In this paper, we analyze a mean-field game model of SIR dynamics (Susceptible, Infected, Recovered) where players can vaccinate. This game admits a unique mean-field equilibrium: The equilibrium strategy of each player is to vaccinate until the proportion of susceptible players drops below some threshold and stop vaccinating thereafter. We also sh...
Dynamic pricing of new products has been extensively studied in monopolistic and oligopolistic markets. But, the optimal control and differential game tools used to investigate the pricing behavior on markets with a finite number of firms are not well-suited to model competitive markets with an infinity of firms. Using a mean-field games approach, ...
In this paper we extend Hitchin-Kobayashi correspondence along holomorphic fibre space and we show that there exists a generalized Hermitian-Einstein metric which is twisted with Weil-Petersson current.
Many interesting shapes appearing in the biological world are formed by the onset of mechanical instability. In this work we consider how the build-up of residual stress can cause a solid to buckle. In all past studies a fictitious (virtual) stress-free state was required to calculate the residual stress. In contrast, we use a model which is simple...
Repetition, Seriality, Temporality are among concepts that undoubtedly refer, in mathematics, to the famous questioning on realism. Repetition highlights identity and non-identity, seriality questions the possibility of decomposition of sequences into identical ones, and temporality addresses the phenomenon of successive actions. The three of them ...
We describe an evaluation/interpolation approach to compute modular polynomials on a Hilbert surface, which parametrizes abelian surfaces with maximal real multiplication. Under some heuristics we obtain a quasi-linear algorithm. The corresponding modular polynomials are much smaller than the ones on the Siegel threefold. We explain how to compute ...
This study puts forward a generalization of the short-time Fourier-based Synchrosqueezing Transform using a new local estimate of instantaneous frequency. Such a technique enables not only to achieve a highly concentrated time-frequency representation for a wide variety of AM-FM multicomponent signals but also to reconstruct their modes with a high...
For compact complex manifolds with vanishing first Chern class that are either Moishezon or compact torus principal bundles over Kähler manifolds, we prove that all holomorphic geometric structures on them, of affine type, are locally homogeneous. For a compact simply connected complex manifold in Fujiki class C, whose dimension is strictly larger ...
We define two algebra automorphisms $T_0$ and $T_1$ of the q-Onsager algebra Bc, which provide an analog of G. Lusztig's braid group action for quantum groups. These automorphisms are used to define root vectors which give rise to a PBW basis for Bc. We show that the root vectors satisfy q-analogs of Onsager's original commutation relations. The pa...
Let A_i, i≥0 be a finite state irreducible aperiodic Markov chain and f a lattice score function such that the average score is negative and positive scores are possible. Define S_0 := 0 and S_k := f(A_1) +...+ f(A_k) the successive partial sums, S^+ the maximal non-negative partial sum, Q_1 the maximal segmental score of the first non-negative exc...
