transition system specifications with negative premises abstract in this article the general approach to plotkin style operational semantics of groote and vaandrager 1989 is extended to transition system specifications tsss with rules that may contain negative premises two problems arise firstly the rules may be inconsistent and secondly it is not obvious how a tss determines a transition relation we present a general method based on the stratification technique in logic programming to prove consistency of a set of rules and we show how a specific transition relation can be associated with a tss in a natural way then a special format for the rules the ntyft ntyxt format is defined it is shown that for this format three important theorems hold the first theorem says that bisimulation is a congruence if all operators are defined using this format the second theorem states that under certain restrictions a tss in ntyft format can be added conservatively to a tss in pure ntyft ntyxt format finally it is shown that the trace congruence for image finite processes induced by the pure ntyft ntyxt format is precisely bisimulation equivalence

well structured transition systems everywhere well structured transition systems wstss are a general class of infinite state systems for which decidability results rely on the existence of a well quasi ordering between states that is compatible with the transitions in this article we provide an extensive treatment of the wsts idea and show several new results our improved definitions allow many examples of classical systems to be seen as instances of wstss

a remark on computing distance functions we propose a new method for the reconstruction of the signed distance function in the context of level set methods the new method is a modification of the algorithm which makes use of the pde equation for the distance function introduced by m sussman p smereka and s osher 1994 j comput phys 119 146 it is based mainly on the use of a truly upwind discretization near the interface comparison with the previous algorithm shows a definite improvement when used with a first order upwind scheme the method provides first order accuracy for the signed distance function in the whole computational domain and second order accuracy in the location of the interface a second order version of the method is also presented

on converse and saturation results for tikhonov regularization of linear ill posed problems in this paper we prove some new converse and saturation results for tikhonov regularization of linear ill posed problems tx y where t is a linear operator between two hilbert spaces

adjoint active surfaces for localization and imaging this paper addresses the problem of localizing and segmenting regions embedded within a surrounding medium by characterizing their boundaries as opposed to imaging the entirety of the volume active surfaces are used to directly reconstruct the shape of the region of interest we describe the procedure for finding the optimal surface which is computed iteratively via gradient descent that exploits the sensitivity of an error minimization functional to changes of the active surface in doing so we introduce the adjoint model to compute the sensitivity and in this respect the method shares common ground with several other disciplines such as optimal control finally we illustrate the proposed active surface technique in the framework of wave propagation governed by the scalar helmholtz equation potential applications include electromagnetics acoustics geophysics nondestructive testing and medical imaging

reconstruction of shapes and impedance functions using few far field measurements we consider the reconstruction of complex obstacles from few far field acoustic measurements the complex obstacle is characterized by its shape and an impedance function distributed along its boundary through robin type boundary conditions this is done by minimizing an objective functional which is the l 2 distance between the given far field information g and the far field of the scattered wave u corresponding to the computed shape and impedance function we design an algorithm to update the shape and the impedance function alternatively along the descent direction of the objective functional the derivative with respect to the shape or the impedance function involves solving the original helmholtz problem and the corresponding adjoint problem where boundary integral methods are used further we implement level set methods to update the shape of the obstacle to combine level set methods and boundary integral methods we perform a parametrization step for a newly updated level set function in addition since the computed shape derivative is defined only on the boundary of the obstacle we extend the shape derivative to the whole domain by a linear transport equation finally we demonstrate by numerical experiments that our algorithm reconstruct both shapes and impedance functions quite accurately for non convex shape obstacles and constant or non constant impedance functions the algorithm is also shown to be robust with respect to the initial guess of the shape the initial guess of the impedance function and even large percentage of noise

the measurement of surface cracks in metals by using a c electric fields this paper describes some recent studies associated with the development of an instrument the crack microgauge at university college london for the detection and measurement of surface cracks in metals by using a c electric currents in the metal surface the design of the instrument has enhanced the accuracy of measurement of surface voltages in the neighbourhood of surface breaking cracks to the point where it is now advantageous to consider the distribution of surface voltages by mathematical analysis this enables better use to be made of the instrument since measurements can then be more accurately interpreted in terms of crack size and geometry in contrast earlier applications of the method relied on the calibration of the instruments against test blocks the first generation of users of the crack microgauge interpreted their readings according to a simple one dimensional normal crack model this however is an oversimplification for cracks of finite aspect ratio and it leads to underestimates of centre line crack depth typically of the order of 30 40 when the aspect ratio is about 3 the first major contribution of the theory was therefore to provide a model for surface current flow around cracks of finite aspect ratio for this purpose a useful unfolding theorem was deduced in cases in which the current skin depth is small compared with crack dimensions this allows the surface field to be unfolded into a plane distribution of potential satisfying laplace s equation and it enables us to obtain solutions for many different crack shapes by using standard mathematical methods an account of these developments is given in xi 2 of this paper the unfolding of the surface field gives the global distribution of surface current around a crack that is on the length scale of the crack dimensions on the length scale of the skin depth however the solutions need modification in the neighbourhood of the surface and interior edges of the crack in developing the unfolding theorem it was argued that these modifications which we describe as corner solutions could be neglected the purpose of this paper is to construct these corner solutions to confirm that this is so the mathematical theory described in xi 2 was developed for the most important case in which cracks develop in planes perpendicular to the surface of the metal it is clear from the construction of that solution however that the unfolding may be applied with the same result to plane cracks inclined to the surface thus the global solution is not able to distinguish the inclination of the crack plane to the surface we shall find however that the corner solutions are sensitive to this inclination and they are given in s 3 for arbitrary angles of inclination these studies suggest therefore that information on crack inclination could be deduced from experimental investigation of these corner solutions since the solutions are found to possess a phase of frac 1 4 pi it might be possible to extract this information by measuring perturbation signals in quadrature with the main field or perhaps by increasing the skin depth so that the scale of the solutions is enhanced for a given specimen this could be done by reducing the frequency of the a c field but if the frequency is reduced significantly the field distributes itself through the interior of the specimen on the scale of the crack dimensions and may no longer be described as a surface distribution further work to describe such field distributions when the skin depth is of the order of the crack depths is in progress

ordered sos process languages for branching and eager bisimulation we present a general and uniform method for defining structural operational semantics sos of process operators by traditional plotkin style transition rules equipped with orderings this new feature allows one to control the order of application of rules when deriving transitions of process terms our method is powerful enough to deal with rules with negative premises and copying we show that rules with orderings called ordered sos rules have the same expressive power as gsos rules we identify several classes of process languages with operators defined by rules with and without orderings in the setting with silent actions and divergence we prove that branching bisimulation and eager bisimulation relations are preserved by all operators in process languages in the relevant classes

mixed normal superconducting states in the presence of strong electric currents we study the ginzburg landau equations in the presence of large electric currents that are smaller than the critical current where the normal state loses its stability for steady state solutions in the large kappa limit we prove that the superconductivity order parameter is exponentially small in a significant part of the domain and simply small in the rest of it similar results are obtained for the time dependent problem in continuation of the paper by the two first authors 3 we conclude by obtaining some weaker results albeit similar for steady state solutions in the large domain limit

decoupling elastic waves and its applications abstract in this paper we consider time harmonic elastic wave scattering governed by the lame system it is known that the elastic wave field can be decomposed into the shear and compressional parts namely the pressure and shear waves that are generally coexisting but propagating at different speeds we consider the third or fourth kind impenetrable scatterer and derive two geometric conditions respectively related to the mean and gaussian curvatures of the boundary surface of the scatterer that can ensure the decoupling of the shear and pressure waves the decoupling results are new to the literature and are of significant interest for their own sake as an interesting application we apply the decoupling results to the uniqueness and stability analysis for inverse elastic scattering problems in determining polyhedral scatterers by a minimal number of far field measurements

level set based topology optimization for electromagnetic dipole antenna design this paper presents a level set framework for a typical electromagnetic design problem of dipole antenna in this study the geometrical configuration of an antenna is represented by the zero level contour of a higher dimensional level set function the governing equation for the induced current flow on a metal surface is the electric field integral equation efie which takes into account the electric component of the incident wave the design objective is formulated in terms of the surface current and incident electric field the normal velocity of the level set model which reflects the sensitivity of the objective function is derived from the adjoint variable method and shape derivative by optimizing the objective function the area with the highest current density to which the voltage feeding should be applied can be reshaped the advantages of adopting the level set technique for electromagnetic design lie in its capacity for capturing sophisticated topological changes and facilitation in mathematical representation of the design configuration the demonstrative examples of dipole antenna design show that the level set method results in a fairly smooth optimization process where the vacuum metal interface gradually attains its optimal configuration a series of design cases with self adjoint and non self adjoint sensitivity analyses are studied and compared to the benchmarking problems in dipole antenna

elan from a rewriting logic point of view elan implements computational systems a concept that combines two first class entities rewrite rules and rewriting strategies elan can be used either as a logical framework or to describe and execute deterministic as well as non deterministic rule based processes with the general goal to make precise a rewriting logic based semantics of elan this paper has three contributions a presentation of the concepts of rules and strategies available in elan an expression of rewrite rules with matching conditions in conditional rewriting logic and finally an enrichment mechanism of a rewrite theory into a strategy theory in conditional rewriting logic

potential theory on lipschitz domains in riemannian manifolds sobolev besov space results and the poisson problem abstract we continue a program to develop layer potential techniques for pde on lipschitz domains in riemannian manifolds building on l p and hardy space estimates established in previous papers here we establish sobolev and besov space estimates on solutions to the dirichlet and neumann problems for the laplace operator plus a potential on a lipschitz domain in a riemannian manifold with a metric tensor smooth of class c 1 for some 0 we treat the inhomogeneous problem and extend it to the setting of manifolds results obtained for the constant coefficient laplace operator on a lipschitz domain in euclidean space with the dirichlet boundary condition by d jerison and c kenig

integrated regulatory networks irns spatially organized biochemical modules in this paper we aim at modeling and analyzing the regulation processes in multi cellular biological systems in particular tissues the modeling framework is a generalization of several existing formalisms in particular it can be seen as an extension of logical regulatory networks a la thomas with information about cells physical state and environment e g their spatial relationships the resulting formalisms called integrated regulatory networks irns is equipped with a transition systems semantics that preserves the possibility of an enumerative and exhaustive state space exploration this paper presents the modeling framework its semantics as well as a prototype implementation that allowed preliminary experiments on some applications related to biology

bisimulation can t be traced in the concurrent language ccs two programs are considered the same if they are bisimilar several years and many researchers have demonstrated that the theory of bisimulation is mathematically appealing and useful in practice however bisimulation makes too many distinctions between programs we consider the problem of adding operations to ccs to make bisimulation fully abstract we define the class of gsos operations generalizing the style and technical advantages of ccs operations we characterize gsos congruence in as a bisimulation like relation called ready simulation bisimulation is strictly finer than ready simulation and hence not a congruence for any gsos language

the singular sources method for an inverse problem with mixed boundary conditions we use the singular sources method to detect the shape of the obstacle in a mixed boundary value problem the basic idea of the method is based on the singular behavior of the scattered field of the incident point sources on the boundary of the obstacle moreover we take advantage of the scattered field estimate by the backprojection operator also we give a uniqueness proof for the shape reconstruction

conditional stability in an inverse problem of determining a non smooth boundary an inverse problem for determining an unknown boundary is discussed we prove conditional stability of logarithmic type for unknown lipschitz boundaries under a priori assumptions the proof is based on estimation of harmonic measures

an axiomatic semantics for esterel in this paper we propose an axiomatic semantics for the synchronous language esterel we begin with giving a structural operational semantics for esterel in terms of a labeled transition system lts we prove that bisimulation on lts states which correspond to esterel programs is a congruence and that our lts reflects the input output behavior of programs so bisimilar programs are distinguished neither by any esterel context nor by the external environment and bisimulation is a reasonable notion of behavioral equivalence in order to characterize equivalent programs we give a set of axioms and we prove that they induce an axiomatization over esterel which is sound and complete modulo bisimulation

stability for an inverse problem in potential theory let d be a subdomain of a bounded domain in r n the conductivity coefficient of d is a positive constant k 1 and the conductivity of d is equal to 1 for a given current density g on we compute the resulting potential u and denote by f the value of u on the general inverse problem is to estimate the location of d from the known measurements of the voltage f if d h is a family of domains for which the hausdorff distance d d d h equal to o h h small then the corresponding measurements f h are o h close to f

balanced risk set matching a new form of matching optimal balanced risk set matching is applied in an observational study of a treatment cystoscopy and hydrodistention given in response to the symptoms of the chronic nonlethal disease interstitial cystitis when a patient receives the treatment at time t that patient is matched to another patient with a similar history of symptoms up to time t who has not received the treatment up to time t this is risk set matching by using a penalty function in integer programming in a new way we force the marginal distributions of symptoms to be balanced in the matched treated and control groups among all balanced matchings we pick the one that is optimal in the sense of minimizing the multivariate pretreatment covariate distance within matched pairs under a simple model for the treatment assignment mechanism we study the sensitivity of the findings to hidden biases in particular we show that a simple conventional sensitivity analysis is appropriate with risk set matching when the

reconstruction of the shape and surface impedance from acoustic scattering data for an arbitrary cylinder the inverse scattering for an obstacle d subset r 2 with mixed boundary condition can be considered as a prototype for radar detection of complex obstacles with coated and noncoated parts of the boundary we construct some indicator functions for this inverse problem using the far field pattern directly without the necessity of transforming the far field to the near field based on careful singularity analysis these indicator functions enable us to reconstruct the shape of the obstacle and distinguish the coated from the noncoated part of the boundary moreover an explicit representation formula for the surface impedance in the coated part of the boundary is also given our reconstruction scheme reveals that the coated part of the obstacle is less visible than the noncoated one which corresponds to the physical fact that the coated boundary absorbs some part of the scattered wave numerics are presented for the reconstruction formulas which show that both the boundary shape and the surface impedan

on stability for a translated obstacle with impedance boundary condition abstract this paper considers an inverse problem of determining the location of a known obstacle and its boundary impedance from one or two incident waves we firstly derive a concrete formula of the far field pattern due to a translation of the obstacle and perturbation of its boundary impedance based on this formula we establish lipschitz stability for the recovery of translation of an obstacle with one incident wave in the special case of obstacle being a ball lipschitz stability for the recovery of both location and its boundary coefficient can be obtained using two incident waves

optimal stability for the inverse problemof multiple cavities abstract we deal with the determination of finitely many cavities in a planar inhomogeneous conductor from one current and voltage measurement collected on the exterior boundary we prove stability estimates under essentially minimal a priori regularity assumptions we construct an explicit example showing the optimality of such stability estimates

recent developments in inverse acoustic scattering theory we survey some of the highlights of inverse scattering theory as it has developed over the last 15 years with emphasis on uniqueness theorems and reconstruction algorithms for time harmonic acoustic waves included in our presentation are numerical experiments using real data and numerical examples of the use of inverse scattering methods to detect buried objects

a new non iterative singular sources method for the reconstruction of piecewise constant media we describe a novel non iterative method for the reconstruction of a piecewise constant inhomogeneous medium in acoustic scattering which we call the singular sources method the basic idea of the method is to use the behaviour of the scattered field for singular incident fields multipoles to calculate the size of the refractive index n at some point z0 on the boundary of the support of the scatterer and then eliminate this value from the data by subtracting a known piecewise constant background medium the paper includes the theory for the singular sources method to locate the unknown support of an inhomogeneous medium for a known inhomogeneous background medium also we give a new uniqueness proof for the reconstruction of a piecewise constant medium in two or three dimensions using techniques that differ from those used to prove previous well known results

a conservative look at operational semantics with variable binding we set up a formal framework to describe transition system specifications in the style of plotkin this framework has the power to express many sortedness general binding mechanisms and substitutions among other notions such as negative hypotheses and unary predicates on terms the framework is used to present a conservativity format in operational semantics which states sufficient criteria to ensure that the extension of a transition system specification with new transition rules does not affect the semantics of the original terms

stability estimates for obstacles in inverse scattering abstract in this paper we estimate distances between two soft obstacles in terms of corresponding scattering amplitudes the estimate is of logarithmic type and it is obtained by using estimates for continuation of solutions of elliptic equations and some methods of potential theory scattering amplitudes are given for one frequency comparable with size of scatterer and for all directions of receiver

stable determination of a crack from boundary measurements we treat the problem of determining a crack inside a conductor when two pairs of current and voltage boundary measurements are given we prove a theorem of continuous dependence from the data

component identification in biochemical pathways biochemical pathways are abstract descriptions of the interactions among the molecular species involved in a cellular process different molecular species mentioned in a pathway often represent different states of the same biological entity such as the unbound and bound states of a certain molecule hence a pathway can be seen as a network of interactions between entities changing state synchronously by means of reactions we consider such biological entities as pathway components we define a semi automatic algorithm to infer the components from their interactions described in the pathway in case the interactions are not sufficient to resolve all the reactions help from a domain expert may be needed to resolve any ambiguity that should arise as an example of application we apply the algorithm to a model of the egf signaling pathway from the literature in order to identify its components from the theoretical point of view we formally prove the correctness of the algorithm its termination under any input pathway and a weak confluence property

a multiwave range test for obstacle reconstructions with unknown physical properties we develop a new multiwave version of the range test for shape reconstruction in inverse scattering theory the range test r potthast et al a range test for determining scatterers with unknown physical properties inverse problems 19 3 2003 533 547 has originally been proposed to obtain knowledge about an unknown scatterer when the far field pattern for only one plane wave is given here we extend the method to the case of multiple waves and show that the full shape of the unknown scatterer can be reconstructed we further will clarify the relation between the range test methods the potential method a kirsch r kress on an integral equation of the first kind in inverse acoustic scattering in inverse problems oberwolfach 1986 internationale schriftenreihe zur numerischen mathematik vol 77 birkhauser basel 1986 pp 93 102 and the singular sources method r potthast point sources and multipoles in inverse scattering theory habilitation thesis gottingen 1999 in particular we propose a new version of the kirsch kress method using the range test and a new approach to the singular sources method based on the range test and potential method numerical examples of reconstructions for all four methods are provided

signed rank statistics for coherent predictions a generalization of wilcoxon s signed rank test is proposed for testing a dose response relationship with one or more outcomes the test is useful in matched observational studies or in nonrandomized experiments that use dose response relationships and predictions about multiple outcomes in an effort to distinguish actual treatment effects from hidden biases a sensitivity analysis indicating whether a dose response relationship or multiple predictions are confirmed with sufficient strength to reduce sensitivity to hidden bias is performed together the test and the sensitivity analysis help to quantify the degree to which a coherent pattern of associations is present or absent and the degree to which this strengthens or fails to strengthen evidence of cause and effect formal properties of tests of this kind are examined the form of the optimal test is determined though this test is not usable because it depends upon the values of the unknown parameters under study also examined are the conditions under which the proposed test resembles the optimal test as well as the impact of various violations of those conditions on power an example involving matched pairs exposed to varying doses of cadmium is considered in detail

stability estimates and reconstructions in inverse acoustic scattering using singular sources abstract the problem of stability for the reconstruction of the scattered field us in the exterior of a scatterer d from far field data u and for the reconstruction of a sound soft or sound hard scatterer d from the far field pattern u x d x d for all incident plane waves is investigated in particular we show how stability estimates are linked to the behaviour of the scattered field s for incident point sources and to special minimum norm solutions for the herglotz wave operator the results can also be used to formulate a method of singular sources for the reconstruction of d which is new in inverse scattering the reconstruction method is described and numerical examples are provided

an adaptive greedy technique for inverse boundary determination problem in this paper the method of fundamental solutions mfs is employed for determining an unknown portion of the boundary from the cauchy data specified on parts of the boundary we propose a new numerical method with adaptive placement of source points in the mfs to solve the inverse boundary determination problem since the mfs source points placement here is not trivial due to the unknown boundary we employ an adaptive technique to choose a sub optimal arrangement of source points on various fictitious boundaries afterwards the standard tikhonov regularization method is used to solve ill conditional matrix equation while the regularization parameter is chosen by the l curve criterion the numerical studies of both open and closed fictitious boundaries are considered it is shown that the proposed method is effective and stable even for data with relatively high noise levels

a convergence analysis of the landweber iteration for nonlinear ill posed problems in this paper we prove that the landweber iteration is a stable method for solving nonlinear ill posed problems for perturbed data with noise level delta we propose a stopping rule that yields the convergence rate o delta 1 2 under appropriate conditions we illustrate these conditions for a few examples

inverse scattering by a continuation method with initial guesses from a direct imaging algorithm a novel continuation method is presented for solving the inverse medium scattering problem of the helmholtz equation which is to reconstruct the shape of the inhomogeneous medium from boundary measurements of the scattered field the boundary data is assumed to be available at multiple frequencies initial guesses are chosen from a direct imaging algorithm multiple signal classification music along with a level set representation at a certain wavenumber where the born approximation may not be valid each update via recursive linearization on the wavenumbers is obtained by solving one forward and one adjoint problem of the helmholtz equation

cpo models for compact gsos languages in this paper we present a general way of giving denotational semantics to a class of languages equipped with an operational semantics that fits the gsos format of bloom istrail and meyer the canonical model used for this purpose will be abramsky s domain of synchronization trees and the denotational semantics automatically generated by our methods will be guaranteed to be fully abstract with respect to the finitely observable part of the bisimulation preorder in the process of establishing the full abstraction result we also obtain several general results on the bisimulation preorder including a complete axiomatization for it and give a novel operational interpretation of gsos languages

mathematical analysis of scattering problems for partially coated obstacles and cracks we consider the scattering problem of time harmonic electromagnetic waves from an infinite cylinder having an open arc and a bounded domain in r2 as cross section to this end we solve a mixed scattering problem for the helmholtz equation in r2 where the scattering object is a combination of an open arc and a bounded obstacle d the well posedness of the solution to the direct scattering problem is established by using the boundary integral equation method and the fredholm theory

a rewriting logic framework for operational semantics of membrane systems existing results in membrane computing refer mainly to p systems characterization of turing computability also to some polynomial solutions to np complete problems by using an exponential workspace created in a biological way in this paper we define an operational semantics of a basic class of p systems and give two implementations of the operational semantics using rewriting logic we present some results regarding these implementations including two operational correspondence results and discuss why these implementations are relevant in order to take advantage of good features of both structural operational semantics and rewriting logic

design sensitivity in observational studies summary outside the field of statistics the literature on observational studies offers advice about research designs or strategies for judging whether or not an association is causal such as multiple operationalism or a dose response relationship these useful suggestions are typically informal and qualitative a quantitative measure design sensitivity is proposed for measuring the contribution such strategies make in distinguishing causal effects from hidden biases several common strategies are then evaluated in terms of their contribution to design sensitivity a related method for computing the power of a sensitivity analysis is also developed

on the electro sensing of weakly electric fish in this paper we are interested in electro sensing inverse problems our objective is to understand the electro perception mechanism of weakly electric fish these species of fish have the ability to recognize the environment around them in complete darkness by generating a weak electrical field at different frequencies and perceiving the transdermal potential perturbation assuming that the target has a known conductivity profile the electro sensing inverse problem consists in recovering the shape and location of the target from measurements of the electric potential over the skin using an original spectral decomposition of the solution to the direct problem in terms of poincare vari ational eigenfunctions we retrieve the cauchy data of the electric potential over the fish skin corresponding to the case where we substitute the target by a perfect conductor with the same shape and position we then identify the target from the recovered cauchy data we derive uniqueness and stability estimates to the considered electro sensing inverse problem the numerical validation of our theoretical approach is realized by reconstructing different targets using synthetic data in dimension two the numerical experiments are conducted using gradient descent optimization algorithms

growth estimates in the hardy sobolev space of an annular domain with applications abstract we give an explicit estimate on the growth of functions in the hardy sobolev space h k 2 g s of an annulus we apply this result first to find an upper bound on the rate of convergence of a recovery interpolation scheme in h 1 2 g s with points located on the outer boundary of g s we also apply this result for the study of a geometric inverse problem namely we derive an explicit upper bound on the area of an unknown cavity in a bounded planar domain from the difference of two electrostatic potentials measured on the boundary when the cavity is present and when it is not

compositional semantics and behavioral equivalences for p systems the aim of the paper is to give a compositional semantics in the style of the structural operational semantics sos and to study behavioral equivalence notions for p systems firstly we consider p systems with maximal parallelism and without priorities we define a process algebra called p algebra whose terms model membranes we equip the algebra with a labeled transition system lts obtained through sos transition rules and we study how some equivalence notions defined over the lts model apply in our case then we consider p systems with priorities and extend the introduced framework to deal with them we prove that our compositional semantics reflects correctly maximal parallelism and priorities

characterization of surface breaking cracks in metal sheets by using ac electric fields a surface breaking crack in a metal sheet may be detected by passing an alternating current through the sheet and making measurements of the potential difference on the sheet s surface the distribution of potential on the metal surface depends on the exact geometry of the crack and the aim of this work is to predict the shape and size of a surface breaking crack from the potential distribution the theoretical model is formulated using the potential and streamfunction as the independent variables and the shape of the lower edge of the crack is determined from the solution of a fredholm integral equation of the first kind this is solved using a minimization technique which suppresses the instability of the equation the method is tested using theoretical distributions of potential from known crack shapes and very good agreement is obtained in each case

a multi frequency inverse source problem this paper is concerned with an inverse source problem that determines the source from measurements of the radiated fields away at multiple frequencies rigorous stability estimates are established when the background medium is homogeneous it is shown that the ill posedness of the inverse problem decreases as the frequency increases under some regularity assumptions on the source function it is further proven that by increasing the frequency the logarithmic stability converts to a linear one for the inverse source problem

stable determination of a scattered wave from its far field pattern the high frequency asymptotics we deal with the stability issue for the determination of outgoing time harmonic acoustic waves from their far field patterns we are especially interested in keeping as explicit as possible the dependence of our stability estimates on the wavenumber of the corresponding helmholtz equation and in understanding the high wavenumber that is frequency asymptotics applications include stability results for the determination from far field data of solutions of direct scattering problems with sound soft obstacles and an instability analysis for the corresponding inverse obstacle problem the key tool consists of establishing precise estimates on the behavior of hankel functions with large argument or order

simulation of spatial p system models spatial p systems are an extension of the p systems formalism in which objects and membranes are embedded into a two dimensional discrete space spatial p systems are characterised by the distinction between ordinary objects and mutually exclusive objects with the constraint that any position can accommodate any number of ordinary objects and at most one mutually exclusive object the presence of mutually exclusive objects makes the simulation of spatial p system models more complex than that of standard p systems in this paper we present a polynomial time algorithm for the simulation of a restricted version of spatial p systems where the restriction consists in considering only mutually exclusive objects and rules having exactly one reactant and one product this version of spatial p systems although very restricted is expressive enough to model interesting biological systems in particular we show how it can be used to simulate two models describing different dynamics of fish populations namely the dynamics of territorial fish and the formation and movement of herring schools in addition the simulation methodology we propose can be adapted to simulate richer versions of spatial p systems

stability of the recovery of surface impedances in inverse scattering abstract the inverse problem we consider is to determine the surface impedance on the boundary of a known obstacle from a knowledge of the far field pattern for the scattering of incident time harmonic plane waves it is well known that this problem has a unique solution 2 but is ill posed 3 we show in this paper that this inverse problem becomes well posed provided that we have an a priori upper bound of the c 1 norm of the surface impedance

numerical implementations of dynamical probe method for non stationary heat equation the dynamical probe method for non stationary heat equation is developed recently which aims to detect an unknown inclusion of conductive material from the boundary measurement data the runge approximation is used to define some indicator function for this method which is a mathematical testing machine to detect the inclusion a numerical realization of the runge approximation is the key to this method by using a regularizing method a realization scheme is given for the runge approximation and numerical examples are given to show the validity of the dynamical probe method

using well structured transition systems to decide divergence for catalytic p systems p systems are a biologically inspired model introduced by gheorghe paun with the aim of representing the structure and the functioning of the cell since their introduction several variants of p systems have been proposed and explored we concentrate on the class of catalytic p systems without priorities associated with the rules we show that the theory of well structured transition systems can be used to decide the divergence problem i e checking for the existence of an infinite computation for such a class of p systems as a corollary we obtain an alternative proof of the nonuniversality of deterministic catalytic p systems an open problem recently solved by ibarra and yen

structural optimization using sensitivity analysis and a level set method in the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level set method for front propagation we implement this method in two and three space dimensions for a model of linear or nonlinear elasticity we consider various objective functions with weight and perimeter constraints the shape derivative is computed by an adjoint method the cost of our numerical algorithm is moderate since the shape is captured on a fixed eulerian mesh although this method is not specifically designed for topology optimization it can easily handle topology changes however the resulting optimal shape is strongly dependent on the initial guess

analytic extension and reconstruction of obstacles from few measurements for elliptic second order operators we deal with an inverse obstacle problem for general second order scalar elliptic operators with real principal part and analytic coefficients near the obstacle we assume that the boundary of the obstacle is a non analytic hypersurface we show that when we put dirichlet boundary conditions one measurement is enough to reconstruct the obstacle in the neumann case we have results only for n 2 3 in general more precisely we show that one measurement is enough for n 2 and we need 3 linearly independent inputs for n 3 however in the case for the helmholtz equation we only need n 1 linearly independent inputs for any n 2 here n is the dimension of the space containing the obstacle these are justified by investigating the analyticity properties of the zero set of a real analytic function in addition we give a reconstruction procedure for each case to recover the shape of obstacle although we state the results for the scattering problems similar results are true for the associated boundary value problems

sensitivity analysis for equivalence and difference in an observational study of neonatal intensive care units in randomized experiments it is sometimes important to demonstrate that two treatments do not differ greatly in their effects or to demonstrate that the treatments have very different effects on one outcome but similar effects on another outcome these demonstrations may take the form of rejecting a null hypothesis of inequivalence in an equivalence test or rejecting a null hypothesis of equal and inequivalent effects on two outcomes the procedures often express a complex hypothesis in terms of component hypotheses and combine the component significance levels to test the complex hypothesis if used in a randomized trial randomization provides valid significance levels for each component test and hence also for the combined procedure in an observational study that is in a study of treatments that were not randomly assigned there is typically concern that significance levels for testing hypotheses about treatment effects may be distorted by failure to control for some unobserved pretreatment cov

the problem of scattering by a partially coated crack abstract in this paper we consider the scattering of an electromagnetic time harmonic plane wave by an infinite cylinder having an open arc in r 2 as the cross section we assume that the arc is divided into two parts and one of the two parts is possibly coated on one side by a material with surface impedance applying potential theory the problem can be reformulated as a boundary integral system we obtain the existence and uniqueness of a solution to the system by using fredholm theory

stable determination of sound hard polyhedral scatterers by a minimal number of scattering measurements the aim of the paper is to establish optimal stability estimates for the determination of sound hard polyhedral scatterers in r n n 2 by a minimal number of far field measurements this work is a significant and highly nontrivial extension of the stability estimates for the determination of sound soft polyhedral scatterers by far field measurements proved by one of the authors to the much more challenging sound hard case the admissible polyhedral scatterers satisfy minimal a priori assumptions of lipschitz type and may include at the same time solid obstacles and screen type components in this case we obtain a stability estimate with n far field measurements important features of such an estimate are that we have an explicit dependence on the parameter h representing the minimal size of the cells forming the boundaries of the admissible polyhedral scatterers and that the modulus of continuity provided the error is small enough with respect to h does not depend on h if we restrict to n 2 3 and to polyhedral obstacles that is to polyhedra then we obtain stability estimates with fewer measurements namely first with n 1 measurements and then with a single measurement in this case the dependence on h is not explicit anymore and the modulus of continuity depends on h as well 2010 mathematics subject classification primary 74j20 74j25 secondary 35r30 35q74

convergence rates of a regularized newton method in sound hard inverse scattering the iteratively regularized gauss newton method is used to solve an inverse acoustic scattering problem with neumann boundary conditions in two space dimensions which is known to be nonlinear and severely ill posed some recent results on the speed of convergence for such problems are considered and numerical experiments yield logarithmic convergence rates as expected moreover we present an efficient method to numerically evaluate the frechet derivative using its characterization as a boundary value problem and prove fast convergence of this method

mathematical basis of scattering problems from penetrable obstacles and cracks we consider a kind of scattering problem which models the scattering of an electromagnetic time harmonic plane wave by an infinite cylinder having an open arc and a penetrable obstacle in r2 as cross section to this end we solve a scattering problem for the helmholtz equation in r2 where the scattering object is a combination of a crack and a penetrable obstacle d and we have dirichlet impedance type boundary condition on and transmission boundary condition on d applying potential theory the problem can be reformulated as a boundary integral system we establish the existence and uniqueness of a weak solution to the system by using the modified fredholm theory

recovering a polyhedral obstacle by a few backscattering measurements abstract we propose an inverse scattering scheme of recovering a polyhedral obstacle in r n n 2 3 by only a few high frequency acoustic backscattering measurements the obstacle could be sound soft or sound hard it is shown that the modulus of the far field pattern in the backscattering aperture possesses a certain local maximum behavior from which one can determine the exterior normal directions of the front sides faces then by using the phaseless backscattering data corresponding to a few incident plane waves with suitably chosen incident directions one can determine the exterior unit normal vector of each side face of the obstacle after the determination of the exterior unit normals the recovery is reduced to a finite dimensional problem of determining a location point of the obstacle and the distance of each side face away from the location point for the latter reconstruction we need to make use of the far field data with phases numerical experiments are also presented to illustrate the effectiveness of the proposed scheme

turning sos rules into equations abstract many process algebras are defined by structural operational semantics sos indeed most such definitions are nicely structured and fit the gsos format of bloom et al j assoc comput mach to appear we give a procedure for converting any gsos language definition to a finite complete equational axiom system possibly with one infinitary induction principle which precisely characterizes strong bisimulation of processes

conditional stability estimation for an inverse boundary problem with non smooth boundary in ℛ in this paper we investigate an inverse problem of determining a shape of a part of the boundary of a bounded domain in r3 by a solution to a cauchy problem of the laplace equation assuming that the unknown part is a lipschitz continuous surface we give a logarithmic conditional stability estimate in determining the part of boundary under reasonably a priori information of an unknown part the keys are the complex extension and estimates for a harmonic measure

numerical solution of an inverse obstacle scattering problem with near field data consider the scattering of an arbitrary time harmonic incident wave by a sound soft obstacle in this paper a novel method is presented for solving the inverse obstacle scattering problem of the two dimensional helmholtz equation which is to reconstruct the obstacle surface by using the near field data the obstacle is assumed to be a small and smooth perturbation of a disc the method uses the transformed field expansion to reduce the boundary value problem into a successive sequence of one dimensional problems which are solved in closed forms by dropping the higher order terms in the power series expansion and truncating the infinite linear system for the first order term the inverse problem is linearized and an approximate but explicit formula is obtained between the fourier coefficients of the solution and data a nonlinear correction algorithm is introduced to improve the accuracy of the reconstructions for large deformations numerical examples show that the method is simple efficient and stable to reconstruct the obstacle with subwavelength resolution

a novel two grid method for semilinear elliptic equations a new finite element discretization technique based on two coarse and fine subspaces is presented for a semilinear elliptic boundary value problem the solution of a nonlinear system on the fine space is reduced to the solution of two small one linear and one nonlinear systems on the coarse space and a linear system on the fine space it is shown both theoretically and numerically that the coarse space can be extremely coarse and still achieve asymptotically optimal approximation as a result the numerical solution of such a nonlinear equation is not significantly more expensive than the solution of one single linearized equation

a comparison of statecharts step semantics the paper studies some variants of statecharts step semantics in the framework of structural operational semantics the chosen framework allows to study precongruence and congruence properties of behavioral preorders and equivalences and to compare with respect to these properties the different step semantics considered

compositional semantics and behavioural equivalences for reaction systems with restriction abstract reaction systems are an abstract model of interactions among biochemical reactions developed around two opposite mechanisms facilitation and inhibition the evolution of a reaction system is driven by the external objects which are sent into the system by the environment at each step in order to increase the modelling expressiveness of the calculus we consider an extension of reaction systems with restriction which allows the hiding of entities such as those occurring inside membranes to this purpose we recently developed the reaction algebra a calculus resembling reaction systems extended with a restriction operator in the present paper three equivalent semantics for the reaction algebra are presented a reduction semantics and two state abstract compositional semantics the reduction semantics is meant to capture the behaviour of reaction algebra models at a high level while the two compositional semantics make the interactive nature of reaction systems explicit the difference between the two compositional semantics lies in how the behaviour with respect to the contextual entities is described one uses an extensional description while the other uses an intensional one we also define in the settings of both compositional semantics a behavioural equivalence subsuming the functional equivalence of reaction systems which is also shown to be congruence thus providing a formal ground to the modular description of models finally as an example of application of the techniques developed in the paper we compare the semantics of two different reaction algebra models of the functioning of the lac operon in the e coli bacterium

nodal sets of eigenfunctions on riemannian manifolds soit m n une variete connexe compacte a metrique riemannienne c soit le laplacien de m soit f une fonction propre reelle de de valeur propre on demontre que la fonction propre f s annule au plus a l ordre c 1 2 pour tout point dans m