by using as mathematical measures the global and the local efficiency we investigate the effects of errors and attacks both on the global and the local properties of the network we show that the global efficiency is a better measure than the characteristic path length to describe the response of complex networks to external factors we find that at variance with random graphs scale free networks display both on a global and on a local scale a high degree of error tolerance and an extreme vulnerability to attacks in fact the global and the local efficiency are unaffected by the failure of some randomly chosen nodes though they are extremely sensitive to the removal of the few nodes which play a crucial role in maintaining the network s connectivity

the problem of π 2 cut introduction abstract we describe an algorithmic method of proof compression based on the introduction of 2 cuts into a cut free lk proof the current approach is based on an inversion of gentzen s cut elimination method and extends former methods for introducing 1 cuts the herbrand instances of a cut free proof of a sequent s are described by a grammar g which encodes substitutions defined in the elimination of quantified cuts we present an algorithm which given a grammar g constructs a 2 cut formula a and a proof of s with one cut on a it is shown that by this algorithm we can achieve an exponential proof compression

a comparative study of several proof procedures abstract in this paper three algorithms for testing the complementarity of a matrix representing a propositional formula are developed in stages any of these algorithms is distinguished from its predecessor by a specific feature linearity jump non normal form which endows it with a provable advantage w r t its performance for well known proof procedures it is shown that they can be simulated by at least one of these algorithms which provides a hierarchy among several atp methods

rigid tree automata and applications we introduce the class of rigid tree automata rta an extension of standard bottom up automata on ranked trees with distinguished states called rigid rigid states define a restriction on the computation of rta on trees rta can test for equality in subtrees reaching the same rigid state rta are able to perform local and global tests of equality between subtrees non linear tree pattern matching and some inequality and disequality tests as well properties like determinism pumping lemma boolean closure and several decision problems are studied in detail in particular the emptiness problem is shown decidable in linear time for rta whereas membership of a given tree to the language of a given rta is np complete our main result is the decidability of whether a given tree belongs to the rewrite closure of an rta language under a restricted family of term rewriting systems whereas this closure is not an rta language this result one of the first on rewrite closure of languages of tree automata with constraints is enabling the extension of model checking procedures based on finite tree automata techniques in particular for the verification of communicating processes with several local non rewritable memories like security protocols finally a comparison of rta with several classes of tree automata with local and global equality tests with dag automata and horn clause formalisms is also provided

hida duality and the iwasawa main conjecture the central result of this paper is a refinement of hida s duality theorem between ordinary varlambda adic modular forms and the universal ordinary hecke algebra in particular we give a sufficient condition for this duality to be integral with respect to particular submodules of the space of ordinary varlambda adic modular forms this refinement allows us to give a simple proof that the universal ordinary cuspidal hecke algebra modulo eisenstein ideal is isomorphic to the iwasawa algebra modulo an ideal related to the kubota leopoldt p adic l function the motivation behind these results stems from a proof of the iwasawa main conjecture over mathbb q by ohta while simple and elegant ohta s proof requires some restrictive hypotheses which we are able to remove using our results

image of λ adic galois representations modulo p let p 5 be a prime if an irreducible component of the spectrum of the big ordinary hecke algebra does not have complex multiplication under mild assumptions we prove that the image of its mod p galois representation contains an open subgroup of open image in new window for the canonical weight variable t this fact appears to be deep as it is almost equivalent to the vanishing of the invariant of the kubota leopoldt p adic l function and the anticyclotomic katz p adic l function another key ingredient of the proof is the anticyclotomic main conjecture proven by rubin mazur tilouine

effect of edge removal on topological and functional robustness of complex networks abstract we study the robustness of several network models subject to edge removal the robustness is measured by the statistics of network breakdowns where a breakdown is defined as the destroying of the total connectedness of a network rather than the disappearance of the giant component we introduce a simple traffic dynamics as the function of a network topology and the total connectedness can be destroyed in the sense of either the topology or the function the overall effect of the topological breakdown and the functional breakdown as well as the relative importance of the topological robustness and the functional robustness are studied under two edge removal strategies

approximation of grammar based compression via recompression in this paper we present a simple linear time algorithm constructing a context free grammar of size o g log n g for the input string where n is the size of the input string and g the size of the optimal grammar generating this string the algorithm works for arbitrary size alphabets but the running time is linear assuming that the alphabet of the input string can be identified with numbers from 1 n c for some constant c otherwise additional cost of o n log is needed algorithms with such an approximation guarantee and running time are known the novelty of this paper is a particular simplicity of the algorithm as well as the analysis of the algorithm which uses a general technique of recompression recently introduced by the author furthermore contrary to the previous results this work does not use the lz representation of the input string in the construction nor in the analysis

asymptotic estimates for efficiency vulnerability and cost for random networks an investigation both analytical and numerical of the values of efficiency vulnerability and cost functions is provided several comparisons among these functions are made following a pairwise strategy and taking into account different efficiency vulnerability and cost functions it is shown in all cases that these magnitudes display strong correlations which are typically piecewise linear in log space as well as universal i e independent of the number of nodes n to a great extent the analytical part of the work develops explicit bounds linking all pairs of such parameters these results are numerically compared with the result of a random testing for erdos renyi networks

algorithmic introduction of quantified cuts abstract we describe a method for inverting gentzen s cut elimination in classical first order logic our algorithm is based on first computing a compressed representation of the terms present in the cut free proof and then cut formulas that realize such a compression finally a proof using these cut formulas is constructed concerning asymptotic complexity this method allows an exponential compression of quantifier complexity the number of quantifier inferences of proofs

on the compressibility of finite languages and formal proofs abstract we consider the minimal number of productions needed for a grammar to cover a finite language l as the grammatical complexity of l we study this measure for several types of word and tree grammars and show that it is closely connected to well known measures for the complexity of formal proofs in first order predicate logic we construct an incompressible sequence of finite word languages and transfer this and several other results about the complexity of word and tree languages to formal proofs

proofs without syntax proofs are traditionally syntactic inductively generated objects this paper presents an abstract mathematical formulation of propositional calcu lus propositional logic in which proofs are combinatorial graph theoretic rather than syntactic it defines a combinatorial proof of a proposition 0 as a graph homomorphism h c g f where g j is a graph associated with and c is a coloured graph the main theorem is soundness and completeness f is true if and only if there exists a combinatorial proof h c g p

concise description of finite languages abstract this paper is a contribution to the theory of grammatical complexity in particular to the following basic question consider some language l and grammars of some type x what is the smallest number of productions of a type x grammar required to generate l this complexity measure the so called x complexity of l has been investigated before we study the more basic case when the languages l considered are finite a case which has been neglected so far we obtain a number of results and insights suggesting that such study is of importance in addition to a number of expected but not necessarily easy to prove results that with type x grammars more productions are necessary than with some other type y grammars even if types x and y define the same family of languages we show that if the limit of certain sequences of finite languages is of type x1 then the type x complexity of each of the finite languages involved must be low

proff search in type theoretic languages an introduction we introduce the main concepts and problems in the theory of proof search in type theoretic languages and survey some specific connected topics we do not claim to cover all of the theoretical and implementation issues in the study of proof search in type theoretic languages rather we present some key ideas and problems starting from well motivated points of departure such as a definition of a type theoretic language or the relationship between languages and proof objects the strong connections between different proof search methods in logics type theories and logical frameworks together with their impact on programming and implementation issues are central in this context

exceptional zero formulae and a conjecture of perrin riou let a mathbf q be an elliptic curve with split multiplicative reduction at a prime p we prove an analogue of a conjecture of perrin riou relating p adic beilinson kato elements to heegner points in a mathbf q and a large part of the rank one case of the mazur tate teitelbaum exceptional zero conjecture for the cyclotomic p adic l function of a more generally let f be the weight two newform associated with a let f infty be the hida family of f and let l p f infty k s be the mazur kitagawa two variable p adic l function attached to f infty we prove a p adic gross zagier formula expressing the quadratic term of the taylor expansion of l p f infty k s at k s 2 1 as a non zero rational multiple of the extended height weight of a heegner point in a mathbf q

new results on computable efficiency and its stability for complex networks the concept of efficiency in a complex dynamic network plays the role of measuring its ability for the exchange of information and its response for the spread of perturbations in diverse applications this concept is strongly related to the topological properties of the network a new framework for the definition of network efficiency is discussed and some of its consequences are established we also consider how the efficiency changes as the network structure evolves by introducing the concept of stability associated to the efficiency of a network as an accurate tool to measure the evolution of a dynamic complex network

the undecidability of simultaneous rigid e unification abstract simultaneous rigid e unification was introduced in 1987 by gallier raatz and snyder it is used in the area of automated reasoning with equality in extension procedures like the tableau method or the connection method many articles in this area assumed the existence of an algorithm for the simultaneous rigid e unification problem there were several faulty proofs of the decidability of this problem in this paper we prove that simultaneous rigid e unification is undecidable as a consequence we obtain the undecidability of the fragment of intuitionistic logic with equality

an algorithm for finding canonical sets of ground rewrite rules in polynomial time in this paper it is shown that there is an algorithm that given by finite set e of ground equations produces a reduced canonical rewriting system r equivalent to e in polynomial time this algorithm based on congruence closure performs simplification steps guided by a total simplification ordering on ground terms and it runs in time o n 3

the geometry of hida families i λ adic de rham cohomology we construct the lambda adic de rham analogue of hida s ordinary lambda adic etale cohomology and of ohta s lambda adic hodge cohomology and by exploiting the geometry of integral models of modular curves over the cyclotomic extension of mathbf q p we give a purely geometric proof of the expected finiteness control and lambda adic duality theorems following ohta we then prove that our lambda adic module of differentials is canonically isomorphic to the space of ordinary lambda adic cuspforms in the sequel cais compos math to appear to this paper we construct the crystalline counterpart to hida s ordinary lambda adic etale cohomology and employ integral p adic hodge theory to prove lambda adic comparison isomorphisms between all of these cohomologies as applications of our work in this paper and cais compos math to appear we will be able to provide a cohomological construction of the family of varphi gamma modules attached to hida s ordinary lambda adic etale cohomology by dee j algebra 235 2 636 664 2001 as well as a new and purely geometric proof of hida s finiteness and control theorems we are also able to prove refinements of the main theorems in mazur and wiles compos math 59 2 231 264 1986 and ohta j reine angew math 463 49 98 1995

a new subsumption method in the connection graph proof procedure compared to most of the other resolution based proof procedures the connection graph proof procedure cgpp is superior due to its effective search space reduction rules a test for subsumption in cgpp is sufficiently efficient in comparison with the standard test but the subsumption with no restriction may cause logical inconsistency the restriction on subsumption to maintain the consistency has been an open problem since it was first noticed in 1981 we define a new subsumption which maintains the logical consistency and provides the graph transformation method which makes c subsume d with the new definition if c subsumes d with the original definition of sumsumption in the subsumption test in cgpp it is essential to find a set of pairwise strongly compatible matching substitutions between literals in two clauses this paper presents an algorithm which finds a set of pairwise strongly compatible matching substitutions efficiently based on both the reduction of possible matching substitutions and bit operations the worst case time complexity of this algorithm is analyzed in terms of the estimated maximal number of string comparisons and it is shown that our complexity is lower than the other algorithms based on the s link test based on the new definition of subsumption and the improved algorithm for the pairwise strongly compatible test an unrestricted subsumption algorithm and a restricted subsumption algorithm are suggested

representing scope in intuitionistic deductions abstract intuitionistic proofs can be segmented into scopes which describe when assumptions can be used in standard descriptions of intuitionistic logic these scopes occupy contiguous regions of proofs this leads to an explosion in the search space for automated deduction because of the difficulty of planning to apply a rule inside a particular scoped region of the proof this paper investigates an alternative representation which assigns scope explicitly to formulas and which is inspired in part by semantics based translation methods for modal deduction this calculus is simple and is justified by direct proof theoretic arguments that transform proofs in the calculus so that scopes match standard descriptions a herbrand theorem established straightforwardly lifts this calculus to incorporate unification the resulting system has no impermutabilities whatsoever rules of inference may be used equivalently anywhere in the proof nevertheless a natural specification describes how terms are to be extracted from its deductions

a note on a problem in the theory of grammatical complexity abstract in this note we answer an open question in the theory of grammatical complexity we show that if l is an infinite context free language then l n the set of words in l of length less than or equal to n can be generated by o l n 2 3 context free productions and if l is an infinite linear language then l n can be generated by o l n linear productions we also show that these bounds are the best possible

iwasawa theory and the eisenstein ideal we verify for each odd prime p 1000 a conjecture of w mccallum and the author s on the surjectivity of pairings on p units constructed out of the cup product on the first galois cohomology group of the maximal unramified outside p extension of q p with p coefficients in the course of the proof we relate several iwasawa theoretic and hida theoretic objects in particular we construct a canonical isomorphism between an eisenstein ideal modulo its square and the second graded piece in an augmentation filtration of a classical iwasawa module over an abelian pro p kummer extension of the cyclotomic zp extension of an abelian field this kummer extension arises from the galois representation on an inverse limit of ordinary parts of first cohomology groups of modular curves that was considered by m ohta in order to give another proof of the iwasawa main conjecture in the spirit of that of b mazur and a wiles in turn we relate the iwasawa module over the kummer extension to the quotient of the tensor product of the classical cyclotomic iwasawa module and the galois group of the kummer extension by the image of a certain reciprocity map that is constructed out of an inverse limit of cup products up the cyclotomic tower we give an application to the structure of the selmer groups of ohta s modular representation taken modulo the eisenstein ideal

theorem proving using equational matings and rigid e unification in this paper it is shown that the method of matings due toandrews and bibel can be extended to first order languages withequality a decidable version of e unification called rigid e unification is introduced and it is shown that the method of equational matings remains completewhen used in conjunction with rigid e unification checking that a familyof mated sets is an equational mating is equivalent to the followingrestricted kind of e unification problem given e a e i m1 i n a family of n finite sets of equations and s u i v i m1 i n a set of n pairsof terms is there a substitution q such that treating each set q e i as a set of ground equations i e holding the variables in q e i rigid q u i and q v i are provably equal from q e i for i 1 n equivalently is there a substitution q such that q u i and q v i can be shown congruent from q e i by the congruence closure method for i 1 n a substitution q solving the above problem is called a rigid e a unifier of s anda pair e a s such that s hassome rigid e a unifier is called an equationalpremating it is show that deciding whether a pair e a s is an equational premating is an np completeproblem

stability and continuity of centrality measures in weighted graphs this paper presents a formal definition of stability for node centrality measures in weighted graphs it is shown that the commonly used measures of degree closeness and eigenvector centrality are stable whereas betweenness centrality is not an alternative definition of the latter that preserves the same centrality notion while satisfying the stability criteria is introduced continuity is presented as a less stringent alternative to stability betweenness centrality is shown to be not only unstable but discontinuous numerical experiments in synthetic random networks and real world data show that in practice stability and continuity imply different levels of robustness in the presence of noisy data in particular the stable betweenness centrality is shown to exhibit resilience against noise that is absent in the discontinuous and unstable standard betweenness centrality while preserving a similar notion of centrality

a comparative analysis of network robustness against different link attacks abstract recently the study of optimizing network robustness has attracted increasing attentions and the constraint that every node s degree cannot be changed is considered although this constraint maintains the node degree distribution consistently in order to reserve the structure of networks it makes the network structure be lack of flexibility since many network structure always transform in the modern society given this consideration in this paper we analyze the robustness of networks through setting a new constraint that is only the number of edges should be unchanged then we use the link robustness index r l as the measure of the network robustness against either random failures or intentional attacks and make a comparative analysis of network robustness against different types of link attacks moreover we use four types of networks as initial networks namely scale free networks random networks regular networks and small world networks the experimental results show that the values of robustness measures for the optimized networks starting from different initial networks are similar under different link attacks but the network topologies may be different that is to say networks with different topologies may have similar robustness in terms of the robustness measures we also find that the optimized networks obtained by one link attack may not robust against other link attacks sometimes even weaker than the original networks therefore before building networks it is better to study which type of link attacks may happen

current flow efficiency of networks abstract many real world networks from infrastructure networks to social and communication networks can be formulated as flow networks how to realistically measure the transport efficiency of these networks is of fundamental importance the shortest path based efficiency measurement has limitations as it assumes that flow travels only along those shortest paths here we propose a new metric named current flow efficiency in which we calculate the average reciprocal effective resistance between all pairs of nodes in the network this metric takes the multipath effect into consideration and is more suitable for measuring the efficiency of many real world flow equilibrium networks moreover this metric can handle a disconnected graph and can thus be used to identify critical nodes and edges from the efficiency loss perspective we further analyze how the topological structure affects the current flow efficiency of networks based on some model and real world networks our results enable a better understanding of flow networks and shed light on the design and improvement of such networks with higher transport efficiency