Optimizing experimental parameters for tracking of diffusing particles

We describe how a single-particle tracking experiment should be designed in order for its recorded trajectories to contain the most information about a tracked particle's diffusion coefficient. The precision of estimators for the diffusion coefficient is affected by motion blur, limited photon statistics, and the length of recorded time-series. We demonstrate for a particle undergoing free diffusion that precision is negligibly affected by motion blur in typical experiments, while optimizing photon counts and the number of recorded frames is the key to precision. Building on these results, we describe for a wide range of experimental scenarios how to choose experimental parameters in order to optimize the precision. Generally, one should choose quantity over quality: experiments should be designed to maximize the number of frames recorded in a time-series, even if this means lower information content in individual frames

Bayesian Active Edge Evaluation on Expensive Graphs

Robots operate in environments with varying implicit structure. For instance, a helicopter flying over terrain encounters a very different arrangement of obstacles than a robotic arm manipulating objects on a cluttered table top. State-of-the-art motion planning systems do not exploit this structure, thereby expending valuable planning effort searching for implausible solutions. We are interested in planning algorithms that actively infer the underlying structure of the valid configuration space during planning in order to find solutions with minimal effort. Consider the problem of evaluating edges on a graph to quickly discover collision-free paths. Evaluating edges is expensive, both for robots with complex geometries like robot arms, and for robots with limited onboard computation like UAVs. Until now, this challenge has been addressed via laziness i.e. deferring edge evaluation until absolutely necessary, with the hope that edges turn out to be valid. However, all edges are not alike in value - some have a lot of potentially good paths flowing through them, and some others encode the likelihood of neighbouring edges being valid. This leads to our key insight - instead of passive laziness, we can actively choose edges that reduce the uncertainty about the validity of paths. We show that this is equivalent to the Bayesian active learning paradigm of decision region determination (DRD). However, the DRD problem is not only combinatorially hard, but also requires explicit enumeration of all possible worlds. We propose a novel framework that combines two DRD algorithms, DIRECT and BISECT, to overcome both issues. We show that our approach outperforms several state-of-the-art algorithms on a spectrum of planning problems for mobile robots, manipulators and autonomous helicopters

Brownian theory of 2D turbulence and generalized thermodynamics

We propose a new parametrization of 2D turbulence based on generalized thermodynamics and Brownian theory. Explicit relaxation equations are obtained that should be easily implementable in numerical simulations for three typical types of turbulent flows. Our parametrization is related to previous ones but it removes their defects and offers attractive new perspectives.Comment: Submitted to Phys. Rev. Let

Kinetic theory of point vortices in two dimensions: analytical results and numerical simulations

We develop the kinetic theory of point vortices in two-dimensional hydrodynamics and illustrate the main results of the theory with numerical simulations. We first consider the evolution of the system "as a whole" and show that the evolution of the vorticity profile is due to resonances between different orbits of the point vortices. The evolution stops when the profile of angular velocity becomes monotonic even if the system has not reached the statistical equilibrium state (Boltzmann distribution). In that case, the system remains blocked in a sort of metastable state with a non standard distribution. We also study the relaxation of a test vortex in a steady bath of field vortices. The relaxation of the test vortex is described by a Fokker-Planck equation involving a diffusion term and a drift term. The diffusion coefficient, which is proportional to the density of field vortices and inversely proportional to the shear, usually decreases rapidly with the distance. The drift is proportional to the gradient of the density profile of the field vortices and is connected to the diffusion coefficient by a generalized Einstein relation. We study the evolution of the tail of the distribution function of the test vortex and show that it has a front structure. We also study how the temporal auto-correlation function of the position of the test vortex decreases with time and find that it usually exhibits an algebraic behavior with an exponent that we compute analytically. We mention analogies with other systems with long-range interactions

Bylaw Governance

This article argues that Delaware corporate law permits shareholders to use bylaws to circumscribe the managerial authority of the board of directors. While shareholders cannot mandate action by the board, they can enact specific prohibitions on its behavior, so long as the board retains enough discretion to implement—in practice, not merely in theory—its managerial policies by other means. The use of such circumscribing bylaws to discourage shirking (or analogous managerial abuses) by the directors or officers resembles the use of negative covenants in debt contracts that seek to prevent the debtor from squandering assets. Bylaw governance thus subtly but significantly reallocates governance power within the corporation, so as to reduce the agency costs of management. Its legal validity should also prompt courts and scholars alike to focus less on the quantity of power wielded by the shareholders, and more on the ways that power can be configured to produce managerial efficiencies

The Licensing Function of Patent Intermediaries

The contemporary patent marketplace is a complex ecosystem comprised of innovators and manufacturers who are often connected by a varied group of intermediaries. While there are a variety of intermediary business models—such as patent assertion entities and defensive aggregators—each facilitates a variant of a similar licensing transaction, connecting a set of patents held by a patent owner with a product or service offered by a prospective licensee. One explanation for the prevalence of intermediaries is that they engage in practices tantamount to arbitrage, acquiring patents and then licensing them at a profit because they enjoy greater success in patent litigation than patent holders would on their own. This paper advances an additional explanation: some intermediaries may serve a function analogous to a platform trading in non-exclusive licenses, overcoming search and valuation costs to facilitate licensing. This paper focuses on the use of two contract terms in intermediaries’ dealings with technology market participants: revenue sharing in patent acquisition and non-exclusive licensing. The Federal Trade Commission’s Patent Entity Activity Study reported that intermediaries used both of these terms. Building on those findings, this paper argues that intermediaries that use both provisions may, under some conditions, operate in a manner analogous to a two-sided platform. First, this paper examines how participants in a technology market would value non-exclusive licenses granted ex post, after the licensed product is already on the market. The paper argues that—in addition to the avoidance of litigation costs— the reduction of uncertainty can also drive licensee demand. Next, the paper proposes that use of revenue sharing allows patent holders to experience network effects from the number of prospective licensees accessed through the intermediary, which may make the intermediary more attractive than licensing unilaterally. Finally, this paper argues that the conduct of a patent licensing intermediary using these contract features can be analogized to the practices of other licensing intermediaries such as performing rights organizations and patent pools. These observations suggest that one explanation for the success of some intermediary models—as well as one aspect of their conduct that may influence competition in technology markets—is their ability to connect patent holders and prospective licensees with a greater number of potential trading partners than they would otherwise be able to connect with on their own