Flocking with discrete symmetry: the 2d Active Ising Model

We study in detail the active Ising model, a stochastic lattice gas where collective motion emerges from the spontaneous breaking of a discrete symmetry. On a 2d lattice, active particles undergo a diffusion biased in one of two possible directions (left and right) and align ferromagnetically their direction of motion, hence yielding a minimal flocking model with discrete rotational symmetry. We show that the transition to collective motion amounts in this model to a bona fide liquid-gas phase transition in the canonical ensemble. The phase diagram in the density/velocity parameter plane has a critical point at zero velocity which belongs to the Ising universality class. In the density/temperature "canonical" ensemble, the usual critical point of the equilibrium liquid-gas transition is sent to infinite density because the different symmetries between liquid and gas phases preclude a supercritical region. We build a continuum theory which reproduces qualitatively the behavior of the microscopic model. In particular we predict analytically the shapes of the phase diagrams in the vicinity of the critical points, the binodal and spinodal densities at coexistence, and the speeds and shapes of the phase-separated profiles.Comment: 20 pages, 25 figure

Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study

Active Brownian particles (ABPs) and Run-and-Tumble particles (RTPs) both self-propel at fixed speed $v$ along a body-axis ${\bf u}$ that reorients either through slow angular diffusion (ABPs) or sudden complete randomisation (RTPs). We compare the physics of these two model systems both at microscopic and macroscopic scales. Using exact results for their steady-state distribution in the presence of external potentials, we show that they both admit the same effective equilibrium regime perturbatively that breaks down for stronger external potentials, in a model-dependent way. In the presence of collisional repulsions such particles slow down at high density: their propulsive effort is unchanged, but their average speed along ${\bf u}$ becomes $v(\rho) < v$. A fruitful avenue is then to construct a mean-field description in which particles are ghost-like and have no collisions, but swim at a variable speed $v$ that is an explicit function or functional of the density $\rho$. We give numerical evidence that the recently shown equivalence of the fluctuating hydrodynamics of ABPs and RTPs in this case, which we detail here, extends to microscopic models of ABPs and RTPs interacting with repulsive forces.Comment: 32 pages, 6 figure

Contracts—Beating Them at Their Own Game: The Business Risk Doctrine and the Broadening Coverage of Commercial General Liability Insurance—Thommes v. Milwaukee Insurance Co.

This note first examines the theory behind the business risk doctrine in analyzing CGL insurance. It then details the supreme court\u27s holding in Thommes, followed by an analysis of that decision. Finally, the note concludes that, whatever problems may exist, the court has devised a manageable approach to CGL insurance coverage

Analyzing P300 Distractors for Target Reconstruction

P300-based brain-computer interfaces (BCIs) are often trained per-user and per-application space. Training such models requires ground truth knowledge of target and non-target stimulus categories during model training, which imparts bias into the model. Additionally, not all non-targets are created equal; some may contain visual features that resemble targets or may otherwise be visually salient. Current research has indicated that non-target distractors may elicit attenuated P300 responses based on the perceptual similarity of these distractors to the target category. To minimize this bias, and enable a more nuanced analysis, we use a generalized BCI approach that is fit to neither user nor task. We do not seek to improve the overall accuracy of the BCI with our generalized approach; we instead demonstrate the utility of our approach for identifying target-related image features. When combined with other intelligent agents, such as computer vision systems, the performance of the generalized model equals that of the user-specific models, without any user specific data.Comment: 4 pages, 3 figure