arXiv subjects

Kurt E. Mitman

Publications and source records attributed to Kurt E. Mitman.

4 recordsLinked to original sources

arXiv2005

Competitive Advantage for Multiple-Memory Strategies in an Artificial Market

We consider a simple binary market model containing $N$ competitive agents. The novel feature of our model is that it incorporates the tendency shown by traders to look for patterns in past price movements over multiple time scales, i.e. {\em multiple memory-lengths}. In the regime where these memory-lengths are all small, the average winnings per agent exceed those obtained for either (1) a pure population where all agents have equal memory-length, or (2) a mixed population comprising sub-populations of equal-memory agents with each sub-population having a different memory-length. Agents who consistently play strategies of a given memory-length, are found to win more on average -- switching between strategies with different memory lengths incurs an effective penalty, while switching between strategies of equal memory does not. Agents employing short-memory strategies can outperform agents using long-memory strategies, even in the regime where an equal-memory system would have favored the use of long-memory strategies. Using the many-body `Crowd-Anticrowd' theory, we obtain analytic expressions which are in good agreement with the observed numerical results. In the context of financial markets, our results suggest that multiple-memory agents have a better chance of identifying price patterns of unknown length and hence will typically have higher winnings.

physics.soc-ph↗

arXiv2003

External Shock Model for the Prompt Phase of Gamma Ray Bursts: Implications for GRB Source Models

An external shock model for the prompt gamma-ray luminous phase of gamma-ray bursts (GRBs) is treated both analytically and numerically. A widely cited derivation claiming that an external shock model for rapidly variable GRBs must be very inefficient employs an incorrect expression for the angular timescale. Numerical results show that variable GRBs can be formed with >10% efficiency to transform the directed kinetic energy of the relativistic fireball to gamma-rays. Successes of the external shock model and difficulties with an internal wind/colliding shell model are summarized. An impulsive external shock model is consistent with the supranova model.

astro-ph↗

arXiv1999

Beaming, Baryon-Loading, and the Synchrotron Self-Compton Component in Gamma-Ray Burst Blast Waves Energized by External Shocks

We present detailed calculations of nonthermal synchrotron and synchrotron self-Compton (SSC) spectra radiated by blast waves that are energized by interactions with a uniform surrounding medium. Radio, optical, X-ray and gamma-ray light curves and spectral indices are calculated for a standard parameter set that yields hard GRB spectra during the prompt emission phase. Because no lateral spreading of the blast-wave is assumed, the calculated temporal breaks represent the sharpest breaks possible from collimated outflows in a uniform surrounding medium. Absence of SSC hardenings in observed GRB X-ray afterglows indicates magnetic field generation toward equipartition as the blast wave evolves. EGRET detections of 100 MeV-GeV photons observed promptly and 90 minutes after GRB 940217 are attributed to nonthermal synchrotron radiation and SSC emission from a decelerating blast wave, respectively. The SSC process will produce prompt TeV emission that could be observed from GRBs with redshifts $z \lesssim 0.1$, provided $γ$-$γ$ opacity in the source is small. Measurements of the time dependence of the 100 MeV-GeV spectral indices with the planned {\it GLAST} mission will chart the evolution of the SSC component and test the external shock scenario. Transient optical and X-ray emissions from misaligned GRBs are generally much weaker than on-axis emissions produced by dirty and clean fireballs that would themselves not trigger a GRB detector; thus detection of long wavelength transients not associated with GRBs will not unambiguously demonstrate GRB beaming.

astro-ph↗

arXiv1999

Short Timescale Variability in the External Shock Model of Gamma Ray Bursts

We have developed a computer model to calculate gamma ray burst (GRB) light curves and efficiencies from the interaction of a single, thin blast wave with clouds in the external medium. Large amplitude, spiky variability occurs when the clouds have radii r << R/Gamma, where R is the mean distance of a cloud from the GRB source and Gamma is the blast-wave Lorentz factor. Efficiencies >~ 10% require a large number of small clouds, each with sufficiently large column densities to extract most of the available blast-wave energy in the region of interaction. For such efficiencies, we find that erratic variability persists in the simulated GRB light curves. If GRB sources are surrounded by clouds with such properties, then short timescale variability of GRBs is possible in the external shock model.

astro-ph↗