We investigate the nonsmooth and nonconvex L1-Potts functional in discrete and continuous time. We show Γ-convergence of discrete L1-Potts functionals toward their continuous counterpart and obtain a convergence statement for the corresponding minimizers as the discretization gets finer. For the discrete L1-Potts problem, we introduce an O(n2) time and O(n) space algorithm to compute an exact m...

We consider a variational model which describes a complex system composed, in its reference configuration, of a periodic distribution of ‘small’ interacting particles immersed in a continuous medium. We describe its macroscopic limit via Gamma-convergence, highlighting different regimes. In particular, we show how the interplay between the particles and the continuum leads, for a critical size ...

Let M‾ be a compact smoothly stratified pseudomanifold with boundary, satisfying the Witt assumption. In this paper we introduce de Rham signature and Hodge of M‾, prove their equality. Next, building also on recent work Albin Gell-Redman, extend Atiyah-Patodi-Singer index theory established in our previous under hypothesis that has stratification depth 1 to general case, establishing particula...

The temporal evolution of ordered γ′(L12)-precipitates and the compositional trajectories during phase-separation γ(face-centered-cubic (f.c.c.))- γ′(L12)-phases are studied in a Ni–0.10Al-0.085Cr-0.02Re (mole-fraction) superalloy, utilizing atom-probe tomography, transmission electron microscopy, Philippe-Voorhees (PV) coarsening model. As grow, excesses Ni, Cr Re, depletion Al γ(f.c.c.)-matri...

We introduce two variations of the cops and robber game on graphs. These games yield invariants in Z+∪{∞} for any connected graph Γ, weak cop number wCop(Γ) strong sCop(Γ). satisfy that sCop(Γ)≤wCop(Γ). Any is finite or a tree has one. new are preserved under small local perturbations graph, specifically, both numbers quasi-isometric More generally, we prove if Δ quasi-retract Γ then wCop(Δ)≤wC...

We prove a refinement of the flat wall theorem Robertson and Seymour to undirected group-labelled graphs (G,γ) where γ assigns each edge an graph G element abelian group Γ. As consequence, we that Γ-nonzero cycles (cycles whose labels sum non-identity Γ) satisfy half-integral Erdős-Pósa property, also recover result Wollan if Γ has no order two, then property. another application, m is odd prim...

A Nash k-colouring is a (S1,…,Sk) such that every vertex of Si adjacent to in Sj, whenever |Sj|≥|Si|. The Number G, denoted by Nn(G), the largest k G admits k-colouring. diminishing greedy that, for all 1≤j<i≤k, |Si|≤|Sj| and Sj. Grundy Γ↓(G), In this paper, we prove some properties Nn Γ↓. We mainly study relations between them other graph parameters as clique number ω, chromatic χ, Γ, maximum ...