Applied Mathematics Research Papers

Vibration and Damping In Distributed Systems

The WKB Method for Eigenvalue Problems I: Space Dimension One. The WKB Method for Eigenvalue Problems II: Multidimensional Spaces. Miscellaneous Methods. Visualization. Remarks on Experimental Determination of Modal Damping Rates in Elastic...

1. Pointwise Control for Distributed Systems

1.1. Introduction. We consider in this chapter systems modeled by Partial Differential Equations of evolution, i.e., evolution distributed systems. We suppose that we can act on the system only at some particular points, this is the so-call...

Regional controllability of distributed systems

Parameter identification in distributed systems: A synthesizing overview

This paper surveys the distributed system parameter identification problem and concludes that it can be treated as a series of largely independent subproblems, each of which must be considered in any attempt to treat the problem in applicat...

Optimal Control of Distributed Systems. Theory and Applications

The existence of solutions to optimal control problems Optimality system for optimal control problems The solvability of boundary value problems for a dense set of data The problem of work minimization in accelerating still fluid to a presc...

Neural Networks for Statistical Modeling

On the Spectral Bias of Neural Networks

Neural networks are known to be a class of highly expressive functions able to fit even random input-output mappings with $100\%$ accuracy. In this work, we present properties of neural networks that complement this aspect of expressivity. ...

Hyperbolic Neural Networks

Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean geomet...

Optimization using neural networks

The design of feedback (or recurrent) neural networks to produce good solutions to complex optimization problems is discussed. The theoretical basis for applying neural networks to optimization problems is reviewed, and a design rule that s...

Neural Networks: A Review from a Statistical Perspective

This paper informs a statistical readership about Artificial Neural Networks (ANNs), points out some of the links with statistical methodology and encourages cross-disciplinary research in the directions most likely to bear fruit. The areas...

Lagrangian Neural Networks

Accurate models of the world are built upon notions of its underlying symmetries. In physics, these symmetries correspond to conservation laws, such as for energy and momentum. Yet even though neural network models see increasing use in the...

Neural networks and statistical techniques: A review of applications

Approximation theory of the MLP model in neural networks

In this survey we discuss various approximation-theoretic problems that arise in the multilayer feedforward perceptron (MLP) model in neural networks. The MLP model is one of the more popular and practical of the many neural network models....

Tensorizing Neural Networks

Deep neural networks currently demonstrate state-of-the-art performance in several domains. At the same time, models of this class are very demanding in terms of computational resources. In particular, a large amount of memory is required b...

Bayesian Learning for Neural Networks

Pattern Recognition and Neural Networks

This 1996 book is a reliable account of the statistical framework for pattern recognition and machine learning. With unparalleled coverage and a wealth of case-studies this book gives valuable insight into both the theory and the enormously...

Understanding Neural Networks as Statistical Tools

Neural networks have received a great deal of attention over the last few years. They are being used in the areas of prediction and classification, areas where regression models and other related statistical techniques have traditionally be...

Hamiltonian Neural Networks

Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models th...

A neural network model for survival data

Neural networks have received considerable attention recently, mostly by non-statisticians. They are considered by many to be very promising tools for classification and prediction. In this paper we present an approach to modelling censored...

Logics of Statements in Context-Category Independent Basics

Based on a formalization of open formulas as statements in context, the paper presents a freshly new and abstract view of logics and specification formalisms. Generalizing concepts like sets of generators in Group Theory, underlying graph o...