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Error-Correcting Codes for Networks, Storage and Computation
Get PDFThe advent of the information age has bestowed upon us three challenges related to the way we deal with data. Firstly, there is an unprecedented demand for transmitting data at high rates. Secondly, the massive amounts of data being collected from various sources needs to be stored across time. Thirdly, there is a need to process the data collected and perform computations on it in order to extract meaningful information out of it. The interconnected nature of modern systems designed to perform these tasks has unraveled new difficulties when it comes to ensuring their resilience against sources of performance degradation. In the context of network communication and distributed data storage, system-level noise and adversarial errors have to be combated with efficient error correction schemes. In the case of distributed computation, the heterogeneous nature of computing clusters can potentially diminish the speedups promised by parallel algorithms, calling for schemes that mitigate the effect of slow machines and communication delay.
This thesis addresses the problem of designing efficient fault tolerance schemes for the three scenarios just described. In the network communication setting, a family of multiple-source multicast networks that employ linear network coding is considered for which capacity-achieving distributed error-correcting codes, based on classical algebraic constructions, are designed. The codes require no coordination between the source nodes and are end to end: except for the source nodes and the destination node, the operation of the network remains unchanged.
In the context of data storage, balanced error-correcting codes are constructed so that the encoding effort required is balanced out across the storage nodes. In particular, it is shown that for a fixed row weight, any cyclic Reed-Solomon code possesses a generator matrix in which the number of nonzeros is the same across the columns. In the balanced and sparsest case, where each row of the generator matrix is a minimum distance codeword, the maximal encoding time over the storage nodes is minimized, a property that is appealing in write-intensive settings. Analogous constructions are presented for a locally recoverable code construction due to Tamo and Barg.
Lastly, the problem of mitigating stragglers in a distributed computation setup is addressed, where a function of some dataset is computed in parallel. Using Reed-Solomon coding techniques, a scheme is proposed that allows for the recovery of the function under consideration from the minimum number of machines possible. The only assumption made on the function is that it is additively separable, which renders the scheme useful in distributed gradient descent implementations. Furthermore, a theoretical model for the run time of the scheme is presented. When the return time of the machines is modeled probabilistically, the model can be used to optimally pick the scheme's parameters so that the expected computation time is minimized. The recovery is performed using an algorithm that runs in quadratic time and linear space, a notable improvement compared to state-of-the-art schemes.
The unifying theme of the three scenarios is the construction of error-correcting codes whose encoding functions adhere to certain constraints. It is shown that in many cases, these constraints can be satisfied by classical constructions. As a result, the schemes presented are deterministic, operate over small finite fields and can be decoded using efficient algorithms.</p
An Experimental and Theoretical Study of Active Flow Control
Get PDFThe accelerating growth of environmental awareness has not stopped at the aerospace industry. The need for greener and more efficient airplanes threatens to outpace the flow of new technology. This has ignited development in several fields, one of which is active flow control (AFC). Active flow control has quickly proven its tremendous potential for real applications. Even though the roots of this technology date back a century, we still lack fundamental understanding. This thesis combines both modern and traditional approaches to lay out a new foundation for future research.
The thesis first focuses on the rising stars of active flow control: the so-called fluidic oscillators or sweeping jet actuators. These devices consist of simple, rigid internal geometries that create a sweeping output jet motion. The fluid dynamic interactions with the internal geometry are studied in detail using high-speed Schlieren imaging. Additionally, the influence of adjacent sweeping jets is investigated. It is revealed that the internal driving mechanism is far stronger than the fluid dynamic interactions at the outlet, resulting in a completely independent jet behavior.
Next, a high-lift airfoil design is combined with active flow control, and an extensive wind tunnel study is carried out. It is shown that for the given wing design active flow control leads to much higher lift benefits when applied to the trailing edge. Applied to the leading edge active flow control disrupts the vortex lift of the high-lift airfoil, resulting in a deleterious lift effect; however, it shows potential for pitch moment control. This project also underlines the advantages of jet-like active flow control over steady blowing actuation at limited available mass flow rates.
The momentum input coefficient as an important parameter in active flow control is discussed in detail, identifying common misconceptions and difficulties that hinder its proper calculation. An innovative, much simpler approach is introduced. This allows a detailed study of the underlying physics, unveiling unknown limitations of active flow control. The approach is then used as a model to derive the novel concept of thermal active flow control. Experimental studies, including a wind tunnel test campaign, are performed to confirm the viability of the concept for practical applications.
The new calculation method of the input momentum coefficient emphasizes its weakness as a similarity parameter in active flow control studies. The extended mass flow coefficient is introduced as a new parameter. It is shown that it can overcome the deficiencies of the input momentum coefficient without suffering other disadvantages. Its further investigation leads to a deeper understanding of active flow control, which is supported by PIV experiments. The main findings of this investigation divide active flow control into three different "states": boundary layer thickening, separation control, and supercirculation.</p
Alkaline Salts of Sodium and Potassium: from C–X Reduction to C–H Functionalization and Beyond
Get PDFThe discovery and contemplations of Gilbert N. Lewis (1875–1946) regarding the concept of electron pair acceptors has led to an improved fundamental understanding of molecular interactions. Lewis’s recognition that acidic character can exist in substances not containing hydrogen (i.e.,
Brønsted acids) led to the classification of a new group of reagents and catalysts for organic synthesis: Lewis acids. Over the last half-century, the application of these reagents and catalysts has in turn led to the discovery of a plethora of new chemical reactions, enabling previously unknown
transformations. It has also been appreciated that electron pair donors (i.e., Lewis bases) are characterized by analogous and opposite behavior. Perhaps most intriguing is that in certain cases Lewis bases are capable of modifying simultaneously the electrophilic and nucleophilic character of
the substance to which they are coordinated. It is also known that neutral tetravalent silicon can act as a Lewis acid for a variety of nucleophiles (i.e., Lewis bases) generating pentavalent Si species; these adducts are observed to have enhanced electrophilicity at Si and enhanced electron density at the ligands bound to silicon. In the case of organosilanes wherein at least one of the groups on silicon is a hydrogen (i.e., a hydrosilane), the reaction with Lewis bases can lead to pentavalent adducts with weakened Si–H bonds wherein the H has enhanced hydridic character. This property has been exploited by researchers in a number of ways, perhaps most prevalently in the development of hydrosilanes as mild reducing agents for the reduction of carbonyl compounds or for the mechanistically-related carbonyl hydrosilylation reaction.
This thesis details the discovery and development of fundamentally new chemical reactivity of silanes enabled by their interaction with basic salts of certain alkali metals (and includes some, but certainly not all of the work that I have performed in this area). First, it was found that specific combinations of hydrosilanes with basic alkali metal salts – in particular KOt-Bu – under certain conditions form exceptionally powerful reductive couples capable of selectively cleaving strong aromatic C–O and C–S bonds with exceptional effectiveness and novel selectivity. Second, I found that certain modifications and elaborations of this chemical system lead to dramatic changes in the operative reaction manifold: from C–X bond cleavage to E–Si bond formation. I determined that this concept of activating hydrosilanes with alkaline salts of the alkali metals can be harnessed for the mild and efficient construction of a wide array of E–Si bond classes by catalytic crossdehydrogenative coupling. Surprisingly, these challenging chemistries all occur in the absence of transition metal species, providing new horizons and opportunities for investigating Earth-abundant elements as catalysts and reagents for a host of applications.</p
Membrane Potential Dynamics of Hippocampal Neurons During Ripples in Awake Mice
Get PDFDuring periods of slow wave sleep and quiet wakefulness, the hippocampal formation generates spontaneous population bursts that are organized as a high-frequency "ripple" oscillation. The neurons that participate in these bursts often replay previously experienced activity patterns encoded during alert behavior, and interfering with ripple generation produces deficits in learning and memory tasks. For these reasons, ripples play a prominent role in theories of memory consolidation and retrieval. While spiking during ripples has been extensively studied, our understanding of the subthreshold behavior of hippocampal neurons during these events remains incomplete. Here, we combine in vivo whole-cell recordings with multisite extracellular and behavioral measurements to study the membrane potential dynamics of hippocampal neurons during ripples in awake mice. We find that the subthreshold depolarization of CA1 pyramidal neurons is uncorrelated with net excitatory input, clarifying the circuit mechanism keeping most neurons silent during ripples. On a finer time scale, the phase delay between intracellular and extracellular ripple oscillations varies systematically with the membrane potential, which is inconsistent with models of intracellular ripple generation involving perisomatic inhibition alone. In addition, we find that membrane potential statistics (mean, variability, distance to threshold) of CA1 pyramidal neurons and dentate granule cells are systematically modulated across brain states, that rapid variations in pupil diameter are reflected in subthreshold fluctuations, and that many neurons begin depolarizing about one second before ripple onset. These results provide evidence that coordinated shifts in the subthreshold dynamics of individual neurons may contribute to the emergence of state-dependent hippocampal activity patterns. Finally, we present evidence that area CA3 provides the major excitatory input to dentate granule cells during ripples and that there are coordinated interactions between hippocampal ripples and population events in the dentate gyrus, both of which inform network-level models of ripple generation
The Divergent Evolution of Earth and Venus
Get PDFVenus and Earth are similar in terms of size and bulk composition, yet their surface conditions are radically different. Earth has hosted plate tectonics and a global magnetic field for billions of years, sustaining water oceans and allowing life to flourish. A thick atmosphere chiefly composed of carbon dioxide, in contrast, drives a greenhouse effect on Venus that would instantly reduce any terrestrial organism to ash. In this thesis, I present several contributions to the debate raging over whether Venus and Earth resembled each other in the past or if unique circumstances placed these celestial siblings on divergent paths from the start. First, I introduce a new process—precipitation of magnesium-rich minerals—that explains the apparent longevity of Earth's dynamo given plausible assumptions about how the core and mantle lose heat. This mechanism relies on high-temperature equilibration in the aftermath of giant impacts, meaning that Earth's violent birth enabled its clement present. The lack of a magnetic field thus indicates that Venus escaped savage bombardment or simply that sluggish mantle convection insulates the core. My analyses of the size and spatial distributions of impact craters suggest that volcanism proceeds planet-wide at gradual rates rather than as catastrophic resurfacing events, which supports a uniformitarian view of Venus. Modeling of enigmatic features called coronae on Venus also sheds light on the properties of the crust and lithosphere that yield a stagnant lid rather than plate tectonics. Finally, I present a thermal history for Venus that is consistent with these and other available constraints. Various uncertainties in my models highlight the pressing need to gather more data relevant to Earth's deep interior and from the most Earth-like planet in our solar system.</p
Nanoscopic Atomic Lattices with Light-Mediated Interactions
Get PDFIntegrating ultracold atoms with nanophotonics enables the exploration of new paradigms in quantum optics and many body physics. Advanced fabrication capabilities for low-loss dielectric materials provide powerful tools to engineer light-matter coupling of photons and atoms. For example, dispersion-engineered photonic crystal waveguides (PCWs) permit not only stable trapping and probing of atoms via interactions with guided mode (GM) light, but also the possibility to study the physics of strong photon-mediated interactions between atoms. This thesis describes the design of a quasi-one-dimensional structure, the alligator photonic crystal waveguide (APCW), which has already allowed for the observation of some of those features.
Furthermore, external illumination schemes allow for the trapping and transport of atoms near the dielectric device. Here, atoms loaded into a one-dimensional optical lattice are transported through the APCW. As the atoms trapped in the lattice approach the APCW, the combination of lattice and GM potential can smoothly guide atoms into the gap between the two dielectric nanobeams. Therefore, the transmission of a weak guided mode probe is modulated at the rate determined by the lattice moving through the APCW. In the near future, single atoms can then be transferred from the moving lattice into optical traps formed in each unit cell by GMs of the APCW. Moreover, a characterization of a simple 2D photonic crystal slabs design is presented.</p
Optimal Sensor Placement for Bayesian Parametric Identification of Structures
Get PDFThere exists a choice in where to place sensors to collect data for Bayesian model updating and system identification of structures. It is desirable to use an available deterministic predictive model, such as a finite-element model, along with prior information on the uncertain model parameters and the uncertain accuracy of the predictive model, to determine which optimal sensor locations should be instrumented in the structure. In this thesis, an information-theoretic framework for optimality is considered.
The mutual information between the uncertain model predictions for the data and the uncertain model parameters is presented as a natural measure of reduction in uncertainty to maximize over sensor configurations. A combinatorial search over all sensor configurations is usually prohibitively expensive. A convex optimization method is developed to provide a fast sub-optimal, but possibly optimal, sensor configuration when certain simplifying assumptions can be made about the chosen stochastic model class for the structure. The optimization method is demonstrated to work for a 50-story uniform shear building, with 20 sensors to be installed.
The stability of optimal sensor configurations under refinement of the mesh of the underlying finite-element model is investigated and related to the choice of prediction-error correlations in the model. An example problem of placement of a single sensor on the continuum of an elastic axial bar is solved analytically.
In order to solve the optimal sensor placement problem in the more general case, numerical estimation of mutual information between the model predictions for the data and the model parameters becomes necessary. To this end, a thermodynamic integration scheme based on path sampling is developed with the aim of estimating the entropy of the data prediction distribution. The scheme is demonstrated to work for an example that uses synthetic data for model class comparison between linear and Duffing oscillator model classes. The thermodynamic integration method is then used to determine the optimal location of a single sensor for a two degree-of-freedom oscillator model.</p
Scattering in N=4 Super Yang Mills and N=8 Supergravity
Get PDFThe scattering amplitudes of planar N = 4 super-Yang-Mills theory (sYM) exhibit a number of remarkable analytic structures, including dual conformal symmetry, logarithmic singularities of integrands, and the absence of poles at infinite loop momentum. None of these properties are apparent from our usual formulation of quantum field theory in terms of Lagrangians and Feynman rules. In the past years, the hidden features inspired a dual formulation for scattering amplitudes that is not built on the two pillars of locality and unitarity. Instead, a new geometric formulation in terms of Grassmannians and the amplituhedron emerged, which is based on the key analytic properties of scattering amplitudes in the planar sector of super-Yang-Mills theory. Starting from geometric concepts, the amplituhedron geometry derives all properties of scattering amplitudes in said theory, including locality and factorization. From a practical perspective, expanding the amplitude in terms of a local diagrams, the amplituhedron construction implies that scattering amplitudes in planar N=4 super-Yang-Mills are fully specified by a surprisingly simple subset of all unitarity cuts. Concretely, integrands are uniquely (up to an overall constant) fixed by demanding their vanishing on all spurious singularities.
Extending an initial proposal by Arkani-Hamed, Bourjaily, Cachazo, and Trnka, we conjecture that the same analytic structures extend beyond the planar limit of N=4 super-Yang-Mills. Furthermore we show that the \dlog and \emph{no pole at infinity} constraints give the key integrand level analytic information contained in dual conformal symmetry in the planar sector. While it is presently unclear how to extend either dual conformal symmetry or the amplituhedron picture beyond the planar sector, our results suggest that related concepts might exist and await discovery.
In order to support our conjectures, we have analyzed several nontrivial multi-loop multi-leg amplitudes. For the nonplanar three-loop four-point and two-loop five point super-Yang-Mills amplitudes, we explicitly construct a complete basis of diagram integrands that has only logarithmic singularities and no poles at infinity. We also give examples at three loops showing how to make the logarithmic singularity properties manifest by writing explicit dlog forms. We give additional evidence at four and five loops supporting the nonplanar logarithmic singularity conjecture. Our investigations show that the singularity structures of planar and nonplanar integrands in N = 4 super-Yang-Mills are strikingly similar. Finally, we express the complete amplitude in terms of our special basis diagrams, with the coefficients determined by the vanishing conditions on the amplitude. By successfully carrying out this procedure, we provide nontrivial evidence that the “zero conditions” also carry over into the nonplanar sector. Our analysis suggests that the concept of the amplituhedron can be extended to the nonplanar sector of N = 4 super-Yang-Mills theory and one might hope to ultimately reformulate more general quantum field theories in a geometric language.
Using the marvelous squaring relation between Yang-Mills and gravity theories discovered by Bern, Carrasco, and Johansson (BCJ), we relate our newly gained knowledge on the Yang-Mills side to properties of gravity. We conjecture that to all loop orders, while N = 8 supergravity has poles at infinity, at least at four points it has only logarithmic singularities at finite locations. We provide nontrivial evidence for these conjectures. We describe the singularity structure of N = 8 supergravity at three loops and beyond.
In order to approach a geometric formulation for scattering in gravitational theories, we retrace the initial steps taken in planar N=4 super-Yang-Mills in the gravitational setting. In particular, we study on-shell diagrams for gravity theories with any number of supersymmetries and find a compact Grassmannian formula in terms of edge variables of the graphs. Unlike in gauge theory where the analogous form involves only dlog-factors, in gravity we find a non-trivial numerator as well as higher degree poles in the edge variables. Based on the structure of the Grassmannian formula for supergravity we conjecture that gravity loop amplitudes also possess similar properties. In particular, we find that there are only logarithmic singularities on cuts with finite loop momentum and that poles at infinity are present.</p
Physics and Applications of Microresonator Solitons and Electro-optic Frequency Combs
Get PDFFrequency combs are having a broad impact on science and technology because they provide a way to coherently link radio/microwave-rate electrical signals with optical-rate signals derived from lasers and atomic transitions. A new, miniature realization, the microcomb, that uses chip-based microresonators can potentially revolutionize instrumentation, time keeping, spectroscopy, and navigation. Microcombs were first demonstrated using a form of cascaded four-wave mixing. However, the recent discovery of dissipative soliton microcombs enables phase-locked spectra with reproducible envelopes, as required in many frequency comb applications. In addition, these solitons are confined in a high-Q microresonator, thereby creating a rich landscape for research in nonlinear optical phenomena. In this thesis, these solitons are demonstrated for the first time in a silica microcavity. Significantly, the device provides a microwave-detectable soliton repetition rate, which is essential to many comb applications. The unusual properties of the solitons are studied from a theoretical viewpoint using a Lagrangian formalism and predictions of the theory are confirmed experimentally. In the course of this work, a new optical soliton, the Stokes soliton, was also discovered. In addition to soliton mode locking, another novel and compact platform, the electro-optical modulation frequency comb, was studied. This type of frequency comb was used to demonstrate a novel electro-optic form of frequency division for stable microwave synthesis. It was also modified to perform astronomical calibration for exoplanet detection at the Keck Observatory in Hawaii.</p
The Women of Othello: Shakespeare's Reinterpretation of "A Moorish Captain"
No full textWilliam Shakespeare’s source for his tragedy Othello is the Italian novella “A Moorish Captain,” written by Giraldi Cinthio in 1565 as part of his work Hecatommithi. Shakespeare’s retelling of the story is particularly interesting because Shakespeare alters the roles of the important female characters of the play