In this thesis we present a model of the interacting agents on the financial market. The agents are represented by a non-Euclidean random graph, where each agent communicate with another with probability p, and the interaction according to the Ising Model. We investigate properties of the model by direct calculations for small graph sizes, and by perfect simulation for larger graph sizes. We also present a model for asset price variation by using the magnetization of the Ising model.

No description available.

The efficiency of parallel tempering Monte Carlo is studied for a two-dimensional Ising system of length L with N=L^2 spins. An external field is used to introduce a difference in free energy between the two low temperature states. It is found that the number of replicas R_opt that optimizes the parallel tempering algorithm scales as the square root of the system size N. For two symmetric low temperature states, the time needed for equilibration is observed to grow as L^2.18. If a significant difference in free energy is present between the two states, this changes to L^1.02. It is therefore established that parallel tempering is sped up by a factor of roughly L if an asymmetry is introduced between the low temperature states. This confirms previously made predictions for the efficiency of parallel tempering. These findings should be especially relevant when using parallel tempering for systems like spin glasses, where no information about the degeneracy of low temperature states is available prior to the simulation.

Problem Statement: The use of pulsed electric fields (PEFs) as a tumor treatment modality is receiving increased traction. A typical clinical procedure involves insertion of a pair of electrodes into the tumor and administration of PEFs (amplitude: ~1 kV/cm; pulse-width: 100 μs). This leaves a zone of complete cell death and a sub-lethal zone where a fraction of the cells survive. There is substantial evidence of an anti-tumor systemic immune profile in animal patients treated with PEFs. However, the mechanism behind such immune profile alterations remains unknown, and the effect of PEFs on cell signaling within sub-lethal zones remains largely unexplored. Moreover, different values of a PEF pulse parameter, for e.g. the pulse-widths of 100 μs and 100 ns, may have different effects on cell signaling. Thus, the challenge of answering the mechanistic questions is compounded by the large PEF parameter space consisting of different combinations of pulse-widths, amplitudes, and exposure times. Intellectual merit: This Ph.D. research provides proof that sub-lethal PEFs can enhance anti-tumor signaling in triple negative breast cancer cells by abrogating thymic stromal lymphopoietin signaling and enhancing stimulatory proteins such as the tumor necrosis factor. Furthermore, experimental evidence produced during this Ph.D. research demonstrates that PEFs may not directly impact the intracellular mitochondrial membrane at clinically relevant field amplitudes. As demonstrated in this work, PEFs may influence the mitochondria via an indirect route such as disruption of the actin cytoskeleton and/or alteration of ionic environment in the cytoplasm due to cell membrane permeabilization. Thus, a reductionist approach to understanding the influence of PEFs on cell signaling is proposed by limiting the study to membrane dynamics. To overcome the problem of investigating the entire PEF parameter space, this Ph.D. research proposes a first-principle thermodynamic approach of scaling the PEF parameter space such that an understanding developed in one regime of PEF pulse parameter values can be used to understand other regimes of the parameter space. Demonstration of the validity of this scaling model is provided by coupling Monte-Carlo methods for density-of-states with the steepest-entropy-ascent quantum thermodynamic framework for the non-equilibrium prediction of the lipid membrane dynamics. / Ph. D. / A complete cure for cancer is still far from being realized despite very promising developments on the front of molecular drug therapy. One promising conceptual approach would be to achieve the ability to re-tune the cancerous signals that drive disease progression. To overcome current challenges in tuning cancerous signaling a paradigm change in cancer treatment is necessary. For example, a treatment strategy to alter cell signaling which leverages both the physical and chemical properties that accompany malignancy may be required. Electric fields, be it in the form of low-amplitude steady state fields or high-amplitude pulsed electric fields (PEFs), can induce distinct physical and chemical effects on cells. Hence, the use of electric fields as a clinical tumor treatment modality is receiving increased traction. However, the effect of these electric fields on cell signaling and cell behavior remains largely unexplored. This Ph.D. work provides experimental evidence that PEFs can directly impact cancerous cell signaling towards a less inflammatory and possibly less cancerous state. Although a noteworthy finding, the data poses another challenging question, i.e., how does the electric field impact cell behavior? Answering this mechanistic question is essential for FDA approval and a broader clinical use of the electric field modalities. An impediment to answering this question is the vast parameter space of electric fields (e.g., amplitude, pulse width, and number of pulses), which makes performing experimental mechanistic studies untenable. It is argued via experimental evidence gathered during this work that applying scaling laws applicable to lipid membranes may provide a solution to reducing the candidate PEF parameters to a manageable number. A non-equilibrium thermodynamic model is proposed that allows studying the behavior of lipid species using scaled electric field parameters. Thus, the v understanding gained via the proposed model can direct the next level of extensive biological assays and animal studies and eventually lead to effective cancer treatments.

<p> LiHoxY1-xF4 is an insulating system where the Ho ions are magnetic. The crystal field gives an Ising character to the Ho ions, and the dominant interaction between them is through magnetic dipolar fields. For x=1, the system is a ferromagnet with a critical temperature of 1.54 K. The critical temperature decreases as x is decreased until x~0.25. At that point the long range order is destroyed, giving rise to a state with some characteristics of spin glass behavior.</p> <p> The study of this system is important because its Ising nature makes it a test ground for theoretical models. Interestingly, not only experiments and theory diverge in many points, but experimental data from different research groups are contradictory. In order to contribute to a clearer experimental picture, we performed μSR measurements in this system and we present our results in this thesis.</p> <p> In the ferromagnetic samples (x=1 and 0.45) we found that the internal field distribution at the muon site is quite broad, even in the x=1 system. Then it is possible that the magnetic field distribution at the Ho ions is broad as well. We show qualitatively how this broadening could explain a feature of the field-temperature phase diagram which is still not understood.</p> <p> For the more diluted samples (x=0.25, 0.12, 0.08, 0.045 and 0.018), we found that they all have the same qualitative behavior as a function of temperature and magnetic field. Our analysis of the data did not show any feature of canonical spin glass behavior. Instead, an analysis using dynamical Kubo-Toyabe functions show a temperature independent fluctuation rate of the Ho moments below ~0.5 K for all these samples. This behavior is characteristic of cooperative paramagnetic systems. We also found that the low temperature fluctuation rate decreases as x is decreased.</p> <p> To analyze the data from LiHoxY1-xF4 we developed microscopic models of μSR signals. These models are presented in this thesis and they correspond to stochastic models of signals using stretched magnetic field distributions; and the modeling of signals from systems with F-μ-F bond formation where the set of bonds does not have cubic symmetry.</p> / Thesis / Doctor of Philosophy (PhD)

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Metal Organic Frameworks (MOFs) exhibit many excellent physical properties including magnetic properties for potential applications in devices. More importantly for the subject of this thesis, MOFs are ideal for the realization of low dimensional magnetism because of the large selection of ligands connecting magnetic centers in making the framework. The materials studied in this thesis include ten magnetic MOFs of the form M(L1)(L2) [M = Cu, Ni, Co, Fe, Mn; L1 = NDC, bpdc, BDC, BODC, N3; L2 = DMF, H2O, TED, bpy]. Polycrystalline powder samples as well as single crystal samples were synthesized. Their crystal structures were determined, and their magnetic and thermodynamic properties were measured and analyzed. Eight of these materials were characterized as 1D magnets and two as 3D magnets. In the 1D case it is found that above Tm [the temperature at which the magnetic susceptibility χ(T) has a peak] the magnetic behavior of MOFs (S ≥ 1) can be well described with the Classical Fisher Model (CFM). Near and below TC the spins take a more definite orientation than allowed for in the CFM and hence the Ising Model (IM) was used for fitting. Both CFM and IM yield fairly consistent intrachain couplings (J) when applied in their appropriate temperature region. To estimate the interchain exchange (J′), the susceptibility for a magnetic chain in the mean field of neighboring chains is used. In all cases, as expected, the ratio of J to J′ was less than 10%. The special case of Cu(N3)2bpy (S = ½) was analyzed with the spin ½ IM. Although the specific heat data (Ctotal) for most of the 1D MOFs showed no clear phase transition, a low temperature fit to the electron-phonon specific heats yielded apparent heavy fermion-like &gamma values on the order of several hundred mJ/mol K2. The lattice specific heat (C lattice) was estimated using a Debye-Einstein hybrid model. Subtracting Clattice from Ctotal, magnetic specific heat (CM) with a broad peak characteristic of low dimensional magnetism was obtained. The peak in CM was at temperature near that expected from χ(T) fits. The J values obtained from the magnetic specific heat fits were in good agreement with those obtained from χ(T) fits. Once the magnetic specific heat was accounted for, γtakes values in the expected range of few mJ/mol K2. For 3D MOFs [Mn(N3)2bpy and Fe(N3)2bpy], the existence of long range canted antiferromagnetic ordering was observed in both magnetic and specific heat measurements with phase transitions at 38 K and 20 K in the case of Mn(N3)2bpy and Fe(N3)2bpy, respectively. These transition temperatures are considered fairly high for molecular based materials. In both Mn(N3)2bpy and Fe(N3)2bpy, the χ(T) data fit well to the Heisenberg model for a diamond-type network. The transition can clearly be seen with an abrupt increase in the magnetization below TC and a shift to a higher temperature in the specific heat when measured under an applied magnetic field. The systematic approach in this work led to the successful estimate of C lattice resulting in meaningful fitting of χ(T) and Cmagnetic to the appropriate theoretical models in magnetism. It also led the discovery of ferrimagnets or canted antiferromagnets M(N3)2bpy with large coercivity and rather high transition temperature. The results of this study have been published in three articles in the Journal of Applied physics, and two manuscripts are under preparation for submission [1-5]. / Physics

In this dissertation, a variable selection method for spatial data is developed. It is assumed that the spatial process is non-stationary as a whole but is piece-wise stationary. The pieces where the spatial process is stationary are called regions. The variable selection approach accounts for two sources of correlation: (1) the spatial correlation of the data within the regions, and (2) the correlation of adjacent regions. The variable selection is carried out by including indicator variables that characterize the significance of the regression coefficients. The Ising distribution as prior for the vector of indicator variables, models the dependence of adjacent regions. We present a case study on brook trout data where the response of interest is the presence/absence of the fish at sites in the eastern United States. We find that the method outperforms the case of the probit regression where the spatial field is assumed stationary and isotropic. Additionally, the method outperformed the case where multiple regions are assumed independent of their neighbors. / Ph. D.

Here, we propose a method for generating a hierarchy of mean-field approximations to study the properties of the driven diffusive Ising model at nonequilibrium steady state. In addition, the present study offers a demonstration of the practical application of the information theoretic methods to a simple interacting nonequilibrium system. The application of maximum entropy principle to the system, which is in contact with a heat reservoir, leads to a minimization principle for the generalized Helmholtz free energy. At every level of approximation the latter is expressed in terms of the corresponding mean—field variables. These play the role of variational parameters. The rate equations for the mean-field variables, which incorporate the dynamics of the system, serve as constraints to the minimization procedure. The method is applicable to high temperatures as well to the low temperature phase coexistence regime and also has the potential for dealing with first-order phase transitions. At low temperatures the free energy is nonconvex and we use a Maxwell construction to find the relevant information for the system. To test the method we carry out numerical calculations at the pair level of approximation for the 2-dimensional driven diffusive Ising model on a square lattice with attractive interactions. The results reproduce quite well all the basic properties of the system as reported from Monte Carlo simulations. / Ph. D.

This thesis explores the theoretical representation of localised electrons in magnetic systems, using Majorana fermions. A motivation is provided for the Majorana fermion representation, which is then developed and applied as a mean-field theory and in the path-integral formalism to the Ising model in transversal-field (TFIM) in one, two and three dimensions, on an orthonormal lattice. In one dimension the development of domain walls precludes long-range order in discrete systems; this is as free energy savings due to entropy outweigh the energetic cost of a domain wall. An argument due to Peierls exists in 2D which allows the formation of domains of ordered spins amidst a disordered background, however, which may be extended to 3D. The forms of the couplings to the bosons used in the Random Phase Analysis (RPA) are considered and an explanation for the non-existence of the phases calculated in this thesis is discussed, in terms of spare degrees of freedom in the Majorana representation. This thesis contains the first known application of Majorana fermions at the RPA level.