reflective inductive inference of recursive functions in this paper we investigate reflective inductive inference of recursive functions a reflective iim is a learning machine that is additionally able to assess its own competence first we formalize reflective learning from arbitrary and from canonical example sequences here we arrive at four different types of reflection reflection in the limit optimistic pessimistic and exact reflection then we compare the learning power of reflective iims with each other as well as with the one of standard iims for learning in the limit for consistent learning of three different types and for finite learning

confident and consistent partial learning of recursive functions abstract partial learning is a criterion where the learner infinitely often outputs one correct conjecture while every other hypothesis is issued only finitely often this paper addresses two variants of partial learning in the setting of inductive inference of functions first confident partial learning requires that the learner also on those functions which it does not learn singles out exactly one hypothesis which is output infinitely often second essentially class consistent partial learning is partial learning with the additional constraint that on the functions to be learnt almost all hypotheses issued are consistent with all the data seen so far the results of the present work are that confident partial learning is more general than explanatory learning incomparable with behaviourally correct learning and closed under union essentially class consistent partial learning is more general than behaviourally correct learning and incomparable with confident partial learning furthermore it is investigated which oracles permit to learn all recursive functions under these criteria for confident partial learning some non high oracles are omniscient for essentially class consistent partial learning all pa complete and all oracles of hyperimmune turing degree are omniscient

mode coupling and generalized hydrodynamics in this paper a general hydrodynamic mode coupling theory of equilibrium fluctuations in simple liquids is developed from molecular considerations the approach developed hem avoids the shortcomings of previous mode coupling theories by adopting a complete hierarchy of equations for the slow modes of a hydrodynamic system and solving it formally through the n ordering approximation scheme developed previously by machta and oppenheim a series is obtained from the hierarchy of equations which allows the generalized transport coeffcicnts to be obtained exactly in the thermodynamic limit up to arbitrary order in the wavevector frequency and mode coupling parameters a self consistent equation for the transport coefficients is formulated up to burnett order in the wavevector and all orders in the mode coupling parameter the results arc similar to phenomenological models used by previous researchers

shape optimal design using b splines abstract shape optimal design of an elastic structure is formulated using a design element technique it is shown that bezier and b spline curves typical of the cad philosophy are well suited to the definition of design elements complex geometries can be described in a very compact way by a small set of design variables and a few design elements because of the b splines flexibility it is no longer necessary to piece design elements together in order to agree with the shape complexity nor to restrict the shape variations moreover the additional optimization constraints that are most often needed to avoid unrealistic designs when the shape variables are the nodal coordinates of a finite element mesh are automatically taken into account in the new formulation an analytical derivation of the sensitivity analysis will be established giving rise to numerical efficiency it will be seen that the resulting optimization problem does not involve highly nonlinear functions with respect to the shape variables so that simple mathematical programming algorithms can be applied to solve it some numerical examples are offered to demonstrate the power and generality of the new approach presented in this paper

rich classes inferable from positive data inductive inference from positive data is shown to be remarkably powerful using the framework of elementary formal systems an elementary formal system efs for short is a kind of logic program on consisting of finitely many axioms any context sensitive language is definable by a restricted efs called a length bounded efs length bounded efss with at most n axioms are considered and it is shown that inductive inference from positive data works successfully for their models as well as for their languages from this it follows that any class of logic programs such as prolog programs corresponding to length bounded efss can be inferred from positive facts

dual methods for optimizing finite element flexural systems abstract modern numerical methods for the optimization of large discretized systems are now well developed and highly efficient in the case of thin walled elastic structures modeled by finite elements however this is not yet true for structures whose components are subject simultaneously to bending and extension loads in this paper the idea of generalized optimality criterion goc set forth in previous papers for bar membrane and pure bending elements is extended to deal with general beam and flat shell elements the modifications brought to the goc result in explicit approximations for the behavior constraints that are correct up to the first order but that exhibit a more complex algebraic form indeed these explicit expressions are no longer merely linear in the reciprocal design variables however they continue to be additively separable and therefore dual methods remain fully applicable just as in the original statement of the goc approach numerical examples will be offered to demonstrate the efficiency of the method presented

properties of noise correlation functions of langevin like equations abstract the stochastic properties of the noise in langevin type equations are studied it is demonstrated that the noise is non gaussian and that the three point noise correlation function has an exponential decay on the slow time scale explicit calculations for systems containing one slow linear variable are carried out using mode coupling techniques the results are easily extended to four and higher order correlation functions and to systems in which there is more than one slow linear variable in particular the noise in the hydrodynamic langevin equations has the properties described above

learning recursive functions a survey studying the learnability of classes of recursive functions has attracted considerable interest for at least four decades starting with gold s 1967 model of learning in the limit many variations modifications and extensions have been proposed these models differ in some of the following the mode of convergence the requirements intermediate hypotheses have to fulfill the set of allowed learning strategies the source of information available to the learner during the learning process the set of admissible hypothesis spaces and the learning goals a considerable amount of work done in this field has been devoted to the characterization of function classes that can be learned in a given model the influence of natural intuitive postulates on the resulting learning power the incorporation of randomness into the learning process the complexity of learning among others on the occasion of rolf wiehagen s 60th birthday the last four decades of research in that area are surveyed with a special focus on rolf wiehagen s work which has made him one of the most influential scientists in the theory of learning recursive functions

a finite element method with mesh separation based approximation technique and its application in modeling crack propagation with adaptive mesh refinement summary this paper presents a fem with mesh separation based approximation technique that separates a standard element into three geometrically independent elements a dual mapping scheme is introduced to couple them seamlessly and to derive the element approximation the novel technique makes it very easy for mesh generation of problems with complex or solution dependent varying geometry it offers a flexible way to construct displacement approximations and provides a unified framework for the fem to enjoy some of the key advantages of the hansbo and hansbo method the meshfree methods the semi analytical fems and the smoothed fem for problems with evolving discontinuities the method enables the devising of an efficient crack tip adaptive mesh refinement strategy to improve the accuracy of crack tip fields both the discontinuities due to intra element cracking and the incompatibility due to hanging nodes resulted from the element refinement can be treated at the elemental level the effectiveness and robustness of the present method are benchmarked with several numerical examples the numerical results also demonstrate that a high precision integral scheme is critical to pass the crack patch test and it is essential to apply local adaptive mesh refinement for low fracture energy problems copyright 2014 john wiley sons ltd

the position of index sets of identifiable sets in the arithmetical hierarchy we prove that every set of partial recursive functions which can be identified by an inductive inference machine is included in some identifiable function set with index set in 3 3 an identifiable set is presented with index set in 2 3 but neither in 2 nor in 2 furthermore we show that there is no nonempty identifiable set with index set in 1 in 1 it is possible to locate this king of set in the last part of the paper we show that the problem to identify all partial recursive functions and the halting problem are of the same degree of unsolvability

on the power of probabilistic strategies in inductive inference abstract inductive inference of programs of recursive functions from input output examples by probabilistic strategies with an a priori bound n n of changes of hypotheses is investigated advantages of probabilistic strategies over deterministic ones are shown concerning their power in principle for every n 2 with probability arbitrarily close to 1 inference of function classes which cannot be inferred by any deterministic strategy with n changes of hypotheses as well as their computational complexity linear speed up of the number of changes of hypotheses necessary for inference by deterministic strategies

probabilistic inductive inference inductive inference machines construct programs for total recursive functions given only example values of the functions probabilistic inductive inference machines are defined and for various criteria of successful inference it is asked whether a probabilistic inductive inference machine can infer larger classes of functions if the inference criterion is relaxed to allow inference with probability at least p 0 p ex and bc it is shown that any class of functions that can be inferred from examples with probability exceeding 1 2 can be inferred deterministically and that for probabilities p 1 2 there is a discrete hierarchy of inferability parameterized by p the power of probabilistic inference strategies is characterized by equating the classes of probabilistically inferable functions with those classes that can be inferred by teams of inductive inference machines a parallel model of inference or by a third model called frequency inference

mode coupling theory of the convective instability abstract a mode coupling theory of free convection in the neighborhood of the linear convective instability is presented a projection operator formalism is used to eliminate the fast hydrodynamic modes from the equations of motion a non linear langevin equation involving only the soft convective mode is obtained the n order expansion scheme developed by machta and oppenheim and the diagrammatic expansion of the resolvent operator developed by lim and kavassalis are used to btain expressions for the mode coupling corrections to the random force correlation up to second order in the mode coupling parameter the effect of this correction on the steady state soft mode correlation is estimated a self consistent approximate evaluation of the steady state soft mode correlation valid to all orders in the mode coupling parameter and very close to the instability threshold is also presented these non classical mode coupling effects are nevertheless too small in magnitude to be observed in a macroscopic experiment

comparison of identification criteria for machine inductive inference abstract a natural pl 1 hierarchy of successively more general criteria of success for inductive inference machines is described based on the size of sets of anomalies in programs synthesized by such machines these criteria are compared to others in the literature some of our results are interpreted as tradeoff results or as showing the inherent relative computational complexity of certain processes and others are interpreted from a positivistic mechanistic philosophical stance as theorems in philosophy of science the techniques of recursive function theory are employed including ordinary and infinitary recursion theorems

refutable language learning with a neighbor system we consider inductive language learning and machine discovery from examples with some errors in the present paper the error or incorrectness we consider is the one described uniformly in terms of a distance over strings firstly we introduce a notion of a recursively generable distance over strings and for a language l we define a k neighbor language l as a language obtained from l by i adding some strings not in l each of which is at most k distant from some string in l and by ii deleting some strings in l each of which is at most k distant from some string not in l then we define a k neighbor system of a base language class as the collection of k neighbor languages of languages in the class and adopt it as a hypothesis space we give formal definitions of k neighbor refutable inferability and discuss necessary and sufficient conditions on such kinds of inference finally as a concrete class inferable in the sense we introduced we consider a language class definable by elementary formal systems efss for short as a main result we show that the language class definable by the so called length bounded efss with at most n axioms is refutable and inferable from complete examples

mode coupling in nonequilibrium granular flow systems in this paper we examine the role of mode coupling in nonequilibrium granular flow systems and derive mode coupling equations for equal time multi linear correlation functions in general nonequilibrium systems by applying n ordering analysis and projection operator techniques the hierarchy of equations obtained is simplified which permits the equal time multilinear averages to be calculated systematically the linear and equal time bilinear nonequilibrium correlation functions are calculated explicitly for a steady state system characterized by a small linear shear flow and uniform number and internal energy densities in this paper we examine the importance of mode coupling l in nonequilibrium systems and investigate the properties of equal time correlations of multilinear densities in steady state granular systems in recent years there has been intense study of the transport properties of granular fluid systems composed of sand or glass beads most of these studies have been semiphenomenological and involve the concept of the coefficient of restitution which is a measure of the inelasticity of collisions among the granular particles composing the fluid as examples of these studies we mention the analytical treatments of jenkins et al 2 and the simulations by walton et al 3 the inelasticity is essential for the treatment of these systems and for comparisons with experimental data 4 the paper is organized as follows using ideas developed to describe brownian motion dynamics 5 in section 2 we obtain a generalized fokkerplanck equation for the distribution function of the translational degrees of freedom of the granular system and thereby derive an effective time displacement operator which determines the time evolution of the distribution function in section 3 we construct a mode coupling theory for a general system whose dynamics are determined by a time displacement operator 0 by considering a generalization of the local equilibrium distribution to describe the

a mode coupling theory of higher order time correlation functions abstract kawasaki s mode coupling theory ann phys 61 1970 1 is used to compute time correlation functions of the form ak0 t0 akn tn where ak t represents some slowly varying quantity the gaussian and bare vertex approximations are made thus yielding extremely simple expressions for these higher order correlation functions these do not contain any bare transport coefficients and suggest relatively simple tests by which the theory could be checked examples relating to light scattering in nonequilibrium systems and the hydrodynamics of simple fluids are presented

refuting learning revisited we consider within the framework of inductive inference the concept of refuting learning as introduced by mukouchi and arikawa where the learner is not only required to learn all concepts in a given class but also has to explicitly refute concepts outside the class in the first part of the paper we consider learning from text and introduce a concept of limit refuting learning that is intermediate between refuting learning and reliable learning we give characterizations for these concepts and show some results about their relative strength and their relation to confident learning in the second part of the paper we consider learning from texts that for some k contain all positive k formulae that are valid in the standard structure determined by the set to be learned in this model the following results are shown for the language with successor any countable axiomatizable class can be limit refuting learned from 1 texts for the language with successor and order any countable axiomatizable class can be reliably learned from 1 texts and can be limit refuting learned from 2 texts whereas the axiomatizable class of all finite sets cannot be limit refuting learned from 1 texts for the full language of arithmetic which contains in addition plus and times for any even k there is an axiomatizable class that can be limit refuting learned from k 1 texts but not from k texts a similar result with k 3 in place of k 1 holds with respect to the language of presburger s arithmetic

learning by switching type of information the present work is dedicated to the study of modes of data presentation in the range between text and informant within the framework of inductive inference in this study the learner alternatingly requests sequences of positive and negative data we define various formalizations of valid data presentations in such a scenario we resolve the relationships between these different formalizations and show that one of these is equivalent to learning from informant we also show a hierarchy formed for each of the formalizations studied by considering the number of switches between requests for positive and negative data

transverse velocity fluctuations in a liquid under steady shear we present an analysis of the transverse velocity fluctuations in an isothermal liquid layer with a uniform shear rate between two parallel horizontal boundaries as a function of the wave number and the reynolds number the results were obtained by solving a stochastic version of the orr sommerfeld equation subject to no slip boundary conditions in a second order galerkin approximation we find that the spatial fourier transform of the transverse velocity fluctuations exhibits a maximum as a function of the horizontal wave number q parallel to this maximum is associated with a crossover from a q parallel to 4 dependence for larger q parallel to to a q parallel to 2 dependence for small q parallel to the q parallel to 4 dependence at larger wave numbers is independent of the boundary conditions but the small q parallel to behavior is strongly affected by the boundary conditions the nonequilibrium enhancement of the intensity of the transverse velocity fluctuations remains finite for all values of the reynolds number but increases approximately with the square of the reynolds number the relation between our results and those obtained by previous authors in the absence of boundary conditions is elucidated

superoperator representation of nonlinear response unifying quantum field and mode coupling theories computing response functions by following the time evolution of superoperators in liouville space whose vectors are ordinary hilbert space operators offers an attractive alternative to the diagrammatic perturbative expansion of many body equilibrium and nonequilibrium green s functions the bookkeeping of time ordering is naturally maintained in real physical time allowing the formulation of wick s theorem for superoperators giving a factorization of higher order response functions in terms of two fundamental green s functions backward propagations and analytic continuations using artificial times keldysh loops and matsubara contours are avoided a generating functional for nonlinear response functions unifies quantum field theory and the classical mode coupling formalism of nonlinear hydrodynamics and may be used for semiclassical expansions classical response functions are obtained without the explicit computation of stability matrices

efficient approximation concepts using second order information the primary goal of this paper is to show how second derivative information can be used in an effective way in structural optimization problems the basic idea is to generate such an information at the expense of only one more virtual load case in the sensitivity analysis part of the finite element code to achieve this goal a primal dual approach is employed that can also be interpreted as a sequential quadratic programming method another objective is to relate the proposed method to the well known family of approximation concepts techniques where the primary optimization problem is transformed into a sequence of non linear explicit subproblems when restricted to diagonal second derivatives the new approach can be viewed as a recursive convex programming method similar to the convex linearization method conlin and to its recent generalization the method of moving asymptotes mma this new method has been successfully tested on simple problems that can be solved in closed form as well as on sizing optimization of trusses in all cases the method converges faster than conlin mma or other approximation techniques based on reciprocal variables

mode coupling theory of hydrodynamics and steady state systems abstract we construct a formal mode coupling theory for hydrodynamic systems which includes contributions from all powers of the hydrodynamic variables this theory is applied to nonequilibrium steady state systems a generalization of the local equilibrium distribution is used to describe the nonequilibrium state this distribution independently constrains all moments of the hydrodynamic variables the infinite hierarchy of equations for the moments of the hydrodynamic variables is truncated using an inverse system size expansion explicit results are obtained for the time correlation functions of fluids with a linear temperature gradient or a linear shear these results agree with previous studies of these steady states

reexamination of the mode coupling scheme for the glass transition abstract within the context of a general mode coupling theory previously developed for the description of equilibrium fluctuations in simple classical fluids we derive an expression for the effective longitudinal viscosity includings couplings to currents so that certain key assumptions inherent in previous work on the glass transition can be analyzed critically we show that the hopping kernels arise from an approximate resummation of the dominant class of diagrams resulting from bilinear modes although the resummed expression for the viscosity obtained in this paper is very similar to the result previously obtained from a kinetic theory approach there are important difference most notably in the form of the vertices connecting the hopping kernels and the lack of subtractions in the kernels representing the cage effect and activated hopping transport using the formalism developed presently we show that the introduction of an initial cut off time in the hopping kernel to obtain a strong temperature dependence for the viscosity amounts to neglecting a class of processes that may be of comparable if not greater importance than the terms explicityly kept in previous work

sizing optimization of truss structures by method of centers and force formulation this paper describes a new approach to optimum weight design of truss structures the force method is incorporated in an optimization algorithm based on the method of center points design variables are the member cross sectional areas and the redundant forces evaluated for each independent loading condition acting on the structure the optimization method utilizes the largest hyperspheres inscribed within the feasible space the method of hyperspheres has been enhanced here to handle the compatibility equality constraints as well by including the analysis step in the optimization cycle there is no longer the need to perform separate structural analyses thus saving computation time the viability and efficiency of the proposed method are demonstrated for truss structures subject to multiple loading conditions and constraints on member stresses nodal displacement and minimum gage numerical results are compared with those reported in the literature

on the intrinsic complexity of learning recursive functions the intrinsic complexity of learning compares the difficulty of learning classes of objects by using some reducibility notion for several types of learning recursive functions both natural complete classes are exhibited and necessary and sufficient conditions for completeness are derived informally a class is complete iff both its topological structure is highly complex while its algorithmic structure is easy some self describing classes turn out to be complete furthermore the structure of the intrinsic complexity is shown to be much richer than the structure of the mind change complexity though in general intrinsic complexity and mind change complexity can behave orthogonally

an optimization design method for large scale structures in this paper based on the mechanical property of structures a unified approximate formula with high precision suitable to several structural response functions and various types of finite elements is introduced first and then an algorithm for solving the nonlinear program is presented this algorithm is not only effective for solving the program constructed by this unified approximate formula but also easy to change the objective function and to solve the structural optimization problem with dual or multiple objective functions