scholarly journals Optimal bounds of classical and non-classical means in terms of Q means

2021 ◽  
Vol 116 (1) ◽  
Author(s):  
Monika Nowicka ◽  
Alfred Witkowski
Keyword(s):  
Broad Class ◽  
Optimal Bounds ◽  
Classical Means

AbstractWe show optimal bounds of the form $$Q_\alpha<M<Q_\beta $$ Q α < M < Q β , where $$\begin{aligned} Q_\alpha (x,y)={\mathsf {A}}(x,y)\frac{{\mathsf {A}}^2(x,y)}{(1-\alpha ){\mathsf {A}}^2(x,y)+\alpha {\mathsf {G}}^2(x,y)} \end{aligned}$$ Q α ( x , y ) = A ( x , y ) A 2 ( x , y ) ( 1 - α ) A 2 ( x , y ) + α G 2 ( x , y ) and M belongs to a broad class of classical homogeneous, symmetric means of two variables.

Contrast From Point Defects in The Infinitesimal Approximation

1980 ◽  
Vol 38 ◽  
pp. 350-351
Author(s):  
L. J. Sykes ◽  
J. J. Hren
Keyword(s):  
Electron Microscope ◽  
Point Defects ◽  
Broad Class ◽  
Stacking Fault ◽  
Crystalline Solids ◽  
Dislocation Loops ◽  
Analytical Expression ◽  
Stacking Fault Tetrahedra

In electron microscope studies of crystalline solids there is a broad class of very small objects which are imaged primarily by strain contrast. Typical examples include: dislocation loops, precipitates, stacking fault tetrahedra and voids. Such objects are very difficult to identify and measure because of the sensitivity of their image to a host of variables and a similarity in their images. A number of attempts have been made to publish contrast rules to help the microscopist sort out certain subclasses of such defects. For example, Ashby and Brown (1963) described semi-quantitative rules to understand small precipitates. Eyre et al. (1979) published a catalog of images for BCC dislocation loops. Katerbau (1976) described an analytical expression to help understand contrast from small defects. There are other publications as well.

Similarity problems of the theory of unsteady concentration boundary layer

1983 ◽  
Vol 48 (10) ◽  
pp. 2751-2766
Author(s):  
Ondřej Wein ◽  
N. D. Kovalevskaya
Keyword(s):  
Boundary Layer ◽  
Approximate Method ◽  
Steady Flow ◽  
Broad Class ◽  
Concentration Boundary Layer ◽  
Concentration Change ◽  
Concentration Boundary ◽  
Flow Problems

Using a new approximate method, transient course of the local and mean diffusion fluxes following a step concentration change on the wall has been obtained for a broad class of steady flow problems.

Disabilities and Well-Being

2019 ◽  
pp. 121-137
Author(s):  
Joshua Shepherd
Keyword(s):  
Broad Class ◽  
Minimally Conscious State ◽  
Well Being ◽  
Conscious State ◽  
Minimally Conscious

This chapter argues for a normative distinction between disabilities that are inherently negative with respect to well-being and disabilities that are inherently neutral. After clarifying terms, the author discusses recent arguments according to which possession of a disability is inherently neutral with respect to well-being. He notes that although these arguments are compelling, they are only intended to cover certain disabilities and, in fact, that there exists a broad class regarding which they do not apply. He then discusses two problem cases: locked-in syndrome and the minimally conscious state, and explains why these are cases in which possession of these disabilities makes one worse off overall. He argues that disabilities that significantly impair control over one’s situation tend to be inherently negative with respect to well-being; other disabilities do not. The upshot is that we must draw an important normative distinction between disabilities that undermine this kind of control and disabilities that do not.

Nearly Exact Bayesian Estimation of Non-linear No-Arbitrage Term-Structure Models*

2021 ◽  
Author(s):  
Marcello Pericoli ◽  
Marco Taboga
Keyword(s):  
Bayesian Estimation ◽  
Term Structure ◽  
Broad Class ◽  
Model Parameters ◽  
State Variables ◽  
Computationally Efficient ◽  
Macroeconomic Factors ◽  
No Arbitrage ◽  
Term Structure Models ◽  
Non Linear

Abstract We propose a general method for the Bayesian estimation of a very broad class of non-linear no-arbitrage term-structure models. The main innovation we introduce is a computationally efficient method, based on deep learning techniques, for approximating no-arbitrage model-implied bond yields to any desired degree of accuracy. Once the pricing function is approximated, the posterior distribution of model parameters and unobservable state variables can be estimated by standard Markov Chain Monte Carlo methods. As an illustrative example, we apply the proposed techniques to the estimation of a shadow-rate model with a time-varying lower bound and unspanned macroeconomic factors.

scholarly journals Hybrid structures applied to ideals in near-rings

2021 ◽  
Author(s):  
B. Elavarasan ◽  
G. Muhiuddin ◽  
K. Porselvi ◽  
Y. B. Jun
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Real World ◽  
Rough Set Theory ◽  
Wide Spectrum ◽  
Hybrid Structure ◽  
Soft Set ◽  
Hybrid Structures ◽  
Classical Mathematics ◽  
Classical Means

AbstractHuman endeavours span a wide spectrum of activities which includes solving fascinating problems in the realms of engineering, arts, sciences, medical sciences, social sciences, economics and environment. To solve these problems, classical mathematics methods are insufficient. The real-world problems involve many uncertainties making them difficult to solve by classical means. The researchers world over have established new mathematical theories such as fuzzy set theory and rough set theory in order to model the uncertainties that appear in various fields mentioned above. In the recent days, soft set theory has been developed which offers a novel way of solving real world issues as the issue of setting the membership function does not arise. This comes handy in solving numerous problems and many advancements are being made now-a-days. Jun introduced hybrid structure utilizing the ideas of a fuzzy set and a soft set. It is to be noted that hybrid structures are a speculation of soft set and fuzzy set. In the present work, the notion of hybrid ideals of a near-ring is introduced. Significant work has been carried out to investigate a portion of their significant properties. These notions are characterized and their relations are established furthermore. For a hybrid left (resp., right) ideal, different left (resp., right) ideal structures of near-rings are constructed. Efforts have been undertaken to display the relations between the hybrid product and hybrid intersection. Finally, results based on homomorphic hybrid preimage of a hybrid left (resp., right) ideals are proved.

scholarly journals Information-Theoretic Generalization Bounds for Meta-Learning and Applications

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 126
Author(s):  
Sharu Theresa Jose ◽  
Osvaldo Simeone
Keyword(s):  
Learning Algorithm ◽  
Broad Class ◽  
Performance Measure ◽  
Training Data ◽  
Learning To Learn ◽  
Data Set ◽  
Information Theoretic ◽  
Meta Learning ◽  
Task Training ◽  
Test Sets

Meta-learning, or “learning to learn”, refers to techniques that infer an inductive bias from data corresponding to multiple related tasks with the goal of improving the sample efficiency for new, previously unobserved, tasks. A key performance measure for meta-learning is the meta-generalization gap, that is, the difference between the average loss measured on the meta-training data and on a new, randomly selected task. This paper presents novel information-theoretic upper bounds on the meta-generalization gap. Two broad classes of meta-learning algorithms are considered that use either separate within-task training and test sets, like model agnostic meta-learning (MAML), or joint within-task training and test sets, like reptile. Extending the existing work for conventional learning, an upper bound on the meta-generalization gap is derived for the former class that depends on the mutual information (MI) between the output of the meta-learning algorithm and its input meta-training data. For the latter, the derived bound includes an additional MI between the output of the per-task learning procedure and corresponding data set to capture within-task uncertainty. Tighter bounds are then developed for the two classes via novel individual task MI (ITMI) bounds. Applications of the derived bounds are finally discussed, including a broad class of noisy iterative algorithms for meta-learning.

scholarly journals Searching for elusive dark sectors with terrestrial and celestial observations

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Roberto Contino ◽  
Kevin Max ◽  
Rashmish K. Mishra
Keyword(s):  
Field Theory ◽  
Broad Class ◽  
High Energy ◽  
Effective Field ◽  
Dark Sector ◽  
Minimum Requirement ◽  
Conformal Field ◽  
Starting Point ◽  
The Standard Model ◽  
Visible Sector

Abstract We consider the possible existence of a SM-neutral and light dark sector coupled to the visible sector through irrelevant portal interactions. Scenarios of this kind are motivated by dark matter and arise in various extensions of the Standard Model. We characterize the dark dynamics in terms of one ultraviolet scale Λuv, at which the exchange of heavy mediator fields generates the portal operators, and by one infrared scale ΛIR, setting the mass gap. At energies ΛIR « E « Λuv the dark sector behaves like a conformal field theory and its phenomenology can be studied model independently. We derive the constraints set on this scenario by high- and low-energy laboratory experiments and by astrophysical observations. Our results are conservative and serve as a minimum requirement that must be fulfilled by the broad class of models satisfying our assumptions, of which we give several examples. The experimental constraints are derived in a manner consistent with the validity of the effective field theory used to define the portal interactions. We find that high-energy colliders give the strongest bounds and exclude UV scales up to a few TeV, but only in specific ranges of the IR scale. The picture emerging from current searches can be taken as a starting point to design a future experimental strategy with broader sensitivity.

scholarly journals Mathematical Properties of Variable Topological Indices

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 43
Author(s):  
José M. Sigarreta
Keyword(s):  
Real Number ◽  
Large Class ◽  
Symmetric Functions ◽  
Topological Indices ◽  
Current Interest ◽  
Zagreb Indices ◽  
Mathematical Properties ◽  
Connectivity Indices ◽  
Optimal Bounds ◽  
New Framework

A topic of current interest in the study of topological indices is to find relations between some index and one or several relevant parameters and/or other indices. In this paper we study two general topological indices Aα and Bα, defined for each graph H=(V(H),E(H)) by Aα(H)=∑ij∈E(H)f(di,dj)α and Bα(H)=∑i∈V(H)h(di)α, where di denotes the degree of the vertex i and α is any real number. Many important topological indices can be obtained from Aα and Bα by choosing appropriate symmetric functions and values of α. This new framework provides new tools that allow to obtain in a unified way inequalities involving many different topological indices. In particular, we obtain new optimal bounds on the variable Zagreb indices, the variable sum-connectivity index, the variable geometric-arithmetic index and the variable inverse sum indeg index. Thus, our approach provides both new tools for the study of topological indices and new bounds for a large class of topological indices. We obtain several optimal bounds of Aα (respectively, Bα) involving Aβ (respectively, Bβ). Moreover, we provide several bounds of the variable geometric-arithmetic index in terms of the variable inverse sum indeg index, and two bounds of the variable inverse sum indeg index in terms of the variable second Zagreb and the variable sum-connectivity indices.

scholarly journals Using Sibling Designs to Understand Neurodevelopmental Disorders: From Genes and Environments to Prevention Programming

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Mark Wade ◽  
Heather Prime ◽  
Sheri Madigan
Keyword(s):  
Neurodevelopmental Disorders ◽  
Broad Class ◽  
Psychosocial Health ◽  
Recurrence Risk ◽  
Autism Spectrum ◽  
Functional Neuroanatomy ◽  
Early Screening ◽  
Environmental Liabilities ◽  
Hyperactivity Disorder ◽  
Significant Bearing

Neurodevelopmental disorders represent a broad class of childhood neurological conditions that have a significant bearing on the wellbeing of children, families, and communities. In this review, we draw on evidence from two common and widely studied neurodevelopmental disorders—autism spectrum disorder (ASD) and attention-deficit hyperactivity disorder (ADHD)—to demonstrate the utility of genetically informed sibling designs in uncovering the nature and pathogenesis of these conditions. Specifically, we examine how twin, recurrence risk, and infant prospective tracking studies have contributed to our understanding of genetic and environmental liabilities towards neurodevelopmental morbidity through their impact on neurocognitive processes and structural/functional neuroanatomy. It is suggested that the siblings of children with ASD and ADHD are at risk not only of clinically elevated problems in these areas, but also of subthreshold symptoms and/or subtle impairments in various neurocognitive skills and other domains of psychosocial health. Finally, we close with a discussion on the practical relevance of sibling designs and how these might be used in the service of early screening, prevention, and intervention efforts that aim to alleviate the negative downstream consequences associated with disorders of neurodevelopment.

scholarly journals Air Learning: a deep reinforcement learning gym for autonomous aerial robot visual navigation

2021 ◽  
Author(s):  
Srivatsan Krishnan ◽  
Behzad Boroujerdian ◽  
William Fu ◽  
Aleksandra Faust ◽  
Vijay Janapa Reddi
Keyword(s):  
Reinforcement Learning ◽  
Embedded System ◽  
Broad Class ◽  
Visual Navigation ◽  
Raspberry Pi ◽  
Latency Distribution ◽  
Hardware In The Loop ◽  
Resource Constrained ◽  
Aerial Robot ◽  
Policy Optimization

AbstractWe introduce Air Learning, an open-source simulator, and a gym environment for deep reinforcement learning research on resource-constrained aerial robots. Equipped with domain randomization, Air Learning exposes a UAV agent to a diverse set of challenging scenarios. We seed the toolset with point-to-point obstacle avoidance tasks in three different environments and Deep Q Networks (DQN) and Proximal Policy Optimization (PPO) trainers. Air Learning assesses the policies’ performance under various quality-of-flight (QoF) metrics, such as the energy consumed, endurance, and the average trajectory length, on resource-constrained embedded platforms like a Raspberry Pi. We find that the trajectories on an embedded Ras-Pi are vastly different from those predicted on a high-end desktop system, resulting in up to $$40\%$$ 40 % longer trajectories in one of the environments. To understand the source of such discrepancies, we use Air Learning to artificially degrade high-end desktop performance to mimic what happens on a low-end embedded system. We then propose a mitigation technique that uses the hardware-in-the-loop to determine the latency distribution of running the policy on the target platform (onboard compute on aerial robot). A randomly sampled latency from the latency distribution is then added as an artificial delay within the training loop. Training the policy with artificial delays allows us to minimize the hardware gap (discrepancy in the flight time metric reduced from 37.73% to 0.5%). Thus, Air Learning with hardware-in-the-loop characterizes those differences and exposes how the onboard compute’s choice affects the aerial robot’s performance. We also conduct reliability studies to assess the effect of sensor failures on the learned policies. All put together, Air Learning enables a broad class of deep RL research on UAVs. The source code is available at: https://github.com/harvard-edge/AirLearning.

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