Search results for "predicate"
showing 10 items of 216 documents
Dimension estimates for the boundary of planar Sobolev extension domains
2020
We prove an asymptotically sharp dimension upper-bound for the boundary of bounded simply-connected planar Sobolev $W^{1,p}$-extension domains via the weak mean porosity of the boundary. The sharpness of our estimate is shown by examples.
Itô calculus extended to systems driven by -stable Lévy white noises (a novel clip on the tails of Lévy motion)
2007
Abstract The paper deals with probabilistic characterization of the response of non-linear systems under α -stable Levy white noise input. It is shown that, by properly selecting a clip in the probability density function of the input, the moments of the increments of Levy motion process remain all of the same order ( d t ) , like the increments of the Compound Poisson process. It follows that the Ito calculus extended to Poissonian input, may also be used for α -stable Levy white noise input processes. It is also shown that, when the clip on the tails of the probability of the increments of the Levy motion approaches to infinity, the Einstein–Smoluchowsky equation is restored. Once these c…
Verbs and Predicates in Ancient Greece
2019
The author starts by reading an excerpt by Symplicius of Cilicia where it is said that Aristotle spoke of the category action established as mere action and taken as a genus. This category was connected with dispositions of the mind corresponding to verbs. Equally there existed mere affection too. It is precisely the verbs that could convey either action or affection, and the two categories action and affection were drawn from the active and passive verbs. These verbs, however, are not the same as those called upright and overturned by the Stoics. While Aristotle took mere action and mere affection into account, the Stoics were interested in predicates, and predicates definitely correspond …
Neural Networks with Multidimensional Cross-Entropy Loss Functions
2019
Deep neural networks have emerged as an effective machine learning tool successfully applied for many tasks, such as misinformation detection, natural language processing, image recognition, machine translation, etc. Neural networks are often applied to binary or multi-class classification problems. In these settings, cross-entropy is used as a loss function for neural network training. In this short note, we propose an extension of the concept of cross-entropy, referred to as multidimensional cross-entropy, and its application as a loss function for classification using neural networks. The presented computational experiments on a benchmark dataset suggest that the proposed approaches may …
Rotation topological factors of minimal $\mathbb {Z}^{d}$-actions on the Cantor set
2006
In this paper we study conditions under which a free minimal Z d -action on the Cantor set is a topological extension of the action of d rotations, either on the product T d of d 1-tori or on a single 1-torus T 1 . We extend the notion of linearly recurrent systems defined for Z-actions on the Cantor set to Z d -actions, and we derive in this more general setting a necessary and sufficient condition, which involves a natural combinatorial data associated with the action, allowing the existence of a rotation topological factor of one of these two types.
THE CAUCHY DUAL AND 2-ISOMETRIC LIFTINGS OF CONCAVE OPERATORS
2018
We present some 2-isometric lifting and extension results for Hilbert space concave operators. For a special class of concave operators we study their Cauchy dual operators and discuss conditions under which these operators are subnormal. In particular, the quasinormality of compressions of such operators is studied.
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.
Development of non-equilibrium Green's functions for use with full interaction in complex systems
2016
We present an ongoing development of an existing code for calculating groundstate, steady-state, and transient properties of many-particle systems. The development involves the addition of the full four-index two electron integrals, which allows for the calculation of transport systems, as well as the extension to multi-level electronic systems, such as atomic and molecular systems and other applications. The necessary derivations are shown, along with some preliminary results and a summary of future plans for the code. peerReviewed
An Extension of the DgLARS Method to High-Dimensional Relative Risk Regression Models
2020
In recent years, clinical studies, where patients are routinely screened for many genomic features, are becoming more common. The general aim of such studies is to find genomic signatures useful for treatment decisions and the development of new treatments. However, genomic data are typically noisy and high dimensional, not rarely outstripping the number of patients included in the study. For this reason, sparse estimators are usually used in the study of high-dimensional survival data. In this paper, we propose an extension of the differential geometric least angle regression method to high-dimensional relative risk regression models.
A complete characterization of all weakly additive measures and of all valuations on the canonical extension of any finite MV-chain
2010
We consider extensions of the unique additive measure on a finite MV-chain to uncertainty measures on its canonical Girard algebra extension. If the underlying MV-chain has more than two non-trivial elements, in a previous paper we have proved the non-existence of strongly additive measure extensions, where strong additivity is defined as additivity not for all disjoint unions but only restricted to the so-called divisible disjoint unions. This negative result motivates to look for weakly additive measure extensions which are defined to be additive only on all MV-subalgebras of the canonical Girard algebra extension. We obtain a characterization of all such MV-subalgebras which are in fact …