TITLE:
Hyperbolic Geometry for Optimal Placement of Patient Assistance Terminals in Wireless Mesh Networks: A Local Data-Driven Approach in Data-Scarce Remote Terrains
AUTHORS:
Felix Davis
KEYWORDS:
Hyperbolic Geometry, Wireless Mesh Networks, Patient Assistance Terminals; Network Topology Design, Smart Healthcare Systems
JOURNAL NAME:
Journal of Biomedical Science and Engineering,
Vol.19 No.1,
January
12,
2026
ABSTRACT: We present a novel framework for optimal placement of Patient Assistance Terminals (PATs) in wireless mesh networks using hyperbolic geometry modeling of remote terrains. The approach models terrain as a hyperbolic plane
ℍ
2
with Poincaré disk representation
D={
z∈ℂ:| z |<1 }
to capture exponential distortions and tree-like hierarchies inherent in hub-centric settlement patterns. Let
G=(
V,ℰ
)
represent the network graph where
V
denotes settlement hubs and internet spots, and
ℰ
encodes connectivity constraints. The optimization objective minimizes
J(
p
)=α
∑
i∈V
1
accessibility
i
(
p
)
+β
∑
(
i,j
)∈ℰ
latency
ij
(
p
)
where
p∈
ℍ
2
represents PAT positions and
(
α,β
)
is multi-objective weights. Distortion-minimizing embeddings
ϕ:G→
ℍ
2
preserve local community knowledge while enabling global optimization. Experimental validation of the framework demonstrates a high reliability in brutal, unforgiving environments through local human knowledge integration, achieving low-latency mesh networks that scale without noise or constraint issues.