Related papers: Boolean Models and Simultaneous Inequalities
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
Variational quantum algorithms (VQAs) utilize a hybrid quantum-classical architecture to recast problems of high-dimensional linear algebra as ones of stochastic optimization. Despite the promise of leveraging near- to intermediate-term…
We establish some linear and nonlinear integral inequalities of Gronwall-Bellman-Bihari type for functions with two independent variables on general time scales. The results are illustrated with examples, obtained by fixing the time scales…
Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in a variety of real-world applications. In dynamical control systems, they appear coupled to a linear input-output system in the form of linear…
The derivatives of a Boolean function are defined up to any order. The Taylor and MacLaurin expansions of a Boolean function are thus obtained. The last corresponds to the ring sum expansion (RSE) of a Boolean function, and is a more…
We propose a formalism to derive the maximal bound of generalized Bell type inequalities and shows that the formalism can be applied to various form of Bell functions. The generic Bell function is defined to generate the combinations of all…
In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can…
Several matrix/operator inequalies are given. Most of them are unexpected extensions of the Araki Log-majorization theorem, obtained thanks to a new log-majorization for positive linear maps and normal operators (Theorem 2.9). The main idea…
The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is…
Using the Carleman linearization technique the continuous iteration of a mapping is studied. Based on the detailed analysis of the Carleman embedding matrix the precise mathematical meaning is given to such notion. The ordinary differential…
Distributed delay equations have been used to model situations in which there is some sort of delay whose duration is uncertain. However, the interpretation of a distributed delay equation is actually very different from that of a delay…
We present a linear program that is capable of determining whether a set of correlations can be captured by a local realistic model. If the correlations can be described by such a model, the linear program outputs a joint probability…
Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…
We consider the Bayesian approach to linear inverse problems when the underlying operator depends on an unknown parameter. Allowing for finite dimensional as well as infinite dimensional parameters, the theory covers several models with…
We derive a Bell-type inequality for observables with arbitrary spectra. For the case of continuous variable systems we propose a possible experimental violation of this inequality, by using squeezed light and homodyne detection together…
Excited states are extracted from lattice correlation functions using a non-uniform prior on the model parameters. Models for both a single exponential and a sum of exponentials are considered, as well as an alternate model for the…
The chapter from the book introduces the delay theory, whose purpose is the modeling of the asynchronous circuits from digital electrical engineering with ordinary and differential pseudo-boolean equations.
Methods of solving big Boolean equations can be broadly classified as algebraic, tabular, numerical and map methods. The most prominent among these classes are the algebraic and map methods. This paper surveys and compares these two types…
Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep…
Scaled Boolean algebras are a category of mathematical objects that arose from attempts to understand why the conventional rules of probability should hold when probabilities are construed, not as frequencies or proportions or the like, but…