Attributed graph similarity from the quantum Jensen-Shannon divergence

One of the most fundamental problem that we face in the graph domain is that of establishing the similarity, or alternatively the distance, between graphs. In this paper, we address the problem of measuring the similarity between attributed graphs. In particular, we propose a novel way to measure the similarity through the evolution of a continuous-time quantum walk. Given a pair of graphs, we create a derived structure whose degree of symmetry is maximum when the original graphs are isomorphic, and where a subset of the edges is labeled with the similarity between the respective nodes. With this compositional structure to hand, we compute the density operators of the quantum systems representing the evolution of two suitably defined quantum walks. We define the similarity between the two original graphs as the quantum Jensen-Shannon divergence between these two density operators, and then we show how to build a novel kernel on attributed graphs based on the proposed similarity measure. We perform an extensive experimental evaluation both on synthetic and real-world data, which shows the effectiveness the proposed approach. © 2013 Springer-Verlag.

Functional Transfer Theorems for Maxima of Stationary Processes

2000 Mathematics Subject Classification: 60G70, 60F12, 60G10.

Efficient computation of decoherent quantum walks through eigenvalue perturbation

A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly,it has been shown that algorithmic properties of quantum walks with decoherence such as the spreading rate are sometimes better than their purely quantum counterparts. Not only quantum walks with decoherence provide a generalization of quantum walks that naturally encompasses both the quantum and classical case, but they also give rise to new and different probability distribution. The application of quantum walks with decoherence to large graphs is limited by the necessity of evolving state vector whose sizes quadratic in the number of nodes of the graph, as opposed to the linear state vector of the purely quantum (or classical) case. In this technical report,we show how to use perturbation theory to reduce the computational complexity of evolving a continuous-time quantum walk subject to decoherence. More specifically, given a graph over n nodes, we show how to approximate the eigendecomposition of the n2×n2 Lindblad super-operator from the eigendecomposition of the n×n graph Hamiltonian.

Martingálmértékek és a várható diszkontált jelenérték szabály (Martingale measures and the law of the discounted present value)

A dolgozatban a legegyszerűbb kérdést feszegetjük: Hogyan kell az árakat meghatározni véletlen jövőbeli kifizetések esetén. A tárgyalás némiképpen absztrakt, de a funkcionálanalízis néhány közismert tételén kívül semmilyen más mélyebb matematikai területre nem kell hivatkozni. A dolgozat kérdése, hogy miként indokolható a várható jelenérték szabálya, vagyis hogy minden jövőbeli kifizetés jelen időpontban érvényes ára a jövőbeli kifizetés diszkontált várható értéke. A dologban az egyetlen csavar az, hogy a várható értékhez tartozó valószínűségi mértékről nem tudunk semmit. Csak annyit tudunk, hogy létezik a matematikai pénzügyek legtöbbet hivatkozott fogalma, a misztikus Q mérték. A dolgozat megírásának legfontosabb indoka az volt, hogy megpróbáltam kiiktatni a megengedett portfólió fogalmát a származtatott termékek árazásának elméletéből. Miként közismert, a származtatott termékek árazásának elmélete a fedezés fogalmára épül. (...) ____ In the article the author discusses some problems of the existence of the martingale measure. In continuous time models one should restrict the set of self financing portfolios and introduce the concept of the admissible portfolios. But to define the admissible portfolios one should either define them under the martingale measure or to turn the set of admissible portfolios to a cone which makes the interpretation of the pricing formula difficult.

Essays on the Dynamic Decisions of Homeowners and Retailers

Urban problems have several features that make them inherently dynamic. Large transaction costs all but guarantee that homeowners will do their best to consider how a neighborhood might change before buying a house. Similarly, stores face large sunk costs when opening, and want to be sure that their investment will pay off in the long run. In line with those concerns, different areas of Economics have made recent advances in modeling those questions within a dynamic framework. This dissertation contributes to those efforts.

Chapter 2 discusses how to model an agent’s location decision when the agent must learn about an exogenous amenity that may be changing over time. The model is applied to estimating the marginal willingness to pay to avoid crime, in which agents are learning about the crime rate in a neighborhood, and the crime rate can change in predictable (Markovian) ways.

Chapters 3 and 4 concentrate on location decision problems when there are externalities between decision makers. Chapter 3 focuses on the decision of business owners to open a store, when its demand is a function of other nearby stores, either through competition, or through spillovers on foot traffic. It uses a dynamic model in continuous time to model agents’ decisions. A particular challenge is isolating the contribution of spillovers from the contribution of other unobserved neighborhood attributes that could also lead to agglomeration. A key contribution of this chapter is showing how we can use information on storefront ownership to help separately identify spillovers.

Finally, chapter 4 focuses on a class of models in which families prefer to live

close to similar neighbors. This chapter provides the first simulation of such a model in which agents are forward looking, and shows that this leads to more segregation than it would have been observed with myopic agents, which is the standard in this literature. The chapter also discusses several extensions of the model that can be used to investigate relevant questions such as the arrival of a large contingent high skilled tech workers in San Francisco, the immigration of hispanic families to several southern American cities, large changes in local amenities, such as the construction of magnet schools or metro stations, and the flight of wealthy residents from cities in the Rust belt, such as Detroit.

Essays on Job Search and Labor Market Dynamics

This dissertation consists of three separate essays on job search and labor market dynamics. In the first essay, “The Impact of Labor Market Conditions on Job Creation: Evidence from Firm Level Data”, I study how much changes in labor market conditions reduce employment fluctuations over the business cycle. Changes in labor market conditions make hiring more expensive during expansions and cheaper during recessions, creating counter-cyclical incentives for job creation. I estimate firm level elasticities of labor demand with respect to changes in labor market conditions, considering two margins: changes in labor market tightness and changes in wages. Using employer-employee matched data from Brazil, I find that all firms are more sensitive to changes in wages rather than labor market tightness, and there is substantial heterogeneity in labor demand elasticity across regions. Based on these results, I demonstrate that changes in labor market conditions reduce the variance of employment growth over the business cycle by 20% in a median region, and this effect is equally driven by changes along each margin. Moreover, I show that the magnitude of the effect of labor market conditions on employment growth can be significantly affected by economic policy. In particular, I document that the rapid growth of the national minimum wages in Brazil in 1997-2010 amplified the impact of the change in labor market conditions during local expansions and diminished this impact during local recessions.

In the second essay, “A Framework for Estimating Persistence of Local Labor

Demand Shocks”, I propose a decomposition which allows me to study the persistence of local labor demand shocks. Persistence of labor demand shocks varies across industries, and the incidence of shocks in a region depends on the regional industrial composition. As a result, less diverse regions are more likely to experience deeper shocks, but not necessarily more long lasting shocks. Building on this idea, I propose a decomposition of local labor demand shocks into idiosyncratic location shocks and nationwide industry shocks and estimate the variance and the persistence of these shocks using the Quarterly Census of Employment and Wages (QCEW) in 1990-2013.

In the third essay, “Conditional Choice Probability Estimation of Continuous- Time Job Search Models”, co-authored with Peter Arcidiacono and Arnaud Maurel, we propose a novel, computationally feasible method of estimating non-stationary job search models. Non-stationary job search models arise in many applications, where policy change can be anticipated by the workers. The most prominent example of such policy is the expiration of unemployment benefits. However, estimating these models still poses a considerable computational challenge, because of the need to solve a differential equation numerically at each step of the optimization routine. We overcome this challenge by adopting conditional choice probability methods, widely used in dynamic discrete choice literature, to job search models and show how the hazard rate out of unemployment and the distribution of the accepted wages, which can be estimated in many datasets, can be used to infer the value of unemployment. We demonstrate how to apply our method by analyzing the effect of the unemployment benefit expiration on duration of unemployment using the data from the Survey of Income and Program Participation (SIPP) in 1996-2007.

Assessment of the Spatial and Temporal Distribution of Functional Connectivity in Resting-State BOLD fMRI

Recent research into resting-state functional magnetic resonance imaging (fMRI) has shown that the brain is very active during rest. This thesis work utilizes blood oxygenation level dependent (BOLD) signals to investigate the spatial and temporal functional network information found within resting-state data, and aims to investigate the feasibility of extracting functional connectivity networks using different methods as well as the dynamic variability within some of the methods. Furthermore, this work looks into producing valid networks using a sparsely-sampled sub-set of the original data.

In this work we utilize four main methods: independent component analysis (ICA), principal component analysis (PCA), correlation, and a point-processing technique. Each method comes with unique assumptions, as well as strengths and limitations into exploring how the resting state components interact in space and time.

Correlation is perhaps the simplest technique. Using this technique, resting-state patterns can be identified based on how similar the time profile is to a seed region’s time profile. However, this method requires a seed region and can only identify one resting state network at a time. This simple correlation technique is able to reproduce the resting state network using subject data from one subject’s scan session as well as with 16 subjects.

Independent component analysis, the second technique, has established software programs that can be used to implement this technique. ICA can extract multiple components from a data set in a single analysis. The disadvantage is that the resting state networks it produces are all independent of each other, making the assumption that the spatial pattern of functional connectivity is the same across all the time points. ICA is successfully able to reproduce resting state connectivity patterns for both one subject and a 16 subject concatenated data set.

Using principal component analysis, the dimensionality of the data is compressed to find the directions in which the variance of the data is most significant. This method utilizes the same basic matrix math as ICA with a few important differences that will be outlined later in this text. Using this method, sometimes different functional connectivity patterns are identifiable but with a large amount of noise and variability.

To begin to investigate the dynamics of the functional connectivity, the correlation technique is used to compare the first and second halves of a scan session. Minor differences are discernable between the correlation results of the scan session halves. Further, a sliding window technique is implemented to study the correlation coefficients through different sizes of correlation windows throughout time. From this technique it is apparent that the correlation level with the seed region is not static throughout the scan length.

The last method introduced, a point processing method, is one of the more novel techniques because it does not require analysis of the continuous time points. Here, network information is extracted based on brief occurrences of high or low amplitude signals within a seed region. Because point processing utilizes less time points from the data, the statistical power of the results is lower. There are also larger variations in DMN patterns between subjects. In addition to boosted computational efficiency, the benefit of using a point-process method is that the patterns produced for different seed regions do not have to be independent of one another.

This work compares four unique methods of identifying functional connectivity patterns. ICA is a technique that is currently used by many scientists studying functional connectivity patterns. The PCA technique is not optimal for the level of noise and the distribution of the data sets. The correlation technique is simple and obtains good results, however a seed region is needed and the method assumes that the DMN regions is correlated throughout the entire scan. Looking at the more dynamic aspects of correlation changing patterns of correlation were evident. The last point-processing method produces a promising results of identifying functional connectivity networks using only low and high amplitude BOLD signals.

A Molecular-scale Programmable Stochastic Process Based On Resonance Energy Transfer Networks: Modeling And Applications

While molecular and cellular processes are often modeled as stochastic processes, such as Brownian motion, chemical reaction networks and gene regulatory networks, there are few attempts to program a molecular-scale process to physically implement stochastic processes. DNA has been used as a substrate for programming molecular interactions, but its applications are restricted to deterministic functions and unfavorable properties such as slow processing, thermal annealing, aqueous solvents and difficult readout limit them to proof-of-concept purposes. To date, whether there exists a molecular process that can be programmed to implement stochastic processes for practical applications remains unknown.

In this dissertation, a fully specified Resonance Energy Transfer (RET) network between chromophores is accurately fabricated via DNA self-assembly, and the exciton dynamics in the RET network physically implement a stochastic process, specifically a continuous-time Markov chain (CTMC), which has a direct mapping to the physical geometry of the chromophore network. Excited by a light source, a RET network generates random samples in the temporal domain in the form of fluorescence photons which can be detected by a photon detector. The intrinsic sampling distribution of a RET network is derived as a phase-type distribution configured by its CTMC model. The conclusion is that the exciton dynamics in a RET network implement a general and important class of stochastic processes that can be directly and accurately programmed and used for practical applications of photonics and optoelectronics. Different approaches to using RET networks exist with vast potential applications. As an entropy source that can directly generate samples from virtually arbitrary distributions, RET networks can benefit applications that rely on generating random samples such as 1) fluorescent taggants and 2) stochastic computing.

By using RET networks between chromophores to implement fluorescent taggants with temporally coded signatures, the taggant design is not constrained by resolvable dyes and has a significantly larger coding capacity than spectrally or lifetime coded fluorescent taggants. Meanwhile, the taggant detection process becomes highly efficient, and the Maximum Likelihood Estimation (MLE) based taggant identification guarantees high accuracy even with only a few hundred detected photons.

Meanwhile, RET-based sampling units (RSU) can be constructed to accelerate probabilistic algorithms for wide applications in machine learning and data analytics. Because probabilistic algorithms often rely on iteratively sampling from parameterized distributions, they can be inefficient in practice on the deterministic hardware traditional computers use, especially for high-dimensional and complex problems. As an efficient universal sampling unit, the proposed RSU can be integrated into a processor / GPU as specialized functional units or organized as a discrete accelerator to bring substantial speedups and power savings.

(Table 1) Active-layer thickness as measured by the Biocomplexity Experiment (BE) for the flooded, drained and control sections in Barrow, Alaska

A continuous time series of annual soil thaw records, extending from 1994 to 2009, is available for comparison with the records of thaw obtained from the Biocomplexity Experiment (BE) for the period 2006-2009. Discontinuous records of thaw at Barrow from wet tundra sites date back to the 1960s. Comparisons between the longer records with the BE observations reveal strong similarities. Records of permafrost temperature, reflecting changes in the annual surface energy exchange, are available from the 1950s for comparison with results from measurement programs begun in 2002. The long-term systematic geocryological investigations at Barrow indicate an increase in permafrost temperature, especially during the last several years. The increase in near-surface permafrost temperature is most pronounced in winter. Marked trends are not apparent in the active-layer record, although subsidence measurements on the North Slope indicate that penetration into the ice-rich layer at the top of permafrost has occurred over the past decade. Active-layer thickness values from the 1960s are generally higher than those from the 1990s, and are very similar to those of the 2000s. Analysis of spatial active-layer observations at representative locations demonstrates significant variations in active-layer thickness between different landscape types, reflecting the influence of vegetation, substrate, microtopography, and, especially, soil moisture. Landscape-specific differences exist in the response of active-layer thickness to climatic forcing. These differences are attributable to the existence of localized controls related to combinations of surface and subsurface characteristics. The geocryological records at Barrow illustrate the importance and effectiveness of sustained, well organized monitoring efforts to document long-term trends.

Distributed Extremum-Seeking Control with Applications to High-Altitude Balloons

The real-time optimization of large-scale systems is a difficult problem due to the need for complex models involving uncertain parameters and the high computational cost of solving such problems by a decentralized approach. Extremum-seeking control (ESC) is a model-free real-time optimization technique which can estimate unknown parameters and can optimize nonlinear time-varying systems using only a measurement of the cost function to be minimized. In this thesis, we develop a distributed version of extremum-seeking control which allows large-scale systems to be optimized without models and with minimal computing power. First, we develop a continuous-time distributed extremum-seeking controller. It has three main components: consensus, parameter estimation, and optimization. The consensus provides each local controller with an estimate of the cost to be minimized, allowing them to coordinate their actions. Using this cost estimate, parameters for a local input-output model are estimated, and the cost is minimized by following a gradient descent based on the estimate of the gradient. Next, a similar distributed extremum-seeking controller is developed in discrete-time. Finally, we consider an interesting application of distributed ESC: formation control of high-altitude balloons for high-speed wireless internet. These balloons must be steered into a favourable formation where they are spread out over the Earth and provide coverage to the entire planet. Distributed ESC is applied to this problem, and is shown to be effective for a system of 1200 ballons subjected to realistic wind currents. The approach does not require a wind model and uses a cost function based on a Voronoi partition of the sphere. Distributed ESC is able to steer balloons from a few initial launch sites into a formation which provides coverage to the entire Earth and can maintain a similar formation as the balloons move with the wind around the Earth.

Evolutionary dynamics under various modes of reproduction

Thesis (Ph.D.)--University of Washington, 2016-08

Likelihood-Based Inference for Partially Observed Multi-Type Markov Branching Processes

Thesis (Ph.D.)--University of Washington, 2016-08

A path-based framework for analyzing large markov models

Reliability and dependability modeling can be employed during many stages of analysis of a computing system to gain insights into its critical behaviors. To provide useful results, realistic models of systems are often necessarily large and complex. Numerical analysis of these models presents a formidable challenge because the sizes of their state-space descriptions grow exponentially in proportion to the sizes of the models. On the other hand, simulation of the models requires analysis of many trajectories in order to compute statistically correct solutions. This dissertation presents a novel framework for performing both numerical analysis and simulation. The new numerical approach computes bounds on the solutions of transient measures in large continuous-time Markov chains (CTMCs). It extends existing path-based and uniformization-based methods by identifying sets of paths that are equivalent with respect to a reward measure and related to one another via a simple structural relationship. This relationship makes it possible for the approach to explore multiple paths at the same time,· thus significantly increasing the number of paths that can be explored in a given amount of time. Furthermore, the use of a structured representation for the state space and the direct computation of the desired reward measure (without ever storing the solution vector) allow it to analyze very large models using a very small amount of storage. Often, path-based techniques must compute many paths to obtain tight bounds. In addition to presenting the basic path-based approach, we also present algorithms for computing more paths and tighter bounds quickly. One resulting approach is based on the concept of path composition whereby precomputed subpaths are composed to compute the whole paths efficiently. Another approach is based on selecting important paths (among a set of many paths) for evaluation. Many path-based techniques suffer from having to evaluate many (unimportant) paths. Evaluating the important ones helps to compute tight bounds efficiently and quickly.

Queueuing system with failures and priorities

Queueing theory provides models, structural insights, problem solutions and algorithms to many application areas. Due to its practical applicability to production, manufacturing, home automation, communications technology, etc, more and more complex systems requires more elaborated models, tech- niques, algorithm, etc. need to be developed. Discrete-time models are very suitable in many situations and a feature that makes the analysis of discrete time systems technically more involved than its continuous time counterparts. In this paper we consider a discrete-time queueing system were failures in the server can occur as-well as priority messages. The possibility of failures of the server with general life time distribution is considered. We carry out an extensive study of the system by computing generating functions for the steady-state distribution of the number of messages in the queue and in the system. We also obtain generating functions for the stationary distribution of the busy period and sojourn times of a message in the server and in the system. Performance measures of the system are also provided.

On the duration of negative surplus

Doutoramento em Matemática