# Peter Louis AntonelliUniversity of Alberta | UAlberta · Department of Mathematical and Statistical Sciences

Peter Louis Antonelli

BS, MS, PHD...all 3 in Mathematics at Home town University: Syracuse University, New York , USA

## About

382

Publications

28,560

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

2,531

Citations

Citations since 2017

Introduction

Additional affiliations

Education

September 1973 - August 1974

June 1968 - June 1970

July 1963 - June 1964

## Publications

Publications (382)

The question: Where does projective geometry fit in generalized geometries like KCC-theory, Lagrange geometry, or Finsler geometry?..is discussed.

Explains why Stratonovich stochastic calculus is the natural one to use for the study of processes on smooth manifolds

KCC-theory of SODE's on manifolds, sprays (SODE's), equations of geodesics in Finsler 2-manifolds, the Finsler metric functional, Euler-Lagrange equations, regular metric tensors, Berwald's frame, angular metric tensor, horizontal and vertical Christoffel symbols and Cartan's torsion tensor, principal scalar, I, projective geometry, Rashevsky's inv...

In order to understand them it will suffice to think about the Berwald Basis { δ i , ´ ∂ i }. If X is a vector field on TM, then one decomposes to obtain "uniquely"(see below) X = X m δ m + ´ X m ´ ∂ m with X m being the HORIZONTAL COMPONENT and the other (with dot) is the VERTICLE COMPONENT. One can formalize this: TTM = HTM ⊕ VTM. A purely vertic...

After brief summaries of several models of evolution of coral/algal symbiosis, stochastic Nelson mechanics is used to prove long-term heat stress can actually benefit scleractinian corals and their symbionts.

A model of L. Margulis' serial endosymbiosis theory, using projective geometry, is shown to be compatible with G.S. Ferreira Jr's recent model of tissue formation, which is based on differential adhesion of cells and Finslerian anholonomic frames describing phenotypic deformation. The Gould-Eldredge theory of punctuated equilibria is herein modelle...

A second order ordinary differential equations model (SODE) of a vegetated riverine ecosystem, amalgamating hydrological equations with ecological equations, is presented for the first time. After formulating plant production equations based on minimization of Medawar Growth Energy , hydrodynamical equations are introduced describing ideal water fl...

Uses the Kron/Kondo engineering method to study a riverine system in the semi-arid of Pernambuco, Brazil

We extend the Eco-strain Model of a Forest, presented previously and based on analogy with continuous media physics, to include the understory Plant Community and the underground Mycorrhizal Network (PC-MN). Using this, we provide a model of carbon cycling, in particular, and nutrient cycling, in general.

A model of tissue formation is presented, extending M. Steinberg's thermodynamic Differential Adhesion Mechanism to include cell membrane structures. Previous work on modeling the Margulis serial endosymbiosis theory of the origin of eukaryote cells is reviewed and a mathematical description of I. E. Wallin's mechanism of symbioticism is presented...

We have shown elsewhere that the classical constant coefficient 2-species ecological population density, N i (t), i = 1, 2, interaction equations for parasitism, mutualism and competition 4 , when augmented with the Volterra production equation, x i (t) = k (i) t 0

A model of tissue formation is presented, extending M. Steinberg's thermodynamic Differential Adhesion Mechanism to include cell membrane structures. Previous work on modeling the Margulis serial endosymbiosis theory of the origin of eukaryote cells is reviewed and a mathematical description of I.E. Wallin's mechanism of symbioticism is presented u...

Somewhat detailed description of our published research from 2003 on.

We extend the Eco-strain Model of a Forest, presented previously and based on analogy with continuous media physics, to include the understory Plant Community and the underground Mycorrhizal Network (PC-MN). Using this, we provide a model of carbon cycling, in particular, and nutrient cycling, in general.

We plan to add a last chapter as well so the final version will be 60 pages or so.

Tissue formation model based on differtial adhesion and nanostructures of cell membranes

Using a quadratic polynomial for exponetial coefficient function, the 3 Finsler gate metrics are listed in table form

Evolution of tissue formation : a model starting with serial endosymbosis of L.Margulis and I. Wallin, using Antonelli/Bucataru anholonomic frames for Kropina space and geometry of the numerator

We extend the Eco-strain Model of a Forest, presented previously and based on analogy with continuous media physics, to include the understory Plant Community and the underground Mycorrhizal Network (PC-MN). Using this, we provide a model of carbon cycling, in particular, and nutrient cycling, in general.

a simple introduction to Strtonovich calculus needed to study Finslerian diffusion is provided.

This PDF replaces the just removed Power Point version of my Independence day talk at UFPE. It is exactly the same.

These are notes(40 pp) of a short course I gave in the Summer,2012, at Dmat, UFPE, Recife.
They were translated into Portuguese by Dr. Claudio Cristino. My original notes were hand written in English.
There are some type-o's caught recently and corrections are indicated in the file.

The role of curvature in Riemannian and Finslerian Markov Diffusions is discussed. Applications in ecology, evolution, epidemiology, genetics and developmental biology are presented, briefly. Refereneces to published papers in the various applications are listed and/or are downloadable.

Randers space used to extend eco-strain in forest modelling so as to the predict carbon cycle . It all depends on Anholonomic frames for plastic deformation of the Allometric spaces in the Finsler gate

UPDATE on the Project: Social Interactions in large Populations of Vertebrates

Finsler scalar curvature plot and projective geometry

Plots Finsler scalar curvature as a surface for particular metrics. Projective geometry is computed.

Graph of Finsler metric, proj.flatness, ..

Research on evolution of singlr celled eukaryotes to multicellular forms leads to this Cosh - class Kropina metric of 2-dimensions. Previously there was known only the linear case.

Some elementary remarks on tensors, covariance and non-integrable deformations, pertinent to the Finsler Gate Theorem

Paper gives a lucid account of the Kron-Kondo method of anholonomy. Furthermore, The Kondo paper can be read at the website of Japan J. Aerodynamical engineering, vol.2,#7, 1954..some Japanese characters are displayed so you can’t read it after you download it, without special reader. Also see the 2nd part in same J but 1953, vol.2 The Kondo part 1...

summary of Antonelli/Rutz projects and their published papers

Further remarks on Non-Riemannian geometries and applications..especially the significance of projective geometry in Finsler's theory, the Darboux- Matsumoto theorem and consequences. Namely, every quadratic 2-spray is projectively Berwald, i.e.,to one of the 3 Berwald classes for dimension 2. If the quadratic spray is not projectively flat, then i...

Comments about Elsevier 's publishing policies. Moreover, the same thing(fired most editors , hired a new set) happened recently with theJournal of Experimental Marine Biology and Ecology..an Elsevier journal..just more evidence of corporate takeover of academia!!

gives some insight into the work of Miron and the Finsler schools

Two remarks on our paper.. Gradient Driven Dynamics on Finsler Manifolds: The Jacobi Action-Metric Theorem and an Application in Ecology

A dynamical model of the environmental impact of transgenic crop on normal varieties in the presence of environmental noise is presented. Previous results used only the deterministic equations to cover external perturbations. Analytical Trophodynamics with spatial diffusion dispersion mechanisms is now augmented with Finslerian noise. We conclued t...

This work can be considered a prequel to our previous paper on coral bleaching induced by global warming. We once again investigate, using Finsler geometry, dynamical energy budget theory and nonlinear modular mechanics, the origin of endosymbiosis, between reef-building corals and the algae. We assume their relationship starts out as entosymbiosis...

Use is made of the Finslerian Diffusion Embedding Theorem of Antonelli and Zastawniack, to study the influence of noise in a model of mamalian plastic Deformation of Phenotypes during maturation, under both normal and non-optimal nutritional programs. Focus is on adipose and skeletal muscle tissues as developed by the authors previously. The main r...

The text is appropriate for 3 rd year undergraduates..who have had linear algebra and 3 semesters of calculus . The required differential geometry is provided within the text proper

Continues the Phd thesis(2nd part) study of Rinaldo V.S. Junior on the analysis of competition between a transgenic crop and its natural variant with the addition of noisy , modeling an uncertain environment . A modified form this paper will appear in the journal, Nonlinear Studies, in the near future.

An over view with historical perspective on allometry ideas is presented. The search for the Holy Grail, or bauplan for ontogenesis goes beyond straight line regressions to try to find cellular dynamical equations relevant to developmental biology and which satisfy the Huxley/Needham allometric law.

Following the Antonelli/Rutz Finsler Gate method, the concept of Allometric Strain is introduced to model plastic deformation of phenotypes in mammalian genomes. Focus is on a model of muscle and adipose (fat) cell populations, which produce hormones adiponectin and IL- 6, which mediate their interactions. The model shows that genetic switching is...

My personal academic history , spanning 1963 to 2015. It is a history of ideas about evolution, ecology, development.There is mention of fFnsler and Riemannian geometry

stochastic Finslerian Volterra-Hamilton systems are used to model noise in the developmental(ontogeny) interaction between muscle and fat tissues seen as populations of cells , each producing a hormone affecting their interplay during growth to adulthood. Two systems are studied one normal and the other a phenotypic deformation due to disease or nu...

stochastic Finslerian Volterra-Hamilton systems are used to model noise in the developmental(ontogeny) interaction between muscle and fat tissues seen as populations of cells , each producing a hormone affecting their interplay during growth to adulthood. Two systems are studied one normal and the other a phenotypic deformation due to disease or nu...

Resumo An Analytical Modular Dynamics (AMD) model of tree stand growth with discounting is investigated using KCC-Theory. Jacobi stability of carbon production is proved. A formal (DEBT) energy expression for the seasonal carbon cycle, obtained and data from the Serto of Northeastern Brazil, is utilized to calibrate the model.

An Analytical Modular Dynamics (AMD) model of tree stand growth with discounting is investigated using KCC-Theory. Jacobi stability of carbon production is proved. A formal (DEBT) energy expression for the seasonal carbon cycle, obtained and data from the Sertão of Northeastern Brazil, is utilized to calibrate the model.

This is the upgraded, journal- ready version of Plastic Deformation: The Role of Allometry and The Golden Ratio. The title has been slightly modified and the bibliography as well. It has been accepted for publication in the Universal Journal of Engineering Mechanics, November 15, 2015

Finsler geometry of Berwald's spaces together with continuum mechanics of deformable media and the Huxley allometric law are used to model growth and maturation of muscle and fatty tissues subjected to plastic deformations induced from the ambient environment. Type-2 diabetes is discussed.

Motivation from Russian history for non-linear modular mechanics models in ecology, evolution, and development of coral reefs and forests is provided. The central role of the Huxley/Needham/Laird allometric law is made plain, by the Finsler Gate Theorem.

Finslerian noise is a Brownian motion theory for Finslerian manifolds having many applications in Biology. Constant connections of 2-dimensions are particularly useful and in this article important aspects of the more general theory of n-dimensions are discussed in detail.

With T. Zastawniack, I lay the rigorous foundations of Brownian Motion on Finsler manifolds. Applications are mainly about coral reef ecology problems in a noisy environment.

Pure theory of Finsler geometry with applications in Physics and biology..

a dozen contributors to various biological problems in ecology and developmental biology. Autotoxin production, coral reef limit cycles, foundations of growth mechanics, Translation of V.Volterra article(1936) and lots more!

GM model shows GM crop severely outcompetes the normal. Deterministic and stochastic methods fro Finsler Geometry are used throughout.

2nd paper of our 4-member team in a series on modelling bleaching and evolution in reef-building coral species. The first paper, published in NONRWA, was the most downloaded paper of 2014. The present work has been submitted.

Phd thesis: submitted, Finslerian noise is added to homogeneously distributed seed crops in competition. First sections already published ..on diffusion reaction due to wind..reaches stable homogeneous distribution on adjacent fields for farming crops

## Questions

Questions (2)

Buss says, it is competition between cell lineages that leads to multicellularity

Plant Allometry: The Scaling of Form and Function,

K.J. Niklas,

U.Chicago Press,1994

## Projects

Projects (17)