Onondaga County Animal Response Team (OnCART): Development & Application

In an effort to better address animal welfare issues, the Onondaga County Department of Emergency Management (OCDEM) initiated the development of an all-volunteer County Animal Response Team (OnCART). • An annex to Onondaga County’s Comprehensive Emergency Management Plan (CEMP) and OnCART Standard Operating Procedures (SOPs) were developed in collaboration with state, county, and local stakeholders. These emergency plans define OnCART’s authority, capabilities and limitations, roles and responsibilities, and command structure. • Following a study of existing CARTs and animal disaster incidents throughout the U.S., a public education and outreach initiative was also initiated. Training modules for OnCART members, first responders and the public, as well as multimedia educational tools were developed in order to increase awareness and preparation within Onondaga County.https://orb.binghamton.edu/mpa_capstone/1026/thumbnail.jp

On monotonicity conditions for Mean Field Games

In this paper we propose two new monotonicity conditions that could serve as sufficient conditions for uniqueness of Nash equilibria in mean field games. In this study we aim for $unconditional\ uniqueness$ that is independent of the length of the time horizon, the regularity of the starting distribution of the agents, or the regularization effect of a non-degenerate idiosyncratic noise. Through a rich class of simple examples we show that these new conditions are not only in dichotomy with each other, but also with the two widely studied monotonicity conditions in the literature, the Lasry-Lions monotonicity and displacement monotonicity conditions.Comment: to appear in J. Funct. Ana

On some mean field games and master equations through the lens of conservation laws

In this manuscript we derive a new nonlinear transport equation written on the space of probability measures that allows to study a class of deterministic mean field games and master equations, where the interaction of the agents happens only at the terminal time. The point of view via this transport equation has two important consequences. First, this equation reveals a new monotonicity condition that is sufficient both for the uniqueness of MFG Nash equilibria and for the global in time well-posedness of master equations. Interestingly, this condition is in general in dichotomy with both the Lasry–Lions and displacement monotonicity conditions, studied so far in the literature. Second, in the absence of monotonicity, the conservative form of the transport equation can be used to define weak entropy solutions to the master equation. We construct several concrete examples to demonstrate that MFG Nash equilibria, whether or not they actually exist, may not be selected by the entropy solutions of the master equation

Sobolev regularity for first order mean field games

In this paper we obtain Sobolev estimates for weak solutions of first order variational Mean Field Game systems with coupling terms that are local functions of the density variable. Under some coercivity conditions on the coupling, we obtain first order Sobolev estimates for the density variable, while under similar coercivity conditions on the Hamiltonian we obtain second order Sobolev estimates for the value function. These results are valid both for stationary and time-dependent problems. In the latter case the estimates are fully global in time, thus we resolve a question which was left open in [23]. Our methods apply to a large class of Hamiltonians and coupling functions