Coherence in Large-Scale Networks: Dimension-Dependent Limitations of Local Feedback

We consider distributed consensus and vehicular formation control problems. Specifically we address the question of whether local feedback is sufficient to maintain coherence in large-scale networks subject to stochastic disturbances. We define macroscopic performance measures which are global quantities that capture the notion of coherence; a notion of global order that quantifies how closely the formation resembles a solid object. We consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1, 2 and higher dimensions, with vehicular platoons corresponding to the 1 dimensional case. A common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures, with a dimensions of 3 being necessary to achieve coherence in consensus and vehicular formations under certain conditions. In particular, we show that it is impossible to have large coherent one dimensional vehicular platoons with only local feedback. We analyze these effects in terms of the underlying energetic modes of motion, showing that they take the form of large temporal and spatial scales resulting in an accordion-like motion of formations. A conclusion can be drawn that in low spatial dimensions, local feedback is unable to regulate large-scale disturbances, but it can in higher spatial dimensions. This phenomenon is distinct from, and unrelated to string instability issues which are commonly encountered in control problems for automated highways.Comment: To appear in IEEE Trans. Automat. Control; 15 pages, 2 figure

A framework for detection and classification of events in neural activity

We present a method for the real time prediction of punctate events in neural activity, based on the time-frequency spectrum of the signal, applicable both to continuous processes like local field potentials (LFP) as well as to spike trains. We test it on recordings of LFP and spiking activity acquired previously from the lateral intraparietal area (LIP) of macaque monkeys performing a memory-saccade task. In contrast to earlier work, where trials with known start times were classified, our method detects and classifies trials directly from the data. It provides a means to quantitatively compare and contrast the content of LFP signals and spike trains: we find that the detector performance based on the LFP matches the performance based on spike rates. The method should find application in the development of neural prosthetics based on the LFP signal. Our approach uses a new feature vector, which we call the 2D cepstrum.Comment: 30 pages, 6 figures; This version submitted to the IEEE Transactions in Biomedical Engineerin

Gauge boson fusion as a probe of inverted hierarchies in supersymmetry

Supersymmetric scenarios with inverted mass hierarchy can be hard to observe at a hadron collider, particularly for the non-strongly interacting sector. We show how the production of stau-pairs via gauge boson fusion, along with hard jets in the high rapidity region, can be instrumental in uncovering the signatures of such scenarios. We demonstrate this both in a model-independent way and with reference to some specific, well-motivated models.Comment: RevTeX4, 4 pages, 2 figures. Final version to appear in Phys.Rev.D Changes in context, figures modified. References added. Conclusions unchange

Project Appraisal and Foreign Exchange Constraints: A Simple Exposition

In an earlier paper, we showed that the value of shadow prices depends on how the government contemplates re- equilibrating the economy to the perturbation associated with any project, except in the extreme case where the government has chosen all policy instruments optimally. Only under restrictive conditions will relative shadow prices for traded goods equal relative international prices. We develop here a general methodology for calculating shadow prices, which expresses the prices as a weighted average of domestic and international prices. The formulae provide the conditions under which the border price rule is valid. For instance, so long as there are non-traded goods, even if the government leaves tariffs unchanged (so that relative domestic prices of traded goods remain unchanged), unless the government completely neutralizes the induced change in domestic income, there will be changes in the prices of non-traded goods. These will preclude the use of the border price rule.

Image Interpretation Using Appraisal Analysis

In geophysical inversion, a significant effort is invested to obtain images of the Earth from finite data. The first step is to obtain an image i.e. solve the inverse problem. This step alone provides significant challenges that are not addressed inthis paper. The next step is to interpret the image in terms of specific questions. For example, what can we say about the average value of a physical property within a certain region of the model? What scale information can we resolve from the data? These questions are problem dependent and may require that inversion be carried out several times to arrive at a satisfactory answer. Therefore the solution to an inverse problem is only a step towards answering these questions. Appraisal analysis of the solution takes the next step by providing a set of tools to judge and select from the possibly infinite suite of images that adequately fit our observations. We discuss the use of point spread functions and averaging kernels in the interpretation of images. We use a controlled source electromagnetic example to demonstrate the methodology

A Classification of First Order Differential Equations

Let $k$ be a differential field of characteristic zero with an algebraically closed field of constants. In this article, we provide a classification of first order differential equations over $k$ and study the algebraic dependence of solutions of a given first order differential equation. Our results generalize parts of the work of Noordman et al. (MR4378074) and complements the work of Freitag et al. (MR4506775).Comment: 20 pages, 3 figure

Experimental evidence that metapopulation structure can accelerate adaptive evolution

Whether the spatial arrangement of a population influences adaptive evolution has been a long-standing question in population genetics. In contrast to standard population genetic models, evolutionary graph theory (EGT) predicts certain topologies amplify (increase) the probability that a beneficial mutation will spread in the population relative to a well-mixed population. Here, we test these predictions empirically by tracking the fixation dynamics of an antibiotic resistant mutant under positive selection as it spreads through networks of different topologies both in vitro and in silico. We show that star-like topologies involving bi-directional dispersal between a central hub and peripheral leaves can be amplifiers of selection relative to a well-mixed network, consistent with the predictions of EGT. We further show that the mechanism responsible for amplification is the reduced probability that a rare beneficial mutant will be lost due to drift when it encounters a new patch. Our results provide the first empirical support for the prediction of EGT that spatial structure can amplify the spread of a beneficial mutation and broadens the conditions under which this phenomenon is thought to occur. We also show the importance of considering the migration rate, which is not independently adjustable in most previous models. More generally, our work underscores the potential importance of spatial structure in governing adaptive evolution by showing how the interplay between spatial structure and evolutionary forces determine the fate of a beneficial mutation. It also points the way towards using network topology to amplify the effects of weakly favoured mutations under directed evolution in industrial applications

Controlled Organocatalytic Ring-Opening Polymerization of ε-Thionocaprolactone

For the first time, the controlled ring-opening polymerization (ROP) of ε-thionocaprolactone (tnCL) is conducted. The organocatalytic ROP of tnCL occurs without carbonyl scrambling, leading to homopoly(ε-thionocaprolactone) (PtnCL). The ROP by base catalysts alone is proposed to proceed via a nucleophilic mechanism, while the addition of an H-bond donating thiourea (TU) is shown to provide excellent reaction control. The increased reaction control provided by the TU occurs in the virtual absence of binding between tnCL and TU, and a mechanistic account for this observation is discussed. The monomer ring strain is measured and found to be similar to δ-valerolactone (VL). Copolymers with VL are synthesized, and the resulting analysis of the copolymer materials properties provides the only known physical characterizations of poly(thio(no)ester-co-ester)s

Dust devils on Earth and Mars: Extension of particle threshold laboratory simulations

Abstract not available