arXiv subjects

Enrique Miranda

Publications and source records attributed to Enrique Miranda.

15 recordsLinked to original sources

arXiv2024

Variability in Resistive Memories

Resistive memories are outstanding electron devices that have displayed a large potential in a plethora of applications such as nonvolatile data storage, neuromorphic computing, hardware cryptography, etc. Their fabrication control and performance have been notably improved in the last few years to cope with the requirements of massive industrial production. However, the most important hurdle to progress in their development is the so-called cycle-to-cycle variability, which is inherently rooted in the resistive switching mechanism behind the operational principle of these devices. In order to achieve the whole picture, variability must be assessed from different viewpoints going from the experimental characterization to the adequation of modeling and simulation techniques. Herein, special emphasis is put on the modeling part because the accurate representation of the phenomenon is critical for circuit designers. In this respect, a number of approaches are used to the date: stochastic, behavioral, mesoscopic..., each of them covering particular aspects of the electron and ion transport mechanisms occurring within the switching material. These subjects are dealt with in this review, with the aim of presenting the most recent advancements in the treatment of variability in resistive memories.

physics.app-ph↗

arXiv2022

Nonlinear desirability theory

Desirability can be understood as an extension of Anscombe and Aumann's Bayesian decision theory to sets of expected utilities. At the core of desirability lies an assumption of linearity of the scale in which rewards are measured. It is a traditional assumption used to derive the expected utility model, which clashes with a general representation of rational decision making, though. Allais has, in particular, pointed this out in 1953 with his famous paradox. We note that the utility scale plays the role of a closure operator when we regard desirability as a logical theory. This observation enables us to extend desirability to the nonlinear case by letting the utility scale be represented via a general closure operator. The new theory directly expresses rewards in actual nonlinear currency (money), much in Savage's spirit, while arguably weakening the founding assumptions to a minimum. We characterise the main properties of the new theory both from the perspective of sets of gambles and of their lower and upper prices (previsions). We show how Allais paradox finds a solution in the new theory, and discuss the role of sets of probabilities in the theory.

cs.AI↗

arXiv2017

Lexicographic choice functions

We investigate a generalisation of the coherent choice functions considered by Seidenfeld et al. (2010), by sticking to the convexity axiom but imposing no Archimedeanity condition. We define our choice functions on vector spaces of options, which allows us to incorporate as special cases both Seidenfeld et al.'s (2010) choice functions on horse lotteries and sets of desirable gambles (Quaeghebeur, 2014), and to investigate their connections. We show that choice functions based on sets of desirable options (gambles) satisfy Seidenfeld's convexity axiom only for very particular types of sets of desirable options, which are in a one-to-one relationship with the lexicographic probabilities. We call them lexicographic choice functions. Finally, we prove that these choice functions can be used to determine the most conservative convex choice function associated with a given binary relation.

cs.AI↗

arXiv2016

Sklar's Theorem in an Imprecise Setting

Sklar's theorem is an important tool that connects bidimensional distribution functions with their marginals by means of a copula. When there is imprecision about the marginals, we can model the available information by means of p-boxes, that are pairs of ordered distribution functions. Similarly, we can consider a set of copulas instead of a single one. We study the extension of Sklar's theorem under these conditions, and link the obtained results to stochastic ordering with imprecision.

math.PR↗

arXiv2015

Desirability and the birth of incomplete preferences

We establish an equivalence between two seemingly different theories: one is the traditional axiomatisation of incomplete preferences on horse lotteries based on the mixture independence axiom; the other is the theory of desirable gambles developed in the context of imprecise probability. The equivalence allows us to revisit incomplete preferences from the viewpoint of desirability and through the derived notion of coherent lower previsions. On this basis, we obtain new results and insights: in particular, we show that the theory of incomplete preferences can be developed assuming only the existence of a worst act---no best act is needed---, and that a weakened Archimedean axiom suffices too; this axiom allows us also to address some controversy about the regularity assumption (that probabilities should be positive---they need not), which enables us also to deal with uncountable possibility spaces; we show that it is always possible to extend in a minimal way a preference relation to one with a worst act, and yet the resulting relation is never Archimedean, except in a trivial case; we show that the traditional notion of state independence coincides with the notion called strong independence in imprecise probability---this leads us to give much a weaker definition of state independence than the traditional one; we rework and uniform the notions of complete preferences, beliefs, values; we argue that Archimedeanity does not capture all the problems that can be modelled with sets of expected utilities and we provide a new notion that does precisely that. Perhaps most importantly, we argue throughout that desirability is a powerful and natural setting to model, and work with, incomplete preferences, even in case of non-Archimedean problems. This leads us to suggest that desirability, rather than preference, should be the primitive notion at the basis of decision-theoretic axiomatisations.

cs.AI↗

arXiv2014

A geometric and game-theoretic study of the conjunction of possibility measures

In this paper, we study the conjunction of possibility measures when they are interpreted as coherent upper probabilities, that is, as upper bounds for some set of probability measures. We identify conditions under which the minimum of two possibility measures remains a possibility measure. We provide graphical way to check these conditions, by means of a zero-sum game formulation of the problem. This also gives us a nice way to adjust the initial possibility measures so their minimum is guaranteed to be a possibility measure. Finally, we identify conditions under which the minimum of two possibility measures is a coherent upper probability, or in other words, conditions under which the minimum of two possibility measures is an exact upper bound for the intersection of the credal sets of those two possibility measures.

math.PR↗

arXiv2014

Multilevel recording in Bi-deficient Pt/BFO/SRO heterostructures based on ferroelectric resistive switching targeting high-density information storage in nonvolatile memories

We demonstrate the feasibility of multilevel recording in Pt/Bi(1-d)FeO3/SrRuO3 capacitors using the ferroelectric resistive switching phenomenon exhibited by the Pt/Bi(1-d)FeO3 interface. A tunable population of up and down ferroelectric domains able to modulate the Schottky barrier height at the Pt/Bi(1-d)FeO3 interface can be achieved by means of either a collection of SET/RESET voltages or current compliances. This programming scheme gives rise to well defined resistance states, which form the basis for a multilevel storage nonvolatile memory.

cond-mat.mes-hall↗

arXiv2014

Irrelevant and independent natural extension for sets of desirable gambles

The results in this paper add useful tools to the theory of sets of desirable gambles, a growing toolbox for reasoning with partial probability assessments. We investigate how to combine a number of marginal coherent sets of desirable gambles into a joint set using the properties of epistemic irrelevance and independence. We provide formulas for the smallest such joint, called their independent natural extension, and study its main properties. The independent natural extension of maximal coherent sets of desirable gambles allows us to define the strong product of sets of desirable gambles. Finally, we explore an easy way to generalise these results to also apply for the conditional versions of epistemic irrelevance and independence. Having such a set of tools that are easily implemented in computer programs is clearly beneficial to fields, like AI, with a clear interest in coherent reasoning under uncertainty using general and robust uncertainty models that require no full specification.

cs.AI↗

arXiv2014

Conservative Inference Rule for Uncertain Reasoning under Incompleteness

In this paper we formulate the problem of inference under incomplete information in very general terms. This includes modelling the process responsible for the incompleteness, which we call the incompleteness process. We allow the process behaviour to be partly unknown. Then we use Walleys theory of coherent lower previsions, a generalisation of the Bayesian theory to imprecision, to derive the rule to update beliefs under incompleteness that logically follows from our assumptions, and that we call conservative inference rule. This rule has some remarkable properties: it is an abstract rule to update beliefs that can be applied in any situation or domain; it gives us the opportunity to be neither too optimistic nor too pessimistic about the incompleteness process, which is a necessary condition to draw reliable while strong enough conclusions; and it is a coherent rule, in the sense that it cannot lead to inconsistencies. We give examples to show how the new rule can be applied in expert systems, in parametric statistical inference, and in pattern classification, and discuss more generally the view of incompleteness processes defended here as well as some of its consequences.

cs.AI↗

arXiv2011

On the connection between probability boxes and possibility measures

We explore the relationship between possibility measures (supremum preserving normed measures) and p-boxes (pairs of cumulative distribution functions) on totally preordered spaces, extending earlier work in this direction by De Cooman and Aeyels, among others. We start by demonstrating that only those p-boxes who have 0-1-valued lower or upper cumulative distribution function can be possibility measures, and we derive expressions for their natural extension in this case. Next, we establish necessary and sufficient conditions for a p-box to be a possibility measure. Finally, we show that almost every possibility measure can be modelled by a p-box. Whence, any techniques for p-boxes can be readily applied to possibility measures. We demonstrate this by deriving joint possibility measures from marginals, under varying assumptions of independence, using a technique known for p-boxes. Doing so, we arrive at a new rule of combination for possibility measures, for the independent case.

math.PR↗

arXiv2010

Analytic model for the surface potential and drain current in negative capacitance field-effect transistors

In 2008, Salahuddin and Datta proposed that a ferroelectric material operating in the negative capacitance region could act as a step-up converter of the surface potential in a MOS structure, opening a new route for the realization of transistors with steeper subthreshold characteristics (S<60 mV/decade). In this letter, a comprehensive physics-based surface potential and drain current model for the negative capacitance field-effect transistor is reported. The model is aimed to evaluate the potentiality of such transistors for low-power switching applications. Moreover it provides a model core for memories devices relying on the hysteretic behavior of the ferroelectric gate insulator.

cond-mat.mes-hall↗

arXiv2009

Exchangeable lower previsions

We extend de Finetti's [Ann. Inst. H. Poincaré 7 (1937) 1--68] notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than (linear) previsions. We derive representation theorems in both the finite and countable cases, in terms of sampling without and with replacement, respectively.

math.PR↗

arXiv2008

Symmetry of models versus models of symmetry

A model for a subject's beliefs about a phenomenon may exhibit symmetry, in the sense that it is invariant under certain transformations. On the other hand, such a belief model may be intended to represent that the subject believes or knows that the phenomenon under study exhibits symmetry. We defend the view that these are fundamentally different things, even though the difference cannot be captured by Bayesian belief models. In fact, the failure to distinguish between both situations leads to Laplace's so-called Principle of Insufficient Reason, which has been criticised extensively in the literature. We show that there are belief models (imprecise probability models, coherent lower previsions) that generalise and include the Bayesian belief models, but where this fundamental difference can be captured. This leads to two notions of symmetry for such belief models: weak invariance (representing symmetry of beliefs) and strong invariance (modelling beliefs of symmetry). We discuss various mathematical as well as more philosophical aspects of these notions. We also discuss a few examples to show the relevance of our findings both to probabilistic modelling and to statistical inference, and to the notion of exchangeability in particular.

math.ST↗

arXiv2008

n-Monotone exact functionals

We study n-monotone functionals, which constitute a generalisation of n-monotone set functions. We investigate their relation to the concepts of exactness and natural extension, which generalise the notions of coherence and natural extension in the behavioural theory of imprecise probabilities. We improve upon a number of results in the literature, and prove among other things a representation result for exact n-monotone functionals in terms of Choquet integrals.

math.FA↗

arXiv2008

Exchangeable lower previsions

We extend de Finetti's (1937) notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than (linear) previsions. We prove representation theorems in both the finite and the countable case, in terms of sampling without and with replacement, respectively. We also establish a convergence result for sample means of exchangeable sequences. Finally, we study and solve the problem of exchangeable natural extension: how to find the most conservative (point-wise smallest) coherent and exchangeable lower prevision that dominates a given lower prevision.

math.PR↗