Spectral geometry with a cut-off: topological and metric aspects

Inspired by regularization in quantum field theory, we study topological and metric properties of spaces in which a cut-off is introduced. We work in the framework of noncommutative geometry, and focus on Connes distance associated to a spectral triple (A, H, D). A high momentum (short distance) cut-off is implemented by the action of a projection P on the Dirac operator D and/or on the algebra A. This action induces two new distances. We individuate conditions making them equivalent to the original distance. We also study the Gromov-Hausdorff limit of the set of truncated states, first for compact quantum metric spaces in the sense of Rieffel, then for arbitrary spectral triples. To this aim, we introduce a notion of "state with finite moment of order 1" for noncommutative algebras. We then focus on the commutative case, and show that the cut-off induces a minimal length between points, which is infinite if P has finite rank. When P is a spectral projection of $D$, we work out an approximation of points by non-pure states that are at finite distance from each other. On the circle, such approximations are given by Fejer probability distributions. Finally we apply the results to Moyal plane and the fuzzy sphere, obtained as Berezin quantization of the plane and the sphere respectively.Comment: Reference added. Minor corrections. Published version. 38 pages, 2 figures. Journal of Geometry and Physics 201

Algebraic description of spacetime foam

A mathematical formalism for treating spacetime topology as a quantum observable is provided. We describe spacetime foam entirely in algebraic terms. To implement the correspondence principle we express the classical spacetime manifold of general relativity and the commutative coordinates of its events by means of appropriate limit constructions.Comment: 34 pages, LaTeX2e, the section concerning classical spacetimes in the limit essentially correcte

Fuzzy model identification and self learning with smooth compositions

This Paper Develops A Smooth Model Identification And Self-Learning Strategy For Dynamic Systems Taking Into Account Possible Parameter Variations And Uncertainties. We Have Tried To Solve The Problem Such That The Model Follows The Changes And Variations In The System On A Continuous And Smooth Surface. Running The Model To Adaptively Gain The Optimum Values Of The Parameters On A Smooth Surface Would Facilitate Further Improvements In The Application Of Other Derivative Based Optimization Control Algorithms Such As Mpc Or Robust Control Algorithms To Achieve A Combined Modeling-Control Scheme. Compared To The Earlier Works On The Smooth Fuzzy Modeling Structures, We Could Reach A Desired Trade-Off Between The Model Optimality And The Computational Load. The Proposed Method Has Been Evaluated On A Test Problem As Well As The Non-Linear Dynamic Of A Chemical Process.This publication was supported in part by project MINECO, TEC2017-88048-C2-2-

How effective are smooth compositions in predictive control of TS fuzzy models?

In This Article, We Study The Structural Properties That Smooth Compositions Bring To Predictive Control Of Ts Fuzzy Models And Examine How They Affect The Uncertainties, Parameter Variations Of The System And Environmental Noises To Die Out. We Have Employed The Smoothness Structure Of Compositions To Convert The Mpc Cost Function Of Ts Fuzzy Model Of The Nonlinear Systems To An Incremental Iterative Algorithm. Hence, The Proposed Algorithm Does Not Linearize The Nonlinear Dynamics, Neither Requires Solving An Np Optimization Problem In Mpc And, Therefore, Is Very Fast And Simple. The Connectivist Identification&#8212 Mpc Approach&#8212 Can Be Employed For The Systems With The Long-Range Horizons. Therefore, The Technique Is Beneficial To The Dead-Time And Non-Minimum Phase Systems. The Stability Analysis Of The Algorithm Has Been Carried Out, And The Performance Of The Smooth Ts Fuzzy Identification&Amp -Controller Scheme To The Classical Ones Has Been Compared On A Non-Min Phase Test Problem With Different Uncertainties And Working Environments, Including (A) The Normal Working Conditions, (B) With The Additive Noises, (C) With The Parametric Changes, (D) With The Additive Time-Varying Disturbances To Demonstrate The Robust Behavior Of The Smooth Compositions

Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators

Loop Quantum Gravity defines the quantum states of space geometry as spin networks and describes their evolution in time. We reformulate spin networks in terms of harmonic oscillators and show how the holographic degrees of freedom of the theory are described as matrix models. This allow us to make a link with non-commutative geometry and to look at the issue of the semi-classical limit of LQG from a new perspective. This work is thought as part of a bigger project of describing quantum geometry in quantum information terms.Comment: 16 pages, revtex, 3 figure

Conference Program

Document provides a list of the sessions, speakers, workshops, and committees of the 32nd Summer Conference on Topology and Its Applications

Hybrid artificial intelligence algorithms for short-term load and price forecasting in competitive electric markets

The liberalization and deregulation of electric markets forced the various participants to accommodate several challenges, including: a considerable accumulation of new generation capacity from renewable sources (fundamentally wind energy), the unpredictability associated with these new forms of generation and new consumption patterns, contributing to further electricity prices volatility (e.g. the Iberian market). Given the competitive framework in which market participants operate, the existence of efficient computational forecasting techniques is a distinctive factor. Based on these forecasts a suitable bidding strategy and an effective generation systems operation planning is achieved, together with an improved installed transmission capacity exploitation, results in maximized profits, all this contributing to a better energy resources utilization. This dissertation presents a new hybrid method for load and electricity prices forecasting, for one day ahead time horizon. The optimization scheme presented in this method, combines the efforts from different techniques, notably artificial neural networks, several optimization algorithms and wavelet transform. The method’s validation was made using different real case studies. The subsequent comparison (accuracy wise) with published results, in reference journals, validated the proposed hybrid method suitability.O processo de liberalização e desregulação dos mercados de energia elétrica, obrigou os diversos participantes a acomodar uma série de desafios, entre os quais: a acumulação considerável de nova capacidade de geração proveniente de origem renovável (fundamentalmente energia eólica), a imprevisibilidade associada a estas novas formas de geração e novos padrões de consumo. Resultando num aumento da volatilidade associada aos preços de energia elétrica (como é exemplo o mercado ibérico). Dado o quadro competitivo em que os agentes de mercado operam, a existência de técnicas computacionais de previsão eficientes, constituí um fator diferenciador. É com base nestas previsões que se definem estratégias de licitação e se efetua um planeamento da operação eficaz dos sistemas de geração que, em conjunto com um melhor aproveitamento da capacidade de transmissão instalada, permite maximizar os lucros, realizando ao mesmo tempo um melhor aproveitamento dos recursos energéticos. Esta dissertação apresenta um novo método híbrido para a previsão da carga e dos preços da energia elétrica, para um horizonte temporal a 24 horas. O método baseia-se num esquema de otimização que reúne os esforços de diferentes técnicas, nomeadamente redes neuronais artificiais, diversos algoritmos de otimização e da transformada de wavelet. A validação do método foi feita em diferentes casos de estudo reais. A posterior comparação com resultados já publicados em revistas de referência, revelou um excelente desempenho do método hibrido proposto

Suboptimality Conditions for Mathematical Programs with Equilibrium Constraints

In this paper we study mathematical programs with equilibrium constraints (MPECs) described by generalized equations in the extended form 0 is an element of the set G(x,y) + Q(x,y), where both mappings G and Q are set-valued. Such models arise, in particular, from certain optimization-related problems governed by variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish new weak and strong suboptimality conditions for the general MPEC problems under consideration in finite-dimensional and infinite-dimensional spaces that do not assume the existence of optimal solutions. This issue is particularly important for infinite-dimensional optimization problems, where the existence of optimal solutions requires quite restrictive assumptions. Our techriiques are mainly based on modern tools of variational analysis and generalized differentiation revolving around the fundamental extremal principle in variational analysis and its analytic counterpart known as the subdifferential variational principle