Valid Inequalities and Facets for Multi-Module (Survivable) Capacitated Network Design Problem

In this dissertation, we develop new methodologies and algorithms to solve the multi-module (survivable) network design problem. Many real-world decision-making problems can be modeled as network design problems, especially on networks with capacity requirements on arcs or edges. In most cases, network design problems of this type that have been studied involve different types of capacity sizes (modules), and we call them the multi-module capacitated network design (MMND) problem. MMND problems arise in various industrial applications, such as transportation, telecommunication, power grid, data centers, and oil production, among many others. In the first part of the dissertation, we study the polyhedral structure of the MMND problem. We summarize current literature on polyhedral study of MMND, which generates the family of the so-called cutset inequalities based on the traditional mixed integer rounding (MIR). We then introduce a new family of inequalities for MMND based on the so-called n-step MIR, and show that various classes of cutset inequalities in the literature are special cases of these inequalities. We do so by studying a mixed integer set, the cutset polyhedron, which is closely related to MMND. We We also study the strength of this family of inequalities by providing some facet-defining conditions. These inequalities are then tested on MMND instances, and our computational results show that these classes of inequalities are very effective for solving MMND problems. Generalizations of these inequalities for some variants of MMND are also discussed. Network design problems have many generalizations depending on the application. In the second part of the dissertation, we study a highly applicable form of SND, referred to as multi-module SND (MM-SND), in which transmission capacities on edges can be sum of integer multiples of differently sized capacity modules. For the first time, we formulate MM-SND as a mixed integer program (MIP) using preconfigured-cycles (p-cycles) to reroute flow on failed edges. We derive several classes of valid inequalities for this MIP, and show that the valid inequalities previously developed in the literature for single-module SND are special cases of our inequalities. Furthermore, we show that our valid inequalities are facet-defining for MM-SND in many cases. Our computational results, using a heuristic separation algorithm, show that these inequalities are very effective in solving MM-SND. In particular they are more effective than compared to using single-module inequalities alone. Lastly, we generalize the inequalities for MMND for other mixed integer sets relaxed from MMND and the cutset polyhedron. These inequalities also generalize several valid inequalities in the literature. We conclude the dissertation by summarizing the work and pointing out potential directions for future research

Optimum Search Schemes for Approximate String Matching Using Bidirectional FM-Index

Finding approximate occurrences of a pattern in a text using a full-text index is a central problem in bioinformatics and has been extensively researched. Bidirectional indices have opened new possibilities in this regard allowing the search to start from anywhere within the pattern and extend in both directions. In particular, use of search schemes (partitioning the pattern and searching the pieces in certain orders with given bounds on errors) can yield significant speed-ups. However, finding optimal search schemes is a difficult combinatorial optimization problem. Here for the first time, we propose a mixed integer program (MIP) capable to solve this optimization problem for Hamming distance with given number of pieces. Our experiments show that the optimal search schemes found by our MIP significantly improve the performance of search in bidirectional FM-index upon previous ad-hoc solutions. For example, approximate matching of 101-bp Illumina reads (with two errors) becomes 35 times faster than standard backtracking. Moreover, despite being performed purely in the index, the running time of search using our optimal schemes (for up to two errors) is comparable to the best state-of-the-art aligners, which benefit from combining search in index with in-text verification using dynamic programming. As a result, we anticipate a full-fledged aligner that employs an intelligent combination of search in the bidirectional FM-index using our optimal search schemes and in-text verification using dynamic programming outperforms today's best aligners. The development of such an aligner, called FAMOUS (Fast Approximate string Matching using OptimUm search Schemes), is ongoing as our future work

Together We Make Sense -- Learning Meta-Sense Embeddings from Pretrained Static Sense Embeddings

Sense embedding learning methods learn multiple vectors for a given ambiguous word, corresponding to its different word senses. For this purpose, different methods have been proposed in prior work on sense embedding learning that use different sense inventories, sense-tagged corpora and learning methods. However, not all existing sense embeddings cover all senses of ambiguous words equally well due to the discrepancies in their training resources. To address this problem, we propose the first-ever meta-sense embedding method -- Neighbour Preserving Meta-Sense Embeddings, which learns meta-sense embeddings by combining multiple independently trained source sense embeddings such that the sense neighbourhoods computed from the source embeddings are preserved in the meta-embedding space. Our proposed method can combine source sense embeddings that cover different sets of word senses. Experimental results on Word Sense Disambiguation (WSD) and Word-in-Context (WiC) tasks show that the proposed meta-sense embedding method consistently outperforms several competitive baselines.Comment: Accepted to Findings of ACL 202

Noisy Correspondence Learning with Meta Similarity Correction

Despite the success of multimodal learning in cross-modal retrieval task, the remarkable progress relies on the correct correspondence among multimedia data. However, collecting such ideal data is expensive and time-consuming. In practice, most widely used datasets are harvested from the Internet and inevitably contain mismatched pairs. Training on such noisy correspondence datasets causes performance degradation because the cross-modal retrieval methods can wrongly enforce the mismatched data to be similar. To tackle this problem, we propose a Meta Similarity Correction Network (MSCN) to provide reliable similarity scores. We view a binary classification task as the meta-process that encourages the MSCN to learn discrimination from positive and negative meta-data. To further alleviate the influence of noise, we design an effective data purification strategy using meta-data as prior knowledge to remove the noisy samples. Extensive experiments are conducted to demonstrate the strengths of our method in both synthetic and real-world noises, including Flickr30K, MS-COCO, and Conceptual Captions.Comment: Accepted at CVPR 202

Noise-Tolerant Learning for Audio-Visual Action Recognition

Recently, video recognition is emerging with the help of multi-modal learning, which focuses on integrating distinct modalities to improve the performance or robustness of the model. Although various multi-modal learning methods have been proposed and offer remarkable recognition results, almost all of these methods rely on high-quality manual annotations and assume that modalities among multi-modal data provide semantically relevant information. Unfortunately, the widely used video datasets are usually coarse-annotated or collected from the Internet. Thus, it inevitably contains a portion of noisy labels and noisy correspondence. To address this challenge, we use the audio-visual action recognition task as a proxy and propose a noise-tolerant learning framework to find anti-interference model parameters against both noisy labels and noisy correspondence. Specifically, our method consists of two phases that aim to rectify noise by the inherent correlation between modalities. First, a noise-tolerant contrastive training phase is performed to make the model immune to the possible noisy-labeled data. To alleviate the influence of noisy correspondence, we propose a cross-modal noise estimation component to adjust the consistency between different modalities. As the noisy correspondence existed at the instance level, we further propose a category-level contrastive loss to reduce its interference. Second, in the hybrid-supervised training phase, we calculate the distance metric among features to obtain corrected labels, which are used as complementary supervision to guide the training. Extensive experiments on a wide range of noisy levels demonstrate that our method significantly improves the robustness of the action recognition model and surpasses the baselines by a clear margin.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Learning Edge Representations via Low-Rank Asymmetric Projections

We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information (from social networks, user-item graphs, knowledge bases, etc.) in many machine learning tasks. Unlike previous work, we (1) explicitly model an edge as a function of node embeddings, and we (2) propose a novel objective, the "graph likelihood", which contrasts information from sampled random walks with non-existent edges. Individually, both of these contributions improve the learned representations, especially when there are memory constraints on the total size of the embeddings. When combined, our contributions enable us to significantly improve the state-of-the-art by learning more concise representations that better preserve the graph structure. We evaluate our method on a variety of link-prediction task including social networks, collaboration networks, and protein interactions, showing that our proposed method learn representations with error reductions of up to 76% and 55%, on directed and undirected graphs. In addition, we show that the representations learned by our method are quite space efficient, producing embeddings which have higher structure-preserving accuracy but are 10 times smaller

Preparation of terminal blend/ grafting activated crumb rubber composite modified asphalt based on response surface methodology

Recycling waste tires, crushing them into crumb rubber (CR) and adding them to asphalt can effectively improve the performance and prolong the service life of asphalt pavement. However, the crumb rubber modified asphalt (CRMA) prepared by aforementioned process is prone to segregation during storage and transportation. The terminal blend rubber asphalt (TB) prepared with fine rubber powder by high-speed shearing at high temperature for long time, which effectively improves the storage stability and working performance of crumb rubber modified asphalt, but reduces the high-temperature performance. In this study, grafting activated crumb rubber (GACR) was incorporated into TB to improve its high temperature performance without impairing storage stability. Using shearing temperature, shearing time and grafting activated crumb rubber content as influencing factors, the response surface method (RSM) was carried out to optimize the preparation process. The results indicated that 180°C was a critical temperature, and the swelling of crumb rubber dominated with the temperature below it, but the desulfurization prevailed with the temperature above it. The extension of time favored the swelling of crumb rubber at low temperature but promoted desulfurization at high temperature. With the increase of crumb rubber content, the high temperature performance of modified asphalt improved whereas the storage stability deteriorated. According to the determination of response values and the prediction of optimal values, the suitable preparation conditions and parameters were recommended as shearing temperature of 190°C, shearing time of 90 min, and GACR content of 15%. The composite modified asphalt prepared through the optimized process showed good high temperature stability and storage stability

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data