Performance Evaluation of Computer and Communication Systems
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This book is the set of lecture notes for a course given at EPFL. It contains all the material needed by an engineer who wishes to evaluate the performance of a computer or communication system.
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Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory.
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics.
In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set. Any set other than the empty set is called non-empty. In some textbooks and popularizations, the empty set is referred to as the "null set".
Learn to optimize on smooth, nonlinear spaces: Join us to build your foundations (starting at "what is a manifold?") and confidently implement your first algorithm (Riemannian gradient descent).
Dans une première partie, nous étudierons d’abord comment résoudre de manière très concrète un problème au moyen d’un algorithme, ce qui nous amènera dans un second temps à une des grandes questions d
Dans une première partie, nous étudierons d’abord comment résoudre de manière très concrète un problème au moyen d’un algorithme, ce qui nous amènera dans un second temps à une des grandes questions d
In this note, we study certain sufficient conditions for a set of minimal klt pairs ( X, triangle) with kappa ( X, triangle) = dim( X ) - 1 to be bounded. ...
European Mathematical Soc-Ems2024
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Soft pneumatic actuators (SPAs) are highly desirable for interactive robotics applications owing to their unconventional properties like high compliance, safe human-machine interaction and adaptable design space. The SPA dynamic behaviour is governed by pn ...
This chapter addresses the alignment of educational robotics (ER) tools with classroom activities. To this end, it first introduces a conceptualization of ER activities describing the relevant cognitive artifacts and the learning theories underlying such a ...