Math Morphing Proximate and Evolutionary Mechanisms
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Chapter 6: Ensemble Forecasting and Atmospheric Predictability
Chapter 6: Ensemble Forecasting and Atmospheric Predictability Introduction Deterministic Chaos (what!?) In 1951 Charney indicated that forecast skill would break down, but he attributed it to model errors and errors in the initial conditions… In the 1960’s the forecasts were skillful for only one day or so. Statistical prediction was equal or better than dynamical predictions, Like it was until now for ENSO predictions! Lorenz wanted to show that statistical prediction could not match prediction with a nonlinear model for the Tokyo (1960) NWP conference So, he tried to find a model that was not periodic (otherwise stats would win!) He programmed in machine language on a 4K memory, 60 ops/sec Royal McBee computer He developed a low-order model (12 d.o.f) and changed the parameters and eventually found a nonperiodic solution Printed results with 3 significant digits (plenty!) Tried to reproduce results, went for a coffee and OOPS! Lorenz (1963) discovered that even with a perfect model and almost perfect initial conditions the forecast loses all skill in a finite time interval: “A butterfly in Brazil can change the forecast in Texas after one or two weeks”. In the 1960’s this was only of academic interest: forecasts were useless in two days Now, we are getting closer to the 2 week limit of predictability, and we have to extract the maximum information Central theorem of chaos (Lorenz, 1960s): a) Unstable systems have finite predictability (chaos) b) Stable systems are infinitely predictable a) Unstable dynamical system b) Stable dynamical -
Complexity” Makes a Difference: Lessons from Critical Systems Thinking and the Covid-19 Pandemic in the UK
systems Article How We Understand “Complexity” Makes a Difference: Lessons from Critical Systems Thinking and the Covid-19 Pandemic in the UK Michael C. Jackson Centre for Systems Studies, University of Hull, Hull HU6 7TS, UK; [email protected]; Tel.: +44-7527-196400 Received: 11 November 2020; Accepted: 4 December 2020; Published: 7 December 2020 Abstract: Many authors have sought to summarize what they regard as the key features of “complexity”. Some concentrate on the complexity they see as existing in the world—on “ontological complexity”. Others highlight “cognitive complexity”—the complexity they see arising from the different interpretations of the world held by observers. Others recognize the added difficulties flowing from the interactions between “ontological” and “cognitive” complexity. Using the example of the Covid-19 pandemic in the UK, and the responses to it, the purpose of this paper is to show that the way we understand complexity makes a huge difference to how we respond to crises of this type. Inadequate conceptualizations of complexity lead to poor responses that can make matters worse. Different understandings of complexity are discussed and related to strategies proposed for combatting the pandemic. It is argued that a “critical systems thinking” approach to complexity provides the most appropriate understanding of the phenomenon and, at the same time, suggests which systems methodologies are best employed by decision makers in preparing for, and responding to, such crises. Keywords: complexity; Covid-19; critical systems thinking; systems methodologies 1. Introduction No one doubts that we are, in today’s world, entangled in complexity. At the global level, economic, social, technological, health and ecological factors have become interconnected in unprecedented ways, and the consequences are immense. -
Object Oriented Programming
No. 52 March-A pril'1990 $3.95 T H E M TEe H CAL J 0 URN A L COPIA Object Oriented Programming First it was BASIC, then it was structures, now it's objects. C++ afi<;ionados feel, of course, that objects are so powerful, so encompassing that anything could be so defined. I hope they're not placing bets, because if they are, money's no object. C++ 2.0 page 8 An objective view of the newest C++. Training A Neural Network Now that you have a neural network what do you do with it? Part two of a fascinating series. Debugging C page 21 Pointers Using MEM Keep C fro111 (C)rashing your system. An AT Keyboard Interface Use an AT keyboard with your latest project. And More ... Understanding Logic Families EPROM Programming Speeding Up Your AT Keyboard ((CHAOS MADE TO ORDER~ Explore the Magnificent and Infinite World of Fractals with FRAC LS™ AN ELECTRONIC KALEIDOSCOPE OF NATURES GEOMETRYTM With FracTools, you can modify and play with any of the included images, or easily create new ones by marking a region in an existing image or entering the coordinates directly. Filter out areas of the display, change colors in any area, and animate the fractal to create gorgeous and mesmerizing images. Special effects include Strobe, Kaleidoscope, Stained Glass, Horizontal, Vertical and Diagonal Panning, and Mouse Movies. The most spectacular application is the creation of self-running Slide Shows. Include any PCX file from any of the popular "paint" programs. FracTools also includes a Slide Show Programming Language, to bring a higher degree of control to your shows. -
Synchronization of Chaotic Systems
Synchronization of chaotic systems Cite as: Chaos 25, 097611 (2015); https://doi.org/10.1063/1.4917383 Submitted: 08 January 2015 . Accepted: 18 March 2015 . Published Online: 16 April 2015 Louis M. Pecora, and Thomas L. Carroll ARTICLES YOU MAY BE INTERESTED IN Nonlinear time-series analysis revisited Chaos: An Interdisciplinary Journal of Nonlinear Science 25, 097610 (2015); https:// doi.org/10.1063/1.4917289 Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data Chaos: An Interdisciplinary Journal of Nonlinear Science 27, 121102 (2017); https:// doi.org/10.1063/1.5010300 Attractor reconstruction by machine learning Chaos: An Interdisciplinary Journal of Nonlinear Science 28, 061104 (2018); https:// doi.org/10.1063/1.5039508 Chaos 25, 097611 (2015); https://doi.org/10.1063/1.4917383 25, 097611 © 2015 Author(s). CHAOS 25, 097611 (2015) Synchronization of chaotic systems Louis M. Pecora and Thomas L. Carroll U.S. Naval Research Laboratory, Washington, District of Columbia 20375, USA (Received 8 January 2015; accepted 18 March 2015; published online 16 April 2015) We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. -
A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons
A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons Eric Berberich, Arno Eigenwillig, Michael Hemmer Susan Hert, Kurt Mehlhorn, and Elmar Schomer¨ [eric|arno|hemmer|hert|mehlhorn|schoemer]@mpi-sb.mpg.de Max-Planck-Institut fur¨ Informatik, Stuhlsatzenhausweg 85 66123 Saarbruck¨ en, Germany Abstract. We give an exact geometry kernel for conic arcs, algorithms for ex- act computation with low-degree algebraic numbers, and an algorithm for com- puting the arrangement of conic arcs that immediately leads to a realization of regularized boolean operations on conic polygons. A conic polygon, or polygon for short, is anything that can be obtained from linear or conic halfspaces (= the set of points where a linear or quadratic function is non-negative) by regularized boolean operations. The algorithm and its implementation are complete (they can handle all cases), exact (they give the mathematically correct result), and efficient (they can handle inputs with several hundred primitives). 1 Introduction We give an exact geometry kernel for conic arcs, algorithms for exact computation with low-degree algebraic numbers, and a sweep-line algorithm for computing arrangements of curved arcs that immediately leads to a realization of regularized boolean operations on conic polygons. A conic polygon, or polygon for short, is anything that can be ob- tained from linear or conic halfspaces (= the set of points where a linear or quadratic function is non-negative) by regularized boolean operations (Figure 1). A regularized boolean operation is a standard boolean operation (union, intersection, complement) followed by regularization. Regularization replaces a set by the closure of its interior and eliminates dangling low-dimensional features. -
A Gentle Introduction to Dynamical Systems Theory for Researchers in Speech, Language, and Music
A Gentle Introduction to Dynamical Systems Theory for Researchers in Speech, Language, and Music. Talk given at PoRT workshop, Glasgow, July 2012 Fred Cummins, University College Dublin [1] Dynamical Systems Theory (DST) is the lingua franca of Physics (both Newtonian and modern), Biology, Chemistry, and many other sciences and non-sciences, such as Economics. To employ the tools of DST is to take an explanatory stance with respect to observed phenomena. DST is thus not just another tool in the box. Its use is a different way of doing science. DST is increasingly used in non-computational, non-representational, non-cognitivist approaches to understanding behavior (and perhaps brains). (Embodied, embedded, ecological, enactive theories within cognitive science.) [2] DST originates in the science of mechanics, developed by the (co-)inventor of the calculus: Isaac Newton. This revolutionary science gave us the seductive concept of the mechanism. Mechanics seeks to provide a deterministic account of the relation between the motions of massive bodies and the forces that act upon them. A dynamical system comprises • A state description that indexes the components at time t, and • A dynamic, which is a rule governing state change over time The choice of variables defines the state space. The dynamic associates an instantaneous rate of change with each point in the state space. Any specific instance of a dynamical system will trace out a single trajectory in state space. (This is often, misleadingly, called a solution to the underlying equations.) Description of a specific system therefore also requires specification of the initial conditions. In the domain of mechanics, where we seek to account for the motion of massive bodies, we know which variables to choose (position and velocity). -
Image Encryption and Decryption Schemes Using Linear and Quadratic Fractal Algorithms and Their Systems
Image Encryption and Decryption Schemes Using Linear and Quadratic Fractal Algorithms and Their Systems Anatoliy Kovalchuk 1 [0000-0001-5910-4734], Ivan Izonin 1 [0000-0002-9761-0096] Christine Strauss 2 [0000-0003-0276-3610], Mariia Podavalkina 1 [0000-0001-6544-0654], Natalia Lotoshynska 1 [0000-0002-6618-0070] and Nataliya Kustra 1 [0000-0002-3562-2032] 1 Department of Publishing Information Technologies, Lviv Polytechnic National University, Lviv, Ukraine [email protected], [email protected], [email protected], [email protected], [email protected] 2 Department of Electronic Business, University of Vienna, Vienna, Austria [email protected] Abstract. Image protection and organizing the associated processes is based on the assumption that an image is a stochastic signal. This results in the transition of the classic encryption methods into the image perspective. However the image is some specific signal that, in addition to the typical informativeness (informative data), also involves visual informativeness. The visual informativeness implies additional and new challenges for the issue of protection. As it involves the highly sophisticated modern image processing techniques, this informativeness enables unauthorized access. In fact, the organization of the attack on an encrypted image is possible in two ways: through the traditional hacking of encryption methods or through the methods of visual image processing (filtering methods, contour separation, etc.). Although the methods mentioned above do not fully reproduce the encrypted image, they can provide an opportunity to obtain some information from the image. In this regard, the encryption methods, when used in images, have another task - the complete noise of the encrypted image. -
Brownian Motion and Relativity Brownian Motion 55
54 My God, He Plays Dice! Chapter 7 Chapter Brownian Motion and Relativity Brownian Motion 55 Brownian Motion and Relativity In this chapter we describe two of Einstein’s greatest works that have little or nothing to do with his amazing and deeply puzzling theories about quantum mechanics. The first,Brownian motion, provided the first quantitative proof of the existence of atoms and molecules. The second,special relativity in his miracle year of 1905 and general relativity eleven years later, combined the ideas of space and time into a unified space-time with a non-Euclidean 7 Chapter curvature that goes beyond Newton’s theory of gravitation. Einstein’s relativity theory explained the precession of the orbit of Mercury and predicted the bending of light as it passes the sun, confirmed by Arthur Stanley Eddington in 1919. He also predicted that galaxies can act as gravitational lenses, focusing light from objects far beyond, as was confirmed in 1979. He also predicted gravitational waves, only detected in 2016, one century after Einstein wrote down the equations that explain them.. What are we to make of this man who could see things that others could not? Our thesis is that if we look very closely at the things he said, especially his doubts expressed privately to friends, today’s mysteries of quantum mechanics may be lessened. As great as Einstein’s theories of Brownian motion and relativity are, they were accepted quickly because measurements were soon made that confirmed their predictions. Moreover, contemporaries of Einstein were working on these problems. Marion Smoluchowski worked out the equation for the rate of diffusion of large particles in a liquid the year before Einstein. -
An Image Cryptography Using Henon Map and Arnold Cat Map
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 05 Issue: 04 | Apr-2018 www.irjet.net p-ISSN: 2395-0072 An Image Cryptography using Henon Map and Arnold Cat Map. Pranjali Sankhe1, Shruti Pimple2, Surabhi Singh3, Anita Lahane4 1,2,3 UG Student VIII SEM, B.E., Computer Engg., RGIT, Mumbai, India 4Assistant Professor, Department of Computer Engg., RGIT, Mumbai, India ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - In this digital world i.e. the transmission of non- 2. METHODOLOGY physical data that has been encoded digitally for the purpose of storage Security is a continuous process via which data can 2.1 HENON MAP be secured from several active and passive attacks. Encryption technique protects the confidentiality of a message or 1. The Henon map is a discrete time dynamic system information which is in the form of multimedia (text, image, introduces by michel henon. and video).In this paper, a new symmetric image encryption 2. The map depends on two parameters, a and b, which algorithm is proposed based on Henon’s chaotic system with for the classical Henon map have values of a = 1.4 and byte sequences applied with a novel approach of pixel shuffling b = 0.3. For the classical values the Henon map is of an image which results in an effective and efficient chaotic. For other values of a and b the map may be encryption of images. The Arnold Cat Map is a discrete system chaotic, intermittent, or converge to a periodic orbit. that stretches and folds its trajectories in phase space. Cryptography is the process of encryption and decryption of 3. -
The Age of Addiction David T. Courtwright Belknap (2019) Opioids
The Age of Addiction David T. Courtwright Belknap (2019) Opioids, processed foods, social-media apps: we navigate an addictive environment rife with products that target neural pathways involved in emotion and appetite. In this incisive medical history, David Courtwright traces the evolution of “limbic capitalism” from prehistory. Meshing psychology, culture, socio-economics and urbanization, it’s a story deeply entangled in slavery, corruption and profiteering. Although reform has proved complex, Courtwright posits a solution: an alliance of progressives and traditionalists aimed at combating excess through policy, taxation and public education. Cosmological Koans Anthony Aguirre W. W. Norton (2019) Cosmologist Anthony Aguirre explores the nature of the physical Universe through an intriguing medium — the koan, that paradoxical riddle of Zen Buddhist teaching. Aguirre uses the approach playfully, to explore the “strange hinterland” between the realities of cosmic structure and our individual perception of them. But whereas his discussions of time, space, motion, forces and the quantum are eloquent, the addition of a second framing device — a fictional journey from Enlightenment Italy to China — often obscures rather than clarifies these chewy cosmological concepts and theories. Vanishing Fish Daniel Pauly Greystone (2019) In 1995, marine biologist Daniel Pauly coined the term ‘shifting baselines’ to describe perceptions of environmental degradation: what is viewed as pristine today would strike our ancestors as damaged. In these trenchant essays, Pauly trains that lens on fisheries, revealing a global ‘aquacalypse’. A “toxic triad” of under-reported catches, overfishing and deflected blame drives the crisis, he argues, complicated by issues such as the fishmeal industry, which absorbs a quarter of the global catch. -
And Nanoemulsions As Vehicles for Essential Oils: Formulation, Preparation and Stability
nanomaterials Review An Overview of Micro- and Nanoemulsions as Vehicles for Essential Oils: Formulation, Preparation and Stability Lucia Pavoni, Diego Romano Perinelli , Giulia Bonacucina, Marco Cespi * and Giovanni Filippo Palmieri School of Pharmacy, University of Camerino, 62032 Camerino, Italy; [email protected] (L.P.); [email protected] (D.R.P.); [email protected] (G.B.); gianfi[email protected] (G.F.P.) * Correspondence: [email protected] Received: 23 December 2019; Accepted: 10 January 2020; Published: 12 January 2020 Abstract: The interest around essential oils is constantly increasing thanks to their biological properties exploitable in several fields, from pharmaceuticals to food and agriculture. However, their widespread use and marketing are still restricted due to their poor physico-chemical properties; i.e., high volatility, thermal decomposition, low water solubility, and stability issues. At the moment, the most suitable approach to overcome such limitations is based on the development of proper formulation strategies. One of the approaches suggested to achieve this goal is the so-called encapsulation process through the preparation of aqueous nano-dispersions. Among them, micro- and nanoemulsions are the most studied thanks to the ease of formulation, handling and to their manufacturing costs. In this direction, this review intends to offer an overview of the formulation, preparation and stability parameters of micro- and nanoemulsions. Specifically, recent literature has been examined in order to define the most common practices adopted (materials and fabrication methods), highlighting their suitability and effectiveness. Finally, relevant points related to formulations, such as optimization, characterization, stability and safety, not deeply studied or clarified yet, were discussed. -
Chaos Theory
By Nadha CHAOS THEORY What is Chaos Theory? . It is a field of study within applied mathematics . It studies the behavior of dynamical systems that are highly sensitive to initial conditions . It deals with nonlinear systems . It is commonly referred to as the Butterfly Effect What is a nonlinear system? . In mathematics, a nonlinear system is a system which is not linear . It is a system which does not satisfy the superposition principle, or whose output is not directly proportional to its input. Less technically, a nonlinear system is any problem where the variable(s) to be solved for cannot be written as a linear combination of independent components. the SUPERPOSITION PRINCIPLE states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually. So that if input A produces response X and input B produces response Y then input (A + B) produces response (X + Y). So a nonlinear system does not satisfy this principal. There are 3 criteria that a chaotic system satisfies 1) sensitive dependence on initial conditions 2) topological mixing 3) periodic orbits are dense 1) Sensitive dependence on initial conditions . This is popularly known as the "butterfly effect” . It got its name because of the title of a paper given by Edward Lorenz titled Predictability: Does the Flap of a Butterfly’s Wings in Brazil set off a Tornado in Texas? . The flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale phenomena.