Robust network formation with biological applications

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F24%3A00376622" target="_blank" >RIV/68407700:21340/24:00376622 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.3934/nhm.2024035" target="_blank" >https://doi.org/10.3934/nhm.2024035</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3934/nhm.2024035" target="_blank" >10.3934/nhm.2024035</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Robust network formation with biological applications

Popis výsledku v původním jazyce

We have provided new results on the structure of optimal transportation networks obtained as minimizers of an energy cost functional posed on a discrete graph. The energy consists of a kinetic (pumping) and a material (metabolic) cost term, constrained by a local mass conservation law. In particular, we have proved that every tree (i.e., graph without loops) represents a local minimizer of the energy with concave metabolic cost. For the linear metabolic cost, we have proved that the set of minimizers contains a loop-free structure. Moreover, we enriched the energy functional such that it accounts also for robustness of the network, measured in terms of the Fiedler number of the graph with edge weights given by their conductivities. We examined fundamental properties of the modified functional, in particular, its convexity and differentiability. We provided analytical insights into the new model by considering two simple examples. Subsequently, we employed the projected subgradient method to find global minimizers of the modified functional numerically. We then presented two numerical examples, illustrating how the optimal graph's structure and energy expenditure depend on the required robustness of the network.

Název v anglickém jazyce

Robust network formation with biological applications

Popis výsledku anglicky

We have provided new results on the structure of optimal transportation networks obtained as minimizers of an energy cost functional posed on a discrete graph. The energy consists of a kinetic (pumping) and a material (metabolic) cost term, constrained by a local mass conservation law. In particular, we have proved that every tree (i.e., graph without loops) represents a local minimizer of the energy with concave metabolic cost. For the linear metabolic cost, we have proved that the set of minimizers contains a loop-free structure. Moreover, we enriched the energy functional such that it accounts also for robustness of the network, measured in terms of the Fiedler number of the graph with edge weights given by their conductivities. We examined fundamental properties of the modified functional, in particular, its convexity and differentiability. We provided analytical insights into the new model by considering two simple examples. Subsequently, we employed the projected subgradient method to find global minimizers of the modified functional numerically. We then presented two numerical examples, illustrating how the optimal graph's structure and energy expenditure depend on the required robustness of the network.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA23-04720S" target="_blank" >GA23-04720S: Jemné vlastnosti funkcí, operátorů a prostorů funkcí</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Networks and Heterogeneous Media

ISSN

1556-1801

e-ISSN

1556-181X

Svazek periodika

19

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

29

Strana od-do

771-799

Kód UT WoS článku

001292088200001

EID výsledku v databázi Scopus

2-s2.0-85202175173