LNCS

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

Utilizing Dependencies to Obtain Subsets of Reachable Sets

Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few. In many of these applications, one requires to compute a reachable set starting within a previously computed reachable set. While it was previously required to re-compute the entire reachable set, we demonstrate that one can leverage the dependencies of states within the previously computed set. As a result, we almost instantly obtain an over-approximative subset of a previously computed reachable set by evaluating analytical maps. The advantages of our novel method are demonstrated for falsification of systems, optimization over reachable sets, and synthesizing safe maneuver automata. In all of these applications, the computation time is reduced significantly

Herbicide-Resistant Crops: Utilities and Limitations for Herbicide-Resistant Weed Management

Since 1996, genetically modified herbicide-resistant (HR) crops, particularly glyphosate-resistant (GR) crops, have transformed the tactics that corn, soybean, and cotton growers use to manage weeds. The use of GR crops continues to grow, but weeds are adapting to the common practice of using only glyphosate to control weeds. Growers using only a single mode of action to manage weeds need to change to a more diverse array of herbicidal, mechanical, and cultural practices to maintain the effectiveness of glyphosate. Unfortunately, the introduction of GR crops and the high initial efficacy of glyphosate often lead to a decline in the use of other herbicide options and less investment by industry to discover new herbicide active ingredients. With some exceptions, most growers can still manage their weed problems with currently available selective and HR crop-enabled herbicides. However, current crop management systems are in jeopardy given the pace at which weed populations are evolving glyphosate resistance. New HR crop technologies will expand the utility of currently available herbicides and enable new interim solutions for growers to manage HR weeds, but will not replace the long-term need to diversify weed management tactics and discover herbicides with new modes of action. This paper reviews the strengths and weaknesses of anticipated weed management options and the best management practices that growers need to implement in HR crops to maximize the long-term benefits of current technologies and reduce weed shifts to difficult-to-control and HR weeds

The l-modular local Langlands correspondence and local constants

Let F be a non-archimedean local field of residual characteristic p , ℓ≠p be a prime number, and WF the Weil group of F . We classify equivalence classes of WF -semisimple Deligne ℓ -modular representations of WF in terms of irreducible ℓ -modular representations of WF , and extend constructions of Artin–Deligne local constants to this setting. Finally, we define a variant of the ℓ -modular local Langlands correspondence which satisfies a preservation of local constants statement for pairs of generic representations

A characterization of the relation between two ℓ\ell -modular correspondences

Let F be a non archimedean local field of residual characteristic p and ℓ a prime number different from p. Let V denote Vignéras’ ℓ-modular local Langlands correspondence [7], between irreducible ℓ-modular representations of GLn(F) and n-dimensional ℓ-modular Deligne representations of the Weil group WF. In [4], enlarging the space of Galois parameters to Deligne representations with non necessarily nilpotent operators allowed us to propose a modification of the correspondence of Vignéras into a correspondence C, compatible with the formation of local constants in the generic case. In this note, following a remark of Alberto Mínguez, we characterize the modification C∘V−1 by a short list of natural properties

Test vectors for local periods

Let E/F be a quadratic extension of non-Archimedean local fields of characteristic zero. An irreducible admissible representation pi of GL(n, E) is said to be distinguished with respect to GL(n, F) if it admits a non-trivial linear form that is invariant under the action of GL(n, F). It is known that there is exactly one such invariant linear form up to multiplication by scalars, and an explicit linear form is given by integrating Whittaker functions over the F-points of the mirabolic subgroup when pi is unitary and generic. In this paper, we prove that the essential vector of [14] is a test vector for this standard distinguishing linear form and that the value of this form at the essential vector is a local L-value. As an application we determine the value of a certain proportionality constant between two explicit distinguishing linear forms. We then extend all our results to the non-unitary generic case