k polystability of q fano varieties admitting kahler einstein metrics it is shown that any possibly singular fano variety x admitting a kahler einstein metric is k polystable thus confirming one direction of the yau tian donaldson conjecture in the setting of mathbb q fano varieties equipped with their anti canonical polarization the proof is based on a new formula expressing the donaldson futaki invariants in terms of the slope of the ding functional along a geodesic ray in the space of all bounded positively curved metrics on the anti canonical line bundle of x one consequence is that a toric fano variety x is k polystable iff it is k polystable along toric degenerations iff 0 is the barycenter of the canonical weight polytope p associated to x the results also extend to the logarithmic setting and in particular to the setting of kahler einstein metrics with edge cone singularities applications to geodesic stability bounds on the ricci potential and perelman s lambda entropy functional on k unstable fano manifolds are also given

commutators and linear spans of projections in certain finite c algebras assume that a is a unital separable simple c algebra with real rank zero stable rank one strict comparison of projections and that its tracial simplex t a has a finite number of extremal points we prove that every self adjoint element a in a with a 0 for all t a is the sum of two commutators in a and that every positive element of a is a linear combination of projections with positive coefficients assume that a is as above but unital and not necessarily unital then an element resp a positive element a of a is a linear combination resp a linear combination with positive coefficients of projections if and only if ra for every t a where denotes the extension of to a tracial weight on a and ra a denotes the range projection of a assume that a is unital and as above but t a has infinitely many extremal points then a is not the linear span of its projections this result settles two open problems of marcoux in 32

lattice preserving maps on lattices of continuous functions abstract lattice preserving maps between sublattices of continuous functions on locally compact spaces e g the functions with compact support are studied these maps though not necessarily linear are related to continuous functions between the underlying locally compact spaces consequences for first countable spaces including an automatic continuity for these lattice maps are provided

universal features in the growth dynamics of religious activities we quantify and analyze the growth dynamics of a religious group in 140 countries for a 47 year period 1959 2005 we find that i the distribution of annual logarithmic growth rates exhibits the same functional form for distinct size scales and ii the standard deviation of growth rates scales with size as a power law both findings hold for distinct measures of religious activity these results are in surprising agreement with those found in the study of economic activities and scientific research suggesting that religious activities are governed by universal growth mechanisms we also compare the empirical findings on religious activities with the predictions of general models recently proposed in the context of complex organizations our findings should provide useful information for a better understanding of the mechanisms governing the growth of religion

orthogonality preservers in c algebras jb algebras and jb triples abstract we study orthogonality preserving operators between c algebras jb algebras and jb triples let t a e be an orthogonality preserving bounded linear operator from a c algebra to a jb triple satisfying that t 1 d is a von neumann regular element then t a e 2 r d every element in t a and d operator commute in the jb algebra e 2 r d and there exists a triple homomorphism s a e 2 r d such that t l d r d s where r d denotes the range tripotent of d in e an analogous result for a being a jb algebra is also obtained when t a b is an operator between two c algebras we show that denoting h t 1 then t orthogonality preserving if and only if there exists a triple homomorphism s a b satisfying h s z s z h h s z s z h and t z l h r h s z 1 2 h r h s z s z r h h this allows us to prove that a bounded linear operator between two c algebras is orthogonality preserving if and only if it preserves zero triple products

effects of mass media on opinion spreading in the sznajd sociophysics model abstract in this work we consider the influence of mass media in the dynamics of the two dimensional sznajd model this influence acts as an external field and it is introduced in the model by means of a probability p of the agents to follow the media opinion we performed monte carlo simulations on square lattices with different sizes and our numerical results suggest a change on the critical behavior of the model with the absence of the usual phase transition for p 0 18 another effect of the probability p is to decrease the average relaxation times that are log normally distributed as in the standard model in addition the values depend on the lattice size l in a power law form l where the power law exponent depends on the probability p

self avoiding walks on scale free networks several kinds of walks on complex networks are currently used to analyze search and navigation in different systems many analytical and computational results are known for random walks on such networks self avoiding walks saw s are expected to be more suitable than unrestricted random walks to explore various kinds of real life networks here we study long range properties of random saw s on scale free networks characterized by a degree distribution p k ensuremath sim k ensuremath ensuremath gamma in the limit of large networks system size n ensuremath rightarrow ensuremath infty the average number s n of saw s starting from a generic site increases as ensuremath mu n with ensuremath mu k 2 k ensuremath 1 for finite n s n is reduced due to the presence of loops in the network which causes the emergence of attrition of the paths for kinetic growth walks the average maximum length l increases as a power of the system size l ensuremath sim n ensuremath alpha with an exponent ensuremath alpha increasing as the parameter ensuremath gamma is raised we discuss the dependence of ensuremath alpha on the minimum allowed degree in the network a similar power law dependence is found for the mean self intersection length of nonreversal random walks simulation results support our approximate analytical calculations

a deterministic small world network created by edge iterations abstract small world networks are ubiquitous in real life systems most previous models of small world networks are stochastic the randomness makes it more difficult to gain a visual understanding on how do different nodes of networks interact with each other and is not appropriate for communication networks that have fixed interconnections here we present a model that generates a small world network in a simple deterministic way our model has a discrete exponential degree distribution we solve the main characteristics of the model

stable maps in higher dimensions we formulate a notion of stability for maps between polarised varieties which generalises kontsevich s definition when the domain is a curve and tian donaldson s definition of k stability when the target is a point we give some examples such as kodaira embeddings and fibrations we prove the existence of a projective moduli space of canonically polarised stable maps generalising the kontsevich alexeev moduli space of stable maps in dimensions one and two we also state an analogue of the yau tian donaldson conjecture in this setting relating stability of maps to the existence of certain canonical kahler metrics

spreading and shortest paths in systems with sparse long range connections spreading according to simple rules e g of fire or diseases and shortest path distances are studied on d dimensional systems with a small density p per site of long range connections small world lattices the volume v t covered by the spreading quantity on an infinite system is exactly calculated in all dimensions as a function of time t from this the average shortest path distance l r can be calculated as a function of euclidean distance r it is found that l r approximately r for r r c the characteristic length r c which governs the behavior of shortest path lengths diverges logarithmically with l for all p 0

biseparating maps between operator algebras we prove that a biseparating map between spaces b e and some other banach algebras is automatically continuous and a multiple of an algebra isomorphism

random geometric graphs we analyze graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present the critical connectivity is found numerically by examining the size of the largest cluster we derive an analytical expression for the cluster coefficient which shows that the graphs are distinctly different from standard random graphs even for infinite dimensionality insights relevant for graph bipartitioning are included

log canonical singularities are du bois a recurring difficulty in the minimal model program mmp is that while log terminal singularities are quite well behaved for instance they are rational log canonical singularities are much more complicated they need not even be cohenmacaulay the aim of this paper is to prove that as conjectured in kol92 1 13 log canonical singularities are du bois the concept of du bois singularities abbreviated as db was introduced by steenbrink in ste83 as a weakening of rationality it is not clear how to define du bois singularities in positive characteristic so we work over a field of characteristic 0 throughout the paper the precise definition is rather involved see 1 10 but our main applications rely only on the following consequence

invariant hypersurfaces of endomorphisms of projective varieties we consider surjective endomorphisms f of degree 1 on projective manifolds x of picard number one and their f 1 stable hypersurfaces v and show that v is rationally chain connected also given is an optimal upper bound for the number of f 1 stable prime divisors on not necessarily smooth projective varieties

percolation and epidemics in a two dimensional small world percolation on two dimensional small world networks has been proposed as a model for the spread of plant diseases in this paper we give an analytic solution of this model using a combination of generating function methods and high order series expansion our solution gives accurate predictions for quantities such as the position of the percolation threshold and the typical size of disease outbreaks as a function of the density of shortcuts in the small world network our results agree with scaling hypotheses and numerical simulations for the same model

biseparating maps and homeomorphic real compactifications abstract if x and y are realcompact and t c x c y is a ring isomorphism then two things happen 1 there is a homeomorphism h of x onto y and 2 t is a composition map for all in c x t h we strengthen that result in propositions 2 and 3 we discard the multiplicative property of t and assume only that t is biseparating in the sense that g 0 t tg 0 it remains true that x is homeomorphic to y but this time if t is also linear it is a weighted composition map for some weight function a in c y t a h

weighted composition operators ofc0 x s abstract in this paper we prove that into isometries and disjointness preserving linear maps from c 0 x into c 0 y are essentially weighted composition operators tf h f for some continuous map and some continuous scalar valued function h

fast monte carlo algorithm for site or bond percolation we describe in detail an efficient algorithm for studying site or bond percolation on any lattice the algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time that scales linearly with the size of the system we demonstrate our algorithm by using it to investigate a number of issues in percolation theory including the position of the percolation transition for site percolation on the square lattice the stretched exponential behavior of spanning probabilities away from the critical point and the size of the giant component for site percolation on random graphs

could any graph be turned into a small world in addition to statistical graph properties diameter degree clustering etc kleinberg the small world phenomenon an algorithmic perspective in proc 32nd acm symp on theory of computing stoc 2000 pp 163 170 showed that a small world can also be seen as a graph in which the routing task can be efficiently and easily done in spite of a lack of global knowledge more precisely in a lattice network augmented by extra random edges but not chosen uniformly a short path of polylogarithmic expected length can be found using a greedy algorithm with a local knowledge of the nodes we call such a graph a navigable small world since short paths exist and can be followed with partial knowledge of the network in this paper we show that a wide class of graphs can be augmented into navigable small worlds

electoral surveys influence on the voting processes a cellular automata model abstract nowadays in societies threatened by atomization selfishness short term thinking and alienation from political life there is a renewed debate about classical questions concerning the quality of democratic decision making in this work a cellular automata model for the dynamics of free elections based on the social impact theory is proposed by using computer simulations power law distributions for the size of electoral clusters and decision time have been obtained the major role of broadcasted electoral surveys in guiding opinion formation and stabilizing the status quo was demonstrated furthermore it was shown that in societies where these surveys are manipulated within the universally accepted statistical error bars even a majoritary opposition could be hindered from reaching power through the electoral path

exact solution of site and bond percolation on small world networks we study percolation on small world networks which has been proposed as a simple model of the propagation of disease the occupation probabilities of sites and bonds correspond to the susceptibility of individuals to the disease and the transmissibility of the disease respectively we give an exact solution of the model for both site and bond percolation including the position of the percolation transition at which epidemic behavior sets in the values of the critical exponents governing this transition the mean and variance of the distribution of cluster sizes disease outbreaks below the transition and the size of the giant component epidemic above the transition

on fano foliations abstract in this paper we address fano foliations on complex projective varieties these are foliations whose anti canonical class k is ample we focus our attention on a special class of fano foliations namely del pezzo foliations on complex projective manifolds we show that these foliations are algebraically integrable with one exceptional case when the ambient space is p n we also provide a classification of del pezzo foliations with mild singularities

brazilian elections voting for a scaling democracy abstract the proportional elections held in brazil in 1998 and 2002 display identical statistical signatures in particular the distribution of votes among candidates includes a power law regime we suggest that the rationale behind this robust scaling invariance is a multiplicative process in which the voter s choice for a candidate is governed by a product of probabilities

bootstrap percolation on a graph with random and local connections let g n p 1 be a superposition of the random graph g n p and a one dimensional lattice the n vertices are set to be on a ring with fixed edges between the consecutive vertices and with random independent edges given with probability p between any pair of vertices bootstrap percolation on a random graph is a process of spread of activation on a given realization of the graph with a given number of initially active nodes at each step those vertices which have not been active but have at least r ge 2 active neighbours become active as well we study the size of the final active set in the limit when n rightarrow infty the parameters of the model are n the size a 0 a 0 n of the initially active set and the probability p p n of the edges in the graph the bootstrap percolation process on g n p was studied earlier here we show that the addition of n local connections to the graph g n p leads to a more narrow critical window for the phase transition preserving however the critical scaling of parameters known for the model on g n p we discover a range of parameters which yields percolation on g n p 1 but not on g n p

ideal adic semi continuity problem for minimal log discrepancies we discuss the ideal adic semi continuity problem for minimal log discrepancies by musta we study the purely log terminal case and prove the semi continuity of minimal log discrepancies when a kawamata log terminal triple deforms in the ideal adic topology

maximal planar networks with large clustering coefficient and power law degree distribution in this article we propose a simple rule that generates scale free networks with very large clustering coefficient and very small average distance these networks are called random apollonian networks rans as they can be considered as a variation of apollonian networks we obtain the analytic results of power law exponent ensuremath gamma 3 and clustering coefficient c frac 46 3 ensuremath 36 phantom rule 0 2em 0ex mathrm ln phantom rule 0 2em 0ex frac 3 2 ensuremath approx 0 74 which agree with the simulation results very well we prove that the increasing tendency of average distance of rans is a little slower than the logarithm of the number of nodes in rans since most real life networks are both scale free and small world networks rans may perform well in mimicking the reality the rans possess hierarchical structure as c k ensuremath sim k ensuremath 1 that are in accord with the observations of many real life networks in addition we prove that rans are maximal planar networks which are of particular practicability for layout of printed circuits and so on the percolation and epidemic spreading process are also studied and the comparisons between rans and barab asi albert ba as well as newman watts nw networks are shown we find that when the network order n the total number of nodes is relatively small as n ensuremath sim 10 4 the performance of rans under intentional attack is not sensitive to n while that of ba networks is much affected by n and the diseases spread slower in rans than ba networks in the early stage of the suseptible infected process indicating that the large clustering coefficient may slow the spreading velocity especially in the outbreaks

scaling behavior in a proportional voting process we perform a statistical analysis on the proportional elections held in brazil in october 1998 we show that the distribution of votes among candidates for the whole country follows a power law n v ensuremath propto v ensuremath ensuremath alpha with ensuremath alpha 1 00 ifmmode pm else textpm fi 0 02 extending over two orders of magnitude the voting distributions for several states of the federation also display scale invariant behavior with ensuremath alpha ensuremath approx 1 we argue that this particular voting system can be modeled as a typical multiplicative process in which the choice of the candidate is governed by a product of probabilities

self organized criticality on small world networks abstract we study the btw height model of self organized criticality on a square lattice with some long range connections giving to the lattice the character of small world network we find that as function of the fraction p of long ranged bonds the power law of the avalanche size and lifetime distribution changes following a crossover scaling law with crossover exponents 2 3 and 1 for size and lifetime respectively

zero product preserving linear maps of ccr c algebras with hausdorff spectrum in this paper we try to attack a conjecture of araujo and jarosz that every bijective linear map between c algebras with both and its inverse 1 preserving zero products arises from an algebra isomorphism followed by a central multiplier we show it is true for ccr c algebras with hausdorff spectrum and in general some special c algebras associated to continuous fields of c algebras

the influence of preferential attachment on evolving networks abstract with the consideration of local events and preferential attachment the extended model proposed by albert and barabasi is studied firstly the extended model is built only by local events it is found that without preferential attachment the networks connectivity distribution decays exponentially for large connectivity and the decaying exponent varies with different probabilities of the addition of new links and rewiring secondly the extended model with partial preferential attachment is studied when preferential attachment only presents in the addition of new links or new nodes there is scale free regime in the phase diagram while preferential attachment is brought into the rewiring there coexist two regimes i e the exponential regime and the scale free regime thirdly fitness is introduced to the extended model with complete preferential attachment it is obtained that the network s connectivity distribution is a result affected by many factors including the fitness the local events and preferential attachment

stable pair tropical and log canonical compactifications of moduli spaces of del pezzo surfaces we give a functorial normal crossing compactification of the moduli space of smooth cubic surfaces entirely analogous to the grothendieck knudsen compactification m 0 n subset overline m 0 n

critical states in political trends how much reliable is a poll on twitter the potts model and the inverse problem in social science abstract in recent years twitter data related to political trends have tentatively been used to make predictions poll about several electoral events given q candidates for an election and a time series of twitts short messages one can extract the q mean trends and the q q 1 2 twitt to twitt correlations and look for the statistical models that reproduce these data on the base of several electoral events and assuming a stationary regime we find out the following i the maximization of the entropy singles out a microscopic model single twitt level that coincides with a q state potts model having suitable couplings and external fields to be determined via an inverse problem from the two sets of data ii correlations decay as 1 n e f f where n e f f is a small fraction of the mean number of twitts iii the simplest statistical models that reproduce these correlations are the multinomial distribution md characterized by q external fields and the mean field potts model mfp characterized by one coupling iv remarkably this coupling turns out to be always close to its critical value this results in a md or mfp model scenario that discriminates between cases in which polls are reliable and not reliable respectively more precisely predictions based on polls should be avoided whenever the data maps to a mfp because anomalous large fluctuations if q 2 or sudden jumps if q 3 in the trends might take place as a result of a second order or a first order phase transition of the mfp respectively

promoting cooperation by local contribution under stochastic win stay lose shift mechanism a b s t r a c t we introduce a stochastic win stay lose shift wsls mechanism into evolutionary prisoner s dilemma on small world networks at each time step after playing with all its immediate neighbors each individual gets a score to evaluate its performance in the game the score is a linear combination of an individual s total payoff i e individual gain from the group and local contribution to its neighbors i e individual donation to the group if one s actual score is not larger than its desired score aspiration it switches current strategy to the opposite one with the probability depending on the difference between the two scores under this stochastic wsls regime we assume that each focal individual gains its fixed score aspiration under the condition of full cooperation in its neighborhood and find that cooperation is significantly enhanced under some certain parameters of the model by studying the evolution of cooperation we also explore the influences of different values of learning rate and intensity of deterministic switch on the evolution of cooperation simulation results show that cooperation level monotonically increases with the relative weight of the local contribution to the score for much low intensity of deterministic switch cooperation is to a large extent independent of learning rate and full cooperation can be reached when relative weight is not less than 0 5 otherwise cooperation level is affected by the value of learning rate besides we find that the cooperation level is not sensitive to the topological parameters to explain these simulation results we provide corresponding analytical results based on mean field approximation and find out that simulationresultsareincloseagreementwiththeanalyticalones ourworkmaybehelpful in understanding the cooperative behavior in social systems based on this stochastic wsls mechanism

isomorphisms of ordered structures of abelian c subalgebras of c algebras abstract the aim of this note is to study the interplay between the jordan structure of c algebra and the structure of its abelian c subalgebras let abel a be a system of unital c subalgebras of a unital c algebra a ordered by set theoretic inclusion we show that any order isomorphism abel a abel b can be uniquely written in the form c c s a i c s a where is a partially linear jordan isomorphism between self adjoint parts of unital c algebras a and b as a corollary we obtain that for certain class of c algebras including von neumann algebras ordered structure of abelian subalgebras completely determines the jordan structure the results extend hitherto known results for abelian c algebras and may be relevant to foundations of quantum theory

dynamics of epidemics on random networks this paper examines how diseases on random networks spread in time the disease is described by a probability distribution function for the number of infected and recovered individuals and the probability distribution is described by a generating function the time development of the disease is obtained by iterating the generating function in cases where the disease can expand to an epidemic the probability distribution function is the sum of two parts one that is static at long times and another whose mean grows exponentially the time development of the mean number of infected individuals is obtained analytically when epidemics occur the probability distributions are very broad and the uncertainty in the number of infected individuals at any given time is typically larger than the mean number of infected individuals

impact of noise and damage on collective dynamics of scale free neuronal networks we study the role of scale free structure and noise in collective dynamics of neuronal networks for this purpose we simulate and study analytically a cortical circuit model with stochastic neurons we compare collective neuronal activity of networks with different topologies classical random graphs and scale free networks we show that in scale free networks with divergent second moment of degree distribution an influence of noise on neuronal activity is strongly enhanced in comparison with networks with a finite second moment a very small noise level can stimulate spontaneous activity of a finite fraction of neurons and sustained network oscillations we demonstrate tolerance of collective dynamics of the scale free networks to random damage in a broad range of the number of randomly removed excitatory and inhibitory neurons a random removal of neurons leads to gradual decrease of frequency of network oscillations similar to the slowing of the alpha rhythm in alzheimer s disease however the networks are vulnerable to targeted attacks a removal of a few excitatory or inhibitory hubs can impair sustained network oscillations

shokurov s acc conjecture for log canonical thresholds on smooth varieties shokurov conjectured that the set of all log canonical thresholds on varieties of bounded dimension satisfies the ascending chain condition in this paper we prove that the conjecture holds for log canonical thresholds on smooth varieties and more generally on locally complete intersection varieties and on varieties with quotient singularities

percolation on a multifractal scale free planar stochastic lattice and its universality class we investigate site percolation on a weighted planar stochastic lattice wpsl which is a multifractal and whose dual is a scale free network percolation is typically characterized by a threshold value p c at which a transition occurs and by a set of critical exponents which describe the critical behavior of the percolation probability p p mean cluster size s p and the correlation length besides the exponent characterizes the cluster size distribution function n s p c and the fractal dimension d f characterizes the spanning cluster we numerically obtain the value of p c and of all the exponents these results suggest that the percolation on wpsl belong to a separate universality class than on all other planar lattices

globally f regular and log fano varieties abstract we prove that every globally f regular variety is log fano in other words if a prime characteristic variety x is globally f regular then it admits an effective q divisor such that k x is ample and x has controlled kawamata log terminal in fact globally f regular singularities a weak form of this result can be viewed as a prime characteristic analog of de fernex and hacon s new point of view on kawamata log terminal singularities in the non q gorenstein case we also prove a converse statement in characteristic zero every log fano variety has globally f regular type our techniques apply also to f split varieties which we show to satisfy a log calabi yau condition we also prove a kawamata viehweg vanishing theorem for globally f regular pairs

cycles and clustering in bipartite networks we investigate the clustering coefficient in bipartite networks where cycles of size three are absent and therefore the standard definition of clustering coefficient cannot be used instead we use another coefficient given by the fraction of cycles with size four showing that both coefficients yield the same clustering properties the new coefficient is computed for two networks of sexual contacts one bipartite and another where no distinction between the nodes is made monopartite in both cases the clustering coefficient is similar furthermore combining both clustering coefficients we deduce an expression for estimating cycles of larger size which improves previous estimations and is suitable for either monopartite and multipartite networks and discuss the applicability of such analytical estimations

adjoint ideals along closed subvarieties of higher codimension in this paper we introduce a notion of adjoint ideal sheaves along closed subvarieties of higher codimension and study its local properties using char acteristic p methods when x is a normal gorenstein closed subvariety of a smooth complex variety a we formulate a restriction property of the adjoint ideal sheaf adj x a of a along x involving the l c i ideal sheaf dx of x the proof relies on a modification of generalized test ideals of hara and yoshida 11

effect of initial concentration and spatial heterogeneity of active agent distribution on opinion dynamics abstract we analyze the effect of spatial heterogeneity in the initial spin distribution on spin dynamics in a three state square lattice divided into spatial cells districts in the spirit of the statistical mechanics of social impact we introduce a dominant influence rule dir according to which in a single update step a chosen node adopts the state determined by the influence of its discussion group formed by the node itself and its neighbors within one or more coordination spheres in contrast to models based on some form of majority rule mr a system governed by the dir is easily trapped in a stable non consensus state if all nodes of the discussion group have the same weight of influence to ensure that a consensus in the dir system is necessarily reached we need to put a stochastic process in the update rule further the stochastic dir model is used as a starting point for understanding the effect of spatial heterogeneity of active agent non zero spin distribution on the exit probabilities initially the positive and negative spins active agents are assigned to some nodes with non uniform spatial distributions while the rest of the nodes remain in the state with spin zero uncommitted voters by varying the relative means and skewness of the initial spin distributions we observe critical behaviors of exit probabilities in finite size systems the critical exponents are obtained by monte carlo simulations the results of numerical simulations are discussed in the context of social dynamics

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

dye s theorem and gleason s theorem for aw algebras abstract we prove that any map between projection lattices of a w algebras a and b where a has no type i 2 direct summand that preserves orthocomplementation and suprema of arbitrary elements is a restriction of a normal jordan homomorphism between a and b this allows us to generalize dye s theorem from von neumann algebras to a w algebras we show that mackey gleason bunce wright theorem can be extended to homogeneous a w algebras of type i the interplay between dye s theorem and gleason s theorem is shown as an application we prove that jordan homomorphisms are commutatively determined another corollary says that jordan parts of a w algebras can be reconstructed from posets of their abelian subalgebras

projectivity of the moduli space of stable log varieties and subadditivity of log kodaira dimension reference epfl article 231100doi 10 1090 jams 871 url http dx doi org 10 1090 jams 871 record created on 2017 09 19 modified on 2017 10 02

structure properties and synchronizability of cobweb like networks abstract the cobweb like network was constructed and its structure properties and synchronizability were studied by numerical simulation and probability theory for cobweb like networks the behaviors of structure properties with the adding probability are similar to those for the small world network however the properties of cobweb like networks also distinctly depend on the spoke ring ratio r with increasing r the average path length decreases and the average clustering coefficient increases simultaneously the connectivity distribution becomes heterogeneous moreover in the case of bounded synchronized region the synchronizability shows complicated behaviors with r and is enhanced favorably at r 2 28 with homogeneous load distribution the reason is that homogeneous load distribution has an advantage over the communication between oscillators which efficiently leads to global synchronization this work could be useful for design and kinetic property research of cobweb like networks

fibered stable varieties reference epfl article 231103doi 10 1090 tran 6386 url http dx doi org 10 1090 tran 6386 record created on 2017 09 19 modified on 2017 10 02

towards boundedness of minimal log discrepancies by the riemann roch theorem we introduce an approach via the riemann roch theorem to the boundedness problem of minimal log discrepancies in fixed dimension after reducing it to the case of a gorenstein terminal singularity firstly we prove that the minimal log discrepancy is bounded if either multiplicity or embedding dimension is bounded secondly we recover the characterization of a gorenstein terminal three fold singularity by reid and the sharp bound for its minimal log discrepancy by markushevich without explicit classification finally we provide the sharp bound for a special four fold singularity whose general hyperplane section has a terminal piece

logistic equation of arbitrary order abstract the paper is concerned with the new logistic equation of arbitrary order which describes the performance of complex executive systems x vs number of tasks n operating at limited resources k at non extensive heterogeneous self organization processes characterized by parameter f in contrast to the classical logistic equation which exclusively relates to the special case of sub extensive homogeneous self organization processes at f 1 the proposed model concerns both homogeneous and heterogeneous processes in sub extensive and super extensive areas the parameter of arbitrary order f where f depends on both the coefficient of external resource utilization u n k where 0 u 1 and the internal microscopic character of realized processes related to the depth of feedback the coefficient directly influences self organization of processes by the change of microscopic parameters v i s i i and z where v i is the number of references visit to the i th component of the system during the service of each task s i is the time of serving the task by the i th component and z is the think time of a given process in the general case of complex system parameters v i s i i and z can have values in the range from 0 to in this way the new equation includes all possible cases of a complex executive system s operation furthermore it allows us to define the optimal matching point between x and n with f as the parameter it also helps to balance the load in complex systems and to equip artificial systems with self optimization mechanisms similar to those observed in natural systems

linear disjointness preservers of w algebras in this paper we give a complete description of the structure of zero product and orthogonality preserving linear maps between w algebras in particular two w algebras are isomorphic if and only if there is a bijective linear map between them preserving their zero product or orthogonality structure in two directions it is also the case when they have equivalent linear and left right ideal structures

the susceptible infected recovered model on a euclidean network we consider a susceptible infected recovered sir epidemic model on a euclidean network in one dimension in which nodes at a distance l are connected with probability p l l in addition to nearest neighbors the topology of the network changes as is varied and its effect on the sir model is studied r t the recovered fraction of population up to time t and the total duration of the epidemic are calculated for different values of the infection probabilities q and a threshold behavior is observed for all up to 2 0 above the threshold value q qc the saturation value rsat attains a finite value both rsat and show scaling behavior in a finite system of size n and qc is constant for 0 qc the results are compared to static percolation phenomena and also to mean field results for finite systems discussions on the properties of the euclidean network are made in the light of the present results

mode locking in small world networks of coupled circle maps abstract we investigate the emergence of mode locking or frequency synchronization in a chain of coupled sine circle maps with randomly distributed parameters and exhibiting the small world property the coupling prescription we adopt considers the nearest and next to the nearest neighbors of a given site as well as randomly chosen non local shortcuts according to a given probability a transition between synchronized and non synchronized patterns is observed as this probability is varied we also study the statistics of the synchronization plateaus evidencing a poisson type distribution

orthogonality and disjointness preserving linear maps between fourier and fourier stieltjes algebras of locally compact groups this paper is devoted to the study of orthogonality and disjointness preserving linear maps between fourier and fourier stieltjes algebras of locally compact groups we show that a linear bijection a g1 a g2 resp b g1 b g2 between two fourier algebras resp fourier stieltjes algebras of locally compact groups will induce a topological group isomorphism between g1 and g2 provided that preserves both disjointness and some kind of orthogonality this improves earlier results of j j font and m s monfared where amenability of the groups or continuity of the linear maps are assumed we also study the structure of bounded and unbounded disjointness preserving linear functionals of fourier algebras in the development general results about disjointness and orthogonality preserving linear maps between c algebras w algebras and their preduals are obtained

irreversible growth of binary mixtures on small world networks binary mixtures growing on small world networks under far from equilibrium conditions are studied by means of extensive monte carlo simulations for any positive value of the shortcut fraction of the network p 0 the system undergoes a continuous order disorder phase transition while it is noncritical in the regular lattice limit p 0 using finite size scaling relations the phase diagram is obtained in the thermodynamic limit and the critical exponents are evaluated the small world networks are thus shown to trigger criticality a phenomenon analogous to similar observations reported recently in the investigation of equilibrium systems

mean field solution of the small world network model the small world network model is a simple model of the structure of social networks which possesses characteristics of both regular lattices and random graphs the model consists of a one dimensional lattice with a low density of shortcuts added between randomly selected pairs of points these shortcuts greatly reduce the typical path length between any two points on the lattice we present a mean field solution for the average path length and for the distribution of path lengths in the model this solution is exact in the limit of large system size and either a large or small number of shortcuts

synchronization diversity and topology of networks of integrate and fire oscillators we study synchronization dynamics of a population of pulse coupled oscillators in particular we focus our attention on the interplay between topological disorder and synchronization features of networks first we analyze synchronization time t in random networks and find a scaling law which relates t to network connectivity then we compare synchronization time for several other topological configurations characterized by a different degree of randomness the analysis shows that regular lattices perform better than a disordered network this fact can be understood by considering the variability in the number of links between two adjacent neighbors this phenomenon is equivalent to having a nonrandom topology with a distribution of interactions and it can be removed by an adequate local normalization of the couplings

spread of opinions and proportional voting election results are determined by numerous social factors that affect the formation of opinion of the voters including the network of interactions between them and the dynamics of opinion influence in this work we study the result of proportional elections using an opinion dynamics model similar to simple opinion spreading over a complex network erd os r enyi barab asi albert regular lattices and randomly augmented lattices are considered as models of the underlying social networks the model reproduces the power law behavior of a number of candidates with a given number of votes found in real elections with the correct slope a cutoff for a larger number of votes and a plateau for a small number of votes it is found that the small world property of the underlying network is fundamental for the emergence of the power law regime

fisher information and the thermodynamics of scale invariant systems abstract we present a thermodynamic formulation for scale invariant systems based on the minimization with constraints of the fisher information measure in such a way a clear analogy between these systems thermal properties and those of gases and fluids is seen to emerge in a natural fashion we focus our attention on the non interacting scenario speaking thus of scale free ideal gases sfigs and present some empirical evidences regarding such disparate systems as electoral results city populations and total citations in physics journals that seem to indicate that sfigs do exist we also illustrate the way in which zipf s law can be understood in a thermodynamical context as the surface of a finite system finally we derive an equivalent microscopic description of our systems which totally agrees with previous numerical simulations found in the literature

a characteristic p analogue of plt singularities and adjoint ideals we introduce a new variant of tight closure and give an interpretation of adjoint ideals via this tight closure as a corollary we prove that a log pair x is plt if and only if the modulo p reduction of x is divisorially f regular for all large p 0 here divisorially f regular pairs are a class of singularities in positive characteristic introduced by hara and watanabe j algebra geom 11 363 392 2002 in terms of frobenius splitting

automatic continuity of biorthogonality preservers between compact c algebras and von neumann algebras abstract we prove that every biorthogonality preserving linear surjection between two dual or compact c algebras or between two von neumann algebras is automatically continuous

scaling and percolation in the small world network model in this paper we study the small world network model of watts and strogatz which mimics some aspects of the structure of networks of social interactions we argue that there is one nontrivial length scale in the model analogous to the correlation length in other systems which is well defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero giving a normal critical point in this limit this length scale governs the crossover from large to small world behavior in the model as well as the number of vertices in a neighborhood of given radius on the network we derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex vertex distance on the network and using series expansion and pad e approximants find an approximate analytic form for the scaling function we calculate the effective dimension of small world graphs and show that this dimension varies as a function of the length scale on which it is measured in a manner reminiscent of multifractals we also study the problem of site percolation on small world networks as a simple model of disease propagation and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms in epidemiological terms the point at which an epidemic occurs the typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph all our analytic results are confirmed by extensive numerical simulations of the model

semi log canonical vs f pure singularities abstract if x is frobenius split then so is its normalization and we explore conditions which imply the converse to do this we recall that given an o x linear map f o x o x it always extends to a map on the normalization of x in this paper we study when the surjectivity of implies the surjectivity of while this doesn t occur generally we show it always happens if certain tameness conditions are satisfied for the normalization map our result has geometric consequences including a connection between f pure singularities and semi log canonical singularities and a more familiar version of the f inversion of adjunction formula

information cascade kirman s ant colony model and kinetic ising model we discuss a voting model in which voters can obtain information from a finite number of previous voters it is the equilibrium process there exist three groups of voters i digital herders and independent voters ii analog herders and independent voters and iii tanh type herders in the case i we show that the solution oscillates between the two states a good bad equilibrium is where a majority of r select the correct wrong candidate we show that there is no phase transition when r is finite if the annealing schedule is adequately slow from finite r to infinite r the voting rate converges only to the good equilibrium in case ii the state of reference votes is equivalent to that of kirman s ant colony model and it follows beta binomial distribution in case iii we show that the model is equivalent to the finite size kinetic ising model if the voters are rational a simple herding experiment of information cascade is conducted information cascade results from the quenching of the kinetic ising model as case i is the limit of case iii when tanh function becomes a step function the phase transition can be observed in infinite size limit we can confirm that there is no phase transition when the reference number r is finite this chapter is based on hisakado and mori physica a 417 63 75 2015

the influence of connectivity on the firing rate in a neuronal network with electrical and chemical synapses a b s t r a c t we study the firing rate properties of a cellular automaton model for a neuronal network with chemical synapses we propose a simple mechanism in which the nonlocal connections are included through electrical and chemical synapses in the latter case we introduce a time delay which produces self sustained activity nonlocal connections or shortcuts are randomly introduced according to a specified connection probability there is a range of connection probabilities for which neuron firing occurs as well as a critical probability for which the firing ceases in the absence of time delay the critical probability for nonlocal shortcuts depends on the network size according to a power law we also compute the firing rate amplification factor by varying both the connection probability and the time delay for different network sizes

hierarchical characterization of complex networks while the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node valuable information about the network topological properties can be obtained by considering further neighborhoods the current work considers the concept of virtual hierarchies established around each node and the respectively defined hierarchical node degree and clustering coefficient introduced in cond mat 0408076 complemented by new hierarchical measurements in order to obtain a powerful set of topological features of complex networks the interpretation of such measurements is discussed including an analytical study of the hierarchical node degree for random networks and the potential of the suggested measurements for the characterization of complex networks is illustrated with respect to simulations of random scale free and regular network models as well as real data airports proteins and word associations the enhanced characterization of the connectivity provided by the set of hierarchical measurements also allows the use of agglomerative clustering methods in order to obtain taxonomies of relationships between nodes in a network a possibility which is also illustrated in the current article

topological bifurcations in a model society of reasonable contrarians people are often divided into conformists and contrarians the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority in practice however the contrarian tendency is rarely followed when there is an overwhelming majority with a given opinion which denotes a social norm such reasonable contrarian behavior is often considered a mark of independent thought and can be a useful strategy in financial markets we present the opinion dynamics of a society of reasonable contrarian agents the model is a cellular automaton of ising type with antiferromagnetic pair interactions modeling contrarianism and plaquette terms modeling social norms we introduce the entropy of the collective variable as a way of comparing deterministic mean field and probabilistic simulations bifurcation diagrams in the mean field approximation the model exhibits bifurcations and a chaotic phase interpreted as coherent oscillations of the whole society however in a one dimensional spatial arrangement one observes incoherent oscillations and a constant average in simulations on watts strogatz networks with a small world effect the mean field behavior is recovered with a bifurcation diagram that resembles the mean field one but where the rewiring probability is used as the control parameter similar bifurcation diagrams are found for scale free networks and we are able to compute an effective connectivity for such networks

sandpile model on an optimized scale free network on euclidean space deterministic sandpile models are studied on a cost optimized barabasi albert ba scale free network whose nodes are the sites of a square lattice for the optimized ba network the sandpile model has the same critical behaviour as the btw sandpile whereas for the un optimized ba network the critical behaviour is mean field like

disjointness preservers of aw algebras abstract in this paper we study bijective linear maps a b between a w algebras preserving either zero products or range orthogonality such a map is automatically continuous and provides an algebra or a algebra isomorphism 1 1 from a onto b our results extend previous works for the case of w algebras and also cover such maps between c algebras satisfying an extra assumption on preserving abelian c subalgebras