A DE BRUIJN'S IDENTITY FOR DEPENDENT RANDOM VARIABLES BASED ON COPULA THEORY

2015 ◽  
Vol 30 (1) ◽  
pp. 125-140 ◽  
Author(s):  
Nayereh Bagheri Khoolenjani ◽  
Mohammad Hossein Alamatsaz
Keyword(s):  
Information Theory ◽  
Heat Equation ◽  
Fisher Information ◽  
Real World ◽  
Input Signal ◽  
Additive Noise ◽  
Differential Entropy ◽  
Copula Theory ◽  
De Bruijn ◽  
Derivatives Of

De Bruijn's identity shows a link between two fundamental concepts in information theory: entropy and Fisher information. In the literature, De Bruijn's identity has been stated under the assumption of independence between input signal and an additive noise. However, in the real world, the noise could be highly dependent on the main signal. The main aim of this paper is, firstly, to extend De bruijn's identity for signal-dependent noise channels and, secondly, to study how Stein and heat identities are related to De bruijn's identity. Thus, new versions of De Bruijn's identity are introduced in the case when input signal and additive noise are dependent and are jointly distributed according to Archimedean and Gaussian copulas. It is shown that in this generalized model, the derivatives of the differential entropy can be expressed in terms of a function of Fisher information. Our finding enfolds the conventional De Bruijn's identity as some remarks. Then, the equivalence among the new De Bruijn-type identity, Stein's identity and heat equation identity is established. The paper concludes with an application of the developed results in information theory.

QALO-MOR: Improved antlion optimizer based on quantum information theory for model order reduction

2021 ◽  
pp. 1-11
Author(s):  
Rosy Pradhan ◽  
Mohammad Rafique Khan ◽  
Prabir Kumar Sethy ◽  
Santosh Kumar Majhi
Keyword(s):  
Information Theory ◽  
Quantum Information ◽  
Real World ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Quantum Information Theory ◽  
Hunting Behavior ◽  
Model Order ◽  
Ant Lion Optimization ◽  
Real World Problems

The field of optimization science is proliferating that has made complex real-world problems easy to solve. Metaheuristics based algorithms inspired by nature or physical phenomena based methods have made its way in providing near-ideal (optimal) solutions to several complex real-world problems. Ant lion Optimization (ALO) has inspired by the hunting behavior of antlions for searching for food. Even with a unique idea, it has some limitations like a slower rate of convergence and sometimes confines itself into local solutions (optima). Therefore, to enhance its performance of classical ALO, quantum information theory is hybridized with classical ALO and named as QALO or quantum theory based ALO. It can escape from the limitations of basic ALO and also produces stability between processes of explorations followed by exploitation. CEC2017 benchmark set is adopted to estimate the performance of QALO compared with state-of-the-art algorithms. Experimental and statistical results demonstrate that the proposed method is superior to the original ALO. The proposed QALO extends further to solve the model order reduction (MOR) problem. The QALO based MOR method performs preferably better than other compared techniques. The results from the simulation study illustrate that the proposed method effectively utilized for global optimization and model order reduction.

A force-matching Stillinger-Weber potential for MoS2: Parameterization and Fisher information theory based sensitivity analysis

2017 ◽  
Vol 122 (24) ◽  
pp. 244301 ◽  
Author(s):  
Mingjian Wen ◽  
Sharmila N. Shirodkar ◽  
Petr Plecháč ◽  
Efthimios Kaxiras ◽  
Ryan S. Elliott ◽  
...  
Keyword(s):  
Information Theory ◽  
Sensitivity Analysis ◽  
Fisher Information ◽  
Force Matching ◽  
Weber Potential

scholarly journals Hexagonal Grid Computation of the Derivatives of the Solution to the Heat Equation by Using Fourth-Order Accurate Two-Stage Implicit Methods

2021 ◽  
Vol 5 (4) ◽  
pp. 203
Author(s):  
Suzan Cival Buranay ◽  
Nouman Arshad ◽  
Ahmed Hersi Matan
Keyword(s):  
Heat Equation ◽  
Fourth Order ◽  
Boundary Value ◽  
Time Variable ◽  
Implicit Methods ◽  
First Order ◽  
Mixed Derivatives ◽  
Hexagonal Grids ◽  
Spatial Derivatives ◽  
Derivatives Of

We give fourth-order accurate implicit methods for the computation of the first-order spatial derivatives and second-order mixed derivatives involving the time derivative of the solution of first type boundary value problem of two dimensional heat equation. The methods are constructed based on two stages: At the first stage of the methods, the solution and its derivative with respect to time variable are approximated by using the implicit scheme in Buranay and Arshad in 2020. Therefore, Oh4+τ of convergence on constructed hexagonal grids is obtained that the step sizes in the space variables x1, x2 and in time variable are indicated by h, 32h and τ, respectively. Special difference boundary value problems on hexagonal grids are constructed at the second stages to approximate the first order spatial derivatives and the second order mixed derivatives of the solution. Further, Oh4+τ order of uniform convergence of these schemes are shown for r=ωτh2≥116,ω>0. Additionally, the methods are applied on two sample problems.

scholarly journals Ecosystem antifragility: Beyond integrity and resilience

2019 ◽  
Author(s):  
Miguel Equihua Zamora ◽  
Mariana Espinosa ◽  
Carlos Gershenson ◽  
Oliver López-Corona ◽  
Mariana Munguia ◽  
...  
Keyword(s):  
Information Theory ◽  
Real World ◽  
Environmental Variability ◽  
Theory Approach ◽  
Ecosystem Resilience ◽  
Ecosystem Response ◽  
Ecosystem Integrity ◽  
Real World Applications ◽  
The Subject ◽  
Robust Systems

We review the concept of ecosystem resilience in its relation to ecosystem integrity from an information theory approach. We summarize the literature on the subject identifying three main narratives: ecosystem properties that enable them to be more resilient; ecosystem response to perturbations; and complexity. We also include original ideas with theoretical and quantitative developments with application examples. The main contribution is a new way to rethink resilience, that is mathematically formal and easy to evaluate heuristically in real-world applications: ecosystem antifragility. An ecosystem is antifragile if it benefits from environmental variability. Antifragility therefore goes beyond robustness or resilience because while resilient/robust systems are merely perturbation-resistant, antifragile structures not only withstand stress but also benefit from it.

Introduction

Hard Reading ◽  
2016 ◽  
pp. 3-5
Author(s):  
Tom Shippey
Keyword(s):  
Information Theory ◽  
Science Fiction ◽  
Cognitive Dissonance ◽  
Real World ◽  
Literature Information ◽  
Process Information ◽  
Whole Process ◽  
Alternative Vision ◽  
Technical Sense ◽  
High Information

This chapter argues that science fiction is hard reading because it requires the reader to process information at a level additional to that required for the reading of all fiction. The vital feature which distinguished the genre is the presence of the novum, a discrete item of information which the reader recognises as not present in the real world. Such items need first to be recognised and then collated to create an alternative vision of reality, the whole process having been described by the critic Darko Suvin as cognitive dissonance: the dissonance demanding recognition, the collation adding the cognitive element. Science fiction is a high information literature, information being used here in the technical sense of information theory.

How to Catch an AI Zombie

2020 ◽  
pp. 439-458
Author(s):  
Susan Schneider
Keyword(s):  
Information Theory ◽  
Natural Language ◽  
Real World ◽  
Phenomenal Consciousness ◽  
Artificial Consciousness ◽  
High Level ◽  
Integrated Information Theory ◽  
Integrated Information

How can we determine if AI is conscious? The chapter begins by illustrating that there are potentially very serious real-world costs to getting facts about AI consciousness wrong. It then proposes a provisional framework for investigating artificial consciousness that involves several tests or markers. One test is the AI Consciousness Test, which challenges an AI with a series of increasingly demanding natural-language interactions. Another test is based on the Integrated Information Theory, developed by Giulio Tononi and others, and considers whether a machine has a high level of “integrated information.” A third test is a Chip Test, where speculatively an individual’s brain is gradually replaced with durable microchips. If this individual being tested continues to report having phenomenal consciousness, the chapter argues that this could be a reason to believe that some machines could have consciousness.

scholarly journals Driving Simulators for Human Vehicle Interaction Design

2015 ◽  
Vol 1 (1) ◽  
pp. 297-306
Author(s):  
Alexandra Tucă ◽  
Valerian Croitorescu ◽  
Mircea Oprean ◽  
Thomas Brandemeir
Keyword(s):  
Real World ◽  
Input Signal ◽  
Interaction Design ◽  
High Frequency ◽  
Driver Behavior ◽  
Low Frequency ◽  
Driving Simulators ◽  
Sensory Inputs ◽  
Frequency Information ◽  
Busy Road

AbstractThe interaction human-vehicle, as well as driver’s behavior are subject long debated in the automotive engineering domain. Driving simulators have an extraordinary important role allowing research that would not be possible to study in real world scenarios.A driver uses his sensory inputs to obtain the required input to base his decision on. The bandwidth of the required input signal should be in accordance to the driver’s task. For simple tasks, like turning on the screen wipers or direction indicator, low frequency information is sufficient. High frequency information is required when cornering on a busy road or when driving in relatively limit situations.The optimal configuration of each sub-system remains a significant cause for debate and still poses a major challenge when considering the ability of simulators to extract realistic driver behavior. If a difference is observed between real and virtual conditions, the factors specifically cause these differences are very difficult to be explained.

INTEGRATION BY PARTS AND SMOOTHNESS OF THE LAW FOR A CLASS OF STOCHASTIC EVOLUTION EQUATIONS

2004 ◽  
Vol 07 (01) ◽  
pp. 89-129 ◽  
Author(s):  
STEFANO BONACCORSI ◽  
MARCO FUHRMAN
Keyword(s):  
Additive Noise ◽  
Evolution Equations ◽  
Transition Probabilities ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Integration By Parts ◽  
Infinite Dimensional ◽  
Integration By Parts Formula ◽  
Derivatives Of ◽  
Logarithmic Derivatives

We consider a Markov process X in a Hilbert space H, solution of a semilinear stochastic evolution equation driven by an infinite-dimensional Wiener process, occurring in the equation as an additive noise. Using techniques of the Malliavin calculus, under suitable assumptions, we prove an integration by parts formula for the transition probabilities νt, t>0 (the laws of Xt). We deduce results on differentiability (i.e. existence of logarithmic derivatives) of νt along a set of directions h∈H which can be described in terms of the coefficients of the equation. The general results are then applied to various classes of non linear stochastic partial differential equations and systems.

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