Phase segregated states in a simple three-state stochastic lattice gas are investigated. A two dimensional finite lattice with periodic boundary conditions is filled with one hole and two oppositely "charged" species of particles, subject to an excluded volume constraint. Starting from a completely disordered initial configuration, a sufficiently large external "electric" field <I>E</I> induces the phase segregation, by separating the charges into two strips and "trapping" the hole at an interface between them. Focusing on the steady state, the scaling properties of an appropriate order parameter, depending on drive and system size, are investigated by mean-field theory and Monte Carlo methods. Density profiles of the two interfaces in the ordered system are studied with the help of Monte Carlo simulations and are found to scale in the field-dependent variable, Ε = 2 tanh <I>E</I> /2), for <I>E</I> ≲ 0.8. For larger values of <I>E</I>, independent approximations of the interfacial profiles, obtained within the framework of mean-field theory, exhibit significant deviations from the Monte Carlo data. Interestingly, the deviations can be reduced significantly by a slight modification of the mean-field theory. / Master of Science

No / In this work we present the work on the equalization algorithms to be used in future orthogonally multiplexed wavelets based multi signaling communication systems. The performance of ZF and MMSE algorithms has been analyzed using SISO and MIMO communication models. The transmitted electromagnetic waves were subjected through Rayleigh multipath fading channel with AWGN. The results showed that the performance of both of the above mentioned algorithms is the same in SISO channel but in MIMO environment MMSE has better performance.

Yes / Underwater communication applications extensively use localization services for object identification. Because of their significant impact on ocean exploration and monitoring, underwater wireless sensor networks (UWSN) are becoming increasingly popular, and acoustic communications have largely overtaken radio frequency (RF) broadcasts as the dominant means of communication. The two localization methods that are most frequently employed are those that estimate the angle of arrival (AOA) and the time difference of arrival (TDoA). The military and civilian sectors rely heavily on UWSN for object identification in the underwater environment. As a result, there is a need in UWSN for an accurate localization technique that accounts for dynamic nature of the underwater environment. Time and position data are the two key parameters to accurately define the position of an object. Moreover, due to climate change there is now a need to constrain energy consumption by UWSN to limit carbon emission to meet net-zero target by 2050. To meet these challenges, we have developed an efficient localization algorithm for determining an object position based on the angle and distance of arrival of beacon signals. We have considered the factors like sensor nodes not being in time sync with each other and the fact that the speed of sound varies in water. Our simulation results show that the proposed approach can achieve great localization accuracy while accounting for temporal synchronization inaccuracies. When compared to existing localization approaches, the mean estimation error (MEE) and energy consumption figures, the proposed approach outperforms them. The MEEs is shown to vary between 84.2154m and 93.8275m for four trials, 61.2256m and 92.7956m for eight trials, and 42.6584m and 119.5228m for twelve trials. Comparatively, the distance-based measurements show higher accuracy than the angle-based measurements.

Portfolio optimization is a process in which the capital is allocated among the portfolio assets such that the return on investment is maximized while the risk is minimized. Portfolio construction and optimization is a complex process and has been an active research area in finance for a long time. For the portfolios with highly correlated assets, the performance of traditional risk-based asset allocation methods such as, the mean-variance (MV) method is limited because it requires an inversion of the covariance matrix of the portfolio to distribute weight among the portfolio assets. Alternatively, a hierarchical clustering-based machine learning method can provide a possible solution to these limitations in portfolio construction because it uses hierarchical relationships between the covariance of assets in a portfolio to distribute the weight and an inversion of the covariance matrix is not required. A comparison of the performance and analyses of the difference in weight distribution of two optimization strategies, the traditional MV method and the hierarchical risk parity method (HRP), which is a machine learning method, on real price historical data has been performed. Also, a comparison of the performance of a simple non-optimization technique called the equal-weight (EW) method to the two optimization methods, the Mean-variance method and HRP method has also been performed. This research supports the idea that HRP is a feasible method to construct portfolios with correlated assets because the performance of HRP is comparable to the performances of the traditional optimization method and the non-optimization method.

Anharmonic lattice dynamics and electron-phonon interactions are crucial to many intriguing physical phenomena in condensed matter physics. In my thesis, I develop theoretical methods and use them to characterize physical properties of model systems and realistic novel materials. First, I introduce vibrational dynamical mean-field theory on models of anharmonic phonons using various impurity solvers, and describe the theoretical extensions to treat non-local interactions. Second, I characterize phononic and excitonic ground state properties of the superatomic semiconductor, Re₆Se₈Cl₂, which exhibits quasi-ballistic exciton dynamics at room temperature. We attribute this behavior to the formation of polarons due to coupling with acoustic phonons and parameterize a Hamiltonian to study the ground state properties. Finally, I introduce a method to calculate the Green’s function that characterizes the equilibrium dynamical properties of polarons. I demonstrate its performance on the Holstein model at finite temperature, and show its applications to systems with general coupling, electron-electron interaction, and anharmonicity.

Making good predictions is a critical feature of decision making in situations such as investing and predicting the spread of diseases. Past literature indicates that people use recent and longer-term trends while making predictions. Nonetheless, less is known about how these factors affect how well people make predictions and the timing of their predictions. Further, identifying factors underlying predictive judgments could be an important behavioral factor in manic-depression, anxiety, substance use, age effects, and understanding how income inequality affects decision making. To understand how people make predictive judgments, we conducted two experiments. In Experiment 1, we used an investment task where participants had to predict the future price of a stock based on an exponential trend of information. We found that participants generally had lower earnings with steeper exponential trends (e.g. slower starting) and delayed their decisions to sell bad stocks with steeper trends. We extended these results in Experiment 2 with an updated task with exponential and inverse exponential trends. Overall, our results suggested that people delayed longer to make their prediction with slower starting exponential trends compared to faster starting inverse exponential trends and delayed their predictions longer with more linear trends compared to more trend trends. When deciding how long to explore, participants incorporated both the average trend and recent trend, though they shifted their responses depending on the overall functional form. These choices were ultimately biased to be optimistic or pessimistic based on whether the trend started fast or slow, respectively. Additionally, we found that participants who self-reported taking more gambling risk and depressive symptoms had a greater tendency to stay with faster starting trends and to leave with slower starting trends, suggesting they were even more optimistic given initially fast starting trends. Results pointing to an optimism bias based on the trend in information available to the participant could suggest that an aspect of sunk-cost fallacy is due to errors in predicting the likelihood of future success based on past information. Our findings help understand the dynamics of how people make predictive judgments over time and could inform future research into the mechanisms people use for prospective decision making. Additionally, future research and potential interventions could account for biases in how people perceive past trends to minimize harmful effects of sunk-cost fallacy when making predictions. / Psychology

Bakgrund: Tidigare studier har påvisat möjligheter till riskjusterad överavkastning genom tillämpandet av multiplar i konstruerandet av portföljer med målsättning att fånga mean-reversal effekten. De genomförda studierna har dock inte beaktat teoretiskt bakomliggande fundamentala variabler. Följaktligen är det av intresse att undersöka i vilken utsträckning en portfölj, sammansatt med hjälp av regression på en multipel, kan härleda avvikelser från jämvikt i aktiepriser och därmed generera högre avkastning än berättigat av risknivån på en effektiv marknad. Syfte: Studien ämnar empiriskt undersöka om aktiers framtida avkastning kan relateras till det värde som härleds genom relationen mellan deras fundamentala multiplar och marknadens faktiska multiplar. Genomförande: Studien härleder med hjälp av regressioner på multiplar aktiers jämviktspris och tillämpar avvikelser från dessa vid konstruktion av portföljer. Slutsats: Resultaten visar att en strategi baserade på regressioner av EV/EBITDA-multipeln kan generera en högre avkastning än berättigat av den effektiva marknadshypotesen under perioden 2006-2016. Liknande resultat har påvisats för P/E-multipeln men dessa kan inte statistiskt säkerställas på 95 % signifikansnivå. När det gäller EV/S-multipeln har inga indikationer på riskjusterad överavkastning påvisats. / Background: Previous studies has presented evidence of abnormal stock returns when applying valuemultiple based strategies in assembling portfolios. The previous studies has not consideredthe fundamental theoretical values that determine the value multiple. As a consequence, it isof interest to examine the performance of portfolios assembled with respect to thesefundamental value drivers. With the use of regression analysis, it is of interest to find out ifportfolios can be constructed that outperform the market portfolio in a sense of risk adjustedreturns. Purpose: This study aims to empirically examine if future stock returns can be derived from therelationship between their fundamentally determined multiples and the market multiple. Implementation: With the help of regression analysis of value multiples this study derives their equilibriumprice of stocks and apply deviation from equilibrium in construction of portfolios. Conclusion: The results indicate that a strategy based on regressions of the EV/EBITDA multiple maygenerate superior risk adjusted portfolio returns than suggested by the efficient markethypothesis during the period between 2006-2016. Similar results was found using the P/Emultiple however these results could not be statistically confirmed. Using the EV/S multipleno risk adjusted abnormal returns could be proven.

Diese Arbeit behandelt zwei Gebiete: stochastische partielle Rückwerts-Differentialgleichungen (BSPDEs) und Mean-Field-Games (MFGs). Im ersten Teil wird über eine stochastische Variante der De Giorgischen Iteration ein Maximumprinzip für quasilineare reflektierte BSPDEs (RBSPDEs) auf allgemeinen Gebieten bewiesen. Als Folgerung erhalten wir ein Maximumprinzip für RBSPDEs auf beschränkten, sowie für BSPDEs auf allgemeinen Gebieten. Abschließend wird das lokale Verhalten schwacher Lösungen untersucht. Im zweiten Teil zeigen wir zunächst die Existenz von Gleichgewichten in MFGs mit singulärer Kontrolle. Wir beweisen, dass die Lösung eines MFG ohne Endkosten und ohne Kosten in der singulären Kontrolle durch die Lösungen eines MFGs mit strikt regulären Kontrollen approximiert werden kann. Die vorgelegten Existenz- und Approximationsresultat basieren entscheidend auf der Wahl der Storokhod M1 Topologie auf dem Raum der Càdlàg-Funktion. Anschließend betrachten wir ein MFG optimaler Portfolioliquidierung unter asymmetrischer Information. Die Lösung des MFG charakterisieren wir über eine stochastische Vorwärts-Rückwärts-Differentialgleichung (FBSDE) mit singulärer Endbedingung der Rückwärtsgleichung oder alternativ über eine FBSDE mit endlicher Endbedingung, jedoch singulärem Treiber. Wir geben ein Fixpunktargument, um die Existenz und Eindeutigkeit einer Kurzzeitlösung in einem gewichteten Funktionenraum zu zeigen. Dies ermöglicht es, das ursprüngliche MFG mit entsprechenden MFGs ohne Zustandsendbedinung zu approximieren. Der zweite Teil wird abgeschlossen mit einem Leader-Follower-MFG mit Zustandsendbedingung im Kontext optimaler Portfolioliquidierung bei hierarchischer Agentenstruktur. Wir zeigen, dass das Problem beider Spielertypen auf singuläre FBSDEs zurückgeführt werden kann, welche mit ähnlichen Methoden wie im vorangegangen Abschnitt behandelt werden können. / The thesis is concerned with two topics: backward stochastic partial differential equations and mean filed games. In the first part, we establish a maximum principle for quasi-linear reflected backward stochastic partial differential equations (RBSPDEs) on a general domain by using a stochastic version of De Giorgi’s iteration. The maximum principle for RBSPDEs on a bounded domain and the maximum principle for BSPDEs on a general domain are obtained as byproducts. Finally, the local behavior of the weak solutions is considered. In the second part, we first establish the existence of equilibria to mean field games (MFGs) with singular controls. We also prove that the solutions to MFGs with no terminal cost and no cost from singular controls can be approximated by the solutions, respectively control rules, for MFGs with purely regular controls. Our existence and approximation results strongly hinge on the use of the Skorokhod M1 topology on the space of càdlàg functions. Subsequently, we consider an MFG of optimal portfolio liquidation under asymmetric information. We prove that the solution to the MFG can be characterized in terms of a forward backward stochastic differential equation (FBSDE) with possibly singular terminal condition on the backward component or, equivalently, in terms of an FBSDE with finite terminal value, yet singular driver. We apply the fixed point argument to prove the existence and uniqueness on a short time horizon in a weighted space. Our existence and uniqueness result allows to prove that our MFG can be approximated by a sequence of MFGs without state constraint. The final result of the second part is a leader follower MFG with terminal constraint arising from optimal portfolio liquidation between hierarchical agents. We show the problems for both follower and leader reduce to the solvability of singular FBSDEs, which can be solved by a modified approach of the previous result.

在線性迴歸分析中，資料的不適當，常導致研究者選擇了不當的模式，為避免此缺失，在分析資料前須先做好診斷工作。本文中將從貝氏觀點提出一些不同的診斷方法以供參考。首先推導出均數移動參數a=(a₁,…,a_k)'的事後分配，並利用a'a/k的事後均數診斷出不當資料點。接著，考慮在個別模式下以β事後分配之總變異及廣義變異為標準，診斷出離群值及具有潛在影響力之觀測值。最後，分別利用(i)β的事後分配(ii)σ²的事後分配(iii)(β,σ²)的聯合事後分配，推導出對應的對稱均方差以做為診斷標準。 / In this thesis, some different diagnostic methodologies for outliers and influential observations from Bayesian point of view are proposed. We firstly derive the marginal posterior distribution of the mean-shift parameter a=(a₁,a_k)¹, then use the posterior mean of a¹a/k to detect the spurious data items. Secondly, we use the posterior total variance and generalized variance of β as diagnostic criterions for outliers and influential observations. Finally, we utilize (i) the posterior distribution of β, (ii) the posterior distribution of σ², and (iii) the joint posterior distribution of β, σ² to find their corresponding symmetric mean square differences , which can be used as diagnostic criterions.

This dissertation designs linear transceivers for the multiuser downlink in multiple-input multiple-output (MIMO) systems. The designs rely on an uplink/downlink duality for the mean squared error (MSE) of each individual data stream. We first consider the design of transceivers assuming channel state information (CSI) at the transmitter. We consider minimization of the sum-MSE over all users subject to a sum power constraint on each transmission. Using MSE duality, we solve a computationally simpler convex problem in a virtual uplink. The transformation back to the downlink is simplified by our demonstrating the equality of the optimal power allocations in the uplink and downlink. Our second set of designs maximize the sum throughput for all users. We establish a series of relationships linking MSE to the signal-to-interference-plus-noise ratios of individual data streams and the information theoretic channel capacity under linear minimum MSE decoding. We show that minimizing the product of MSE matrix determinants is equivalent to sum-rate maximization, but we demonstrate that this problem does not admit a computationally efficient solution. We simplify the problem by minimizing the product of mean squared errors (PMSE) and propose an iterative algorithm based on alternating optimization with near-optimal performance. The remainder of the thesis considers the more practical case of imperfections in CSI. First, we consider the impact of delay and limited-rate feedback. We propose a system which employs Kalman prediction to mitigate delay; feedback rate is limited by employing adaptive delta modulation. Next, we consider the robust design of the sum-MSE and PMSE minimizing precoders with delay-free but imperfect estimates of the CSI. We extend the MSE duality to the case of imperfect CSI, and consider a new optimization problem which jointly optimizes the energy allocations for training and data stages along with the sum-MSE/PMSE minimizing transceivers. We prove the separability of these two problems when all users have equal estimation error variances, and propose several techniques to address the more challenging case of unequal estimation errors.