Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 

Saved Queries

Sign in to use this feature.

Search Filter Reset All

Years

Between: -

Subjects

remove_circle_outline
Add Subjects Reset
Select Subjects

Journals

remove_circle_outline
remove_circle_outline
Add Journals Reset
Select Journals

Article Types

remove_circle_outline
Add Article Types Reset
Select Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Countries / Regions Reset
Select Countries / Regions
Update Search
share announcement

Search Results (2)

Search Parameters:
Keywords = explicit piecewise affine solutions

Order results
Result details
Results per page
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
13 pages, 660 KB  
Article
Periodic Solutions in a Simple Delay Differential Equation
by Anatoli Ivanov and Sergiy Shelyag
Math. Comput. Appl. 2024, 29(3), 36; https://doi.org/10.3390/mca29030036 - 12 May 2024
Cited by 2 | Viewed by 2511
Abstract
A simple-form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback coefficient. The periodic solutions are built explicitly in [...] Read more.
A simple-form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback coefficient. The periodic solutions are built explicitly in the case with piecewise constant nonlinearities involved. The periodic dynamics are shown to persist under small perturbations of the equation, which make it smooth. The theoretical results are verified through extensive numerical simulations. Full article
(This article belongs to the Special Issue Recent Advances and New Challenges in Coupled Systems and Networks: Theory, Modelling, and Applications)
►▼ Show Figures

Figure 1

18 pages, 751 KB  
Article
Aiding Dictionary Learning Through Multi-Parametric Sparse Representation
by Florin Stoican and Paul Irofti
Algorithms 2019, 12(7), 131; https://doi.org/10.3390/a12070131 - 28 Jun 2019
Cited by 4 | Viewed by 4949
Abstract
The ℓ 1 relaxations of the sparse and cosparse representation problems which appear in the dictionary learning procedure are usually solved repeatedly (varying only the parameter vector), thus making them well-suited to a multi-parametric interpretation. The associated constrained optimization problems differ only through [...] Read more.
The ℓ 1 relaxations of the sparse and cosparse representation problems which appear in the dictionary learning procedure are usually solved repeatedly (varying only the parameter vector), thus making them well-suited to a multi-parametric interpretation. The associated constrained optimization problems differ only through an affine term from one iteration to the next (i.e., the problem’s structure remains the same while only the current vector, which is to be (co)sparsely represented, changes). We exploit this fact by providing an explicit, piecewise affine with a polyhedral support, representation of the solution. Consequently, at runtime, the optimal solution (the (co)sparse representation) is obtained through a simple enumeration throughout the non-overlapping regions of the polyhedral partition and the application of an affine law. We show that, for a suitably large number of parameter instances, the explicit approach outperforms the classical implementation. Full article
(This article belongs to the Special Issue Dictionary Learning Algorithms and Applications)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying article 1-50 on page 1 of 1.
Back to TopTop