Search results for " inequality."

A nonhomogeneous nonlocal elasticity model

2006

Nonlocal elasticity with nonhomogeneous elastic moduli and internal length is addressed within a thermodynamic framework suitable to cope with continuum nonlocality. The Clausius–Duhem inequality, enriched by the energy residual, is used to derive the state equations and all other thermodynamic restrictions upon the constitutive equations. A phenomenological nonhomogeneous nonlocal (strain difference-dependent) elasticity model is proposed, in which the stress is the sum of two contributions, local and nonlocal, respectively governed by the standard elastic moduli tensor and the (symmetric positive-definite) nonlocal stiffness tensor. The inhomogeneities of the elastic moduli and of the int…

A True Extension of the Markov Inequality to Negative Random Variables

2020

The Markov inequality is a classical nice result in statistics that serves to demonstrate other important results as the Chebyshev inequality and the weak law of large numbers, and that has useful applications in the real world, when the random variable is unspecified, to know an upper bound for the probability that an variable differs from its expectation. However, the Markov inequality has one main flaw: its validity is limited to nonnegative random variables. In the very short note, we propose an extension of the Markov inequality to any non specified random variable. This result is completely new.

Charged oxygen interstitials in corundum: first principles simulations

2016

Combining supercell models and hybrid B3PW exchange-correlation functionals, ab initio simulations on quasi-stable configurations of interstitial ions in α-Al2O3 (corundum) crystals and possible migration trajectories have been modelled. We have studied crystalline distortion around migrating including interatomic distances and the effective atomic charges, as well as redistributions of the electronic density. Unlike neutral interstitial atom Oi studied by us previously, migrating ion does not form dumbbells with the nearest regular oxygen ions, due to the strong Coulomb interaction with the nearest cations as well as stronger repulsion between and adjacent regular ions. We have also estima…

2017

Summary Background The UN's Sustainable Development Goals (SDGs) are grounded in the global ambition of "leaving no one behind". Understanding today's gains and gaps for the health-related SDGs is essential for decision makers as they aim to improve the health of populations. As part of the Global Burden of Diseases, Injuries, and Risk Factors Study 2016 (GBD 2016), we measured 37 of the 50 health-related SDG indicators over the period 1990–2016 for 188 countries, and then on the basis of these past trends, we projected indicators to 2030. Methods We used standardised GBD 2016 methods to measure 37 health-related indicators from 1990 to 2016, an increase of four indicators since GBD 2015. W…

A tour of the theory of absolutely minimizing functions

2004

A detailed analysis of the class of absolutely minimizing functions in Euclidean spaces and the relationship to the infinity Laplace equation

A new paradigm for pattern classification: Nearest Border Techniques

2013

Published version of a chapter in the book: AI 2013: Advances in Artificial Intelligence. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-319-03680-9_44 There are many paradigms for pattern classification. As opposed to these, this paper introduces a paradigm that has not been reported in the literature earlier, which we shall refer to as the Nearest Border (NB) paradigm. The philosophy for developing such a NB strategy is as follows: Given the training data set for each class, we shall first attempt to create borders for each individual class. After that, we advocate that testing is accomplished by assigning the test sample to the class whose border it lies closest to…

Semmes surfaces and intrinsic Lipschitz graphs in the Heisenberg group

2018

A Semmes surface in the Heisenberg group is a closed set $S$ that is upper Ahlfors-regular with codimension one and satisfies the following condition, referred to as Condition B. Every ball $B(x,r)$ with $x \in S$ and $0 < r < \operatorname{diam} S$ contains two balls with radii comparable to $r$ which are contained in different connected components of the complement of $S$. Analogous sets in Euclidean spaces were introduced by Semmes in the late $80$'s. We prove that Semmes surfaces in the Heisenberg group are lower Ahlfors-regular with codimension one and have big pieces of intrinsic Lipschitz graphs. In particular, our result applies to the boundary of chord-arc domains and of redu…

Modality-specific dysfunctional neural processing of social-abstract and non-social-concrete information in schizophrenia

2021

Highlights • Social/non-social information processing in three modalities was investigated in SZ. • SZ showed reduced activation for social information only in gesture modality. • Reduced activation in SZ was observed for non-social information only in speech. • Neural Neural processing in bimodal condition is not different between patients and controls.

Rapid categorization of sound objects in anesthetized rats as indexed by the electrophysiological mismatch response

2014

It is not known whether animals can, similarly to humans, categorize auditory objects based on an abstract rule in combining their physical features. We recorded local-field potentials from the dura above the primary auditory cortex in urethane-anesthetized rats presented with sound series occasionally violating a rule (e.g., "the higher the frequency, the weaker the intensity"). In a separate control condition, the same frequency and intensity levels were applied in the sound objects, but they obeyed no rule. Responses found selectively to the violations of the rule suggest that an abstract rule was represented in the rat brain, enabling auditory categorization.

2017

The Cognitive reserve (CR) hypothesis was put forward to account for the variability in cognitive performance of patients with similar degrees of brain pathology. Compensatory neural activity within the frontal lobes has often been associated with CR. For the first time we investigated the independent effects of two CR proxies, education and NART IQ, on measures of executive function, fluid intelligence, speed of information processing, verbal short term memory (vSTM), naming, and perception in a sample of 86 patients with focal, unilateral frontal lesions and 142 healthy controls. We fitted multiple linear regression models for each of the cognitive measures and found that only NART IQ pre…