Inductive Program Synthesis via Iterative Forward-Backward Abstract Interpretation

A key challenge in example-based program synthesis is the gigantic search space of programs. To address this challenge, various work proposed to use abstract interpretation to prune the search space. However, most of existing approaches have focused only on forward abstract interpretation, and thus cannot fully exploit the power of abstract interpretation. In this paper, we propose a novel approach to inductive program synthesis via iterative forward-backward abstract interpretation. The forward abstract interpretation computes possible outputs of a program given inputs, while the backward abstract interpretation computes possible inputs of a program given outputs. By iteratively performing the two abstract interpretations in an alternating fashion, we can effectively determine if any completion of each partial program as a candidate can satisfy the input-output examples. We apply our approach to a standard formulation, syntax-guided synthesis (SyGuS), thereby supporting a wide range of inductive synthesis tasks. We have implemented our approach and evaluated it on a set of benchmarks from the prior work. The experimental results show that our approach significantly outperforms the state-of-the-art approaches thanks to the sophisticated abstract interpretation techniques

Compassion beyond boundaries, solidarity beyond beliefs : responding to the suffering peoples of Asia interreligiously - a comparative study of Christian and Buddhist perspectives

Thesis advisor: Margaret GuiderThis thesis is informed by the reality of human suffering as it manifests itself globally throughout the world, regionally in Asia, particularly East Asia, and more specifically in the context of Korea. Globally speaking, the complexities of human suffering as well as the qualitative and quantitative magnitude of human suffering are beyond the understanding and control of individuals, groups and nations. Mindful of this reality, the thesis asserts that there exists an urgent need for interreligious cooperation among adherents of all religions of the world so that together they may find ways of responding to those who suffer. It argues that interreligious cooperation directed toward the alleviation and prevention of human suffering is not an option but an obligation to all adherents of all religions. The thesis takes as its particular focus the interreligious cooperation of Christians and Buddhists. It asserts that while Christians and Buddhists have distinctive and differentiated understandings of the nature and meaning of human suffering, both religions share a common concern for and commitment to those who suffer.Thesis (STL) — Boston College, 2011.Submitted to: Boston College. School of Theology and Ministry.Discipline: Sacred Theology

On Optimal Consistency-Robustness Trade-Off for Learning-Augmented Multi-Option Ski Rental

The learning-augmented multi-option ski rental problem generalizes the classical ski rental problem in two ways: the algorithm is provided with a prediction on the number of days we can ski, and the ski rental options now come with a variety of rental periods and prices to choose from, unlike the classical two-option setting. Subsequent to the initial study of the multi-option ski rental problem (without learning augmentation) due to Zhang, Poon, and Xu, significant progress has been made for this problem recently in particular. The problem is very well understood when we relinquish one of the two generalizations -- for the learning-augmented classical ski rental problem, algorithms giving best-possible trade-off between consistency and robustness exist; for the multi-option ski rental problem without learning augmentation, deterministic/randomized algorithms giving the best-possible competitiveness have been found. However, in presence of both generalizations, there remained a huge gap between the algorithmic and impossibility results. In fact, for randomized algorithms, we did not have any nontrivial lower bounds on the consistency-robustness trade-off before. This paper bridges this gap for both deterministic and randomized algorithms. For deterministic algorithms, we present a best-possible algorithm that completely matches the known lower bound. For randomized algorithms, we show the first nontrivial lower bound on the consistency-robustness trade-off, and also present an improved randomized algorithm. Our algorithm matches our lower bound on robustness within a factor of e/2 when the consistency is at most 1.086.Comment: 16 pages, 2 figure

Improved Learning-Augmented Algorithms for the Multi-Option Ski Rental Problem via Best-Possible Competitive Analysis

In this paper, we present improved learning-augmented algorithms for the multi-option ski rental problem. Learning-augmented algorithms take ML predictions as an added part of the input and incorporates these predictions in solving the given problem. Due to their unique strength that combines the power of ML predictions with rigorous performance guarantees, they have been extensively studied in the context of online optimization problems. Even though ski rental problems are one of the canonical problems in the field of online optimization, only deterministic algorithms were previously known for multi-option ski rental, with or without learning augmentation. We present the first randomized learning-augmented algorithm for this problem, surpassing previous performance guarantees given by deterministic algorithms. Our learning-augmented algorithm is based on a new, provably best-possible randomized competitive algorithm for the problem. Our results are further complemented by lower bounds for deterministic and randomized algorithms, and computational experiments evaluating our algorithms' performance improvements.Comment: 23 pages, 1 figur

Changes in Cytokine Expression after Electroacupuncture in Neuropathic Rats

The production of proinflammatory cytokines including interleukin-1 (IL-1), interleukin-6 (IL-6), and tumor necrosis factor-α (TNF-α) plays a key role in chronic pain such as neuropathic pain. We investigated changes in cytokine expression in injured peripheral nerves and dorsal root ganglia (DRG) following electroacupuncture (EA) treatment. Neuropathic pain was induced by peripheral nerve injury to the left hind limb of Sprague-Dawley rats under pentobarbital anesthesia. Two weeks later, the nerve-injured rats were treated by EA for 10 minutes. The expression levels of IL-1β, IL-6, and TNF-α in peripheral nerves and DRG of neuropathic rats were significantly increased in nerve-injured rats. However, after EA, the cytokine expression levels were noticeably decreased in peripheral nerves and DRG. These results suggest that EA stimulation can reduce the levels of proinflamtory cytokines elevated after nerve injury

Basic Principles and Practical Applications of the Cahn–Hilliard Equation

The celebrated Cahn–Hilliard (CH) equation was proposed to model the process of phase separation in binary alloys by Cahn and Hilliard. Since then the equation has been extended to a variety of chemical, physical, biological, and other engineering fields such as spinodal decomposition, diblock copolymer, image inpainting, multiphase fluid flows, microstructures with elastic inhomogeneity, tumor growth simulation, and topology optimization. Therefore, it is important to understand the basic mechanism of the CH equation in each modeling type. In this paper, we review the applications of the CH equation and describe the basic mechanism of each modeling type with helpful references and computational simulation results

Efficient 3D Volume Reconstruction from a Point Cloud Using a Phase-Field Method

We propose an explicit hybrid numerical method for the efficient 3D volume reconstruction from unorganized point clouds using a phase-field method. The proposed three-dimensional volume reconstruction algorithm is based on the 3D binary image segmentation method. First, we define a narrow band domain embedding the unorganized point cloud and an edge indicating function. Second, we define a good initial phase-field function which speeds up the computation significantly. Third, we use a recently developed explicit hybrid numerical method for solving the three-dimensional image segmentation model to obtain efficient volume reconstruction from point cloud data. In order to demonstrate the practical applicability of the proposed method, we perform various numerical experiments

The mixed-valent titanium phosphate, Li2Ti2(PO4)3, dilithium dititanium(III/IV) tris­(orthophosphate)

The mixed-valent titanium phosphate, Li2Ti2(PO4)3, has been prepared by the reactive halide flux method. The title compound is isostructural with Li2TiM(PO4)3 (M = Fe, Cr) and Li2FeZr(PO4)3 and has the same 3 ∞[Ti2(PO4)3]2− framework as the previously reported Li3- xM 2(PO4)3 phases. The framework is built up from corner-sharing TiO6 octa­hedra and PO4 tetra­hedra, one of which has 2 symmetry. The Li+ ions are located on one crystallographic position and reside in the vacancies of the framework. They are surrounded by four O atoms in a distorted tetra­hedral coordination. The classical charge-balance of the title compound can be represented as Li+ 2(Ti3+/Ti4+)(PO4 3−)3