Towards conditional RNAi : shape and sequence transduction with small conditional RNAs

RNA interference (RNAi) is a powerful biological pathway allowing for sequence-specific knockdown of any gene of interest. While RNAi is a proven tool for probing gene function in biological circuits, it is limited by being constitutively ON and executes the logical operation: silence gene Y. To provide greater control over post-transcriptional gene silencing, we propose engineering a biological logic gate to implement “conditional RNAi.” Such a logic gate would silence gene Y only upon the expression of gene X, a completely unrelated gene, executing the logic: if gene X is transcribed, silence independent gene Y. Silencing of gene Y could be confined to a specific time and/or tissue by appropriately selecting gene X.

To implement the logic of conditional RNAi, we present the design and experimental validation of three nucleic acid self-assembly mechanisms which detect a sub-sequence of mRNA X and produce a Dicer substrate specific to gene Y. We introduce small conditional RNAs (scRNAs) to execute the signal transduction under isothermal conditions. scRNAs are small RNAs which change conformation, leading to both shape and sequence signal transduction, in response to hybridization to an input nucleic acid target. While all three conditional RNAi mechanisms execute the same logical operation, they explore various design alternatives for nucleic acid self-assembly pathways, including the use of duplex and monomer scRNAs, stable versus metastable reactants, multiple methods of nucleation, and 3-way and 4-way branch migration.

We demonstrate the isothermal execution of the conditional RNAi mechanisms in a test tube with recombinant Dicer. These mechanisms execute the logic: if mRNA X is detected, produce a Dicer substrate targeting independent mRNA Y. Only the final Dicer substrate, not the scRNA reactants or intermediates, is efficiently processed by Dicer. Additional work in human whole-cell extracts and a model tissue-culture system delves into both the promise and challenge of implementing conditional RNAi in vivo.

Part 1: Longitudinal static and dynamic effects in semiconductor lasers. Part II: Spectral characteristics of passively mode-locked quantum well lasers

In the first part of this thesis a study of the effect of the longitudinal distribution of optical intensity and electron density on the static and dynamic behavior of semiconductor lasers is performed. A static model for above threshold operation of a single mode laser, consisting of multiple active and passive sections, is developed by calculating the longitudinal optical intensity distribution and electron density distribution in a self-consistent manner. Feedback from an index and gain Bragg grating is included, as well as feedback from discrete reflections at interfaces and facets. Longitudinal spatial holeburning is analyzed by including the dependence of the gain and the refractive index on the electron density. The mechanisms of spatial holeburning in quarter wave shifted DFB lasers are analyzed. A new laser structure with a uniform optical intensity distribution is introduced and an implementation is simulated, resulting in a large reduction of the longitudinal spatial holeburning effect.

A dynamic small-signal model is then developed by including the optical intensity and electron density distribution, as well as the dependence of the grating coupling coefficients on the electron density. Expressions are derived for the intensity and frequency noise spectrum, the spontaneous emission rate into the lasing mode, the linewidth enhancement factor, and the AM and FM modulation response. Different chirp components are identified in the FM response, and a new adiabatic chirp component is discovered. This new adiabatic chirp component is caused by the nonuniform longitudinal distributions, and is found to dominate at low frequencies. Distributed feedback lasers with partial gain coupling are analyzed, and it is shown how the dependence of the grating coupling coefficients on the electron density can result in an enhancement of the differential gain with an associated enhancement in modulation bandwidth and a reduction in chirp.

In the second part, spectral characteristics of passively mode-locked two-section multiple quantum well laser coupled to an external cavity are studied. Broad-band wavelength tuning using an external grating is demonstrated for the first time in passively mode-locked semiconductor lasers. A record tuning range of 26 nm is measured, with pulse widths of typically a few picosecond and time-bandwidth products of more than 10 times the transform limit. It is then demonstrated that these large time-bandwidth products are due to a strong linear upchirp, by performing pulse compression by a factor of 15 to a record pulse widths as low 320 fs.

A model for pulse propagation through a saturable medium with self-phase-modulation, due to the a-parameter, is developed for quantum well material, including the frequency dependence of the gain medium. This model is used to simulate two-section devices coupled to an external cavity. When no self-phase-modulation is present, it is found that the pulses are asymmetric with a sharper rising edge, that the pulse tails have an exponential behavior, and that the transform limit is 0.3. Inclusion of self-phase-modulation results in a linear upchirp imprinted on the pulse after each round-trip. This linear upchirp is due to a combination of self-phase-modulation in a gain section and absorption of the leading edge of the pulse in the saturable absorber.

Conditional independence in quantum many-body systems

In this thesis, I will discuss how information-theoretic arguments can be used to produce sharp bounds in the studies of quantum many-body systems. The main advantage of this approach, as opposed to the conventional field-theoretic argument, is that it depends very little on the precise form of the Hamiltonian. The main idea behind this thesis lies on a number of results concerning the structure of quantum states that are conditionally independent. Depending on the application, some of these statements are generalized to quantum states that are approximately conditionally independent. These structures can be readily used in the studies of gapped quantum many-body systems, especially for the ones in two spatial dimensions. A number of rigorous results are derived, including (i) a universal upper bound for a maximal number of topologically protected states that is expressed in terms of the topological entanglement entropy, (ii) a first-order perturbation bound for the topological entanglement entropy that decays superpolynomially with the size of the subsystem, and (iii) a correlation bound between an arbitrary local operator and a topological operator constructed from a set of local reduced density matrices. I also introduce exactly solvable models supported on a three-dimensional lattice that can be used as a reliable quantum memory.

Topics in gravitational-wave science : macroscopic quantum mechanics and black hole physics

The theories of relativity and quantum mechanics, the two most important physics discoveries of the 20th century, not only revolutionized our understanding of the nature of space-time and the way matter exists and interacts, but also became the building blocks of what we currently know as modern physics. My thesis studies both subjects in great depths --- this intersection takes place in gravitational-wave physics.

Gravitational waves are "ripples of space-time", long predicted by general relativity. Although indirect evidence of gravitational waves has been discovered from observations of binary pulsars, direct detection of these waves is still actively being pursued. An international array of laser interferometer gravitational-wave detectors has been constructed in the past decade, and a first generation of these detectors has taken several years of data without a discovery. At this moment, these detectors are being upgraded into second-generation configurations, which will have ten times better sensitivity. Kilogram-scale test masses of these detectors, highly isolated from the environment, are probed continuously by photons. The sensitivity of such a quantum measurement can often be limited by the Heisenberg Uncertainty Principle, and during such a measurement, the test masses can be viewed as evolving through a sequence of nearly pure quantum states.

The first part of this thesis (Chapter 2) concerns how to minimize the adverse effect of thermal fluctuations on the sensitivity of advanced gravitational detectors, thereby making them closer to being quantum-limited. My colleagues and I present a detailed analysis of coating thermal noise in advanced gravitational-wave detectors, which is the dominant noise source of Advanced LIGO in the middle of the detection frequency band. We identified the two elastic loss angles, clarified the different components of the coating Brownian noise, and obtained their cross spectral densities.

The second part of this thesis (Chapters 3-7) concerns formulating experimental concepts and analyzing experimental results that demonstrate the quantum mechanical behavior of macroscopic objects - as well as developing theoretical tools for analyzing quantum measurement processes. In Chapter 3, we study the open quantum dynamics of optomechanical experiments in which a single photon strongly influences the quantum state of a mechanical object. We also explain how to engineer the mechanical oscillator's quantum state by modifying the single photon's wave function.

In Chapters 4-5, we build theoretical tools for analyzing the so-called "non-Markovian" quantum measurement processes. Chapter 4 establishes a mathematical formalism that describes the evolution of a quantum system (the plant), which is coupled to a non-Markovian bath (i.e., one with a memory) while at the same time being under continuous quantum measurement (by the probe field). This aims at providing a general framework for analyzing a large class of non-Markovian measurement processes. Chapter 5 develops a way of characterizing the non-Markovianity of a bath (i.e.,whether and to what extent the bath remembers information about the plant) by perturbing the plant and watching for changes in the its subsequent evolution. Chapter 6 re-analyzes a recent measurement of a mechanical oscillator's zero-point fluctuations, revealing nontrivial correlation between the measurement device's sensing noise and the quantum rack-action noise.

Chapter 7 describes a model in which gravity is classical and matter motions are quantized, elaborating how the quantum motions of matter are affected by the fact that gravity is classical. It offers an experimentally plausible way to test this model (hence the nature of gravity) by measuring the center-of-mass motion of a macroscopic object.

The most promising gravitational waves for direct detection are those emitted from highly energetic astrophysical processes, sometimes involving black holes - a type of object predicted by general relativity whose properties depend highly on the strong-field regime of the theory. Although black holes have been inferred to exist at centers of galaxies and in certain so-called X-ray binary objects, detecting gravitational waves emitted by systems containing black holes will offer a much more direct way of observing black holes, providing unprecedented details of space-time geometry in the black-holes' strong-field region.

The third part of this thesis (Chapters 8-11) studies black-hole physics in connection with gravitational-wave detection.

Chapter 8 applies black hole perturbation theory to model the dynamics of a light compact object orbiting around a massive central Schwarzschild black hole. In this chapter, we present a Hamiltonian formalism in which the low-mass object and the metric perturbations of the background spacetime are jointly evolved. Chapter 9 uses WKB techniques to analyze oscillation modes (quasi-normal modes or QNMs) of spinning black holes. We obtain analytical approximations to the spectrum of the weakly-damped QNMs, with relative error O(1/L^2), and connect these frequencies to geometrical features of spherical photon orbits in Kerr spacetime. Chapter 11 focuses mainly on near-extremal Kerr black holes, we discuss a bifurcation in their QNM spectra for certain ranges of (l,m) (the angular quantum numbers) as a/M → 1. With tools prepared in Chapter 9 and 10, in Chapter 11 we obtain an analytical approximate for the scalar Green function in Kerr spacetime.

Lattice quantum codes and exotic topological phases of matter

This thesis addresses whether it is possible to build a robust memory device for quantum information. Many schemes for fault-tolerant quantum information processing have been developed so far, one of which, called topological quantum computation, makes use of degrees of freedom that are inherently insensitive to local errors. However, this scheme is not so reliable against thermal errors. Other fault-tolerant schemes achieve better reliability through active error correction, but incur a substantial overhead cost. Thus, it is of practical importance and theoretical interest to design and assess fault-tolerant schemes that work well at finite temperature without active error correction.

In this thesis, a three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite temperature is possible, at least to some extent. When quantum information is encoded into a highly entangled ground state of this model and subjected to thermal errors, the errors remain easily correctable for a long time without any active intervention, because a macroscopic energy barrier keeps the errors well localized. As a result, stored quantum information can be retrieved faithfully for a memory time which grows exponentially with the square of the inverse temperature. In contrast, for previously known types of topological quantum storage in three or fewer spatial dimensions the memory time scales exponentially with the inverse temperature, rather than its square.

This spin model exhibits a previously unexpected topological quantum order, in which ground states are locally indistinguishable, pointlike excitations are immobile, and the immobility is not affected by small perturbations of the Hamiltonian. The degeneracy of the ground state, though also insensitive to perturbations, is a complicated number-theoretic function of the system size, and the system bifurcates into multiple noninteracting copies of itself under real-space renormalization group transformations. The degeneracy, the excitations, and the renormalization group flow can be analyzed using a framework that exploits the spin model's symmetry and some associated free resolutions of modules over polynomial algebras.

The interplay of localization and interactions in quantum many-body systems

Disorder and interactions both play crucial roles in quantum transport. Decades ago, Mott showed that electron-electron interactions can lead to insulating behavior in materials that conventional band theory predicts to be conducting. Soon thereafter, Anderson demonstrated that disorder can localize a quantum particle through the wave interference phenomenon of Anderson localization. Although interactions and disorder both separately induce insulating behavior, the interplay of these two ingredients is subtle and often leads to surprising behavior at the periphery of our current understanding. Modern experiments probe these phenomena in a variety of contexts (e.g. disordered superconductors, cold atoms, photonic waveguides, etc.); thus, theoretical and numerical advancements are urgently needed. In this thesis, we report progress on understanding two contexts in which the interplay of disorder and interactions is especially important.

The first is the so-called “dirty” or random boson problem. In the past decade, a strong-disorder renormalization group (SDRG) treatment by Altman, Kafri, Polkovnikov, and Refael has raised the possibility of a new unstable fixed point governing the superfluid-insulator transition in the one-dimensional dirty boson problem. This new critical behavior may take over from the weak-disorder criticality of Giamarchi and Schulz when disorder is sufficiently strong. We analytically determine the scaling of the superfluid susceptibility at the strong-disorder fixed point and connect our analysis to recent Monte Carlo simulations by Hrahsheh and Vojta. We then shift our attention to two dimensions and use a numerical implementation of the SDRG to locate the fixed point governing the superfluid-insulator transition there. We identify several universal properties of this transition, which are fully independent of the microscopic features of the disorder.

The second focus of this thesis is the interplay of localization and interactions in systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting (“ergodic”) phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.

Quantum error correction with biased noise

Quantum computing offers powerful new techniques for speeding up the calculation of many classically intractable problems. Quantum algorithms can allow for the efficient simulation of physical systems, with applications to basic research, chemical modeling, and drug discovery; other algorithms have important implications for cryptography and internet security.

At the same time, building a quantum computer is a daunting task, requiring the coherent manipulation of systems with many quantum degrees of freedom while preventing environmental noise from interacting too strongly with the system. Fortunately, we know that, under reasonable assumptions, we can use the techniques of quantum error correction and fault tolerance to achieve an arbitrary reduction in the noise level.

In this thesis, we look at how additional information about the structure of noise, or "noise bias," can improve or alter the performance of techniques in quantum error correction and fault tolerance. In Chapter 2, we explore the possibility of designing certain quantum gates to be extremely robust with respect to errors in their operation. This naturally leads to structured noise where certain gates can be implemented in a protected manner, allowing the user to focus their protection on the noisier unprotected operations.

In Chapter 3, we examine how to tailor error-correcting codes and fault-tolerant quantum circuits in the presence of dephasing biased noise, where dephasing errors are far more common than bit-flip errors. By using an appropriately asymmetric code, we demonstrate the ability to improve the amount of error reduction and decrease the physical resources required for error correction.

In Chapter 4, we analyze a variety of protocols for distilling magic states, which enable universal quantum computation, in the presence of faulty Clifford operations. Here again there is a hierarchy of noise levels, with a fixed error rate for faulty gates, and a second rate for errors in the distilled states which decreases as the states are distilled to better quality. The interplay of of these different rates sets limits on the achievable distillation and how quickly states converge to that limit.

Design, specification, and synthesis of aircraft electric power systems control logic

Cyber-physical systems integrate computation, networking, and physical processes. Substantial research challenges exist in the design and verification of such large-scale, distributed sensing, ac- tuation, and control systems. Rapidly improving technology and recent advances in control theory, networked systems, and computer science give us the opportunity to drastically improve our approach to integrated flow of information and cooperative behavior. Current systems rely on text-based spec- ifications and manual design. Using new technology advances, we can create easier, more efficient, and cheaper ways of developing these control systems. This thesis will focus on design considera- tions for system topologies, ways to formally and automatically specify requirements, and methods to synthesize reactive control protocols, all within the context of an aircraft electric power system as a representative application area.

This thesis consists of three complementary parts: synthesis, specification, and design. The first section focuses on the synthesis of central and distributed reactive controllers for an aircraft elec- tric power system. This approach incorporates methodologies from computer science and control. The resulting controllers are correct by construction with respect to system requirements, which are formulated using the specification language of linear temporal logic (LTL). The second section addresses how to formally specify requirements and introduces a domain-specific language for electric power systems. A software tool automatically converts high-level requirements into LTL and synthesizes a controller.

The final sections focus on design space exploration. A design methodology is proposed that uses mixed-integer linear programming to obtain candidate topologies, which are then used to synthesize controllers. The discrete-time control logic is then verified in real-time by two methods: hardware and simulation. Finally, the problem of partial observability and dynamic state estimation is ex- plored. Given a set placement of sensors on an electric power system, measurements from these sensors can be used in conjunction with control logic to infer the state of the system.

Quantum optomechanics with silicon nanostructures

Mechanical resonators are the most basic and ubiquitous physical systems known. In on-chip form, they are used to process high frequency signals in every cell phone, television, and laptop. They have also been in the last few decades in different shapes and forms, a critical part of progress in quantum information sciences with kilogram-scale mirrors for gravitational wave detection measuring motion at its quantum limits, and the motion of single ions being used to link qubits for quantum computation.

Optomechanics is a field primarily concerned with coupling light to the motion of mechanical structures. This thesis contains descriptions of recent work with mechanical systems in the megahertz to gigahertz frequency range, formed by nanofabricating novel photonic/phononic structures on a silicon chip. These structures are designed to have both optical and mechanical resonances, and laser light is used to address and manipulate their motional degrees of freedom through radiation pressure forces. We laser cool these mechanical resonators to their ground states, and observe for the first time the quantum zero-point motion of a nanomechanical resonator. Conversely, we show that engineered mechanical resonances drastically modify the optical response of our structures, creating large effective optical nonlinearities not present in bulk silicon. We experimentally demonstrate aspects of these nonlinearities by proposing and observing ``electromagnetically induced transparency'' and light slowed down to 6 m/s, as well as wavelength conversion, and generation of nonclassical optical radiation. Finally, the application of optomechanics to longstanding problems in quantum and classical communications are proposed and investigated.

Interacting single atoms with nanophotonics for chip-integrated quantum networks

Underlying matter and light are their building blocks of tiny atoms and photons. The ability to control and utilize matter-light interactions down to the elementary single atom and photon level at the nano-scale opens up exciting studies at the frontiers of science with applications in medicine, energy, and information technology. Of these, an intriguing front is the development of quantum networks where N >> 1 single-atom nodes are coherently linked by single photons, forming a collective quantum entity potentially capable of performing quantum computations and simulations. Here, a promising approach is to use optical cavities within the setting of cavity quantum electrodynamics (QED). However, since its first realization in 1992 by Kimble et al., current proof-of-principle experiments have involved just one or two conventional cavities. To move beyond to N >> 1 nodes, in this thesis we investigate a platform born from the marriage of cavity QED and nanophotonics, where single atoms at ~100 nm near the surfaces of lithographically fabricated dielectric photonic devices can strongly interact with single photons, on a chip. Particularly, we experimentally investigate three main types of devices: microtoroidal optical cavities, optical nanofibers, and nanophotonic crystal based structures. With a microtoroidal cavity, we realized a robust and efficient photon router where single photons are extracted from an incident coherent state of light and redirected to a separate output with high efficiency. We achieved strong single atom-photon coupling with atoms located ~100 nm near the surface of a microtoroid, which revealed important aspects in the atom dynamics and QED of these systems including atom-surface interaction effects. We present a method to achieve state-insensitive atom trapping near optical nanofibers, critical in nanophotonic systems where electromagnetic fields are tightly confined. We developed a system that fabricates high quality nanofibers with high controllability, with which we experimentally demonstrate a state-insensitive atom trap. We present initial investigations on nanophotonic crystal based structures as a platform for strong atom-photon interactions. The experimental advances and theoretical investigations carried out in this thesis provide a framework for and open the door to strong single atom-photon interactions using nanophotonics for chip-integrated quantum networks.

Quantum simulation of enzyme catalysis

Separating the dynamics of variables that evolve on different timescales is a common assumption in exploring complex systems, and a great deal of progress has been made in understanding chemical systems by treating independently the fast processes of an activated chemical species from the slower processes that proceed activation. Protein motion underlies all biocatalytic reactions, and understanding the nature of this motion is central to understanding how enzymes catalyze reactions with such specificity and such rate enhancement. This understanding is challenged by evidence of breakdowns in the separability of timescales of dynamics in the active site form motions of the solvating protein. Quantum simulation methods that bridge these timescales by simultaneously evolving quantum and classical degrees of freedom provide an important method on which to explore this breakdown. In the following dissertation, three problems of enzyme catalysis are explored through quantum simulation.

Fermionic quantum systems. Part I: Phase transitions in quantum dots. Part II: Nuclear matter on a lattice

In the first part I perform Hartree-Fock calculations to show that quantum dots (i.e., two-dimensional systems of up to twenty interacting electrons in an external parabolic potential) undergo a gradual transition to a spin-polarized Wigner crystal with increasing magnetic field strength. The phase diagram and ground state energies have been determined. I tried to improve the ground state of the Wigner crystal by introducing a Jastrow ansatz for the wave function and performing a variational Monte Carlo calculation. The existence of so called magic numbers was also investigated. Finally, I also calculated the heat capacity associated with the rotational degree of freedom of deformed many-body states and suggest an experimental method to detect Wigner crystals.

The second part of the thesis investigates infinite nuclear matter on a cubic lattice. The exact thermal formalism describes nucleons with a Hamiltonian that accommodates on-site and next-neighbor parts of the central, spin-exchange and isospin-exchange interaction. Using auxiliary field Monte Carlo methods, I show that energy and basic saturation properties of nuclear matter can be reproduced. A first order phase transition from an uncorrelated Fermi gas to a clustered system is observed by computing mechanical and thermodynamical quantities such as compressibility, heat capacity, entropy and grand potential. The structure of the clusters is investigated with the help two-body correlations. I compare symmetry energy and first sound velocities with literature and find reasonable agreement. I also calculate the energy of pure neutron matter and search for a similar phase transition, but the survey is restricted by the infamous Monte Carlo sign problem. Also, a regularization scheme to extract potential parameters from scattering lengths and effective ranges is investigated.

Branes and supersymmetric quantum field theories

Since the discovery of D-branes as non-perturbative, dynamic objects in string theory, various configurations of branes in type IIA/B string theory and M-theory have been considered to study their low-energy dynamics described by supersymmetric quantum field theories.

One example of such a construction is based on the description of Seiberg-Witten curves of four-dimensional N = 2 supersymmetric gauge theories as branes in type IIA string theory and M-theory. This enables us to study the gauge theories in strongly-coupled regimes. Spectral networks are another tool for utilizing branes to study non-perturbative regimes of two- and four-dimensional supersymmetric theories. Using spectral networks of a Seiberg-Witten theory we can find its BPS spectrum, which is protected from quantum corrections by supersymmetry, and also the BPS spectrum of a related two-dimensional N = (2,2) theory whose (twisted) superpotential is determined by the Seiberg-Witten curve. When we don’t know the perturbative description of such a theory, its spectrum obtained via spectral networks is a useful piece of information. In this thesis we illustrate these ideas with examples of the use of Seiberg-Witten curves and spectral networks to understand various two- and four-dimensional supersymmetric theories.

First, we examine how the geometry of a Seiberg-Witten curve serves as a useful tool for identifying various limits of the parameters of the Seiberg-Witten theory, including Argyres-Seiberg duality and Argyres-Douglas fixed points. Next, we consider the low-energy limit of a two-dimensional N = (2, 2) supersymmetric theory from an M-theory brane configuration whose (twisted) superpotential is determined by the geometry of the branes. We show that, when the two-dimensional theory flows to its infra-red fixed point, particular cases realize Kazama-Suzuki coset models. We also study the BPS spectrum of an Argyres-Douglas type superconformal field theory on the Coulomb branch by using its spectral networks. We provide strong evidence of the equivalence of superconformal field theories from different string-theoretic constructions by comparing their BPS spectra.

Control of dynamical systems with temporal logic specifications

This thesis is motivated by safety-critical applications involving autonomous air, ground, and space vehicles carrying out complex tasks in uncertain and adversarial environments. We use temporal logic as a language to formally specify complex tasks and system properties. Temporal logic specifications generalize the classical notions of stability and reachability that are studied in the control and hybrid systems communities. Given a system model and a formal task specification, the goal is to automatically synthesize a control policy for the system that ensures that the system satisfies the specification. This thesis presents novel control policy synthesis algorithms for optimal and robust control of dynamical systems with temporal logic specifications. Furthermore, it introduces algorithms that are efficient and extend to high-dimensional dynamical systems.

The first contribution of this thesis is the generalization of a classical linear temporal logic (LTL) control synthesis approach to optimal and robust control. We show how we can extend automata-based synthesis techniques for discrete abstractions of dynamical systems to create optimal and robust controllers that are guaranteed to satisfy an LTL specification. Such optimal and robust controllers can be computed at little extra computational cost compared to computing a feasible controller.

The second contribution of this thesis addresses the scalability of control synthesis with LTL specifications. A major limitation of the standard automaton-based approach for control with LTL specifications is that the automaton might be doubly-exponential in the size of the LTL specification. We introduce a fragment of LTL for which one can compute feasible control policies in time polynomial in the size of the system and specification. Additionally, we show how to compute optimal control policies for a variety of cost functions, and identify interesting cases when this can be done in polynomial time. These techniques are particularly relevant for online control, as one can guarantee that a feasible solution can be found quickly, and then iteratively improve on the quality as time permits.

The final contribution of this thesis is a set of algorithms for computing feasible trajectories for high-dimensional, nonlinear systems with LTL specifications. These algorithms avoid a potentially computationally-expensive process of computing a discrete abstraction, and instead compute directly on the system's continuous state space. The first method uses an automaton representing the specification to directly encode a series of constrained-reachability subproblems, which can be solved in a modular fashion by using standard techniques. The second method encodes an LTL formula as mixed-integer linear programming constraints on the dynamical system. We demonstrate these approaches with numerical experiments on temporal logic motion planning problems with high-dimensional (10+ states) continuous systems.

Signal transduction, regulation, and developmental logic of EGFR signalling in C. elegans

RTKs-mediated signaling systems and the pathways with which they interact (e.g., those initiated by G protein-mediated signaling) involve a highly cooperative network that sense a large number of cellular inputs and then integrate, amplify, and process this information to orchestrate an appropriate set of cellular responses. The responses include virtually all aspects of cell function, from the most fundamental (proliferation, differentiation) to the most specialized (movement, metabolism, chemosensation). The basic tenets of RTK signaling system seem rather well established. Yet, new pathways and even new molecular players continue to be discovered. Although we believe that many of the essential modules of RTK signaling system are rather well understood, we have relatively little knowledge of the extent of interaction among these modules and their overall quantitative importance.

My research has encompassed the study of both positive and negative signaling by RTKs in C. elegans. I identified the C. elegans S0S-1 gene and showed that it is necessary for multiple RAS-mediated developmental signals. In addition, I demonstrated that there is a SOS-1-independent signaling during RAS-mediated vulval differentiation. By assessing signal outputs from various triple mutants, I have concluded that this SOS-1-independent signaling is not mediated by PTP-2/SHP-2 or the removal of inhibition by GAP-1/ RasGAP and it is not under regulation by SLI-1/Cb1. I speculate that there is either another exchange factor for RASor an as yet unidentified signaling pathway operating during RAS-mediated vulval induction in C. elegans.

In an attempt to uncover the molecular mechanisms of negative regulation of EGFR signaling by SLI-1/Cb1, I and two other colleagues codiscovered that RING finger domain of SLI-1 is partially dispensable for activity. This structure-function analysis shows that there is an ubiquitin protein ligase-independent activity for SLI-1 in regulating EGFR signaling. Further, we identified an inhibitory tyrosine of LET-23/ EGFR requiring sli-1(+)for its effects: removal of this tyrosine closely mimics loss of sli-1 but not loss of other negative regulator function.

By comparative analysis of two RTK pathways with similar signaling mechanisms, I have found that clr-1, a previously identified negative regulator of egl-15 mediated FGFR signaling, is also involved in let-23 EGFR signaling. The success of this approach promises a similar reciprocal test and could potentially extend to the study of other signaling pathways with similar signaling logic.

Finally, by correlating the developmental expression of lin-3 EGF to let-23 EGFR signaling activity, I demonstrated the existence of reciprocal EGF signaling in coordinating the morphogenesis of epithelia. This developmental logic of EGF signaling could provide a basis to understand a universal mechanism for organogenesis.