Scaling Relationships of Gaussian Processes

Asset returns conforming to a Gaussian random walk are characterised by the temporal independence of the moments of the distribution. Employing currency returns, this note demonstrates the conditions that are necessary for risk to be estimated in this manner.Scaling; Volatility; Currency Returns

Thinking about Thinking about Thinking about Thinking (about Poker)

Remember that childhood game “Odds or Evens” you used to play in order to settle important disputes such as who gets the last slice of pizza? There was only one element of skill to that game: trying to figure out what the other person would throw. But that wasn’t easy. If your opponent was savvy, that meant trying to figure out what he thought you were going to throw. And that sometimes meant figuring out what he thought you thought he was going to throw. Philosophers call this “thought attribution,” and top poker players are remarkably good at it. The ability to attribute thoughts to other people is especially important in the No-Limit Texas Hold’em tournaments that have, through television and the Internet, swept the globe in recent years. What is required to succeed in this game is not merely attributing “first-order” thoughts to other players, but attributing to them thoughts about your thoughts about their thoughts. In fact, that’s the minimum. The kind of thinking done by the very best players (T. J. Cloutier, Howard Lederer, and Daniel Negreanu are especially good at it) is much more complex than that. In this paper, I explore the light that recent philosophical work on thought attribution sheds on the kind of thinking that goes on at the expert poker table. The paper should be revealing to poker experts and novices alike. And it should be of interest to philosophers interested in poker or thought attribution. The essay is published in Poker and Philosophy, a volume of Open Court's Popular Culture and Philosophy Series. The goal of the series is to introduce philosophical themes to non-philosophers by way of particular topics of interest (in this case poker)

Countering Domestic Violent Extremism Through a Whole-of-society Approach

PI: Jonathan Ellis, Student, Embry-Riddle Aeronautical University, Daytona Beach, FL Co-PIs/Research Team: Student Team, Spring 2021, Introduction to Homeland Security 110-01 Daytona Beach, FL Presentation: Countering domestic violent extremism through a whole-of-society approach, a case study of first- and second-year college students and renewed inclusivity Domestic terrorists represent a growing share of the threat Americans face today. Domestic terrorists include racially- and ethnically motivated violent extremism, antigovernment and anti-authority violent extremism, and other violent extremist ideologies. The situation surrounding COVID-19 has also created an environment that could accelerate some individuals’ mobilization to targeted violence or terrorist activities. This project takes a whole-of-society approach to identify and prevent targeted violence anywhere and in any form. Using funding from a government agency, the HS-110 class at Daytona Beach was challenged to consider not only how they might counter targeted violence and terrorism but also how to empower positive initiatives that advocate for community connectedness and inclusivity. The research encompassed in this study targets college students in their first and second years, who may be spending time more time indoors due to COVID restrictions, and therefore are statistically more likely to be influenced and/or targeted by nefarious online groups. The researchers also identified a benchmark of existing audience sentiment, determined their attitudes, and the behavior change they desired. Through a strategic outreach program, the research team challenged students to spend time doing an activity away from their computers, and incentivized that activity through branding, competition, and an award structure. They then used a combination of tools to periodically examine progress and examine whether or not there had been an attitudinal shift, behavior change, and/or conversion to action within the defined target audience

D-Brane Recoil Mislays Information

We discuss the scattering of a light closed-string state off a $D$ brane, taking into account quantum recoil effects on the latter, which are described by a pair of logarithmic operators. The light-particle and $D$-brane subsystems may each be described by a world-sheet with an external source due to the interaction between them. This perturbs each subsystem away from criticality, which is compensated by dressing with a Liouville field whose zero mode we interpret as time. The resulting evolution equations for the $D$ brane and the closed string are of Fokker-Planck and modified quantum Liouville type, respectively. The apparent entropy of each subsystem increases as a result of the interaction between them, which we interpret as the loss of information resulting from non-observation of the other entangled subsystem. We speculate on the possible implications of these results for the propagation of closed strings through a dilute gas of virtual $D$ branes.Comment: 34 pages, LaTeX, 2 figures (included

Recombination Algorithms and Jet Substructure: Pruning as a Tool for Heavy Particle Searches

We discuss jet substructure in recombination algorithms for QCD jets and single jets from heavy particle decays. We demonstrate that the jet algorithm can introduce significant systematic effects into the substructure. By characterizing these systematic effects and the substructure from QCD, splash-in, and heavy particle decays, we identify a technique, pruning, to better identify heavy particle decays into single jets and distinguish them from QCD jets. Pruning removes protojets typical of soft, wide angle radiation, improves the mass resolution of jets reconstructing a heavy particle decay, and decreases the QCD background. We show that pruning provides significant improvements over unpruned jets in identifying top quarks and W bosons and separating them from a QCD background, and may be useful in a search for heavy particles.Comment: 33 pages, 42 figure

Asymptotic behavior of the finite-size magnetization as a function of the speed of approach to criticality

The main focus of this paper is to determine whether the thermodynamic magnetization is a physically relevant estimator of the finite-size magnetization. This is done by comparing the asymptotic behaviors of these two quantities along parameter sequences converging to either a second-order point or the tricritical point in the mean-field Blume--Capel model. We show that the thermodynamic magnetization and the finite-size magnetization are asymptotic when the parameter $\alpha$ governing the speed at which the sequence approaches criticality is below a certain threshold $\alpha_0$. However, when $\alpha$ exceeds $\alpha_0$, the thermodynamic magnetization converges to 0 much faster than the finite-size magnetization. The asymptotic behavior of the finite-size magnetization is proved via a moderate deviation principle when $0\alpha_0$. To the best of our knowledge, our results are the first rigorous confirmation of the statistical mechanical theory of finite-size scaling for a mean-field model.Comment: Published in at http://dx.doi.org/10.1214/10-AAP679 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Ginzburg-Landau Polynomials and the Asymptotic Behavior of the Magnetization Near Critical and Tricritical Points

For the mean-field version of an important lattice-spin model due to Blume and Capel, we prove unexpected connections among the asymptotic behavior of the magnetization, the structure of the phase transitions, and a class of polynomials that we call the Ginzburg-Landau polynomials. The model depends on the parameters n, beta, and K, which represent, respectively, the number of spins, the inverse temperature, and the interaction strength. Our main focus is on the asymptotic behavior of the magnetization m(beta_n,K_n) for appropriate sequences (beta_n,K_n) that converge to a second-order point or to the tricritical point of the model and that lie inside various subsets of the phase-coexistence region. The main result states that as (beta_n,K_n) converges to one of these points (beta,K), m(beta_n,K_n) ~ c |beta - beta_n|^gamma --> 0. In this formula gamma is a positive constant, and c is the unique positive, global minimum point of a certain polynomial g that we call the Ginzburg-Landau polynomial. This polynomial arises as a limit of appropriately scaled free-energy functionals, the global minimum points of which define the phase-transition structure of the model. For each sequence (beta_n,K_n) under study, the structure of the global minimum points of the associated Ginzburg-Landau polynomial mirrors the structure of the global minimum points of the free-energy functional in the region through which (beta_n,K_n) passes and thus reflects the phase-transition structure of the model in that region. The properties of the Ginzburg-Landau polynomials make rigorous the predictions of the Ginzburg-Landau phenomenology of critical phenomena, and the asymptotic formula for m(beta_n,K_n) makes rigorous the heuristic scaling theory of the tricritical point.Comment: 70 pages, 8 figure

Particle Physics at Future Colliders

The search for physics beyond the Standard Model motivates new high-energy accelerators, which will require high luminosities in order to produce interesting new heavy particles. Using the Higgs boson and supersymmetry as examples, we discuss the capabilities of the LHC and $e^+ e^-$ linear colliders in the TeV and multi-TeV energy ranges to discover and study new particles