Physical Sciences and Mathematics Commons^™

Facing The Sun, Frank Prendergast, Muiris O'Sullivan, Ken Williams, Gabriel Cooney

Articles

December 2017 marked 50 years since archaeologist Michael J. O’Kelly first observed the solar illumination of the burial chamber in the Neolithic passage tomb at Newgrange during the period of the winter solstice. O’Kelly subsequently recorded direct sunlight entering Newgrange through the ‘especially contrived slit which lies under the roof-box at the outer end of the passage roof’ on 21 December 1969. The discovery of this historic phenomenon, dating back over 5,000 years, captured the public interest and imagination at that time and ever since. In this major article published in the Winter 2017 edition of Archaeology Ireland (date of …

Mode-Sum Prescription For Vacuum Polarization In Black Hole Spacetimes In Even Dimensions, Peter Taylor, Cormac Doran

Articles

We present a mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically symmetric black hole spacetimes in even dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher even dimensions, building upon a previous scheme we developed for odd dimensions. Things are more complicated here since the even-dimensional propagator possesses logarithmic singularities which must be regularized. However, in spite of this complication, the regularization parameters can be computed in closed form in arbitrary even dimensions and for arbitrary metric function f(r). As an explicit example of our method, we …

Mode-Sum Prescription For Vacuum Polarization In Black Hole Spacetimes In Even Dimensions, Peter Taylor, Cormac Breen

Articles

We present a mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically symmetric black hole spacetimes in even dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher even dimensions, building upon a previous scheme we developed for odd dimensions. Things are more complicated here since the even-dimensional propagator possesses logarithmic singularities which must be regularized. However, in spite of this complication, the regularization parameters can be computed in closed form in arbitrary even dimensions and for arbitrary metric function f(r). As an explicit example of our method, we …

An Analysis Of The Application Of Simplified Silhouette To The Evaluation Of K-Means Clustering Validity, Fei Wang, Hector-Hugo Franco-Penya, John D. Kelleher, John Pugh, Robert J. Ross

Conference papers

Silhouette is one of the most popular and effective internal measures for the evaluation of clustering validity. Simplified Silhouette is a computationally simplified version of Silhouette. However, to date Simplified Silhouette has not been systematically analysed in a specific clustering algorithm. This paper analyses the application of Simplified Silhouette to the evaluation of k-means clustering validity and compares it with the k-means Cost Function and the original Silhouette from both theoretical and empirical perspectives. The theoretical analysis shows that Simplified Silhouette has a mathematical relationship with both the k-means Cost Function and the original Silhouette, while empirically, we show that …

Mathematical Competencies Of Third Level Students: A Review, Colm Mcguinness

The ITB Journal

Many lecturers of mathematics and related disciplines in Ireland and internationally believe there has been a gradual decline in mathematical competencies of students presenting for first year at third level educational establishments. Some of the evidence to support this view is reviewed, along with the types of solutions being applied in Ireland and the UK. Attention is drawn to the explicit and implicit decline in standards potentially associated with some of the solutions, particularly for short courses involving mathematics.

Motor Preparation Rather Than Decision-Making Differentiates Parkinson’S Disease Patients With And Without Freezing Of Gait, John Butler, Conor Fearon, Isabelle Killane, Saskia M. Waechter, Richard B. Reilly, Timothy Lynch

Articles

Objective: Freezing of gait (FOG) is a brief, episodic phenomenon affecting over half of people with Parkinson’s disease (PD) and leads to significant morbidity. The pathophysiology of FOG remains poorly understood but is associated with deficits in cognitive function and motor preparation.

Method: We studied 20 people with PD (10 with FOG, 10 without FOG) and performed a timed response target detection task while electroencephalographic data were acquired. We analysed the data to detect and examine cortical markers of cognitive decision making (P3b or centroparietal positivity, CPP) and motor readiness potential. We analysed current source density (CSD) to increase spatial …

Dialectric Materials With Memory 1: Minimum And General Free Energies., Scott Glascow, John Murrough Golden

Articles

A general tensor isothermal theory of free energies and free enthalpies for dielectrics is presented, corresponding to linear constitutive relations with memory. Starting from the general equations of continuum thermodynamics, various properties of and constraints on free energy/enthalpy functionals in dielectric media are noted. It is well-known that free enthalpies are particularly convenient in that their properties are closely analogous with those of free energies in mechanics, though different in crucial ways. General constitutive equations with memory are determined from a given free enthalpy. The form of the relaxation function, which occurs in these constitutive equations, is discussed from a …

A Dressing Method For Soliton Solutions Of The Camass-Holm Equation, Rossen Ivanov, Tony Lyons, Nigel Orr

Conference papers

The soliton solutions of the Camassa-Holm equation are derived by the implementation of the dressing method. The form of the one and two soliton solutions coincides with the form obtained by other methods.

Stochastic Modelling For Levy Distributed Systems, Jonathan Blackledge, T Raja Rani

Articles

The purpose of this paper is to examine a range of results that can be derived from Einstein’s evolution equation focusing on (but not in an exclusive sense) the effect of introducing a L´evy distribution. In this context, we examine the derivation (as derived from the Einstein’s evolution equation) of the classical and fractional diffusion equations, the classical and generalised Kolmogorov-Feller equations, the evolution of self-affine stochastic fields through the fractional diffusion equation and the fractional Schr¨odinger equation, the fractional Poisson equation (for the time independent case), and, a derivation of the Lyapunov exponent. In this way, we provide a …

Dressing Method For The Degasperis-Procesi Equation, Rossen Ivanov

Articles

The soliton solutions of the Degasperis–Procesi equations are constructed by the implementation of the dressing method. The form of the one and two soliton solutions coincides with the form obtained by Hirota's method.

G-Strands On Symmetric Spaces, Alexis Arnaudin, Darryl Holm, Rossen Ivanov

Articles

We study the G-strand equations that are extensions of the classical chiral model of particle physics in the particular setting of broken symmetries described by symmetric spaces. These equations are simple field theory models whose configuration space is a Lie group, or in this case a symmetric space. In this class of systems, we derive several models that are completely integrable on finite dimensional Lie group G, and we treat in more detail examples with symmetric space SU(2)/S1 and SO(4)/SO(3). The latter model simplifies to an apparently new integrable nine-dimensional system. We …

Generalised Hopficity And Products Of The Integers, Brendan Goldsmith

Articles

Hopfian groups have been a topic of interest in alge-braic settings for many years. In this work a natural generalizationof the notion, so-called R-Hopficity is introduced. Basic propertiesof R-Hopfian groups are developed and the question of whether ornot infinite direct products of copies of the integers are R-Hopfian isconsidered. An unexpected result is that the answer to this purelyalgebraic question depends on the set theory assumed.

Hamiltonian Model For Coupled Surface And Internal Waves In The Presence Of Currents, Rossen Ivanov

Articles

We examine a two dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface. The two media are separated by a free common interface. The gravity driven surface and internal water waves (at the common interface between the media) in the presence of a depth-dependent current are studied under certain physical assumptions. Both media are considered incompressible and with prescribed vorticities. Using the Hamiltonian approach the Hamiltonian of the system is constructed in terms of ’wave’ variables and the equations of motion are calculated. The resultant equations of motion …

Hamiltonian Dynamics Of Cosmological Quintessence Models, Rossen Ivanov, Emil Prodanov

Articles

The time-evolution dynamics of two nonlinear cosmological real gas models has been reexamined in detail with methods from the theory of Hamiltonian dynamical systems. These examples are FRWL cosmologies, one based on a gas, satisfying the van der Waals equation and another one based on the virial expansion gas equation. The cosmological variables used are the expansion rate, given by the Hubble parameter, and the energy density. The analysis is aided by the existence of global first integral as well as several special (second) integrals in each case. In addition, the global first integral can serve as a Hamiltonian for …

Dielectric Materials With Memory Ii: Free Energies In Non- Magnetic Materials, Scott Glascow, John Murrough Golden

Articles

An isothermal theory of free energies and free enthalpies, corresponding to linear constitutive relations with memory, is presented for isotropic non-magnetic materials. This is a second paper, following recent work on a general tensor theory of isothermal dielectrics and on the form of the minimum free energy. Both papers are based on continuum thermodynamics. For a standard choice of relaxation function, the minimum and maximum free energies are given explicitly, using a method previously developed in a mechanics context. Also, a new family of intermediate free energy functionals is derived for dielectrics. All these are solutions of a constrained optimization …

Disrupted Superior Collicular Activity May Reveal Cervical Dystonia Disease Pathomechanisms, Eavan Mc Govern, Owen Killian, Shruti Narasimham, Brendan T. Quinlivan, John Butler, Rebecca B. Beck, Ines M. Beiser, Laura W. Williams, Ronan P.M. Killeen, Michael A. Farrell, Seán O'Riordan, Richard B. Reilly, Michael J. Hutchinson

Articles

Cervical dystonia is a common neurological movement disorder characterised by muscle contractions causing abnormal movements and postures affecting the head and neck. The neural networks underpinning this condition are incompletely understood. While animal models suggest a role for the superior colliculus in its pathophysiology, this link has yet to be established in humans. The present experiment was designed to test the hypothesis that disrupted superior collicular processing is evident in affected patients and in relatives harbouring a disease-specific endophenotype (abnormal temporal discrimination). The study participants were 16 cervical dystonia patients, 16 unaffected first-degree relatives with abnormal temporal discrimination, 16 unaffected …

Disrupted Superior Collicular Activity May Reveal Cervical Dystonia Disease Pathomechanisms, Eavan M. Mcgovern, Owen Killian, Shruti Narashimham, Brendan Quinlivan, John Butler, Rebecca Beck, Ines Beiser, Laura W. Williams, Ronan P. Killeen, Michael Farrell, Sean O'Riordan, Richard B. Reilly, Michael Hutchinson

Articles

Cervical dystonia is a common neurological movement disorder characterised by muscle contractions causing abnormal movements and postures affecting the head and neck. The neural networks underpinning this condition are incompletely understood. While animal models suggest a role for the superior colliculus in its pathophysiology, this link has yet to be established in humans. The present experiment was designed to test the hypothesis that disrupted superior collicular processing is evident in affected patients and in relatives harbouring a disease-specific endophenotype (abnormal temporal discrimination). The study participants were 16 cervical dystonia patients, 16 unaffected first-degree relatives with abnormal temporal discrimination, 16 unaffected …

Disrupted Superior Collicular Activity May Reveal Cervical Dystonia Disease Pathomechanisms, Eavan Mcgovern, Owen Killian, Shruti Narasimham, Brendan Quinlivan, John Butler, Rebecca Beck, Ines Beiser, Laura Williams, Ronan P. Kileen, Michael Farrell, Sean O'Riordan, Richard B. Reilly, Michael Hutchinson

Articles

Cervical dystonia is a common neurological movement disorder characterised by muscle contractions causing abnormal movements and postures afecting the head and neck. The neural networks underpinning this condition are incompletely understood. While animal models suggest a role for the superior colliculus in its pathophysiology, this link has yet to be established in humans. The present experiment was designed to test the hypothesis that disrupted superior collicular processing is evident in afected patients and in relatives harbouring a disease-specifc endophenotype (abnormal temporal discrimination). The study participants were 16 cervical dystonia patients, 16 unafected frst-degree relatives with abnormal temporal discrimination, 16 unafected …

On Integrable Wave Interactions And Lax Pairs On Symmetric Spaces, Vladimir S. Gerdjikov, Georgi G. Grahovski, Rossen Ivanov

Articles

No abstract provided.

A Comparison Of Stimulus Presentation Methods In Temporal Discrimination Testing, Eavan M. Mcgovern, John Butler, Ines Beiser, Laura Williams, Brendan Quinlivan, Shruti Narasiham, Rebecca Beck, Sean O'Riordan, Richard B. Reilly, Michael Hutchinson

Articles

The temporal discrimination threshold (TDT) is the shortest time interval at which an individual detects two stimuli to be asynchronous (normal  =  30-50 ms). It has been shown to be abnormal in patients with disorders affecting the basal ganglia including adult onset idiopathic focal dystonia (AOIFD). Up to 97% of patients have an abnormal TDT with age- and sex-related penetrance in unaffected relatives, demonstrating an autosomal dominant inheritance pattern. These findings support the use of the TDT as a pre-clinical biomarker for AOIFD. The usual stimulus presentation method involves the presentation of progressively asynchronous stimuli; when three sequential stimuli are …

R-Hopfian And L-Co-Hopfian Abelian Groups, Brendan Goldsmith, Katao Gong

Articles

The notions of Hopfian and co-Hopfian groups are well known in both non-commutative and Abelian group theory. In this work we begin a systematic investigation of natural generalizations of these concepts and, in the case of Abelian p-groups, give a complete characterization of the generalizations in terms of the original concepts.

Epidemiological, Clinical And Genetic Aspects Of Adult Onset Isolated Focal Dystonia In Ireland, L. Williams, E. Mcgovern, O. Kimmich, A. Molloy, I. Beiser, John Butler, F. Molloy, P. Logan, D.G. Healy, T. Lynch, R. Walsh, L. Cassidy, P. Moriarty, H. Moore, T. Mcswiney, C. Walsh, S. O'Riordan, M. Hutchinson

Articles

Background: Adult onset idiopathic isolated focal dystonia presents with a number of phenotypes. Reported prevalence rates vary considerably; well-characterized cohorts are important to our understanding of this disorder.

Aim: To perform a nationwide epidemiological study of adult onset idiopathic isolated focal dystonia in the Republic of Ireland.

Methods: Patients with adult onset idiopathic isolated focal dystonia were recruited from multiple sources. Diagnosis was based on assessment by a neurologist with an expertise in movement disorders. When consent was obtained, a number of clinical features including family history were assessed.

Results: On the prevalence date there were 592 individuals in Ireland …

Information Hiding With Data Diffusion Using Convolutional Encoding For Super-Encryption, Jonathan Blackledge, Paul Tobin, J. Myeza, C.M. Adolfo

Articles

The unification of data encryption with information hiding methods continues to receive significant attention because of the importance of protecting encrypted information by making it covert. This is because one of the principal limitations in any cryptographic system is that encrypted data flags the potential importance of the data (i.e. the plaintext information that has been encrypted) possibly leading to the launch of an attack which may or may not be successful. Information hiding overcomes this limitation by making the data (which may be the plaintext or the encrypted plaintext) imperceptible, the security of the hidden information being compromised if …

Mind The Gap: An Initial Analysis Of The Transition Of A Second Level Curriculum Reform To Higher Education, Michael Carr, Fiona Faulkner, Cormac Breen, Mark Prendergast

Articles

This article details an initial analysis of the transition of a second level curriculum reform to higher education in Ireland. The reform entitled ‘Project Maths’ involved changes to what second level students learn in mathematics, how they learn it, and how they are assessed. Changes were rolled out nationally on a phased basis in September 2010. Students who were taught and assessed through the new curriculum first entered third level education in September 2012. It is important that third level mathematics lecturers are aware of the changes to the curriculum since certain topics such as vectors and matrices are no …