non upper semicontinuity of algebraic dimension for families of compact complex manifolds in this note we show that in a certain subfamily of the kuranishi family of any half inoue surface the algebraic dimensions of the fibers jump downwards at special points of the parameter space showing that the upper semicontinuity of algebraic dimensions in any sense does not hold in general for families of compact non kahler manifolds in the kahler case the upper semicontinuity always holds true in a certain weak sense

stein compacts in levi flat hypersurfaces we explore connections between geometric properties of the levi foliation of a levi flat hypersurface m and holomorphic convexity of compact sets in m or bounded in part by m applications include extendability of cauchy riemann functions solvability of the b equation approximation of cauchy riemann and holomorphic functions and global regularity of the neumann operator

spreading dynamics of forget remember mechanism we study extensively the forget remember mechanism frm for message spreading originally introduced in eur phys j b 62 247 2008 epjbfy1434 602810 1140 epjb e2008 00139 4 the freedom of specifying forget remember functions governing the frm can enrich the spreading dynamics to a very large extent the master equation is derived for describing the frm dynamics by applying the mean field techniques we have shown how the steady states can be reached under certain conditions which agrees well with the monte carlo simulations the distributions of forget and remember times can be explicitly given when the forget remember functions take linear or exponential forms which might shed some light on understanding the temporal nature of diseases like flu for time dependent frm there is an epidemic threshold related to the frm parameters we have proven that the mean field critical transmissibility for the sis model and the critical transmissibility for the sir model are the lower and the the upper bounds of the critical transmissibility for the frm model respectively

on the cr structure of compact group orbits associated with bounded symmetric domains let e be a complex vector space of finite dimension and let k gl e be a compact connected subgroup then for fixed a e the orbit k k a is a real analytic submanifold of e that inherits various structures from e for instance choosing a k invariant positive definite inner product x y on e makes k a riemannian manifold on which k acts transitively by isometries on the other hand k inherits from e a cauchy riemann structure cr structure that is given by the distribution of the maximal complex subspaces hx k tx k itx k of the real tangent spaces tx k e x k together with the complex structure on every hx k multiplication by i the subspace hx k is called the holomorphic tangent space to k at x see 9 and 4 as general references for cr manifolds of interest for the geometry of the orbit k k a with respect to its cr structure is the study of the cr functions or more generally cr mappings on k i e of smooth functions f k c that satisfy the tangential cauchy riemann differential equations in the sense that the restriction of the differential df to every holomorphic tangent space is complex linear for instance all holomorphic functions defined in an open neighbourhood of k e give by restriction real analytic cr functions on k actually we deal with the more general continuous cr functions on k which satisfy by definition the tangential cr equations in the distribution sense or equivalently which are locally uniform limits of sequences of smooth cr functions due to the approximation theorem of baouenditreves 6 in this context it is of interest to determine the space of all

holomorphic functions on bundles over annuli we consider a family big e m d m big of holomorphic bundles constructed as follows from any given m in gl n mathbb z we associate a multiplicative automorphism varphi of mathbb c n now let d subseteq mathbb c n be a varphi invariant stein reinhardt domain then em d m is defined as the flat bundle over the annulus of modulus m 0 with fiber d and monodromy varphi we show that the function theory on em d m depends nontrivially on the parameters m m and d our main result is that e m d m text is stein if and only if m log rho m leq 2 pi 2 where m denotes the max of the spectral radii of m and m 1 as corollaries we 1 obtain a classification result for reinhardt domains in all dimensions 2 establish a similarity between two known counterexamples to a question of j p serre and 3 suggest a potential reformulation of a disproved conjecture of siu y t

inoue surfaces and the chern ricci flow we investigate the chern ricci flow an evolution equation of hermitian metrics on inoue surfaces these are non kahler compact complex surfaces of type class vii we show that after an initial conformal change the flow always collapses the inoue surface to a circle at infinite time in the sense of gromov hausdorff

logarithmic moduli spaces for surfaces of class vii in this paper we describe logarithmic moduli spaces of pairs s d consisting of a minimal surface s of class vii with second betti number b2 0 together with a reduced maximal divisor d of b2 rational curves the special case of enoki surfaces has already been considered by dloussky and kohler we use normal forms for the action of the fundamental group of s d and for the associated holomorphic contraction mathbb c 0 to mathbb c 0

epidemic dynamics in finite size scale free networks many real networks present a bounded scale free behavior with a connectivity cutoff due to physical constraints or a finite network size we study epidemic dynamics in bounded scale free networks with soft and hard connectivity cutoffs the finite size effects introduced by the cutoff induce an epidemic threshold that approaches zero at increasing sizes the induced epidemic threshold is very small even at a relatively small cutoff showing that the neglection of connectivity fluctuations in bounded scale free networks leads to a strong overestimation of the epidemic threshold we provide the expression for the infection prevalence and discuss its finite size corrections the present paper shows that the highly heterogeneous nature of scale free networks does not allow the use of homogeneous approximations even for systems of a relatively small number of nodes

epidemics and percolation in small world networks we study some simple models of disease transmission on small world networks in which either the probability of infection by a disease or the probability of its transmission is varied or both the resulting models display epidemic behavior when the infection or transmission probability rises above the threshold for site or bond percolation on the network and we give exact solutions for the position of this threshold in a variety of cases we confirm our analytic results by numerical simulation

on the metric structure of non kahler complex surfaces we give a characterization of a locally conformally kahler l c k metric with parallel lee form on a compact complex surface using the kodaira classification of surfaces we classify the compact complex surfaces admitting such structures this gives a classification of sasakian structures on compact three manifolds a weak version of the above mentioned characterization leads to an explicit construction of l c k metrics on all hopf surfaces we characterize the locally homogeneous l c k metrics on geometric complex surfaces and we prove that some inoue surfaces do not admit any l c k metric

uniqueness and approximation of solutions of first order non linear equations guy metivier d6partement de math6matiques universit6 rennes i f 35042 rennes c6dex france this paper is devoted to non linear first order analytic partial differential equa tions and contains the proof of the following results a uniqueness of c 2 complex valued solutions to the non characteristic cauchy problem b any c 2 solution is the limit of a sequence of analytic solutions of the same equation for linear equations of any order a is of course well known 7 and b which is also well known in the constant coefficients case 8 has also been proved for wide classes of equations see baouendi treves 3 4 baouendi rothschild 23 for non linear equations the situation is quite different and so far only the first order case has been investigated indeed in that case baouendi goulaouic and treves 1 have already proved a and b in the semilinear case and a either in dimension 2 or when the cauchy data is analytic so the aim of this paper is to extend their result to a general first order non linear equation leaving still completely open the problem for higher order equations as in 1 the proofs given in this paper rely on the analysis of the hamil tonian field of the equation the new point is that we are able to produce directly a formula expressing any smooth enough solution in terms of its cauchy data uniqueness follows at once in the linear case this formula is exactly the one given in baouendi treves 3 and gives in the same time the approximation property here we still derive this property from the mentioned formula but because of the nonlinearity the arguments are just a little more complicated this paper was completed while the author was visiting at rutgers university

on surfaces of class vii 0 with numerically anticanonical divisor we consider minimal compact complex surfaces s with betti numbers b 1 and n bi 0 a theorem of donaldson gives n exceptional line bundles we prove that if in a deformation these line bundles have sections s is a degeneration of blown up hopf surfaces besides if there exists an integer m 1 and a flat line bundle f such that h s mk 0 these surfaces admit no nonconstant mero morphic functions the major problem in classification of non kahlerian surfaces is to achieve the classification of surfaces s of class viij all known surfaces of this class contain global spherical shells gss i e admit a biholomorphic map ip u v from a neighbourhood u c c2 0 of the sphere 53 db2 onto an open set v such that i f s3 does not disconnect s are there other surfaces in first section we investigate the general situation a theorem of donaldson 13 gives a z base of 2 s z such that b of s these line bundles form families we propose the following conjecture which can be easily checked for surfaces with gss

bihermitian structures on complex surfaces proc london math soc 3 79 1999 414 428 we correct the statements of theorem 1 and corollary 2 of the above mentioned paper and provide a new argument for corollary 2 we also update some parts of the paper in the light of recent major developments in the theory of bihermitian structures due to m gualtieri and n hitchin

intermittent social distancing strategy for epidemic control we study the critical effect of an intermittent social distancing strategy on the propagation of epidemics in adaptive complex networks we characterize the effect of our strategy in the framework of the susceptible infected recovered model in our model based on local information a susceptible individual interrupts the contact with an infected individual with a probability ensuremath sigma and restores it after a fixed time t b we find that depending on the network topology in our social distancing strategy there exists a cutoff threshold ensuremath sigma c beyond which the epidemic phase disappears our results are supported by a theoretical framework and extensive simulations of the model furthermore we show that this strategy is very efficient because it leads to a susceptible herd behavior that protects a large fraction of susceptible individuals we explain our results using percolation arguments

phase transitions in the quadratic contact process on complex networks the quadratic contact process qcp is a natural extension of the well studied linear contact process where infected 1 individuals infect susceptible 0 neighbors at rate ensuremath lambda and infected individuals recover 1 0 at rate 1 in the qcp a combination of two 1 s is required to effect a 0 1 change we extend the study of the qcp which so far has been limited to lattices to complex networks we define two versions of the qcp vertex centered vqcp and edge centered eqcp with birth events 1 ensuremath 0 ensuremath 1 1 ensuremath 1 ensuremath 1 and 1 ensuremath 1 ensuremath 0 1 ensuremath 1 ensuremath 1 respectively where ensuremath represents an edge we investigate the effects of network topology by considering the qcp on random regular erd ifmmode mbox h o else h o fi s r enyi and power law random graphs we perform mean field calculations as well as simulations to find the steady state fraction of occupied vertices as a function of the birth rate we find that on the random regular and erd ifmmode mbox h o else h o fi s r enyi graphs there is a discontinuous phase transition with a region of bistability whereas on the heavy tailed power law graph the transition is continuous the critical birth rate is found to be positive in the former but zero in the latter

noise induced dissipation in lebesgue measure preserving maps on d dimensional torus we consider dissipative systems resulting from the gaussian and alpha stable noise perturbations of measure preserving maps on the d dimensional torus we study the dissipation time scale and its physical implications as the noise level e vanishes we show that nonergodic maps give rise to an o 1 e dissipation time whereas ergodic toral automorphisms including cat maps and their d dimensional generalizations have an o ln 1 e dissipation time with a constant related to the minimal dimensionally averaged entropy among the automorphism s irreducible blocks our approach reduces the calculation of the dissipation time to a nonlinear arithmetic optimization problem which is solved asymptotically by means of some fundamental theorems in theories of convexity diophantine approximation and arithmetic progression we show that the same asymptotic can be reproduced by degenerate noises as well as mere coarse graining we also discuss the implication of the dissipation time in kinematic dynamo

locally conformally kahler manifolds admitting a holomorphic conformal flow a manifold m is locally conformally kahler lck if it admits a kahler covering tilde m with monodromy acting by holomorphic homotheties let m be an lck manifold admitting a holomorphic conformal flow of diffeomorphisms lifted to a non isometric homothetic flow on tilde m we show that m admits an automorphic potential and the monodromy group of its conformal weight bundle is mathbb z

the mathematics of infectious diseases many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases threshold theorems involving the basic reproduction number r 0 the contact number sigma and the replacement number r are reviewed for the classic sir epidemic and endemic models similar results with new expressions for r 0 are obtained for mseir and seir endemic models with either continuous age or age groups values of r 0 and sigma are estimated for various diseases including measles in niger and pertussis in the united states previous models with age structure heterogeneity and spatial structure are surveyed

une construction elementaire des surfaces d inoue hirzebruch 0 introduction 663 1 surfaces d inoue hirzebruch et th6or6me principal 664 2 application aux champs de vecteurs globaux et fibr6 canonique 668 3 rev ements et automorphismes des surfaces de kato 673 4 d monstration du th or me principal 681 r6f6rences 682

network topology inference from infection statistics abstract we introduce a mathematical framework for identification of network topology based on data collected from infectious sis process occurring on a network an exact expression for the weight of each network link existing or not as a function of infectious statistics is obtained an algorithm for proper implementation of the analyzed concept is suggested and the validity of the obtained result is confirmed by numerical simulations performed on a number of synthetic computer generated networks

infinite bubbling in non kahlerian geometry in a holomorphic family x b b in b of non kahlerian compact manifolds the holomorphic curves representing a fixed 2 homology class do not form a proper family in general the deep source of this fundamental difficulty in non kahler geometry is the explosion of the area phenomenon the area of a curve c b subset x b in a fixed 2 homology class can diverge as b b0 this phenomenon occurs frequently in the deformation theory of class vii surfaces for instance it is well known that any minimal gss surface x0 is a degeneration of a 1 parameter family of simply blown up primary hopf surfaces x z z in d setminus 0 so one obtains non proper families of exceptional divisors e z subset x z whose area diverge as z 0 our main goal is to study in detail this non properness phenomenon in the case of class vii surfaces we will prove that under certain technical assumptions a lift widetilde e z of ez in the universal cover widetilde x z does converge to an effective divisor widetilde e 0 in widetilde x 0 but this limit divisor is not compact we prove that this limit divisor is always bounded towards the pseudo convex end of widetilde x 0 and that when x0 is a minimal surface with global spherical shell it is given by an infinite series of compact rational curves whose coefficients can be computed explicitly this phenomenon degeneration of a family of compact curves to an infinite union of compact curves should be called infinite bubbling we believe that such a decomposition result holds for any family of class vii surfaces whose generic fiber is a blown up primary hopf surface this statement would have important consequences for the classification of class vii surfaces

local solvability for top degree forms in a class of systems of vector fields we study the local exactness at the top degree level in the differential complex defined by a smooth locally integrable structure of rank n in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i if z denotes a local first integral of the structure it is proved that the vanishing of the local cohomology in degree n is implied by the absence of compact connected components of the fibers z const this adds one more result towards the verification of a conjecture due to f treves regarding the vanishing of the local cohomology of such complexes of differential operators

collapsing of the chern ricci flow on elliptic surfaces we investigate the chern ricci flow an evolution equation of hermitian metrics generalizing the kahler ricci flow on elliptic bundles over a riemann surface of genus greater than one we show that starting at any gauduchon metric the flow collapses the elliptic fibers and the metrics converge to the pullback of a kahler einstein metric from the base some of our estimates are new even for the kahler ricci flow a consequence of our result is that on every minimal non kahler surface of kodaira dimension one the chern ricci flow converges in the sense of gromov hausdorff to an orbifold kahler einstein metric on a riemann surface

donaldson theory on non kahlerian surfaces and class vii surfaces with b2 1 we prove that any class vii surface with b2 1 has curves this implies the global spherical shell conjecture in the case b2 1

the hartogs phenomenon on weakly pseudoconcave hypersurfaces in 2002 henkin and michel proved a local hartogs phenomenon for real analytic cr functions on real analytic weakly pseudoconcave cr manifolds the aim of the present article is to remove the assumptions on real analyticity in the case of weakly pseudoconcave hypersurfaces m subset mathbb c n if m is a graph of class mathcal c 2 and n 3 a global theorem is proved for the extension of holomorphic germs along m if the appearing domains have nicely shaped boundary a hartogs theorem even holds for continuous cr functions where the difference to the case of holomorphic germs relies on the possible presence of lower dimensional cr orbits levi flat hypersurfaces in mathbb c 2 require a separate treatment here an affirmative answer is given to the question of tomassini whether 2 spheres bound 3 balls in m

on compact complex surfaces of kahler rank one the kahler rank of compact complex surfaces was introduced by harvey and lawson in their 1983 paper on kahler manifolds as a measure of kahlerianity here we give a partial classification of compact complex surfaces of kahler rank 1 these are either elliptic surfaces or hopf surfaces or they admit a holomorphic foliation of a very special type as a consequence we give an affirmative answer to the question raised by harvey and lawson whether the kahler rank is a bimeromorphic invariant

on boundary properties of solutions of complex vector fields abstract this work presents results on the boundary properties of solutions of a complex planar smooth vector field l classical results in the h p theory of holomorphic functions of one variable are extended to the solutions of a class of nonelliptic complex vector fields

a property of the functions and distributions annihilated by a locally integrable system of complex vector fields page introduction 387 1 basic notation and ingredients 389 2 approximation and constancy on the fibers of the classical solutions of the homogeneous equations 393 3 first consequences and interpretation of the fundamental theorem 398 4 distribution solutions of the homogeneous equations 402 5 regularity of the solutions of the homogeneous equations 409 6 example of a system that is analytic hypo elliptic but not co hypo elliptic 413 references 420

global homotopy with ck estimates for a family of compact regular q pseudoconcave cr manifolds let m 0 be a compact regular q pseudoconcave cr submanifold of a complex manifold g and open image in new window a holomorphic vector bundle on g such that dim open image in new window for some fixed r q we prove a global homotopy formula with c k estimates for r cohomology of open image in new window on arbitrary cr submanifold m close enough to m 0

epidemic threshold determined by the first moments of network with alternating degree distributions abstract during the alternating day night cycle people have differing behavior and hence different connection patterns such as going to work or home shopping and so on hence the true topological structure of human contact networks are not only time varying but also exhibit certain distribution regularity in this paper we will investigate epidemic spreading on time varying human contact networks which follow one degree distribution during daytime but another at night based on sis susceptible infected susceptible propagation mechanism we study the epidemic threshold of this network with alternating distributions a surprising result is that for the discrete time case the epidemic threshold is determined only by the first moments of the two alternating degree distributions if the degree of each node is constant for all nights a similar result is valid for the continuous time case if the duration is sufficiently small this work shows that the spreading dynamics of time varying networks with alternating distributions is completely different from the widely studied case of static spreading networks

survival time of the susceptible infected susceptible infection process on a graph the survival time t is the longest time that a virus a meme or a failure can propagate in a network using the hitting time of the absorbing state in an uniformized embedded markov chain of the continuous time susceptible infected susceptible sis markov process we derive an exact expression for the average survival time e t of a virus in the complete graph kn and the star graph k1 n 1 by using the survival time instead of the average fraction of infected nodes we propose a new method to approximate the sis epidemic threshold c that at least for kn and k1 n 1 correctly scales with the number of nodes n and that is superior to the epidemic threshold 1 c 1 1 of the n intertwined mean field approximation where 1 is the spectral radius of the adjacency matrix of the graph g although this new approximation of the epidemic threshold offers a more intuitive understanding of the sis process it remains difficult to compare outbreaks in different graph types for example the survival in an arbitrary graph seems upper bounded by the complete graph and lower bounded by the star graph as a function of the normalized effective infection rate 1 c however when the average fraction of infected nodes is used as a basis for comparison the virus will survive in the star graph longer than in any other graph making the star graph the worst case graph instead of the complete graph finally in non markovian sis the distribution of the spreading attempts over the infectious period of a node influences the survival time even if the expected number of spreading attempts during an infectious period the non markovian equivalent of the effective infection rate is kept constant both early and late infection attempts lead to shorter survival times interestingly just as in markovian sis the survival times appear to be exponentially distributed regardless of the infection and curing time distributions

the pseudo effective cone of a non kahlerian surface and applications we describe the positive cone and the pseudo effective cone of a non kahlerian surface we use these results for two types of applications

conformal duality and compact complex surfaces on etudie les structures demi conformement plates sur une variete de riemann a 4 dimensions m g avec l hypothese supplementaire que m est complexe

instantons and curves on class vii surfaces we develop a general strategy based on gauge theoretical methods to prove existence of curves on class vii surfaces we prove that for b 2 2 every minimal class vii surface has a cycle of rational curves hence by a result of nakamura is a global deformation of a one parameter family of blown up primary hopf surfaces the case b 2 1 was solved in a previous article the fundamental object intervening in our strategy is the moduli space m pst 0 k of polystable bundles with c 2 0 det k for large b 2 the geometry of this moduli space becomes very complicated the case b 2 2 treated here in detail requires new ideas and difficult techniques of both complex geometric and gauge theoretical nature we explain the substantial obstacles which must be overcome in order to extend our methods to the case b 2 3

epidemic threshold for the susceptible infectious susceptible model on random networks we derive an analytical expression for the critical infection rate r c of the susceptible infectious susceptible sis disease spreading model on random networks to obtain r c we first calculate the probability of reinfection defined as the probability of a node to reinfect the node that had earlier infected it we then derive r c from using percolation theory we show that is governed by two effects i the requirement from an infecting node to recover prior to its reinfection which depends on the sis disease spreading parameters and ii the competition between nodes that simultaneously try to reinfect the same ancestor which depends on the network topology

smooth deformations of singular contractions of class vii surfaces we consider normal compact surfaces y obtained from a minimal class vii surface x by contraction of a cycle c of r rational curves with c 2 0 our main result states that if the obtained cusp is smoothable then y is globally smoothable the proof is based on a vanishing theorem for h 2 theta y if r b 2 x any smooth small deformation of y is rational and if r b 2 x i e when x is a half inoue surface any smooth small deformation of y is an enriques surface the condition the cusp is smoothable in our main theorem can be checked in terms of the intersection numbers of the cycle using the looijenga conjecture which has recently become a theorem therefore this is a decidable condition we prove that this condition is always satisfied if r b 2 x leqslant 11 therefore the singular surface y obtained by contracting a cycle c of r rational curves in a minimal class vii surface x with r b 2 x leqslant 11 is always smoothable by rational surfaces the statement holds even for unknown class vii surfaces

on the integrals of a singular real analytic differential form in ⁿ in this paper we study the constancy on the fibers for the continuous integrals of a complex valued real analytic differential form in rn then we prove an isomorphism result between the space of smooth integrals and a space built from spaces of whitney functions

second look at the spread of epidemics on networks in an important paper newman phys rev e66 016128 2002 claimed that a general network based stochastic susceptible infectious removed sir epidemic model is isomorphic to a bond percolation model where the bonds are the edges of the contact network and the bond occupation probability is equal to the marginal probability of transmission from an infected node to a susceptible neighbor in this paper we show that this isomorphism is incorrect and define a semidirected random network we call the epidemic percolation network that is exactly isomorphic to the sir epidemic model in any finite population in the limit of a large population i the distribution of self limited outbreak sizes is identical to the size distribution of small out components ii the epidemic threshold corresponds to the phase transition where a giant strongly connected component appears iii the probability of a large epidemic is equal to the probability that an initial infection occurs in the giant in component and iv the relative final size of an epidemic is equal to the proportion of the network contained in the giant out component for the sir model considered by newman we show that the epidemic percolation network predicts the same mean outbreak size below the epidemic threshold the same epidemic threshold and the same final size of an epidemic as the bond percolation model however the bond percolation model fails to predict the correct outbreak size distribution and probability of an epidemic when there is a nondegenerate infectious period distribution we confirm our findings by comparing predictions from percolation networks and bond percolation models to the results of simulations in the appendix we show that an isomorphism to an epidemic percolation network can be defined for any time homogeneous stochastic sir model

thin discs and a morera theorem for cr functions f z dz 0 for every closed curve in d there are generalizations of this theorem to domains and real hypersurfaces in cn see a and gs and references there in this paper we obtain a version of the morera theorem for cr functions on manifolds of higher codimension let m be a smooth real manifold in cn recall that m is generic if the tangent space tz m spans the whole space cn for z m a cr function on m is a continuous function that satisfies the weak tangential cauchy riemann equations an analytic disc is a continuous mapping a cn holomorphic in the standard disc c 1 we say that the disc a is attached to m if it maps the circle b to m that is a b m let f be a continuous function on a real manifold m cn we say that f has the morera property with respect to an analytic disc a attached to m if

epidemic threshold for the sirs model on the networks abstract we study the phase transition from the persistence phase to the extinction phase for the sirs susceptible infected refractory susceptible model of diseases spreading on the networks we derive an analytical expression for the probability of the descendants to reinfect their ancestors we find that in the case of the recovery time r is larger than the infection time i the infection will flow directionally from the ancestors to descendants however the descendants will be unable to reinfect their ancestors during the time of their illness this behavior leads us to deduce that if the infection rate is high enough so that any infected node on the network infects all its neighbors during its infection time then the sirs model on the network evolves to extinction state where all the nodes on the network become susceptible moreover we assert that in order to the disease spreads frequently throughout the nodes of the networks the loops on the network are necessary which means the clustering coefficient will play an important role in this model hence unlike the other models such as sis model and sir model the sirs model has two critical thresholds which separate the persistence phase from the extinction phase when i r i e for fixed values of i and r there are two critical points for infection rate 1 and 2 where epidemic persists in between of those two points we confirm those results numerically with the simulation of a regular one dimensional sirs system and small world network