Probabilistic analysis of algorithms for dual bin packing problems

In the dual bin packing problem, the objective is to assign items of given size to the largest possible number of bins, subject to the constraint that the total size of the items assigned to any bin is at least equal to 1. We carry out a probabilistic analysis of this problem under the assumption that the items are drawn independently from the uniform distribution on [0, 1] and reveal the connection between this problem and the classical bin packing problem as well as to renewal theory.

Renderings of the Abyss: some changing nineteenth-century literary perceptions of the animal / human divide.

The aim of this thesis is to amalgamate philosophy and history of science with literature to achieve an overview of changing ideas of the animal/human divide during the nineteenth century. Drawing on the ideas of Jacques Derrida, Friedrich Nietzsche, Julia Kristeva and Giorgio Agamben. I consider this divide and its contents, often regarded as an abyss. The study is written like a time line, starting at the beginning of the nineteenth century and finishing at the end. I split the nineteenth century into four time periods centred around the emergence of Darwinian theory, considered by this study to be the single most prolific scientific event to have occurred during the nineteenth century. These time frames are the pre-Darwinian, the early Darwinian, the late Darwinian and the post-Darwinian. The study is split into four chapters which coincide with these time frames, covering four different novels which exemplify contextually relevant ideas of the abyss. These are Frankenstein by Mary Shelley, Moby-Dick by Herman Melville, Crime and Punishment by Fyodor Dostoevsky and The Island of Doctor Moreau by H.G. Wells. During the course of this study I consider various ideas applied by the authors about the abyssal limits and what they consist of. These include considerations on reason, society, morality and spirituality, all ideas used in various different manners to attempt to explain the abyss. From these various deliberations I formulate a conclusion which takes into account the various nuances which would have effected each of the writer’s formulations of the abyss

Kondo Effect in Fermi Systems with a Gap: A Renormalization Group Study

We present the results of a Wilson Renormalization Group study of the single-impurity Kondo and Anderson models in a system with a gap in the conduction electron spectrum. The behavior of the impurity susceptibility and the zero-frequency response function, $T>$ are discussed in the cases with and without particle-hole symmetry. In addition, for the asymmetric Anderson model the correlation functions, $<\vec S \cdot\vec \sigma (0)>$,$$, and$$ are computed.Comment: 10 pages, 10 figure

Nutrient Estimation from 24-Hour Food Recalls Using Machine Learning and Database Mapping: A Case Study with Lactose.

The Automated Self-Administered 24-Hour Dietary Assessment Tool (ASA24) is a free dietary recall system that outputs fewer nutrients than the Nutrition Data System for Research (NDSR). NDSR uses the Nutrition Coordinating Center (NCC) Food and Nutrient Database, both of which require a license. Manual lookup of ASA24 foods into NDSR is time-consuming but currently the only way to acquire NCC-exclusive nutrients. Using lactose as an example, we evaluated machine learning and database matching methods to estimate this NCC-exclusive nutrient from ASA24 reports. ASA24-reported foods were manually looked up into NDSR to obtain lactose estimates and split into training (n = 378) and test (n = 189) datasets. Nine machine learning models were developed to predict lactose from the nutrients common between ASA24 and the NCC database. Database matching algorithms were developed to match NCC foods to an ASA24 food using only nutrients ("Nutrient-Only") or the nutrient and food descriptions ("Nutrient + Text"). For both methods, the lactose values were compared to the manual curation. Among machine learning models, the XGB-Regressor model performed best on held-out test data (R2 = 0.33). For the database matching method, Nutrient + Text matching yielded the best lactose estimates (R2 = 0.76), a vast improvement over the status quo of no estimate. These results suggest that computational methods can successfully estimate an NCC-exclusive nutrient for foods reported in ASA24

LSEMINK: A Modified Newton-Krylov Method for Log-Sum-Exp Minimization

This paper introduces LSEMINK, an effective modified Newton-Krylov algorithm geared toward minimizing the log-sum-exp function for a linear model. Problems of this kind arise commonly, for example, in geometric programming and multinomial logistic regression. Although the log-sum-exp function is smooth and convex, standard line search Newton-type methods can become inefficient because the quadratic approximation of the objective function can be unbounded from below. To circumvent this, LSEMINK modifies the Hessian by adding a shift in the row space of the linear model. We show that the shift renders the quadratic approximation to be bounded from below and that the overall scheme converges to a global minimizer under mild assumptions. Our convergence proof also shows that all iterates are in the row space of the linear model, which can be attractive when the model parameters do not have an intuitive meaning, as is common in machine learning. Since LSEMINK uses a Krylov subspace method to compute the search direction, it only requires matrix-vector products with the linear model, which is critical for large-scale problems. Our numerical experiments on image classification and geometric programming illustrate that LSEMINK considerably reduces the time-to-solution and increases the scalability compared to geometric programming and natural gradient descent approaches. It has significantly faster initial convergence than standard Newton-Krylov methods, which is particularly attractive in applications like machine learning. In addition, LSEMINK is more robust to ill-conditioning arising from the nonsmoothness of the problem. We share our MATLAB implementation at https://github.com/KelvinKan/LSEMINK

Theories for multiple resonances

Two microscopic theories for multiple resonances in nuclei are compared, n-particle-hole RPA and quantized Time-Dependent Hartree-Fock (TDHF). The Lipkin-Meshkov-Glick model is used as test case. We find that quantized TDHF is superior in many respects, except for very small systems.Comment: 14 Pages, 3 figures available upon request

An extended overview of natural gas use embodied in world economy and supply chains: Policy implications from a time series analysis

As an extension of our previous study on natural gas use in world economy (Kan et al., Energy Policy 124 (2019) 215–225), this paper explores policy implications based on a time series analysis uncovering the evolution of natural gas use embodied in global supply chains during 2000-2011. Due to increasing gas supply from gas-rich regions to gas-scarce regions and outsourcing of energy-intensive industries, trade imbalance of embodied natural gas is intensifying globally, corresponding to strengthening gas resource relocation and environmental stress shift. Regarding trade patterns, EU and Russia remain the leading (net) importer and exporter of embodied gas, respectively. And global trade relations are diversifying over time, with more suppliers and recipients joining the international trade. Based on the New Policies Scenario provided by IEA, a long term forecast of embodied gas use illustrates need to prepare for a world with changing energy mix, with respect to growing availability of low-cost natural gas and robust demand growth coming from emerging economies, especially China, who is struggling to fight against air pollution through coal-to-gas switch. Potential room to expand natural gas utilization is also targeted, and the expansion requires coordination of all the agents in global supply chains