adjoint based predictor corrector sequential convex programming for parametric nonlinear optimization this paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint based predictor corrector sequential convex programming after presenting the algorit

global smoothing of calabi yau threefolds yoshinori namikawa i j h m steenbrink 2 i department of mathematics sophia university kioi cho tokyo 102 japan 2 mathematical institute university of nijmegen toernooiveld 6525 ed nijmegen the netherlands oblatum 10 x 1994 13 vi 1995 introduction friedman fr has studied the relationship between local and global deforma tions of a threefold z with isolated hypersurface singularities which admits small resolutions one of his main results is as follows let z be a moishezon threefold with only ordinary double points pl p assume that the canon ical line bundle

on the stability of extensions of tangent sheaves on kahler einstein fano calabi yau pairs let s be a smooth projective variety and delta a simple normal crossing mathbb q divisor with coefficients in 0 1 for any ample mathbb q line bundle l over s we denote by mathscr e l the extension sheaf of the orbifold tangent sheaf t s log delta by the structure sheaf mathcal o s with the extension class c 1 l we prove the following two results these results generalize tian s result where k s is ample and delta emptyset we give two applications of these results the first is to study a question by borbon spotti about the relationship between local euler numbers and normalized volumes of log canonical surface singularities we prove that the two invariants differ only by a factor 4 when the log canonical pair is an orbifold cone over a marked riemann surface in particular we complete the computation of langer s local euler numbers for any line arrangements in mathbb c 2 the second application is to derive miyaoka yau type inequalities on k semistable log smooth fano pairs and calabi yau pairs which generalize some chern number inequalities proved by song wang

hochschild cohomology and atiyah classes abstract in this paper we prove that on a smooth algebraic variety the hkr morphism twisted by the square root of the todd genus gives an isomorphism between the sheaf of poly vector fields and the sheaf of poly differential operators both considered as derived gerstenhaber algebras in particular we obtain an isomorphism between hochschild cohomology and the cohomology of poly vector fields which is compatible with the lie bracket and the cupproduct the latter compatibility is an unpublished result by kontsevich our proof is set in the framework of lie algebroids and so applies without modification in much more general settings as well

on mordell weil groups of isotrivial abelian varieties over function fields we show that the mordell weil rank of an isotrivial abelian variety with cyclic holonomy depends only on the fundamental group of the complement to the discriminant provided the discriminant has singularities in cm class introduced here this class of singularities includes all unibranched plane curves singularities as a corollary we describe a family of simple jacobians over the field of rational functions in two variables for which the mordell weil rank is arbitrarily large

mordell weil lattices and toric decompositions of plane curves we extend results of cogolludo agustin and libgober relating the alexander polynomial of a plane curve c with the mordell weil rank of certain isotrivial families of jacobians over mathbf p 2 of discriminant c in the second part we introduce a height pairing on the 2 3 6 quasi toric decompositions of a plane curve we use this pairing and the results in the first part of the paper to construct a pair of degree 12 curves with 30 cusps and alexander polynomial t 2 t 1 but with distinct height pairing we use the height pairing to show that these curves from a zariski pair

numerical methods for optimum experimental design in dae systems subject of this paper is the design of optimal experiments for chemical processes described by nonlinear dae models the optimization aims at maximizing the statistical quality of a parameter estimate from experimental data this leads to optimal control problems with an unusual and intricate objective function which depends implicitly on first derivatives of the solution of the underlying dae we treat these problems by the direct approach and solve them using a structured sqp method the required first and second derivatives of the solution of the dae are computed very efficiently by a special coupling of the techniques of internal numerical differentiation and automatic differentiation the performance of our approach is demonstrated for an application to chemical reaction kinetics

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

the coolidge nagata conjecture let e p2 be a complex rational cuspidal curve contained in the projective plane the coolidge nagata conjecture asserts that e is cremona equivalent to a line that is it is mapped onto a line by some birational transformation of p2 the second author recently analyzed the log minimal model program run for the pair x 12d where x d p2 e is a minimal resolution of singularities and as a corollary he proved the conjecture in the case when more than one irreducible curve in p2 e is contracted by the process of minimalization we prove the conjecture in the remaining cases

loss of superlinear convergence for an sqp type method with conic constraints in this short note we consider a sequential quadratic programming sqp type method with conic subproblems and compare this method with a standard sqp method in which the conic constraint is linearized at each step for both approaches we restrict our attention to convex subproblems since these are easy to solve and guarantee a certain global descent property using the example of a simple nonlinear program nlp and its conic reformulation we show that the sqp method with conic subproblems displays a slower rate of convergence than standard sqp methods we then explain why an sqp subproblem that is based on a better approximation of the feasible set of the nlp results in a much slower algorithm

sampling decisions in optimum experimental design in the light of pontryagin s maximum principle optimum experimental design oed problems are optimization problems in which an experimental setting and decisions on when to measure the so called sampling design are to be determined such that a follow up parameter estimation yields accurate results for model parameters in this paper we use the interpretation of oed as optimal control problems with a very particular structure for the analysis of optimal sampling decisions we introduce the information gain function motivated by an analysis of necessary conditions of optimality we highlight differences between problem formulations and propose to use a linear penalization of sampling decisions to overcome the intrinsic ill conditioning of oed the results of this paper are independent from the actual numerical method to compute the solution to the oed problem and of the question of local and global optima

the coolidge nagata conjecture part i let e p2 be a complex rational cuspidal curve contained in the projective plane and let x d p2 e be the minimal log resolution of singularities applying the log minimal model program to x 12d we prove that if e has more than two singular points or if d which is a tree of rational curves has more than six maximal twigs or if p2 e is not of log general type then e is cremona equivalent to a line i e the coolidge nagata conjecture for e holds we show also that if e is not cremona equivalent to a line then the morphism onto the minimal model contracts at most one irreducible curve not contained in d

parameter estimation for differential equations a generalized smoothing approach summary we propose a new method for estimating parameters in models that are defined by a system of non linear differential equations such equations represent changes in system outputs by linking the behaviour of derivatives of a process to the behaviour of the process itself current methods for estimating parameters in differential equations from noisy data are computationally intensive and often poorly suited to the realization of statistical objectives such as inference and interval estimation the paper describes a new method that uses noisy measurements on a subset of variables to estimate the parameters defining a system of non linear differential equations the approach is based on a modification of data smoothing methods along with a generalization of profiled estimation we derive estimates and confidence intervals and show that these have low bias and good coverage properties respectively for data that are simulated from models in chemical engineering and neurobiology the performance of the method is demonstrated by using real world data from chemistry and from the progress of the autoimmune disease lupus

chern classes of reflexive sheaves on normal surfaces we define chern classes of reflexive sheaves using wahl s relative local chern classes of vector bundles the main result of the paper bounds contributions of singularities of a sheaf to the riemann roch formula using it we are able to prove inequality in wahl s conjecture on relative asymptotic rr formula for rank 2 vector bundles moreover we prove that if wahl s conjecture is true for a singularity then it is true for any its quotient this implies wahl s conjecture for quotient singularities and for quotients of cones over elliptic curves

formality and kontsevich duflo type theorems for lie pairs newcommand poly operatorname poly bullet newcommand td operatorname td l a nabla frac 1 2 newcommand cx 1 operatorname tot big gamma lambda bullet a vee otimes r mathcal 1 poly big newcommand cy 1 mathbb h bullet operatorname ce a mathcal 1 poly kontsevich s formality theorem states that there exists an l infty quasi isomorphism from the dgla t poly m of polyvector fields on a smooth manifold m to the dgla d poly m of polydifferential operators on m which extends the classical hochschild kostant rosenberg map in this paper we extend kontsevich s formality theorem to lie pairs a framework which includes a range of diverse geometric contexts such as complex manifolds foliations and mathfrak g manifolds the spaces cx t and cx d associated with a lie pair l a each carry an l infty algebra structure canonical up to l infty isomorphism these two spaces serve as replacements for the spaces of polyvector fields and polydifferential operators respectively their corresponding cohomology groups cy t and cy d admit canonical gerstenhaber algebra structures we establish the following formality theorem for lie pairs there exists an l infty quasi isomorphism from cx t to cx d whose first taylor coefficient is equal to operatorname hkr circ td here td acts on cx t by contraction furthermore we prove a kontsevich duflo type theorem for lie pairs the hochschild kostant rosenberg map twisted by the square root of the todd class of the lie pair l a is an isomorphism of gerstenhaber algebras from cy t to cy d as applications we establish formality theorems and kontsevich duflo type theorems for complex manifolds foliations and mathfrak g manifolds in the case of complex manifolds we recover the kontsevich duflo theorem of complex geometry

optimal experimental design for parameter estimation in column outflow experiments 1 inverse modeling is increasingly used for water flow and reactive solute transport in the unsaturated zone to determine unknown parameters e g soil hydraulic parameters degradation rates or dispersion coefficients however experimental data are frequently not suitable for parameter estimation leading instead to practically singular estimation problems optimal experimental design aims at identifying experimental conditions and sampling schemes that deliver measurement data which are most sensitive to unknown parameters a new numerical approach to optimize experimental designs for parameter estimation in coupled partial differential equations pdes and ordinary differential equation odes arising from transport and degradation processes is presented the optimal experimental design problem is embedded in the framework of optimal control theory this results in an intricate nonlinear constrained optimization problem that is solved by a direct approach based on a structured sqp method these methods are used to investigate several scenarios for a column outflow experiment in a simulation study simultaneously experimental conditions such as irrigation schemes substance concentrations and sampling schemes are optimized result is an enormous reduction of parameter uncertainty additionally it is demonstrated that it is possible to estimate both soil hydraulic and solute transport parameters together in one experiment on the basis of leachate data only the usefulness of the numerical approach for practical applications is discussed

an equation based algorithmic differentiation technique for differential algebraic equations this work presents a novel algorithmic differentiation ad approach for sensitivity analysis of differential algebraic equation systems daes for the first time the algorithmic specification of a computationally memory efficient equation based ad technique is presented this approach is mainly targeting equation based modeling and simulation tools capable of constructing high level models using state of the art object oriented modeling principles the approach is based on fundamental tree algorithms that are even manually applicable on implicit equation systems of long formulas the main building blocks of model components by applying the presented forward differentiation scheme on a given dae efficient representation of sensitivity equation systems sess is computed parameter sensitivities are evaluated by direct integration of the derived sess to overcome the runtime performance drawback of direct numerical integration a system decomposition approach is recommended it is shown that the runtime performance using modern variable step integration methods tends to achieve the expected theoretical complexity of the forward differentiation scheme under few realistic assumptions

the alternating descent conditional gradient method for sparse inverse problems we propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable observation models such models arise in many practical problems including superres

a proximal method for composite minimization we consider minimization of functions that are compositions of convex or prox regular functions possibly extended valued with smooth vector functions a wide variety of important optimization problems fall into this framework we describe an algorithmic framework based on a subproblem constructed from a linearized approximation to the objective and a regularization term properties of local solutions of this subproblem underlie both a global convergence result and an identification property of the active manifold containing the solution of the original problem preliminary computational results on both convex and nonconvex examples are promising

a continuation gmres method for fast computation of nonlinear receding horizon control in this paper a fast numerical algorithm for nonlinear receding horizon control is proposed the control input is updated by a differential equation to trace the solution of an associated state dependent two point boundary value problem a linear equation involved in the differential equation is solved by the generalized minimum residual method one of the krylov subspace methods with jacobians approximated by forward differences the error in the entire algorithm is analyzed and is shown to be bounded under some conditions the proposed algorithm is applied to a two link arm whose dynamics is highly nonlinear simulation results show that the proposed algorithm is faster than the conventional algorithms

a optimal design of experiments for infinite dimensional bayesian linear inverse problems with regularized ell_0 sparsification we present an efficient method for computing a optimal experimental designs for infinite dimensional bayesian linear inverse problems governed by partial differential equations pdes specifically we address the problem of optimizing the location of sensors at which observational data are collected to minimize the uncertainty in the parameters estimated by solving the inverse problem where the uncertainty is expressed by the trace of the posterior covariance computing optimal experimental designs oeds is particularly challenging for inverse problems governed by computationally expensive pde models with infinite dimensional or after discretization high dimensional parameters to alleviate the computational cost we exploit the problem structure and build a low rank approximation of the parameter to observable map preconditioned with the square root of the prior covariance operator the availability of this low rank surrogate relieves our method from expensive pde solves when evaluating the op

pbw for an inclusion of lie algebras abstract let h g be an inclusion of lie algebras with quotient h module n there is a natural degree filtration on the h module u g u g h whose associated graded h module is isomorphic to s n we give a necessary and sufficient condition for the existence of a splitting of this filtration in turn such a splitting yields an isomorphism between the h modules u g u g h and s n for the diagonal embedding h h h the condition is automatically satisfied and we recover the classical poincare birkhoff witt theorem the main theorem and its proof are direct translations of results in algebraic geometry obtained using an ad hoc dictionary this suggests the existence of a unified framework allowing the simultaneous study of lie algebras and of algebraic varieties and a closely related work in this direction is on the way

a robust optimization approach to experimental design for model discrimination of dynamical systems a high ranking goal of interdisciplinary modeling approaches in science and engineering are quantitative prediction of system dynamics and model based optimization quantitative modeling has to be closely related to experimental investigations if the model is supposed to be used for mechanistic analysis and model predictions typically before an appropriate model of an experimental system is found different hypothetical models might be reasonable and consistent with previous knowledge and available data the parameters of the models up to an estimated confidence region are generally not known a priori therefore one has to incorporate possible parameter configurations of different models into a model discrimination algorithm which leads to the need for robustification in this article we present a numerical algorithm which calculates a design of experiments allowing optimal discrimination of different hypothetic candidate models of a given dynamical system for the most inappropriate worst case parameter configurations within a parameter range the design comprises initial values system perturbations and the optimal placement of measurement time points the number of measurements as well as the time points are subject to design the statistical discrimination criterion is worked out rigorously for these settings a derivation from the kullback leibler divergence as optimization objective is presented for the case of discontinuous heaviside functions modeling the measurement decision which are replaced by continuous approximations during the optimization procedure the resulting problem can be classified as a semi infinite optimization problem which we solve in an outer approximations approach stabilized by a suggested homotopy strategy whose efficiency is demonstrated we present the theoretical framework algorithmic realization and numerical results

the bogomolov miyaoka yau inequality for logarithmic surfaces in positive characteristic we generalize bogomolov s inequality for higgs sheaves and the bogomolov miyaoka yau inequality in positive characteristic to the logarithmic case we also generalize shepherd barron s results on bogomolov s inequality on surfaces of special type from rank 2 to the higher rank case we use these results to show some examples of smooth nonconnected curves on smooth rational surfaces that cannot be lifted modulo p2 these examples contradict some claims by xie

equivariant lefschetz number of differential operators let g be a compact lie group acting on a compact complex manifold m by holomorphic transformations we prove a trace density formula for the g lefschetz number of a holomorphic differential operator on m we generalize the recent results of engeli and the first author to orbifolds

a semismooth newton method with multidimensional filter globalization for l_1 optimization due to their property of enhancing the sparsity of solutions l 1 regularized optimization problems have developed into a highly dynamic research area with a wide range of applications we present a class of methods for l 1 regularized optimization problems that are based on a combination of semismooth newton steps a filter globalization and shrinkage thresholding steps a multidimensional filter framework is used to control the acceptance and to evaluate the quality of the semismooth newton steps if the current newton iterate is rejected a shrinkage thresholding based step with quasi armijo stepsize rule is used instead global convergence and transition to local q superlinear convergence for both convex and nonconvex objective functions are established we present numerical results and comparisons with several state of the art methods that show the efficiency and competitiveness of the proposed method

fedosov dg manifolds associated with lie pairs given any pair l a of lie algebroids we construct a differential graded manifold l 1 oplus l a q which we call fedosov dg manifold we prove that the homological vector field q constructed on l 1 oplus l a by the fedosov iteration method arises as a byproduct of the poincare birkhoff witt map established in 18 finally using the homological perturbation lemma we establish a quasi isomorphism of dolgushev fedosov type the differential graded algebras of functions on the dg manifolds a 1 d a and l 1 oplus l a q are homotopy equivalent

algebraic constructions in the category of lie algebroids the aim of this paper is to give the first general and abstract treatment of the algebraic properties of lie algebroids the concept of lie algebroid was introduced in 1967 by pradines ls as the basic infinitesimal invariant of a differentiable groupoid the construction of the lie algebroid of a differentiable groupoid is a direct generalization of the construction of the lie algebra of a lie group and 183 described a full lie theory for differentiable groupoids and lie algebroids encompassing many phenomena in the foundations of differential geometry a more detailed account and further references are given in 13 however at this stage the algebraic properties of lie algebroids were not pursued in 13 iii section 2 iv section 11 one of us gave a fairly detailed account of the abstract algebra of lie algebroids over a fixed base lie algebroids are vector bundles with several additional structures and a category of lie algebroids on a given base and morphisms which preserve that base has properties similar to those of the category of lie algebras using this algebra it was demonstrated in 13 that the lie theory of a category of locally trivial differentiable lie groupoids over a fixed base and the corresponding category of transitive lie algebroids over that base is coextensive with the standard theory of connections in principal bundles we now propose to show that the lie functor from the category of all differentiable groupoids over arbitrary bases and arbitrary smooth morphisms to the category of all lie algebroids preserves the basic algebraic constructions known to be possible in the category of differentiable groupoids the main work is to give abstract formulations of the corresponding lie algebroid concepts the groupoid results with which we

rozansky witten type invariants from symplectic lie pairs we introduce symplectic structures on lie pairs of real or complex lie algebroids as studied by chen et al from atiyah classes to homotopy leibniz algebras arxiv 1204 1075 2012 encompassing homogeneous symplectic spaces symplectic manifolds with a mathfrak g action and holomorphic symplectic manifolds we show that to each such symplectic lie pair are associated rozansky witten type invariants of three manifolds and knots given respectively by weight systems on trivalent and chord diagrams

hypersurfaces with defect abstract a projective hypersurface x p n has defect if h i x h i p n for some i n 2 n 2 in a suitable cohomology theory this occurs for example when x p 4 is not q factorial we show that hypersurfaces with defect tend to be very singular in characteristic 0 we present a lower bound on the tjurina number where x is allowed to have arbitrary isolated singularities for x with mild singularities we prove a similar result in positive characteristic as an application we obtain an estimate on the asymptotic density of hypersurfaces without defect over a finite field

adjoint sensitivity analysis for nonsmooth differential algebraic equation systems an adjoint sensitivity method is presented for nonsmooth semiexplicit differential algebraic equation systems ndaes of index 1 the adjoint sensitivity system is derived for a generalization of mayer type functionals subject to ndae constraints opposed to classical mayer type functionals that depend on the differential and algebraic variables evaluated only at the initial and final times the generalization depends additionally on the evaluation at multiple interior time points the derived adjoint sensitivity method extends and builds on the method for smooth daes by cao et al siam j sci comput 24 2003 pp 1076 1089 and on the method for nonsmooth odes by ruban j comput systems sci internat 36 1997 pp 536 542

kontsevich s graph complex grt and the deformation complex of the sheaf of polyvector fields we generalize kontsevich s construction of l1 derivations of polyvector elds from the ane space to an arbitrary smooth algebraic variety more precisely we construct a map in the homotopy category from kontsevich s graph complex to the deformation complex of the sheaf of polyvector elds on a smooth algebraic variety we show that the action of deligne drinfeld

cuspidal plane curves syzygies and a bound on the mw rank abstract let c z f be a reduced plane curve of degree 6k with only nodes and ordinary cusps as singularities let i be the ideal of the points where c has a cusp let s b i s a i s s i be a minimal resolution of i we show that b i 5 k from this we obtain that the mordell weil rank of the elliptic threefold w y 2 x 3 f equals 2 i b i 5 k using this we find an upper bound for the mordell weil rank of w which is 1 18 125 73 2302 106 73 k l o t and we find an upper bound for the exponent of t 2 t 1 in the alexander polynomial of c which is 1 36 125 73 2302 106 73 k l o t this improves a recent bound of cogolludo and libgober almost by a factor 2

from atiyah classes to homotopy leibniz algebras a celebrated theorem of kapranov states that the atiyah class of the tangent bundle of a complex manifold x makes t x 1 into a lie algebra object in d x the bounded below derived category of coherent sheaves on x furthermore kapranov proved that for a kahler manifold x the dolbeault resolution omega bullet 1 t x 1 0 of t x 1 is an l algebra in this paper we prove that kapranov s theorem holds in much wider generality for vector bundles over lie pairs given a lie pair l a i e a lie algebroid l together with a lie subalgebroid a we define the atiyah class e of an a module e as the obstruction to the existence of an a compatible l connection on e we prove that the atiyah classes l a and e respectively make l a 1 and e 1 into a lie algebra and a lie algebra module in the bounded below derived category d mathcal a where mathcal a is the abelian category of left mathcal u a modules and mathcal u a is the universal enveloping algebra of a moreover we produce a homotopy leibniz algebra and a homotopy leibniz module stemming from the atiyah classes of l a and e and inducing the aforesaid lie structures in d mathcal a

approximation of elliptic control problems in measure spaces with sparse solutions optimal control problems in measure spaces governed by elliptic equations are considered for distributed and neumann boundary control which are known to promote sparse solutions optimality conditions are derived and some of the structural properties of their solutions in particular sparsity are discussed a framework for their approximation is proposed which is efficient for numerical computations and for which we prove convergence and provide error estimates

the geometry of sporadic c embeddings into c2 abstract a closed algebraic embedding of c c 1 0 into c 2 is sporadic if for every curve a c 2 isomorphic to an affine line the intersection with c is at least 2 non sporadic embeddings have been classified there are very few known sporadic embeddings we establish geometric and algebraic tools to classify them based on the analysis of the minimal log resolution x d p 2 u where u is the closure of c on p 2 we show in particular that one can choose coordinates on c 2 in which the type at infinity of the c and the self intersection of its proper transform on x are sharply limited

a quasi infinite horizon nonlinear model predictive control scheme with guaranteed stability we present in this paper a novel nonlinear model predictive control scheme that guarantees asymptotic closed loop stability the scheme can be applied to both stable and unstable systems with input constraints the objective functional to be minimized consists of an integral square error ise part over a finite time horizon plus a quadratic terminal cost the terminal state penalty matrix of the terminal cost term has to be chosen as the solution of an appropriate lyapunov equation furthermore the setup includes a terminal inequality constraint that forces the states at the end of the finite prediction horizon to lie within a prescribed terminal region if the jacobian linearization of the nonlinear system to be controlled is stabilizable we prove that feasibility of the open loop optimal control problem at time t 0 implies asymptotic stability of the closed loop system the size of the region of attraction is only restricted by the requirement for feasibility of the optimization problem due to the input and terminal inequality constraints and is thus maximal in some sense

real time nonlinear optimization as a generalized equation we establish results for the problem of tracking a time dependent manifold arising in real time optimization by casting this as a parametric generalized equation we demonstrate that if points along a solution manifold are consistently strongly regular it is possible to track the manifold approximately by solving a single linear complementarity problem lcp at each time step we derive sufficient conditions guaranteeing that the tracking error remains bounded to second order with the size of the time step even if the lcp is solved only approximately we use these results to derive a fast augmented lagrangian tracking algorithm and demonstrate the developments through a numerical case study

on surfaces of general type with maximal albanese dimension abstractgiven a minimal surface s equipped with a generically nite map to an abelianvariety and c s a rational or an elliptic curve we show that the canonical degreeof c is bounded by four times the self intersection of the canonical divisor of s asa corollary we obtain the niteness of rational and elliptic curves with an optimaluniform bound on their canonical degrees on any surface of general type with twolinearly independent regular one forms 1 1 introduction the object of this paper is to give an e ective bound on the canonical degrees of rationaland elliptic curves on a minimal surface of general type with generically nite albanese maplinearly in terms of the canonical volume of the surface here the canonical degree is thedegree with respect to the canonical polarization of the surface and the self intersection ofthis polarization is the canonical volume we will work in the complex analytic setting so that all varieties are complex analytic wewill assume the rudiments from the the theory of classi cation of complex projective surfacesas found for example in 3 we call a smooth projective surface to be of maximal albanesedimension if its albanese map is generically nite n b this terminology is di erent fromthat introduced in 21 we recall that any smooth projective surface s of maximal albanesedimension admits a morphism to a minimal one whose canonical divisor pulls back to thepositive part p of the zariski decomposition of the canonical divisor k of s and the canonicalvolume of s is by de nition vol k p

experimental design for biological systems many problems in biology are governed by a dynamical system of differential equations with unknown parameters to have a meaningful representation of the system these parameters need to be evaluated from observations experimentalists face the dilemma between accuracy of the parameters and costs of an experiment the choice of the design of an experiment is important if we are to recover precise model parameters it is important to know when and what kind of observations should be taken taking the wrong measurement can lead to inaccurate estimation of parameters thus resulting in inaccurate representations of the dynamical system each experiment has its own specific challenges however optimization methods form the basic computational tool to address eminent questions of optimal experimental design in this paper we present a methodology for the design of such experiments that can optimally recover parameters in a dynamical system biological systems in particular we show that the problem can be cast as a stochastic bilevel optimization problem we then develop an effective algorithm that allows for the solution of the design problem the advantages of our approach are demonstrated on a few basic biological models as well as a design problem for the energy metabolism to estimate insulin resistance

when is the self intersection of a subvariety a fibration abstract we provide a necessary and sufficient condition for the derived self intersection of a smooth subscheme inside a smooth scheme to be a fibration over the subscheme as a consequence we deduce a generalized hkr isomorphism we also investigate the relationship of our result to path spaces in homotopy theory buchweitz flenner formality in algebraic geometry and draw parallels with similar results in lie theory and symplectic geometry

partitioned variable metric updates for large structured optimization problems this paper presents a minimization method based on the idea of partitioned updating of the hessian matrix in the case where the objective function can be decomposed in a sum of convex element functions this situation occurs in a large class of practical problems including nonlinear finite elements calculations some theoretical and algorithmic properties of the update are discussed and encouraging numerical results are presented

lyapunov spectrum of ball quotients with applications to commensurability questions we determine the lyapunov spectrum of ball quotients arising from cyclic coverings the computations are performed by rewriting the sum of lyapunov exponents as ratios of intersection numbers and by the analysis of the period map near boundary divisors as a corollary we complete the classification of commensurability classes of all presently known non arithmetic ball quotients

on the local convergence of adjoint broyden methods the numerical solution of nonlinear equation systems is often achieved by so called quasi newton methods they preserve the rapid local convergence of newton s method at a significantly reduced cost per step by successively approximating the system jacobian though low rank updates we analyze two variants of the recently proposed adjoint broyden update which for the first time combines the classical least change property with heredity on affine systems however the new update does require the evaluation of so called adjoint vectors namely products of the transposed jacobian with certain dual direction vectors the resulting quasi newton method is linear contravariant in the sense of deuflhard newton methods for nonlinear equations springer heidelberg 2006 and it is shown here to be locally and q superlinearly convergent our numerical results on a range of test problems demonstrate that the new method usually outperforms newton s and broyden s method in terms of runtime and iterations count respectively

a sparse control approach to optimal sensor placement in pde constrained parameter estimation problems we present a systematic approach to the optimal placement of finitely many sensors in order to infer a finite dimensional parameter from point evaluations of the solution of an associated parameter dependent elliptic pde the quality of the corresponding least squares estimator is quantified by properties of the asymptotic covariance matrix depending on the distribution of the measurement sensors we formulate a design problem where we minimize functionals related to the size of the corresponding confidence regions with respect to the position and number of pointwise measurements the measurement setup is modeled by a positive borel measure on the spatial experimental domain resulting in a convex optimization problem for the algorithmic solution a class of accelerated conditional gradient methods in measure space is derived which exploits the structural properties of the design problem to ensure convergence towards sparse solutions convergence properties are presented and the presented results are illustrated by numerical experiments

optimal bounds for t singularities in stable surfaces abstract we explicitly bound t singularities on normal projective surfaces w with one singularity and k w ample this bound depends only on k w 2 and it is optimal when w is not rational we classify and realize surfaces attaining the bound for each nonnegative kodaira dimension of the minimal resolution of w this answers effectiveness of bounds see 1 2 17 for those surfaces