Related papers: Time-Frequency Analysis (Lecture Notes)
We report on a course project in which students submit weekly probabilistic forecasts of two weather variables and one financial variable. This real-time format allows students to engage in practical forecasting, which requires a diverse…
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is…
These are Notes prepared for nine lectures given at the Mathematical Sciences Research Institute, MSRI, Berkeley during the period January--March 1995. It is a pleasant duty to record here my gratitude to MSRI, and its staff, for making…
The Fourier spectrum at a fractional period is often examined when extracting features from biological sequences and time series. It reflects the inner information structure of the sequences. A fractional period is not uncommon in time…
These lecture notes are intended to cover some introductory topics in stochastic simulation for scientific computing courses offered by the IT department at Uppsala University, as taught by the author. Basic concepts in probability theory…
Data analysis is a powerful tool in all experimental sciences. Statistical methods, such as sampling theory, computer technologies necessary for handling large amounts of data, skill in analysing information contained in different types of…
The aim of this book is to give a rigorous introduction for the graduate students to Analysis on Wiener space, a subject which has grown up very quickly these recent years under the new impulse of the Stochastic Calculus of Variations of…
This set of lecture notes constitutes the free textbook project I initiated towards the end of Summer 2015, while preparing for the Fall 2015 Analytical Methods in Physics course I taught to upper level undergraduates at the University of…
How few parameters do we really need to forecast a periodic time series? An hourly electricity series, reshaped as a 24-row matrix with one column per day, is approximately rank-1: a daily shape modulated by a daily level (median centered…
Late Winter Lecture Notes, Short Course (10 hours) of Relativistic Astrophysics held at the Department of Physics and Astronomy of the University of Padova, March 13-17, 2017. Third version.
These are introductory lecture notes on Mather's theory for Tonelli Lagrangian and Hamiltonian systems. They are based on a series of lectures given by the author at Universit\`a degli Studi di Napoli "Federico II" (April 2009), at…
We introduce methods and theory for fractionally cointegrated curve time series. We develop a variance-ratio test to determine the dimensions associated with the nonstationary and stationary subspaces. For each subspace, we apply a local…
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…
These lecture notes provide a comprehensive introduction to Quantitative Methods in Finance (QMF), designed for graduate students in finance and economics with heterogeneous programming backgrounds. The material develops a unified toolkit…
This paper presents a web application for visualizing the tonality of a piece of music -- the organization of its chords and scales -- at a high level of abstraction and with coordinated playback. The application applies the discrete…
Recent developments in frequency metrology and optical clocks have been based on electronic transitions in atoms and singly charged ions as references. These systems have enabled relative frequency uncertainties at a level of a few parts in…
This is a survey on the subject of the title corresponding to three lectures I gave in June 2001 at the Workshop on Fourier Analysis and Convexity, at the Universita di Milano-Biccoca.
This is a report of a course on modern physics designed and taught to undergraduate science and engineering students in the Spring of 2013. The course, meant for freshmen, attempts to integrate statistical mechanics into non-classical…
The notes contain a streamlined account on stability of univariate polynomials and related problems
Frequency domain representation of time series feature offers a concise representation for handling real-world time series data with inherent complexity and dynamic nature. However, current frequency-based methods with complex operations…