When Stuck, Flip a Coin:New Algorithms for Large-Scale Tasks

Many modern services need to routinely perform tasks on a large scale. This prompts us to consider the following question: How can we design efficient algorithms for large-scale computation? In this thesis, we focus on devising a general strategy to address the above question. Our approaches use tools from graph theory and convex optimization, and prove to be very effective on a number of problems that exhibit locality. A recurring theme in our work is to use randomization to obtain simple and practical algorithms. The techniques we developed enabled us to make progress on the following questions: - Parallel Computation of Approximately Maximum Matchings. We put forth a new approach to computing $O(1)$-approximate maximum matchings in the Massively Parallel Computation (MPC) model. In the regime in which the memory per machine is $\Theta(n)$, i.e., linear in the size of the vertex-set, our algorithm requires only $O((\log \log{n})^2)$ rounds of computations. This is an almost exponential improvement over the barrier of $\Omega(\log {n})$ rounds that all the previous results required in this regime. - Parallel Computation of Maximal Independent Sets. We propose a simple randomized algorithm that constructs maximal independent sets in the MPC model. If the memory per machine is $\Theta(n)$ our algorithm runs in $O(\log \log{n})$ MPC-rounds. In the same regime, all the previously known algorithms required $O(\log{n})$ rounds of computation. - Network Routing under Link Failures. We design a new protocol for stateless message-routing in $k$-connected graphs. Our routing scheme has two important features: (1) each router performs the routing decisions based only on the local information available to it; and, (2) a message is delivered successfully even if arbitrary $k-1$ links have failed. This significantly improves upon the previous work of which the routing schemes tolerate only up to $k/2 - 1$ failed links in $k$-connected graphs. - Streaming Submodular Maximization under Element Removals. We study the problem of maximizing submodular functions subject to cardinality constraint $k$, in the context of streaming algorithms. In a regime in which up to $m$ elements can be removed from the stream, we design an algorithm that provides a constant-factor approximation for this problem. At the same time, the algorithm stores only $O(k \log^2{k} + m \log^3{k})$ elements. Our algorithm improves quadratically upon the prior work, that requires storing $O(k \cdot m)$ many elements to solve the same problem. - Fast Recovery for the Separated Sparsity Model. In the context of compressed sensing, we put forth two recovery algorithms of nearly-linear time for the separated sparsity signals (that naturally model neural spikes). This improves upon the previous algorithm that had a quadratic running time. We also derive a refined version of the natural dynamic programming (DP) approach to the recovery of the separated sparsity signals. This DP approach leads to a recovery algorithm that runs in linear time for an important class of separated sparsity signals. Finally, we consider a generalization of these signals into two dimensions, and we show that computing an exact projection for the two-dimensional model is NP-hard

Angle-resolved photoemission spectroscopic properties of quasi-one-dimensional crystals

Abstract Electronic properties of low-dimensional systems — and particularly quasi-one-dimensional systems — together with related correlated electron phenomena have for quite some time been at the very frontier of condensed matter physics. The interest ranges from purely fundamental reasons, since the reduced dimension offers a unique possibility of direct calculation of many-body problems, to nowadays very intense interest in functional nano-systems. Angle-resolved photoemission spectroscopy (ARPES) is arguably the most direct probe of the physical properties of solids, which arise from low-energy electronic excitations. With the present state-of-the-art high energy/angle resolution detectors, it allows a direct insight into the most subtle effects of electron correlations. All the results presented in this Thesis are the first ARPES measurements on several inorganic chain-like materials that are, or are related to Peierls conductors. These quasi-one-dimensional correlated materials typically exhibit non-Fermi liquid like properties that are at the same time incompatible with any of the existing singular Fermi liquid scenarios (such as Luttinger liquid). In that respect the aim is twofold: to reveal the new physics arising from direct electronic structure measurements, and secondly, to compare the emerging models for the spectroscopic features with the new findings. More specifically, the Thesis focuses on the influence of the electron-phonon coupling on the observed excitations. A quasi-one-dimensional insulating compound K0.33MoO3, known as molybdenum red bronze, is closely related to the blue bronze K0.3MoO3, a 1D Peierls conductor. We disclose the details of the electron structure and reveal the important role of defect induced states. The small mobile polaron scenario describes well the blue bronze, and this picture is further strengthened, as we discuss here, by the spectroscopic similarities with the red bronze. Then we present measurements on two transition metal trichalcogenides: ZrTe3 and TaSe3. The first is a Peierls compound whose peculiar Fermi surface hides its low-dimensional character. The latter, strikingly, even though it does not exhibit any instability, shows spectroscopic similarities with the Peierls conductors, thereby demonstrating the importance of electron-phonon interactions in this material, as well as the general importance of the particularities of the Fermi surface in setting the conditions for an electronic instability. Finally, we report the results on one of the most intriguing materials in the field — BaVS3. This correlated electron system demonstrates a wealth of complex, poorly understood phases. Extensive experimental findings cannot easily be put together into a coherent picture. Our direct electronic structure measurements suggest that the puzzling electronic properties are due to the interplay of the 1D states and a narrow localized band. We find supporting evidence for a one-dimensional instability driving the metal-insulator transition at 69 K and propose its realization through a mechanism of interband nesting. We conclude that there is a direct link between the observed non-Fermi liquid features and the intrinsic characteristics of 1D Peierls conductors and/or one-dimensionality in general. The influence of electron-phonon coupling in conjunction with the reduced dimensionality leads to spectroscopic features that hide the realizations of the singular behavior. However, a detailed modeling of the new data presented here is necessary to place them in the framework of the emerging theories

Vanadium, niobium and tantalum by XPS

We present high-resolution XPS spectra of elemental vanadium, niobium and tantalum sputter-cleaned by Ar^+ ions. The energy scales are shown without applying any corrections, and the position of the Fermi level was verified to be at zero binding energy within better than 0.1 eV, as determined from the Fermi edge measurement

Reduction of thermal conductivity in phononic nanomesh structures

Controlling the thermal conductivity of a material independently of its electrical conductivity continues to be a goal for researchers working on thermoelectric materials for use in energy applications and in the cooling of integrated circuits. In principle, the thermal conductivity κ and the electrical conductivity σ may be independently optimized in semiconducting nanostructures because different length scales are associated with phonons (which carry heat) and electric charges (which carry current). Phonons are scattered at surfaces and interfaces, so κ generally decreases as the surface-to-volume ratio increases. In contrast, σ is less sensitive to a decrease in nanostructure size, although at sufficiently small sizes it will degrade through the scattering of charge carriers at interfaces. Here, we demonstrate an approach to independently controlling κ based on altering the phonon band structure of a semiconductor thin film through the formation of a phononic nanomesh film. These films are patterned with periodic spacings that are comparable to, or shorter than, the phonon mean free path. The nanomesh structure exhibits a substantially lower thermal conductivity than an equivalently prepared array of silicon nanowires, even though this array has a significantly higher surface-to-volume ratio. Bulk-like electrical conductivity is preserved. We suggest that this development is a step towards a coherent mechanism for lowering thermal conductivity

A Distributed Algorithm for Partitioned Robust Submodular Maximization

Abstract—In this paper, we consider the problem of maximizing a monotone submodular function subject to a cardinality constraint, with two added twists: The computation is distributed across a number of machines, and we require the solution to be robust against adversarial removals. We provide two versions of a partitioned robust algorithm for this problem, with the difference amounting to whether or not the centralized machine is informed (only in the final stage of the algorithm) which elements will be removed. In both of these cases, we provide a novel constant-factor approximation guarantee with respect to the optimal algorithm. Finally, we validate our algorithms via numerical experiments on real-world data sets in influence maximization and data summarization

MICROSTRUCTURE INFLUENCE ON FRICTION BEHAVIOR OF THE TI6AL4V BIOMEDICAL ALLOY AT LOW LOADS

Dynamic friction coefficient (COF) between Ti6Al4V and Al2O3 was analyzed under low loads (100 mN, 250 mN, 500 mN, 750 mN, 1000 mN), sliding speed (4 mm/s, 8 mm/s, 12 mm/s) at dry contact and in the Ringer's solution. Different Ti6Al4V microstructures were studied: Sample 1 - fully lamellar; Sample 2 - martensitic; sample 3 - equiaxed; and sample 4 - globular microstructure. The maximum COF values varied as: 0.4 - 1.23 (Sample 1), 0.5 – 2.8 (Sample 2), 0.4 – 1.1 (Sample 3), and 0.4 – 2.3 (Sample 4). Lamellar and martensitic microstructures were not beneficial for the tribological response since they exhibited severe wear and very high COF values. The globular Ti alloy microstructure showed extremely high COF and wear under dry conditions. In general, water quenching was not a favorable treatment for tribological behavior. The lowest COF values and wear volumes were exhibited in the case of equiaxed microstructure

Corrosion behavior of compocasted ZA27/SiCp composites in sodium chloride solution

The corrosion behavior of particulate ZA27/SiCp composites in an aerated sodium chloride solution was studied. The composites were synthesized via compocasting with addition of 1, 3 and 5 wt.% SiC particles in the matrix alloy. Composite samples were immersed for 30 days in the 3.5 wt.% NaCl solution open to the atmospheric air. Surface appearance and microstructure of the composites were examined by means of optical microscopy and scanning electron microscopy, while corrosion rates of the composites were determined using the weight loss method. It was revealed that SiC particles were not influenced by corrosion. General uniform corrosion occurred in the composite matrices, mainly in the region of the η phase. Local corrosion was noticed in micro-cracks and near clusters of particulate reinforcements. Results of microstructural examinations and immersion test indicate a slightly lower corrosion resistance of the ZA27/SiCp composites compared to that of the matrix alloy

Combining reactive sputtering and rapid thermal processing for synthesis and discovery of metal oxynitrides

Recent efforts have demonstrated enhanced tailoring of material functionality with mixed anion materials, yet exploratory research with mixed anion chemistries is limited by the sensitivity of these materials to synthesis conditions. Synthesis of a particular metal oxynitride compound by traditional reactive annealing requires specific, limited ranges of both oxygen and nitrogen chemical potentials to establish equilibrium between the solid-state material and a reactive atmosphere. Using Ta–O–N as an example system, we describe a combination of reactive sputter deposition and rapid thermal processing (RTP) for synthesis of mixed anion inorganic materials. Heuristic optimization of reactive gas pressures to attain a desired anion stoichiometry is discussed, and the ability of RTP to enable amorphous to crystalline transitions without preferential anion loss is demonstrated through the controlled synthesis of nitride, oxide, and oxynitride phases