Using theory of mind

The ability to flexibly predict others' behaviors has been ascribed to a theory of mind (ToM) system. Most research has focused on formal conceptual definitions of such a system, and the question of whom to credit with a ToM. In this article, I suggest shifting perspective from formal definitions to a usage-based approach. This approach views action within human interaction as central to the emergence and continuous development of the ability to flexibly predict others' behaviors. Addressing the current debate about whether infants have a ToM, I illustrate how infants use flexible action expectations to interact with others appropriately. I also discuss the continuous development of ToM and its natural structure from a usage-based perspective

Ghost circles in lattice Aubry-Mather theory

Monotone lattice recurrence relations such as the Frenkel-Kontorova lattice, arise in Hamiltonian lattice mechanics as models for fe?rromagnetism and as discretization of elliptic PDEs. Mathematically, they are a multidimensional counterpart of monotone twist maps. They often admit a variational structure, so that the solutions are the stationary points of a formal action function. Classical Aubry-Mather theory establishes the existence of a large collection of solutions of any rotation vector. For irrational rotation vectors this is the well-known Aubry-Mather set. It consists of global minimizers and it may have gaps. In this paper, we study the gradient flow of the formal action function and we prove that every Aubry-Mather set can be interpolated by a continuous gradient-flow invariant family, the so-called "ghost circle". The existence of ghost circles is first proved for rational rotation vectors and Morse action functions. The main technical result is a compactness theorem for ghost circles, based on a parabolic Harnack inequality for the gradient flow, which implies the existence of ghost circles of arbitrary rotation vectors and for arbitrary actions. As a consequence, we can give a simple proof of the fact that when an Aubry-Mather set has a gap, then this gap must be parametrized by minimizers, or contain a non-minimizing solution.Comment: 39 pages, 1 figur

Ghost circles in lattice Aubry-Mather theory

Monotone lattice recurrence relations such as the Frenkel-Kontorova lattice, arise in Hamiltonian lattice mechanics as models for fe?rromagnetism and as discretization of elliptic PDEs. Mathematically, they are a multidimensional counterpart of monotone twist maps. They often admit a variational structure, so that the solutions are the stationary points of a formal action function. Classical Aubry-Mather theory establishes the existence of a large collection of solutions of any rotation vector. For irrational rotation vectors this is the well-known Aubry-Mather set. It consists of global minimizers and it may have gaps. In this paper, we study the gradient flow of the formal action function and we prove that every Aubry-Mather set can be interpolated by a continuous gradient-flow invariant family, the so-called "ghost circle". The existence of ghost circles is first proved for rational rotation vectors and Morse action functions. The main technical result is a compactness theorem for ghost circles, based on a parabolic Harnack inequality for the gradient flow, which implies the existence of ghost circles of arbitrary rotation vectors and for arbitrary actions. As a consequence, we can give a simple proof of the fact that when an Aubry-Mather set has a gap, then this gap must be parametrized by minimizers, or contain a non-minimizing solution.Comment: 39 pages, 1 figur

An algebraic approach to energy problems I - continuous Kleene ω-algebras ‡

Energy problems are important in the formal analysis of embedded or autonomous systems. With the purpose of unifying a number of approaches to energy problems found in the literature, we introduce energy automata. These are finite automata whose edges are labeled with energy functions that define how energy levels evolve during transitions. Motivated by this application and in order to compute with energy functions, we introduce a new algebraic structure of *-continuous Kleene ω-algebras. These involve a *-continuous Kleene algebra with a *-continuous action on a semimodule and an infinite product operation that is also *-continuous. We define both a finitary and a non-finitary version of *-continuous Kleene ω-algebras. We then establish some of their properties, including a characterization of the free finitary *-continuous Kleene ω-algebras. We also show that every *-continuous Kleene ω-algebra gives rise to an iteration semiring-semimodule pair

Dilemas das redes de cooperação interorganizacionais e a formação dos profissionais de saúde. O caso da Enfermagem

Supported by the indispensability of the resource sharing, health care organizations and university teaching organizations search for understanding platforms and action schemes to better respond to the learning needs in loco of the nursing students’ clinical training, the professionals’ continuous training as well as the demands of their community. Bearing in mind such assumptions there is a need for the promotion of such debate and of the sociological discussion about the logic cooperation network between university and health care organizations, questioning on one hand, the different government forms of the network actions, and on the other hand, the emancipator strategy towards knowledge development and susceptible of generating health capital. To answer these questions we made our research in twelve organizations (eleven are health organisations and one higher nursing education) using qualitative methodologies and also the network analysis techniques, namely through the use of the applications UCINET and NETDRAW. In this study we unveiled the structure; content and dynamic of the established inter organizational relations, checking the existence of a cooperation supported by a formal and informal relation network, which use norms, but also in symbolic and ideological values related to the profession, but also the of trust and friendship relations who were themselves conditioners of their functioning

Compiling Elementary Mathematical Functions into Finite Chemical Reaction Networks via a Polynomialization Algorithm for ODEs

The Turing completeness result for continuous chemical reaction networks (CRN) shows that any computable function over the real numbers can be computed by a CRN over a finite set of formal molecular species using at most bimolecular reactions with mass action law kinetics. The proof uses a previous result of Turing completeness for functions defined by polynomial ordinary differential equations (PODE), the dualrail encoding of real variables by the difference of concentration between two molecular species, and a back-end quadratization transformation to restrict to elementary reactions with at most two reactants. In this paper, we present a polynomialization algorithm of quadratic time complexity to transform a system of elementary differential equations in PODE. This algorithm is used as a front-end transformation to compile any elementary mathematical function, either of time or of some input species, into a finite CRN. We illustrate the performance of our compiler on a benchmark of elementary functions relevant to CRN design problems in synthetic biology specified by mathematical functions. In particular, the abstract CRN obtained by compilation of the Hill function of order 5 is compared to the natural CRN structure of MAPK signalling networks