Search results for "Monotonic function"
showing 10 items of 87 documents
Error detecting in inductive inference
1995
Several well-known inductive inference strategies change the actual hypothesis only when they discover that it “provably misclassifies” an example seen so far. This notion is made mathematically precise and its general power is characterized. In spite of its strength it is shown that this approach is not of universal power. Consequently, then hypotheses are considered which “unprovably misclassify” examples and the properties of this approach are studied. Among others it turns out that this type is of the same power as monotonic identification. Then it is shown that universal power can be achieved only when an unbounded number of alternations of these dual types of hypotheses is allowed. Fi…
Dual types of hypotheses in inductive inference
2006
Several well-known inductive inference strategies change the actual hypothesis only when they discover that it “provably misclassifies” an example seen so far. This notion is made mathematically precise and its general power is characterized. In spite of its strength it is shown that this approach is not of “universal” power. Consequently, then hypotheses are considered which “unprovably misclassify” examples and the properties of this approach are studied. Among others it turns out that this type is of the same power as monotonic identification. Finally, it is shown that “universal” power can be achieved only when an unbounded number of alternations of these dual types of hypotheses is all…
Solving Two-Person Zero-Sum Stochastic Games With Incomplete Information Using Learning Automata With Artificial Barriers
2021
Learning automata (LA) with artificially absorbing barriers was a completely new horizon of research in the 1980s (Oommen, 1986). These new machines yielded properties that were previously unknown. More recently, absorbing barriers have been introduced in continuous estimator algorithms so that the proofs could follow a martingale property, as opposed to monotonicity (Zhang et al., 2014), (Zhang et al., 2015). However, the applications of LA with artificial barriers are almost nonexistent. In that regard, this article is pioneering in that it provides effective and accurate solutions to an extremely complex application domain, namely that of solving two-person zero-sum stochastic games that…
A formal proof of the e-optimality of discretized pursuit algorithms
2015
Learning Automata (LA) can be reckoned to be the founding algorithms on which the field of Reinforcement Learning has been built. Among the families of LA, Estimator Algorithms (EAs) are certainly the fastest, and of these, the family of discretized algorithms are proven to converge even faster than their continuous counterparts. However, it has recently been reported that the previous proofs for ??-optimality for all the reported algorithms for the past three decades have been flawed. We applaud the researchers who discovered this flaw, and who further proceeded to rectify the proof for the Continuous Pursuit Algorithm (CPA). The latter proof examines the monotonicity property of the proba…
Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension
2017
A fundamental problem in the dimension theory of self-affine sets is the construction of high- dimensional measures which yield sharp lower bounds for the Hausdorff dimension of the set. A natural strategy for the construction of such high-dimensional measures is to investigate measures of maximal Lyapunov dimension; these measures can be alternatively interpreted as equilibrium states of the singular value function introduced by Falconer. Whilst the existence of these equilibrium states has been well-known for some years their structure has remained elusive, particularly in dimensions higher than two. In this article we give a complete description of the equilibrium states of the singular …
Some approximation properties of ( p , q ) $(p,q)$ -Bernstein operators
2016
This paper is concerned with the $(p,q)$ -analog of Bernstein operators. It is proved that, when the function is convex, the $(p,q)$ -Bernstein operators are monotonic decreasing, as in the classical case. Also, some numerical examples based on Maple algorithms that verify these properties are considered. A global approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem are proved.
A strategy for the finite element modeling of FRP-confined concrete columns subjected to preload
2018
Abstract Compressive behavior of columns strengthened by means of an outer elastic confinement provided e.g. by fiber-reinforced polymer (FRP) jackets has become a main topic in the field of structural retrofitting. In details, the problem of the response assessment of strengthened columns is still under study. Many analytical formulations have been proposed to describe the compressive behavior of confined concrete under both monotonic and cyclic loads. However, the effect of a stress/strain level in the columns already present prior to apply the confinement has been generally neglected until now, also because of the lack of well defined strategies of modeling. In this frame, here, (1) a FE…
Cohesive–frictional interface constitutive model
2009
AbstractIn the framework of numerical analysis of joined bodies, the present paper is devoted to the constitutive modeling, via an interface kinematic formulation, of mechanical behaviour of internal adhesive layers. The proposed interface constitutive model couples a cohesive behaviour, based on the damage mechanics theory, with a frictional one, defined in a non-associative plasticity framework. Namely, the interface formulation follows the transition of the adhesive material from the sound elastic condition to the fully cracked one. This formulation is able to model, by means of a specific interpretation of the damage variable and in a relevant mathematical setting, the interface interme…
Analysis-oriented stress–strain model of CRFP-confined circular concrete columns with applied preload
2018
The compressive behavior of FRP-confined concrete is a current issue in the field of structural retrofitting. The available models well predict the stress–strain behavior under monotonic and cyclic loads. However, in the practical applications, columns that need an increasing of bearing capacity are often strengthened under serviceability load conditions, with a stress and strain state that could change the response of the reinforced systems with respect to the case of the unloaded state. In this paper, the compressive behavior of circular FRP-confined concrete columns with preload is analyzed with the introduction of a modified analysis-oriented model. Differently from the classical formul…
Analytical Prediction of the Flexural Response of External RC Joints with Smooth Rebars
2018
Nel presente lavoro viene presentato un modello analitico in forma chiusa in grado di riprodurre la risposta flessionale monotonica di nodi esterni trave-colonna in c.a. con armature lisce. La colonna viene sottoposta a carico verti-cale costante e la trave ad una forza laterale crescente monotonicamente applicata all’estremità. Il modello si basa sul comportamen-to flessionale di trave e colonna adottando un modello di cerniera plasticità concentrata che include lo scorrimento delle armature della trave. Si assume un dominio sforzo normale-momento bilineare semplificato da cui viene derivato il momento ultimo associato alla forza assiale di progetto. Per il nodo viene adottato un modello c…