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.

Engineering nucleic acid mechanisms for regulation and readout of gene expression : conditional Dicer substrate formation and sensitive multiplexed northern blots

Nucleic acids are most commonly associated with the genetic code, transcription and gene expression. Recently, interest has grown in engineering nucleic acids for biological applications such as controlling or detecting gene expression. The natural presence and functionality of nucleic acids within living organisms coupled with their thermodynamic properties of base-pairing make them ideal for interfacing (and possibly altering) biological systems. We use engineered small conditional RNA or DNA (scRNA, scDNA, respectively) molecules to control and detect gene expression. Three novel systems are presented: two for conditional down-regulation of gene expression via RNA interference (RNAi) and a third system for simultaneous sensitive detection of multiple RNAs using labeled scRNAs.

RNAi is a powerful tool to study genetic circuits by knocking down a gene of interest. RNAi executes the logic: If gene Y is detected, silence gene Y. The fact that detection and silencing are restricted to the same gene means that RNAi is constitutively on. This poses a significant limitation when spatiotemporal control is needed. In this work, we engineered small nucleic acid molecules that execute the logic: If mRNA X is detected, form a Dicer substrate that targets independent mRNA Y for silencing. This is a step towards implementing the logic of conditional RNAi: If gene X is detected, silence gene Y. We use scRNAs and scDNAs to engineer signal transduction cascades that produce an RNAi effector molecule in response to hybridization to a nucleic acid target X. The first mechanism is solely based on hybridization cascades and uses scRNAs to produce a double-stranded RNA (dsRNA) Dicer substrate against target gene Y. The second mechanism is based on hybridization of scDNAs to detect a nucleic acid target and produce a template for transcription of a short hairpin RNA (shRNA) Dicer substrate against target gene Y. Test-tube studies for both mechanisms demonstrate that the output Dicer substrate is produced predominantly in the presence of a correct input target and is cleaved by Dicer to produce a small interfering RNA (siRNA). Both output products can lead to gene knockdown in tissue culture. To date, signal transduction is not observed in cells; possible reasons are explored.

Signal transduction cascades are composed of multiple scRNAs (or scDNAs). The need to study multiple molecules simultaneously has motivated the development of a highly sensitive method for multiplexed northern blots. The core technology of our system is the utilization of a hybridization chain reaction (HCR) of scRNAs as the detection signal for a northern blot. To achieve multiplexing (simultaneous detection of multiple genes), we use fluorescently tagged scRNAs. Moreover, by using radioactive labeling of scRNAs, the system exhibits a five-fold increase, compared to the literature, in detection sensitivity. Sensitive multiplexed northern blot detection provides an avenue for exploring the fate of scRNAs and scDNAs in tissue culture.

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.

On the solution of first excursion problems by simulation with applications to probabilistic seismic performance assessment

In a probabilistic assessment of the performance of structures subjected to uncertain environmental loads such as earthquakes, an important problem is to determine the probability that the structural response exceeds some specified limits within a given duration of interest. This problem is known as the first excursion problem, and it has been a challenging problem in the theory of stochastic dynamics and reliability analysis. In spite of the enormous amount of attention the problem has received, there is no procedure available for its general solution, especially for engineering problems of interest where the complexity of the system is large and the failure probability is small.

The application of simulation methods to solving the first excursion problem is investigated in this dissertation, with the objective of assessing the probabilistic performance of structures subjected to uncertain earthquake excitations modeled by stochastic processes. From a simulation perspective, the major difficulty in the first excursion problem comes from the large number of uncertain parameters often encountered in the stochastic description of the excitation. Existing simulation tools are examined, with special regard to their applicability in problems with a large number of uncertain parameters. Two efficient simulation methods are developed to solve the first excursion problem. The first method is developed specifically for linear dynamical systems, and it is found to be extremely efficient compared to existing techniques. The second method is more robust to the type of problem, and it is applicable to general dynamical systems. It is efficient for estimating small failure probabilities because the computational effort grows at a much slower rate with decreasing failure probability than standard Monte Carlo simulation. The simulation methods are applied to assess the probabilistic performance of structures subjected to uncertain earthquake excitation. Failure analysis is also carried out using the samples generated during simulation, which provide insight into the probable scenarios that will occur given that a structure fails.

Quantifying Earthquake Collapse Risk of Tall Steel Moment Frame Buildings Using Rupture-to-Rafters Simulations

There is a sparse number of credible source models available from large-magnitude past earthquakes. A stochastic source model generation algorithm thus becomes necessary for robust risk quantification using scenario earthquakes. We present an algorithm that combines the physics of fault ruptures as imaged in laboratory earthquakes with stress estimates on the fault constrained by field observations to generate stochastic source models for large-magnitude (Mw 6.0-8.0) strike-slip earthquakes. The algorithm is validated through a statistical comparison of synthetic ground motion histories from a stochastically generated source model for a magnitude 7.90 earthquake and a kinematic finite-source inversion of an equivalent magnitude past earthquake on a geometrically similar fault. The synthetic dataset comprises of three-component ground motion waveforms, computed at 636 sites in southern California, for ten hypothetical rupture scenarios (five hypocenters, each with two rupture directions) on the southern San Andreas fault. A similar validation exercise is conducted for a magnitude 6.0 earthquake, the lower magnitude limit for the algorithm. Additionally, ground motions from the Mw7.9 earthquake simulations are compared against predictions by the Campbell-Bozorgnia NGA relation as well as the ShakeOut scenario earthquake. The algorithm is then applied to generate fifty source models for a hypothetical magnitude 7.9 earthquake originating at Parkfield, with rupture propagating from north to south (towards Wrightwood), similar to the 1857 Fort Tejon earthquake. Using the spectral element method, three-component ground motion waveforms are computed in the Los Angeles basin for each scenario earthquake and the sensitivity of ground shaking intensity to seismic source parameters (such as the percentage of asperity area relative to the fault area, rupture speed, and risetime) is studied.

Under plausible San Andreas fault earthquakes in the next 30 years, modeled using the stochastic source algorithm, the performance of two 18-story steel moment frame buildings (UBC 1982 and 1997 designs) in southern California is quantified. The approach integrates rupture-to-rafters simulations into the PEER performance based earthquake engineering (PBEE) framework. Using stochastic sources and computational seismic wave propagation, three-component ground motion histories at 636 sites in southern California are generated for sixty scenario earthquakes on the San Andreas fault. The ruptures, with moment magnitudes in the range of 6.0-8.0, are assumed to occur at five locations on the southern section of the fault. Two unilateral rupture propagation directions are considered. The 30-year probabilities of all plausible ruptures in this magnitude range and in that section of the fault, as forecast by the United States Geological Survey, are distributed among these 60 earthquakes based on proximity and moment release. The response of the two 18-story buildings hypothetically located at each of the 636 sites under 3-component shaking from all 60 events is computed using 3-D nonlinear time-history analysis. Using these results, the probability of the structural response exceeding Immediate Occupancy (IO), Life-Safety (LS), and Collapse Prevention (CP) performance levels under San Andreas fault earthquakes over the next thirty years is evaluated.

Furthermore, the conditional and marginal probability distributions of peak ground velocity (PGV) and displacement (PGD) in Los Angeles and surrounding basins due to earthquakes occurring primarily on the mid-section of southern San Andreas fault are determined using Bayesian model class identification. Simulated ground motions at sites within 55-75km from the source from a suite of 60 earthquakes (Mw 6.0 − 8.0) primarily rupturing mid-section of San Andreas fault are considered for PGV and PGD data.

1. Ultrasonic studies of binary liquid structure in the critical region. Theory and experiment for the 2,6-lutidine/water system. 2. Hartree-Fock calculations of electric polarizabilities of some simple atoms and molecules, and their practicality. 3. Calculation of vibrational transition probabilities in collinear atom-diatom and diatom-diatom collisions with Lennard-Jones interaction

Part 1. Many interesting visual and mechanical phenomena occur in the critical region of fluids, both for the gas-liquid and liquid-liquid transitions. The precise thermodynamic and transport behavior here has some broad consequences for the molecular theory of liquids. Previous studies in this laboratory on a liquid-liquid critical mixture via ultrasonics supported a basically classical analysis of fluid behavior by M. Fixman (e. g., the free energy is assumed analytic in intensive variables in the thermodynamics)--at least when the fluid is not too close to critical. A breakdown in classical concepts is evidenced close to critical, in some well-defined ways. We have studied herein a liquid-liquid critical system of complementary nature (possessing a lower critical mixing or consolute temperature) to all previous mixtures, to look for new qualitative critical behavior. We did not find such new behavior in the ultrasonic absorption ascribable to the critical fluctuations, but we did find extra absorption due to chemical processes (yet these are related to the mixing behavior generating the lower consolute point). We rederived, corrected, and extended Fixman's analysis to interpret our experimental results in these more complex circumstances. The entire account of theory and experiment is prefaced by an extensive introduction recounting the general status of liquid state theory. The introduction provides a context for our present work, and also points out problems deserving attention. Interest in these problems was stimulated by this work but also by work in Part 3.

Part 2. Among variational theories of electronic structure, the Hartree-Fock theory has proved particularly valuable for a practical understanding of such properties as chemical binding, electric multipole moments, and X-ray scattering intensity. It also provides the most tractable method of calculating first-order properties under external or internal one-electron perturbations, either developed explicitly in orders of perturbation theory or in the fully self-consistent method. The accuracy and consistency of first-order properties are poorer than those of zero-order properties, but this is most often due to the use of explicit approximations in solving the perturbed equations, or to inadequacy of the variational basis in size or composition. We have calculated the electric polarizabilities of H₂, He, Li, Be, LiH, and N₂ by Hartree-Fock theory, using exact perturbation theory or the fully self-consistent method, as dictated by convenience. By careful studies on total basis set composition, we obtained good approximations to limiting Hartree-Fock values of polarizabilities with bases of reasonable size. The values for all species, and for each direction in the molecular cases, are within 8% of experiment, or of best theoretical values in the absence of the former. Our results support the use of unadorned Hartree-Pock theory for static polarizabilities needed in interpreting electron-molecule scattering data, collision-induced light scattering experiments, and other phenomena involving experimentally inaccessible polarizabilities.

Part 3. Numerical integration of the close-coupled scattering equations has been carried out to obtain vibrational transition probabilities for some models of the electronically adiabatic H₂-H₂ collision. All the models use a Lennard-Jones interaction potential between nearest atoms in the collision partners. We have analyzed the results for some insight into the vibrational excitation process in its dependence on the energy of collision, the nature of the vibrational binding potential, and other factors. We conclude also that replacement of earlier, simpler models of the interaction potential by the Lennard-Jones form adds very little realism for all the complication it introduces. A brief introduction precedes the presentation of our work and places it in the context of attempts to understand the collisional activation process in chemical reactions as well as some other chemical dynamics.