BUILDING EFFICIENT AND COST-EFFECTIVE CLOUD-BASED BIG DATA MANAGEMENT SYSTEMS

In today’s big data world, data is being produced in massive volumes, at great velocity and from a variety of different sources such as mobile devices, sensors, a plethora of small devices hooked to the internet (Internet of Things), social networks, communication networks and many others. Interactive querying and large-scale analytics are being increasingly used to derive value out of this big data. A large portion of this data is being stored and processed in the Cloud due the several advantages provided by the Cloud such as scalability, elasticity, availability, low cost of ownership and the overall economies of scale. There is thus, a growing need for large-scale cloud-based data management systems that can support real-time ingest, storage and processing of large volumes of heterogeneous data. However, in the pay-as-you-go Cloud environment, the cost of analytics can grow linearly with the time and resources required. Reducing the cost of data analytics in the Cloud thus remains a primary challenge. In my dissertation research, I have focused on building efficient and cost-effective cloud-based data management systems for different application domains that are predominant in cloud computing environments. In the first part of my dissertation, I address the problem of reducing the cost of transactional workloads on relational databases to support database-as-a-service in the Cloud. The primary challenges in supporting such workloads include choosing how to partition the data across a large number of machines, minimizing the number of distributed transactions, providing high data availability, and tolerating failures gracefully. I have designed, built and evaluated SWORD, an end-to-end scalable online transaction processing system, that utilizes workload-aware data placement and replication to minimize the number of distributed transactions that incorporates a suite of novel techniques to significantly reduce the overheads incurred both during the initial placement of data, and during query execution at runtime. In the second part of my dissertation, I focus on sampling-based progressive analytics as a means to reduce the cost of data analytics in the relational domain. Sampling has been traditionally used by data scientists to get progressive answers to complex analytical tasks over large volumes of data. Typically, this involves manually extracting samples of increasing data size (progressive samples) for exploratory querying. This provides the data scientists with user control, repeatable semantics, and result provenance. However, such solutions result in tedious workflows that preclude the reuse of work across samples. On the other hand, existing approximate query processing systems report early results, but do not offer the above benefits for complex ad-hoc queries. I propose a new progressive data-parallel computation framework, NOW!, that provides support for progressive analytics over big data. In particular, NOW! enables progressive relational (SQL) query support in the Cloud using unique progress semantics that allow efficient and deterministic query processing over samples providing meaningful early results and provenance to data scientists. NOW! enables the provision of early results using significantly fewer resources thereby enabling a substantial reduction in the cost incurred during such analytics. Finally, I propose NSCALE, a system for efficient and cost-effective complex analytics on large-scale graph-structured data in the Cloud. The system is based on the key observation that a wide range of complex analysis tasks over graph data require processing and reasoning about a large number of multi-hop neighborhoods or subgraphs in the graph; examples include ego network analysis, motif counting in biological networks, finding social circles in social networks, personalized recommendations, link prediction, etc. These tasks are not well served by existing vertex-centric graph processing frameworks whose computation and execution models limit the user program to directly access the state of a single vertex, resulting in high execution overheads. Further, the lack of support for extracting the relevant portions of the graph that are of interest to an analysis task and loading it onto distributed memory leads to poor scalability. NSCALE allows users to write programs at the level of neighborhoods or subgraphs rather than at the level of vertices, and to declaratively specify the subgraphs of interest. It enables the efficient distributed execution of these neighborhood-centric complex analysis tasks over largescale graphs, while minimizing resource consumption and communication cost, thereby substantially reducing the overall cost of graph data analytics in the Cloud. The results of our extensive experimental evaluation of these prototypes with several real-world data sets and applications validate the effectiveness of our techniques which provide orders-of-magnitude reductions in the overheads of distributed data querying and analysis in the Cloud.

Quantitative Derivation of Effective Evolution Equations for the Dynamics of Bose-Einstein Condensates

This thesis proves certain results concerning an important question in non-equilibrium quantum statistical mechanics which is the derivation of effective evolution equations approximating the dynamics of a system of large number of bosons initially at equilibrium (ground state at very low temperatures). The dynamics of such systems are governed by the time-dependent linear many-body Schroedinger equation from which it is typically difficult to extract useful information due to the number of particles being large. We will study quantitatively (i.e. with explicit bounds on the error) how a suitable one particle non-linear Schroedinger equation arises in the mean field limit as number of particles N → ∞ and how the appropriate corrections to the mean field will provide better approximations of the exact dynamics. In the first part of this thesis we consider the evolution of N bosons, where N is large, with two-body interactions of the form N³ᵝv(Nᵝ⋅), 0≤β≤1. The parameter β measures the strength and the range of interactions. We compare the exact evolution with an approximation which considers the evolution of a mean field coupled with an appropriate description of pair excitations, see [18,19] by Grillakis-Machedon-Margetis. We extend the results for 0 ≤ β < 1/3 in [19, 20] to the case of β < 1/2 and obtain an error bound of the form p(t)/Nᵅ, where α>0 and p(t) is a polynomial, which implies a specific rate of convergence as N → ∞. In the second part, utilizing estimates of the type discussed in the first part, we compare the exact evolution with the mean field approximation in the sense of marginals. We prove that the exact evolution is close to the approximate in trace norm for times of the order o(1)√N compared to log(o(1)N) as obtained in Chen-Lee-Schlein [6] for the Hartree evolution. Estimates of similar type are obtained for stronger interactions as well.

MULTI-BAND BOSE HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONS

Experiments with ultracold atoms in optical lattice have become a versatile testing ground to study diverse quantum many-body Hamiltonians. A single-band Bose-Hubbard (BH) Hamiltonian was first proposed to describe these systems in 1998 and its associated quantum phase-transition was subsequently observed in 2002. Over the years, there has been a rapid progress in experimental realizations of more complex lattice geometries, leading to more exotic BH Hamiltonians with contributions from excited bands, and modified tunneling and interaction energies. There has also been interesting theoretical insights and experimental studies on “un- conventional” Bose-Einstein condensates in optical lattices and predictions of rich orbital physics in higher bands. In this thesis, I present our results on several multi- band BH models and emergent quantum phenomena. In particular, I study optical lattices with two local minima per unit cell and show that the low energy states of a multi-band BH Hamiltonian with only pairwise interactions is equivalent to an effec- tive single-band Hamiltonian with strong three-body interactions. I also propose a second method to create three-body interactions in ultracold gases of bosonic atoms in a optical lattice. In this case, this is achieved by a careful cancellation of two contributions in the pair-wise interaction between the atoms, one proportional to the zero-energy scattering length and a second proportional to the effective range. I subsequently study the physics of Bose-Einstein condensation in the second band of a double-well 2D lattice and show that the collision aided decay rate of the con- densate to the ground band is smaller than the tunneling rate between neighboring unit cells. Finally, I propose a numerical method using the discrete variable repre- sentation for constructing real-valued Wannier functions localized in a unit cell for optical lattices. The developed numerical method is general and can be applied to a wide array of optical lattice geometries in one, two or three dimensions.