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Signals on Networks: Random Asynchronous and Multirate Processing, and Uncertainty Principles
Get PDFThe processing of signals defined on graphs has been of interest for many years, and finds applications in a diverse set of fields such as sensor networks, social and economic networks, and biological networks. In graph signal processing applications, signals are not defined as functions on a uniform time-domain grid but they are defined as vectors indexed by the vertices of a graph, where the underlying graph is assumed to model the irregular signal domain. Although analysis of such networked models is not new (it can be traced back to the consensus problem studied more than four decades ago), such models are studied recently from the view-point of signal processing, in which the analysis is based on the "graph operator" whose eigenvectors serve as a Fourier basis for the graph of interest. With the help of graph Fourier basis, a number of topics from classical signal processing (such as sampling, reconstruction, filtering, etc.) are extended to the case of graphs.
The main contribution of this thesis is to provide new directions in the field of graph signal processing and provide further extensions of topics in classical signal processing. The first part of this thesis focuses on a random and asynchronous variant of "graph shift," i.e., localized communication between neighboring nodes. Since the dynamical behavior of randomized asynchronous updates is very different from standard graph shift (i.e., state-space models), this part of the thesis focuses on the convergence and stability behavior of such random asynchronous recursions. Although non-random variants of asynchronous state recursions (possibly with non-linear updates) are well-studied problems with early results dating back to the late 60's, this thesis considers the convergence (and stability) in the statistical mean-squared sense and presents the precise conditions for the stability by drawing parallels with switching systems. It is also shown that systems exhibit unexpected behavior under randomized asynchronicity: an unstable system (in the synchronous world) may be stabilized simply by the use of randomized asynchronicity. Moreover, randomized asynchronicity may result in a lower total computational complexity in certain parameter settings. The thesis presents applications of the random asynchronous model in the context of graph signal processing including an autonomous clustering of network of agents, and a node-asynchronous communication protocol that implements a given rational filter on the graph.
The second part of the thesis focuses on extensions of the following topics in classical signal processing to the case of graph: multirate processing and filter banks, discrete uncertainty principles, and energy compaction filters for optimal filter design. The thesis also considers an application to the heat diffusion over networks.
Multirate systems and filter banks find many applications in signal processing theory and implementations. Despite the possibility of extending 2-channel filter banks to bipartite graphs, this thesis shows that this relation cannot be generalized to M-channel systems on M-partite graphs. As a result, the extension of classical multirate theory to graphs is nontrivial, and such extensions cannot be obtained without certain mathematical restrictions on the graph. The thesis provides the necessary conditions on the graph such that fundamental building blocks of multirate processing remain valid in the graph domain. In particular, it is shown that when the underlying graph satisfies a condition called M-block cyclic property, classical multirate theory can be extended to the graphs.
The uncertainty principle is an essential mathematical concept in science and engineering, and uncertainty principles generally state that a signal cannot have an arbitrarily "short" description in the original basis and in the Fourier basis simultaneously. Based on the fact that graph signal processing proposes two different bases (i.e., vertex and the graph Fourier domains) to represent graph signals, this thesis shows that the total number of nonzero elements of a graph signal and its representation in the graph Fourier domain is lower bounded by a quantity depending on the underlying graph. The thesis also presents the necessary and sufficient condition for the existence of 2-sparse and 3-sparse eigenvectors of a connected graph. When such eigenvectors exist, the uncertainty bound is very low, tight, and independent of the global structure of the graph.
The thesis also considers the classical spectral concentration problem. In the context of polynomial graph filters, the problem reduces to the polynomial concentration problem studied more generally by Slepian in the 70's. The thesis studies the asymptotic behavior of the optimal solution in the case of narrow bandwidth. Different examples of graphs are also compared in order to show that the maximum energy compaction and the optimal filter depends heavily on the graph spectrum.
In the last part, the thesis considers the estimation of the starting time of a heat diffusion process from its noisy measurements when there is a single point source located on a known vertex of a graph with unknown starting time. In particular, the Cramér-Rao lower bound for the estimation problem is derived, and it is shown that for graphs with higher connectivity the problem has a larger lower bound making the estimation problem more difficult.</p
Transition Metal-Catalyzed Enantioselective Alpha Functionalization of Nitrogen and Oxygen-Containing Heterocycles
Get PDFResearch in the Stoltz group is focused on the development of synthetic methods for the preparation of stereochemically rich molecules and the total synthesis of complex natural products. One major theme of our group’s methods development is transition-metal catalyzed α-functionalization of carbonyl derivatives, with a particular focus on the development of allylic alkylation protocols. Although the α-functionalization of carbonyl derivatives such as enolates, has been extensively studied, the use of nitrogen and oxygen- containing heterocycles, such as lactams and lactones, remains under- developed. These types of nucleophiles are significantly more reactive, and in the case of the γ-butyrolactones and γ-lactams, may be smaller in size. Because of these differences, the conditions that have been developed for the functionalization of carbonyl derivatives such as ketones does not translate well to these nucleophiles. Furthermore, within the context of enantioselective functionalization, the unique characteristics of these nucleophiles necessitates the development of large, bulky ligands that enable the formation of a very well-defined chiral environment around the transition metal catalyst. This thesis mainly describes strategies that have been developed for the enantioselective α-functionalization of nitrogen and oxygen-containing heterocycles, with a particular focus on the γ-lactams and γ-butyrolactones.</p
Prebiotic Fingerprints
Get PDFMeteorites contain organic compounds that occur in all known life. These compounds, commonly referred to as prebiotic compounds, include α-amino acids and are most prevalent on carbonaceous chondrites. As carbonaceous chondrites are pristine samples from early in the solar system that have not had living organisms on them, we can study the chemistry that produced α-amino acids on them to better understand the processes by which they might have formed on early Earth or on other bodies. Multiple syntheses have been put forth as routes to form amino acids on meteorites and include ice-grain chemistry on interstellar ices and Strecker synthesis in meteorite parent bodies. Prior measurements of molecular-average carbon isotope ratios (¹³C/¹²C) have found ¹³C enrichments of up to 53‰ in certain α-amino acids and molecular-average hydrogen isotope ratios (D/H) have found enrichments of 100s of ‰. With this data, it has been suggested that Strecker synthesis—a synthesis in which an aldehyde or ketone reacts with ammonia and cyanide to produce an α-aminonitrile that is hydrolyzed into an α-amino amide and then an α-amino acid—is the primary pathway to produce α-amino acids on aqueously altered meteorites.
Here, we develop an instrument that can measure site-specific isotope ratios (SSIR) for carbon — that is the ¹²C/¹³C at each site in a molecule — and use it to first constrain the site-specific isotope effects associated with Strecker synthesis and then the carbon SSIR of an alanine sample extracted from the Murchison meteorite. The instrument, the Q-Exactive Orbitrap, is a Fourier Transform Mass Spectrometer that has resolution of 240,000 full width-half maximum and can measure site-specific carbon isotope ratios on samples as small as 1 picomole. When we use it to measure the carbon SSIR in multiple samples of alanine produced by Strecker synthesis, we find a -20 ‰ equilibrium isotope effect between the product alanine's C-2 site (amine carbon, ¹³C-depleted) reactant acetaldehyde’s carbonyl carbon (¹³C-enriched), a potential -15 ‰ kinetic isotope effect on the C-1 site (eventual carboxyl carbon) for the first hydrolysis of α-aminopropanenitrile (¹³C-enriched) into alaninamide (¹³C-depleted), and a -15.4 ‰ kinetic isotope effect on the C-1 carbon for the second hydrolysis step in which α-alaninamide (¹³C-enriched) becomes alanine (¹³C-depleted). Through conventional isotope ratio mass spectrometry, we also measure a +56.4 ‰ equilibrium isotope effect between ammonia (¹⁵N-depleted) and the amine site on alanine (¹⁵N-enriched). When we measure the sample of alanine from the Murchison meteorite, we find site-specific carbon isotope ratios of -29 ± 10 ‰, 142 ± 20 ‰, and -36 ± 20 ‰ for the C-1, C-2, and C-3 (methyl) sites, respectively. This pattern agrees with the hypothesis that Strecker synthesis created alanine in Murchison. Combining these data with the isotope effects found for Strecker synthesis, we find initial site values of -7 ± 10 ‰, 162 ± 20 ‰, and 36 ± 20 ‰ for the C-1, C-2, and C-3 sites, respectively. With these values, we create a model of potential organic synthesis on the Murchison parent body that predicts the molecular-average δ¹³C values of 19 other prebiotic compounds.
Finally, we create a model that uses the previously measured molecular average carbon and deuterium isotope ratios for organics on Murchison to create models that predict site-specific and molecular average isotope ratios for organic compounds. This model finds that organic compounds with have methyl sites that are enriched in deuterium by up to 3000 ‰ relative to other sites in the compound and that the degree of enrichment scales both with a compound class’s solubility in water and with a sample’s degree of aqueous alteration and terrestrial weathering. These patterns suggest that a primordial ISM-derived deuterium signal exchanges with water and that the methyl site hosts the highest amount of this enrichment due to its low acidity. The carbon model demonstrates that using only the aldehyde and cyanide values measured on Murchison and isotope effects inferred from other studies, we can predict 59 of 82 organic compounds on it (72%) that have δ¹³C values spanning over 149 ‰ with an average residual of 6 ‰. To achieve this level of prediction, the model combines Strecker synthesis, reductive amination, and oxidation of aldehydes to create straight-chain α-H hydroxy and amino acids, amines, and monocarboxylic acids with subsequent formaldehyde addition to these compounds to create branches.</p
Stability of Photo-Electrochemical Interface for Solar Fuels
Get PDFPhotoelectrochemical (PEC) water splitting is a promising approach to convert renewable solar energy to clean hydrogen (H2) fuels in one simple step. Although Ⅲ-Ⅴ semiconductors are attractive candidates as light-absorbers in tandem solar-fuel devices, their long-term stability for the hydrogen-evolution reaction (HER) in either acidic or alkaline aqueous electrolytes needs to be established. Chapter 2-5 of this thesis first aims at revealing the underlying corrosion chemistry for a variety of Ⅲ-Ⅴ semiconductors specifically under the HER conditions, offering a rational understanding towards the stability of semiconductor photoelectrode.
In Chapter 2, we start from p-InP and reveal its susceptibility to cathodic photocorrosion forming metallic In0, which however can be completely mitigated by the presence of Pt catalyst due to kinetic stabilization. We also show that the resulting PEC performance of p-InP/Pt electrodes is sensitive to the changes in surface stoichiometry, whereas an InOx-rich surface developed in KOH caused a substantial degradation in the current density-potential (J-E) behavior. In Chapter 3, we discovered that a non-stoichiometric and As0-rich surface of p-GaAs, resulting from a galvanic corrosion by Pt, led to mid-gap surface states as well as a complete loss in photoactivity. In Chapter 4-5, we demonstrate similar kinetic stabilization applied to both p-InGaP2/Pt and pn+-InGaP2/Pt photocathodes for the HER at both pH 0 and pH 14. Additionally, we found that the corrosion of underlying GaAs substrates for the pn+-InGaP2/Pt photocathodes at positive potentials caused damage of structural integrity as well as instability in electrode performance. Altogether these works underscore the mutual dependence of the physical and electrochemical stability of semiconductor photoelectrodes during the HER, which also need to be considered separately. Moreover, both catalytic kinetics and surface stoichiometry are crucial factors for defining long-term corrosion chemistry for semiconductor photoelectrode.
In Chapter 6-7, we further explore solar fuels beyond H2, namely electrochemical N2-to-NH3 conversion. We first establish a new analytical method to isotopically quantify the concentrations of 15NH3 in aqueous solutions with a high sensitivity and a low limit-of-detection of <1 μM. Further we applied this advanced method to rigorously verify the electrocatalytic activity of a CoMo electrode for reducing N2(g) to NH3. We show that the additional ammonia detected in electrolyte was instead attributed to the corrosion of N impurities present in the CoMo electrode under cathodic bias, thus giving false positive results. These works emphasize the importance of both rigorous product analysis and experiment design in further catalyst development.</p
Understanding Imperfections and Instabilities in Crystals via Physics-Based and Data-Driven Models
Get PDFIn crystals, atoms are arranged in a periodic manner in space. However in reality, imperfections and instabilities exist and this repeated arrangement is never perfect. The coupling between crystal defects, lattice instabilities, other defects like domain walls and domain patterns, and material properties generates interesting phenomena that can be leveraged on for future materials design. Nevertheless, the coupling of different scales and processes also makes the modeling and understanding of these materials an open challenge. This thesis examines these various aspects of crystalline solids through the development of both physics-based and data-driven computational models at the appropriate length scales.
Above-bandgap photovoltaic (PV) effect has been observed experimentally in multi-domain ferroelectric perovskites, but the underlying working mechanisms are not well understood. The first part of the thesis presents a device model to study the role of ferroelectric domain walls in the observed PV effect. The model accounts for the intricate interplay between ferroelectric polarization, space charges, photo-generation, and electronic transport. When applied to bismuth ferrite, results show a significant electric potential step across both 71° and 109° domain walls, which in turn contributes to the PV effect. The domain-wall-driven PV effect is further shown to be additive in nature, allowing for the possibility of generating the above-bandgap voltage.
In the second part, we present a lattice model incorporating random fields and long-range interactions where a frustrated state emerges at a specific composition, but is suppressed elsewhere. The model is motivated by perovskite solid solutions, and explains the phase diagram in such materials including the morphotropic phase boundary (MPB) that plays a critical role in applications for its enhanced dielectric, piezoelectric, and optical properties. Further, the model also suggests the possibility of entirely new phenomena by exploiting MPBs.
The final part of the thesis focuses on constructing data-driven models from first principles calculations, particularly density functional theory (DFT) for studying crystalline materials. Specifically we propose an approach that exploits machine learning to approximate electronic fields in crystalline solids subjected to deformation. When demonstrated on magnesium---a promising light weight structural material---our model predicts the energy and electronic fields to the level of chemical accuracy, and it even captures lattice instabilities. This DFT-based machine learning approach can be very useful in methods that require repeated DFT calculations of unit cell subjected to strain, especially multi-resolution studies of crystal defects and strain engineering that is emerging as a widely used method for tuning material properties.</p
Principles for Designing Robust and Stable Synthetic Microbial Consortia
Get PDFEngineering stable microbial consortia with robust functions are useful in many areas, including bioproduction and human health. Robust and stable properties depend on proper control of dynamics ranging from single cell-level to population-environment interactions. In this thesis, I discuss principles of building microbial consortia with synthetic circuits in two design scenarios.
First, for one microbial population, strong disturbances in environments often severely perturb cell states and lead to heterogeneous responses. Single cell-level design of control circuits may fail to induce a uniform response as needed. I demonstrate that cell-cell signaling systems can facilitate coordination among cells and achieve robust population-level behaviors. Moreover, I show that heterogeneity can be harnessed for robust adaptation at population-level via a bistable state switch.
Second, multi-pecies consortia are intrinsically unstable due to competitive exclusion. Previous theoretical investigations based on models of pairwise interactions mainly explored what interaction network topology ensures stable coexistence. Yet neglecting detailed interaction mechanisms and spatial context results in contradictory predictions. Focusing on chemical-mediated interaction, I show that detailed mechanisms of chemical consumption/accumulation and chemical-induced growth/death, interaction network topology and spatial structures of environments all are critical factors to maintain stable coexistence. With a two population-system, I demonstrate that the same interaction network topology can exhibit qualitatively different or even opposite behaviors due to interaction mechanisms and spatial conditions.</p
Twinkle, Twinkle, Little Stars: Shedding Light on the Population of Galactic Gravitational Wave Sources
Get PDFTime domain surveys are revolutionizing our understanding of compact binary systems containing a white dwarf and another compact object at short orbital periods. These extreme binaries are astrophysical laboratories which can probe compact object physics, the nature of Type Ia supernova progenitors, accretion physics, tidal physics, the process of binary evolution, and they will dominate the population of objects the Laser Interferometer Space Antenna (LISA) will detect. In this thesis, I present substantial advances in the discovery and characterization of compact binaries using the Zwicky Transient Facility (ZTF). This work has resulted in a ten-fold increase in the discovery rate of such binaries compared to previous work in the field, and has helped lay the groundwork for discovering and characterizing these sources using other facilities, such as the the Transiting Exoplanet Survey Satellite (TESS), the upcoming Vera Rubin Observatory (VRO) and eventually LISA itself.</p
Complexity Reduction of Fluid-Structure Systems at Low Forcing Frequencies
Get PDFThis thesis addresses complexity reduction in periodic fluid-structure systems at low forcing frequencies. A novel quasi-steady time scaling framework is developed to relate the dynamics of a forced system to a corresponding unforced system.
Particle Image Velocimetry and dye flow visualization are used to study the streamwise-oscillating cylinder's wake at a mean Reynolds number of 900. Forcing frequencies both one and two orders of magnitude below the stationary shedding frequency are considered. Forcing amplitudes are such that the instantaneous Reynolds number remains above the critical value at all times. It is shown that this forcing regime is synonymous with the development of both frequency and amplitude modulation in the wake. While frequency modulation is linked to vortex shedding, amplitude modulation arises due to symmetric reorganization of the wake at certain phases in the forcing cycle. Furthermore, Dynamic Mode Decomposition is used to extract underlying flow structures and quasi-steady time scaling is employed to relate dynamics to the corresponding unforced system. Specifically, forcing regimes where quasi-steady shedding can develop are identified and time is scaled to transform the system to resemble the stationary cylinder at the same mean Reynolds number.
Experimental flowfields are also used to analyze the wake of a surface mounted hemisphere subject to a highly pulsatile freestream, characterized by a forcing amplitude equal to the mean. Although this flow sees regular shedding of hairpin vortices in the unforced case, pulsatile forcing leads to significant deviations. For a nominal mean Reynolds number of 1000, analysis of the wake shows that forcing at a frequency much smaller than that associated with hairpin shedding can lead to frequency modulated shedding. Consequently, time scaling is employed to reduce system complexity associated with hairpin shedding and to relate wake dynamics to the analogous unforced system.</p
Stability and Protective Coatings of Semiconductor Electrodes for Solar Fuel Devices
Get PDFClimate change and increasing global energy consumption drive the need for clean and renewable alternatives to fossil fuels. Photoelectrochemical solar fuel devices offer a potential solution to capture and store clean and renewable solar energy in chemical bonds. Nevertheless, degradation of semiconductor electrodes is one of the major impediments to the implementation of practical stable solar fuels systems.
erein, we investigate the corrosion mechanisms and the corrosion kinetics of CdTe and ZnTe cathodes under the conditions for hydrogen-evolution reaction in strong acid and strong alkaline media. The effects of catalyst over-layer on CdTe’s and ZnTe’s corrosion pathways are discussed as well as potential protective coatings for ZnTe cathodes. Then, we address the original physical pinhole defects in amorphous a TiO₂ grown by atomic-layer deposition (ALD) on GaAs anodes. In addition, we explore new pinhole formation during electrochemical experiments and provide simulation for the propagation of the corroding GaAs substrate after new exposure to the electrolyte through microscopic pinholes. Finally, we develop a fabrication procedure for GaAs micro-island structures to provide defect isolation on the a TiO₂ film. The micro-island structures combined with dissolution measurements of the ALD a TiO₂ films were used to study the distribution and the evolution of pinholes from pre-existing defect spots in the protective coatings.</p
Modernization of Monoclonal Antibody Screening and Protein-interaction Assays
Get PDFIn this research, multiplexed bead-based technology was employed to develop a high-throughput monoclonal antibody production method and to refine a protein-protein interaction (PPI) assay for interactome screening. Hybridoma supernatants produced from mice injected with multiple antigens were screened with color-coded, antigen-coupled beads in a semi-automated workflow. Two monoclonal antibodies, each demonstrating high specificity and strong binding, were produced. To our knowledge, these results are the first demonstrated usage of multiplexed suspension bead-based screening as a critical component of high-throughput antibody production. The technology was also utilized as a PPI assay due to its numerous advantages over ELISA-based screens. We studied interactions of the extracellular domains of the Beat and Side protein families, whose members control neuromuscular specificity in Drosophila melanogaster and form a highly-connected interaction network. We demonstrated that a screen utilizing avidin-captured bait was superior to a screen utilizing Protein A-captured bait and deorphanized five proteins within the network, namely Beat 1b, Beat 3a, Beat 3c, Side 5, and Side 8.</p