un phenomene de hartogsdans les varietes projectives in this article we study univalent open subsets u hookrightarrow v mathrm dim v geq 2 assuming v setminus bar u to be pseudoconcave in andreotti s sense we prove an hartogs s kugelsatz theorem for such open sets let u an open subset in v such that v setminus bar u is a pseudoconcave domain in the sense of andreotti then u contains a maximal compact hypersurface h moreover any meromorphic section s of a vector bundle f over v defined on a neighborhood of partial overset 0 overline u extends on u setminus h and if s is holomorphic then s extends meromorphically to u with a polar set in h

the abundance of unknots in various models of polymer loops a veritable zoo of different knots is seen in the ensemble of looped polymer chains whether created computationally or observed in vitro at short loop lengths the spectrum of knots is dominated by the trivial knot unknot the fractional abundance of this topological state in the ensemble of all conformations of the loop of n segments follows a decaying exponential form exp n n0 where n0 marks the crossover from a mostly unknotted i e topologically simple to a mostly knotted i e topologically complex ensemble in the present work we use computational simulation to look closer into the variation of n0 for a variety of polymer models among models examined n0 is smallest about 240 for the model with all segments of the same length it is somewhat larger 305 for gaussian distributed segments and can be very large up to many thousands when the segment length distribution has a fat power law tail

application of statistical physics to politics abstract the concept and technics of real space renormalization group are applied to study majority rule voting in hierarchical structures it is found that democratic voting can lead to totalitarianism by keeping in power a small minority conditions of this paradox are analyzed and singled out indeed majority rule produces critical thresholds to absolute power values of these thresholds can vary from 50 up to at least 77 the associated underlying mechanism could provide an explanation for both former apparent eternity of communist leaderships and their sudden collapse

an opinion formation model with dissipative structure abstract we propose an opinion formation model which includes both the influence of internal motivation and dissipation active agents adopt their neighbors opinions according to a simplified set of rules but they may gradually lose their interests in the discussion and drop out of it on the other hand inert agents can become active by initial activation or internal motivation from neighbors and participate in the discussion the initial activation is usually due to occurrence of a social event the internal motivation opinion update and dissipation procedure take place simultaneously we apply the voter rule in our model and carry out analysis and numerical simulations results show if nonzero dissipation stays below a threshold value the system evolves to a balance state where the average concentration of one opinion is equal to that of the other with dissipation a number of small size opinion clusters exist in the end but the system gains a fast relaxation rate the final average opinion is closely related to the dissipation intensity and the length of time for initial activation

szego kernel asymptotics and morse inequalities on cr manifolds let x be an abstract compact orientable cr manifold of dimension 2n 1 n 2 and let l k be the k th tensor power of a cr complex line bundle l over x we assume that condition y q holds at each point of x in this paper we obtain a scaling upper bound for the szego kernel on 0 q forms with values in l k for large k after integration this gives weak morse inequalities analogues of the holomorphic morse inequalities of demailly by a refined spectral analysis we obtain also strong morse inequalities we apply the strong morse inequalities to the embedding of some convex concave manifolds

average size of random polygons with fixed knot topology we have evaluated by numerical simulation the average size r k of random polygons of fixed knot topology k ensuremath emptyset 3 1 3 1 ensuremath sharp 4 1 and we have confirmed the scaling law r k 2 ensuremath sim n 2 ensuremath nu k for the number n of polygonal nodes in a wide range n 100 char21 2200 the best fit gives 2 ensuremath nu k ensuremath simeq 1 11 char21 1 16 with good fitting curves in the whole range of n the estimate of 2 ensuremath nu k is consistent with the exponent of self avoiding polygons in a limited range of n n ensuremath gtrsim 600 however we have another fit with 2 ensuremath nu k ensuremath simeq 1 01 char21 1 07 which is close to the exponent of random polygons

opinion polarization in the receipt accept sample model abstract the zaller theory of opinion formation is reformulated with one free parameter which measures the largest possible ideological distance which can be made by a citizen in one mental step our numerical results show the transient effects i the political awareness measured by the number of received messages increases with time first exponentially later linearly ii for small correlations are present between previously and newly received messages iii these correlation lead to a hyperdiffusion effect in the space of attitudes of messages citizens with small are more prone to extremal opinions

the hartogs extension theorem on n 1 complete complex spaces employing morse theory for the global control of monodromy and the method of analytic discs for local extension we establish a version of the global hartogs extension theorem in a singular setting for every domain d of an n 1 complete normal complex space x of pure dimension n 2 and for every compact set k in d such that d k is connected holomorphic or meromorphic functions in d k extend holomorphically or meromorphically to d normality is an unvavoidable assumption for holomorphic extension but we show that meromorphic extension holds on a reduced globally irreducible not necessarily normal x of pure dimension n 2 provided that the regular part of d k is connected

the impact of network characteristics on the diffusion of innovations abstract this paper studies the influence of network topology on the speed and reach of new product diffusion while previous research has focused on comparing network types this paper explores explicitly the relationship between topology and measurements of diffusion effectiveness we study simultaneously the effect of three network metrics the average degree the relative degree of social hubs i e the ratio of the average degree of highly connected individuals to the average degree of the entire population and the clustering coefficient a novel network generation procedure based on random graphs with a planted partition is used to generate 160 networks with a wide range of values for these topological metrics using an agent based model we simulate diffusion on these networks and check the dependence of the net present value npv of the number of adopters over time on the network metrics we find that the average degree and the relative degree of social hubs have a positive influence on diffusion this result emphasizes the importance of high network connectivity and strong hubs the clustering coefficient has a negative impact on diffusion a finding that contributes to the ongoing controversy on the benefits and disadvantages of transitivity these results hold for both monopolistic and duopolistic markets and were also tested on a sample of 12 real networks

an opinion diffusion model with clustered early adopters abstract we propose an opinion dynamic model which studies the adoption process of new opinions or ideas by agents the proposed model allows the observation range of an agent to be expanded in square lattices the agent s opinion update process is not only influenced by a neighbor s choice but also by the whole environment that can be observed the model shows a different result with the normal coda model if adopters initial opinions equal 0 6 and individual observation probability equals 0 65 then diffusions with clustered early adopters are 3 faster than those with randomly scattered ones introducing the bounded confidence concept into our model leads to appearance of freezing effect in opinion dynamics

limits of analogy between self avoidance and topology driven swelling of polymer loops the work addresses the analogy between trivial knotting and excluded volume in looped polymer chains of moderate length where the effects of knotting are small a simple expression for the swelling seen in trivially knotted loops is described and shown to agree with simulation data contrast between this expression and the well known expression for excluded volume polymers leads to a graphical mapping of excluded volume to trivial knots which may be useful for understanding where the analogy between the two physical forms is valid the work also includes description of a new method for the computational generation of polymer loops via conditional probability although computationally intensive this method generates loops without statistical bias and thus is preferable to other loop generation routines in the region of interest

scaling behavior of random knots using numerical simulations we investigate how overall dimensions of random knots scale with their length we demonstrate that when closed non self avoiding random trajectories are divided into groups consisting of individual knot types then each such group shows the scaling exponent of 0 588 that is typical for self avoiding walks however when all generated knots are grouped together their scaling exponent becomes equal to 0 5 as in non self avoiding random walks we explain here this apparent paradox we introduce the notion of the equilibrium length of individual types of knots and show its correlation with the length of ideal geometric representations of knots we also demonstrate that overall dimensions of random knots with a given chain length follow the same order as dimensions of ideal geometric representations of knots

probability theory of random polygons from the quaternionic viewpoint we build a new probability measure on closed space and plane polygons the key construction is a map given by hausmann and knutson using the hopf map on quaternions from the complex stiefel manifold of 2 frames in n space to the space of closed n gons in 3 space of total length 2 our probability measure on polygon space is defined by pushing forward haar measure on the stiefel manifold by this map a similar construction yields a probability measure on plane polygons that comes from a real stiefel manifold the edgelengths of polygons sampled according to our measures obey beta distributions this makes our polygon measures different from those usually studied which have gaussian or fixed edgelengths one advantage of our measures is that we can explicitly compute expectations and moments for chord lengths and radii of gyration another is that direct sampling according to our measures is fast linear in the number of edges and easy to code some of our methods will be of independent interest in studying other probability measures on polygon spaces we define an edge set ensemble ese to be the set of polygons created by rearranging a given set of n edges a key theorem gives a formula for the average over an ese of the squared lengths of chords skipping k vertices in terms of k n and the edgelengths of the ensemble this allows one to easily compute expected values of squared chord lengths and radii of gyration for any probability measure on polygon space invariant under rearrangements of edges 2014 wiley periodicals inc

un phenomene de hartogs dans les varietes projectives let v be a projective manifold dimv 2 let z be an open subset in v which is pseudoconcave see 1 letm z be the field of meromorphic functions on z according to andreotti 1 m z is a finite extension ofm v hence meromorphic functions on a pseudoconcave domain in a projective manifold are algebraic in 3 theorem 3 2 1 we claimed that they are rationals this claim is false counterexamples can be found in 6 chapter 5 page 199 or in 2 chapter 9 example 9 1 in order to state ahartogs theoremon a projectivemanifold wemust take care of algebraic multivaluedness we state corrected versions of main theorem 3 2 4 in 3 and of corollary 6 of 4 first we work with a pseudoconcave domain z such that m z m v then we use a primitive element to reduce to the first case theorem let v be a projective manifold dimv 2 let u be an open subset in v such that v is pseudoconcave in the sense of andreotti and the boundary of u is connected let h be the maximal compact reduced divisor in u see 3 assume meromorphic functions on v are rationals let f v be a holomorphic vector bundle then any meromorphic section of f defined on a connected neighborhood w of u extends as a meromorphic section of f over u moreover if that section is holomorphic on w then its extension is holomorphic on u h

spreading of families in cyclic predator prey models we study the spreading of families in two dimensional multispecies predator prey systems in which species cyclically dominate each other in each time step randomly chosen individuals invade one of the nearest sites of the square lattice eliminating their prey initially all individuals get a family name which will be carried on by their descendants monte carlo simulations show that the systems with several species n 3 4 5 are asymptotically approaching the behavior of the voter model i e the survival probability of families the mean size of families and the mean square distance of descendants from their ancestor exhibits the same scaling behavior the scaling behavior of the survival probability of families has a logarithmic correction in case of the voter model this correction depends on the number of species while cyclic predator prey models behave like the voter model with infinite species it is found that changing the rates of invasions does not change this asymptotic behavior as an application a three species system with a fourth species intruder is also discussed

fixation and consensus times on a network a unified approach we investigate a set of stochastic models of biodiversity population genetics language evolution and opinion dynamics on a network within a common framework each node has a state 0 x i 1 with interactions specified by strengths m ij for any set of m ij we derive an approximate expression for the mean time to reach fixation or consensus all x i 0 or 1 remarkably in a case relevant to language change this time is independent of the network structure

the generation of random equilateral polygons freely jointed random equilateral polygons serve as a common model for polymer rings reflecting their statistical properties under theta conditions to generate equilateral polygons researchers employ many procedures that have been proved or at least are believed to be random with respect to the natural measure on the space of polygonal knots as a result the random selection of equilateral polygons as well as the statistical robustness of this selection is of particular interest in this research we study the key features of four popular methods the polygonal folding the crankshaft rotation the hedgehog and the triangle methods in particular we compare the implementation and efficacy of these procedures especially in regards to the population distribution of polygons in the space of polygonal knots the distribution of edge vectors the local curvature and the local torsion in addition we give a rigorous proof that the crankshaft rotation method is ergodic

finite size and asymptotic behaviors of the gyration radius of knotted cylindrical self avoiding polygons several nontrivial properties are shown for the mean square radius of gyration r k 2 of ring polymers with a fixed knot type k through computer simulation we discuss both finite size and asymptotic behaviors of the gyration radius under the topological constraint for self avoiding polygons consisting of n cylindrical segments with radius r we find that the average size of ring polymers with the knot k can be much larger than that of no topological constraint the effective expansion due to the topological constraint depends strongly on the parameter r that is related to the excluded volume the topological expansion is particularly significant for the small r case where the simulation result is associated with that of random polygons with the knot k

asymptotics of knotted lattice polygons we use monte carlo methods to investigate the asymptotic behaviour of the number and mean square radius of gyration of polygons in the simple cubic lattice with fixed knot type let be the number of n edge polygons of a fixed knot type in the cubic lattice and let be the mean square radius of gyration of all the polygons counted by if we assume that where is the growth constant of polygons of knot type and is the entropic exponent of polygons of knot type then our numerical data are consistent with the relation where is the unknot and is the number of prime factors of the knot if we assume that then our data are consistent with both and being independent of these results support the claims made in janse van rensburg and whittington 1991a 24 3935 and orlandini et al 1996 29 l299 1998 topology and geometry in polymer science ima volumes in mathematics and its applications berlin springer