Mechanical fluctuations suppress the threshold of soft-glassy solids : the secular drift scenario

We propose a dynamical mechanism leading to the fluidization of soft-glassy amorphous mate-rial driven below the yield-stress by external mechanical fluctuations. The model is based on the combination of memory effect and non-linearity, leading to an accumulation of tiny effects over a long-term. We test this scenario on a granular packing driven mechanically below the Coulomb threshold. We bring evidences for an effective viscous response directly related to small stress modulations in agreement with the theoretical prediction of a generic secular drift

Turning bacteria suspensions into a "superfluid"

The rheological response under simple shear of an active suspension of Escherichia coli is determined in a large range of shear rates and concentrations. The effective viscosity and the time scales characterizing the bacterial organization under shear are obtained. In the dilute regime, we bring evidences for a low shear Newtonian plateau characterized by a shear viscosity decreasing with concentration. In the semi-dilute regime, for particularly active bacteria, the suspension display a "super-fluid" like transition where the viscous resistance to shear vanishes, thus showing that macroscopically, the activity of pusher swimmers organized by shear, is able to fully overcome the dissipative effects due to viscous loss

Incidence coloring game and arboricity of graphs

An incidence of a graph $G$ is a pair $(v,e)$ where $v$ is a vertex of $G$ and $e$ an edge incident to $v$. Two incidences $(v,e)$ and $(w,f)$ are adjacent whenever $v = w$, or $e = f$, or $vw = e$ or $f$. The incidence coloring game [S.D. Andres, The incidence game chromatic number, Discrete Appl. Math. 157 (2009), 1980-1987] is a variation of the ordinary coloring game where the two players, Alice and Bob, alternately color the incidences of a graph, using a given number of colors, in such a way that adjacent incidences get distinct colors. If the whole graph is colored then Alice wins the game otherwise Bob wins the game. The incidence game chromatic number $i_g(G)$ of a graph $G$ is the minimum number of colors for which Alice has a winning strategy when playing the incidence coloring game on $G$. Andres proved that %$\lceil 3/2 \Delta(G)\rceil \le$i_g(G) \le 2\Delta(G) + 4k - 2$for every$k$-degenerate graph$G$.$a(G)$of a graph$G$is the minimum number of forests into which its set of edges can be partitioned.$G$is$k$-degenerate, then$a(G) \le k \le 2a(G) - 1$. We show in this paper that$i_g(G) \le \lfloor\frac{3\Delta(G) - a(G)}{2}\rfloor + 8a(G) - 2$for every graph$G$, where$a(G)$stands for the arboricity of$G$, thus improving the bound given by Andres since$a(G) \le k$for every$k$-degenerate graph$G$. Since there exists graphs with$i_g(G) \ge \lceil\frac{3\Delta(G)}{2}\rceil$, the multiplicative constant of our bound is best possible.Comment: 10 page

Learning circuits with few negations

Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in any circuit computing them, a complexity measure that interpolates between monotone functions and the class of all functions. We study this generalization of monotonicity from the vantage point of learning theory, giving near-matching upper and lower bounds on the uniform-distribution learnability of circuits in terms of the number of negations they contain. Our upper bounds are based on a new structural characterization of negation-limited circuits that extends a classical result of A. A. Markov. Our lower bounds, which employ Fourier-analytic tools from hardness amplification, give new results even for circuits with no negations (i.e. monotone functions)