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Visual Computations in the Superior Colliculus
Get PDFThis thesis presents two projects related to large-scale extracellular recordings of neural signals. The first project asks how the brain sifts the onslaught of sensory information to identify the few bits that are relevant for guiding behavior. This question is studied in the context of the looming reaction, an innate defensive behavior against an approaching aerial predator. Interestingly, the mouse responds very selectively to the looming stimulus regardless of changes in orthogonal features, such as its position. The neural basis of this phenomenon is investigated with extracellular recordings in the superior colliculus, a midbrain visual area known to mediate the looming reaction. A detailed analysis of the difference between the superficial and deeper layers of the superior colliculus highlights a core function of visual processing: to discard information intelligently.
The second project presents electrode pooling, a novel method to increase the yield of extracellular recordings with the modern silicon electrode array. The fundamental constraint of wire volume in these devices is identified, and a solution that makes use of the switching circuitry and the sparseness of the neural signal in the time axis is described. Specifically, the method proposes to intelligently choose many recording sites that carry signal and connect them to a single wire via manipulating the switches. This pooled recording is subsequently un-mixed by a spike-sorting algorithm. The method is implemented in a state-of-the-art silicon neural probe, and its effect on signal and noise is analyzed by theory and experiment. Recommendations on the design of silicon devices are made to facilitate the incorporation of this method in the future.</p
Tethered Motion Planning for a Rappelling Robot
Get PDFThe Jet Propulsion Laboratory and Caltech developed the Axel rover to investigate and demonstrate the potential for tethered extreme terrain mobility, such as allowing access to science targets on the steep crater walls of other planets. Tether management is a key issue for Axel and other rappelling rovers. Avoiding tether entanglement constrains the robot's valid motions to the set of outgoing and returning path pairs that are homotopic to each other. In the case of a robot on a steep slope, a motion planner must additionally ensure that this ascent-descent path pair is feasible, based on the climbing forces provided by the tether. This feasibility check relies on the taut tether configuration, which is the shortest path in the homotopy class of the ascent-descent path pair.
This dissertation presents a novel algorithm for tethered motion planning in extreme terrains, produced by combining shortest-homotopic-path algorithms from the topology and computational geometry communities with traditional graph search methods. The resulting tethered motion planning algorithm searches for this shortest path, checks for feasibility, and then generates waypoints for an ascent-descent path pair in the same homotopy class. I demonstrate the implementation of this algorithm on a Martian crater data set such as might be seen for a typical mission. By searching only for the shortest path, and ordering that search according to a heuristic, this algorithm proceeds more efficiently than previous tethered path-planning algorithms for extreme terrain.
Frictional tether-terrain interaction may cause dangerously intermittent and unstable tether obstacles, which can be categorized based on their stability. Force-balance equations from the rope physics literature provide a set of tether and terrain conditions for static equilibrium, which can be used to determine if a given tether configuration will stick to a given surface based on tether tension. By estimating the tension of Axel's tether when driving, I divide potential tether tension obstacles into the following categories: acting as obstacles, acting as non-obstacles, and hazardous intermittent obstacles where it is uncertain whether the tether would slip or stick under normal driving tension variance. This dissertation describes how to modify the obstacle map as the categorization of obstacles fluctuates, and how to alter a motion plan around the dangerous tether friction obstacles. Together, these algorithms and methods form a framework for tethered motion planning on extreme terrain.</p
Generalizations of a Theorem of Hecke
Get PDFLet p > 3 be an odd prime, p ≡ 3 mod 4 and let π⁺, π⁻ be the pair of cuspidal representations of SL₂(𝔽p). It is well known by Hecke that the difference mπ⁺ - mπ⁻ in the multiplicities of these two irreducible representations occurring in the space of weight 2 cusps forms with respect to the principal congruence subgroup Γ(p), equals the class number h(-p) of the imaginary quadratic field ℚ(√(-p)).
This thesis consists of two main parts. In the first part, we extend Hecke's result to all fundamental discriminants of imaginary quadratic fields, including the even case. The proof is geometric in nature and uses the holomorphic Lefschetz number.
In the second part, we consider generalizations to groups with higher ℚ-rank. In particular, we focus on the rank 2 special unitary group SU(2, 2). On the representation theory side, we prove the regular unipotent classes have positive contribution to an alternating sum of multiplicities of certain irreducible cuspidal representations of SU(2, 2) over the finite field of p elements. We also show that the semisimple classes have zero contribution, which is again a direct generalization of the SL₂ case. To obtain these two results, we make use of the Deligne-Lusztig theory and the connection of the traces to the Gelfand-Graev representations.</p
Transition Metal Complexes for Challenging Reductive Transformations: From Nitrogen Fixation Catalysts to Photoreductants
Get PDFTransition metal complexes are routinely employed as catalysts for the reductive cleavage of a diverse array of strong chemical bonds. Two notable research areas that exemplify such utility are nitrogen fixation, involving cleavage of the notoriously unreactive triple bond of dinitrogen (N₂) to form ammonia (NH₃), and photoredox catalysis, wherein powerful photoreductants generated by visible light excitation facilitate challenging reduction steps in a host of synthetic organic transformations. This thesis focuses on a number of structure-function studies conducted on group 8 transition metal complexes that catalyze N₂-to-NH₃ conversion, commonly referred to as the nitrogen reduction reaction (N₂RR), and on homoleptic tungsten(0) arylisocyanides that, among their many attractive qualities, possess highly reducing electronically excited states. These comparative studies provide fundamental insight into critical design features which can guide efforts to improve existing N₂RR or photocatalysts or rationally tailor them for specific applications.
Chapter 2 details the effect apical Lewis acidic atom substitution in P₃XFe platforms (X = B, Al, Ga) has on structure, bonding, and N₂RR activity. Structural, spectroscopic, electrochemical, and computational studies reveal that all three P₃XFe systems possess similar electronic structures, degrees of N₂ activation, and geometric flexibility, but P₃AlFe and P₃GaFe display significantly lower N₂RR efficiencies than P₃BFe when treated with HBArF₄/KC₈ or [H₂NPh₂][OTf]/Cp*₂Co at –78 °C in Et₂O.
Chapter 3 reports on isostructural tris(phosphino)silyl Ru and Os complexes that mediate catalytic N₂RR. The study of the homologous, isostructural series of complexes P₃SiM (M = Fe, Ru, Os) helps delineate important factors for N₂RR catalyst design. Low-temperature protonation of P₃SiOs–N₂⁻ yields P₃SiOs=NNH₂⁺, representing the first instance of an Os–N₂ species being converted to a protonated Os–NxHy product.
Chapter 4 communicates a novel series of homoleptic tungsten(0) photoactive complexes supported by fused-ring (CN-1-(2-iPr)-Naph) or alkynyl-bridged (CNDippCCAr) arylisocyanide ligands. Systematic studies establish facile electronic variation of the CNDippCCAr platform as a straightforward method by which to rationally modulate the ground- and excited-state properties of W(CNDippCCAr)₆ complexes. The photophysical properties of W(CN-1-(2-iPr)-Naph)₆ reveal potential benefits of utilizing fused-ring arylisocyanide ligands in the design of this class of photosensitizers.</p
Chemical Tools for Studying O-GlcNAc Glycosylation at the Systems Level
Get PDFThe addition of O-linked β-N-acetylglucosamine (O-GlcNAc) to intracellular serine and threonine residues is a ubiquitous post-translational modification (PTM) found in all higher eukaryotes. Like other PTMs, it is finely regulated in response to stimuli and dysregulated in multiple diseases. However, unlike other PTMs, methods to detect and profile the dynamics of O-GlcNAc glycosylation are still in their infancy. Herein, we discuss the background, development, and application of new chemical tools that have allowed for some of the first systems-level investigations of O-GlcNAcylation in different cells, organ systems, and disease states. We also significantly advance established techniques for the detection and monitoring of O-GlcNAc on proteins of interest. Using these new techniques, we first uncover a novel O-GlcNAcylation site on Cdk5 and show that this site can dynamically regulate Cdk5 activity in the context of neurodegenerative disease. Next, we apply novel chemical, mass spectrometric, and computational tools to, for the first time, uncover cellular networks engaged by O-GlcNAcylation in vivo. Finally, we undertake the systematic optimization of mass spectrometry based O-GlcNAcomics and use these new insights to significantly advance our understanding of O-GlcNAcylation dynamics in metabolic diseases of the liver. Overall, the techniques developed and data generated herein are closing the methodological and intellectual gaps between the study of O-GlcNAc glycosylation and that of other PTMs.</p
Nanophotonic Phenomena in Dielectric Photonic Crystals
Get PDFPhotonic crystals are periodic optical nanostructures with varying dielectric constant that allow light flow to be controlled and manipulated much in a similar way to electrons within a semiconductor crystal. These nanostructures tend to have a spatially varying refractive index on the order of the wavelength of light to be manipulated. 1D and 2D photonic crystals have already garnered significant attention in the realm of thin-film optics, while 3D photonic crystals have been thus far limited in application, due to difficulties in fabrication and a lack of available materials for fabrication.
In this work, we first explore 1D and 2D photonic crystals based on the concept of a guided mode resonance, which manifests as a narrow near-unity resonance in reflection or transmission that arise from the coupling of an incident wave into a leaky waveguide mode via a grating vector that is subsequently re-radiated. Such a resonance is well-suited for multi- and hyper- spectral filtering applications in the infrared. We designed a platform consisting of amorphous Si arrays embedded in SiO2 in simulation and experiment for application as narrow stopband filters. We present the tunability of the spectral characteristics of the resonance in these arrays through variation of array geometric parameters in simulation and experiment. Guided mode resonance designs often consider only the case of an infinite array, where the leaky waveguide mode can propagate laterally for hundreds of periods, allowing for this mode to eventually scatter out of the array giving rise to the characteristic narrow near-unity rapid spectral variations of a GMR. With an insufficient number of periods, the quality factor and thus the optical filtering performance is greatly diminished. Thus, we further extend our analysis to compact periodic arrays of finite size, which are required for high spatial resolution snapshot imaging, and introduce array designs that operate under finite size limitations in the near-infrared.
We then transition to 3D photonic crystals, exploring the use of an additive manufacturing process to directly fabricate nanocrystalline rutile TiO2 with ~100 nm resolution. Though TiO2 was chosen as the model material, the key to this work is that a similar process can be used to print many different materials, enabling future applications of 3D photonic crystals. The focus here is the additive manufacturing of high index materials such as TiO2, and its potential for photonic applications is demonstrated by characterizing the optical band gap of 3D PhC TiO2 structures printed with this method. We present a system where the ability to print high refractive index 3D photonic crystals would be useful, by studying 3D polymer-germanium core-shell structures that should exhibit all-angle negative refraction in the mid-infrared regime.</p
Multimodal Analysis of Cell Types in a Hypothalamic Node Controlling Social Behavior in Mice
Get PDFThe advent and recent advances of single-cell RNA sequencing (scRNA-seq) have yielded transformative insights into our understanding of cellular diversity in the central nervous system (CNS) with unprecedented detail. However, due to current experimental and computational limitations on defining transcriptomic cell types (T-types) and the multiple phenotypic features of cell types in the CNS, an integrative and multimodal approach should be required for the comprehensive classification of cell types.
To this end, performing multimodal analysis of scRNA-seq in hypothalamus would be very beneficial in that hypothalamus, controlling homeostatic and innate survival behaviors which known to be highly conserved across a wide range of species and encoded in hard-wired brain circuits, is likely to display the more straightforward relationship between transcriptomic identity, axonal projections, and behavioral activation, respectively. In my dissertation, I have been focused on the cell type characterizations of a hypothalamic node controlling innate social behavior in mice, the ventrolateral subdivision of the ventromedial hypothalamus (VMHvl). VMHvl only contains ~4,000 neurons per hemisphere in mice but due to its behavioral, anatomical, and molecular heterogeneity, which T-types in VMHvl are related to connectivity and behavioral function is largely unknown.
In Chapter II, I described my main thesis work to perform scRNA-seq in VMHvl using two independent platforms: SMART-seq2 (~4,500 neurons sequenced) and 10x (~78,000 neurons sequenced). Specifically, 17 joint VMHvl T-types including several sexually dimorphic clusters were identified by canonical correlation analysis (CCA) in Seurat, and the majority of them were validated by multiplexed single-molecule FISH (seqFISH). Correspondence between transcriptomic identity, and axonal projections or behavioral activation, respectively, was also investigated. Immediate early gene analysis identified T-types exhibiting preferential responses to intruder males versus females but only rare examples of behavior-specific activation. Unexpectedly, many VMHvl T-types comprise a mixed population of neurons with different projection target preferences. Overall our analysis revealed that, surprisingly, few VMHvl T-types exhibit a clear correspondence with behavior-specific activation and connectivity.
In Chapter III, I will discuss about future directions for a deeper and better understanding of VMHvl cell types. Briefly, my previous data from whole-cell patch clamp recording in VMHvl slices suggested that there were at least 4 distinct electrophysiological cell types (E-types). Additionally, two distinct neuromodulatory effects on VMHvl were observed (persistently activated by vasopressin/oxytocin vs. silenced by nitric oxide) by monitoring populational activities using two-photon Ca2+ imaging in slices. Based on the results from the first part and combined with advanced molecular techniques (e.g. Patch-seq and CRISPR-Cas9), we can further dissect out the cellular diversity in VMHvl and their functional implications.</p
Convex Relaxations for Graph and Inverse Eigenvalue Problems
Get PDFThis thesis is concerned with presenting convex optimization based tractable solutions for three fundamental problems:
1. Planted subgraph problem: Given two graphs, identifying the subset of vertices of the larger graph corresponding to the smaller one.
2. Graph edit distance problem: Given two graphs, calculating the number of edge/vertex additions and deletions required to transform one graph into the other.
3. Affine inverse eigenvalue problem: Given a subspace ε ⊂ 𝕊ⁿ and a vector of eigenvalues λ ∈ ℝⁿ, finding a symmetric matrix with spectrum λ contained in ε.
These combinatorial and algebraic problems frequently arise in various application domains such as social networks, computational biology, chemoinformatics, and control theory. Nevertheless, exactly solving them in practice is only possible for very small instances due to their complexity. For each of these problems, we introduce convex relaxations which succeed in providing exact or approximate solutions in a computationally tractable manner.
Our relaxations for the two graph problems are based on convex graph invariants, which are functions of graphs that do not depend on a particular labeling. One of these convex relaxations, coined the Schur-Horn orbitope, corresponds to the convex hull of all matrices with a given spectrum, and plays a prominent role in this thesis. Specifically, we utilize relaxations based on the Schur-Horn orbitope in the context of the planted subgraph problem and the graph edit distance problem. For both of these problems, we identify conditions under which the Schur-Horn orbitope based relaxations exactly solve the corresponding problem with overwhelming probability. Specifically, we demonstrate that these relaxations turn out to be particularly effective when the underlying graph has a spectrum comprised of few distinct eigenvalues with high multiplicities. In addition to relaxations based on the Schur-Horn orbitope, we also consider outer-approximations based on other convex graph invariants such as the stability number and the maximum-cut value for the graph edit distance problem. On the other hand, for the inverse eigenvalue problem, we investigate two relaxations arising from a sum of squares hierarchy. These relaxations have different approximation qualities, and accordingly induce different computational costs. We utilize our framework to generate solutions for, or certify unsolvability of the underlying inverse eigenvalue problem.
We particularly emphasize the computational aspect of our relaxations throughout this thesis. We corroborate the utility of our methods with various numerical experiments.</p
Mechanisms of Phenazine-Mediated Extracellular Electron Transfer by Pseudomonas aeruginosa
Get PDFExtracellular electron transfer (EET), the process whereby cells access electron acceptors or donors that reside many cell lengths away, enables metabolic activity by microorganisms, particularly under oxidant-limited conditions that occur in multicellular bacterial biofilms. Although different mechanisms underpin this process in individual organisms, a potentially widespread strategy involves extracellular electron shuttles, redox-active metabolites that are secreted and recycled by diverse bacteria. Here, I first review general aspects of the electron shuttling strategy, such as the chemical diversity and potential distribution of electron shuttle producers and users, and the costs associated with electron shuttle biosynthesis. Then I address the long-standing question: how do these electron shuttles catalyze electron transfer within biofilms without being lost to the environment? I show that phenazine electron shuttles mediate efficient EET through interactions with extracellular DNA (eDNA) in Pseudomonas aeruginosa biofilms, which are important in nature and disease. Retention of pyocyanin (PYO) and phenazine carboxamide in the biofilm matrix is facilitated by binding to eDNA. In vitro, different phenazines can exchange electrons in the presence or absence of DNA and phenazines can participate directly in redox reactions through DNA; the biofilm eDNA can also support rapid electron transfer between redox-active intercalators. Electrochemical measurements of biofilms indicate that retained PYO supports an efficient redox cycle with rapid EET and slow loss from the biofilm. Together, these results establish that eDNA facilitates phenazine metabolic processes in P. aeruginosa biofilms, suggesting a model for how extracellular electron shuttles achieve retention and efficient EET in biofilms.</p
Utilitarian Calculations and the Moral Status of Strong AI
No full textWhen, if ever, does a robot or other advanced AI system deserve the same moral consideration as a human being? From a philosophical perspective, addressing this question requires us to examine utilitarian theory and its most powerful tool, moral calculations, with some care. From a human’s perspective, the response to this question is very closely tied to the formulation of a broader criterion for full moral status, so it has important implications for the morality of actions toward humans and animals too – not just toward AI. And, from an android’s perspective, our answer to this question could be, without exaggeration, a matter of deactivation or continuation, of life or death. In this paper, I will use the backdrop of utilitarianism to make a case for my own answer. Sentience alone, I claim, is a sufficient condition for an AI system to have full moral status