Let X be a set of multicolored points in the plane such that no three points are collinear and each color appears on at most ⌈|X|/2⌉ points. We show the existence of a non-crossing properly colored geometric perfect matching on X (if |X| is even), and the existence of a non-crossing properly colored geometric spanning tree with maximum degree at most 3 on X. Moreover, we show the existence of a...

Membrane transporters actively translocate their substrate by undergoing large-scale structural transitions between inward- (IF) and outward-facing (OF) states ('alternating-access' mechanism). Despite extensive structural studies, atomic-level mechanistic details of such structural transitions, and as importantly, their coupling to chemical events supplying the energy, remain amongst the most ...

We address the induced matching enumeration problem. An edge set M is an induced matching of a graph G = (V,E). The enumeration of matchings are widely studied in literature, but the induced matching has not been paid much attention. A straightforward algorithm takes O (|V |) time for each solution, that is coming from the time to generate a subproblem. We investigated local structures that ena...

This paper explores equilibrium and optimal matching behavior in constant returns to scale search economies with heterogeneous agents. We show that optimal matching behavior may involve a nontrivial limit cycle, and that there may exist a continuum of cyclical perfect foresight equilibria. These results hold for a generic set of parameter values. They are due to a trading externality (Diamond 1...

The behavior of a one-dimensional thermoelastic rod is modeled and analyzed. The rod is held fixed and at constant temperature at one end, while at the other end it is free to separate from or make contact with a rigid wall. At this free end we impose a pressure and gap-dependent thermal boundary condition. This condition, known as the Barber condition, couples the thermal and elastic problems....

We undertake a study on computing Hamiltonian alternating cycles and paths on bicolored point sets. This has been an intensively studied problem, not always with a solution, when the paths and cycles are also required to be plane. In this paper, we relax the constraint on the cycles and paths from being plane to being 1-plane, and deal with the same type of questions as those for the plane case...