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Pseudorandomness of the Sticky Random Walk
Get PDFWe extend the pseudorandomness of random walks on expander graphs using the sticky random walk. Golowich and Vadhan recently showed that expander random walks can fool all symmetric functions in total variation distance (TVD) up to an O(λ pp) error in total variation distance, where lambda is the second largest eigenvalue of the expander and p is the size of the arbitrary alphabet used to label the vertices. It has been conjectured that the dependency on the pp term is not tight.
In this paper, we resolve the conjecture in the affirmative for a family of expanders. We present a generalization of Guruswami and Kumar's sticky random walk for which prior results predicts a TVD upper bound of O(λ pp) using a Fourier analytic approach. For this family of graphs, we use a combinatorial approach involving the Krawtchouk functions to derive a strengthened TVD of O(λ). Furthermore, we present equivalencies between instances of the generalized sticky random walk, and, using linear-algebraic techniques, show that the generalized sticky random walk is an infinite family of expanders.</p
Multicellular Circuit Design in Mammalian Cells
Get PDFMulticellular circuits control the development of multicellular organisms, through programming processes such as cell proliferation, cell differentiation, cell movement, and cell signaling. A fundamental goal of biology is to understand the design principles of these multicellular circuits, and use these principles to design synthetic multicellular systems for therapeutic purposes. Top-down approaches, for example analyzing embryos bearing genetic mutations, have identified key genes in many multicellular circuits, but are challenging to study these circuits in an isolated context and in a quantitative and systematic manner. An alternative, complementary approach is to engineer or reconstitute multicellular circuits from bottom-up, which allows us to overcome the limitations of top-down approach and gain quantitative insights into multicellular circuit design. In this thesis, we use this bottom-up approach to explore the design principles of two multicellular circuits. In the first project, we took inspiration from two prevalent features from natural multistable circuits, namely competitive protein-protein interactions and positive autoregulation, to design a synthetic multistable circuit architecture called MultiFate. Both in the model and in the experiment, MultiFate circuits generate multiple cellular states, each stable for weeks, allow control over state-switching and state stability, and can be easily expanded to generate more states. In the second project, we use a gradient reconstitution system to systematically analyze a gradient modulation circuit consisting of BMP4 and its modulators, Chordin, Twsg and BMP-1. We found that the circuit can give rise to diverse gradient modulation capabilities. In particular, the full circuit is sufficient for active ligand shuttling and generation of non-monotonic displaced gradient. These multicellular circuits could provide a foundation for engineering synthetic multicellular systems in mammalian cells.</p
A Neural Network Model of an Insect's Wing Hinge Reveals How Steering Muscles Control Flight
Get PDFThe flight system of the fly is remarkable. A fly can execute an escape maneuver in milliseconds, compensate for wing damage when half of the wing is missing, fly in turbulent conditions, and migrate over large distances. While there are many factors that contribute to the robustness and versatility of insect flight, it is the mechanical encoding of wing motion in the wing hinge that allows flies to rapidly and accurately change wing motion over a large dynamic range. The wing hinge consists of several hardened skeletal elements, named sclerites, and a set of twelve steering muscles are attached to some of these components within the exoskeleton. Due to the anatomical complexity and minute size of the sclerites, the way in which the steering muscles alter the mechanical encoding of wing motion in the hinge is poorly understood.
Using genetically encoded calcium indicators and high-speed videography, is is possible to simultaneously image steering muscle activity and wing motion. In order to extract wing pose from the high-speed video frames, an automated tracking algorithm was developed, that used a neural network and model fitting to accurately reconstruct the wing kinematics. The synchronous recordings of wing motion and steering muscle activity were used to train a convolutional neural network that learned to accurately predict the wing kinematics from muscle activity patterns. After training, the convolutional neural network was used to perform virtual experiments, revealing how the steering muscles regulate wing motion. Correlation analysis revealed that the 12 steering muscles have highly correlated activity. The correlation of muscle activity can be approximated well by a 12D-plane, in which all activity has to reside.
To study the function of the sclerites, a bottleneck was introduced in the convolutional neural network. The bottleneck consists of five neurons, or latent parameters, four parameters corresponding to the state of the different sclerites, on which the steering muscles act, and one parameter representing the wingbeat frequency. This so called latent network predicts both the changes in wing motion and muscle activity patterns as a function of sclerite state. The predicted wing motion as a function of sclerite state matches with previous anatomy and electrophysiology studies for the basalare, first axillary and third axillary sclerites. The fourth axillary sclerite has not been studied before, but shows an antagonistic relationship between the hg1,2 and hg3,4 muscles, resulting in a strong decrease and increase, respectively, of stroke amplitude, deviation and wing pitch angles.
By replaying the wing kinematics of the virtual experiments on a dynamically scaled robotic fly, a model of the aerodynamic and inertial control forces as a function of steering muscle activity was constructed. This control force model was subsequently integrated in a state-space system of fly flight, which in turn was integrated in a model predictive control simulation that was used to simulate free flight maneuvers. The body motion, steering muscle activity, and wing kinematics of the model predictive control simulations were strikingly similar to the recorded maneuvers of free-flying flies.
The integrative, multi-disciplinary approach that was used to reveal the mechanical logic of the wing hinge, and the control problem that a fly needs to solve to stay airborne, are both unprecedented in prior literature. The methodologies and models of this study will be a valuable resource in future research on how the fly's nervous system controls the complex behavior that is flight.</p
Modeling Deformations of Active Rods, Ribbons, and Plates
Get PDFSlender structures are mechanical components which have at least one spatial dimension much smaller than another. Some canonical examples are beams, rods, ribbons, plates, and shells. Although these systems have been studied for many centuries, the focus of development has generally been limited to small strains and the onset of buckling modes. Outside of this regime, both geometric and material non-linearities contribute significant complexity to the analytical and computational techniques which can be applied to these problems. Despite this, large deformations demonstrate tremendous potential in engineering applications, particularly with soft materials. This thesis examines various methods of modeling slender structures. We focus on large strain behaviors, often accentuated by spontaneous strains generated with active materials. These systems demonstrate a wide range of interesting and useful behaviors, such as bifurcations, snap-through, and cyclic deformations.</p
Control and State-Estimation of Jump Stochastic Systems by Learning Recurrent Spatiotemporal Patterns
Get PDFThis thesis establishes control and estimation architectures that combine both model-based and model-free methods by theoretically characterizing several types of jump stochastic systems (JSSs), i.e., systems with random and repetitive jump phenomena. By expanding the capabilities of model-based stochastic control and estimation, there is potential for artificial intelligence to be implemented as a supplement to theory-influenced design instead of being used end-to-end. We begin by deriving sufficient conditions for stochastic incremental stability for nonlinear systems perturbed by two types of non-Gaussian noise: 1) shot noise processes represented as compound Poisson processes, and 2) finite-measure Lévy processes constructed as affine combinations of Gaussian white and Poisson shot noise processes. We then present a controller architecture based on a concept we call pattern-learning for prediction (PLP) for discrete-time/discrete-event systems, in which we can take advantage of the fact that the underlying jump process is a sequence of random variables that occurs as repeated patterns of interest. Finally, we demonstrate control and estimation for JSSs in three real-world applications. First, we consider the control of networks with dynamic topology (e.g., power grid with fault-tolerance to downed lines), for which PLP is integrated with variations of the novel system-level synthesis framework for disturbance-rejection. Second, we perform congestion control of vehicle traffic flow over metropolitan intersection networks, for which PLP is extended to pattern-learning with memory and prediction (PLMP) via the inclusion of episodic control, designed to reduce memory consumption by exploiting structural symmetries and temporal repetition in the network. Third, we perform estimation and forecasting (the dual problem to control) for epidemic spread throughout a population network under jump phenomena such as superspreader effects and the emergence of variant viruses. Our results indicate that learning patterns in the jump process makes controller/observer design efficient in data-consumption and computation time, which suggests that it can potentially be used for other JSSs in the real world
Studies on Off-Nominal Rotor Aerodynamics for eVTOL Aircraft
Get PDFAs electric Vertical Takeoff and Landing (eVTOL) aircraft become increasingly common, improved understanding of rotor aerodynamics in off-nominal conditions becomes ever more important. A better fundamental understanding of these effects can help inform vehicle design, leading to lower power consumption and improved performance. This thesis will cover a selection of topics to gain a better understanding of the expected rotor aerodynamics associated with use in this class of vehicle, as well as the development of tools to aid in the studies and an analysis of the impact of the effects.
To consider special effects on a rotor in hover on such a vehicle, Chapter 2 is the study of obstructions in the upstream of a propeller, representing the effects of a wing or fuselage blocking a propeller’s inlet. The next is the effect of forward flight on the forces produced by a rotor. Lifting rotors are often used in eVTOL aircraft as the craft transitions to forward flight, so a study of their performance in forward flight as well as a model are presented in Chapter 3. Having examined rotor-wing interactions in hover and isolated rotor performance in forward flight, the next step is to examine rotor-wing interactions in forward flight. Chapter 6 shows the design of an integrated test stand for studying the aerodynamic interactions between lifting propellers and a wing in low-speed, transitional forward flight, as well as the subsequent results.
This thesis also describes the development and implementation of two tools to aid in the work herein. The first (Chapter 4) is a rapid, low-cost method of extracting the geometry of a propeller using photogrammetry which is subsequently used in simulations. The second (Chapter 5) is low-cost and accessible multi-axis force sensor used in the integrated test stand for propeller-wing interaction studies. To assess the impact of the findings, the experimental results and models developed are then taken into consideration by applying them to models of existing eVTOL aircraft in Chapter 7. The change in modeling of hover and transition performance is studied with and without the additional modeling.</p
Nanoscale Field Emission Devices for High-Temperature and High-Frequency Operation
Get PDFField emission—the quantum-mechanical tunneling of electrons from the surface of a material into vacuum by means of a strong electric field—has been studied for over a century. However, the usage of devices based on this mechanism has been limited to a handful of niche applications such as high-power RF systems and field emission displays. The preference for solid-state devices relies on their low cost, long lifetimes, reduced power consumption, ease of integrability, and simple and scalable fabrication. Nonetheless, with the advent of modern fabrication techniques, it has been possible to build field emission devices with nanoscale dimensions that offer several advantages over traditional semiconductor devices. The use of vacuum allows ballistic transport with no lattice scattering. As device capacitance can be engineered by tuning the geometry, these devices are appealing for high-frequency operation. Vacuum is also inherently immune to harsh operating conditions such as high temperature and radiation, which is desirable for aerospace, nuclear, and military applications. In addition, even though field emission requires substantial electric fields, by exploiting the nanoscale gaps that can be easily fabricated with state-of-the-art lithographic capabilities, we can expect operating voltages comparable to CMOS. Thus, vacuum emission devices have the potential to greatly improve upon the limitations of current technologies.
In this work, we experimentally demonstrate various design paradigms to develop nanoscale field emission devices for high-temperature environments and high-frequency operation. First, we propose suspended lateral two- and four-terminal devices. By removing the underlying solid substrate, we aim to increase the resistance of the leakage current pathways that emerge at elevated temperatures. Tungsten is the chosen electrode material due to its low work function and ability to withstand high temperatures. Our next architecture consists of a multi-tip two-terminal array, which exclusively relies on the inherent fast response of field emission. Due to the strong non-linearity in the emission characteristic, frequency mixing is measured. Lastly, we combine field emission with plasmonics to conceive devices that can be modulated both electrically and optically at telecommunication wavelength. By taking advantage of the strong confinement and significant optical field enhancement of surface plasmon polaritons, we seek to minimize the applied voltages required for field emission as well as the necessary laser powers for photoemission towards the development of high-speed, low-power, nanoscale optoelectronic systems.</p
Ultrafast Optical Control of Order Parameters in Quantum Materials
Get PDFDeveloping protocols to realize quantum phases that are not accessible thermally and to manipulate material properties on demand is one of the central problems of modern condensed matter physics. Impulsive electromagnetic stimulus provides an extensive playground not only to exert desired control over the material macroscopic properties but also to optically detect the underlying microscopic mechanisms. Two indispensable components form the cornerstone to realize these goals: a meticulous comprehension of light-induced phenomena and a suitable and versatile platform.
Abundant photoinduced phenomena emerge upon light irradiation. A collective oscillation of order parameter can be launched and probed in the weak perturbation regime; further increasing light intensity can transiently modulate the free-energy landscape, inducing a suppression, enhancement, reversal, and switch of order parameters; in the strong non-perturbative excitation regime, the system can be driven nonlinearly with microscopic coupling parameters modified. Understanding these light driven emergent phenomena lays the foundation of optical control and novel functionalities.
Quantum materials, embodying a large portfolio of topological and strongly correlated compounds, afford an exceptional venue to realize optical control. Owing to the complex interplay between the charge, spin, orbital, and lattice degrees of freedom, a rich phase diagram can be generated with various phases that are selectively and independently accessible via optical perturbations. They hence offer a wealth of opportunities to not only improve our comprehension of the underlying physics but also develop the next generation of ultrafast technologies.
In Chapter I of this thesis, I will first cover a multitude of light-induced emergent phenomena in quantum materials under the framework of time-dependent Landau theory, Keldysh theory, and Floquet theory, and then introduce several canonical microscopic models to quantitatively rationalize the intra- and interactions between different degrees of freedom in quantum materials. As the necessary theoretical background is established, three main experimental techniques that have been extensively utilized in my research: time-resolved reflectivity and Kerr effect, time-resolved second harmonic generation rotational anisotropy, and coherent phonon spectroscopy will be introduced in Chapter II. In Chapter III, I will demonstrate that a light-induced topological phase transition can be engendered concomitant with an inverse-Peierls structural phase transition in elemental Te. In Chapter IV, I will describe signatures of ultrafast reversal of excitonic order in excitonic insulator candidate Ta2NiSe5 and substantiate a manipulation of the reversal as well as the Higgs mode with tailored light pulses. In Chapter V, a light-induced switch of spin-orbit-coupled quadrupolar order in multiband Mott insulator Ca2RuO4 will be introduced. In Chapter VI, a Keldysh tuning of nonlinear carrier excitation and Floquet bandwidth renormalization in strongly driven Ca2RuO4 will be covered.</p
Mechanical Response of Lattice Structures under High Strain-Rate and Shock Loading
Get PDFLattice structures are a class of architected cellular materials composed of similar unit cells with structural components of rods, plates, or sheets. Current additive manufacturing (AM) techniques allow control and tunability of unit cell geometries, which enable lattice structures to demonstrate exceptional mechanical properties such as high stiffness- and strength-to-mass ratios and energy absorption. Lattice structures exist on two length scales corresponding to the unit cell and continuum material, and therefore demonstrate mechanical behavior dependent on structural geometry and base material. These effects extend to the dynamic regime where lattice structures demonstrate distinct deformation modes under varying strain-rate loading. Experimental investigation of the dynamic and shock compression behavior of lattice structures remains largely unstudied and is the central focus of this thesis where the high strain-rate, transient dynamic, and shock compression behaviors of different topologies of lattice materials are explored.
The first part of this thesis investigates the high strain-rate behavior of lattice structures via polymeric Kelvin lattices with rod- and plate-based geometries and relative densities of 15-30%. High strain-rate behavior is characterized by deformation modes similar to that of low strain-rate behavior. High strain-rate experiments (1000/s) are performed and validated using a viscoelastic polycarbonate split-Hopkinson (Kolsky) pressure bar system coupled with high-speed imaging. Both low and high strain-rate experiments show the formation of a localized deformation band which initiates in the middle of the specimen. Strain-rate effects of lattice specimens are observed to correlate with effects of the base polymer material and mechanical properties depend strongly on the relative density of the lattice specimen and exhibit distinct scaling with geometry type (rod, plate) and loading rate despite a similar unit cell shape. Explicit finite element simulations with a tensile failure material model are then used to validate deformation modes and scaling/property trends, and match those observed in experiments.
The second part of this thesis explores the transient dynamic and transition to shock compression behavior of lattice structures using polymeric lattices with cubic, Kelvin, and octet-truss topologies with relative densities of about 8%. Transient dynamic behavior is characterized by a compaction wave initiating at an impact surface and additional deformation bands with modes similar to low strain-rate modes of deformation. Dynamic testing is conducted through gas gun direct impact experiments (25 - 70 m/s) with high-speed imaging coupled with digital image correlation (DIC) and a polycarbonate Hopkinson pressure bar. Full-field DIC measurements are used to characterize distinct mechanical behaviors induced by topology such as elastic wave speeds, deformation modes, and particle velocities. At lower impact velocities, a transient dynamic response is observed. At higher impact velocities, shock compression behavior occurs and is characterized by a sole compaction wave initiating and propagating from the impact surface of the lattice. One-dimensional continuum shock theory with Eulerian forms of the Rankine-Hugoniot jump conditions is used with full-field measurements to quantify a non-steady shock response and the varied effect of topology on material behaviors.
The final part of this thesis examines the steady-state shock compression behavior of lattice structures through stainless steel 316L (SS316L) octet-truss lattices with relative densities of 10-30%. Powder gun plate impact experiments (270 - 390 m/s) with high-speed imaging and DIC are conducted and reveal a two-wave structure consisting of an elastic precursor wave and a planar compaction (shock) wave. Local shock parameters of lattice structures are defined using full-field DIC measurements and a linear shock velocity (us) versus particle velocity (up) relation is found to approximate measurements with a unit slope and linear fit constant equal to the crushing speed. One-dimensional continuum shock analysis is again performed using Eulerian forms of the Rankine-Hugoniot jump conditions to extract relevant mechanical quantities. Explicit finite element simulations of the lattice specimens using the Johnson-Cook constitutive model exhibit similar shock behavior to experiments. The simulations reveal a linear us-up relation and corresponding Hugoniot calculations agree with experimental trends. Notably, 1D shock theory is applied to simulations without resorting to a us-up relation for the base material, which characterizes this deformation regime and compaction wave as a `structural shock.'
Major contributions of this thesis include experimental demonstration of ranged strain-rate behaviors for lattice structures of various base materials and topologies including low strain-rate, high strain-rate, transient dynamic, and shock compression regimes; use of full-field quantitative visualization techniques for local mechanical behavior and shock analysis; and finally, characterization of a 'structural' shock compression regime in lattice structures.</p
Developing Tools for Neurobiology: The Retina as a Neuropharmacology Testbed & Electrode Pooling to Boost Extracellular Array Recording
Get PDFThis thesis presents two tool development projects for neurobiology and one explorative project to find organizing principles for autism.
The first project (Chap 2, Retina as Probe) was conceived to tackle the problem that there hasn’t been a reliable model system for system-level neuropharmacology. We introduce a testbed for this: the mammalian retina. The retina involves many of the known neurotransmitters and modulators. Yet its synaptic wiring is well understood, and quantitative models exist to explain its input-output functions. One can connect the systems-level effects to the underlying cellular and molecular causes. To demonstrate the retina’s use, we explored the effects of a range of general anesthetics on the light responses of the mouse retina. At sub-anesthetic doses, we found that certain anesthetics exert a paradoxical effect: they increase the light response of some retinal neurons and suppress the response of others. Notably, this occurred for alcohols and ketamine but not for isoflurane. We traced these effects to transmitter release at a specific synapse and, in one case, to a specific presynaptic ion channel. All the anesthetics silenced the output of the retina completely at concentrations similar to their effective dose for anesthesia in humans. Sedatives reduced retinal sensitivity but did not silence it. Finally, we used specific drugs that target hypothesized molecular mechanisms to probe how much they each contribute to anesthesia of the retina.
The second project which attempted to probe the principles of autism (Chap 3) was conceptually a direct extension of the retina as a testbed. Similar to the situation in seeking for what the mechanism of general anesthesia is, the field of autism research also lacks a good testbed but for systemically comparing gene mutation - circuit defect - behavior outcomes. Similarly, we utilized the retina as a platform to identify circuit defects in four different autism model mice and followed through the different mouse line’s behavior readouts using our lab’s maze navigation paradigm. We discovered that the different autism mouse lines varied in the retinal circuits and varied in their navigation preferences. Nevertheless, unlike the anesthetic project, there wasn’t a simple mechanism to explain why or how these differences are coupled together.
The last project, Electrode Pooling, (Chap 4) aimed to boost the yield of extracellular recording electrode arrays with a novel method we named electrode pooling. The per-implant yield of extracellular recording leaped significantly from the order of tens to the order of hundreds when engineers built multiple electrode arrays based on silicon technology to replace tetrode wires. Unfortunately, this yield-per-site is already maxed out with modern silicon technology. The constraint of the yield is mainly biological, as explained in the chapter, and thus could not be further advanced by improving the manufacturing processes of semiconductors. Our solution utilized an approach that multiplexed the array recording sites (not the bottleneck) onto the readout wires with accompanying filters (the actual bottleneck). Specifically, the method proposes intelligently choosing many recording sites that carry signals and connecting them to a single wire via manipulating the switches and later un-mixed with a spike-sorting algorithm. We demonstrated the first proof-of-principle study that shows that one could get more single-neuron recordings per implant site with electrode pooling, and made recommendations on the hardware design that could facilitate the advancement of probes that use pooling algorithms.</p