asymptotic enumeration of rna secondary structure based on the new representation of rna secondary structures we obtain the basic relations about secondary structures with a prescribed size m for hairpin loops and minimum stack length l furthermore we make an asymptotic analysis on rna secondary structures with certain additional constrains

density functional theory and optimal transportation with coulomb cost we present here novel insight into exchange correlation functionals in density functional theory based on the viewpoint of optimal transport we show that in the case of two electrons and in the semiclassical limit the exact exchange correlation functional reduces to a very interesting functional of novel form which depends on an optimal transport map t associated with a given density since the above limit is strongly correlated the limit functional yields insight into electron correlations we prove the existence and uniqueness of such an optimal map for any number of electrons and each and determine the map explicitly in the case when is radially symmetric

moduli spaces and macromolecules techniques from moduli spaces are applied to biological macromolecules the first main result provides new a priori constraints on protein geometry discovered empirically and confirmed computationally the second main result identifies up to homotopy the natural moduli space of several interacting rna molecules with the riemann moduli space of a surface with several boundary components in each fixed genus applications to rna folding prediction are discussed the mathematical and biological frameworks are surveyed and presented from first principles

minimization for conditional simulation relationship to optimal transport in this paper we consider the problem of generating independent samples from a conditional distribution when independent samples from the prior distribution are available although there are exact methods for sampling from the posterior e g markov chain monte carlo or acceptance rejection these methods tend to be computationally demanding when evaluation of the likelihood function is expensive as it is for most geoscience applications as an alternative in this paper we discuss deterministic mappings of variables distributed according to the prior to variables distributed according to the posterior although any deterministic mappings might be equally useful we will focus our discussion on a class of algorithms that obtain implicit mappings by minimization of a cost function that includes measures of data mismatch and model variable mismatch algorithms of this type include quasi linear estimation randomized maximum likelihood perturbed observation ensemble kalman filter and ensemble of perturbed analyses 4d var when the prior pdf is gaussian and the observation operators are linear we show that these minimization based simulation methods solve an optimal transport problem with a nonstandard cost function when the observation operators are nonlinear however the mapping of variables from the prior to the posterior obtained from those methods is only approximate errors arise from neglect of the jacobian determinant of the transformation and from the possibility of discontinuous mappings

an asymptotic closed form microstrip surface green s function for the efficient moment method analysis of mutual coupling in microstrip antennas a relatively simple closed form asymptotic representation for the single layer microstrip dyadic surface green s function is developed the large parameter in this asymptotic development is proportional to the lateral separation between the source and field points along the air dielectric interface this asymptotic solution remains surprisingly accurate even for very small a few tenths of a free space wavelength lateral separation of the source and field points thus using the present asymptotic approximation of the green s function can lead to a very efficient moment method mm solution for the currents on an array of microstrip antenna patches and feed lines numerical results based on the efficient mm analysis using the present closed form asymptotic approximation to the microstrip surface green s function are given for the mutual coupling between a pair of printed dipoles on a single layer grounded dielectric slab the accuracy of the latter calculation is confirmed by comparison with numerical results based on a mm analysis which employs an exact integral representation for the microstrip green s function

on the equation y2 x x2 p generators are found for the group of rational points on the title curve for all primes p 5 mod 8 less than 1 000 the rank is always i in accordance with conjectures of selmer and mordell some of the generators are rather large

a pde approach to a 2 dimensional matching problem we prove asymptotic results for 2 dimensional random matching problems in particular we obtain the leading term in the asymptotic expansion of the expected quadratic transportation cost for empirical measures of two samples of independent uniform random variables in the square our technique is based on a rigorous formulation of the challenging pde ansatz by caracciolo et al phys rev e 90 012118 2014 that linearizes the monge ampere equation

torsion algebraic cycles and complex cobordism atiyah and hirzebruch gave the first counterexamples to the hodge conjecture with integral coefficients 3 that conjecture predicted that every integral cohomology class of hodge type p p on a smooth projective variety should be the class of an algebraic cycle but atiyah and hirzebruch found additional topological properties which must be satisfied by the integral cohomology class of an algebraic cycle here we provide a more systematic explanation for their results by showing that the classical cycle map from algebraic cycles modulo algebraic equivalence to integral cohomology factors naturally through a topologically defined ring which is richer than integral cohomology the new ring is based on complex cobordism a well developed topological theory which has been used only rarely in algebraic geometry since hirzebruch used it to prove the riemann roch theorem 17 this factorization of the classical cycle map implies the topological restrictions on algebraic cycles found by atiyah and hirzebruch it goes beyond their work by giving a topological method to show that the classical cycle map can be noninjective as well as nonsurjective the kernel of the classical cycle map is called the griffiths group and the topological proof here that the griffiths group can be nonzero is the first proof of this fact which does not use hodge theory the proof here gives nonzero torsion elements in the griffiths group whereas griffiths s hodge theoretic proof gives nontorsion elements 13 this topological argument also gives examples of algebraic cycles in the kernel of various related cycle maps where few or no examples were known before thus answering some questions posed by colliot thelene and schoen 8 p 14 37 p 13 colliot thelene asked in particular whether the map ch2 x n h4 x z n is injective for all smooth complex projective varieties x here ch x is the group of codimension i algebraic cycles modulo rational equivalence the first examples where colliot thelene s map is not injective were found by kollar and van geemen see 4 p 135 very recently bloch and esnault found examples defined over number fields 7 over nonalgebraically closed fields k there are other examples of smooth projective varieties xk with ch2 xk n hg4t xk z n not injective due to colliot thelene and sansuc as reinterpreted by salberger see 9 and 8 remark 7 6 1 and parimala and suresh 31 these elements of ch2 xk n are not shown to remain nonzero in ch2 xc n however here our topological method

zero temperature properties of rna secondary structures we analyze different microscopic rna models at zero temperature we discuss both the most simple model which suffers a large degeneracy of the ground state and models in which the degeneracy has been removed in a more or less severe manner we calculate low energy density of states using a coupling perturbing method where the ground state of a modified hamiltonian that repels the original ground state is determined we evaluate scaling exponents starting from measurements of overlaps and energy differences in the case of models without accidental degeneracy of the ground state we are able to clearly establish the existence of a glassy phase with ensuremath theta ensuremath simeq 1 3 87 15 aa 64 60 fr

rational points on pencils of conics and quadrics with many degenerate fibres for any pencil of conics or higher dimensional quadrics over q with all degenerate bres dened over q we show that the brauer manin obstruction controls weak approximation the proof is based on the hasse principle and weak approximation for some special intersections of quadrics over q which is a consequence of recent advances in additive combinatorics

free boundaries in optimal transport and monge ampere obstacle problems given compactly supported 0 f g 2 l 1 r n the problem of trans porting a fraction m min kfkl1 kgkl1 of the mass of f onto g as cheaply as possible is considered where cost per unit mass transported is given by a cost function c typically quadratic c x y x y 2 2 this question is shown to be equivalent to a double obstacle problem for the monge ampere equation for which sucient conditions are given to guarantee uniqueness of the solution such as f vanishing on sptg in the quadratic case the part of f to be transported increases monotonically with m and if sptf and sptg are separated by a hyperplane h then this part will separated from the balance of f by a semiconcave lipschitz graph over the hyperplane if f f and g g are bounded away from zero and infinity on separated strictly convex domains r n for the quadratic cost this graph is shown to be a c 1 loc hypersurface in whose normal coincides with the direction transported the optimal map between f and g is shown to be holder continuous up to this free bound ary and to those parts of the fixed boundary which map to locally convex parts of the path connected target region

quadratic stochastic euclidean bipartite matching problem we propose a new approach for the study of the quadratic stochastic euclidean bipartite matching problem between two sets of n points each n 1 the points are supposed independently randomly generated on a domain r d with a given distribution x on in particular we derive a general expression for the correlation function and for the average optimal cost of the optimal matching a previous ansatz for the matching problem on the flat hypertorus is obtained as a particular case

analytical technique to evaluate the asymptotic part of the impedance matrix of sommerfeld type integrals the propagation of electromagnetic waves in a grounded dielectric slab has numerous applications in printed antenna technology and in the analysis of microwave and millimeter wave integrated circuits for the accurate analysis of microstrip dipoles and circuits based on the moment of method mom a crucial step is the precise evaluation of the impedance matrix elements which contain the integration of sommerfeld type integrals the integral transform method with the asymptotic extraction technique is formulated for calculating a sommerfeld type integral problem this formulation allows the infinite double integral of the asymptotic part of the impedance matrix to be transformed into a finite one dimensional 1 d integral this finite 1 d integral contains a spherical legendre function and can be easily evaluated numerically after the singular part of the integral is performed analytically it is shown that the proposed method dramatically reduces the computation time and improves the accuracy over the conventional method to evaluate the asymptotic part of impedance matrix

enumeration of rna structures by matrix models we enumerate the number of rna contact structures according to their genus i e the topological character of their pseudoknots by using a recently proposed matrix model formulation for the rna folding problem we obtain exact results for the simple case of an rna molecule with an infinitely flexible backbone in which any arbitrary pair of bases is allowed we analyze the distribution of the genus of pseudoknots as a function of the total number of nucleotides along the phosphate sugar backbone

rna matrix models with external interactions and their asymptotic behavior we study a matrix model of rna in which an external perturbation on n nucleotides is introduced in the action of the partition function of the polymer chain the effect of the perturbation appears in the exponential generating function of the partition function as a factor exp 1 n alpha l where alpha is the ratio of strengths of the original to the perturbed term and l is the length of the chain the asymptotic behavior of the genus distribution functions as a function of length for the matrix model with interaction is analyzed numerically for all n l it is found that as n alpha l is increased from 0 to 1 the term 3 sup l in the number of diagrams a sub l g alpha sup at a fixed length l genus g and alpha goes to 2 sup l 3 n alpha l sup l for any n alpha l and the total number of diagrams n sub alpha sup at a fixed length l and alpha but independent of genus g undergoes a change in the factor exp radical l to 1 exp 1 n alpha l radical l for any n alpha l however the exponent l of the dominant length dependent term in a sub l g alpha sup stays unchanged hence the universality is robust to changes in the interaction alpha the distribution functions alsomore exhibit unusual behavior at small lengths less

some convergence considerations in space domain moment method analysis of a class of wide band microstrip antennas the method of moments mom analysis of probe fed rectangular microstrip patches requires the inclusion of a probe to patch attachment mode expansion function when the substrate thickness d spl ges 0 02 spl lambda where spl lambda is the free space wavelength the results for the input impedance showed increased divergence with measurements when the attachment mode was omitted from the full wave analysis the attachment mode can be expressed as an infinite eigenfunction series that increases the fill time of the impedance matrix in an mom analysis in an earlier investigation the infinite eigenfunction series was reduced to a residue series that required one or two terms compared to about 55 terms for the eigenfunction series in this paper the convergence properties of the eigenfunction and residue series are investigated in view of rigorous mom analysis the relative errors resulting from replacing the eigenfunction by the residue series for the attachment mode are compared by numerically evaluating a class of two dimensional 2 d spatial integrals shown to be closely related to the elements of an mom impedance matrix additionally the computation times for the evaluation of these integrals for the two forms of the attachment mode expansion function are also included based on the superior convergence properties of the residue series for the attachment mode expansion function it is mathematically justified that this form can readily be used for analytic reduction of the spatial reaction integrals from four to 2 d forms this feature allows further reduction of the fill time of the mom impedance matrix suggesting the possibility of developing an efficient space domain mom technique for modeling of wide band microstrip antennas

phase transition in random planar diagrams and rna type matching we study the planar matching problem defined by a symmetric random matrix with independent identically distributed entries taking values zero and one we show that the existence of a perfect planar matching structure is possible only above a certain critical density p c of allowed contacts i e of ones using a formulation of the problem in terms of dyck paths and a matrix model of planar contact structures we provide an analytical estimation for the value of the transition point p c in the thermodynamic limit this estimation is close to the critical value p c 0 379 obtained in numerical simulations based on an exact dynamical programming algorithm we characterize the corresponding critical behavior of the model and discuss the relation of the perfect imperfect matching transition to the known molten glass transition in the context of random rna secondary structure formation in particular we provide strong evidence supporting the conjecture that the molten glass transition at t 0 occurs at p c

one dimensional euclidean matching problem exact solutions correlation functions and universality we discuss the equivalence relation between the euclidean bipartite matching problem on the line and on the circumference and the brownian bridge process on the same domains the equivalence allows us to compute the correlation function and the optimal cost of the original combinatorial problem in the thermodynamic limit moreover we solve also the minimax problem on the line and on the circumference the properties of the average cost and correlation functions are discussed

the dyck bound in the concave 1 dimensional random assignment model we consider models of assignment for random n blue points and n red points on an interval of length 2n in which the cost for connecting a blue point in x to a red point in y is the concave function x y p for 0 1 where the optimal matching is trivially determined here the optimization is non trivial the purpose of this paper is to introduce a special configuration that we call the dyck matching and to study its statistical properties we compute exactly the average cost in the asymptotic limit of large n together with the first subleading correction the scaling is remarkable it is of order n for p 1 2 and it is universal for a wide class of models we conjecture that the average cost of the dyck matching has the same scaling in n as the cost of the optimal matching and we produce numerical data in support of this conjecture we hope to produce a proof of this claim in future work

a finiteness theorem for zero cycles over p adic fields let r be a henselian discrete valuation ring let x be a regular projective flat scheme over spec r with generalized semistable reduction we prove a bijectivity theorem for etale cycle class maps of the chow group of 1 cycles on x as an application we prove a finiteness theorem for the chow group of 0 cycles on a projective smooth variety over a p adic field

exact solutions to the transportation problem on the line given distributions w of production and v of consumption on the line the monge kantorovich problem is to decide which producer should supply each consumer in order to minimize the total transportation costs here cost will be assumed to be a strictly concave function of the distance which translates into an economy of scale for longer trips and may encourage cross hauling the resulting solutions display a hierarchical structure that reflects a striking separation into local and global scales also found in the real world moreover this structure can be exploited to reduce the infinite dimensional linear problem to a convex minimization in m variables where 2 m 2 counts the number of times that w v changes sign a combinatorial algorithm is then derived which yields exact solutions by optimizing a certain finite sequence of convex separable network flows

solution for a bipartite euclidean traveling salesman problem in one dimension the traveling salesman problem is one of the most studied combinatorial optimization problems because of the simplicity in its statement and the difficulty in its solution we characterize the optimal cycle for every convex and increasing cost function when the points are thrown independently and with an identical probability distribution in a compact interval we compute the average optimal cost for every number of points when the distance function is the square of the euclidean distance we also show that the average optimal cost is not a self averaging quantity by explicitly computing the variance of its distribution in the thermodynamic limit moreover we prove that the cost of the optimal cycle is not smaller than twice the cost of the optimal assignment of the same set of points interestingly this bound is saturated in the thermodynamic limit

planar diagrams from optimization for concave potentials we propose a toy model of a heteropolymer chain capable of forming planar secondary structures typical for rna molecules in this model the sequential intervals between neighboring monomers along a chain are considered as quenched random variables and energies of nonlocal bonds are assumed to be concave functions of those intervals a few factors are neglected the contribution of loop factors to the partition function the variation in energies of different types of complementary nucleotides the stacking interactions and constraints on the minimal size of loops however the model captures well the formation of folded structures without pseudoknots in an arbitrary sequence of nucleotides using the optimization procedure for a special class of concave type potentials borrowed from optimal transport analysis we derive the local difference equation for the ground state free energy of the chain with the planar rna like architecture of paired links we consider various distribution functions of intervals between neighboring monomers truncated gaussian and scale free and demonstrate the existence of a topological crossover from sequential to essentially nested configurations of paired links

fokker planck equations for a free energy functional or markov process on a graph the classical fokker planck equation is a linear parabolic equation which describes the time evolution of the probability distribution of a stochastic process defined on a euclidean space corresponding to a stochastic process there often exists a free energy functional which is defined on the space of probability distributions and is a linear combination of a potential and an entropy in recent years it has been shown that the fokker planck equation is the gradient flow of the free energy functional defined on the riemannian manifold of probability distributions whose inner product is generated by a 2 wasserstein distance in this paper we consider analogous matters for a free energy functional or markov process defined on a graph with a finite number of vertices and edges if n 2 is the number of vertices of the graph we show that the corresponding fokker planck equation is a system of nnonlinear ordinary differential equations defined on a riemannian manifold of probability distributions however in contrast to stochastic processes defined on euclidean spaces the situation is more subtle for discrete spaces we have different choices for inner products on the space of probability distributions resulting in different fokker planck equations for the same process it is shown that there is a strong connection but there are also substantial discrepancies between the systems of ordinary differential equations and the classical fokker planck equation on euclidean spaces furthermore both systems of ordinary differential equations are gradient flows for the same free energy functional defined on the riemannian manifolds of probability distributions with different metrics some examples are also discussed

families of rationally connected varieties recall that a proper variety x is said to be rationally connected if two general points p q x are contained in the image of a map g p x this is clearly a birationally invariant property when x is smooth this turns out to be equivalent to the a priori weaker condition that two general points can be joined by a chain of rational curves and also to the a priori stronger condition that for any finite subset x there is a map g p x whose image contains and such that gtx is an ample bundle

on the fibration method for zero cycles and rational points conjectures on the existence of zero cycles on arbitrary smooth projective varieties over number elds were proposed by colliot th el ene sansuc kato and saito in the 1980 s we prove that these conjectures are compatible with brations for brations into rationally connected varieties over a curve in particular they hold for the total space of families of homogeneous spaces of linear groups with connected geometric stabilisers we prove the analogous result for rational points conditionally on a conjecture on locally split values of polynomials which a recent work of matthiesen establishes in the case of linear polynomials over the rationals

scaling hypothesis for the euclidean bipartite matching problem ii correlation functions we analyze the random euclidean bipartite matching problem on the hypertorus in d dimensions with quadratic cost and we derive the two point correlation function for the optimal matching using a proper ansatz introduced by caracciolo et al phys rev e 90 012118 2014 to evaluate the average optimal matching cost we consider both the grid poisson matching problem and the poisson poisson matching problem we also show that the correlation function is strictly related to the green s function of the laplace operator on the hypertorus

finite size corrections in the random assignment problem we analytically derive in the context of the replica formalism the first finite size corrections to the average optimal cost in the random assignment problem for a quite generic distribution law for the costs we show that when moving from a power law distribution to a mathrm ensuremath gamma distribution the leading correction changes both in sign and in its scaling properties we also examine the behavior of the corrections when approaching a ensuremath delta function distribution by using a numerical solution of the saddle point equations we provide predictions that are confirmed by numerical simulations

pathologies of the brauer manin obstruction it had long been suspected that varieties x over a number field k without k points but with a non empty brauer manin set x ak are fairly common the first examples were found in 27 and then in 2 an earlier conditional example is given in 21 one should also expect that there are many varieties x without k points for which the etale brauer manin set x ak x ak is non empty we refer to 19 or 29 for the definition of these subsets of the space x ak of adeles of x different methods to construct such varieties have been found recently in 19 poonen constructs a threefold x with a surjective morphism to a curve c that has exactly one k point p and the fibre xp has points everywhere locally but not globally in poonen s example xp is a smooth ch telet surface the trick with a curve with just one rational point was also used in 11 where the fibres of x c are curves of high genus and xp is a singular curve which geometrically is a union of projective lines in retrospect one could note that the examples in 27 and 2 are families of genus 1 curves parameterised by elliptic curves of mordell weil rank 0 in this paper we propose more flexible methods to construct such examples we show that the varieties x such that x k and x ak include the following

on solutions to the mass transfer problem this paper studies the monge kantorovich mass transfer mt problem on metric spaces with possibly unbounded cost function conditions are given under which the mt problem is solvable and furthermore an optimal solution can be obtained as the weak limit of a sequence of optimal solutions to suitably approximating mt problems

duality theorems for marginal problems given topological spaces x1 xn with product space x probability measures i on xi together with a real function h on x define a marginal problem as well as a dual problem using an extended version of choquet s theorem on capacities an analogue of the classical duality theorem of linear programming is established imposing only weak conditions on the topology of the spaces xi and the measurability resp boundedness of the function h applications concern among others measures with given support stochastic order and general marginal problems

good reduction of the brauer manin obstruction for a smooth and projective variety over a number field with torsion free geometric picard group and finite transcendental brauer group we show that only the archimedean places the primes of bad reduction and the primes dividing the order of the transcendental brauer group can turn up in the description of the brauer manin set ams subject classification 14f22 14g05 11g35 11g25

problems of optimal transportation on the circle and their mechanical applications abstract we consider a mechanical problem concerning a 2d axisymmetric body moving forward on the plane and making slow turns of fixed magnitude about its axis of symmetry the body moves through a medium of non interacting particles at rest and collisions of particles with the body s boundary are perfectly elastic billiard like the body has a blunt nose a line segment orthogonal to the symmetry axis it is required to make small cavities with special shape on the nose so as to minimize its aerodynamic resistance this problem of optimizing the shape of the cavities amounts to a special case of the optimal mass transportation problem on the circle with the transportation cost being the squared euclidean distance we find the explicit solution for this problem when the amplitude of rotation is smaller than a fixed critical value and give a numerical solution otherwise as a by product we get explicit description of the solution for a class of optimal transportation problems on the circle

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

rational solutions of certain equations involving norms let k be an algebraic closure of k in the case when p t has at most one root in k the open subset of the affine variety 1 given by p t y o is a principal homogeneous space under an algebraic k torus in this case it is well known that the brauer manin obstruction is the only obstruction to the hasse principle and weak approximation on any smooth projective model of this variety colliot th l ne and sansuc csanl in this paper we prove the same result when p t has exactly two roots in k and no other roots in k and k is the field of rational numbers q an immediate change of variables then reduces 1 to the equation ta

extrapolation methods for sommerfeld integral tails a review is presented of the extrapolation methods for accelerating the convergence of sommerfeld type integrals i e semi infinite range integrals with bessel function kernels which arise in problems involving antennas or scatterers embedded in planar multilayered media attention is limited to partition extrapolation procedures in which the sommerfeld integral is evaluated as a sum of a series of partial integrals over finite subintervals and is accelerated by an extrapolation method applied over the real axis tail segment spl alpha spl infin of the integration path where spl alpha 0 is selected to ensure that the integrand is well behaved an analytical form of the asymptotic truncation error or the remainder which characterizes the convergence properties of the sequence of partial sums and serves as a basis for some of the most efficient extrapolation methods is derived several extrapolation algorithms deemed to be the most suitable for the sommerfeld integrals are described and their performance is compared it is demonstrated that the performance of these methods is strongly affected by the horizontal displacement of the source and field points spl rho and by the choice of the subinterval break points furthermore it is found that some well known extrapolation techniques may fail for a number of values of spl rho and ways to remedy this are suggested finally the most effective extrapolation methods for accelerating sommerfeld integral tails are recommended

anomalous scaling of the optimal cost in the one dimensional random assignment problem we consider the random euclidean assignment problem on the line between two sets of n random points independently generated with the same probability density function varrho the cost of the matching is supposed to be dependent on a power p 1 of the euclidean distance of the matched pairs we discuss an integral expression for the average optimal cost for n gg 1 that generalizes a previous result obtained for p 2 we also study the possible divergence of the given expression due to the vanishing of the probability density function the provided regularization recipe allows us to recover the proper scaling law for the cost in the divergent cases and possibly some of the involved coefficients the possibility that the support of varrho is a disconnected interval is also analysed we exemplify the proposed procedure and we compare our predictions with the results of numerical simulations

enumeration of chord diagrams on many intervals and their non orientable analogs two types of connected chord diagrams with chord endpoints lying in a collection of ordered and oriented real segments are considered here the real segments may contain additional bivalent vertices in one model but not in the other in the former case we record in a generating function the number of fatgraph boundary cycles containing a fixed number of bivalent vertices while in the latter we instead record the number of boundary cycles of each fixed length second order non linear algebraic partial differential equations are derived which are satisfied by these generating functions in each case giving efficient enumerative schemes moreover these generating functions provide multi parameter families of solutions to the kp hierarchy for each model there is furthermore a non orientable analog and each such model likewise has its own associated differential equation the enumerative problems we solve are interpreted in terms of certain polygon gluings as specific applications we discuss models of several interacting rna molecules we also study a matrix integral which computes numbers of chord diagrams in both orientable and non orientable cases in the model with bivalent vertices and the large n limit is computed using techniques of free probability

surjectivity of the total clifford invariant and brauer dimension abstract a celebrated theorem of merkurjev that the 2 torsion of the brauer group is represented by clifford algebras of quadratic forms is in general false when the base is no longer a field the first counterexamples when the base is among certain arithmetically subtle hyperelliptic curves over local fields were constructed by parimala scharlau and sridharan we prove that considering clifford algebras of all line bundle valued quadratic forms such counterexamples disappear and we recover merkurjev s theorem in these cases for any smooth curve over a local field or any smooth surface over a finite field the 2 torsion of the brauer group is always represented by clifford algebras of line bundle valued quadratic forms

zero cycles on rational surfaces over number fields let x be a smooth projective geometrically integral surface defined over a perfect field k let kbe an algebraic closure of k and f be the function field of x k x then x is said to be rational if f is a purely transcendental extension of k the tame symbols define a map from ke f to the sum of function fields h k 7 of all irreducible divisors 7 on x let m be the cokernel of this map if k is a number field and kv the completion at a place v of k let kv be an algebraic closure of kv and m the corresponding cokernel for k x x further let i i i l k m be the kernel of the natural map from hl gal k k m to i h1 gal k v kv my in 5 w colliot th616ne and sansuc conjectured that

random euclidean matching problems in one dimension we discuss the optimal matching solution for both the assignment problem and the matching problem in one dimension for a large class of convex cost functions we consider the problem in a compact set with the topology both of the interval and of the circumference afterwards we assume the points positions to be random variables identically and independently distributed on the considered domain we analytically obtain the average optimal cost in the asymptotic regime of very large number of points n and some correlation functions for a power law type cost function in the form c z z p both in the p 1 case and in the p 1 whereas in both cases it is a constant when p 0 finally our predictions are compared with the results of numerical simulations

strong duality of the monge kantorovich mass transfer problem in metric spaces this paper studies the monge kantorovich mass transfer mt problem on metric spaces and with an unbounded cost function conditions are given under which the strong duality condition holds that is mt and its dual mt are both solvable and their optimal values coincide

on chow and brauer groups of a product of mumford curves let c1 cd be mumford curves defined over a finite extension of open image in new window and let x c1 cd we shall show the following 1 the cycle map ch0 x n h2d x n d is injective for any non zero integer n 2 the kernel of the canonical map ch0 x hom br x open image in new window defined by the brauer manin pairing coincides with the maximal divisible subgroup in ch0 x

descent on fibrations over the projective line we formulate a general set up for the descent method of j l colliot thelene and j j sansuc applied to varieties fibred over the projective line over a number field this makes it possible to prove that the manin obstruction to the hasse principle and weak approximation is the only one provided there are only few degenerate fibres usually two three in some cases and that sufficiently many smooth fc fibres satisfy the hasse principle and weak approximation we introduce a new concept of what should be called a degenerate fibre the so called split fibres the property which depends only on the generic fibre and not on the choice of a particular model this yields a simpler and more general approach to the previous results of that kind 0 introduction motivated by hasse s theorem on quadratic forms one says that the hasse principle holds for a family of geometrically integral smooth and proper varieties over a number field k9 if for every member of this family the existence of rational points over all the completions of k implies the existence of a rational point the fact that the hasse principle holds for some family signif icantly simplifies the study of its arithmetic because the problem of determining whether or not there is a rational point is then reduced to a finite number of

fast transport optimization for monge costs on the circle consider the problem of optimally matching two measures on the circle or equivalently two periodic measures on the real line and suppose the cost of matching two points satisfies the monge condition we introduce a notion of locally optimal transport plan motivated by the weak kam aubry mather theory and show that all locally optimal transport plans are conjugate to shifts and that the cost of a locally optimal transport plan is a convex function of a shift parameter this theory is applied to a transportation problem arising in image processing for two sets of point masses on the circle both of which have the same total mass find an optimal transport plan with respect to a given cost function satisfying the monge condition in the circular case the sorting strategy fails to provide a unique candidate solution and a naive approach requires a quadratic number of operations for the case of n real valued point masses we present an o n log epsilon algorithm that approximates the optimal cost within epsilon when all masses are integer multiples of 1 m the algorithm gives an exact solution in o n log m operations

rna substructure as a random matrix ensemble combinatorial analysis of a certain abstraction of rna structures has been studied to investigate their statistics our approach regards the backbone of secondary structures as an alternate sequence of paired and unpaired sets of nucleotides which can be described by a random matrix model we obtain the generating function of the structures using the hermitian matrix model with the chebyshev polynomial of the second kind and analyze the statistics with respect to the number of stems to match the experimental findings of the statistical behavior we consider the structures in a grand canonical ensemble and find a fugacity value corresponding to an appropriate number of stems

analytical evaluation of the asymptotic impedance matrix of a grounded dielectric slab with roof top functions an analytical technique is derived to solve the asymptotic part of impedance matrix elements for printed circuit structures using roof top subdomain expansions the key to this problem is the analytical transformation from an infinite double integral to a suitable finite one dimensional 1 d integral the newly developed formula is applied to the monostatic radar cross section rcs of a microstrip patch comparisons are made with measurements and conventional method of moments predictions

lichtenbaum tate duality for varieties over p adic fields s lichtenbaum has proved in l1 that there is a nondegenerate pairing pic c x br c br k q z 1 between the picard group and the brauer group of a nonsingular projective curve c over a p adic field k a finite extension of the p adic numbers qp his proof consists of a reduction via explicit cocycle calculations in galois cohomology to a combination of tate duality for group schemes over p adic fields and the autoduality of the jacobian of a smooth curve in this paper we will reconstruct the above duality as a purely formal combination of a generalized form of tate duality over p adic fields and a form of poincar e duality for curves over arbitrary fields of characteristic zero this gives a more conceptual proof of lichtenbaum s result and an analogue in higher dimensions

the geometry of optimal transportation introduction 113 1 summary of main results 120 2 background on optimal measures 126 part i strictly convex costs 133 3 existence and uniqueness of optimal maps 133 4 characterization of the optimal map 137 part ii costs which are strictly concave as a function of d i s t a n c e 141 5 the role of optimal maps 141 6 uniqueness of optimal solutions 144 part iii appendices 148 a legendre transforms and conjugate costs 148 b examples of c concave potentials 152 c regularity of c concave potentials 154 references 159