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Type-I Fractons -- Foliation in Non-Abelian Models
Get PDFIn this thesis, we present recent contributions to the study of Type-I non-abelian fracton models, which led us to propose the notion of generalized foliated fracton orders that captures the universal properties of both abelian and non-abelian Type-I fracton models.
Fracton models are known for their exotic properties such as point-like excitations with restricted mobilities and robust topological ground state degeneracy that grows sub-extensively with the system size. A multitude of Type-I fracton models whose excitations obey either abelian or non-abelian fusion rules have recently been constructed. Among them, a large number of the abelian fracton models have been shown to possess foliation structures, where models of different system sizes can be related through the addition / removal of an entire piece of topologically ordered system on a sub-dimensional manifold via the action of a finite-depth local unitary circuit. In this thesis, this is referred to as the original foliation renormalization group (RG) scheme, which leads us to the notion of original foliation fracton orders. The Ising cage-net model and other similar non-abelian models are closely related to these abelian models in terms of their excitation structures and coupled layers construction etc. However, it was not known whether their fracton orders can also be understood within the original foliation framework. We address this problem in this thesis.
In Chapter 2, we show that the Ising cage-net model does not fit into the original definition of foliated fracton orders, by calculating its ground state degeneracy. We realize that there exists naturally a more general way to define foliation -- the generalized foliation scheme (Chapter 3). The Ising cage-net and other similar non-abelian fracton models are foliated according to this generalized scheme. In the generalized foliation scheme, the RG transformation is defined by, from the excitation perspective, the condensation of planons / gauging subsystem symmetries. In terms of quantum circuits, this RG transformation is equivalent to a sequential linear-depth circuit that acts near a sub-dimensional manifold. With this definition, we can study phase relation of the Ising cage-net with other known fracton models. In Chapter 4, via gauging composite subsystem symmetries, we further show that the Ising cage-net belongs to the same generalized foliated fracton phases as the prototypical X-cube model. Furthermore, gauging composite subsystem symmetries opens up a new route to constructing non-abelian fracton models hosting exotic non-abelian fractons. An example is the tri-Ising-fracton model (Sec. 4.5).</p
Chasing Metamorphic Supernovae with Zwicky Transient Facility, SEDM-KP, and AI
Get PDFModern time-domain astronomy has entered a data-rich era. Propelled by wide-field, high-cadence surveys like the Zwicky Transient Facility (ZTF) have vastly expanded our understanding of supernova (SN) diversity. However, the surge in discoveries has led to a classification bottleneck, particularly for spectroscopic follow-up, hindering the timely identification of rare or unusual transients. This thesis focuses on a class of unusually long-lived SNe with bumpy light curves, and also addresses the broader classification challenge through instrumentation and the application of artificial intelligence.
Two rare SN classes are examined in depth through systematic samples: (i) SNe Ia-CSM, which initially have SNe Ia-like spectra but later transform into Type IIn-like SNe strongly interacting with circumstellar material (CSM), challenging our understanding of their progenitor systems; and (ii) double-peaked stripped-envelope supernovae (SESNe), where multiple light curve peaks suggest contributions from diverse energy sources including double-nickel distribution, CSM interaction, or magnetar engines. I derive constraints on the observed rates of SNe Ia-CSM with the systematic sample, and identify spectroscopic features that can differentiate between the strongly-interacting spectra of SNe Ia-CSM from SNe IIn. I discuss the diversity of double-peaked SESN light curves in the context of the plethora of suggested powering mechanisms and derive light curve properties that can help narrow down the possibilities.
To enable more effective discovery and classification of such events, this thesis also presents instrumental and computational advances. I detail the commissioning of a new low-resolution robotic spectrograph, SEDM-KP, on the Kitt Peak 84-inch telescope, designed to extend spectroscopic classification to fainter transients. Additionally, I introduce a deep-learning-based tool, CCSNscore, which achieves high accuracy in automated core-collapse supernova classification from low-resolution spectra, significantly reducing human workload and latency in reporting.
Together, these contributions advance our ability to identify, classify, and study the growing zoo of transient phenomena and lay the groundwork for managing the deluge of discoveries anticipated in the Rubin Observatory era.</p
Neural Network Models of Learning and Generalization
Get PDFNeural networks have emerged as powerful models for understanding both biological and artificial intelligence. This thesis investigates fundamental principles of learning and generalization across four interconnected domains, bridging insights from theoretical neuroscience and machine learning to advance our understanding of intelligent systems.
Chapter I addresses a central question in associative learning: how do neural circuits learn to associate concepts with one another? We combine two cortical inductive biases, namely mixed selectivity and predictive learning in compartmentalized neurons, to explain how the cortical architecture may confer significant evolutionary advantages for efficient learning and packing multiple associations within the same neuronal population. Our model achieves stimulus substitution, where neurons respond identically to a conditioned stimulus as they would to the associated unconditioned stimulus, a feat in which traditional, Hebb-based learning rules fail.
Chapter II pivots from the static mappings between concepts learned in Chapter I to explore how neural systems develop the precise synaptic connectivity required to establish dynamic mappings for path integration—the ability to maintain an internal sense of location without external cues. Applied to the Drosophila head direction system, our model develops connectivity patterns strikingly similar to those observed experimentally, with Continuous Attractor (CAN) dynamics emerging naturally from learning. This offers a novel perspective on how precisely calibrated neural circuits can develop through experience, rather than requiring genetic pre-specification, and explains experimental findings where animals adapt their internal representation when sensory experience changes.
In Chapter III, we establish a theoretical framework explaining how disentangled representations—internal models that isolate independent factors of variation in the world—emerge from multi-task learning. We prove that any system competent at multiple related tasks must implicitly represent the underlying latent variables in a linearly decodable form. We experimentally confirm all major theoretical predictions, and reveal a fundamental connection between task diversity and representation quality, particularly explaining why modern transformer models may develop human-interpretable concepts. Furthermore, our work suggests that the massively parallel cortical architecture may be a key facilitator in the development of representations that enable the impressive zero-shot generalization ability that humans possess.
Finally, Chapter IV proposes leveraging Large Language Models (LLMs) as cognitive tools for evaluating latent factor hypotheses for psychology, leveraging the theoretical insights from Chapter III. It suggests that the self-consistency of an LLM's responses given hypothesized psychological factors could serve as a metric for psychological latent factor hypothesis evaluation. While preliminary, this approach represents a novel computational methodology for psychology that could transform how hypotheses for human cognition are developed and refined.
Continuous attractors display prominently in this thesis (Chapters II and III), yet these concepts are misunderstood, particularly in the experimental literature. Hence, in Appendix D of this thesis we provide important considerations about the detection and quantification of Continuous Attractors (CANs) from experimental data, considerations particularly important in order to avoid confusion when it comes to these concepts, leading to wasted efforts and resources in the experimental neuroscience community.
Together, these investigations reveal complementary aspects of how intelligent systems develop useful, generalizable representations through learning. From biologically plausible learning rules to abstract computational principles, this thesis demonstrates how neural networks can illuminate fundamental mechanisms of intelligence across natural and artificial systems, contributing to a unified science of Neural Computation.</p
Application of Ultrafast Spectroscopy Techniques to Probe Correlated Ion Hopping Mechanisms in Solid-State Ion Conductors
No full textSuperionic conductors, or solid-state ion conductors that surpass the ionic con- ductivity of its liquid counterpart, can enable more energy dense batteries, robust artificial ion pumps, and optimized fuel cells. The mechanisms enabling superionic conductivity still remain elusive, though many-body correlations between the mi- grating ions, lattice vibrational modes, and charge screening clouds have all been posited to greatly enhance ionic conduction. Most spectroscopic techniques cannot directly probe and validate the role of such correlations due to their inability to transiently resolve these ultrafast dynamics occurring at picosecond timescales. In this work, we develop an ultrafast technique that measures the time-resolved change in impedance while a light source ranging from UV to THz frequencies selectively excites an ion-coupled correlation. The technique is used to compare the relative changes in impedance of a solid-state Li⁺ conductor Li0.5La0.5TiO3 (LLTO) before and after light excitation to elucidate the role of charge screening clouds, optical phonons, and acoustic phonons on ion migration. From our techniques, we deter- mine that electronic screening and rocking phonon-mode interactions significantly dominate the ion migration pathway of LLTO compared to acoustic phonons. Al- though we only present one case study, our technique can extend to O²⁻, H⁺, or other charge carrier transport phenomena where ultrafast correlations control transport. Furthermore, the temporal relaxation of the measured impedance can distinguish ion transport effects caused by many-body correlations, optical heating, correlation, and memory behavior
Seismic Probes of Stellar Mergers and Magnetism
Get PDFStellar pulsations can do what most other astrophysical observables cannot: directly probe internal stellar properties. This thesis consolidates work investigating how stellar oscillation modes are affected by two common but "noncanonical" pieces of stellar physics: mergers and magnetism.
The earlier chapters develop "seismic stellar merger genealogy," the application of seismology to the discovery of stellar merger remnants. In Chapter II, I show that red giants which have engulfed close, main-sequence companions possess unusual gravity-mode period spacings, indicating their binary origin. I identify two dozen promising merger remnant candidates in archival Kepler data, roughly consistent with expected stellar merger rates. In Chapter III, I study the evolution and properties of the red-giant-like stars which result from coalescences of accreting helium-core white dwarf systems. These merger remnants display distinctive seismic and chemical properties, particularly during the core helium-burning phase as the result of an especially violent helium flash.
The later chapters develop "seismic stellar magnetometry," the application of seismology to the measurement of stellar magnetic fields. In Chapter IV, I calculate the morphology of high-radial-order gravity modes under the influence of strong magnetic fields. The eigenfunctions exhibit two morphological features at which energy dissipation may be strong, in agreement with the suppressed dipole modes observed in many red giants.
In Chapter V, I apply the same method to calculate the gravity-mode period spacing pattern under a strong magnetic field. The perturbative theory developed for weak fields underestimates the true frequency shifts to gravity modes caused by strong magnetic fields. In Chapter VI, I model the behavior of stochastic pulsators whose magnetic fields are strong enough to misalign their pulsations from the rotation axis. Even in the presence of stochasticity, the light curves of such oblique pulsators indefinitely retain some phase information in a way that can be used to identify them. In Chapter VII, I place upper bounds on the near-surface magnetic fields of a sample of white dwarfs based on the non-detection of magnetic features in their pulsation spectra. Although these constraints vary significantly with white dwarf structure and mode periods, they are consistently much stronger than the megagauss-scale magnetic fields to which spectroscopy is sensitive.</p
Construction of Long, Complex, and Diverse DNA Sequences
No full textThe DNA molecule encodes the information required for biological systems to carry out a broad range of functions. The understanding of this relationship has sparked inquiries across vast fields of biology and biological engineering as we read, edit, and write the genetic information of organisms. Great advancements have been made toward these pursuits, from revolutions in DNA reading with long read sequencing and the ability to generate terabytes of data from a single run to the breakthroughs in DNA editing with the major advancements in CRISPR/Cas technologies over the last decade. However, writing DNA, as the ability to construct DNA of any length, complexity, or diversity, lags significantly behind our capacity for reading and editing.
DNA oligo synthesis can only reach short lengths of a few hundred nucleotides of single stranded DNA. The field of DNA assembly develops the methods for stitching together DNA oligos and DNA fragments into larger constructs. The current field applies a broad range of approaches that each occupy their own niche due to their unique set of advantages and disadvantages. No existing technique is able to assemble a large number of DNA fragments simultaneously with high accuracy and without placing restrictions on the sequences being assembled. This is because all existing DNA assembly technologies rely on the information contained within the complementary sequences of the DNA molecules being constructed to direct the assembly.
To meet the demand for robust DNA assembly, we have developed a new DNA assembly technique named Sidewinder which separates the information that guides assembly from the final assembled sequence using DNA 3-Way junctions. We demonstrate the transformative nature of the Sidewinder technique with highly robust and accurate assembly of complex DNA sequences of both high GC and high repeats, a 40-piece multi-fragment assembly, a parallel construction of multiple distinct genes in the same reaction, and construction of a combinatorial library with a large number of diversified positions across the entire length of the gene for high coverage of a library of 442,368 variants.
Where Sidewinder excels at the assembly of oligos to the kilobase scale, we have made a series of advancements to an existing 2-Way junction assembly technique, USER cloning, for the accurate and efficient assembly of PCR-based DNA inputs. We characterize these improvements with a series of assemblies where we achieve an average accuracy over 95%, gain 3 orders of magnitude increase in yield of transformants, and conduct large multi-fragment assemblies beyond what was previously possible with the technique. We then interface these two state-of-the-art capacities for the rapid and efficient construction of a complex 10 kilobase sequence de novo and entirely cell-free.</p
Novel Electronic and Optoelectronic Interactions in Two-Dimensional Materials
No full textTwo-dimensional (2D) materials host a rich set of emerging physical phenomena such as superconductivity, ferroelectricity, quantum magnetism, and circular dichroism. Moreover, these phenomena are highly tunable by crystalline composition variations and crystalline structural phase modifications and are sensitive to external conditions such as temperature, magnetic field and optical excitation, substrate and gate tuning. Therefore, 2D material-based devices are highly desirable for modern electronic and optoelectronic devices applications. In this thesis, we employed a fully scalable approach to synthesize materials and fabricate 2D material-based devices such as those based on graphene and 1H-Molybdenum disulfide (1H-MoS2), and explore their electronic and optoelectronic properties in cryogenic conditions under various excitation sources, such as external magnetic field and structured light.
In the first part of the thesis (Chapters 2 and 3), we provide experimental details for achieving nanoscale strain engineering of monolayer (ML)-graphene and demonstrate that periodic patterns of nanoscale strain distributions in ML-graphene can lead to local giant pseudomagnetic fields as well as global modifications to the electronic properties of ML-graphene, including strain-induced valley Hall and anomalous Hall effects in the absence of external magnetic fields, nonlocal valley-polarized currents and evidence of quantum valley Hall effect under external magnetic field. These findings suggest new approaches towards developing emerging quantum states with tunable electronic correlation based on graphene straintronics.
The second part of the thesis (Chapters 4 and 5) focus more on the semiconducting monolayer transition metal dichalcogenides (ML-TMDs), whose broken inversion symmetry and strong spin-orbit coupling result in spin-valley lock-in effects so that the valley degeneracy may be lifted by external magnetic fields, potentially leading to real-space structural transformation.
In Chapter 4, we report magnetic field (B)-induced giant electric hysteretic responses to back-gate voltages in ML-MoS₂ field-effect transistors (FETs) on SiO₂/Si at temperatures < 20 K. The observed hysteresis increases with |B| up to 12 T and is tunable by varying the temperature. Raman spectroscopic and scanning tunneling microscopic studies reveal significant lattice expansion with increasing |B| at 4.2 K, and this lattice expansion becomes asymmetric in ML-MoS₂ FETs on rigid SiO₂/Si substrates, leading to out-of-plane mirror symmetry breaking and the emergence of a tunable out-of-plane ferroelectric-like polar order. This broken symmetry-induced polarization in ML-MoS₂ shows typical ferroelectric butterfly hysteresis in piezo-response force microscopy, adding ML-MoS₂ to the single-layer material family that exhibit out-of-plane polar order-induced ferroelectricity, which is promising for such technological applications as cryo-temperature ultracompact non-volatile memories, memtransistors, and ultrasensitive magnetic field sensors. Moreover, the polar effect induced by asymmetric lattice expansion may be further generalized to other ML-TMDs and achieved by nanoscale strain engineering of the substrate without magnetic fields.
In Chapter 5, we further demonstrate the design and application of a novel instrument that integrates scanning spectroscopic photocurrent measurements with structured light of controlled spin and orbital angular momentum. For structured photons with wavelengths between 500 nm to 700 nm, this instrument can perform spatially resolved photocurrent measurements of 2D materials or thin crystals under magnetic fields up to ±14 Tesla, at temperatures from 300 K down to 3 K, with either spin angular momentum (SAM) ℓħ or orbital angular momentum (OAM) ± ℓħ (where ℓ = 1, 2, 3… is the topological charge), and over a (35x25) µm² area with ~ 1 µm spatial resolution. These capabilities of the instrument are exemplified by magneto-photocurrent spectroscopic measurements of monolayer 2H-MoS₂ field-effect transistors, which not only reveal the excitonic spectra but also demonstrate monotonically increasing photocurrents with increasing |ℓ| as well as excitonic Zeeman splitting and an enhanced Landé g-factor due to the enhanced formation of intervalley dark excitons under magnetic field. These studies thus demonstrate the versatility of the scanning photocurrent spectrometry for investigating excitonic physics, optical selection rules, and optoelectronic responses of novel quantum materials and engineered quantum devices to structured light.
Finally, we summarize the research accomplishments of this thesis work in Chapter 6 and discuss the outlook for new research directions associated with these 2D quantum materials.</p
Percolation on Transitive Graphs
No full textPercolation on a transitive graph is an idealized mathematical model for a homogeneous system undergoing a phase transition. We will investigate how the geometry of an infinite transitive graph determines whether percolation undergoes a phase transition, and if so, at what critical point. Building on these ideas, we will develop a new theory of percolation on finite transitive graphs. This theory unifies the percolation phase transition on infinite transitive graphs with the giant-cluster phase transition in the celebrated Erdős-Rényi model from combinatorics
Anthropogenic Emissions and the Future of Our Atmosphere: I. Cyclohexanol Chemistry and Aerosol Formation in an Environmental Chamber II. K₂CO₃-Based Sorbent Development and Testing in a Packed Bed Reactor for CO₂ Capture
No full textChapter 1 presents experimental studies conducted in an environmental chamber, alongside mechanistic modeling, to quantify aerosol formation from the gas-phase pollutant cyclohexanol. The calculated aerosol mass yields, which are higher than measured and predicted values of similar 6-carbon species, indicates the importance of functionalization, and interaction between functional groups (not just carbon number), on aerosol forming potential. Chapter 2 describes the construction and characterization of a mini-industrial scale packed-bed reactor, loaded with K₂CO₃-impregnated particles for CO₂ capture. Chapters 3 and 4 describe the formulation of durable high-capacity K₂CO₃-based sorbents using wet activated granulation and extrusion spheronization, respectively. In short, capture of point source CO₂ via K₂CO₃ sorbent is demonstrated to be feasible and even economical in the near future.</p
A Study on the Content, Format, and Implementation of Neural Representations That Underlie Flexible Human Cognition
No full textHumans are the most capable cognitive generalists to walk the earth. They have a remarkable capacity for flexibility reallocating cognitive resources to rapidly acquire and execute an effectively infinite number of tasks. By utilizing the opportunity to record single-neuron activity in the frontal and temporal lobes of awake, behaving neurosurgical patients, we aim to elucidate the principles by which task representations are organized at the neural-circuit level to give rise to flexible cognition and behavior.
Our research program consists of four inter-related projects, each of which seeks to clarify the content, format, and single-neuron implementation of the representations that underlie different aspects of cognition and behavior that are uniquely human. In the first project, we demonstrate that the emergence of disentangled task representations in the hippocampus correlate with the ability of an individual to discover and perform inference on the state of latent context variables in their environment. In the second project, we describe differences in the temporal stability of instructed task representations in the hippocampus and medial frontal cortex, and show that they rely on persistent activity of single-neurons that lasts for 1-2 orders of magnitude longer than is typically studied in working-memory tasks. In the third project, we study the neural mechanisms of task-switching costs, and show that the state of medial frontal cortical context-representing neurons immediately following instructions is predictive of switching cost. In the fourth project, we evaluate the extent to which frontal cortical task representations inherit the compositional structure of natural language, and attempt to predict the neural representation of novel tasks as patients perform zero-shot generalization in a large task space.
Together, these projects constitute a first step in understanding the neural computations that underlie cognitive processing used by humans to solve complex, multi-task environments.</p