Results 151 to 160 of about 219,337 (309)

On Bounds for Norms of Reparameterized ReLU Artificial Neural Network Parameters: Sums of Fractional Powers of the Lipschitz Norm Control the Network Parameter Vector

open access: yesMathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT It is an elementary fact in the scientific literature that the Lipschitz norm of the realization function of a feedforward fully connected rectified linear unit (ReLU) artificial neural network (ANN) can, up to a multiplicative constant, be bounded from above by sums of powers of the norm of the ANN parameter vector.
Arnulf Jentzen, Timo Kröger
wiley   +1 more source

On piecewise linear approximation of quadratic functions

open access: yes, 2000
The authors discuss piecewise linear approximation to an \(n\)-variate quadratic function. The approximation is linear on the simplices of a triangulation. The problem considered is the following. Given a quadratic polynomial, find the piecewise linear approximation such that the \(L^\infty\)-norm is below a certain tolerance and such that the number ...
Pottmann, Helmut   +4 more
openaire   +2 more sources

Hybrid Reaction–Diffusion Epidemic Models: Dynamics and Emergence of Oscillations

open access: yesMathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT In this paper, we construct a hybrid epidemic mathematical model based on a reaction–diffusion system of the SIR (susceptible‐infected‐recovered) type. This model integrates the impact of random factors on the transmission rate of infectious diseases, represented by a probabilistic process acting at discrete time steps.
Asmae Tajani   +2 more
wiley   +1 more source

Space‐Time FEM Solution of Dynamic Contact Problem With Discontinuous Velocity for Multiple Impact of Deformed Bar Using PDAS Method

open access: yesMathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT A class of one‐dimensional impact and dynamic contact problems taking into account non‐smooth velocities is studied. The new space‐time finite element approximation of dynamic variational inequalities is suggested. The non‐smooth solution for the impact of an obstacle by an elastic bar and its energy conservation under persistency conditions ...
Victor A. Kovtunenko   +2 more
wiley   +1 more source

Analysis of a Mathematical Model of Marital Satisfaction

open access: yesMathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT A large number of marriages end in divorce. In this paper, we present a model for the emotional state of a couple based on bilinear ordinary differential equations. We study the effect of changes of each individual's self‐emotional state on the couple's state.
Benito Chen‐Charpentier   +2 more
wiley   +1 more source

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