Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Applied Mathematics (89)
- Partial Differential Equations (58)
- Non-linear Dynamics (57)
- Physics (36)
- Engineering (25)
-
- Fluid Dynamics (19)
- Dynamic Systems (15)
- Education (14)
- Medicine and Health Sciences (14)
- Analysis (13)
- Astrophysics and Astronomy (12)
- Dynamical Systems (10)
- Ordinary Differential Equations and Applied Dynamics (10)
- Statistics and Probability (10)
- Algebra (9)
- Cosmology, Relativity, and Gravity (9)
- Computer Sciences (8)
- Life Sciences (8)
- Quantum Physics (8)
- Social and Behavioral Sciences (8)
- Applied Mechanics (7)
- Applied Statistics (7)
- Elementary Particles and Fields and String Theory (7)
- Mechanical Engineering (7)
- Electrical and Computer Engineering (6)
- Neuroscience and Neurobiology (6)
- Numerical Analysis and Computation (6)
- Oceanography and Atmospheric Sciences and Meteorology (6)
- Keyword
-
- Solitons (17)
- Abelian groups (16)
- Mathematics (10)
- KdV equation (8)
- Endomorphism rings (7)
-
- Integrable systems (7)
- Peakons (7)
- Equatorial undercurrent (6)
- Internal waves (6)
- Lax Pair (6)
- Eddies (5)
- Free energy (5)
- Integrability (5)
- Soliton theory (5)
- Stokes flow (5)
- Thermodynamics (5)
- Transitivity (5)
- Abelian p-groups (4)
- Algebra (4)
- Camassa-Holm equation (4)
- Constant vorticity (4)
- Cubic equation (4)
- Epidemiology (4)
- Fluid dynamics (4)
- Hamiltonian system (4)
- Inverse Scattering (4)
- Lax pair (4)
- Memory effects (4)
- Root bounds (4)
- Shear flow (4)
- Publication Year
- Publication
- Publication Type
Articles 121 - 150 of 356
Full-Text Articles in Mathematics
Information Hiding With Data Diffusion Using Convolutional Encoding For Super-Encryption, Jonathan Blackledge, Paul Tobin, J. Myeza, C.M. Adolfo
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 …
Mode-Sum Prescription For The Vacuum Polarization In Odd Dimensions, Peter Taylor, Cormac Breen
Mode-Sum Prescription For The Vacuum Polarization In Odd Dimensions, Peter Taylor, Cormac Breen
Articles
We present a new mode-sum regularization prescription for computing the vacuum polarization of a scalar field in static spherically-symmetric black hole spacetimes in odd dimensions. This is the first general and systematic approach to regularized vacuum polarization in higher dimensions. Remarkably, the regularization parameters can be computed in closed form in arbitrary dimensions and for arbitrary metric function $f(r)$. In fact, we show that in spite of the increasing severity and number of the divergences to be regularized, the method presented is mostly agnostic to the number of dimensions. Finally, as an explicit example of our method, we show plots …
An Examination Of The Neural Unreliability Thesis Of Autism, John Butler, Sophie Molholm, Gizely Andrade, John J. Foxe
An Examination Of The Neural Unreliability Thesis Of Autism, John Butler, Sophie Molholm, Gizely Andrade, John J. Foxe
Articles
An emerging neuropathological theory of Autism, referred to here as “the neural unreliability thesis,” proposes greater variability in moment-to-moment cortical representation of environmental events, such that the system shows general instability in its impulse response function. Leading evidence for this thesis derives from functional neuroimaging, a methodology ill-suited for detailed assessment of sensory transmission dynamics occurring at the millisecond scale. Electrophysiological assessments of this thesis, however, are sparse and unconvincing. We conducted detailed examination of visual and somatosensory evoked activity using high-density electrical mapping in individuals with autism (N = 20) and precisely matched neurotypical controls (N = 20), recording …
Hawking Radiation Screening And Penrose Process Shielding In The Kerr Black Hole, Eamon Mccaughey
Hawking Radiation Screening And Penrose Process Shielding In The Kerr Black Hole, Eamon Mccaughey
Articles
The radial motion of massive particles in the equatorial plane of aKerr black hole is considered. Screening of the Hawking radiation and shielding of the Penrose process are examined (both inside and outside the ergosphere) and their effect on the evaporation of the black hole is studied. In particular, the locus and width of a classically forbidden region and their dependence on the particle’s angular momentum and energy is analysed. Tunneling of particles between the boundaries of this region is considered and the transmission coefficient determined.
Second Order Approximation For Heat Conduction: Dissipation Principle And Free Energies, Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden, Barbara Lazzari
Second Order Approximation For Heat Conduction: Dissipation Principle And Free Energies, Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden, Barbara Lazzari
Articles
In the context of new models of heat conduction, the second-order approximation of Tzou’s theory, derived by Quintanilla and Racke, has been studied recently by two of the present authors, where it was proved equivalent to a fading memory material. The importance of determining free energy functionals for such materials, and indeed for any material with memory, is emphasized. Because the kernel does not satisfy certain convexity restrictions that allow us to obtain various traditional free energies for materials with fading memory, it is necessary to restrict the study to the minimum and related free energies, which do not require …
Atypical Visual And Somatosensory Adaptation In Schizophrenia-Spectrum Disorders, Gizely Andrade, John Butler, Gregory Peter, Sophie Molholm, John J. Foxe
Atypical Visual And Somatosensory Adaptation In Schizophrenia-Spectrum Disorders, Gizely Andrade, John Butler, Gregory Peter, Sophie Molholm, John J. Foxe
Articles
Neurophysiological investigations in patients with schizophrenia consistently show early sensory processing deficits in the visual system. Importantly, comparable sensory deficits have also been established in healthy first-degree biological relatives of patients with schizophrenia and in first-episode drug-naive patients. The clear implication is that these measures are endophenotypic, related to the underlying genetic liability for schizophrenia. However, there is significant overlap between patient response distributions and those of healthy individuals without affected first-degree relatives. Here we sought to develop more sensitive measures of sensory dysfunction in this population, with an eye to establishing endophenotypic markers with better predictive capabilities. We used …
Bayesian Exponential Random Graph Models With Nodal Random Effects, Stephanie Thiemichen, Nial Friel, Alberto Caimo, Goeran Kauermann
Bayesian Exponential Random Graph Models With Nodal Random Effects, Stephanie Thiemichen, Nial Friel, Alberto Caimo, Goeran Kauermann
Articles
We extend the well-known and widely used Exponential Random Graph Model (ERGM) by including nodal random effects to compensate for heterogeneity in the nodes of a network. The Bayesian framework for ERGMs proposed by Caimo and Friel (2011) yields the basis of our modelling algorithm. A central question in network models is the question of model selection and following the Bayesian paradigm we focus on estimating Bayes factors. To do so we develop an approximate but feasible calculation of the Bayes factor which allows one to pursue model selection. Two data examples and a small simulation study illustrate our mixed …
Free Energies For Singleton Minimal States, John Murrough Golden
Free Energies For Singleton Minimal States, John Murrough Golden
Articles
It is assumed that any free energy funcuon exhibits strict periodic benav10r tor histories that have been periodic for all past times. This is not the case for the work function, which, however, has the usual defining properties of a free energy. Fonns given m fairly recent years for the minimum and related free energies of linear materials with memory have this property. Materials for which the minimal states are all singletons are those for which at least some of the singularities of the Fourier transfonn of the relaxation function are not isolated. For such materials, the maximum free energy …
Application Of Virtual Reality Head Mounted Display For Investigation Of Movement: A Novel Effect Of Orientation Of Attention, Brendan Quinlivan, John Butler, Ines Beiser, Laura Williams, Eavan Mcgovern, Sean O'Riordan, Michael Hutchinson, Richard Reilly
Application Of Virtual Reality Head Mounted Display For Investigation Of Movement: A Novel Effect Of Orientation Of Attention, Brendan Quinlivan, John Butler, Ines Beiser, Laura Williams, Eavan Mcgovern, Sean O'Riordan, Michael Hutchinson, Richard Reilly
Articles
Objective. To date human kinematics research has relied on video processing, motion capture and magnetic search coil data acquisition techniques. However, the use of head mounted display virtual reality systems, as a novel research tool, could facilitate novel studies into human movement and movement disorders. These systems have the unique ability of presenting immersive 3D stimulus while also allowing participants to make ecologically valid movement-based responses. Approach. We employed one such system (Oculus Rift DK2) in this study to present visual stimulus and acquire head-turn data from a cohort of 40 healthy adults. Participants were asked to complete head movements …
Bayesian Exponential Random Graph Modeling Of Whole-Brain Structural Networks Across Lifespan, Michel Sinke, Rick Dijkhuizen, Alberto Caimo, Cornelis Stam, Willem Otte
Bayesian Exponential Random Graph Modeling Of Whole-Brain Structural Networks Across Lifespan, Michel Sinke, Rick Dijkhuizen, Alberto Caimo, Cornelis Stam, Willem Otte
Articles
No abstract provided.
Hamiltonian Formulation For Wave-Current Interactions In Stratified Rotational Flows, Adrian Constantin, Rossen Ivanov, Calin-Iulian Martin
Hamiltonian Formulation For Wave-Current Interactions In Stratified Rotational Flows, Adrian Constantin, Rossen Ivanov, Calin-Iulian Martin
Articles
We show that the Hamiltonian framework permits an elegant formulation of the nonlinear governing equations for the coupling between internal and surface waves in stratified water flows with piecewise constant vorticity.
On The N-Wave Equations With Pt-Symmetry, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov
On The N-Wave Equations With Pt-Symmetry, Vladimir Gerdjikov, Georgi Grahovski, Rossen Ivanov
Articles
We study extensions of N-wave systems with PT-symmetry. The types of (nonlocal) reductions leading to integrable equations invariant with respect to P- (spatial reflection) and T- (time reversal) symmetries is described. The corresponding constraints on the fundamental analytic solutions and the scattering data are derived. Based on examples of 3-wave (related to the algebra sl(3,C)) and 4-wave (related to the algebra so(5,C)) systems, the properties of different types of 1- and 2-soliton solutions are discussed. It is shown that the PT symmetric 3-wave equations may have regular multi-soliton solutions for some specific choices of their parameters.
The Dynamics Of Flat Surface Internal Geophysical Waves With Currents, Alan Compelli, Rossen Ivanov
The Dynamics Of Flat Surface Internal Geophysical Waves With Currents, Alan Compelli, Rossen Ivanov
Articles
A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or thermocline in the ocean. The system is considered as being bounded at the bottom and top by a flatbed and wave-free surface respectively. A current profile with depth-dependent currents in each domain is considered. The Hamiltonian of the system is determined and expressed in terms of canonical wave-related variables. Limiting behavior is examined and compared to that of other known models. The linearised …
Unique Characterization Of Materials With Memory, John Murrough Golden
Unique Characterization Of Materials With Memory, John Murrough Golden
Articles
In general, materials with linear memory constitutive relations are characterized by a relaxation function. This leads to a situation where the free energy for most materials with memory is not unique. There is a convex set of free energy functionals with a minimum and a maximum element. An alternative procedure is proposed which characterizes a material by the kernel of the rate of dissipation functional. Using some recent results, we find that a unique free energy and relaxation function may then be deduced. An example is given for discrete spectrum materials. Also, the new results are used to show that …
The Neural Dynamics Of Somatosensory Processing And Adaptation Across Childhood: A High-Density Electrical Mapping Study, Neha Uppal, John J. Foxe, John Butler, Frantzy Acluche, Sophie Molholm
The Neural Dynamics Of Somatosensory Processing And Adaptation Across Childhood: A High-Density Electrical Mapping Study, Neha Uppal, John J. Foxe, John Butler, Frantzy Acluche, Sophie Molholm
Articles
Young children are often hyperreactive to somatosensory inputs hardly noticed by adults, as exemplified by irritation to seams or labels in clothing. The neurodevelopmental mechanisms underlying changes in sensory reactivity are not well understood. Based on the idea that neurodevelopmental changes in somatosensory processing and/or changes in sensory adaptation might underlie developmental differences in somatosensory reactivity, high-density electroencephalography was used to examine how the nervous system responds and adapts to repeated vibrotactile stimulation over childhood. Participants aged 6–18 yr old were presented with 50-ms vibrotactile stimuli to the right wrist over the median nerve at 5 blocked interstimulus intervals (ranging …
Mathematics Learning Support Across A Multi-Campus Institution: A Prototype Of Virtual Support, Cormac Breen, Ciaran O'Sullivan, Damian Cox
Mathematics Learning Support Across A Multi-Campus Institution: A Prototype Of Virtual Support, Cormac Breen, Ciaran O'Sullivan, Damian Cox
Articles
In this paper, a study on Mathematics Learning Support (MLS) that was undertaken across three institutes intending to form the Technological University for Dublin is outlined. This study consisted of a survey that was circulated to both staff and students in each of the three institutes. The survey had two objectives. Firstly it sought to identify the students’ needs for MLS in each of the three institutes. Secondly, it sought to ascertain the preferred method of provision of MLS, on a scale ranging from exclusively online, to exclusively in person. Following on the results of this survey it was decided …
The Minimum And Other Free Energies For Non-Linear Materials With Memory., John Murrough Golden
The Minimum And Other Free Energies For Non-Linear Materials With Memory., John Murrough Golden
Articles
Expressions are obtained for free energies of materials with a certain type of non-linear constitutive relation. In particular, the minimum and related free energies are considered in some detail. Minimal states are defined for these materials, and it is shown that any free energy yielding a linear constitutive equation that is a functional of the minimal state has a counterpart in the non-linear case which is also a minimal state functional in this more general context. These results are explored for simple examples, including discrete spectrum materials.
Audiovisual Processing Is Abnormal In Parkinson's Disease And Correlates With Freezing Of Gait And Disease Duration, Conor Fearon, John Butler, Louise Newman, Timothy Lynch, Richard B. Reilly
Audiovisual Processing Is Abnormal In Parkinson's Disease And Correlates With Freezing Of Gait And Disease Duration, Conor Fearon, John Butler, Louise Newman, Timothy Lynch, Richard B. Reilly
Articles
Background: Sensory and perceptual disturbances progress with disease duration in Parkinson’s disease (PD) and probably contribute to motor deficits such as bradykinesia and gait disturbances, including freezing of gait (FOG). Simple reaction time tests are ideal to explore sensory processing, as they require little cognitive processing. Multisensory integration is the ability of the brain to integrate sensory information from multiple modalities into a single coherent percept, which is crucial for complex motor tasks such as gait. 9 10 11 12 13 Objectives: The aims of this study were to: 1. Assess differences in unisensory (auditory and visual) and multisensory processing …
Free Energies And Minimal States For Scalar Linear Viscoelasticity, Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
Free Energies And Minimal States For Scalar Linear Viscoelasticity, Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
Articles
The concept of a minimal state was introduced in recent decades, based on earlier work by Noll. The property that a given quantity is a functional of the minimal state is of central interest in the present work. Using a standard representation of a free energy associated with a linear memory constitutive relation, a new condition, involving linear functionals, is derived which, if satisfied, ensures that the free energy is a functional of the minimal state. Using this result and recent work on constructing free energy functionals, it is shown that if the kernel of the rate of dissipation functional …
Age-Related Sexual Dimorphism In Temporal Discrimination And In Adult-Onset Dystonia Suggests Gabaergic Mechanisms, John Butler, Ines M. Beiser, Laura Williams, Eavan Mcgovern, Fiona Molloy, Timothy Lynch, Dan G. Healy, Helena Moore, Richard Walsh, Richard B. Reilly, Sean O'Riordan, Cathal Walsh, Michael Hutchinson
Age-Related Sexual Dimorphism In Temporal Discrimination And In Adult-Onset Dystonia Suggests Gabaergic Mechanisms, John Butler, Ines M. Beiser, Laura Williams, Eavan Mcgovern, Fiona Molloy, Timothy Lynch, Dan G. Healy, Helena Moore, Richard Walsh, Richard B. Reilly, Sean O'Riordan, Cathal Walsh, Michael Hutchinson
Articles
Background: Adult-onset isolated focal dystonia (AOIFD) presenting in early adult life is more frequent in men, whereas in middle age it is female predominant. Temporal discrimination, an endophenotype of adult-onset idiopathic isolated focal dystonia, shows evidence of sexual dimorphism in healthy participants. Objectives: We assessed the distinctive features of age-related sexual dimorphism of (i) sex ratios in dystonia phenotypes and (ii) sexual dimorphism in temporal discrimination in unaffected relatives of cervical dystonia patients. Methods: We performed (i) a meta-regression analysis of the proportion of men in published cohorts of phenotypes of adult-onset dystonia in relation to their mean age of …
Congruent Visual Speech Enhances Entrainment To Continuous Auditory Speech In Noise-Free Conditions, Michael Crosse, John S. Butler, Edmumd Lalor
Congruent Visual Speech Enhances Entrainment To Continuous Auditory Speech In Noise-Free Conditions, Michael Crosse, John S. Butler, Edmumd Lalor
Articles
Congruent audiovisual speech enhances our ability to comprehend a speaker, even in noise-free conditions. When incongruent auditory and visual information is presented concurrently, it can hinder a listener’s perception and even cause him or her to perceive information that was not presented in either modality. Efforts to investigate the neural basis of these effects have often focused on the special case of discrete audiovisual syllables that are spatially and temporally congruent, with less work done on the case of natural, continuous speech. Recent electrophysiological studies have demonstrated that cortical response measures to continuous auditory speech can be easily obtained using …
On Mikhailov's Reduction Group, Tihomir Valchev
On Mikhailov's Reduction Group, Tihomir Valchev
Articles
We present a generalization of the notion of reduction group which allows one to study in a uniform way certain classes of nonlocal $S$-integrable equations like Ablowitz-Musslimani's nonlocal Schr\"odinger equation. Another aspect of the proposed generalization is the possibility to derive in a systematic way solutions to S-integrable equations with prescribed symmetries.
Multivariate Statistical Methodologies Applied In Biomedical Raman Spectroscopy: Assessing The Validity Of Partial Least Squares Regression Using Simulated Model Datasets., Mark Keating
Articles
Raman spectroscopy is fast becoming a valuable analytical tool in a number of biomedical scenarios, most notably disease diagnostics. Importantly, the technique has also shown increasing promise in the assessment of drug interactions on a cellular and subcellular level, particularly when coupled with multivariate statistical analysis. However, an important consideration, both with Raman spectroscopy and the associated statistical methodologies, is the accuracy of these techniques and more specifically the sensitivities which can be achieved and ultimately the limits of detection of the various methods. The purpose of this study is thus the construction of a model simulated data set with …
Exploring The Unknown: Electrophysiological And Behavioural Measures Of Visuospatial Learning, Brendan Quinlivan, John Butler, Abdur R. Ridwan, Ines Beiser, Laura Williams, Eavan Mcgovern, Sean O'Riordan, Michael Hutchinson, Richard B. Reilly
Exploring The Unknown: Electrophysiological And Behavioural Measures Of Visuospatial Learning, Brendan Quinlivan, John Butler, Abdur R. Ridwan, Ines Beiser, Laura Williams, Eavan Mcgovern, Sean O'Riordan, Michael Hutchinson, Richard B. Reilly
Articles
Visuospatial memory describes our ability to temporarily store and manipulate visual and spatial information, and is employed for a wide variety of complex cognitive tasks. Here, a visuospatial learning task requiring fine motor control is employed to investigate visuospatial learning in a group of typically developing adults. Electrophysiological and behavioural data are collected during a target location task under two experimental conditions: Target Learning and Target Cued. Movement times (MTs) are employed as a behavioural metric of performance, while dynamic P3b amplitudes and power in the alpha band (approximately 10 Hz) are explored as electrophysiological metrics during visuospatial learning. Results …
Simultaneous Modelling Of Initial Conditions And Time Heterogeneity In Dynamic Networks: An Application To Foreign Direct Investments, Johan Koskinen, Alberto Caimo, Alessandro Lomi
Simultaneous Modelling Of Initial Conditions And Time Heterogeneity In Dynamic Networks: An Application To Foreign Direct Investments, Johan Koskinen, Alberto Caimo, Alessandro Lomi
Articles
In dynamic networks, the presence of ties are subject both to endogenous network dependencies and spatial dependencies. Current statistical models for change over time are typically defined relative to some initial condition, thus skirting the issue of where the first network came from. Additionally, while these longitudinal network models may explain the dynamics of change in the network over time, they do not explain the change in those dynamics. We propose an extension to the longitudinal exponential random graph model that allows for simultaneous inference of the changes over time and the initial conditions, as well as relaxing assumptions of …
Investigating The Engagement Of Mature Students With Mathematics Learning Support, Cormac Breen, Michael Carr, Mark Prendergast
Investigating The Engagement Of Mature Students With Mathematics Learning Support, Cormac Breen, Michael Carr, Mark Prendergast
Articles
The Maths Learning Support Centre (MLSC) in the Dublin Institute of Technology (DIT) provides free mathematical support to all DIT students. This support is primarily delivered through a drop-in service, where students can receive one-to-one tuition, without an appointment, in any area of mathematics. In the first semester of the 2013/14 academic year, a significant proportion of students that availed of this drop-in service were mature students enrolled in Engineering programmes. This is of particular interest as mature students constitute a relatively small proportion of the total student body, motivating a deeper study of the reasons for the high levels …
Vacuum Polarization On The Brane, Cormac Breen, Matthew Hewitt,, Elizabeth Winstanley, Adrian Ottewill
Vacuum Polarization On The Brane, Cormac Breen, Matthew Hewitt,, Elizabeth Winstanley, Adrian Ottewill
Articles
We compute the renormalized expectation value of the square of a massless, conformally coupled, quantum scalar field on the brane of a higher-dimensional black hole. Working in the AADD braneworld scenario, the extra dimensions are flat and we assume that the compactification radius is large compared with the size of the black hole. The four-dimensional on-brane metric corresponds to a slice through a higher-dimensional Schwarzschild-Tangherlini black hole geometry and depends on the number of bulk space-time dimensions. The quantum scalar field is in a thermal state at the Hawking temperature. An exact, closed-form expression is derived for the renormalized expectation …
Maximizing The Impact Of Digital Supports In Mathematics Learning Support In Higher Education – An Overview Of The 9th Annual Imlsn Workshop, Cormac Breen, Anthony Cronin
Maximizing The Impact Of Digital Supports In Mathematics Learning Support In Higher Education – An Overview Of The 9th Annual Imlsn Workshop, Cormac Breen, Anthony Cronin
Articles
In this article we give a short description of the 9th Annual Workshop of the Irish Mathematics Learning Support Network (IMLSN). The workshop theme was ‘Maximizing the impact of digital supports in Mathematics Learning Support in Higher Education’. We briefly describe the Irish Mathematics Learning Support Network (IMLSN) and outline the factors that motivated this workshop theme. We will also discuss the presentations, some of the issues that were raised during the workshop and we close with some brief conclusions on this very successful event.
Efficient Computational Strategies For Doubly Intractable Problems With Applications To Bayesian Social Networks, Alberto Caimo, Antonietta Mira
Efficient Computational Strategies For Doubly Intractable Problems With Applications To Bayesian Social Networks, Alberto Caimo, Antonietta Mira
Articles
Powerful ideas recently appeared in the literature are adjusted and combined to design improved samplers for doubly intractable target distributions with a focus on Bayesian exponential random graph models. Different forms of adaptive Metropolis–Hastings proposals (vertical, horizontal and rectangular) are tested and merged with the delayed rejection (DR) strategy with the aim of reducing the variance of the resulting Markov chain Monte Carlo estimators for a given computational time. The DR is modified in order to integrate it within the approximate exchange algorithm (AEA) to avoid the computation of intractable normalising constant that appears in exponential random graph models. This …
Derivatives Pricing With Accelerated Trinomial Trees, Conall O'Sullivan, Stephen O'Sullivan
Derivatives Pricing With Accelerated Trinomial Trees, Conall O'Sullivan, Stephen O'Sullivan
Articles
Accelerated Trinomial Trees (ATTs) are a derivatives pricing lattice method that circumvent the restrictive time step condition inherent in standard trinomial trees and explicit finite difference methods (FDMs) in which the time step must scale with the square of the spatial step. ATTs consist of L uniform supersteps each of which contains an inner lattice/trinomial tree with N non-uniform subtime steps. Similarly to implicit FDMs, the size of the superstep in ATTs, a function of N, are constrained primarily by accuracy demands. ATTs can price options up to N times faster than standard trinomial trees (explicit FDMs). ATTs can be …