Autorregresive conditional volatility, skewness and kurtosis

This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram-Charlier series expansion of the normal density function for the error term, which is easier to estimate than the non-central t distribution proposed by Harvey and Siddique (1999). Moreover, this approach accounts for time-varying skewness and kurtosis while the approach by Harvey and Siddique (1999) only accounts for nonnormal skewness. We apply this method to daily returns of a variety of stock indices and exchange rates. Our results indicate a significant presence of conditional skewness and kurtosis. It is also found that specifications allowing for time-varying skewness and kurtosis outperform specifications with constant third and fourth moments.

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.