scholarly journals Flows in strongly regular periodic dynamic resource networks

2021 ◽  
Vol 31 (3) ◽  
pp. 458-470
Author(s):  
V.A. Skorokhodov ◽  
D.O. Sviridkin
Keyword(s):  
Resource Allocation ◽  
Limit State ◽  
Dynamic Networks ◽  
Dynamic Network ◽  
Limit States ◽  
Resource Network ◽  
Strongly Regular ◽  
Dynamic Resource ◽  
Resource Networks ◽  
Time Resource

This paper is devoted to studying the processes of resource allocation in dynamic resource networks. In such networks, the capacities of the arcs depend on time. Resource allocation in the network occurs in discrete time. The resource of each vertex is distributed only between adjacent vertices according to some rules. The study of the processes of resource redistribution in such networks is carried out. The main goal is to develop methods for finding the limit state (distribution) of a resource in a dynamic resource network. It is shown that the approach based on the construction of an auxiliary network is also applicable to reduce the problem of resource allocation in a dynamic network to a similar problem in an auxiliary network. Theorems on the existence of a limit state on an auxiliary graph are proved for strongly regular periodic dynamical networks. To find the limit states, one can use the approaches which are developed for the shortest path problem in dynamic networks.

scholarly journals Single-Threshold Model Resource Network and Its Double-Threshold Modifications

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1444
Author(s):  
Liudmila Zhilyakova
Keyword(s):  
Threshold Model ◽  
General Characteristic ◽  
Threshold Value ◽  
Homogeneous Markov Chain ◽  
Limit States ◽  
Infinitely Divisible ◽  
Resource Network ◽  
Basic Model ◽  
Operation Rules ◽  
Resource Networks

A resource network is a non-classical flow model where the infinitely divisible resource is iteratively distributed among the vertices of a weighted digraph. The model operates in discrete time. The weights of the edges denote their throughputs. The basic model, a standard resource network, has one general characteristic of resource amount—the network threshold value. This value depends on graph topology and weights of edges. This paper briefly outlines the main characteristics of standard resource networks and describes two its modifications. In both non-standard models, the changes concern the rules of receiving the resource by the vertices. The first modification imposes restrictions on the selected vertices’ capacity, preventing them from accumulating resource surpluses. In the second modification, a network with so-called greedy vertices, on the contrary, vertices first accumulate resource themselves and only then begin to give it away. It is noteworthy that completely different changes lead, in general, to the same consequences: the appearance of a second threshold value. At some intervals of resource values in networks, their functioning is described by a homogeneous Markov chain, at others by more complex rules. Transient processes and limit states in networks with different topologies and different operation rules are investigated and described.

SAFER model: Strategic allocation of fundamental epidemic resources

2020 ◽  
Author(s):  
B W Weston ◽  
Z N Swingen ◽  
S Gramann ◽  
D Pojar
Keyword(s):  
Resource Allocation ◽  
Real Time ◽  
Community Based ◽  
Broad Distribution ◽  
Census Tracts ◽  
Milwaukee County ◽  
Strategic Allocation ◽  
Four Quadrant ◽  
Time Resource ◽  
Critical Resources

Abstract Background To describe the Strategic Allocation of Fundamental Epidemic Resources (SAFER) model as a method to inform equitable community distribution of critical resources and testing infrastructure. Methods The SAFER model incorporates a four-quadrant design to categorize a given community based on two scales: testing rate and positivity rate. Three models for stratifying testing rates and positivity rates were applied to census tracts in Milwaukee County, Wisconsin: using median values (MVs), cluster-based classification and goal-oriented values (GVs). Results Each of the three approaches had its strengths. MV stratification divided the categories most evenly across geography, aiding in assessing resource distribution in a fixed resource and testing capacity environment. The cluster-based stratification resulted in a less broad distribution but likely provides a truer distribution of communities. The GVs grouping displayed the least variation across communities, yet best highlighted our areas of need. Conclusions The SAFER model allowed the distribution of census tracts into categories to aid in informing resource and testing allocation. The MV stratification was found to be of most utility in our community for near real time resource allocation based on even distribution of census tracts. The GVs approach was found to better demonstrate areas of need.

scholarly journals DNA-based constitutional dynamic networks as functional modules for logic gates and computing circuit operations

2021 ◽  
Vol 12 (15) ◽  
pp. 5473-5483
Author(s):  
Zhixin Zhou ◽  
Jianbang Wang ◽  
R. D. Levine ◽  
Francoise Remacle ◽  
Itamar Willner
Keyword(s):  
Nucleic Acid ◽  
Dynamic Networks ◽  
Dynamic Network ◽  
Logic Gates ◽  
Functional Modules ◽  
Logic Operations

A nucleic acid-based constitutional dynamic network (CDN) provides a single functional computational module for diverse input-guided logic operations and computing circuits.

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