Physical Sciences and Mathematics Commons^™

A Review Of The Fractal Market Hypothesis For Trading And Market Price Prediction, Jonathan Blackledge, Marc Lamphiere

Articles

This paper provides a review of the Fractal Market Hypothesis (FMH) focusing on financial times series analysis. In order to put the FMH into a broader perspective, the Random Walk and Efficient Market Hypotheses are considered together with the basic principles of fractal geometry. After exploring the historical developments associated with different financial hypotheses, an overview of the basic mathematical modelling is provided. The principal goal of this paper is to consider the intrinsic scaling properties that are characteristic for each hypothesis. In regard to the FMH, it is explained why a financial time series can be taken to be …

Multicomponent Fokas-Lenells Equations On Hermitian Symmetric Spaces, Vladimir Gerdjikov, Rossen Ivanov

Articles

Multi-component integrable generalizations of the Fokas-Lenells equation, associated with each irreducible Hermitian symmetric space are formulated. Description of the underlying structures associated to the integrability, such as the Lax representation and the bi-Hamiltonian formulation of the equations is provided. Two reductions are considered as well, one of which leads to a nonlocal integrable model. Examples with Hermitian symmetric spaces of all classical series of types A.III, BD.I, C.I and D.III are presented in details, as well as possibilities for further reductions in a general form.

Five-Wave Resonances In Deep Water Gravity Waves: Integrability, Numerical Simulations And Experiments, Dan Lucas, Marc Perlin, Dian-Yong Liu, Shane Walsh, Rossen Ivanov, Miguel D. Bustamante

Articles

In this work we consider the problem of finding the simplest arrangement of resonant deep water gravity waves in one-dimensional propagation, from three perspectives: Theoretical, numerical and experimental. Theoretically this requires using a normal-form Hamiltonian that focuses on 5-wave resonances. The simplest arrangement is based on a triad of wave vectors K₁ + K₂ = K₃ (satisfying specific ratios) along with their negatives, corresponding to a scenario of encountering wave packets, amenable to experiments and numerical simulations. The normal-form equations for these encountering waves in resonance are shown to be non-integrable, but they admit an integrable reduction …

Isolation Intervals Of The Real Roots Of The Parametric Cubic Equation, Emil Prodanov

Articles

The isolation intervals of the real roots of the real symbolic monic cubic polynomial $p(x) = x^3 + a x^2 + b x + c$ are found in terms of simple functions of the coefficients of the polynomial (such as: $-a$, $-a/3$, $-c/b$, $\pm \sqrt{-b}$, when $b$ is negative), and the roots of some auxiliary quadratic equations whose coefficients are also simple functions of the coefficients of the cubic. All possible cases are presented with clear and very detailed diagrams. It is very easy to identify which of these diagrams is the relevant one for any given cubic equation and …

A Method For Locating The Real Roots Of The Symbolic Quintic Equation Using Quadratic Equations, Emil Prodanov

Articles

A method is proposed with which the locations of the roots of the monic symbolic quintic polynomial $x^5 + a_4 x^4 + a_3 x^3 + a_2 x^2 + a_1 x + a_0$ can be determined using the roots of two {\it resolvent} quadratic polynomials: $q_1(x) = x^2 + a_4 x + a_3$ and $q_2(x) = a_2 x^2 + a_1 x + a_0$, whose coefficients are exactly those of the quintic polynomial. The different cases depend on the coefficients of $q_1(x)$ and $q_2(x)$ and on some specific relationships between them. The method is illustrated with the full analysis of one of …

On Newton's Rule Of Signs, Emil Prodanov

Articles

Analysing the cubic sectors of a real polynomial of degree n, a minor modification of Newton’s Rule of signs is proposed with which stricter upper limits on the number of real roots can be found. A new necessary condition for reality of the roots of a polynomial is also proposed. Relationship between the quadratic elements of the polynomial is established through its roots and those of its derivatives. Some aspects of polynomial discriminants are also discussed.

Climate Change Impacts On Wind Energy Generation In Ireland, Eadaoin Doddy Clarke, Conor Sweeney, Frank Mcdermott, Seánie Griffin, Joao Monteiro Correia, Paul Nolan, Laura Cooke

Articles

An ensemble of high-resolution regional climate model simulation data is used to examine the impacts of climate change on offshore and onshore wind energy genera- tion in Ireland. Two Representative Concentration Pathway (RCP) scenarios (RCP 4.5 and 8.5) are analysed for the mid-term (2041–2060) and the long-term (2081–2100) future. Wind energy is projected to decrease (≤2%) overall in future climate scenarios. Changes are evident by mid-century and are more pronounced by late 21st century, particularly for RCP 8.5 offshore. Seasonally, wind energy is projected to decrease by less than 6% in summer and to increase slightly in winter (up to …

Abelian P-Groups With Minimal Full Inertia, Brendan Goldsmith, Luigi Salce

Articles

The class of abelian p-groups with minimal full inertia, that is, satisfying the property that fully inert subgroups are commensurable with fully invariant subgroups is investigated, as well as the class of groups not satisfying this property; it is known that both the class of direct sums of cyclic groups and that of torsion-complete groups are of the first type. It is proved that groups with “small" endomorphism ring do not satisfy the property and concrete examples of them are provided via Corner’s realization theorems. Closure properties with respect to direct sums of the two classes of groups are also …

On P-Adic Modules With Isomorphic Endomorphism Algebras, Brendan Goldsmith, Noel White

Articles

We investigate pairs of modules over the ring of p-adic integers having isomorphic endomorphism algebras. In many cases this forces the modules to be isomorphic but there are two exceptional situations where isomorphism does not follow.

On The Evolution Equation For Modelling The Covid-19 Pandemic, Jonathan Blackledge

Books/Book chapters

The paper introduces and discusses the evolution equation, and, based exclusively on this equation, considers random walk models for the time series available on the daily confirmed Covid-19 cases for different countries. It is shown that a conventional random walk model is not consistent with the current global pandemic time series data, which exhibits non-ergodic properties. A self-affine random walk field model is investigated, derived from the evolutionary equation for a specified memory function which provides the non-ergodic fields evident in the available Covid-19 data. This is based on using a spectral scaling relationship of the type 1/ωα where ω …

Neurophysiological Correlates Of Dual Tasking In People With Parkinson's Disease And Freezing Of Gait, Conor Fearon, John Butler, Saskia Waechter, Isabelle Killane, Simon Kelly, Richard B Reilly, Timothy Lynch

Articles

Freezing of gait in people with Parkinson's disease (PwP) is associated with executive dysfunction and motor preparation deficits. We have recently shown that electrophysiological markers of motor preparation, rather than decision-making, differentiate PwP with freezing of gait (FOG +) and without (FOG -) while sitting. To examine the effect of locomotion on these results, we measured behavioural and electrophysiological responses in PwP with and without FOG during a target response time task while sitting (single-task) and stepping-in-place (dual-task). Behavioural and electroencephalographic data were acquired from 18 PwP (eight FOG +) and seven young controls performing the task while sitting and …

Quotient-Transitivity And Cyclic Subgroup-Transitivity, Brendan Goldsmith, Ketao Gong

Articles

We introduce two new notions of transitivity for Abelian 𝑝-groups based on isomorphism of quotients rather than the classical use of equality of height sequences associated with Abelian 𝑝-group theory. Unlike the classical theory where “most” groups are transitive, these new notions lead to much smaller classes, but even these classes are sufficiently large to be interesting.

A Hybrid Agent-Based And Equation Based Model For The Spread Of Infectious Diseases, Elizabeth Hunter, Brian Mac Namee, John D. Kelleher

Articles

Both agent-based models and equation-based models can be used to model the spread of an infectious disease. Equation-based models have been shown to capture the overall dynamics of a disease outbreak while agent-based models are able to capture heterogeneous characteristics of agents that drive the spread of an outbreak. However, agent-based models are computationally intensive. To capture the advantages of both the equation-based and agent-based models, we create a hybrid model where the disease component of the hybrid model switches between agent-based and equation-based. The switch is determined using the number of agents infected. We first test the model at …

New Bounds On The Real Polynomial Roots, Emil M. Prodanov

Articles

The presented analysis determines several new bounds on the roots of the equation $a_n x^n + a_{n−1} x^{n−1} + · · · + a_0 = 0$ (with $a_n > 0$). All proposed new bounds are lower than the Cauchy bound max $\{ 1, sum_{j=0}^{n-1} | a_j / a_n | \}$. Firstly, the Cauchy bound formula is derived by presenting it in a new light — through a recursion. It is shown that this recursion could be exited at earlier stages and, the earlier the recursion is terminated, the lower the resulting root bound will be. Following a separate analysis, it is …

Italian Sociologists: A Community Of Disconnected Groups, Aliakbar Akbaritabar, Vincent Traag, Alberto Caimo, Flaminio Squazzoni

Articles

Examining coauthorship networks is key to study scientific collaboration patterns and structural characteristics of scientific communities. Here, we studied coauthorship networks of sociologists in Italy, using temporal and multi-level quantitative analysis. By looking at publications indexed in Scopus, we detected research communities among Italian sociologists. We found that Italian sociologists are fractured in many disconnected groups. The giant connected component of the Italian sociology could be split into five main groups with a mixture of three main disciplinary topics: sociology of culture and communication (present in two groups), economic sociology (present in three groups) and general sociology (present in three …

On The Socles Of Fully Inert Subgroups Of Abelian P-Groups, Andrey R. Chekhlov, Peter V. Danchev, Brendan Goldsmith

Articles

We define the so-called fully inert socle-regular and weakly fully inert socle-regular Abelian p-groups and study them with respect to certain of their numerous interesting properties. For instance, we prove that in the case of groups of length ! these two group classes coincide but that in the case of groups of length ! + 1 they differ. Some structural and characterization results are also obtained. The work generalizes concepts which have been of interest recently in the theory of entropy in algebra and builds on recent investigations by the second and third named authors in Arch. Math. Basel (2009) …

Aspects Of Quantum Theory In General Relativity And Cosmology, Eamon Mccaughey

Doctoral

After a brief introduction to Cosmology some quantum aspects of General Relativity and cosmology are presented. The radial motion of a massive particles in the ergosphere of the Kerr Black Hole is considered. Screening of Hawking radiation and shielding of the Penrose process is examined in the context of the region of negative energy inside the ergosphere. Tunnelling of such particles between the boundaries of the classically forbidden region will be considered and the transmission coefficient determined. The evolution of Primordial black holes in standard and Loop Quantum Cosmology is reviewed. A stability analysis of Einstein’s universe in both classical …

New Estimates For The Number Of Integer Polynomials With Given Discriminants, Natalia Budarina, Vasilii Bernik, Hugh O'Donnell

Articles

In this paper, we propose a new method of upper bounds for the number of integer polynomials of the fourth degree with a given discriminant. By direct calculation similar results were established by H. Davenport and D. Kaliada for polynomials of second and third degrees.

Saperi: Approaching Gender Gap Using Spatial Ability Training Week In High-School Context, Maria Giulia Ballatore, Gavin Duffy, Sheryl Sorby, Anita Tabacco

Articles

Maria Giulia Ballatore, Gavin Duffy, Sheryl Sorby, and Anita Tabacco. 2020. SAperI: approaching gender gap using Spatial Ability training week in high-school context. In Eighth International Conference on Technological Ecosystems for Enhancing Multiculturality (TEEM’20), October 21–23, 2020, Salamanca, Spain. ACM, New York, NY, USA, 7 pages. https://doi.org/10.1145/3434780.3436577

Swirling Fluid Flow In Flexible, Expandable Elastic Tubes: Variational Approach, Reductions And Integrability, Rossen Ivanov, Vakhtang Putkaradze

Articles

Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In real-life applications like blood flow, a swirl in the fluid often plays an important role, presenting an additional complexity not described by previous theoretical models. We present a theory for the dynamics of the interaction between elastic tubes and swirling fluid flow. The equations are derived using a variational principle, with the incompressibility constraint of the fluid giving rise to a pressure-like term. In order to connect this work with the previous literature, we consider the case of inextensible and …

On The Intermediate Long Wave Propagation For Internal Waves In The Presence Of Currents, Joseph Cullen, Rossen Ivanov

Articles

A model for the wave motion of an internal wave in the presence of current in the case of intermediate long wave approximation is studied. The lower layer is considerably deeper, with a higher density than the upper layer. The flat surface approximation is assumed. The fluids are incompressible and inviscid. The model equations are obtained from the Hamiltonian formulation of the dynamics in the presence of a depth-varying current. It is shown that an appropriate scaling leads to the integrable Intermediate Long Wave Equation (ILWE). Two limits of the ILWE leading to the integrable Benjamin-Ono and KdV equations are …

Camassa-Holm Cuspons, Solitons And Their Interactions Via The Dressing Method, Rossen Ivanov, Tony Lyons, Nigel Orr

Articles

A dressing method is applied to a matrix Lax pair for the Camassa–Holm equation, thereby allowing for the construction of several global solutions of the system. In particular, solutions of system of soliton and cuspon type are constructed explicitly. The interactions between soliton and cuspon solutions of the system are investigated. The geometric aspects of the Camassa–Holm equation are re-examined in terms of quantities which can be explicitly constructed via the inverse scattering method.

Designing A National Blended Learning Program For “Out‑Of‑Field” Mathematics Teacher Professional Development, Merrilyn Goos, John O’Donoghue, Máire Ní Ríordáin, Fiona Faulkner, Tony Hall, Niamh O'Meara

Articles

“Out-of-field” teaching refers to the practice of assigning secondary school teachers to teach subjects that do not match their training or education. This practice is an issue of concern in many countries around the world, and seems particularly prevalent in the teaching of mathematics. The aim of this paper is to analyse the design principles underpinning the development and delivery of a blended learning program of professional development for out-of-field teachers of secondary school mathematics in Ireland. Three theoretical frameworks inform our analysis of the blended learning design. The first identifies critical dimensions of blended learning environments as a boundary …

A Mathematical Model For Visco-Ferromagnetic Materials, Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden

Articles

Visco-ferromagnetic materials represented by non-local constitutive equation are considered in the paper. We use fractional derivatives in order to describe memory and spatial effects. Also, thermodynamic principles are formulated and studied.

Integrable Negative Flows Of The Heisenberg Ferromagnet Equation Hierarchy, Rossen Ivanov

Articles

We study the negative flows of the hierarchy of the integrable Heisenberg ferromagnet model and their soliton solutions. The first negative flow is related to the so-called short pulse equation. We provide a framework which generates Lax pairs for the other members of the hierarchy. The application of the dressing method is illustrated with the derivation of the one-soliton solution.

Classification Of The Real Roots Of The Quartic Equation And Their Pythagorean Tunes, Emil Prodanov

Articles

Presented is a two-tier analysis of the location of the real roots of the general quartic equation x4+ax3+bx2+cx+d=0 with real coefficients and the classification of the roots in terms of a, b, c, and d, without using any numerical approximations. Associated with the general quartic, there is a number of subsidiary quadratic equations (resolvent quadratic equations) whose roots allow this systematization as well as the determination of the bounds of the individual roots of the quartic. In many cases the root isolation intervals are found. The second tier of the analysis uses two subsidiary cubic equations (auxiliary cubic equations) and …

Stability Analysis Of Einstein's Universe In Loop Quantum Cosmology, Eamon Mccaughey

Articles

A stability analysis of Einstein’s universe in both classical General Relativity and semiclassical Loop Quantum Cosmology regimes is presented. The stability properties of the General Relativity model are significantly altered due to Loop Quantum Gravity corrections. Comparisons between both dynamical systems are considered on the basis of these modifications. The Loop Quantum Cosmology solutions are restricted to an open universe model (k = -1) and represent a cyclic universe. The integrals of motion for both systems are found and their Hamiltonian structure determined.

Modelling Interactions Among Offenders: A Latent Space Approach For Interdependent Ego-Networks, Isabella Gollini, Alberto Caimo, Paolo Campana

Articles

Illegal markets are notoriously difficult to study. Police data offer an increasingly exploited source of evidence. However, their secondary nature poses challenges for researchers. A key issue is that researchers often have to deal with two sets of actors: targeted and non-targeted. This work develops a latent space model for interdependent ego-networks purposely created to deal with the targeted nature of police evidence. By treating targeted offenders as egos and their contacts as alters, the model (a) leverages on the full information available and (b) mirrors the specificity of the data collection strategy. The paper then applies this approach to …

Phase-Only Digital Encryption, Jonathan Blackledge, Western Govere, Dumisani Sibanda

Articles

Abstract—We study then-dimensional deconvolution prob-lem associated with an impulse response function and an(additive) noise function that are both characterised by thesame phase-only stochastic spectrum. In this case, it is shownthat the deconvolution problem becomes well-posed and has ageneral solution that is both exact and unique, subject to are-normalisation condition relating to the scale of the solution.While the phase-only spectral model considered is of limitedvalue in general (in particular, problems arising in the fieldsof digital signal processing and communications engineering,specifically with regard to the retrieval of information fromnoise), its application to digital cryptography has potential.One of the reasons for this (as …

Sustainable Energy Governance In South Tyrol (Italy): A Probabilistic Bipartite Network Model, Jessica Belest, Laura Secco, Elena Pisani, Alberto Caimo

Articles

At the national scale, almost all of the European countries have already achieved energy transition targets, while at the regional and local scales, there is still some potential to further push sustainable energy transitions. Regions and localities have the support of political, social, and economic actors who make decisions for meeting existing social, environmental and economic needs recognising local specificities.

These actors compose the sustainable energy governance that is fundamental to effectively plan and manage energy resources. In collaborative relationships, these actors share, save, and protect several kinds of resources, thereby making energy transitions deeper and more effective.

This research …