scholarly journals A Formal Account of Structuring Motor Actions With Sensory Prediction for a Naive Agent

2020 ◽  
Vol 7 ◽  
Author(s):  
Jean-Merwan Godon ◽  
Sylvain Argentieri ◽  
Bruno Gas
Keyword(s):  
Sufficient Conditions ◽  
Combinatorial Structure ◽  
Prediction Function ◽  
Formal Framework ◽  
Sensory Predictions ◽  
Spatial Displacements ◽  
Motor Actions ◽  
Sensory Prediction ◽  
Sensorimotor Contingency

For naive robots to become truly autonomous, they need a means of developing their perceptive capabilities instead of relying on hand crafted models. The sensorimotor contingency theory asserts that such a way resides in learning invariants of the sensorimotor flow. We propose a formal framework inspired by this theory for the description of sensorimotor experiences of a naive agent, extending previous related works. We then use said formalism to conduct a theoretical study where we isolate sufficient conditions for the determination of a sensory prediction function. Furthermore, we also show that algebraic structure found in this prediction can be taken as a proxy for structure on the motor displacements, allowing for the discovery of the combinatorial structure of said displacements. Both these claims are further illustrated in simulations where a toy naive agent determines the sensory predictions of its spatial displacements from its uninterpreted sensory flow, which it then uses to infer the combinatorics of said displacements.

scholarly journals Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems

2012 ◽  
Vol 22 (4) ◽  
pp. 451-465 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Transfer Function ◽  
Linear Systems ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Diagram Method ◽  
State Variable ◽  
Discrete Time Systems ◽  
Time Systems ◽  
Time Linear

A new modified state variable diagram method is proposed for determination of positive realizations with reduced numbers of delays and without delays of linear discrete-time systems for a given transfer function. Sufficient conditions for the existence of the positive realizations of given proper transfer function are established. It is shown that there exists a positive realization with reduced numbers of delays if there exists a positive realization without delays but with greater dimension. The proposed methods are demonstrated on a numerical example.

Positive stable realizations of discrete-time linear systems

2012 ◽  
Vol 60 (3) ◽  
pp. 605-616
Author(s):  
T. Kaczorek
Keyword(s):  
Transfer Function ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Asymptotically Stable ◽  
Numerical Examples ◽  
Discrete Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems ◽  
Time Linear

Abstract The problem of existence and determination of the set of positive asymptotically stable realizations of a proper transfer function of linear discrete-time systems is formulated and solved. Necessary and sufficient conditions for existence of the set of the realizations are established. A procedure for computation of the set of realizations are proposed and illustrated by numerical examples.

Arithmetical Semigroup Rings

1980 ◽  
Vol 32 (6) ◽  
pp. 1361-1371 ◽  
Author(s):  
Bonnie R. Hardy ◽  
Thomas S. Shores
Keyword(s):  
Principal Ideal ◽  
Sufficient Conditions ◽  
Forthcoming Paper ◽  
Semigroup Ring ◽  
Necessary And Sufficient Conditions ◽  
Semigroup Rings ◽  
Principal Ideal Ring ◽  
Arithmetical Semigroup ◽  
Necessary And Sufficient

Throughout this paper the ring R and the semigroup S are commutative with identity; moreover, it is assumed that S is cancellative, i.e., that S can be embedded in a group. The aim of this note is to determine necessary and sufficient conditions on R and S that the semigroup ring R[S] should be one of the following types of rings: principal ideal ring (PIR), ZPI-ring, Bezout, semihereditary or arithmetical. These results shed some light on the structure of semigroup rings and provide a source of examples of the rings listed above. They also play a key role in the determination of all commutative reduced arithmetical semigroup rings (without the cancellative hypothesis on S) which will appear in a forthcoming paper by Leo Chouinard and the authors [4].

scholarly journals CREDIT RISK PREMIA AND QUADRATIC BSDEs WITH A SINGLE JUMP

2010 ◽  
Vol 13 (07) ◽  
pp. 1103-1129 ◽  
Author(s):  
STEFAN ANKIRCHNER ◽  
CHRISTOPHETTE BLANCHET-SCALLIET ◽  
ANNE EYRAUD-LOISEL
Keyword(s):  
Credit Risk ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Risk Premia ◽  
Contingent Claims ◽  
Quadratic Growth ◽  
Utility Preferences ◽  
Random Times ◽  
Uniqueness Theory

This paper is concerned with the determination of credit risk premia of defaultable contingent claims by means of indifference valuation principles. Assuming exponential utility preferences we derive representations of indifference premia of credit risk in terms of solutions of Backward Stochastic Differential Equations (BSDE). The class of BSDEs needed for that representation allows for quadratic growth generators and jumps at random times. Since the existence and uniqueness theory for this class of BSDEs has not yet been developed to the required generality, the first part of the paper is devoted to fill that gap. By using a simple constructive algorithm, and known results on continuous quadratic BSDEs, we provide sufficient conditions for the existence and uniqueness of quadratic BSDEs with discontinuities at random times.

Types of simple α-recursively enumerable sets

1976 ◽  
Vol 41 (3) ◽  
pp. 681-694
Author(s):  
Anne Leggett ◽  
Richard A. Shore
Keyword(s):  
Lattice Theory ◽  
Lattice Structure ◽  
Sufficient Conditions ◽  
Recursion Theory ◽  
Recursively Enumerable ◽  
Countable Ordinal ◽  
Congruence Relations ◽  
General Program ◽  
Simple Sets

One general program of α-recursion theory is to determine as much as possible of the lattice structure of (α), the lattice of α-r.e. sets under inclusion. It is hoped that structure results will shed some light on whether or not the theory of (α) is decidable with respect to a suitable language for lattice theory. Fix such a language ℒ.Many of the basic results about the lattice structure involve various sorts of simple α-r.e. sets (we use definitions which are definable in ℒ over (α)). It is easy to see that simple sets exist for all admissible α. Chong and Lerman [1] have found some necessary and some sufficient conditions for the existence of hhsimple α-r.e. sets, although a complete determination of these conditions has not yet been made. Lerman and Simpson [9] have obtained some partial results concerning r-maximal α-r.e. sets. Lerman [6] has shown that maximal α-r.e. sets exist iff a is a certain sort of constructibly countable ordinal. Lerman [5] has also investigated the congruence relations, filters, and ideals of (α). Here various sorts of simple sets have also proved to be vital tools. The importance of simple α-r.e. sets to the study of the lattice structure of (α) is hence obvious.Lerman [6, Q22] has posed the following problem: Find an admissible α for which all simple α-r.e. sets have the same 1-type with respect to the language ℒ. The structure of (α) for such an α would be much less complicated than that of (ω). Lerman [7] showed that such an α could not be a regular cardinal of L. We show that there is no such admissible α.

Empathy, Honesty, and Integrity in the Therapist

2020 ◽  
Author(s):  
Jeffrey H. D. Cornelius-White ◽  
Gillian Proctor
Keyword(s):  
Sufficient Conditions ◽  
Therapist Attitudes ◽  
Carl Rogers ◽  
Empathic Understanding ◽  
Unconditional Positive Regard ◽  
Therapy Relationship ◽  
Necessary And Sufficient ◽  
Fully Functioning

Empathy, honesty, and integrity are essential concepts to ensure the quality of the therapy relationship and the client’s trust in the therapist. This chapter situates these concepts in relation to the necessary and sufficient conditions for therapy proposed by Carl Rogers in the late 1950s, and particularly in relation to the therapist attitudes of empathic understanding, unconditional positive regard, and congruence. In person-centered therapy (PCT), empathy is a moral, not instrumental, practice that nondirectively protects the self-determination of the client. It exemplifies power with others, avoiding power over others, and facilitating power from within, by providing a conduit for non-possessive love, the active ingredient in PCT. Honesty in PCT involves the sincerity of the therapist’s unconditional empathy and the transparence to be a full person in relation to a client. Integrity refers not only to the disciplined moral practice of empathy, but an extensional, fully functioning maturation.

scholarly journals Exchange de Risques entre Assureurs et Theorie des Jeux

1977 ◽  
Vol 9 (1-2) ◽  
pp. 155-180 ◽  
Author(s):  
Jean Lemaire
Keyword(s):  
Shapley Value ◽  
Sufficient Conditions ◽  
Pareto Optimal ◽  
Existence Of A Solution ◽  
The Shapley Value ◽  
Théorie Des Jeux ◽  
Person Game ◽  
Reinsurance Market ◽  
Value Concept

SummaryA theorem of Borch characterizing Pareto-optimal treaties in a reinsurance market is extended to the case of non-differentiable utilities. Sufficient conditions for the existence of a solution to the equations are established. The problem is then shown to be identical to the determination of the value of a cooperative non-transferable m-person game. We show how to compute the Shapley value of this game, then we introduce a new value concept. An example illustrates both methods.

The problem of dirichlet for quasilinear elliptic differential equations with many independent variables

1969 ◽  
Vol 264 (1153) ◽  
pp. 413-496 ◽  
Keyword(s):  
Dirichlet Problem ◽  
Differential Equations ◽  
Elliptic Equations ◽  
Sufficient Conditions ◽  
Central Position ◽  
Second Primary ◽  
Elliptic Differential Equations ◽  
High Level ◽  
Quasilinear Elliptic

This paper is concerned with the existence of solutions of the Dirichlet problem for quasilinear elliptic partial differential equations of second order, the conclusions being in the form of necessary conditions and sufficient conditions for this problem to be solvable in a given domain with arbitrarily assigned smooth boundary data. A central position in the discussion is played by the concept of global barrier functions and by certain fundamental invariants of the equation. With the help of these invariants we are able to distinguish an important class of ‘ regularly elliptic5 equations which, as far as the Dirichlet problem is concerned, behave comparably to uniformly elliptic equations. For equations which are not regularly elliptic it is necessary to impose significant restrictions on the curvatures of the boundaries of the underlying domains in order for the Dirichlet problem to be generally solvable; the determination of the precise form of these restrictions constitutes a second primary aim of the paper. By maintaining a high level of generality throughout, we are able to treat as special examples the minimal surface equation, the equation for surfaces having prescribed mean curvature, and a number of other non-uniformly elliptic equations of classical interest.

scholarly journals A Formal Framework for Speedup Learning from Problems and Solutions

1996 ◽  
Vol 4 ◽  
pp. 445-475 ◽  
Author(s):  
P. Tadepalli ◽  
B. K. Natarajan
Keyword(s):  
Problem Solving ◽  
Sufficient Conditions ◽  
Theoretical Work ◽  
Pac Learning ◽  
Speedup Learning ◽  
Conditions For Learning ◽  
Control Rules ◽  
Formal Framework ◽  
Problems And Solutions ◽  
Probably Approximately Correct

Speedup learning seeks to improve the computational efficiency of problem solving with experience. In this paper, we develop a formal framework for learning efficient problem solving from random problems and their solutions. We apply this framework to two different representations of learned knowledge, namely control rules and macro-operators, and prove theorems that identify sufficient conditions for learning in each representation. Our proofs are constructive in that they are accompanied with learning algorithms. Our framework captures both empirical and explanation-based speedup learning in a unified fashion. We illustrate our framework with implementations in two domains: symbolic integration and Eight Puzzle. This work integrates many strands of experimental and theoretical work in machine learning, including empirical learning of control rules, macro-operator learning, Explanation-Based Learning (EBL), and Probably Approximately Correct (PAC) Learning.

Sign in / Sign up

Export Citation Format

Share Document