On the role of higher-order nonlinearities in implementing second-order hologram-based associative memories

2015 ◽  
Vol 24 (3) ◽  
pp. 230-234 ◽  
Author(s):  
P. V. Polyanskii ◽  
Ch. V. Felde ◽  
A. V. Konovchuk ◽  
M. V. Oleksyuk
Keyword(s):  
Higher Order ◽  
Second Order ◽  
Associative Memories

AUTONOMY AND HIERARCHY

2003 ◽  
Vol 20 (2) ◽  
pp. 156-176 ◽  
Author(s):  
Michael E. Bratman
Keyword(s):  
Free Will ◽  
Higher Order ◽  
Second Order ◽  
Original Version ◽  
Autonomous Action ◽  
Original Proposal

In autonomous action the agent herself directs and governs the action. But what is it for the agent herself to direct and to govern? One theme in a series of articles by Harry G. Frankfurt is that we can make progress in answering this question by appeal to higher-order conative attitudes. Frankfurt's original version of this idea is that in acting of one's own free will, one is not acting simply because one desires so to act. Rather, it is also true that this desire motivates one's action because one desires that this desire motivate one's action. This latter desire about the motivational role of one's desire is a second-order desire. It is, in particular, what Frankfurt calls a second-order “volition.” And, according to Frankfurt's original proposal, acting of one's own free will involves in this way such second-order, and sometimes yet higher order, volitions.

Influence of the higher-order nonlinearities in embodying the second-order holographic associative memories

2015 ◽  
Author(s):  
Peter V. Polyanskii ◽  
Christina V. Felde ◽  
Alexey V. Konovchuk ◽  
Maxim V. Oleksyuk
Keyword(s):  
Higher Order ◽  
Second Order ◽  
Associative Memories

scholarly journals Cortical Contributions to Higher-Order Conditioning: A Review of Retrosplenial Cortex Function

2021 ◽  
Vol 15 ◽  
Author(s):  
Danielle I. Fournier ◽  
Han Yin Cheng ◽  
Siobhan Robinson ◽  
Travis P. Todd
Keyword(s):  
Brain Structures ◽  
Neutral Stimulus ◽  
Higher Order ◽  
Retrosplenial Cortex ◽  
Second Order ◽  
Future Research ◽  
Cortical Region ◽  
Sensory Preconditioning ◽  
Order Conditioning

In higher-order conditioning paradigms, such as sensory preconditioning or second-order conditioning, discrete (e.g., phasic) or contextual (e.g., static) stimuli can gain the ability to elicit learned responses despite never being directly paired with reinforcement. The purpose of this mini-review is to examine the neuroanatomical basis of high-order conditioning, by selectively reviewing research that has examined the role of the retrosplenial cortex (RSC) in sensory preconditioning and second-order conditioning. For both forms of higher-order conditioning, we first discuss the types of associations that may occur and then review findings from RSC lesion/inactivation experiments. These experiments demonstrate a role for the RSC in sensory preconditioning, suggesting that this cortical region might contribute to higher-order conditioning via the encoding of neutral stimulus-stimulus associations. In addition, we address knowledge gaps, avenues for future research, and consider the contribution of the RSC to higher-order conditioning in relation to related brain structures.

Higher‐order Logic

2009 ◽  
Author(s):  
Stewart Shapiro
Keyword(s):  
Philosophy Of Mathematics ◽  
Higher Order ◽  
Second Order ◽  
Order Logic ◽  
First Order Logic ◽  
Higher Order Logic ◽  
First Order ◽  
Deductive Systems ◽  
Second Order Logic

The philosophical literature contains numerous claims on behalf of and numerous claims against higher-order logic. Virtually all of the issues apply to second-order logic (vis-à-vis first-order logic), so this article focuses on that. It develops the syntax of second-order languages and present typical deductive systems and model-theoretic semantics for them. This will help to explain the role of higher-order logic in the philosophy of mathematics. It is assumed that the reader has at least a passing familiarity with the theory and metatheory of first-order logic.

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

scholarly journals Preserving the Shape of Functions by Applying Multidimensional Schoenberg-Type Operators

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1016
Author(s):  
Camelia Liliana Moldovan ◽  
Radu Păltănea
Keyword(s):  
Applied Sciences ◽  
Degree Of Approximation ◽  
Higher Order ◽  
Second Order ◽  
Dimensional Case ◽  
Moduli Of Continuity ◽  
One Dimensional ◽  
Multidimensional Generalization ◽  
The One

The paper presents a multidimensional generalization of the Schoenberg operators of higher order. The new operators are powerful tools that can be used for approximation processes in many fields of applied sciences. The construction of these operators uses a symmetry regarding the domain of definition. The degree of approximation by sequences of such operators is given in terms of the first and the second order moduli of continuity. Extending certain results obtained by Marsden in the one-dimensional case, the property of preservation of monotonicity and convexity is proved.

scholarly journals Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

2021 ◽  
Vol 502 (3) ◽  
pp. 3976-3992
Author(s):  
Mónica Hernández-Sánchez ◽  
Francisco-Shu Kitaura ◽  
Metin Ata ◽  
Claudio Dalla Vecchia
Keyword(s):  
Fourth Order ◽  
Large Scale ◽  
Equations Of Motion ◽  
Large Scale Structure ◽  
Real Space ◽  
Higher Order ◽  
Second Order ◽  
Scale Structure ◽  
Integration Schemes ◽  
Reconstruction Methods

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

scholarly journals Higher-order Recursion Schemes and Collapsible Pushdown Automata: Logical Properties

2021 ◽  
Vol 22 (2) ◽  
pp. 1-37
Author(s):  
Christopher H. Broadbent ◽  
Arnaud Carayol ◽  
C.-H. Luke Ong ◽  
Olivier Serre
Keyword(s):  
Model Checking ◽  
Free Variable ◽  
Higher Order ◽  
Second Order ◽  
Effective Solution ◽  
Parity Games ◽  
Transition Graphs ◽  
Second Order Logic ◽  
Pushdown Automata ◽  
Monadic Second Order Logic

This article studies the logical properties of a very general class of infinite ranked trees, namely, those generated by higher-order recursion schemes. We consider, for both monadic second-order logic and modal -calculus, three main problems: model-checking, logical reflection (a.k.a. global model-checking, that asks for a finite description of the set of elements for which a formula holds), and selection (that asks, if exists, for some finite description of a set of elements for which an MSO formula with a second-order free variable holds). For each of these problems, we provide an effective solution. This is obtained, thanks to a known connection between higher-order recursion schemes and collapsible pushdown automata and on previous work regarding parity games played on transition graphs of collapsible pushdown automata.

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