modeling and analysis of timed petri nets using heaps of pieces the authors show that safe timed petri nets can be represented by special automata over the max semiring which compute the height of heaps of pieces this extends to the timed case the classical representation a la mazurkiewicz of the behavior of safe petri nets by trace monoids and trace languages for a subclass including all safe free choice petri nets we obtain reduced heap realizations using structural properties of the net covering by safe state machine components the authors illustrate the heap based modeling by the typical case of safe jobshops for a periodic schedule the authors obtain a heap based throughput formula which is simpler to compute than its traditional timed event graph version particularly if one is interested in the successive evaluation of a large number of possible schedules

a measure valued differentiation approach to sensitivities of quantiles quantiles play an important role in modelling quality of service in the service industry and in modelling risk in the financial industry the recent discovery that efficient simulation based estimators can be obtained for quantile sensitivities has led to an intensive search for sample path differentiation based estimators for quantile sensitivities in this paper we present a novel approach to quantile sensitivity estimation our approach elaborates on the concept of measure valued differentiation thereby we overcome the main obstacle of the sample path approach which is the requirement that the sample cost have to be lipschitz continuous with respect to the parameter of interest specifically we perform a sensitivity analysis of the value at risk in financial models in addition we discuss an application of our sensitivity estimator to queueing networks

horizontal visibility graphs exact results for random time series networks this procedure allows us to apply methods of complex network theory for characterizing time series in this work we present the horizontal visibility algorithm a geometrically simpler and analytically solvable version of our former algorithm focusing on the mapping of random series series of independent identically distributed random variables after presenting some properties of the algorithm we present exact results on the topological properties of graphs associated with random series namely the degree distribution the clustering coefficient and the mean path length we show that the horizontal visibility algorithm stands as a simple method to discriminate randomness in time series since any random series maps to a graph with an exponential degree distribution of the shape pk 1 32 3 k 2 independent of the probability distribution from which the series was generated accordingly visibility graphs with other pk are related to nonrandom series numerical simulations confirm the accuracy of the theorems for finite series in a second part we show that the method is able to distinguish chaotic series from independent and identically distributed i i d theory studying the following situations i noise free low dimensional chaotic series ii low dimensional noisy chaotic series even in the presence of large amounts of noise and iii high dimensional chaotic series coupled map lattice without needs for additional techniques such as surrogate data or noise reduction methods finally heuristic arguments are given to explain the topological properties of chaotic series and several sequences that are conjectured to be random are analyzed

log canonical thresholds of certain fano hypersurfaces we study log canonical thresholds on quartic threefolds quintic fourfolds and double spaces as an important application we show that they have kahler einstein metrics if they are general

nonlinear dynamics delay times and embedding windows in order to construct an embedding of a nonlinear time series one must choose an appropriate delay time d often d is estimated using the autocorrelation function however this does not treat the nonlinearity appropriately and it may yield an incorrect value for d on the other hand the correct value of d can be found from the mutual information but this process is rather cumbersome computationally here we suggest a simpler method for estimating d using the correlation integral we call this the c c method and we test it on several nonlinear time series obtaining estimates of d in agreement with those obtained using the mutual information furthermore some researchers have suggested that one should not choose a fixed delay time d independent of the embedding dimension m but rather one should choose an appropriate value for the delay time window w d m 1 which is the total time spanned by the components of each embedded point unfortunately w cannot be estimated using the autocorrelation function or the mutual information and no standard procedure for estimating w has emerged however we show that the c c method can also be used to estimate w basically w is the optimal time for independence of the data while d is the first locally optimal time as tests we apply the c c method to the lorenz system a three dimensional irrational torus the rossler system and the rabinovich fabrikant system we also demonstrate the robustness of this method to the presence of noise c 1999 elsevier science b v all rights reserved

jumping coefficients and spectrum of a hyperplane arrangement in an earlier version of this paper written by the second named author we showed that the jumping coefficients of a hyperplane arrangement depend only on the combinatorial data of the arrangement as conjectured by musta for this we proved a similar assertion on the spectrum after this first proof was written the first named author found a more conceptual proof using the hirzebruch riemann roch theorem where the assertion on the jumping numbers was proved without reducing to that for the spectrum in this paper we improve these methods and show that the jumping numbers and the spectrum are calculable in low dimensions without using a computer in the reduced case we show that these depend only on fewer combinatorial data and give completely explicit combinatorial formulas for the jumping coefficients and part of the spectrum in the case the ambient dimension is 3 or 4 we also give an analogue of musta s formula for the spectrum

analytic approximations of plurisubharmonic singularities we study several classes of isolated singularities of plurisubharmonic functions that can be approximated by analytic singularities with control over their residual monge ampere masses they are characterized in terms of green functions for demailly s approximations relative types and valuations furthermore the classes are shown to appear when studying graded families of ideals of analytic functions and the corresponding asymptotic multiplier ideals

a bound of lengths of chains of minimal rational curves on fano manifolds of picard number 1 abstract in this paper we investigate the minimal length of chains of minimal rational curves needed to join two general points on a fano manifold of picard number 1 under mild assumptions in particular we give a sharp bound of the length by a fundamental argument as an application we compute the length for fano manifolds of dimension 7

characterization of chaotic dynamic behavior in the gas liquid slug flow using directed weighted complex network analysis abstract understanding the nonlinear and complex dynamics underlying the gas liquid slug flow is a significant but challenging problem we systematically carried out gas liquid two phase flow experiments for measuring the time series of flow signals which is studied in terms of the mapping from time series to complex networks in particular we construct directed weighted complex networks dwcn from time series and then associate different aspects of chaotic dynamics with the topological indices of the dwcn and further demonstrate that the dwcn can be exploited to detect unstable periodic orbits of low periods examples using time series from classical chaotic systems are provided to demonstrate the effectiveness of our approach we construct and analyze numbers of dwcns for different gas liquid flow patterns and find that our approach can quantitatively distinguish different experimental gas liquid flow patterns furthermore the dwcn analysis indicates that slug flow shows obvious chaotic behavior and its unstable periodic orbits reflect the intermittent quasi periodic oscillation behavior between liquid slug and large gas slug these interesting and significant findings suggest that the directed weighted complex network can potentially be a powerful tool for uncovering the underlying dynamics leading to the formation of the gas liquid slug flow

a nadel vanishing theorem for metrics with minimal singularities on big line bundles abstract the purpose of this paper is to establish a nadel vanishing theorem for big line bundles with multiplier ideal sheaves of singular metrics admitting an analytic zariski decomposition such as metrics with minimal singularities and siu s metrics for this purpose we apply the theory of harmonic integrals and generalize enoki s proof of kollar s injectivity theorem moreover we investigate the asymptotic behavior of harmonic forms with respect to a family of regularized metrics

seshadri constants on abelian varieties we show that on a complex abelian variety of dimension two or greater the seshadri constant of an ample line bundle is at least one moreover the seshadri constant is equal to one if and only if the polarized abelian variety splits as a product of a principally polarized elliptic curve and a polarized abelian subvariety of codimension one we also examine the case when the seshadri constant is not one and obtain lower bounds when the dimension of the abelian variety is small

kahler einstein metrics for some quasi smooth log del pezzo surfaces recently johnson and kollar determined the complete list of anti canonically embedded quasi smooth log del pezzo surfaces in weighted projective 3 spaces they also proved that many of those surfaces admit a kahler einstein metric and that some of them do not have tigers the aim of this paper is to settle the question of the existence of kahler einstein metrics and tigers for those surfaces for which the question was left open in order to do so we will use techniques developed earlier by nadel demailly and kollar

motif distributions in phase space networks for characterizing experimental two phase flow patterns with chaotic features the dynamics of two phase flows have been a challenging problem in nonlinear dynamics and fluid mechanics we propose a method to characterize and distinguish patterns from inclined water oil flow experiments based on the concept of network motifs that have found great usage in network science and systems biology in particular we construct from measured time series phase space complex networks and then calculate the distribution of a set of distinct network motifs to gain insight we first test the approach using time series from classical chaotic systems and find a universal feature motif distributions from different chaotic systems are generally highly heterogeneous our main finding is that the distributions from experimental two phase flows tend to be heterogeneous as well suggesting the underlying chaotic nature of the flow patterns calculation of the maximal lyapunov exponent provides further support for this motif distributions can thus be a feasible tool to understand the dynamics of realistic two phase flow patterns

a differential calculus for random matrices with applications to max linear stochastic systems we introduce the concept of weak differentiability for random matrices and thereby obtain closed form analytical expressions for derivatives of functions of random matrices more specifically we develop a calculus of weak differentiation for random matrices that resembles the standard calculus of differentiation our formalism enables us to algebraically calculate derivatives of finite horizon performance measures of stochastic event graphs more precisely we develop a theory of weak differentiation for max linear systems the resulting derivatives provide unbiased estimators for gradients of finite horizon performance measures for various types of max linear systems we compute these estimators explicitly and state the corresponding gradient estimation algorithm

time series and dependent variables we present a new method for analyzing time series which is designed to extract inherent deterministic dependencies in the series the method is particularly suited to series with broad band spectra such as chaotic series with or without noise we derive quantities j e based on conditional probabilities whose magnitude roughly speaking is an indicator of the extent to which the kth element in the series is a deterministic function of the k j th element to within a measurement uncertainty e we apply our method to a number of deterministic time series generated by chaotic processes such as the tent logistic and h non maps as well as to sequences of quasi random numbers in all cases the 6j correctly indicate the expected dependencies we also show that the j are robust to the addition of substantial noise in a deterministic process in addition we derive a predictability index which is a measure of the extent to which a time series is predictable given some tolerance e finally we discuss the behavior of the 6i as e approaches zero

a numerical criterion for very ample line bundles let x be a projective algebraic manifold of dimension n and let l be an ample line bundle over x we give a numerical criterion ensuring that the adjoint bundle kx l is very ample the sufficient conditions are expressed in terms of lower bounds for the intersection numbers l y over subvarieties y of x in the case of surfaces our criterion gives universal bounds and is only slightly weaker than i reider s criterion when dimx 3 and codimy 2 the lower bounds for l y involve a numerical constant which depends on the geometry of x by means of an iteration process it is finally shown that 2kx ml is very ample form 12n our approach is mostly analytic and based on a combination of hormander s l estimates for the operator lelong number theory and the aubin calabi yau theorem

blowing up and desingularizing constant scalar curvature kahler manifolds this paper is concerned with the existence of constant scalar curvature kahler metrics on blow ups at finitely many points of compact manifolds which already carry constant scalar curvature kahler metrics we also consider the desingularization of isolated quotient singularities of compact orbifolds which carry constant scalar curvature kahler metrics

scaling analysis of phase fluctuations in experimental three phase flows abstract the characterization of complex patterns arising from three phase e g oil gas water flows is an important problem with significant engineering and industrial applications based solely on measured conductance fluctuation signals from experimental three phase flows we propose a method to characterize and distinguish three commonly observed flow patterns using the phase characterization method we first calculate the instantaneous phase from the signals then through performing a scaling analysis detrended fluctuation analysis dfa we extract scaling behaviors associated with the phase fluctuations and find that the dfa scaling exponent is sensitive to the transition among different flow patterns which can be used to characterize nonlinear dynamics of the three phase flow from a novel perspective we investigate the three phase flow in terms of phase characterization and scaling analysis the results indicate that our method can provide new insights into the exploration of complex mechanism in flow pattern transition the effectiveness of the method is demonstrated and its broader applicability is articulated

horizontal visibility graphs transformed from fractional brownian motions topological properties versus the hurst index abstract nonlinear time series analysis aims at understanding the dynamics of stochastic or chaotic processes in recent years quite a few methods have been proposed to transform a single time series to a complex network so that the dynamics of the process can be understood by investigating the topological properties of the network we study the topological properties of horizontal visibility graphs constructed from fractional brownian motions with different hurst indexes h 0 1 special attention has been paid to the impact of the hurst index on topological properties it is found that the clustering coefficient c decreases when h increases we also found that the mean length l of the shortest paths increases exponentially with h for fixed length n of the original time series in addition l increases linearly with respect to n when h is close to 1 and in a logarithmic form when h is close to 0 although the occurrence of different motifs changes with h the motif rank pattern remains unchanged for different h adopting the node covering box counting method the horizontal visibility graphs are found to be fractals and the fractal dimension d b decreases with h furthermore the pearson coefficients of the networks are positive and the degree degree correlations increase with degree which indicate that the horizontal visibility graphs are assortative with the increase of h the pearson coefficient decreases first and then increases in which the turning point is around h 0 6 the presence of both fractality and assortativity in the horizontal visibility graphs converted from fractional brownian motions is different from many cases where fractal networks are usually disassortative

the boundedness of degree of fano varieties with picard number one contents 0 introduction 1 rational curves 1 1 deformation theory of morphisms 1 2 free rational curves 1 3 the invariant d m 2 special subvarieties in fano varieties of large degree 2 1 the statement 2 2 a siegel type lemma 2 3 multiplicity subspaces 2 4 the product theorem part i 2 5 the product theorem part ii 2 6 the proof 3 the covering lemma 4 collections of subsets 4 1 base change and push forward 4 2 an example 4 3 universally open morphisms 4 4 flat families 5 proof of theorem a

lengths of chains of minimal rational curves on fano manifolds abstract in this paper we consider a natural question how many minimal rational curves are needed to join two general points on a fano manifold x of picard number 1 in particular we study the minimal length of such chains in the cases where the dimension of x is at most 5 the coindex of x is at most 3 and x equips with a structure of a double cover as an application we give a better bound on the degree of fano 5 folds of picard number 1

statistical properties of visibility graph of energy dissipation rates in three dimensional fully developed turbulence abstract we study the statistical properties of complex networks constructed from time series of energy dissipation rates in three dimensional fully developed turbulence using the visibility algorithm the degree distribution is found to have a power law tail with the tail exponent 3 0 the exponential relation between the number of the boxes n b and the box size l b based on the edge covering box counting method illustrates that the network is not self similar which is also confirmed by the hub hub attraction according to the visibility algorithm in addition it is found that the skeleton of the visibility network exhibits excellent allometric scaling with the scaling exponent 1 163 0 005

ricci flow and the metric completion of the space of kahler metrics we consider the space of kahler metrics as a riemannian submanifold of the space of riemannian metrics and study the associated submanifold geometry in particular we show that the intrinsic and extrinsic distance functions are equivalent we also determine the metric completion of the space of kahler metrics making contact with recent generalizations of the calabi yau theorem due to dinew and guedj zeriahi as an application we obtain a new analytic stability criterion for the existence of a kahler einstein metric on a fano manifold in terms of the ricci flow and the distance function we also prove that the kahler ricci flow converges as soon as it converges in the metric sense

some discretizations of geometric evolution equations and the ricci iteration on the space of kahler metrics we propose the study of certain discretizations of geometric evolution equations as an approach to the study of the existence problem of some elliptic partial differential equations of a geometric nature as well as a means to obtain interesting dynamics on certain infinite dimensional spaces we illustrate the fruitfulness of this approach in the context of the ricci flow as well as another flow in kahler geometry we introduce and study dynamical systems related to the ricci operator on the space of kahler metrics that arise as discretizations of these flows we pose some problems regarding their dynamics we point out a number of applications to well studied objects in kahler and conformal geometry such as constant scalar curvature metrics kahler ricci solitons nadel type multiplier ideal sheaves balanced metrics the moser trudinger onofri inequality energy functionals and the geometry and structure of the space of kahler metrics e g we obtain a new sharp inequality strengthening the classical moser trudinger onofri inequality on the two sphere

stationarity and nonstationarity in time series analysis abstract in this paper we introduce a new class of methods to test model and describe nonstationary processes to frame these methods we generalize the dynamical description of autonomous systems to the case of nonautonomous systems of particular interest are systems for which the driving force is recurrent for these systems we describe a method to find recurrences and to improve the statistics in reconstructing the tine series and consequently to improve the predictability another objective is a proper description of the nonstationarity all these methods are applied to four examples

existence of kahler einstein metrics and multiplier ideal sheaves on del pezzo surfaces we apply nadel s method of multiplier ideal sheaves to show that every complex del pezzo surface of degree at most six whose automorphism group acts without fixed points has a kahler einstein metric in particular all del pezzo surfaces of degree 4 5 or 6 and certain special del pezzo surfaces of lower degree are shown to have a kahler einstein metric these existence statements are not new but the proofs given in the present paper are less involved than earlier ones by siu tian and tian yau

effectiveness of demailly s strong openness conjecture and related problems in this article stimulated by the effectiveness in berndtsson s solution of the openness conjecture and continuing our solution of demailly s strong openness conjecture we discuss conditions to guarantee the effectiveness of the conjecture and establish such an effectiveness result we explicitly point out a lower semicontinuity property of plurisubharmonic functions with a multiplier which is implicitly contained in guan and zhou 2014 arxiv 1401 7158 we also obtain optimal effectiveness of the conjectures of demailly kollar and jonsson mustat respectively

multiplier ideal sheaves and kahler einstein metrics of positive scalar curvature we present a method for proving the existence of kiihler einstein metrics of positive scalar curvature on certain compact complex manifolds and use the method to produce a large class of examples of compact kiihler einstein manifolds of positive scalar curvature suppose that m is a compact complex manifold of positive first chern class as is well known the existence of a kiihler einstein metric on m is equivalent to the existence of a solution to a certain complex monge ampere equation on m to solve this complex mongeampere equation by the method of continuity one needs only to establish the appropriate zeroth order a priori estimate suppose now that m does not admit a kiihler einstein metric so that the zeroth order a priori estimate fails to hold from this lack of an estimate we extract various global algebro geometric properties of m by introducing a coherent sheaf of ideals j on m called the multiplier ideal sheaf which carefully measures the extent to which the estimate fails the sheaf y is analogous to the subelliptic multiplier ideal sheaf that j j kohn introduced over a decade ago to obtain sufficient conditions for subellipticity of the d neumann problem now j is a global algebro geometric object on m and it so happens that j satisfies a number of highly nontrivial global algebro geometric conditions including a cohomology vanishing theorem in particular the complex analytic subspace v c m cut out by j is nonempty connected and has arithmetic genus zero if v is zero dimensional then it is a single reduced point while if v is one dimensional then its support is a tree of smooth rational curves the logarithmic geometric genus of m v always vanishes these considerations place nontrivial global algebro geometric restric

uncovering dynamic behaviors underlying experimental oil water two phase flow based on dynamic segmentation algorithm abstract characterizing complex dynamic behaviors arising from various inclined oil water two phase flow patterns is a challenging problem in the fields of nonlinear dynamics and fluid mechanics we systematically carried out inclined oil water two phase flow experiments for measuring the time series conductance fluctuating signals of different flow patterns we using the dynamic segmentation algorithm incorporating with phase space reconstruction analyze the measured experimental signals to uncover the dynamic behaviors underlying different flow patterns specifically given a time series from a two phase flow we move a sliding pointer over the time series and for each position of the pointer we calculate the dynamic difference measure of the phase space orbits generated from the segment to the left and to the right of the pointer a number of experimental signals under different flow conditions are investigated in order to reveal the dynamical characteristics of inclined oil water flows the results indicate that the heterogeneity of dynamic difference measure series is sensitive to the transition among different flow patterns and the standard deviation of dynamic difference measure series can yield quantitative insights into the nonlinear dynamics of the two phase flow these properties render the dynamic segmentation algorithm based approach particularly useful for uncovering the dynamic behaviors of inclined oil water two phase flows

seshadri exceptional foliations the maximal seshadri number l of an ample line bundle l on a smooth projective variety x measures the local positivity of the line bundle l at a general point of x by refining the method of ein kuchle lazarsfeld lower bounds on l are obtained in terms of ln n dim x for a class of varieties the main idea is to show that if a certain lower bound is violated there exists a non trivial foliation on the variety whose leaves are covered by special curves in a number of examples one can show that such foliations must be trivial and obtain lower bounds for l the examples include the hyperplane line bundle on a smooth surface in 3 and ample line bundles on smooth threefolds of picard number 1

rationally connected varieties over local fields let x be a proper variety defined over a field k following ma we say that two points x x x k are r equivalent if they can be connected by a chain of rational curves defined over k cf 4 1 in essence two points are r equivalent if they are obviously rationally equivalent several authors have proved finiteness results over local and global fields cubic hypersurfaces ma sd linear algebraic groups ct sa vo1 gi vo2 rational surfaces ct co ct1 ct sk1 quadric bundles and intersections of two quadrics ct sa sd pa su r equivalence is only interesting if there are plenty of rational curves on x at least over k such varieties have been studied in the series of papers komi mo1 ko mi mo3 see also ko1 there are many a priori different ways of defining what plenty of rational curves should mean fortunately many of these turn out to be equivalent and this leads to the notion of rationally connected varieties see ko mi mo2 ko1 iv 3 ko2 4 1 2

kahler einstein metrics on complex surfaces with c 1 0 various estimates of the lower bound of the holomorphic invariant m defined in t are given here by using branched coverings potential estimates and lelong numbers of positive d closed 1 1 currents of certain type etc these estimates are then applied to produce kahler einstein metrics on complex surfaces withc1 0 in particular we prove that there are kahler einstein structures withc1 0 on any manifold of differential type cp 2 overline ncp 2 3 leqq n leqq 8

toric plurisubharmonic functions and analytic adjoint ideal sheaves in the first part of this paper we study the properties of some particular plurisubharmonic functions namely the toric ones the main result of this part is a precise description of their multiplier ideal sheaves which generalizes the algebraic case studied by howald in the second part almost entirely independent of the first one we generalize the notion of the adjoint ideal sheaf used in algebraic geometry to the analytic setting this enables us to give an analogue of howald s theorem for adjoint ideals attached to monomial ideals finally using the local ohsawa takegoshi manivel theorem we prove the existence of the so called generalized adjunction exact sequence which enables us to recover a weak version of the global extension theorem of manivel for compact kahler manifolds

siu s lemma optimal l 2 extension and applications to twisted pluricanonical sheaves we prove a general version of siu s lemma for plurisubharmonic functions with nontrivial multiplier ideal sheaves and use it to prove an optimal l 2 extension theorem and an optimal l frac 2 m extension theorem for kahler fibrations these results are used to prove the positivity of twisted relative pluricanonical bundles and their direct images for kahler fibrations and to answer a comparison question about singular metrics of twisted pluricanonical bundles

analytical framework for recurrence network analysis of time series recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems while there are already many successful applications ranging from medicine to paleoclimatology a solid theoretical foundation of the method has still been missing so far here we interpret an ensuremath varepsilon recurrence network as a discrete subnetwork of a continuous graph with uncountably many vertices and edges corresponding to the system s attractor this step allows us to show that various statistical measures commonly used in complex network analysis can be seen as discrete estimators of newly defined continuous measures of certain complex geometric properties of the attractor on the scale given by ensuremath varepsilon in particular we introduce local measures such as the ensuremath varepsilon clustering coefficient mesoscopic measures such as ensuremath varepsilon motif density path based measures such as ensuremath varepsilon betweennesses and global measures such as ensuremath varepsilon efficiency this new analytical basis for the so far heuristically motivated network measures also provides an objective criterion for the choice of ensuremath varepsilon via a percolation threshold and it shows that estimation can be improved by so called node splitting invariant versions of the measures we finally illustrate the framework for a number of archetypical chaotic attractors such as those of the bernoulli and logistic maps periodic and two dimensional quasiperiodic motions and for hyperballs and hypercubes by deriving analytical expressions for the novel measures and comparing them with data from numerical experiments more generally the theoretical framework put forward in this work describes random geometric graphs and other networks with spatial constraints which appear frequently in disciplines ranging from biology to climate science

multiplier ideal sheaves and existence of kahler einstein metrics of positive scalar curvature abstract to study c0a priori estimates for solutions to certain complex monge ampere equations i introduce a coherent sheaf of ideals and show that it satisfies various global algebrogeometric conditions including a cohomology vanishing theorem this technique is used to establish the existence of kahler einstein metrics of positive scalar curvature on a very large class of compact complex manifolds

a nadel vanishing theorem via injectivity theorems the purpose of this paper is to establish nadel type vanishing theorems with multiplier ideal sheaves of singular metrics admitting an analytic zariski decomposition such as metrics with minimal singularities and siu s metrics for this purpose we generalize kollar s injectivity theorem to an injectivity theorem for line bundles equipped with singular metrics by making use of the theory of harmonic integrals moreover we give asymptotic cohomology vanishing theorems for high tensor powers of line bundles