Community sense and response systems

The proliferation of smartphones and other internet-enabled, sensor-equipped consumer devices enables us to sense and act upon the physical environment in unprecedented ways. This thesis considers Community Sense-and-Response (CSR) systems, a new class of web application for acting on sensory data gathered from participants' personal smart devices. The thesis describes how rare events can be reliably detected using a decentralized anomaly detection architecture that performs client-side anomaly detection and server-side event detection. After analyzing this decentralized anomaly detection approach, the thesis describes how weak but spatially structured events can be detected, despite significant noise, when the events have a sparse representation in an alternative basis. Finally, the thesis describes how the statistical models needed for client-side anomaly detection may be learned efficiently, using limited space, via coresets.

The Caltech Community Seismic Network (CSN) is a prototypical example of a CSR system that harnesses accelerometers in volunteers' smartphones and consumer electronics. Using CSN, this thesis presents the systems and algorithmic techniques to design, build and evaluate a scalable network for real-time awareness of spatial phenomena such as dangerous earthquakes.

Efficient methods for empirical tests of behavioral economics theories in laboratory and field experiments

In the quest for a descriptive theory of decision-making, the rational actor model in economics imposes rather unrealistic expectations and abilities on human decision makers. The further we move from idealized scenarios, such as perfectly competitive markets, and ambitiously extend the reach of the theory to describe everyday decision making situations, the less sense these assumptions make. Behavioural economics has instead proposed models based on assumptions that are more psychologically realistic, with the aim of gaining more precision and descriptive power. Increased psychological realism, however, comes at the cost of a greater number of parameters and model complexity. Now there are a plethora of models, based on different assumptions, applicable in differing contextual settings, and selecting the right model to use tends to be an ad-hoc process. In this thesis, we develop optimal experimental design methods and evaluate different behavioral theories against evidence from lab and field experiments.

We look at evidence from controlled laboratory experiments. Subjects are presented with choices between monetary gambles or lotteries. Different decision-making theories evaluate the choices differently and would make distinct predictions about the subjects' choices. Theories whose predictions are inconsistent with the actual choices can be systematically eliminated. Behavioural theories can have multiple parameters requiring complex experimental designs with a very large number of possible choice tests. This imposes computational and economic constraints on using classical experimental design methods. We develop a methodology of adaptive tests: Bayesian Rapid Optimal Adaptive Designs (BROAD) that sequentially chooses the "most informative" test at each stage, and based on the response updates its posterior beliefs over the theories, which informs the next most informative test to run. BROAD utilizes the Equivalent Class Edge Cutting (EC²) criteria to select tests. We prove that the EC² criteria is adaptively submodular, which allows us to prove theoretical guarantees against the Bayes-optimal testing sequence even in the presence of noisy responses. In simulated ground-truth experiments, we find that the EC² criteria recovers the true hypotheses with significantly fewer tests than more widely used criteria such as Information Gain and Generalized Binary Search. We show, theoretically as well as experimentally, that surprisingly these popular criteria can perform poorly in the presence of noise, or subject errors. Furthermore, we use the adaptive submodular property of EC² to implement an accelerated greedy version of BROAD which leads to orders of magnitude speedup over other methods.

We use BROAD to perform two experiments. First, we compare the main classes of theories for decision-making under risk, namely: expected value, prospect theory, constant relative risk aversion (CRRA) and moments models. Subjects are given an initial endowment, and sequentially presented choices between two lotteries, with the possibility of losses. The lotteries are selected using BROAD, and 57 subjects from Caltech and UCLA are incentivized by randomly realizing one of the lotteries chosen. Aggregate posterior probabilities over the theories show limited evidence in favour of CRRA and moments' models. Classifying the subjects into types showed that most subjects are described by prospect theory, followed by expected value. Adaptive experimental design raises the possibility that subjects could engage in strategic manipulation, i.e. subjects could mask their true preferences and choose differently in order to obtain more favourable tests in later rounds thereby increasing their payoffs. We pay close attention to this problem; strategic manipulation is ruled out since it is infeasible in practice, and also since we do not find any signatures of it in our data.

In the second experiment, we compare the main theories of time preference: exponential discounting, hyperbolic discounting, "present bias" models: quasi-hyperbolic (α, β) discounting and fixed cost discounting, and generalized-hyperbolic discounting. 40 subjects from UCLA were given choices between 2 options: a smaller but more immediate payoff versus a larger but later payoff. We found very limited evidence for present bias models and hyperbolic discounting, and most subjects were classified as generalized hyperbolic discounting types, followed by exponential discounting.

In these models the passage of time is linear. We instead consider a psychological model where the perception of time is subjective. We prove that when the biological (subjective) time is positively dependent, it gives rise to hyperbolic discounting and temporal choice inconsistency.

We also test the predictions of behavioral theories in the "wild". We pay attention to prospect theory, which emerged as the dominant theory in our lab experiments of risky choice. Loss aversion and reference dependence predicts that consumers will behave in a uniquely distinct way than the standard rational model predicts. Specifically, loss aversion predicts that when an item is being offered at a discount, the demand for it will be greater than that explained by its price elasticity. Even more importantly, when the item is no longer discounted, demand for its close substitute would increase excessively. We tested this prediction using a discrete choice model with loss-averse utility function on data from a large eCommerce retailer. Not only did we identify loss aversion, but we also found that the effect decreased with consumers' experience. We outline the policy implications that consumer loss aversion entails, and strategies for competitive pricing.

In future work, BROAD can be widely applicable for testing different behavioural models, e.g. in social preference and game theory, and in different contextual settings. Additional measurements beyond choice data, including biological measurements such as skin conductance, can be used to more rapidly eliminate hypothesis and speed up model comparison. Discrete choice models also provide a framework for testing behavioural models with field data, and encourage combined lab-field experiments.

On the local Tamagawa number conjecture for Tate motives

There is a wonderful conjecture of Bloch and Kato that generalizes both the analytic Class Number Formula and the Birch and Swinnerton-Dyer conjecture. The conjecture itself was generalized by Fukaya and Kato to an equivariant formulation. In this thesis, I provide a new proof for the equivariant local Tamagawa number conjecture in the case of Tate motives for unramified fields, using Iwasawa theory and (φ,Γ)-modules, and provide some work towards extending the proof to tamely ramified fields.

Efficient methods for stochastic optimal control

The Hamilton Jacobi Bellman (HJB) equation is central to stochastic optimal control (SOC) theory, yielding the optimal solution to general problems specified by known dynamics and a specified cost functional. Given the assumption of quadratic cost on the control input, it is well known that the HJB reduces to a particular partial differential equation (PDE). While powerful, this reduction is not commonly used as the PDE is of second order, is nonlinear, and examples exist where the problem may not have a solution in a classical sense. Furthermore, each state of the system appears as another dimension of the PDE, giving rise to the curse of dimensionality. Since the number of degrees of freedom required to solve the optimal control problem grows exponentially with dimension, the problem becomes intractable for systems with all but modest dimension.

In the last decade researchers have found that under certain, fairly non-restrictive structural assumptions, the HJB may be transformed into a linear PDE, with an interesting analogue in the discretized domain of Markov Decision Processes (MDP). The work presented in this thesis uses the linearity of this particular form of the HJB PDE to push the computational boundaries of stochastic optimal control.

This is done by crafting together previously disjoint lines of research in computation. The first of these is the use of Sum of Squares (SOS) techniques for synthesis of control policies. A candidate polynomial with variable coefficients is proposed as the solution to the stochastic optimal control problem. An SOS relaxation is then taken to the partial differential constraints, leading to a hierarchy of semidefinite relaxations with improving sub-optimality gap. The resulting approximate solutions are shown to be guaranteed over- and under-approximations for the optimal value function. It is shown that these results extend to arbitrary parabolic and elliptic PDEs, yielding a novel method for Uncertainty Quantification (UQ) of systems governed by partial differential constraints. Domain decomposition techniques are also made available, allowing for such problems to be solved via parallelization and low-order polynomials.

The optimization-based SOS technique is then contrasted with the Separated Representation (SR) approach from the applied mathematics community. The technique allows for systems of equations to be solved through a low-rank decomposition that results in algorithms that scale linearly with dimensionality. Its application in stochastic optimal control allows for previously uncomputable problems to be solved quickly, scaling to such complex systems as the Quadcopter and VTOL aircraft. This technique may be combined with the SOS approach, yielding not only a numerical technique, but also an analytical one that allows for entirely new classes of systems to be studied and for stability properties to be guaranteed.

The analysis of the linear HJB is completed by the study of its implications in application. It is shown that the HJB and a popular technique in robotics, the use of navigation functions, sit on opposite ends of a spectrum of optimization problems, upon which tradeoffs may be made in problem complexity. Analytical solutions to the HJB in these settings are available in simplified domains, yielding guidance towards optimality for approximation schemes. Finally, the use of HJB equations in temporal multi-task planning problems is investigated. It is demonstrated that such problems are reducible to a sequence of SOC problems linked via boundary conditions. The linearity of the PDE allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to satisfy a complex temporal logic specification.

Velocity resolved - scalar modeled simulations of high Schmidt number turbulent transport

The objective of this thesis is to develop a framework to conduct velocity resolved - scalar modeled (VR-SM) simulations, which will enable accurate simulations at higher Reynolds and Schmidt (Sc) numbers than are currently feasible. The framework established will serve as a first step to enable future simulation studies for practical applications. To achieve this goal, in-depth analyses of the physical, numerical, and modeling aspects related to Sc>>1 are presented, specifically when modeling in the viscous-convective subrange. Transport characteristics are scrutinized by examining scalar-velocity Fourier mode interactions in Direct Numerical Simulation (DNS) datasets and suggest that scalar modes in the viscous-convective subrange do not directly affect large-scale transport for high Sc. Further observations confirm that discretization errors inherent in numerical schemes can be sufficiently large to wipe out any meaningful contribution from subfilter models. This provides strong incentive to develop more effective numerical schemes to support high Sc simulations. To lower numerical dissipation while maintaining physically and mathematically appropriate scalar bounds during the convection step, a novel method of enforcing bounds is formulated, specifically for use with cubic Hermite polynomials. Boundedness of the scalar being transported is effected by applying derivative limiting techniques, and physically plausible single sub-cell extrema are allowed to exist to help minimize numerical dissipation. The proposed bounding algorithm results in significant performance gain in DNS of turbulent mixing layers and of homogeneous isotropic turbulence. Next, the combined physical/mathematical behavior of the subfilter scalar-flux vector is analyzed in homogeneous isotropic turbulence, by examining vector orientation in the strain-rate eigenframe. The results indicate no discernible dependence on the modeled scalar field, and lead to the identification of the tensor-diffusivity model as a good representation of the subfilter flux. Velocity resolved - scalar modeled simulations of homogeneous isotropic turbulence are conducted to confirm the behavior theorized in these a priori analyses, and suggest that the tensor-diffusivity model is ideal for use in the viscous-convective subrange. Simulations of a turbulent mixing layer are also discussed, with the partial objective of analyzing Schmidt number dependence of a variety of scalar statistics. Large-scale statistics are confirmed to be relatively independent of the Schmidt number for Sc>>1, which is explained by the dominance of subfilter dissipation over resolved molecular dissipation in the simulations. Overall, the VR-SM framework presented is quite effective in predicting large-scale transport characteristics of high Schmidt number scalars, however, it is determined that prediction of subfilter quantities would entail additional modeling intended specifically for this purpose. The VR-SM simulations presented in this thesis provide us with the opportunity to overlap with experimental studies, while at the same time creating an assortment of baseline datasets for future validation of LES models, thereby satisfying the objectives outlined for this work.

Radioautographic method of determination of number of bacteria in water-bodies [Translation from: Informatsionnyi Byulleten Biologiya Vnutrennikh Vod No.26, 65-67, 1975]

The radioautographic method of determination of the number of autotrophic microorganisms was initially suggested for counting methane-oxidizing bacteria. With the help of this method colonies of hydrogen-oxidizing bacteria are differentiated even more clearly from heterotrophic. Under laboratory conditions it was shown that colonies grown on membrane filters from a pure culture of thionic bacteria on a nutrient medium with radio- active carbonate, give better prints on film. This method was tested by the authors for determining the number of these bacteria in the meromictic Lake Vae de San Juan during the expedition to Cuba in the summer of 1973. The study showed that that the thionic bacteria are found throughout the pelagial. It proved that the thionic bacteria can be well considered in water-bodies by the radioautographic method.

Number of phase levels of a Talbot array illuminator

The number of phase levels of a Talbot array illuminator is an important factor in the estimation of practical fabrication complexity and cost. We show that the number it) of phase levels of a Talbot array illuminator has a simple relationship to the prime number. When there is an alternative pi -phase modulation in the output array, the relations are similar. (C) 2001 Optical Society of America OCIS codes: 070.6760, 050.1950, 050.1980.

Part I: Latent heat of vaporization of n-decane. Part II: Heat and mass transfer from a cylinder placed in a turbulent air stream - Sherwood and Frössling numbers as a function of free stream turbulence level and Reynolds number

Part I

The latent heat of vaporization of n-decane is measured calorimetrically at temperatures between 160° and 340°F. The internal energy change upon vaporization, and the specific volume of the vapor at its dew point are calculated from these data and are included in this work. The measurements are in excellent agreement with available data at 77° and also at 345°F, and are presented in graphical and tabular form.

Part II

Simultaneous material and energy transport from a one-inch adiabatic porous cylinder is studied as a function of free stream Reynolds Number and turbulence level. Experimental data is presented for Reynolds Numbers between 1600 and 15,000 based on the cylinder diameter, and for apparent turbulence levels between 1.3 and 25.0 per cent. n-heptane and n-octane are the evaporating fluids used in this investigation.

Gross Sherwood Numbers are calculated from the data and are in substantial agreement with existing correlations of the results of other workers. The Sherwood Numbers, characterizing mass transfer rates, increase approximately as the 0.55 power of the Reynolds Number. At a free stream Reynolds Number of 3700 the Sherwood Number showed a 40% increase as the apparent turbulence level of the free stream was raised from 1.3 to 25 per cent.

Within the uncertainties involved in the diffusion coefficients used for n-heptane and n-octane, the Sherwood Numbers are comparable for both materials. A dimensionless Frössling Number is computed which characterizes either heat or mass transfer rates for cylinders on a comparable basis. The calculated Frössling Numbers based on mass transfer measurements are in substantial agreement with Frössling Numbers calculated from the data of other workers in heat transfer.

On the number of generations of tendipes in collective ponds in Kuibyshchevskoi district [Translation from: C.R. Acad.Sci. U.R.S.S. 95, 1113-1115, 1954]

Three ponds were chosen for this study. The two lower ones were of 2 - 4 hectares in area, the depth of the littoral zone was 2.5 - 3 metres at the time of maximum flooding and the mud which covered the floor of the ponds was homogeneous and autochthonous in nature with very few vegetable remnants. The ponds which were originally set up in 1950. were intended for water supply and populated with Crucian Carp (for human consumption). A survey was done in the ponds in order to establish number and biomass of Tendipes semireductus. The author concludes that in these ponds T.semireductus has 2-3 generations per year.

Deep near-infrared spectroscopy of high-redshift galaxies: the physical growth of passive systems

The assembly history of massive galaxies is one of the most important aspects of galaxy formation and evolution. Although we have a broad idea of what physical processes govern the early phases of galaxy evolution, there are still many open questions. In this thesis I demonstrate the crucial role that spectroscopy can play in a physical understanding of galaxy evolution. I present deep near-infrared spectroscopy for a sample of high-redshift galaxies, from which I derive important physical properties and their evolution with cosmic time. I take advantage of the recent arrival of efficient near-infrared detectors to target the rest-frame optical spectra of z > 1 galaxies, from which many physical quantities can be derived. After illustrating the applications of near-infrared deep spectroscopy with a study of star-forming galaxies, I focus on the evolution of massive quiescent systems.

Most of this thesis is based on two samples collected at the W. M. Keck Observatory that represent a significant step forward in the spectroscopic study of z > 1 quiescent galaxies. All previous spectroscopic samples at this redshift were either limited to a few objects, or much shallower in terms of depth. Our first sample is composed of 56 quiescent galaxies at 1 < z < 1.6 collected using the upgraded red arm of the Low Resolution Imaging Spectrometer (LRIS). The second consists of 24 deep spectra of 1.5 < z < 2.5 quiescent objects observed with the Multi-Object Spectrometer For Infra-Red Exploration (MOSFIRE). Together, these spectra span the critical epoch 1 < z < 2.5, where most of the red sequence is formed, and where the sizes of quiescent systems are observed to increase significantly.

We measure stellar velocity dispersions and dynamical masses for the largest number of z > 1 quiescent galaxies to date. By assuming that the velocity dispersion of a massive galaxy does not change throughout its lifetime, as suggested by theoretical studies, we match galaxies in the local universe with their high-redshift progenitors. This allows us to derive the physical growth in mass and size experienced by individual systems, which represents a substantial advance over photometric inferences based on the overall galaxy population. We find a significant physical growth among quiescent galaxies over 0 < z < 2.5 and, by comparing the slope of growth in the mass-size plane dlogR_e/dlogM_∗ with the results of numerical simulations, we can constrain the physical process responsible for the evolution. Our results show that the slope of growth becomes steeper at higher redshifts, yet is broadly consistent with minor mergers being the main process by which individual objects evolve in mass and size.

By fitting stellar population models to the observed spectroscopy and photometry we derive reliable ages and other stellar population properties. We show that the addition of the spectroscopic data helps break the degeneracy between age and dust extinction, and yields significantly more robust results compared to fitting models to the photometry alone. We detect a clear relation between size and age, where larger galaxies are younger. Therefore, over time the average size of the quiescent population will increase because of the contribution of large galaxies recently arrived to the red sequence. This effect, called progenitor bias, is different from the physical size growth discussed above, but represents another contribution to the observed difference between the typical sizes of low- and high-redshift quiescent galaxies. By reconstructing the evolution of the red sequence starting at z ∼ 1.25 and using our stellar population histories to infer the past behavior to z ∼ 2, we demonstrate that progenitor bias accounts for only half of the observed growth of the population. The remaining size evolution must be due to physical growth of individual systems, in agreement with our dynamical study.

Finally, we use the stellar population properties to explore the earliest periods which led to the formation of massive quiescent galaxies. We find tentative evidence for two channels of star formation quenching, which suggests the existence of two independent physical mechanisms. We also detect a mass downsizing, where more massive galaxies form at higher redshift, and then evolve passively. By analyzing in depth the star formation history of the brightest object at z > 2 in our sample, we are able to put constraints on the quenching timescale and on the properties of its progenitor.

A consistent picture emerges from our analyses: massive galaxies form at very early epochs, are quenched on short timescales, and then evolve passively. The evolution is passive in the sense that no new stars are formed, but significant mass and size growth is achieved by accreting smaller, gas-poor systems. At the same time the population of quiescent galaxies grows in number due to the quenching of larger star-forming galaxies. This picture is in agreement with other observational studies, such as measurements of the merger rate and analyses of galaxy evolution at fixed number density.

A kinetic theory description for external spherical flows with arbitrary Knudsen number by a moment method

The Maxwell integral equations of transfer are applied to a series of problems involving flows of arbitrary density gases about spheres. As suggested by Lees a two sided Maxwellian-like weighting function containing a number of free parameters is utilized and a sufficient number of partial differential moment equations is used to determine these parameters. Maxwell's inverse fifth-power force law is used to simplify the evaluation of the collision integrals appearing in the moment equations. All flow quantities are then determined by integration of the weighting function which results from the solution of the differential moment system. Three problems are treated: the heat-flux from a slightly heated sphere at rest in an infinite gas; the velocity field and drag of a slowly moving sphere in an unbounded space; the velocity field and drag torque on a slowly rotating sphere. Solutions to the third problem are found to both first and second-order in surface Mach number with the secondary centrifugal fan motion being of particular interest. Singular aspects of the moment method are encountered in the last two problems and an asymptotic study of these difficulties leads to a formal criterion for a "well posed" moment system. The previously unanswered question of just how many moments must be used in a specific problem is now clarified to a great extent.

Small scale turbulence in high Karlovitz number premixed flames

The purpose of this thesis is to characterize the behavior of the smallest turbulent scales in high Karlovitz number (Ka) premixed flames. These scales are particularly important in the two-way coupling between turbulence and chemistry and better understanding of these scales will support future modeling efforts using large eddy simulations (LES). The smallest turbulent scales are studied by considering the vorticity vector, ω, and its transport equation.

Due to the complexity of turbulent combustion introduced by the wide range of length and time scales, the two-dimensional vortex-flame interaction is first studied as a simplified test case. Numerical and analytical techniques are used to discern the dominate transport terms and their effects on vorticity based on the initial size and strength of the vortex. This description of the effects of the flame on a vortex provides a foundation for investigating vorticity in turbulent combustion.

Subsequently, enstrophy, ω² = ω • ω, and its transport equation are investigated in premixed turbulent combustion. For this purpose, a series of direct numerical simulations (DNS) of premixed n-heptane/air flames are performed, the conditions of which span a wide range of unburnt Karlovitz numbers and turbulent Reynolds numbers. Theoretical scaling analysis along with the DNS results support that, at high Karlovitz number, enstrophy transport is controlled by the viscous dissipation and vortex stretching/production terms. As a result, vorticity scales throughout the flame with the inverse of the Kolmogorov time scale, τ_η, just as in homogeneous isotropic turbulence. As τ_η is only a function of the viscosity and dissipation rate, this supports the validity of Kolmogorov’s first similarity hypothesis for sufficiently high Ka numbers (Ka ≳ 100). These conclusions are in contrast to low Karlovitz number behavior, where dilatation and baroclinic torque have a significant impact on vorticity within the flame. Results are unaffected by the transport model, chemical model, turbulent Reynolds number, and lastly the physical configuration.

Next, the isotropy of vorticity is assessed. It is found that given a sufficiently large value of the Karlovitz number (Ka ≳ 100) the vorticity is isotropic. At lower Karlovitz numbers, anisotropy develops due to the effects of the flame on the vortex stretching/production term. In this case, the local dynamics of vorticity in the strain-rate tensor, S, eigenframe are altered by the flame. At sufficiently high Karlovitz numbers, the dynamics of vorticity in this eigenframe resemble that of homogeneous isotropic turbulence.

Combined, the results of this thesis support that both the magnitude and orientation of vorticity resemble the behavior of homogeneous isotropic turbulence, given a sufficiently high Karlovitz number (Ka ≳ 100). This supports the validity of Kolmogorov’s first similarity hypothesis and the hypothesis of local isotropy under these condition. However, dramatically different behavior is found at lower Karlovitz numbers. These conclusions provides/suggests directions for modeling high Karlovitz number premixed flames using LES. With more accurate models, the design of aircraft combustors and other combustion based devices may better mitigate the detrimental effects of combustion, from reducing CO₂ and soot production to increasing engine efficiency.

Localization of sources of human evoked responses

The evoked response, a signal present in the electro-encephalogram when specific sense modalities are stimulated with brief sensory inputs, has not yet revealed as much about brain function as it apparently promised when first recorded in the late 1940's. One of the problems has been to record the responses at a large number of points on the surface of the head; thus in order to achieve greater spatial resolution than previously attained, a 50-channel recording system was designed to monitor experiments with human visually evoked responses.

Conventional voltage versus time plots of the responses were found inadequate as a means of making qualitative studies of such a large data space. This problem was solved by creating a graphical display of the responses in the form of equipotential maps of the activity at successive instants during the complete response. In order to ascertain the necessary complexity of any models of the responses, factor analytic procedures were used to show that models characterized by only five or six independent parameters could adequately represent the variability in all recording channels.

One type of equivalent source for the responses which meets these specifications is the electrostatic dipole. Two different dipole models were studied: the dipole in a homogeneous sphere and the dipole in a sphere comprised of two spherical shells (of different conductivities) concentric with and enclosing a homogeneous sphere of a third conductivity. These models were used to determine nonlinear least squares fits of dipole parameters to a given potential distribution on the surface of a spherical approximation to the head. Numerous tests of the procedures were conducted with problems having known solutions. After these theoretical studies demonstrated the applicability of the technique, the models were used to determine inverse solutions for the evoked response potentials at various times throughout the responses. It was found that reliable estimates of the location and strength of cortical activity were obtained, and that the two models differed only slightly in their inverse solutions. These techniques enabled information flow in the brain, as indicated by locations and strengths of active sites, to be followed throughout the evoked response.