Latent Space and Social Psychological Models of Diffusion

The problem of social diffusion has animated sociological thinking on topics ranging from the spread of an idea, an innovation or a disease, to the foundations of collective behavior and political polarization. While network diffusion has been a productive metaphor, the reality of diffusion processes is often muddier. Ideas and innovations diffuse differently from diseases, but, with a few exceptions, the diffusion of ideas and innovations has been modeled under the same assumptions as the diffusion of disease. In this dissertation, I develop two new diffusion models for "socially meaningful" contagions that address two of the most significant problems with current diffusion models: (1) that contagions can only spread along observed ties, and (2) that contagions do not change as they spread between people. I augment insights from these statistical and simulation models with an analysis of an empirical case of diffusion - the use of enterprise collaboration software in a large technology company. I focus the empirical study on when people abandon innovations, a crucial, and understudied aspect of the diffusion of innovations. Using timestamped posts, I analyze when people abandon software to a high degree of detail.

To address the first problem, I suggest a latent space diffusion model. Rather than treating ties as stable conduits for information, the latent space diffusion model treats ties as random draws from an underlying social space, and simulates diffusion over the social space. Theoretically, the social space model integrates both actor ties and attributes simultaneously in a single social plane, while incorporating schemas into diffusion processes gives an explicit form to the reciprocal influences that cognition and social environment have on each other. Practically, the latent space diffusion model produces statistically consistent diffusion estimates where using the network alone does not, and the diffusion with schemas model shows that introducing some cognitive processing into diffusion processes changes the rate and ultimate distribution of the spreading information. To address the second problem, I suggest a diffusion model with schemas. Rather than treating information as though it is spread without changes, the schema diffusion model allows people to modify information they receive to fit an underlying mental model of the information before they pass the information to others. Combining the latent space models with a schema notion for actors improves our models for social diffusion both theoretically and practically.

The empirical case study focuses on how the changing value of an innovation, introduced by the innovations' network externalities, influences when people abandon the innovation. In it, I find that people are least likely to abandon an innovation when other people in their neighborhood currently use the software as well. The effect is particularly pronounced for supervisors' current use and number of supervisory team members who currently use the software. This case study not only points to an important process in the diffusion of innovation, but also suggests a new approach -- computerized collaboration systems -- to collecting and analyzing data on organizational processes.

Undersampled Critical Branching Processes on Small-World and Random Networks Fail to Reproduce the Statistics of Spike Avalanches

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent t~3=2. Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.

Managing Rentals with Usage-Based Loss

Motivated by new and innovative rental business models, this paper develops a novel discrete-time model of a rental operation with random loss of inventory due to customer use. The inventory level is chosen before the start of a finite rental season, and customers not immediately served are lost. Our analysis framework uses stochastic comparisons of sample paths to derive structural results that hold under good generality for demands, rental durations, and rental unit lifetimes. Considering different \recirculation" rules | i.e., which rental unit to choose to meet each demand | we prove the concavity of the expected profit function and identify the optimal recirculation rule. A numerical study clarifies when considering rental unit loss and recirculation rules matters most for the inventory decision: Accounting for rental unit loss can increase the expected profit by 7% for a single season and becomes even more important as the time horizon lengthens. We also observe that the optimal inventory level in response to increasing loss probability is non-monotonic. Finally, we show that choosing the optimal recirculation rule over another simple policy allows more rental units to be profitably added, and the profit-maximizing service level increases by up to 6 percentage points.

Dynamic instabilities in scalar neural field equations with space-dependent delays

In this paper we consider a class of scalar integral equations with a form of space-dependent delay. These non-local models arise naturally when modelling neural tissue with active axons and passive dendrites. Such systems are known to support a dynamic (oscillatory) Turing instability of the homogeneous steady state. In this paper we develop a weakly nonlinear analysis of the travelling and standing waves that form beyond the point of instability. The appropriate amplitude equations are found to be the coupled mean-field Ginzburg-Landau equations describing a Turing-Hopf bifurcation with modulation group velocity of O(1). Importantly we are able to obtain the coefficients of terms in the amplitude equations in terms of integral transforms of the spatio-temporal kernels defining the neural field equation of interest. Indeed our results cover not only models with axonal or dendritic delays but those which are described by a more general distribution of delayed spatio-temporal interactions. We illustrate the predictive power of this form of analysis with comparison against direct numerical simulations, paying particular attention to the competition between standing and travelling waves and the onset of Benjamin-Feir instabilities.

Relating bisimulations with attractors in boolean network models

When studying a biological regulatory network, it is usual to use boolean network models. In these models, boolean variables represent the behavior of each component of the biological system. Taking in account that the size of these state transition models grows exponentially along with the number of components considered, it becomes important to have tools to minimize such models. In this paper, we relate bisimulations, which are relations used in the study of automata (general state transition models) with attractors, which are an important feature of biological boolean models. Hence, we support the idea that bisimulations can be important tools in the study some main features of boolean network models.We also discuss the differences between using this approach and other well-known methodologies to study this kind of systems and we illustrate it with some examples.

Undersampled Critical Branching Processes on Small-World and Random Networks Fail to Reproduce the Statistics of Spike Avalanches

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent t~3=2. Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.

Forecasting exchange rates in the presence of instabilities

Many exchange rate papers articulate the view that instabilities constitute a major impediment to exchange rate predictability. In this thesis we implement Bayesian and other techniques to account for such instabilities, and examine some of the main obstacles to exchange rate models' predictive ability. We first consider in Chapter 2 a time-varying parameter model in which fluctuations in exchange rates are related to short-term nominal interest rates ensuing from monetary policy rules, such as Taylor rules. Unlike the existing exchange rate studies, the parameters of our Taylor rules are allowed to change over time, in light of the widespread evidence of shifts in fundamentals - for example in the aftermath of the Global Financial Crisis. Focusing on quarterly data frequency from the crisis, we detect forecast improvements upon a random walk (RW) benchmark for at least half, and for as many as seven out of 10, of the currencies considered. Results are stronger when we allow the time-varying parameters of the Taylor rules to differ between countries. In Chapter 3 we look closely at the role of time-variation in parameters and other sources of uncertainty in hindering exchange rate models' predictive power. We apply a Bayesian setup that incorporates the notion that the relevant set of exchange rate determinants and their corresponding coefficients, change over time. Using statistical and economic measures of performance, we first find that predictive models which allow for sudden, rather than smooth, changes in the coefficients yield significant forecast improvements and economic gains at horizons beyond 1-month. At shorter horizons, however, our methods fail to forecast better than the RW. And we identify uncertainty in coefficients' estimation and uncertainty about the precise degree of coefficients variability to incorporate in the models, as the main factors obstructing predictive ability. Chapter 4 focus on the problem of the time-varying predictive ability of economic fundamentals for exchange rates. It uses bootstrap-based methods to uncover the time-specific conditioning information for predicting fluctuations in exchange rates. Employing several metrics for statistical and economic evaluation of forecasting performance, we find that our approach based on pre-selecting and validating fundamentals across bootstrap replications generates more accurate forecasts than the RW. The approach, known as bumping, robustly reveals parsimonious models with out-of-sample predictive power at 1-month horizon; and outperforms alternative methods, including Bayesian, bagging, and standard forecast combinations. Chapter 5 exploits the predictive content of daily commodity prices for monthly commodity-currency exchange rates. It builds on the idea that the effect of daily commodity price fluctuations on commodity currencies is short-lived, and therefore harder to pin down at low frequencies. Using MIxed DAta Sampling (MIDAS) models, and Bayesian estimation methods to account for time-variation in predictive ability, the chapter demonstrates the usefulness of suitably exploiting such short-lived effects in improving exchange rate forecasts. It further shows that the usual low-frequency predictors, such as money supplies and interest rates differentials, typically receive little support from the data at monthly frequency, whereas MIDAS models featuring daily commodity prices are highly likely. The chapter also introduces the random walk Metropolis-Hastings technique as a new tool to estimate MIDAS regressions.

Towards automation of constellation management with analytical models for collision avoidance

The growing interest for constellation of small, less expensive satellites is bringing space junk and traffic management to the attention of space community. At the same time, the continuous quest for more efficient propulsion systems put the spotlight on electric (low thrust) propulsion as an appealing solution for collision avoidance. Starting with an overview of the current techniques for conjunction assessment and avoidance, we then highlight the possible problems when a low thrust propulsion is used. The need for accurate propagation model shows up from the conducted simulations. Thus, aiming at propagation models with low computational burden, we study the available models from the literature and propose an analytical alternative to improve propagation accuracy. The model is then tested in the particular case of a tangential maneuver. Results show that the proposed solution significantly improve on state of the art methods and is a good candidate to be used in collision avoidance operations. For instance to propagate satellite uncertainty or optimizing avoidance maneuver when conjunction occurs within few (3-4) orbits from measurements time.

Turbulence in collisionless plasmas: statistical analysis from numerical simulations with pressure anisotropy

In recent years, we have experienced increasing interest in the understanding of the physical properties of collisionless plasmas, mostly because of the large number of astrophysical environments (e. g. the intracluster medium (ICM)) containing magnetic fields that are strong enough to be coupled with the ionized gas and characterized by densities sufficiently low to prevent the pressure isotropization with respect to the magnetic line direction. Under these conditions, a new class of kinetic instabilities arises, such as firehose and mirror instabilities, which have been studied extensively in the literature. Their role in the turbulence evolution and cascade process in the presence of pressure anisotropy, however, is still unclear. In this work, we present the first statistical analysis of turbulence in collisionless plasmas using three-dimensional numerical simulations and solving double-isothermal magnetohydrodynamic equations with the Chew-Goldberger-Low laws closure (CGL-MHD). We study models with different initial conditions to account for the firehose and mirror instabilities and to obtain different turbulent regimes. We found that the CGL-MHD subsonic and supersonic turbulences show small differences compared to the MHD models in most cases. However, in the regimes of strong kinetic instabilities, the statistics, i.e. the probability distribution functions (PDFs) of density and velocity, are very different. In subsonic models, the instabilities cause an increase in the dispersion of density, while the dispersion of velocity is increased by a large factor in some cases. Moreover, the spectra of density and velocity show increased power at small scales explained by the high growth rate of the instabilities. Finally, we calculated the structure functions of velocity and density fluctuations in the local reference frame defined by the direction of magnetic lines. The results indicate that in some cases the instabilities significantly increase the anisotropy of fluctuations. These results, even though preliminary and restricted to very specific conditions, show that the physical properties of turbulence in collisionless plasmas, as those found in the ICM, may be very different from what has been largely believed.

Recovery of the star formation history of the LMC from the VISTA survey of the Magellanic system

The VISTA near infrared survey of the Magellanic System (VMC) will provide deep YJK(s) photometry reaching stars in the oldest turn-off point throughout the Magellanic Clouds (MCs). As part of the preparation for the survey, we aim to access the accuracy in the star formation history (SFH) that can be expected from VMC data, in particular for the Large Magellanic Cloud (LMC). To this aim, we first simulate VMC images containing not only the LMC stellar populations but also the foreground Milky Way (MW) stars and background galaxies. The simulations cover the whole range of density of LMC field stars. We then perform aperture photometry over these simulated images, access the expected levels of photometric errors and incompleteness, and apply the classical technique of SFH-recovery based on the reconstruction of colour-magnitude diagrams (CMD) via the minimisation of a chi-squared-like statistics. We verify that the foreground MW stars are accurately recovered by the minimisation algorithms, whereas the background galaxies can be largely eliminated from the CMD analysis due to their particular colours and morphologies. We then evaluate the expected errors in the recovered star formation rate as a function of stellar age, SFR(t), starting from models with a known age-metallicity relation (AMR). It turns out that, for a given sky area, the random errors for ages older than similar to 0.4 Gyr seem to be independent of the crowding. This can be explained by a counterbalancing effect between the loss of stars from a decrease in the completeness and the gain of stars from an increase in the stellar density. For a spatial resolution of similar to 0.1 deg(2), the random errors in SFR(t) will be below 20% for this wide range of ages. On the other hand, due to the lower stellar statistics for stars younger than similar to 0.4 Gyr, the outer LMC regions will require larger areas to achieve the same level of accuracy in the SFR( t). If we consider the AMR as unknown, the SFH-recovery algorithm is able to accurately recover the input AMR, at the price of an increase of random errors in the SFR(t) by a factor of about 2.5. Experiments of SFH-recovery performed for varying distance modulus and reddening indicate that these parameters can be determined with (relative) accuracies of Delta(m-M)(0) similar to 0.02 mag and Delta E(B-V) similar to 0.01 mag, for each individual field over the LMC. The propagation of these errors in the SFR(t) implies systematic errors below 30%. This level of accuracy in the SFR(t) can reveal significant imprints in the dynamical evolution of this unique and nearby stellar system, as well as possible signatures of the past interaction between the MCs and the MW.

Communication structure of cortical networks

Large-scale cortical networks exhibit characteristic topological properties that shape communication between brain regions and global cortical dynamics. Analysis of complex networks allows the description of connectedness, distance, clustering, and centrality that reveal different aspects of how the network's nodes communicate. Here, we focus on a novel analysis of complex walks in a series of mammalian cortical networks that model potential dynamics of information flow between individual brain regions. We introduce two new measures called absorption and driftness. Absorption is the average length of random walks between any two nodes, and takes into account all paths that may diffuse activity throughout the network. Driftness is the ratio between absorption and the corresponding shortest path length. For a given node of the network, we also define four related measurements, namely in-and out-absorption as well as in-and out-driftness, as the averages of the corresponding measures from all nodes to that node, and from that node to all nodes, respectively. We find that the cat thalamo-cortical system incorporates features of two classic network topologies, Erdos-Renyi graphs with respect to in-absorption and in-driftness, and configuration models with respect to out-absorption and out-driftness. Moreover, taken together these four measures separate the network nodes based on broad functional roles (visual, auditory, somatomotor, and frontolimbic).

Two-component Abelian sandpile models

In one-component Abelian sandpile models, the toppling probabilities are independent quantities. This is not the case in multicomponent models. The condition of associativity of the underlying Abelian algebras imposes nonlinear relations among the toppling probabilities. These relations are derived for the case of two-component quadratic Abelian algebras. We show that Abelian sandpile models with two conservation laws have only trivial avalanches.

The random barrier-crossing problem

This paper addresses the time-variant reliability analysis of structures with random resistance or random system parameters. It deals with the problem of a random load process crossing a random barrier level. The implications of approximating the arrival rate of the first overload by an ensemble-crossing rate are studied. The error involved in this so-called ""ensemble-crossing rate"" approximation is described in terms of load process and barrier distribution parameters, and in terms of the number of load cycles. Existing results are reviewed, and significant improvements involving load process bandwidth, mean-crossing frequency and time are presented. The paper shows that the ensemble-crossing rate approximation can be accurate enough for problems where load process variance is large in comparison to barrier variance, but especially when the number of load cycles is small. This includes important practical applications like random vibration due to impact loadings and earthquake loading. Two application examples are presented, one involving earthquake loading and one involving a frame structure subject to wind and snow loadings. (C) 2007 Elsevier Ltd. All rights reserved.

Volumetric reconstruction of the mean flow around circular cylinders fitted with strakes

The volumetric reconstruction technique presented in this paper employs a two-camera stereoscopic particle image velocimetry (SPIV) system in order to reconstruct the mean flow behind a fixed cylinder fitted with helical strakes, which are commonly used to suppress vortex-induced vibrations (VIV). The technique is based on the measurement of velocity fields at equivalent adjacent planes that results in pseudo volumetric fields. The main advantage over proper volumetric techniques is the avoidance of additional equipment and complexity. The averaged velocity fields behind the straked cylinders and the geometrical periodicity of the three-start configuration are used to further simplify the reconstruction process. Two straked cylindrical models with the same pitch (p = 10d) and two different heights (h = 0.1 and 0.2d) are tested. The reconstructed flow shows that the strakes introduce in the wake flow a well-defined wavelength of one-third of the pitch. Measurements of hydrodynamic forces, fluctuating velocity, vortex formation length, and vortex shedding frequency show the interdependence of the wake parameters. The vortex formation length is increased by the strakes, which is an important effect for the suppression of vortex-induced vibrations. The results presented complement previous investigations concerning the effectiveness of strakes as VIV suppressors and provide a basis of comparison to numerical simulations.

Residuals for log-Burr XII regression models in survival analysis

In this paper, we compare three residuals to assess departures from the error assumptions as well as to detect outlying observations in log-Burr XII regression models with censored observations. These residuals can also be used for the log-logistic regression model, which is a special case of the log-Burr XII regression model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to the modified martingale-type residual in log-Burr XII regression models with censored data.