Statistical physics

How one behaves after interacting with a friend may not be the same as before
the interaction began What factors a ect the formation of social interactions
between people and, once formed, how do social interactions leave lasting changes on
individual behavior? In this dissertation, a thorough review and conceptual synthesis
is provided Major features of coordination dynamics are demonstrated with
examples from both the intrapersonal and interpersonal coordination literature that
are interpreted via a conceptual scheme, the causal loops of coordination dynamics
An empirical, behavioral study of interpersonal coordination was conducted to
determine which spontaneous patterns of coordination formed and whether a remnant
of the interaction ensued ("social memory") To assess social memory in dyads, the
behavior preceding and following episodes of interaction was compared In the
experiment, pairs of people sat facing one another and made continuous flexion-extension finger movements while a window acted as a shutter to control
whether partners saw each other's movements Thus, vision ("social contact") allowed
spontaneous information exchange between partners through observation Each trial consisted of three successive intervals lasting twenty seconds: without social contact
("me and you"), with social contact ("us"), and again without ("me and you")
During social contact, a variety of patterns was observed ranging from phase coupling
to transient or absent collective behavior Individuals also entered and exited social
coordination differently In support of social memory, compared to before social
contact, after contact ended participants tended to remain near each other's
movement frequency Furthermore, the greater the stability of coupling, the more
similar the partners' post-interactional frequencies were Proposing that the
persistence of behavior in the absence of information exchange was the result of prior
frequency adaptation, a mathematical model of human movement was implemented
with Haken-Kelso-Bunz oscillators that reproduced the experimental findings, even
individual dyadic patterns Parametric manipulations revealed multiple routes to
persistence of behavior via the interplay of adaptation and other HKB model
parameters The experimental results, the model, and their interpretation form the
basis of a proposal for future research and possible therapeutic applications

The main objective of this thesis is to simulate, evaluate and discuss several
methods for pricing European-style options. The Black-Scholes model has long been
considered the standard method for pricing options. One of the downfalls of the
Black-Scholes model is that it is strictly continuous and does not incorporate discrete
jumps. This thesis will consider two alternate Levy models that include discretized
jumps; The Merton Jump Diffusion and Kou's Double Exponential Jump Diffusion.
We will use each of the three models to price real world stock data through software
simulations and explore the results.Keywords: Levy Processes, Brownian motion, Option pricing, Simulation, Black-Scholes, Merton Jump Diffusion, Kou, Kou's Double Exponential Jump Diffusion.

Three new approaches to the clustering of data sets are presented. They are heuristic methods and represent forms of unsupervised (non-parametric) clustering. Applied to an unknown set of data these methods automatically determine the number of clusters and their location using no a priori assumptions. All are based on analogies with different physical phenomena. The first technique, named the Percolation Clustering Algorithm, embodies a novel variation on the nearest-neighbor algorithm focusing on the connectivity between sample points. Exploiting the equivalence with a percolation process, this algorithm considers data points to be surrounded by expanding hyperspheres, which bond when they touch each other. Once a sequence of joined spheres spans an entire cluster, percolation occurs and the cluster size remains constant until it merges with a neighboring cluster. The second procedure, named Nucleation and Growth Clustering, exploits the analogy with nucleation and growth which occurs in island formation during epitaxial growth of solids. The original data points are nucleation centers, around which aggregation will occur. Additional "ad-data" that are introduced into the sample space, interact with the data points and stick if located within a threshold distance. These "ad-data" are used as a tool to facilitate the detection of clusters. The third method, named Discrete Deposition Clustering Algorithm, constrains deposition to occur on a grid, which has the advantage of computational efficiency as opposed to the continuous deposition used in the previous method. The original data form the vertexes of a sparse graph and the deposition sites are defined to be the middle points of this graphs edges. Ad-data are introduced on the deposition site and the system is allowed to evolve in a self-organizing regime. This allows the simulation of a phase transition and by monitoring the specific heat capacity of the system one can mark out a "natural" criterion for validating the partition. All of these techniques are competitive with existing algorithms and offer possible advantages for certain types of data distributions. A practical application is presented using the Percolation Clustering Algorithm to determine the taxonomy of the Dow Jones Industrial Average portfolio. The statistical properties of the correlation coefficients between DJIA components are studied along with the eigenvalues of the correlation matrix between the DJIA components.