TY - JOUR AB - Many animals use antimicrobials to prevent or cure disease [1,2]. For example, some animals will ingest plants with medicinal properties, both prophylactically to prevent infection and therapeutically to self-medicate when sick. Antimicrobial substances are also used as topical disinfectants, to prevent infection, protect offspring and to sanitise their surroundings [1,2]. Social insects (ants, bees, wasps and termites) build nests in environments with a high abundance and diversity of pathogenic microorganisms — such as soil and rotting wood — and colonies are often densely crowded, creating conditions that favour disease outbreaks. Consequently, social insects have evolved collective disease defences to protect their colonies from epidemics. These traits can be seen as functionally analogous to the immune system of individual organisms [3,4]. This ‘social immunity’ utilises antimicrobials to prevent and eradicate infections, and to keep the brood and nest clean. However, these antimicrobial compounds can be harmful to the insects themselves, and it is unknown how colonies prevent collateral damage when using them. Here, we demonstrate that antimicrobial acids, produced by workers to disinfect the colony, are harmful to the delicate pupal brood stage, but that the pupae are protected from the acids by the presence of a silk cocoon. Garden ants spray their nests with an antimicrobial poison to sanitize contaminated nestmates and brood. Here, Pull et al show that they also prophylactically sanitise their colonies, and that the silk cocoon serves as a barrier to protect developing pupae, thus preventing collateral damage during nest sanitation. AU - Pull, Christopher AU - Metzler, Sina AU - Naderlinger, Elisabeth AU - Cremer, Sylvia ID - 55 IS - 19 JF - Current Biology TI - Protection against the lethal side effects of social immunity in ants VL - 28 ER - TY - JOUR AB - We consider large random matrices X with centered, independent entries but possibly di erent variances. We compute the normalized trace of f(X)g(X∗) for f, g functions analytic on the spectrum of X. We use these results to compute the long time asymptotics for systems of coupled di erential equations with random coe cients. We show that when the coupling is critical, the norm squared of the solution decays like t−1/2. AU - Erdös, László AU - Krüger, Torben H AU - Renfrew, David T ID - 181 IS - 3 JF - SIAM Journal on Mathematical Analysis TI - Power law decay for systems of randomly coupled differential equations VL - 50 ER - TY - JOUR AB - We construct quantizations of multiplicative hypertoric varieties using an algebra of q-difference operators on affine space, where q is a root of unity in C. The quantization defines a matrix bundle (i.e. Azumaya algebra) over the multiplicative hypertoric variety and admits an explicit finite étale splitting. The global sections of this Azumaya algebra is a hypertoric quantum group, and we prove a localization theorem. We introduce a general framework of Frobenius quantum moment maps and their Hamiltonian reductions; our results shed light on an instance of this framework. AU - Ganev, Iordan V ID - 322 JF - Journal of Algebra TI - Quantizations of multiplicative hypertoric varieties at a root of unity VL - 506 ER - TY - GEN AB - Implementation of the inference method in Matlab, including three applications of the method: The first one for the model of ant motion, the second one for bacterial chemotaxis, and the third one for the motion of fish. AU - Bod’Ová, Katarína AU - Mitchell, Gabriel AU - Harpaz, Roy AU - Schneidman, Elad AU - Tkačik, Gašper ID - 9831 TI - Implementation of the inference method in Matlab ER - TY - CONF AB - We address the problem of analyzing the reachable set of a polynomial nonlinear continuous system by over-approximating the flowpipe of its dynamics. The common approach to tackle this problem is to perform a numerical integration over a given time horizon based on Taylor expansion and interval arithmetic. However, this method results to be very conservative when there is a large difference in speed between trajectories as time progresses. In this paper, we propose to use combinations of barrier functions, which we call piecewise barrier tube (PBT), to over-approximate flowpipe. The basic idea of PBT is that for each segment of a flowpipe, a coarse box which is big enough to contain the segment is constructed using sampled simulation and then in the box we compute by linear programming a set of barrier functions (called barrier tube or BT for short) which work together to form a tube surrounding the flowpipe. The benefit of using PBT is that (1) BT is independent of time and hence can avoid being stretched and deformed by time; and (2) a small number of BTs can form a tight over-approximation for the flowpipe, which means that the computation required to decide whether the BTs intersect the unsafe set can be reduced significantly. We implemented a prototype called PBTS in C++. Experiments on some benchmark systems show that our approach is effective. AU - Kong, Hui AU - Bartocci, Ezio AU - Henzinger, Thomas A ID - 142 TI - Reachable set over-approximation for nonlinear systems using piecewise barrier tubes VL - 10981 ER -