A Multi-Dimensional Width-Bounded Geometric Separator and its Applications to Protein Folding

We used a divide-and-conquer algorithm to recursively solve the two-dimensional problem of protein folding of an HP sequence with the maximum number of H-H contacts. We derived both lower and upper bounds for the algorithmic complexity by using the newly introduced concept of multi-directional width-bounded geometric separator. We proved that for a grid graph G with n grid points P, there exists a balanced separator A subseteq P$ such that A has less than or equal to 1.02074 sqrt{n} points, and G-A has two disconnected subgraphs with less than or equal to {2over 3}n nodes on each subgraph. We also derive a 0.7555sqrt {n} lower bound for our balanced separator. Based on our multidirectional width-bounded geometric separator, we found that there is an O(n^{5.563sqrt{n}}) time algorithm for the 2D protein folding problem in the HP model. We also extended the upper bound results to rectangular and triangular lattices

Adaptive Methods for Robust Document Image Understanding

A vast amount of digital document material is continuously being produced as part of major digitization efforts around the world. In this context, generic and efficient automatic solutions for document image understanding represent a stringent necessity. We propose a generic framework for document image understanding systems, usable for practically any document types available in digital form. Following the introduced workflow, we shift our attention to each of the following processing stages in turn: quality assurance, image enhancement, color reduction and binarization, skew and orientation detection, page segmentation and logical layout analysis. We review the state of the art in each area, identify current defficiencies, point out promising directions and give specific guidelines for future investigation. We address some of the identified issues by means of novel algorithmic solutions putting special focus on generality, computational efficiency and the exploitation of all available sources of information. More specifically, we introduce the following original methods: a fully automatic detection of color reference targets in digitized material, accurate foreground extraction from color historical documents, font enhancement for hot metal typesetted prints, a theoretically optimal solution for the document binarization problem from both computational complexity- and threshold selection point of view, a layout-independent skew and orientation detection, a robust and versatile page segmentation method, a semi-automatic front page detection algorithm and a complete framework for article segmentation in periodical publications. The proposed methods are experimentally evaluated on large datasets consisting of real-life heterogeneous document scans. The obtained results show that a document understanding system combining these modules is able to robustly process a wide variety of documents with good overall accuracy

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

Ion and Molecule Transport in Membrane Systems

Membranes play an enormous role in our life. Biological cell membranes control the fluxes of substances in and out of cells. Artificial membranes are widely used in numerous applications including “green” separation processes in chemistry, agroindustry, biology, medicine; they are used as well in energy generation from renewable sources. They largely mimic the structure and functions of biological membranes. The similarity in the structure leads to the similarity in the properties and the approaches to study the laws governing the behavior of both biological and artificial membranes. In this book, some physico-chemical and chemico-physical aspects of the structure and behavior of biological and artificial membranes are investigated

Large bichromatic point sets admit empty monochromatic 4-gons

We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its interior. We show that any bichromatic set of n ≥ 5044 points in R2 in general position determines at least one empty, monochromatic quadrilateral (and thus linearly many).Postprint (published version

Machine Learning Framework for Causal Modeling for Process Fault Diagnosis and Mechanistic Explanation Generation

Machine learning models, typically deep learning models, often come at the cost of explainability. To generate explanations of such systems, models need to be rooted in first-principles, at least mechanistically. In this work we look at a gamete of machine learning models based on different levels of process knowledge for process fault diagnosis and generating mechanistic explanations of processes. In chapter 1, we introduce the thesis using a range of problems from causality, explainability, aiming towards the goal of generating mechanistic explanations of process systems. Chapter 2 looks at an approach for generating causal models purely through data-centric approach, with minimal process knowledge with respect to equipment connectivity and identifying causality in the domains. These causal models generated can be utilized for process fault diagnosis. Chapter 3 and chapter 4 show how deep learning models can be used for both classification for process fault diagnosis and regression. We see that depending on the hyperparameters, i.e., purely the breadth and depth of a neural network, the learned hidden representations vary from a simple set of features, to more complex sets of features. While these hidden representations may be exploited to aid in classification and regression problems, the true explanations of these representations do not correlate with mechanisms in the system of interest. There is thus a requirement to add more mechanistic information about the features generated to aid in explainability. Chapter 5 shows how incorporating process knowledge can aid in generating such mechanistic explanations based on automated variable transformations. In this chapter we show how process knowledge can be used to generate features, or model forms to generate explainable models. These models have the ability of extracting the true models of the system from the model knowledge provided