302 research outputs found

    The Global Riverine Hydrokinetic Resource

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    Systems and Algorithms for Dynamic Graph Processing

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    Data generated from human and systems interactions could be naturally represented as graph data. Several emerging applications rely on graph data, such as the semantic web, social networks, bioinformatics, finance, and trading among others. These applications require graph querying capabilities which are often implemented in graph database management systems (GDBMS). Many GDBMSs have capabilities to evaluate one-time versions of recursive or subgraph queries over static graphs – graphs that do not change or a single snapshot of a changing graph. They generally do not support incrementally maintaining queries as graphs change. However, most applications that employ graphs are dynamic in nature resulting in graphs that change over time, also known as dynamic graphs. This thesis investigates how to build a generic and scalable incremental computation solution that is oblivious to graph workloads. It focuses on two fundamental computations performed by many applications: recursive queries and subgraph queries. Specifically, for subgraph queries, this thesis presents the first approach that (i) performs joins with worstcase optimal computation and communication costs; and (ii) maintains a total memory footprint almost linear in the number of input edges. For recursive queries, this thesis studies optimizations for using differential computation (DC). DC is a general incremental computation that can maintain the output of a recursive dataflow computation upon changes. However, it requires a prohibitively large amount of memory because it maintains differences that track changes in queries input/output. The thesis proposes a suite of optimizations that are based on reducing the number of these differences and recomputing them when necessary. The techniques and optimizations in this thesis, for subgraph and recursive computations, represent a proposal for how to build a state-of-the-art generic and scalable GDBMS for dynamic graph data management

    Sum-of-squares representations for copositive matrices and independent sets in graphs

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    A polynomial optimization problem asks for minimizing a polynomial function (cost) given a set of constraints (rules) represented by polynomial inequalities and equations. Many hard problems in combinatorial optimization and applications in operations research can be naturally encoded as polynomial optimization problems. A common approach for addressing such computationally hard problems is by considering variations of the original problem that give an approximate solution, and that can be solved efficiently. One such approach for attacking hard combinatorial problems and, more generally, polynomial optimization problems, is given by the so-called sum-of-squares approximations. This thesis focuses on studying whether these approximations find the optimal solution of the original problem.We investigate this question in two main settings: 1) Copositive programs and 2) parameters dealing with independent sets in graphs. Among our main new results, we characterize the matrix sizes for which sum-of-squares approximations are able to capture all copositive matrices. In addition, we show finite convergence of the sums-of-squares approximations for maximum independent sets in graphs based on their continuous copositive reformulations. We also study sum-of-squares approximations for parameters asking for maximum balanced independent sets in bipartite graphs. In particular, we find connections with the Lovász theta number and we design eigenvalue bounds for several related parameters when the graphs satisfy some symmetry properties.<br/

    Distinct Difference Configurations in Groups

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    Radiative Forcing & Feedback through the Lens of Solar Geoengineering

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    Global, annual mean surface temperature continues to rise in the wake of the Paris Agreement goal of limiting warming to 2.C and pursing efforts to limit warming to less than 1.5 C. Research paradigms have arisen to analyze projections of future warming, as well as understanding the drivers of anthropogenic climate change since the preindustrial era. One such paradigm is the characterization of anthropogenic emissions of greenhouse gases as an external radiative forcing on the climate system, as well as feedbacks from the climate response to forcing that augment the rate in which the Earth system reestablishes energy balance. As surface temperatures rise, solar geoengineering has been proposed as a means to deliberately alter Earth’s energy balance and achieve Paris Agreement goals through reducing the amount of incoming shortwave radiation from reaching the surface. Through the lens of the conventional forcing-feedback framework, solar geoengineering is challenging to frame due to the purposeful introduction of an external forcing in order to suppress surface warming, and therefore feedback. Furthermore, the potential for multiple external forcings via solar geoengineering to produce feedbacks from an energetic perspective, even in the absence of surface warming, is poorly understood. This thesis attempts to adapt the forcing-feedback paradigm to define potential radiative feedbacks on the climate system as a result of solar geoengineering through three studies. First, we perform an analyses of radiative forcing and feedback between two versions of the Canadian Earth System Model (CanESM) to understand what is physically driving differences in surface warming. We find little difference in radiative forcing from increased CO2 between the two model versions. More positive radiative feedbacks produce a larger amount of warming in CanESM5, primarily from a reduction boundary layer clouds across the equatorial Pacific that reduced the Earth’s albedo to a greater extent. This analysis was essential to understand how radiative feedbacks, specifically from clouds, can impact the rate surface warming. Next, we analyzed radiative forcing from both increased CO2 and a reduced solar constant using the Community Earth System Model (CESM). We find that the magnitude of solar forcing required to offset the positive radiative forcing from quadrupling CO2 is sensitive to radiative adjustments from both forcings. Radiative adjustments, which are climate responses from an external forcing in the absence of surface warming that impact Earth’s energy balance, as a result of reductions in cloud fraction had a dampening effect on the reduction of the solar constant. This work informed how solar constant tuning, which we used as a proxy for more realistic representations of solar geoengineering, can produce changes in cloud fraction that impact planetary albedo and therefore the amount solar forcing required to achieve energy balance. Finally, we extend the work of the first two studies by defining and investigating potential geoengineering radiative feedbacks in a transient solar geoengineering experiment using CESM. We reduce the solar constant over time in an idealized geoengineering experiment that maintains near-zero global mean surface warming in the wake of increasing CO2 and find a decreasing trend in optically thick tropical clouds. Reductions in cloud fraction reduced planetary albedo, which further decreased the amount of solar forcing needed to achieve the same net energy reduction at the surface, thus producing a positive radiative feedback loop in absence of global mean surface warming. This work highlights the need to understand potential feedbacks from realizable methods of solar geoengineering such as stratosphere aerosol injections

    Biophysical methods bridging signal pathway architecture and dynamics in multigenerational bacterial processes

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    Cells sense their environment and process changes through intracellular signaling networks to coordinate behavioral changes, such as cell fate decisions. In bacterial systems, these changes often occur over time periods longer than a single cell cycle. While we are now able to experimentally track and monitor these behavioral changes over multiple generations, we have a limited conceptual understanding of how these decisions are mediated by signaling pathways. Here, I present two projects that build predictive frameworks for understanding signaling pathway dynamics over multiple generations informed by the signal network architectures. In the first section, I use computational simulations to understand how signaling pathway architecture controls the duration over which related cells maintain similar concentrations of signaling pathway components following division from a common mother cell. I find that signal amplification is a requirement for similarity between related cells. In the second section, I take a joint theory-experiment approach to analyze the accumulation timescale of the signaling molecule cyclic di-GMP during biofilm initiation in the soil bacterium B. subtilis. Here I predict that the accumulation occurs over many generations, suggesting the possibility cyclic di-GMP is used as a cellular timer mechanism during biofilm initiation. These results both explain previous experimental findings as well as generate new predictions for how signaling pathways mediate single-cell behaviors in bacterial populations. Together, my work demonstrates the power of a joint theory-experiment approach to understand the long-term, dynamical behavior of intracellular signaling pathways by linking their architecture to their dynamical function

    LIPIcs, Volume 258, SoCG 2023, Complete Volume

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    LIPIcs, Volume 258, SoCG 2023, Complete Volum

    Polynomial optimization: matrix factorization ranks, portfolio selection, and queueing theory

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    Inspired by Leonhard Euler’s belief that every event in the world can be understood in terms of maximizing or minimizing a specific quantity, this thesis delves into the realm of mathematical optimization. The thesis is divided into four parts, with optimization acting as the unifying thread. Part 1 introduces a particular class of optimization problems called generalized moment problems (GMPs) and explores the moment method, a powerful tool used to solve GMPs. We introduce the new concept of ideal sparsity, a technique that aids in solving GMPs by improving the bounds of their associated hierarchy of semidefinite programs. Part 2 focuses on matrix factorization ranks, in particular, the nonnegative rank, the completely positive rank, and the separable rank. These ranks are extensively studied using the moment method, and ideal sparsity is applied (whenever possible) to enhance the bounds on these ranks and speed-up their computation. Part 3 centers around portfolio optimization and the mean-variance-skewness kurtosis (MVSK) problem. Multi-objective optimization techniques are employed to uncover Pareto optimal solutions to the MVSK problem. We show that most linear scalarizations of the MVSK problem result in specific convex polynomial optimization problems which can be solved efficiently. Part 4 explores hypergraph-based polynomials emerging from queueing theory in the setting of parallel-server systems with job redundancy policies. By exploiting the symmetry inherent in the polynomials and some classical results on matrix algebras, the convexity of these polynomials is demonstrated, thereby allowing us to prove that the polynomials attain their optima at the barycenter of the simplex.<br/

    Finding a perfect matching of F2n\mathbb{F}_2^n with prescribed differences

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    We consider the following question by Balister, Gy\H{o}ri and Schelp: given 2n12^{n-1} nonzero vectors in F2n\mathbb{F}_2^n with zero sum, is it always possible to partition the elements of F2n\mathbb{F}_2^n into pairs such that the difference between the two elements of the ii-th pair is equal to the ii-th given vector for every ii? An analogous question in Fp\mathbb{F}_p, which is a case of the so-called "seating couples" problem, has been resolved by Preissmann and Mischler in 2009. In this paper, we prove the conjecture in F2n\mathbb{F}_2^n in the case when the number of distinct values among the given difference vectors is at most n2logn1n-2\log n-1, and also in the case when at least a fraction 12+ε\frac12+\varepsilon of the given vectors are equal (for all ε>0\varepsilon>0 and nn sufficiently large based on ε\varepsilon).Comment: 18 page
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