Aberration-corrected three-dimensional positioning with a single-shot metalens array

Three-dimensional (3D) positioning with the correction of imaging aberrations in the photonic platform remains challenging. Here, we combine techniques from nanophotonics and machine vision to significantly improve the imaging and positioning performance. We use a titanium dioxide metalens array operating in the visible region to realize multipole imaging and introduce a cross-correlation-based gradient descent algorithm to analyze the intensity distribution in the image plane. This corrects the monochromatic aberrations to improve the imaging quality. Analysis of the two-dimensional aberration-corrected information in the image plane enables the 3D coordinates of the object to be determined with a measured relative accuracy of 0.60%-1.31%. We also demonstrate the effectiveness of the metalens array for arbitrary incident polarization states. Our approach is single-shot, compact, aberration-corrected, polarization-insensitive, and paves the way for future integrated photonic robotic vision systems and intelligent sensing platforms that are feasible on the submillimeter scale, such as face recognition, autonomous vehicles, microrobots, and wearable intelligent devices.National Key Research and Development Program of China (2016YFA0301102, 2017YFA0303800); China National Funds for Distinguished Young Scientists (11925403); National Natural Science Foundation of China (11904183, 11904181, 11974193, 91856101, 11774186, 21421001); Natural Science Foundation of Tianjin City for Distinguished Young Scientists (18JCJQJC45700); National Postdoctoral Program for Innovative Talents (BX20180148); China Postdoctoral Science Foundation (2018M640224, 2018M640229)

Identifying Non-Sublattice Equivalence Classes Induced by an Attribute Reduction in FCA

The detection of redundant or irrelevant variables (attributes) in datasets becomes essential in different frameworks, such as in Formal Concept Analysis (FCA). However, removing such variables can have some impact on the concept lattice, which is closely related to the algebraic structure of the obtained quotient set and their classes. This paper studies the algebraic structure of the induced equivalence classes and characterizes those classes that are convex sublattices of the original concept lattice. Particular attention is given to the reductions removing FCA's unnecessary attributes. The obtained results will be useful to other complementary reduction techniques, such as the recently introduced procedure based on local congruences

The Foundation of Pattern Structures and their Applications

This thesis is divided into a theoretical part, aimed at developing statements around the newly introduced concept of pattern morphisms, and a practical part, where we present use cases of pattern structures. A first insight of our work clarifies the facts on projections of pattern structures. We discovered that a projection of a pattern structure does not always lead again to a pattern structure. A solution to this problem, and one of the most important points of this thesis, is the introduction of pattern morphisms in Chapter4. Pattern morphisms make it possible to describe relationships between pattern structures, and thus enable a deeper understanding of pattern structures in general. They also provide the means to describe projections of pattern structures that lead to pattern structures again. In Chapter5 and Chapter6, we looked at the impact of morphisms between pattern structures on concept lattices and on their representations and thus clarified the theoretical background of existing research in this field. The application part reveals that random forests can be described through pattern structures, which constitutes another central achievement of our work. In order to demonstrate the practical relevance of our findings, we included a use case where this finding is used to build an algorithm that solves a real world classification problem of red wines. The prediction accuracy of the random forest is better, but the high interpretability makes our algorithm valuable. Another approach to the red wine classification problem is presented in Chapter 8, where, starting from an elementary pattern structure, we built a classification model that yielded good results

Innovative Apatite/Bioactive Glass-based materials for biomedical applications

Musculoskeletal-related problems are nowadays one of the main concerns in healthcare, due to tumors, traumatology, osteoporosis and others pathologies, especially considering ageing populations. These diseases and induced defects affect millions of people worldwide. An important scientific effort was dedicated, in the past decades, to the development of bonegrafts materials as alternatives to allo- and autografts, due to the drawbacks associated with the employment of the latter ones (as for instance, transmission complications as well as immunological rejection and morbidity). Scientific research focused on synthetic bone graft displaying suitable properties is an actual hot topic. In this context, calcium phosphates (in particular hydroxyapatite) and bioactive glasses, recently gained much attention due to their characteristics as promising materials for the treatment of non-self-healing bone defects. Indeed, they display biocompatibility, good bioactivity and non-toxicity. Despite these, clinical application of hydroxyapatite- and bioactive glass-derived materials is still limited, and further development of such materials is needed. The main aim of this work is then to contribute to solve some of the drawbacks displayed by these classes of materials (related to their composition, synthesis and manufacturing), to provide possible useful insights about howto limit/overcome them. In the present thesis, beyond the state of the art, it was attempted to tackle various problems related to the development of innovative materials for hard tissue engineering

Congruencias y factorización como herramientas de reducción en el análisis de conceptos formales

Desde su introducción a principios de los años ochenta por B. Ganter y R. Wille, el Análisis de Conceptos Formales (FCA, de sus siglas en inglés) ha sido una de las herramientas matemáticas para el análisis de datos que más desarrollo ha experimentado. El FCA es una teoría matemática que determina estructuras conceptuales entre conjuntos de datos. En particular, las bases de datos se interpretan formalmente en esta teoría con la noción de contexto, que viene determinado por un conjunto de objetos, un conjunto de atributos y una relación entre ambos conjuntos. Las herramientas que proporciona el FCA permiten manipular adecuadamente los datos y extraer información relevante de ellos. Una de las líneas de investigación con más importancia es la reducción del conjunto de atributos que contienen estos conjuntos de datos, preservando la información esencial y eliminando la redundancia que puedan contener. La reducción de atributos también ha sido estudiada en otros ambientes, como en la Teoría de Conjuntos Rugosos, así como en las distintas generalizaciones difusas de ambas teorías. En el FCA, se ha demostrado que cuando se lleva a cabo una reducción de atributos de un contexto formal, se induce una relación de equivalencia sobre el conjunto de conceptos del contexto original. Esta relación de equivalencia inducida tiene una particularidad, sus clases de equivalencia tienen una estructura de semirretículo superior con un elemento máximo, es decir, no forman estructuras algebraicas cerradas, en general. En esta tesis estudiamos cómo es posible complementar las reducciones de atributos dotando a las clases de equivalencia con una estructura algebraica cerrada. La noción de congruencia consigue este propósito, sin embargo, el uso de este tipo de relación de equivalencia puede desembocar en una gran pérdida de información debido a que las clases de equivalencia agrupan demasiados conceptos. Para abordar este problema, en esta tesis se introduce una noción debilitada de congruencia que denominamos congruencia local. La congruencia local da lugar a clases de equivalencia con estructura de subretículo convexo, siendo más flexible a la hora de agrupar conceptos pero manteniendo propiedades interesantes desde un punto de vista algebraico. Se presenta una discusión general de los principales resultados relativos al estudio y aplicación de las congruencias locales que se han obtenido a lo largo de la investigación desarrollada durante la tesis. En particular, se introduce la noción de congruencia local junto con un análisis de las propiedades que satisface, así como una relación de orden sobre el conjunto de las clases de equivalencia. Además, realizamos un análisis profundo del impacto que genera el uso de las congruencias locales en el FCA, tanto en el contexto formal como en el retículo de conceptos. En este análisis identificamos aquellas clases de equivalencia de la relación inducida por una reducción de atributos, sobre las cuales actuaría la congruencia local, realizando una agrupación de conceptos diferente para obtener subretículos convexos. Adicionalmente, llevamos a cabo un estudio sobre el uso de las congruencias locales cuando en la reducción de atributos considerada se han eliminado todos los atributos innecesarios del contexto, obtienen resultados interesantes. Presentamos diversos mecanismos que permiten calcular congruencias locales y aplicarlas sobre retículos de conceptos, detallando las modificaciones que se realizan sobre el contexto formal para proporcionar un método de reducción basado en congruencias locales. Por otra parte, otra de las estrategias que nos permite reducir la complejidad del análisis de los contextos formales son los mecanismos de factorización. Los procedimientos utilizados para factorizar permiten dividir un contexto en dos o más subcontextos formales de menor tamaño, pudiéndose estudiar por separado más fácilmente. Se presenta un estudio preliminar sobre la factorización de contextos formales difusos usando operadores modales, que no se ha publicado aún en una revista. Estos operadores modales ya han sido utilizados para extraer subcontextos independientes de un contexto formal clásico obteniéndose así una factorización del contexto original. En esta tesis estudiamos también diversas propiedades que nos ayudan a comprender mejor cómo funciona la descomposición de tablas de datos booleanos, para luego realizar una adaptación de dichas propiedades al marco de trabajo multiadjunto. El estudio de estas propiedades generales en el marco de trabajo multiadjunto será de gran relevancia para poder obtener en el futuro un procedimiento que nos permita factorizar contextos formales multiadjuntos. Por tanto, la obtención de mecanismos de factorización de contextos multiadjuntos será clave para el análisis y tratamiento de grandes bases de dato

Physical Vapor Deposited Biomedical Coatings

The book outlines a series of developments made in the manufacturing of bio-functional layers via Physical Vapour-Deposited (PVD) technologies for application in various areas of healthcare. The scrutinized PVD methods include Radio-Frequency Magnetron Sputtering (RF-MS), Cathodic Arc Evaporation, Pulsed Electron Deposition and its variants, Pulsed Laser Deposition, and Matrix-Assisted Pulsed Laser Evaporation (MAPLE) due to their great promise, especially in dentistry and orthopaedics. These methods have yet to gain traction for industrialization and large-scale application in biomedicine. A new generation of implant coatings can be made available by the (1) incorporation of organic moieties (e.g., proteins, peptides, enzymes) into thin films using innovative methods such as combinatorial MAPLE, (2) direct coupling of therapeutic agents with bioactive glasses or ceramics within substituted or composite layers via RF-MS, or (3) innovation in high-energy deposition methods, such as arc evaporation or pulsed electron beam methods

On Pattern Setups and Pattern Multistructures

Modern order and lattice theory provides convenient mathematical tools for pattern mining, in particular for condensed irredundant representations of pattern spaces and their efficient generation. Formal Concept Analysis (FCA) offers a generic framework , called pattern structures, to formalize many types of patterns, such as itemsets, intervals, graph and sequence sets. Moreover, FCA provides generic algorithms to generate irredundantly all closed patterns, the only condition being that the pattern space is a meet-semilattice. This does not always hold, e.g., for sequential and graph patterns. Here, we discuss pattern setups consisting of descriptions making just a partial order. Such a framework can be too broad, causing several problems, so we propose a new model, dubbed pattern multistructure, lying between pattern setups and pattern structures, which relies on multilattices. Finally, we consider some techniques , namely completions, transforming pattern setups to pattern structures using sets/antichains of patterns