A Branch and Price Algorithm for List Coloring Problem

Coloring problems in graphs have been used to model a wide range of real applications. In particular, the List Coloring Problem generalizes the well-known Graph Coloring Problem for which many exact algorithms have been developed. In this work, we present a Branch-and-Price algorithm for the weighted version of the List Coloring Problem, based on the one developed by Mehrotra and Trick (1996) for the Graph Coloring Problem. This version considers non-negative weights associated to each color and it is required to assign a color to each vertex from predetermined lists in such a way the sum of weights of the assigned colors is minimum. Computational experiments show the good performance of our approach, being able to comfortably solve instances whose graphs have up to seventy vertices. These experiences also bring out that the hardness of the instances of the List Coloring Problem does not seem to depend only on quantitative parameters such as the size of the graph, its density, and the size of list of colors, but also on the distribution of colors present in the lists.Fil: Lucci, Mauro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Nasini, Graciela Leonor. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Severin, Daniel Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina10th Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS 2019)Belo HorizonteBrasilCoordenação de Aperfeiçoamento de Pessoal de Nivel SuperiorConselho Nacional de Desenvolvimento Científico e Técnologico do BrasilUniversidade Federal de Minas Gerai

Optimal Planning of Container Terminal Operations

Due to globalization and international trade, moving goods using a mixture of transportation modes has become a norm; today, large vessels transport 95% of the international cargos. In the first part of this thesis, the emphasis is on the sea-land intermodal transport. The availability of different modes of transportation (rail/road/direct) in sea-land intermodal transport and container flows (import, export, transhipment) through the terminal are considered simultaneously within a given planning time horizon. We have also formulated this problem as an Integer Programming (IP) model and the objective is to minimise storage cost, loading and transportation cost from/to the customers. To further understand the computational complexity and performance of the model, we have randomly generated a large number of test instances for extensive experimentation of the algorithm. Since, CPLEX was unable to find the optimal solution for the large test problems; a heuristic algorithm has been devised based on the original IP model to find near „optimal‟ solutions with a relative error of less than 4%. Furthermore, we developed and implemented Lagrangian Relaxation (LR) of the IP formulation of the original problem. The bounds derived from LR were improved using sub-gradient optimisation and computational results are presented. In the second part of the thesis, we consider the combined problems of container assignment and yard crane (YC) deployment within the container terminal. A new IP formulation has been developed using a unified approach with the view to determining optimal container flows and YC requirements within a given planning time horizon. We designed a Branch and Cut (B&C) algorithm to solve the problem to optimality which was computationally evaluated. A novel heuristic approach based on the IP formulation was developed and implemented in C++. Detailed computational results are reported for both the exact and heuristic algorithms using a large number of randomly generated test problems. A practical application of the proposed model in the context of a real case-study is also presented. Finally, a simulation model of container terminal operations based on discrete-event simulation has been developed and implemented with the view of validating the above optimisation model and using it as a test bed for evaluating different operational scenarios

Montana Kaimin, May 5, 1978

Student newspaper of the University of Montana, Missoula.https://scholarworks.umt.edu/studentnewspaper/7782/thumbnail.jp

Quantum phases of interacting bosons in optical lattices

This thesis presents a theoretical analysis of the phase diagram of ultracold bosons in a lattice and interacting with long-range interac- tions. The theoretical model is an extended Bose-Hubbard model and describes the dynamics of ultracold atoms in optical lattices realised in present experimental platforms. We consider here two situations, where either the long-range forces are global and emerge from the coupling with a high-finesse cavity, or they decay with the interparti- cle distance and can be due to Rydberg interactions or to the atoms permanent dipoles. We determine the ground state in one and two dimensions using mean-field treatments. In one dimension we comple- ment our studies using numerical programs based on tensor networks. We focus in particular on parameters for which the hopping induced by the kinetic energy competes with the interaction-induced corre- lated hopping between lattice sites. We analyse the superfluid phases emerging from the competition of these two mechanisms, and identify the parameters, where the two processes destructively interfere. For power-law interactions this quantum interference leads to insulating phases at relatively large kinetic energies, where one would otherwise expect superfluidity. When correlated tunnelling is due to the global potential of a resonator, the ground state is a self-organised topological insulator.Diese Arbeit präsentiert eine theoretische Analyse des Phasendiagramms von ultrakalten Bosonen in einem Gitter, die langreichweitige Wechselwirkungen erfahren. Das theoretische Modell ist ein erweitertes Bose-Hubbard Modell und beschreibt die Dynamik von ultrakalten Atomen in einem optischen Gitter, wie sie in heutigen Experimenten realisiert werden kann. Wir betrachten hier zwei Situationen: Zum einen sind die langreichweitigen Kräfte global und entstehen aus der Kopplung mit einem Resonator. Zum anderen zerfällt das Wechselwirkungspotential mit dem Abstand zwischen den Teilchen, wie es zwischen Rydbergatomen oder Atomen mit einem permanenten Dipolmoment auftritt. Wir bestimmen den Grundzustand in einer und zwei Dimensionen durch Mean-Field Analysen. In einer Dimension benutzen wir zudem ein auf Tensornetzwerken basierendes numerisches Programm. Wir betrachten insbesondere Parameter, für die das durch die kinetische Energie induzierte Tunneln mit dem von der Wechselwirkung induzierten Tunneln konkurriert. Wir analysieren die superfluiden Phasen, die sich aus dieser Kompetition ergeben, und identifizieren die Parameter, bei denen die beiden Prozesse destruktiv interferieren. Für die mit dem Abstand zerfallenden Wechselwirkungen führt diese Quanteninterferenz zu Isolatoren in Parameterbereichen, in denen man sonst Superfluidität erwarten würde. Wenn das Tunneln vom globalen Potential herrührt, ist der Grundzustand ein selbstorganisierter topologischer Isolator

Computational Methods For Comparative Non-coding Rna Analysis: From Structural Motif Identification To Genome-wide Functional Classification

Recent advances in biological research point out that many ribonucleic acids (RNAs) are transcribed from the genome to perform a variety of cellular functions, rather than merely acting as information carriers for protein synthesis. These RNAs are usually referred to as the non-coding RNAs (ncRNAs). The versatile regulation mechanisms and functionalities of the ncRNAs contribute to the amazing complexity of the biological system. The ncRNAs perform their biological functions by folding into specific structures. In this case, the comparative study of the ncRNA structures is key to the inference of their molecular and cellular functions. We are especially interested in two computational problems for the comparative analysis of ncRNA structures: the alignment of ncRNA structures and their classification. Specifically, we aim to develop algorithms to align and cluster RNA structural motifs (recurrent RNA 3D fragments), as well as RNA secondary structures. Thorough understanding of RNA structural motifs will help us to disassemble the huge RNA 3D structures into functional modules, which can significantly facilitate the analysis of the detailed molecular functions. On the other hand, efficient alignment and clustering of the RNA secondary structures will provide insights for the understanding of the ncRNA expression and interaction in a genomic scale. In this dissertation, we will present a suite of computational algorithms and software packages to solve the RNA structural motif alignment and clustering problem, as well as the RNA iii secondary structure alignment and clustering problem. The summary of the contributions of this dissertation is as follows. (1) We developed RNAMotifScan for comparing and searching RNA structural motifs. Recent studies have shown that RNA structural motifs play an essential role in RNA folding and interaction with other molecules. Computational identification and analysis of RNA structural motifs remain to be challenging tasks. Existing motif identification methods based on 3D structure may not properly compare motifs with high structural variations. We present a novel RNA structural alignment method for RNA structural motif identi- fication, RNAMotifScan, which takes into consideration the isosteric (both canonical and non-canonical) base-pairs and multi-pairings in RNA structural motifs. The utility and accuracy of RNAMotifScan are demonstrated by searching for Kink-turn, C-loop, Sarcin-ricin, Reverse Kink-turn and E-loop motifs against a 23s rRNA (PDBid: 1S72), which is well characterized for the occurrences of these motifs. (2) We improved upon RNAMotifScan by incorporating base-stacking information and devising a new branch-and-bound algorithm called RNAMotifScanX. Model-based search of RNA structural motif has been focused on finding instances with similar 3D geometry and base-pairing patterns. Although these methods have successfully identified many of the true motif instances, each of them has its own limitations and their accuracy and sensitivity can be further improved. We introduce a novel approach to model the RNA structural motifs, which incorporates both base-pairing and base-stacking information. We also develop a new algorithm to search for known motif instances with the consideration of both base-pairing and base-stacking information. Benchmarking of RNAMotifScanX on searching known RNA structural motifs including kink-turn, C-loop, sarcin-ricin, reverse kink-turn, and E-loop iv clearly show improved performances compared to its predecessor RNAMotifScan and other state-of-the-art RNA structural motif search tools. (3) We develop an RNA structural motif clustering and de novo identification pipeline called RNAMSC. RNA structural motifs are the building blocks of the complex RNA architecture. Identification of non-coding RNA structural motifs is a critical step towards understanding of their structures and functionalities. We present a clustering approach for de novo RNA structural motif identification. We applied our approach on a data set containing 5S, 16S and 23S rRNAs and rediscovered many known motifs including GNRA tetraloop, kink-turn, C-loop, sarcin-ricin, reverse kink-turn, hook-turn, E-loop and tandem-sheared motifs, with higher accuracy than the currently state-of-the-art clustering method. More importantly, several novel structural motif families have been revealed by our novel clustering analysis. (4) We propose an improved RNA structural clustering pipeline that takes into account the length-dependent distribution of the structural similarity measure. We also devise a more efficient and robust CLique finding CLustering algorithm (CLCL), to replace the traditional hierarchical clustering approach. Benchmark of the proposed pipeline on Rfam data clearly demonstrates over 10% performance gain, when compared to a traditional hierarchical clustering pipeline. We applied this new computational pipeline to cluster the posttranscriptional control elements in fly 3’-UTR. The ncRNA elements in the 3’ untranslated regions (3’-UTRs) are known to participate in the genes’ post-transcriptional regulation, such as their stability, translation efficiency, and subcellular localization. Inferring co-expression patterns of the genes by clustering their 3’-UTR ncRNA elements will provide invaluable knowledge for further studies of their functionalities and interactions under specific physiological processes. v (5) We develop an ultra-efficient RNA secondary structure alignment algorithm ERA by using a sparse dynamic programming technique. Current advances of the next-generation sequencing technology have revealed a large number of un-annotated RNA transcripts. Comparative study of the RNA structurome is an important approach to assess the biological functionalities of these RNA transcripts. Due to the large sizes and abundance of the RNA transcripts, an efficient and accurate RNA structure-structure alignment algorithm is in urgent need to facilitate the comparative study. By using the sparse dynamic programming technique, we devised a new alignment algorithm that is as efficient as the tree-based alignment algorithms, and as accurate as the general edit-distance alignment algorithms. We implemented the new algorithm into a program called ERA (Efficient RNA Alignment). Benchmark results indicate that ERA can significantly speedup RNA structure-structure alignments compared to other state-of-the-art RNA alignment tools, while maintaining high alignment accuracy. These novel algorithms have led to the discovery of many novel RNA structural motif instances, which have significantly deepened our understanding to the RNA molecular functions. The genome-wide clustering of ncRNA elements in fly 3’-UTR has predicted a cluster of genes that are responsible for the spermatogenesis process. More importantly, these genes are very likely to be co-regulated by their common 3’-UTR elements. We anticipate that these algorithms and the corresponding software tools will significantly promote the comparative ncRNA research in the futur

Hierarchical dynamics of individual RNA helix base pair formation and disruption

This thesis explores the RNA folding problem using single-molecule field effect transistors (smFETs) to measure the lifetimes of individual RNA base-pairing rearrangements. In the course of this research, considerable computational, chemical, and engineering contributions were developed so that the single-molecule measurements could be conducted and quantified. These advancements have allowed, on the basis of the smFET data collected herein, the quantification of a kinetic model for RNA stem-loop structures which has been generalized to quantitatively explore the phenomenological observation that an RNA found in the bacillus subtilis strain acts as a metabolite-sensing switch, allowing RNA polymerase to transcribe the messenger RNA when the metabolite is present and preventing transcription when the metabolite is absent. Together, the data presented quantify a simple model for the base pairing rearrangements that underlie RNA folding