We analyze a continuous and discrete symmetries of the maximum lifetime problem in two dimensional sensor networks. We show, how a symmetry of the network and invariance of the problem under a given transformation group G can be utilized to simplify its solution. We prove, that for a G-invariant maximum lifetime problem there exists a G-invariant solution. Constrains which follow from the G-inv...

We construct fundamental domains for arithmetic subgroups of Γ = GL2(Fq [t]). Given ∆ ⊇ Γ(a) we construct a contracted form T of the Bruhat-Tits tree T and a fundamental domain F of ∆ acting on T. We define a lift of F to F ⊂ T called the “bipartite” lift. We show that F is a fundamental domain of ∆ acting on T precisely when F is “∆-compressed.”

We show how a number of second order time-dependent partial differential equations can be solved numerically by reformulating them in terms of inhomogeneous modified Helmholtz equations. Using recently derived analytic particular solutions for these equations, the resulting boundary value problems can be reduced to solving homogeneous Helmholtz equations which can be done effectively using the ...

In this paper, we first introduce a generalized modeling and analysis framework to explore the fundamental interactions between user association, coverage probability and link rate in a millimeter wave (mmWave) heterogeneous network (HetNet) in which there are multiple tiers of the ultra-highfrequency (UHF) macrocell and small cell base stations (BSs) and a single tier of mmWave small cell BSs....

We start from a study of the density-potential relation for classical homeoids in terms of an asymptotic expansion for small deviations from spherical symmetry. We then show that such expansion is a useful device that allows us to construct a variety of exact density-potential pairs with spheroidal, toroidal, or triaxial shapes for which the deviation from spherical symmetry is finite. As concr...

In this paper, we use local feature transformations estimated in the matching process as initial seeds for 2D homography estimation. The number of testing hypotheses is equal to the number of matches, naturally enabling a full search over the hypothesis space. Using this property, we develop an iterative algorithm that clusters the matches under the common 2D homography into one group, i.e., fe...

In this work we provide a space complexity analysis of the core language of the LogicGuard framework. Our approach is to abstract away from the formula structure of the core language in order to construct invariants for a recursive function. This final recursive function provided an upper bound for the number of instances of the monitor that need to be kept in memory over any duration of time. ...