Dynamical Solution of the On-Line Minority Game

We solve the dynamics of the on-line minority game, with general types of decision noise, using generating functional techniques a la De Dominicis and the temporal regularization procedure of Bedeaux et al. The result is a macroscopic dynamical theory in the form of closed equations for correlation- and response functions defined via an effective continuous-time single-trader process, which are exact in both the ergodic and in the non-ergodic regime of the minority game. Our solution also explains why, although one cannot formally truncate the Kramers-Moyal expansion of the process after the Fokker-Planck term, upon doing so one still finds the correct solution, that the previously proposed diffusion matrices for the Fokker-Planck term are incomplete, and how previously proposed approximations of the market volatility can be traced back to ergodicity assumptions.Comment: 25 pages LaTeX, no figure

Generating Functional Analysis of the Dynamics of the Batch Minority Game with Random External Information

We study the dynamics of the batch minority game, with random external information, using generating functional techniques a la De Dominicis. The relevant control parameter in this model is the ratio $\alpha=p/N$ of the number $p$ of possible values for the external information over the number $N$ of trading agents. In the limit $N\to\infty$ we calculate the location $\alpha_c$ of the phase transition (signaling the onset of anomalous response), and solve the statics for $\alpha>\alpha_c$ exactly. The temporal correlations in global market fluctuations turn out not to decay to zero for infinitely widely separated times. For $\alpha<\alpha_c$ the stationary state is shown to be non-unique. For $\alpha\to 0$ we analyse our equations in leading order in $\alpha$, and find asymptotic solutions with diverging volatility \sigma=\order(\alpha^{-{1/2}}) (as regularly observed in simulations), but also asymptotic solutions with vanishing volatility \sigma=\order(\alpha^{{1/2}}). The former, however, are shown to emerge only if the agents' initial strategy valuations are below a specific critical value.Comment: 15 pages, 6 figures, uses Revtex. Replaced an old version of volatility graph that. Rephrased and updated some reference

A proposal for a coordinated effort for the determination of brainwide neuroanatomical connectivity in model organisms at a mesoscopic scale

In this era of complete genomes, our knowledge of neuroanatomical circuitry remains surprisingly sparse. Such knowledge is however critical both for basic and clinical research into brain function. Here we advocate for a concerted effort to fill this gap, through systematic, experimental mapping of neural circuits at a mesoscopic scale of resolution suitable for comprehensive, brain-wide coverage, using injections of tracers or viral vectors. We detail the scientific and medical rationale and briefly review existing knowledge and experimental techniques. We define a set of desiderata, including brain-wide coverage; validated and extensible experimental techniques suitable for standardization and automation; centralized, open access data repository; compatibility with existing resources, and tractability with current informatics technology. We discuss a hypothetical but tractable plan for mouse, additional efforts for the macaque, and technique development for human. We estimate that the mouse connectivity project could be completed within five years with a comparatively modest budget.Comment: 41 page

Chromatic periodic activity down to 120 MHz in a Fast Radio Burst

Fast radio bursts (FRBs) are extragalactic astrophysical transients whose brightness requires emitters that are highly energetic, yet compact enough to produce the short, millisecond-duration bursts. FRBs have thus far been detected between 300 MHz and 8 GHz, but lower-frequency emission has remained elusive. A subset of FRBs is known to repeat, and one of those sources, FRB 20180916B, does so with a 16.3 day activity period. Using simultaneous Apertif and LOFAR data, we show that FRB 20180916B emits down to 120 MHz, and that its activity window is both narrower and earlier at higher frequencies. Binary wind interaction models predict a narrower periodic activity window at lower frequencies, which is the opposite of our observations. Our detections establish that low-frequency FRB emission can escape the local medium. For bursts of the same fluence, FRB 20180916B is more active below 200 MHz than at 1.4 GHz. Combining our results with previous upper-limits on the all-sky FRB rate at 150 MHz, we find that there are 3-450 FRBs/sky/day above 50 Jy ms at 90% confidence. We are able to rule out the scenario in which companion winds cause FRB periodicity. We also demonstrate that some FRBs live in clean environments that do not absorb or scatter low-frequency radiation.Comment: 50 pages, 14 figures, 3 tables, submitte

The Cutting Power of Preparation

In a strategic game, a curb set [Basu and Weibull, Econ.Letters 36 (1991) 141-146] is a product set of pure strategies containing all best responses to every possible belief restricted to this set.Prep sets [Voorneveld, Games Econ. Behav. 48 (2004) 403-414] relax this condition by only requiring the presence of at least one best response to such a belief.The purpose of this paper is to provide sufficient conditions under which minimal prep sets give sharp predictions.These conditions are satisfied in many economically relevant classes of games, including supermodular games, potential games, and congestion games with player-specific payoffs.In these classes, minimal curb sets generically have a large cutting power as well, although it is shown that there are relevant subclasses of coordination games and congestion games where minimal curb sets have no cutting power at all and simply consist of the entire strategy space.

A fast radio burst with submillisecond quasi-periodic structure

Fast radio bursts (FRBs) are extragalactic radio transients of extraordinary luminosity. Studying the diverse temporal and spectral behaviour recently observed in a number of FRBs may help to determine the nature of the entire class. For example, a fast spinning or highly magnetised neutron star (NS) might generate the rotation-powered acceleration required to explain the bright emission. Periodic, subsecond components suggesting such rotation were recently reported in one FRB, and may also exist in two more. Here we report the discovery of FRB 20201020A with Apertif, an FRB that shows five components regularly spaced by 0.411 ms. This submillisecond structure in FRB 20201020A carries important clues about the progenitor of this FRB specifically, and potentially about the progenitors of FRBs in general. We therefore contrast its features to what is seen in other FRBs and pulsars, and to the predictions of some FRB models. We present a timing analysis of the FRB 20201020A components carried out in order to determine the significance of the periodicity. We compare these against the timing properties of the previously reported CHIME FRBs with subsecond quasi-periodic components, and against two Apertif bursts from repeating FRB 20180916B, which show complex time-frequency structure. We find the periodicity of FRB 20201020A to be marginally significant at 2.4σ. Its repeating subcomponents cannot be explained as pulsar rotation because the required spin rate of over 2 kHz exceeds the limits set by typical NS equations of state and observations. The fast periodicity is also in conflict with a compact object merger scenario. However, these quasi-periodic components could be caused by equidistant emitting regions in the magnetosphere of a magnetar. The submillisecond spacing of the components in FRB 20201020A, the smallest observed so far in a one-off FRB, may rule out both a NS spin period and binary mergers as the direct source of quasi-periodic FRB structure

The Apertif Radio Transient System (ARTS): Design, commissioning, data release, and detection of the first five fast radio bursts

Fast radio bursts (FRBs) must be powered by uniquely energetic emission mechanisms. This requirement has eliminated a number of possible source types, but several remain. Identifying the physical nature of FRB emitters arguably requires good localisation of more detections, as well as broad-band studies enabled by real-time alerting. In this paper, we present the Apertif Radio Transient System (ARTS), a supercomputing radio-telescope instrument that performs real-time FRB detection and localisation on the Westerbork Synthesis Radio Telescope (WSRT) interferometer. It reaches coherent-addition sensitivity over the entire field of the view of the primary-dish beam. After commissioning results verified that the system performed as planned, we initiated the Apertif FRB survey (ALERT). Over the first 5 weeks we observed at design sensitivity in 2019, we detected five new FRBs, and interferometrically localised each of them to 0.4–10 sq. arcmin. All detections are broad band, very narrow, of the order of 1 ms in duration, and unscattered. Dispersion measures are generally high. Only through the very high time and frequency resolution of ARTS are these hard-to-find FRBs detected, producing an unbiased view of the intrinsic population properties. Most localisation regions are small enough to rule out the presence of associated persistent radio sources. Three FRBs cut through the halos of M31 and M33. We demonstrate that Apertif can localise one-off FRBs with an accuracy that maps magneto-ionic material along well-defined lines of sight. The rate of one every ~7 days ensures a considerable number of new sources are detected for such a study. The combination of the detection rate and localisation accuracy exemplified by the first five ARTS FRBs thus marks a new phase in which a growing number of bursts can be used to probe our Universe