K-Formal Concept Analysis as linear algebra over idempotent semifields

We report on progress in characterizing K-valued FCA in algebraic terms, where K is an idempotent semifield. In this data mining-inspired approach, incidences are matrices and sets of objects and attributes are vectors. The algebraization allows us to write matrix-calculus formulae describing the polars and the fixpoint equations for extents and intents. Adopting also the point of view of the theory of linear operators between vector spaces we explore the similarities and differences of the idempotent semimodules of extents and intents with the subspaces related to a linear operator in standard algebra. This allows us to shed some light into Formal Concept Analysis from the point of view of the theory of linear operators over idempotent semimodules. In the opposite direction, we state the importance of FCA-related concepts for dual order homomorphisms of linear spaces over idempotent semifields, specially congruences, the lattices of extents, intents and formal concepts

The Singular Value Decomposition over Completed Idempotent Semifields

In this paper, we provide a basic technique for Lattice Computing: an analogue of the Singular Value Decomposition for rectangular matrices over complete idempotent semifields (i-SVD). These algebras are already complete lattices and many of their instances—the complete schedule algebra or completed max-plus semifield, the tropical algebra, and the max-times algebra—are useful in a range of applications, e.g., morphological processing. We further the task of eliciting the relation between i-SVD and the extension of Formal Concept Analysis to complete idempotent semifields (K-FCA) started in a prior work. We find out that for a matrix with entries considered in a complete idempotent semifield, the Galois connection at the heart of K-FCA provides two basis of left- and right-singular vectors to choose from, for reconstructing the matrix. These are join-dense or meet-dense sets of object or attribute concepts of the concept lattice created by the connection, and they are almost surely not pairwise orthogonal. We conclude with an attempt analogue of the fundamental theorem of linear algebra that gathers all results and discuss it in the wider setting of matrix factorization.This research was funded by the Spanish Government-MinECo project TEC2017-84395-P and the Dept. of Research and Innovation of Madrid Regional Authority project EMPATIA-CM (Y2018/TCS-5046)

Pattern Recognition

Pattern recognition is a very wide research field. It involves factors as diverse as sensors, feature extraction, pattern classification, decision fusion, applications and others. The signals processed are commonly one, two or three dimensional, the processing is done in real- time or takes hours and days, some systems look for one narrow object class, others search huge databases for entries with at least a small amount of similarity. No single person can claim expertise across the whole field, which develops rapidly, updates its paradigms and comprehends several philosophical approaches. This book reflects this diversity by presenting a selection of recent developments within the area of pattern recognition and related fields. It covers theoretical advances in classification and feature extraction as well as application-oriented works. Authors of these 25 works present and advocate recent achievements of their research related to the field of pattern recognition

Guideline on therapeutic dentistry for the 5-th term

РУКОВОДСТВАСТОМАТОЛОГИЯ ЛЕЧЕБНО-ВОССТАНОВИТЕЛЬНАЯСТОМАТОЛОГИЯ ТЕРАПЕВТИЧЕСКАЯИНОСТРАННЫЕ СТУДЕНТЫУЧЕБНО-МЕТОДИЧЕСКИЕ ПОСОБИЯПособие составлено в соответствии с учебной программой для медицинских вузов по терапевтической стоматологии. Предназначено для внутреннего использования

Mobile Robots Navigation

Mobile robots navigation includes different interrelated activities: (i) perception, as obtaining and interpreting sensory information; (ii) exploration, as the strategy that guides the robot to select the next direction to go; (iii) mapping, involving the construction of a spatial representation by using the sensory information perceived; (iv) localization, as the strategy to estimate the robot position within the spatial map; (v) path planning, as the strategy to find a path towards a goal location being optimal or not; and (vi) path execution, where motor actions are determined and adapted to environmental changes. The book addresses those activities by integrating results from the research work of several authors all over the world. Research cases are documented in 32 chapters organized within 7 categories next described

Energy and performance-optimized scheduling of tasks in distributed cloud and edge computing systems

Infrastructure resources in distributed cloud data centers (CDCs) are shared by heterogeneous applications in a high-performance and cost-effective way. Edge computing has emerged as a new paradigm to provide access to computing capacities in end devices. Yet it suffers from such problems as load imbalance, long scheduling time, and limited power of its edge nodes. Therefore, intelligent task scheduling in CDCs and edge nodes is critically important to construct energy-efficient cloud and edge computing systems. Current approaches cannot smartly minimize the total cost of CDCs, maximize their profit and improve quality of service (QoS) of tasks because of aperiodic arrival and heterogeneity of tasks. This dissertation proposes a class of energy and performance-optimized scheduling algorithms built on top of several intelligent optimization algorithms. This dissertation includes two parts, including background work, i.e., Chapters 3–6, and new contributions, i.e., Chapters 7–11. 1) Background work of this dissertation. Chapter 3 proposes a spatial task scheduling and resource optimization method to minimize the total cost of CDCs where bandwidth prices of Internet service providers, power grid prices, and renewable energy all vary with locations. Chapter 4 presents a geography-aware task scheduling approach by considering spatial variations in CDCs to maximize the profit of their providers by intelligently scheduling tasks. Chapter 5 presents a spatio-temporal task scheduling algorithm to minimize energy cost by scheduling heterogeneous tasks among CDCs while meeting their delay constraints. Chapter 6 gives a temporal scheduling algorithm considering temporal variations of revenue, electricity prices, green energy and prices of public clouds. 2) Contributions of this dissertation. Chapter 7 proposes a multi-objective optimization method for CDCs to maximize their profit, and minimize the average loss possibility of tasks by determining task allocation among Internet service providers, and task service rates of each CDC. A simulated annealing-based bi-objective differential evolution algorithm is proposed to obtain an approximate Pareto optimal set. A knee solution is selected to schedule tasks in a high-profit and high-quality-of-service way. Chapter 8 formulates a bi-objective constrained optimization problem, and designs a novel optimization method to cope with energy cost reduction and QoS improvement. It jointly minimizes both energy cost of CDCs, and average response time of all tasks by intelligently allocating tasks among CDCs and changing task service rate of each CDC. Chapter 9 formulates a constrained bi-objective optimization problem for joint optimization of revenue and energy cost of CDCs. It is solved with an improved multi-objective evolutionary algorithm based on decomposition. It determines a high-quality trade-off between revenue maximization and energy cost minimization by considering CDCs’ spatial differences in energy cost while meeting tasks’ delay constraints. Chapter 10 proposes a simulated annealing-based bees algorithm to find a close-to-optimal solution. Then, a fine-grained spatial task scheduling algorithm is designed to minimize energy cost of CDCs by allocating tasks among multiple green clouds, and specifies running speeds of their servers. Chapter 11 proposes a profit-maximized collaborative computation offloading and resource allocation algorithm to maximize the profit of systems and guarantee that response time limits of tasks are met in cloud-edge computing systems. A single-objective constrained optimization problem is solved by a proposed simulated annealing-based migrating birds optimization. This dissertation evaluates these algorithms, models and software with real-life data and proves that they improve scheduling precision and cost-effectiveness of distributed cloud and edge computing systems

Saving Bones: a direct comparison of FTIR-ATR, whole bone percent nitrogen, and NIR

89th Annual Meeting of the American-Association-of-Physical-Anthropologists (AAPA), Los Angeles, CA, APR 15-18, 202