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Outer billiards provides a toy model for planetary motion and exhibits intricate and mysterious behavior even for seemingly simple examples. It is a dynamical system in which a particle in the plane moves around the outside of a convex shape according to a scheme that is reminiscent of ordinary billiards. The Plaid Model, which is a self-contained sequel to Richard Schwartz's Outer Billiards on Kites, provides a combinatorial model for orbits of outer billiards on kites.Schwartz relates these orbits to such topics as polytope exchange transformations, renormalization, continued fractions, corner percolation, and the Truchet tile system. The combinatorial model, called "the plaid model," has a self-similar structure that blends geometry and elementary number theory. The results were discovered through computer experimentation and it seems that the conclusions would be extremely difficult to reach through traditional mathematics.The book includes an extensive computer program that allows readers to explore materials interactively and each theorem is accompanied by a computer demo.

Hyperbolic spaces. --- Singularities (Mathematics) --- Transformations (Mathematics) --- Geometry, Plane. --- Plane geometry --- Algorithms --- Differential invariants --- Geometry, Differential --- Geometry, Algebraic --- Hyperbolic complex manifolds --- Manifolds, Hyperbolic complex --- Spaces, Hyperbolic --- Geometry, Non-Euclidean --- 1-dimensional wordlines. --- Bad Tile Lemma. --- Box Theorem. --- Copy Lemma. --- Copy Theorem. --- Curve Turning Theorem. --- Graph Master Picture Theorem. --- Graph Master Theorem. --- Graph Reconstruction Lemma. --- Grid Geometry Lemma. --- Grid Supply Lemma. --- Horizontal Lemma. --- Intertwining Lemma. --- Master Picture Theorem. --- Matching Criterion. --- Orbit Equivalence Theorem. --- PET. --- Plaid Master Picture Theorem. --- Projection Theorem. --- Quasi-Isomorphism Theorem. --- Rectangle Lemma. --- Renormalization Theorem. --- Segment Lemma. --- Truchet Comparison Theorem. --- Truchet tile system. --- Vertical Lemma. --- anchor point. --- arithmetic alignment. --- arithmetic graph. --- auxiliary lemmas. --- capacities. --- capacity sequence. --- capacity. --- checkerboard partition. --- classifying map. --- compactification. --- congruence. --- continued fractions. --- convex polygon. --- convex polytopes. --- corner percolation. --- east edges. --- elementary number theory. --- embedded loops. --- equidistribution. --- even rational parameter. --- fundamental surface. --- geometric alignment. --- geometry. --- graph grid. --- grid lines. --- horizontal case. --- integer square. --- intersection points. --- kites. --- kits. --- lemma. --- lemmas. --- light point. --- light points. --- linear algebra. --- low capacity lines. --- map. --- maps. --- mass sequence. --- masses. --- number theory. --- orbit. --- oriented lines. --- outer billiards map. --- outer billiards. --- parallel lines. --- parallelotope. --- particle lines. --- pixelated spacetime diagrams. --- pixelated spacetime. --- pixilation. --- plaid PET map. --- plaid model. --- plaid polygon. --- plaid polygons. --- plane. --- planetary motion. --- planetary orbits. --- polygon. --- polytope exchange transformations. --- polytopes. --- prism structure. --- prism. --- proof. --- quarter turn compositions. --- remote adjacency. --- renormalization. --- scale information. --- sequences. --- slanting lines. --- spaces. --- spacetime diagrams. --- spacetime plaid surfaces. --- special billiards orbits. --- square tiling. --- stacking blocks. --- structural result. --- symmetries. --- symmetry. --- technical lemma. --- theorems. --- vertical case. --- vertical particles.

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This book presents an interesting sample of the latest advances in optimization techniques applied to electrical power engineering. It covers a variety of topics from various fields, ranging from classical optimization such as Linear and Nonlinear Programming and Integer and Mixed-Integer Programming to the most modern methods based on bio-inspired metaheuristics. The featured papers invite readers to delve further into emerging optimization techniques and their real application to case studies such as conventional and renewable energy generation, distributed generation, transport and distribution of electrical energy, electrical machines and power electronics, network optimization, intelligent systems, advances in electric mobility, etc.

n/a --- Stackelberg game --- MILP --- optimal congestion threshold --- magnetic field mitigation --- simulation --- multi-objective particle swarm optimization --- virtual power plant --- internal defect --- day-ahead load forecasting --- neural network --- modular predictor --- multi-objective particle swarm optimization algorithm --- stochastic optimization --- dragonfly algorithm --- unit commitment --- metaheuristic --- multi-population method (MP) --- optimization --- tabu search --- considerable decomposition --- loss minimization --- active distribution system --- islanded microgrid --- dynamic solving framework --- feature selection --- electric energy costs --- power factor compensation --- dependability --- interactive load --- overhead --- energy internet --- evolutionary computation --- wind power --- developed grew wolf optimizer --- underground --- ETAP --- fuzzy algorithm --- electric vehicles --- Schwarz’s equation --- evolutionary algorithms --- electric power contracts --- congestion management --- optimizing-scenarios method --- building energy management system --- particle encoding method --- ringdown detection --- HOMER software --- DC optimal power flow --- prosumer --- constrained parameter estimation --- distributed generations (DGs) --- strong track filter (STF) --- transient stability --- calibration --- cost minimization --- radiance --- decentralized and collaborative optimization --- hybrid renewable energy system --- renewable energy sources --- rural electrification --- distribution network reconfiguration --- interval variables --- optimization methods --- particle swarm optimization --- hierarchical scheduling --- micro grid --- AC/DC hybrid active distribution --- consensus --- artificial bee colony --- CCHP system --- data center --- support vector machine --- affinity propagation clustering --- extended Kalman filter --- affine arithmetic --- linear discriminant analysis (LDA) --- current margins --- heterogeneous networks --- Cameroon --- hybrid method --- distributed heat-electricity energy management --- discrete wind driven optimization --- fitness function --- cross-entropy --- GenOpt --- wind energy --- demand uncertainty --- UC --- off-design performance --- genetic algorithm --- energy storage --- the biomimetic membrane computing --- power system optimization --- electric vehicle --- power architectures --- economic load dispatch problem (ELD) --- runner-root algorithm (RRA) --- Cable joint --- battery energy storage system --- load curtailment --- integration assessment --- power system unit commitment --- artificial lighting --- power flow --- hybrid membrane computing --- two-point estimation method --- low-voltage networks --- demand bidding --- non-sinusoidal circuits --- energy flow model --- power transfer distribution factors --- sustainability --- HVAC system --- voltage deviation --- street light points --- radial basis function --- energy storage system --- charging/discharging --- power systems --- intelligent scatter search --- MV/LV substation --- optimal power flow --- stochastic state estimation --- eight searching sub-regions --- chaos optimization algorithm (COA) --- mutual information theory --- inter-turn shorted-circuit fault (ISCF) --- C&I particle swarm optimization --- multiobjective optimization --- passive shielding --- sub-Saharan Africa --- micro-phasor measurement unit --- geometric algebra --- bio-inspired algorithms --- adaptive consensus algorithm --- energy management --- PCS efficiency --- multi-stakeholders --- generalized generation distribution factors --- the genetic algorithm based P system --- JAYA algorithm --- thermal probability density --- power optimization --- pumped-hydro energy storage --- smart grid --- two-stage feature selection --- piecewise linear techniques --- photovoltaic --- SOCP relaxations --- switched reluctance machine (SRM) --- optimal reactive power dispatch --- optimal operation --- controllable response --- off-grid --- active shielding --- transformer-fault diagnosis --- IEEE Std. 80-2000 --- principal component analysis --- demand response --- Schwarz's equation