Automated design of self-stabilization

Self-stabilization is a property of a distributed system such that, regardless of the legitimacy of its current state, the system behavior shall eventually reach a legitimate state and shall remain legitimate thereafter. The elegance of self-stabilization stems from the fact that it distinguishes distributed systems by a strong fault tolerance property against arbitrary state perturbations. The difficulty of designing and reasoning about self-stabilization has been witnessed by many researchers; most of the existing techniques for the verification and design of self-stabilization are either brute-force, or adopt manual approaches non-amenable to automation. In this dissertation, we first investigate the possibility of automatically designing self-stabilization through global state space exploration. In particular, we develop a set of heuristics for automating the addition of recovery actions to distributed protocols on various network topologies. Our heuristics equally exploit the computational power of a single workstation and the available parallelism on computer clusters. We obtain existing and new stabilizing solutions for classical protocols like maximal matching, ring coloring, mutual exclusion, leader election and agreement. Second, we consider a foundation for local reasoning about self-stabilization; i.e., study the global behavior of the distributed system by exploring the state space of just one of its components. It turns out that local reasoning about deadlocks and livelocks is possible for an interesting class of protocols whose proof of stabilization is otherwise complex. In particular, we provide necessary and sufficient conditions – verifiable in the local state space of every process – for global deadlock- and livelock-freedom of protocols on ring topologies. Local reasoning potentially circumvents two fundamental problems that complicate the automated design and verification of distributed protocols: (1) state explosion and (2) partial state information. Moreover, local proofs of convergence are independent of the number of processes in the network, thereby enabling our assertions about deadlocks and livelocks to apply on rings of arbitrary sizes without worrying about state explosion.

Applications of finite geometries to designs and codes

This dissertation concerns the intersection of three areas of discrete mathematics: finite geometries, design theory, and coding theory. The central theme is the power of finite geometry designs, which are constructed from the points and t-dimensional subspaces of a projective or affine geometry. We use these designs to construct and analyze combinatorial objects which inherit their best properties from these geometric structures. A central question in the study of finite geometry designs is Hamada’s conjecture, which proposes that finite geometry designs are the unique designs with minimum p-rank among all designs with the same parameters. In this dissertation, we will examine several questions related to Hamada’s conjecture, including the existence of counterexamples. We will also study the applicability of certain decoding methods to known counterexamples. We begin by constructing an infinite family of counterexamples to Hamada’s conjecture. These designs are the first infinite class of counterexamples for the affine case of Hamada’s conjecture. We further demonstrate how these designs, along with the projective polarity designs of Jungnickel and Tonchev, admit majority-logic decoding schemes. The codes obtained from these polarity designs attain error-correcting performance which is, in certain cases, equal to that of the finite geometry designs from which they are derived. This further demonstrates the highly geometric structure maintained by these designs. Finite geometries also help us construct several types of quantum error-correcting codes. We use relatives of finite geometry designs to construct infinite families of q-ary quantum stabilizer codes. We also construct entanglement-assisted quantum error-correcting codes (EAQECCs) which admit a particularly efficient and effective error-correcting scheme, while also providing the first general method for constructing these quantum codes with known parameters and desirable properties. Finite geometry designs are used to give exceptional examples of these codes.

Development of Optically Based pH Sensing Hydrogel and Controlled Nitric Oxide Release Polymer

Nitric oxide has the potential to greatly improve intravascular measurements by locally inhibiting thrombus formation and dilating blood vessels. pH, the partial pressure of oxygen, and the partial pressure of carbon dioxide are three arterial blood parameters that are of interest to clinicians in the intensive care unit that can benefit from an intravascular sensor. This work explores fabrication of absorbance and fluorescence based pH sensing chemistry, the sensing chemistries' compatibility with nitric oxide, and a controllable nitric oxide releasing polymer. The pH sensing chemistries utilized various substrates, dyes, and methods of immobilization. Absorbance sensing chemistries used sol-gels, fumed silica particles, mesoporous silicon oxide, bromocresol purple, phenol red, bromocresol green, physical entrapment, molecular interactions, and covalent linking. Covalently linking the dyes to fumed silica particles and mesoporous silicon oxide eliminated leaching in the absorbance sensing chemistries. The structures of the absorbance dyes investigated were similar and bromocresol green in a sol-gel was tested for compatibility with nitric oxide. Nitric oxide did not interfere with the use of bromocresol green in a pH sensor. Investigated fluorescence sensing chemistries utilized silica optical fibers, poly(allylamine) hydrogel, SNARF-1, molecular interactions, and covalent linking. SNARF-1 covalently linked to a modified poly(allylamine) hydrogel was tested in the presence of nitric oxide and showed no interference from the nitric oxide. Nitric oxide release was controlled through the modulation of a light source that cleaved the bond between the nitric oxide and a sulfur atom in the donor. The nitric oxide donor in this work is S-nitroso-N-acetyl-D-penicillamine which was covalently linked to a silicone rubber made from polydimethylsiloxane. It is shown that the surface flux of nitric oxide released from the polymer films can be increased and decreased by increasing and decreasing the output power of the LED light source. In summary, an optical pH sensing chemistry was developed that eliminated the chronic problem of leaching of the indicator dye and showed no reactivity to nitric oxide released, thereby facilitating the development of a functional, reliable intravascular sensor.

COMPUTATIONAL ANALYSIS OF THE AEROELASTIC DYNAMICS OF A WIND TURBINE BLADE WITH VARIABLE-SPEED STALL CONTROL

The accuracy of simulating the aerodynamics and structural properties of the blades is crucial in the wind-turbine technology. Hence the models used to implement these features need to be very precise and their level of detailing needs to be high. With the variety of blade designs being developed the models should be versatile enough to adapt to the changes required by every design. We are going to implement a combination of numerical models which are associated with the structural and the aerodynamic part of the simulation using the computational power of a parallel HPC cluster. The structural part models the heterogeneous internal structure of the beam based on a novel implementation of the Generalized Timoshenko Beam Model Technique.. Using this technique the 3-D structure of the blade is reduced into a 1-D beam which is asymptotically equivalent. This reduces the computational cost of the model without compromising its accuracy. This structural model interacts with the Flow model which is a modified version of the Blade Element Momentum Theory. The modified version of the BEM accounts for the large deflections of the blade and also considers the pre-defined structure of the blade. The coning, sweeping of the blade, tilt of the nacelle and the twist of the sections along the blade length are all computed by the model which aren’t considered in the classical BEM theory. Each of these two models provides feedback to the other and the interactive computations lead to more accurate outputs. We successfully implemented the computational models to analyze and simulate the structural and aerodynamic aspects of the blades. The interactive nature of these models and their ability to recompute data using the feedback from each other makes this code more efficient than the commercial codes available. In this thesis we start off with the verification of these models by testing it on the well-known benchmark blade for the NREL-5MW Reference Wind Turbine, an alternative fixed-speed stall-controlled blade design proposed by Delft University, and a novel alternative design that we proposed for a variable-speed stall-controlled turbine, which offers the potential for more uniform power control and improved annual energy production.. To optimize the power output of the stall-controlled blade we modify the existing designs and study their behavior using the aforementioned aero elastic model.

ON THE DIGITAL-POLITICAL TOPOGRAPHY OF MUSIC

The persuasive power of music is often relegated to the dimension of pathos: that which moves us emotionally. Yet, the music commodity is now situated in and around the liminal spaces of digitality. To think about how music functions, how it argues across media, and how it moves us, we must examine its material and immaterial realities as they present themselves to us and as we so create them. This dissertation rethinks the relationship between rhetoric and music by examining the creation, performance, and distribution of music in its material and immaterial forms to demonstrate its persuasive power. While both Plato and Aristotle understood music as a means to move men toward virtue, Aristotle tells us in his Laws, through the Athenian Stranger, that the very best kinds of music can help guide us to truth. From this starting point, I assess the historical problem of understanding the rhetorical potential of music as merely that which directs or imitates the emotions: that which “Soothes the savage breast,” as William Congreve writes. By furthering work by Vickers and Farnsworth, who suggest that the Baroque fascination with applying rhetorical figures to musical figures is an insufficient framework for assessing the rhetorical potential of music, I demonstrate the gravity of musical persuasion in its political weight, in its violence—the subjective violence of musical torture at Guantanamo and the objective, ideological violence of music—and in what Jacques Attali calls the prophetic nature of music. I argue that music has a significant function, and as a non-discursive form of argumentation, works on us beyond affect. Moreover, with the emergence of digital music distribution and domestic digital recording technologies, the digital music commodity in its material and immaterial forms allows for ruptures in the former methods of musical composition, production, and distribution and in the political potential of music which Jacques Attali describes as being able to foresee new political realities. I thus suggest a new theoretical framework for thinking about rhetoric and music by expanding on Lloyd Bitzer’s rhetorical situation, by offering the idea of “openings” to the existing exigence, audience, and constraints. The prophetic and rhetorical power of music in the aleatoric moment can help provide openings from which new exigencies can be conceived. We must, therefore, reconsider the role of rhetorical-musical composition for the citizen, not merely as a tool for entertainment or emotional persuasion, but as an arena for engaging with the political.