Search results for "Calculus"

Sequencing ancient calcified dental plaque shows changes in oral microbiota with dietary shifts of the Neolithic and Industrial revolutions

2013

The importance of commensal microbes for human health is increasingly recognized, yet the impacts of evolutionary changes in human diet and culture on commensal microbiota remain almost unknown. Two of the greatest dietary shifts in human evolution involved the adoption of carbohydrate-rich Neolithic (farming) diets (beginning ∼10,000 years before the present) and the more recent advent of industrially processed flour and sugar (in ∼1850). Here, we show that calcified dental plaque (dental calculus) on ancient teeth preserves a detailed genetic record throughout this period. Data from 34 early European skeletons indicate that the transition from hunter-gatherer to farming shifted the oral m…

Symbolic and conceptual representation of dynamic scenes: Interpreting situation calculus on conceptual spaces

2001

In (Chella et al. [1,2]) we proposed a framework for the representation of visual knowledge, with particular attention to the analysis and the representation of scenes with moving objects and people. One of our aims is a principled integration of the models developed within the artificial vision community with the propositional knowledge representation systems developed within symbolic AI. In the present note we show how the approach we adopted fits well with the representational choices underlying one of the most popular symbolic formalisms used in cognitive robotics, namely the situation calculus.

Stochastic dynamics of nonlinear systems with a fractional power-law nonlinear term: The fractional calculus approach

2011

Fractional power-law nonlinear drift arises in many applications of engineering interest, as in structures with nonlinear fluid viscous–elastic dampers. The probabilistic characterization of such structures under external Gaussian white noise excitation is still an open problem. This paper addresses the solution of such a nonlinear system providing the equation governing the evolution of the characteristic function, which involves the Riesz fractional operator. An efficient numerical procedure to handle the problem is also proposed.

Pseudo-force method for a stochastic analysis of nonlinear systems

1996

Nonlinear systems, driven by external white noise input processes and handled by means of pseudo-force theory, are transformed through simple coordinate transformation to quasi-linear systems. By means of Itô stochastic differential calculus for parametric processes, a finite hierarchy for the moment equations of these systems can be exactly obtained. Applications of this procedure to the first-order differential equation with cubic nonlinearity and to the Duffing oscillator show the versatility of the proposed method. The accuracy of the proposed procedure improves by making use of the classical equivalent linearization technique.

ON THE FUNDAMENTAL THEOREM OF CALCULUS FOR FRACTAL SETS

2015

The aim of this paper is to formulate the best version of the Fundamental theorem of Calculus for real functions on a fractal subset of the real line. In order to do that an integral of Henstock–Kurzweil type is introduced.

An introduction to Cheeger's differentiation theory

2015

Il Filtro Integrale Auto-Regressivo Continuo (I-ARC) per l’Analisi di Strutture Esposte al Vento

2010

In questo studio viene proposto un metodo per la rappresentazione di processi aleatori Gaussiani e stazionari, utile a modellare la turbolenza della velocità del vento, introducendo la versione integrale del modello auto-regressivo discreto già proposto in precedenza. La rappresentazione di un processo aleatorio di assegnata funzione di correlazione viene condotta integrando un’equazione integro-differenziale in cui viene coinvolto un nucleo, che rappresenta la memoria del processo, in presenza di un rumore bianco Gaussiano. La soluzione dell’equazione rappresenta un campione del processo aleatorio della turbolenza della velocità del vento. E’ stato mostrato che il modello I-ARC fornisce, n…

Sur les problèmes d'optimisation structurelle

2000

We discuss existence theorems for shape optimization and material distribution problems. The conditions that we impose on the unknown sets are continuity of the boundary, respectively a certain measurability hypothesis. peerReviewed

Using Wave Propagation Simulations and Convolutional Neural Networks to Retrieve Thin Film Thickness from Hyperspectral Images

2021

Ill-posed inversion problems are one of the major challenges when there is a need to combine measurements with the theory and numerical model. In this study, we demonstrate the use of wave propagation simulations to train a convolutional neural network (CNN) for retrieving sub-wavelength thickness profiles of thin film coatings from hyperspectral images. The simulations are produced by solving numerically one-dimensional wave equation with a method based on Discrete Exterior Calculus (DEC). This approach provides a powerful tool to produce large sets of training data for the neural network. CNN was verified by simulated verification sets and measured reflectance spectra, both of which showe…

Regularly Algebraizable Logics

2001

A sentential logic (S, C) is regularly algebraizable (alias 1-algebraizable) if it possesses a non-empty system E(p, q) of equivalence sentences such that E(p, q) ⊆ C(p, q).