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.

Control of wettability of carbon nanotube array by reversible dry oxidation for superhydrophobic coating and supercapacitor applications

In this thesis, dry chemical modification methods involving UV/ozone, oxygen plasma, and vacuum annealing treatments are explored to precisely control the wettability of CNT arrays. By varying the exposure time of these treatments the surface concentration of oxygenated groups adsorbed on the CNT arrays can be controlled. CNT arrays with very low amount of oxygenated groups exhibit a superhydrophobic behavior. In addition to their extremely high static contact angle, they cannot be dispersed in DI water and their impedance in aqueous electrolytes is extremely high. These arrays have an extreme water repellency capability such that a water droplet will bounce off of their surface upon impact and a thin film of air is formed on their surface as they are immersed in a deep pool of water. In contrast, CNT arrays with very high surface concentration of oxygenated functional groups exhibit an extreme hydrophilic behavior. In addition to their extremely low static contact angle, they can be dispersed easily in DI water and their impedance in aqueous electrolytes is tremendously low. Since the bulk structure of the CNT arrays are preserved during the UV/ozone, oxygen plasma, and vacuum annealing treatments, all CNT arrays can be repeatedly switched between superhydrophilic and superhydrophobic, as long as their O/C ratio is kept below 18%.

The effect of oxidation using UV/ozone and oxygen plasma treatments is highly reversible as long as the O/C ratio of the CNT arrays is kept below 18%. At O/C ratios higher than 18%, the effect of oxidation is no longer reversible. This irreversible oxidation is caused by irreversible changes to the CNT atomic structure during the oxidation process. During the oxidation process, CNT arrays undergo three different processes. For CNT arrays with O/C ratios lower than 40%, the oxidation process results in the functionalization of CNT outer walls by oxygenated groups. Although this functionalization process introduces defects, vacancies and micropores opening, the graphitic structure of the CNT is still largely intact. For CNT arrays with O/C ratios between 40% and 45%, the oxidation process results in the etching of CNT outer walls. This etching process introduces large scale defects and holes that can be obviously seen under TEM at high magnification. Most of these holes are found to be several layers deep and, in some cases, a large portion of the CNT side walls are cut open. For CNT arrays with O/C ratios higher than 45%, the oxidation process results in the exfoliation of the CNT walls and amorphization of the remaining CNT structure. This amorphization process can be implied from the disappearance of C-C sp2 peak in the XPS spectra associated with the pi-bond network.

The impact behavior of water droplet impinging on superhydrophobic CNT arrays in a low viscosity regime is investigated for the first time. Here, the experimental data are presented in the form of several important impact behavior characteristics including critical Weber number, volume ratio, restitution coefficient, and maximum spreading diameter. As observed experimentally, three different impact regimes are identified while another impact regime is proposed. These regimes are partitioned by three critical Weber numbers, two of which are experimentally observed. The volume ratio between the primary and the secondary droplets is found to decrease with the increase of Weber number in all impact regimes other than the first one. In the first impact regime, this is found to be independent of Weber number since the droplet remains intact during and subsequent to the impingement. Experimental data show that the coefficient of restitution decreases with the increase of Weber number in all impact regimes. The rate of decrease of the coefficient of restitution in the high Weber number regime is found to be higher than that in the low and moderate Weber number. Experimental data also show that the maximum spreading factor increases with the increase of Weber number in all impact regimes. The rate of increase of the maximum spreading factor in the high Weber number regime is found to be higher than that in the low and moderate Weber number. Phenomenological approximations and interpretations of the experimental data, as well as brief comparisons to the previously proposed scaling laws, are shown here.

Dry oxidation methods are used for the first time to characterize the influence of oxidation on the capacitive behavior of CNT array EDLCs. The capacitive behavior of CNT array EDLCs can be tailored by varying their oxygen content, represented by their O/C ratio. The specific capacitance of these CNT arrays increases with the increase of their oxygen content in both KOH and Et4NBF4/PC electrolytes. As a result, their gravimetric energy density increases with the increase of their oxygen content. However, their gravimetric power density decreases with the increase of their oxygen content. The optimally oxidized CNT arrays are able to withstand more than 35,000 charge/discharge cycles in Et4NBF4/PC at a current density of 5 A/g while only losing 10% of their original capacitance.

Limits and tradeoffs in the control of autocatalytic systems

Despite the complexity of biological networks, we find that certain common architectures govern network structures. These architectures impose fundamental constraints on system performance and create tradeoffs that the system must balance in the face of uncertainty in the environment. This means that while a system may be optimized for a specific function through evolution, the optimal achievable state must follow these constraints. One such constraining architecture is autocatalysis, as seen in many biological networks including glycolysis and ribosomal protein synthesis. Using a minimal model, we show that ATP autocatalysis in glycolysis imposes stability and performance constraints and that the experimentally well-studied glycolytic oscillations are in fact a consequence of a tradeoff between error minimization and stability. We also show that additional complexity in the network results in increased robustness. Ribosome synthesis is also autocatalytic where ribosomes must be used to make more ribosomal proteins. When ribosomes have higher protein content, the autocatalysis is increased. We show that this autocatalysis destabilizes the system, slows down response, and also constrains the system’s performance. On a larger scale, transcriptional regulation of whole organisms also follows architectural constraints and this can be seen in the differences between bacterial and yeast transcription networks. We show that the degree distributions of bacterial transcription network follow a power law distribution while the yeast network follows an exponential distribution. We then explored the evolutionary models that have previously been proposed and show that neither the preferential linking model nor the duplication-divergence model of network evolution generates the power-law, hierarchical structure found in bacteria. However, in real biological systems, the generation of new nodes occurs through both duplication and horizontal gene transfers, and we show that a biologically reasonable combination of the two mechanisms generates the desired network.

Optical bistability via amplitude and phase control of a microwave field

We investigate the steady-state optical bistability behavior in a three-level A-type atomic system closed by a microwave field under the condition that the applied fields are in resonance with corresponding atomic transitions. It is shown that the bistable hysteresis cycles can be controlled by both the amplitude and the phase of the microwave field. (c) 2006 Elsevier B.V. All rights reserved.

Optimization of single attosecond x-ray pulses by genetic algorithm control of the chirp and initial phase of 5 fs laser pulses

We show that the peak intensity of single attosecond x-ray pulses is enhanced by 1 or 2 orders of magnitude, the pulse duration is greatly compressed, and the optimal propagation distance is shortened by genetic algorithm optimization of the chirp and initial phase of 5 fs laser pulses. However, as the laser intensity increases, more efficient nonadiabatic self-phase matching can lead to a dramatically enhanced harmonic yield, and the efficiency of optimization decreases in the enhancement and compression of the generated attosecond pulses. (c) 2006 Optical Society of America.

Different patterns of uptake and depuration of cadmium by periphyton community and a grazer species (Physa sp.): A mesocosm evalution

Widespread pollution by heavy metals generated by various industries has serious adverse effects on human health and the environment. Cadmium is a heavy metal recognised as one of the most hazardous environmental pollutants. It is a non-essential and non-beneficial element to organisms, causing toxicity and other deleterious effects on various components of the aquatic environment. The ability of algal periphyton to concentrate cadmium from fresh water is well known. Moreover, periphyton communities are able to accumulate large amounts of cadmium despite its low concentration in fresh water. Many researchers use algal periphyton as an indicator of water quality in aquatic environments. In the present study, the authors ask two basic questions: Does cadmium accumulate along a food chain consisting of the periphyton community and a grazer species (Physa sp.) under semi-natural conditions provided by artificial streams? If not, which one can better indicate the water quality?

Keys to families of Cladocera and to subfamilies, genera, species and subspecies of Macrothricidae and Moinidae [Translation from: Leningrad, Fauna SSSR, Crustacea 1 (3), 1971]

Identification keys to families of Cladocera and to subfamilies, genera, species and subspecies of Macrothricidae and Moinidae are given. This translation does not include ecological notes or illustrations.

Dangeardia sporapiculata n.sp., the term 'apiculus' and the species limitation of some chytrids [Translation from: Sydowia 16 324-330, 1963]

Taxonomic observations are given on Dangeardia sporapiculata n. sp. Furthermore the term 'apiculus' and the species limitation of some chytrids are being discussed. It is concluded that the newly described species Dangeardia sporapiculata does not fit satisfactorily into the present system of phlyctidiacee, because their characteristics do not agree exactly with any genus.

Robust Control of Evolutionary Dynamics

The application of principles from evolutionary biology has long been used to gain new insights into the progression and clinical control of both infectious diseases and neoplasms. This iterative evolutionary process consists of expansion, diversification and selection within an adaptive landscape - species are subject to random genetic or epigenetic alterations that result in variations; genetic information is inherited through asexual reproduction and strong selective pressures such as therapeutic intervention can lead to the adaptation and expansion of resistant variants. These principles lie at the center of modern evolutionary synthesis and constitute the primary reasons for the development of resistance and therapeutic failure, but also provide a framework that allows for more effective control.

A model system for studying the evolution of resistance and control of therapeutic failure is the treatment of chronic HIV-1 infection by broadly neutralizing antibody (bNAb) therapy. A relatively recent discovery is that a minority of HIV-infected individuals can produce broadly neutralizing antibodies, that is, antibodies that inhibit infection by many strains of HIV. Passive transfer of human antibodies for the prevention and treatment of HIV-1 infection is increasingly being considered as an alternative to a conventional vaccine. However, recent evolution studies have uncovered that antibody treatment can exert selective pressure on virus that results in the rapid evolution of resistance. In certain cases, complete resistance to an antibody is conferred with a single amino acid substitution on the viral envelope of HIV.

The challenges in uncovering resistance mechanisms and designing effective combination strategies to control evolutionary processes and prevent therapeutic failure apply more broadly. We are motivated by two questions: Can we predict the evolution to resistance by characterizing genetic alterations that contribute to modified phenotypic fitness? Given an evolutionary landscape and a set of candidate therapies, can we computationally synthesize treatment strategies that control evolution to resistance?

To address the first question, we propose a mathematical framework to reason about evolutionary dynamics of HIV from computationally derived Gibbs energy fitness landscapes -- expanding the theoretical concept of an evolutionary landscape originally conceived by Sewall Wright to a computable, quantifiable, multidimensional, structurally defined fitness surface upon which to study complex HIV evolutionary outcomes.

To design combination treatment strategies that control evolution to resistance, we propose a methodology that solves for optimal combinations and concentrations of candidate therapies, and allows for the ability to quantifiably explore tradeoffs in treatment design, such as limiting the number of candidate therapies in the combination, dosage constraints and robustness to error. Our algorithm is based on the application of recent results in optimal control to an HIV evolutionary dynamics model and is constructed from experimentally derived antibody resistant phenotypes and their single antibody pharmacodynamics. This method represents a first step towards integrating principled engineering techniques with an experimentally based mathematical model in the rational design of combination treatment strategies and offers predictive understanding of the effects of combination therapies of evolutionary dynamics and resistance of HIV. Preliminary in vitro studies suggest that the combination antibody therapies predicted by our algorithm can neutralize heterogeneous viral populations despite containing resistant mutations.