Diego Caratelli is associate professor at the Department of Electrical Engineering, Eindhoven University of Technology, and CTO at The Antenna Company in Eindhoven, The Netherlands.  His main specialisations are Antenna design, electromagnetics and mathematics.  He is co-founder of The Antenna Company where he is Chief Technology Officer CTO.  

Dominik Chapman currently works as a software engineer for the companies Imaging Solutions (industrial photo printers) and Viesus (image processing, AI). He has worked in various software industries, including signal processing (audio, image, radio- and microwaves), flight simulators, and multimedia installations, but also has extensive expertise a musician, sound engineer, stage manager, and visual artist. Since he discovered the n-gon waves in about 2000 he explores the relationships of geometry, audio, visual, and perception. He published his initial work on n-gon waves for the first time at the ICMC|SMC conference in Athens in 2014. Since he studied Music Computing at Goldsmiths University in London he is developing software for various research collaborations in audiovisuals and music. This ongoing work led to a research collaboration with mathematician and biologist Johan Gielis and composer Rexleigh Bunyard. Together they explore the audiovisual phenomena and musical applications of Gielis transformations. 

Abstract

A few audio and visual applications that feature supershape oscillators already exist. It appears none of those applications uses supershape polygons as oscillators. Like points on a circle can be connected by lines to create polygons inscribed to a circle, supershape polygons can be created from connecting points on a supershape. Depending on the type of linear interpolation used to connect the points different audiovisual effects are perceived and an audiovisual phenomenon can be observed: The same or a similar polygon can be visualised with different types of digitised audio waveforms played back on an electronic audio device with its audio outputs connected to the x and y inputs of a digital or analogue oscilloscope. An audiovisual database and a moebius strip-like interface for supershape oscillators that use various types of interpolations can be used as tools for musical and visual compositions and improvisations. Using supershape oscillators in a musical context leads to music theoretical investigations that may also provide a basis for further audiovisual explorations.  

Annie Cuyt is prof. em. at University of Antwerp and driving force for the consoritium within the EU project Expower (www.expower.eu), focusing on Multi-exponential analysis.  Joint work with Wen-shin Lee.

Abstract

We discuss how sparse interpolation in computer algebra and exponential analysis in digital signal processing can cross-fertilize and lead to new results.

The Nyquist constraint  is the digital signal processing equivalent of stating that the argument of a complex exponential can only be retrieved uniquely under specific conditions the condition. It governs signal processing since the beginning of the 20-th century. In the past two decades this constraint was  first broken with the use of randomly collected signal samples and later for use with uniform samples. The latter method closely relates to the original version of the exponential data fitting algorithm

published in 1795 by the French mathematician de Prony, which is often cited in sparse interpolation research. Besides avoiding the Nyquist constraint, the new result also solves a number of remaining open problems in exponential analysis, which we plan to discuss. All of the above can be generalized in several ways, to the use of more functions besides the exponential on the one hand, and to the solution of multi-dimensional versions of this inverse problem on the other.

G. Dattoli was ENEA Researcher Research Center Frascati,  Italy, and has been involved in different research projects, including high energy accelerators, free electron lasers, and applied mathematics. Dr. Dattoli has received the FEL Prize Award for his outstanding achievements in the field.

Abstract

The theory of special polynomials has been recently revisited through the application of methods, employing abstract operator theory. Within this framework the  relevant theory has been reduced to straightforward algebraic manipulations of operators realizing a Weyl-Heisenberg algebra. The low factorial polynomials have noticeable elements of interest, since they are the natural framework in which the theory of difference equations can be placed. In this talk we discuss the relevant theory, employing the afore mentioned point of view. We also underscore that non-linear difference equations of the logistic type can be comprised  within the same formalism. A few physical applications are discussed.

J. Gielis is visiting professor at the University of Antwerp, department of Bioscience Engineering. He is also cofounder of Genicap Beheer BV and Antenna Company, where he is currently vicepresident of Research and Materials.

Abstract: In this talk I give an overview of 25 years of Superformula aka Gielis Transformations, and the many nice collaborations which evolved esp. over the last decade.  Various connections to the speakers or this symposium will be highlighted.

Erhan Güler is assoc. professor of mathematics at Bartin University (Turkey). Güler received his PhD degree in Mathematics and worked with Prof. H.Hilmi Hacısalihoğlu and Prof. Yusuf Yaylı from Ankara Un., Turkey (2007-2010), with Prof. Franki Dillen at Katholieke Leuven Un., Belgium (2011-2012), and many others. Recently, his work focuses on helicoidal, rotational, minimal, one-sided, algebraic (hyper)surfaces in space forms, and on elimination theory.

Abstract:  

We characterize helicoidal hypersurfaces in Minkowski four-space 𝔼^4_1 based on their axis of rotation. There exist three distinct types of helicoidal hypersurfaces. We deduce expressions for their curvatures, including Gaussian and mean curvatures, and provide illustrative examples of these hypersurfaces. To conclude, we establish a theorem that classifies helicoidal hypersurfaces with timelike axes, meeting the condition Δ𝐇=𝐴𝐇.

Matthew He, Ph.D., is Professor of the Halmos College of Arts and Sciences of Nova Southeastern University, Florida, USA. He received the World Academy of Sciences Achievement Awards in recognition of his research contributions in the field of computing in 2003 and 2010.  Dr. Matthew He has authored and edited 25 books and conference proceedings and published over 100 research papers in the areas of mathematics, bioinformatics, computer vision, information theory, math and engineering techniques in medical and biological sciences. 

Abstract:  

In recent scientific and technological advances, many boundaries among science, engineering and social systems are cross-linked in the face of combinations of knowledge and tools as demonstrated in the areas of scientific computing, network computing, bio-molecular computing, quantum computing, soft computing, most recently perceptual computing, and general artificial intelligence. Human thoughts are at the core of the latest scientific computing advances and development. Understanding the true nature of human thoughts and their mathematical patterns will be essential and critical. This talk presents three principles of the Brain-Mind Relationship recently proposed by Giorgio A. Ascoli in 2015 and briefly provides an overview of Paul and Elder's model (in 1999 on the universal structure of human thought and the centrality of thinking. In order to explore mathematical structure of human thought, we briefly summarize Ulf Grenander’s work “A Calculus of Ideas: A Mathematical Study of Human Thought” (in 2012). We then introduce a key concept of Thinking Kernels as geometric structure of human thought and draw the connections between Neural Spikes with Zeros of mathematics via an integration of fuzzy logic and binary logic (Fuzzinary Logic). Furthermore, we present a Central Dogma of Human Thoughts connecting internal black box of thinking kernels and external open box of thinking expressions via middle gray box of thinking flows

Miao-Jung Yvonne Ou is a Professor in the Department of Mathematical Sciences, University of Delaware, USA. Her research interests are in applied analysis, inverse problems, homogenization and mathematical material sciences.

Abstract

Fractional time derivatives have been applied in many applications such as anomalous diffusion and electromagnetic waves in dispersive media due to its ability to describe non-classic phenomena. However, it is nonlocal in time by definition and poses challenges in developing a numerical solver. There are many types of fractional time derivatives - Caputo derivative, Riemann-Liouville derivatives, Caputo-Fabrizio, etc. Despite of the difference in them, they are all defined as a time convolution operator with a kernel. The kernel function has to satisfy a causality condition, which means its Fourier Laplace transform has to be a Herglotz-Nevanlinna function. This link can be utilized not only to reveal the physical meaning of these fractional time derivatives but also inform about a time-domain quadrature for handling the convolution term in a numerical solver. In this talk, all the above will be explained and a numerical example will be given

B. Palmer is professor of mathematics at Idaho State University at Pocatello.  His main interests are in anisotropic energy surfaces and functionals.

Abstract

We study critical surfaces for the Euler-Helfrich energy which contains the squared L2 norm of the sum of the mean curvature H and the spontaneous curvature co, coupled to the elastic energy of the boundary curve. This functional is used to model the morphology of lipid bilayers with pores. When the spontaneous curvature is non negative, we characterize those cases where the infimum of this energy is finite for topological annuli and we find the minimizer in the cases that it exists. Results for topological discs are also given. Bifurcation of solutions of the Helfrich model will also be discussed. The results are joint work with Álvaro Pámpano.

Paolo E. Ricci was professor of mathematics at La Sapienze University in Rome. Presently he is professor at  International Telematic University UniNettuno, Roma, Italia. He received the Simon Stevin Prize for Geometry in 2015.

Abstract   

An exponential function has the property of invariance with respect to a given

differential operator since it is an eigenfunction of that one. This can be generalized to fractional exponentials. Another example is given by the Laguerrian exponential function which is invariant with respect to the Laguerrian derivative. Using such unusual types of exponentials, new models of population dynamics are studied. The results are joint work with Diego Caratelli.

Pejian Shi is at Bamboo Research Institute, College of Ecology and Environment, Nanjing Forestry University, #159 Longpan Road, Xuanwu District, Nanjing 210037, P. R. China

Abstract: 

The performance equation proposed by Raymond B. Huey is initially used to describe the effect of temperature on the behavior of poikilotherms, and it can generate symmetrical and asymmetrical curves. The Lorenz curve describes the relationship between the cumulative proportion of household income and the cumulative proportion of households. Although the Lorenz curve has been widely used in economics to calculate the Gini coefficient, which quantifies the inequality of household income, prior studies focus on the statistical characteristics that the curve represents, and consider it as a cumulative distribution function. The shape of the Loren curve has not attracted sufficient attention. After rotating the Lorenz curve by 135 degrees counterclockwise and then right shifting it to a distance of the square root of 2, we find that the rotated and right-shifted Lorenz curves in fruit size and leaf size at the individual plant level follow the performance equation or its generalized version. In addition, the validity of the generalized performance equation was tested using the tree size data at the quadrat level for the forest census data. We believe that the generalized performance equation is promising to quantify the inequality of plant size, plant organ or tissue size.

I. Tavkhelidze is professor of mathematics at the Faculty of Exact and Natural Sciences,  Iv.Javakhishvili Tbilisi State University, Georgia. His main interests are differential equations and geometrization of topology.

Abstract

GML - bodies with any m and n parameters, whose radial cross-section is a regular m-polygon, are discussed in the report. The regularity of how many and what type of flat geometric figures are formed for any SS-cut (with a straight knife) on the radial cross-section of the GML-body has been found.

David has an undergraduate degree in Chemical Physics from University College London, and a Ph.D in Theoretical Chemistry from the University of Cambridge. Following a post-doctoral fellowship focused on numerical methods in electronic structure calculations, David transitioned into the pharmaceutical industry and spent many years providing computational support and solutions to drug discovery programs. David currently works at Chemical Computing Group (CCG), the makers of the MOE molecular modeling platform. 

Abstract

Our understanding of quantum phenomena often begins with simple ‘particle-in-a-box’ style problems, the solutions of which introduce the student to foundational quantum concepts such as degeneracy and quantization. In the current work, these model problems are explored in a variety of ways. This framework allows the interested student to orient the diverse multidisciplinary literature that has evolved around these problems. Finally, through consideration of the shape element of the syntax, the superformula – a simple extension of the equation describing a circle – is introduced and discussed.