Public city bus services across various developing cities inhabit multiple stay-locations on the routes due to ad-hoc bus stops to provide on-demand passenger boarding and alighting services. Characterizing these stay-locations is essential to correctly develop models for bus transit patterns used in various digital navigation services. In this poster, we create a deep learning-driven methodology to characterize ad-hoc stay-locations over bus routes based on crowd-sensing contextual information. Experiments over 720km of bus travel data in a semi-urban city in India indicate promising results from the model in terms of good detection accuracy.

The Borsuk-Ulam theorem is a fundamental result in algebraic topology, with applications to various areas of Mathematics. A classical application of the Borsuk-Ulam theorem is the Ham Sandwich theorem: The volumes of any n compact sets in R^n can always be simultaneously bisected by an (n-1)-dimensional hyperplane. In this paper, we demonstrate the equivalence between the Borsuk-Ulam theorem and the Ham Sandwich theorem. The main technical result we show towards establishing the equivalence is the following: For every odd polynomial restricted to the hypersphere f:S^n->R, there exists a compact set A in R^{n+1}, such that for every x in S^n we have f(x)=vol(A cap H^+) - vol(A cap H^-), where H is the oriented hyperplane containing the origin with x as the normal. A noteworthy aspect of the proof of the above result is the use of hyperspherical harmonics. Finally, using the above result we prove that there exist constants n_0, epsilon_0>0 such that for every n>= n_0 and epsilon <= epsilon_0/sqrt{48n}, any query algorithm to find an epsilon-bisecting (n-1)-dimensional hyperplane of n compact set in [-n^4.51,n^4.51]^n, even with success probability 2^-Omega(n), requires 2^Omega(n) queries.