Browsing Department of Electronics, Computing & Maths by Title
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On the characterization of periodic complex Horadam sequencesHoradam sequences are secondorder linear recurrence sequences which depend on a family of four parameters (two in the defining recursion itself, and two initial values). In this article we find necessary and sufficient conditions for the periodicity of complex Horadam sequences, under general initial values, characterizing sequence behavior for degenerate and nondegenerate characteristic solution types. Inner and outer boundaries for regions containing periodic orbits are also determined.

On the characterization of periodic generalized Horadam sequencesThe Horadam sequence is a direct generalization of the Fibonacci numbers in the complex plane, which depends on a family of four complex parameters: two recurrence coefficients and two initial conditions. In this article a computational matrixbased method is developed to formulate necessary and sufficient conditions for the periodicity of generalized complex Horadam sequences, which are generated by higher order recurrences for arbitrary initial conditions. The asymptotic behaviour of generalized Horadam sequences generated by roots of unity is also examined, along with upper boundaries for the disc containing periodic orbits. Some applications are suggested, along with a number of future research directions.

On the evaluation of sums of exponentiated multiples of generalized Catalan number linear combinations using a hypergeometric approachInfinite series comprising exponentiated multiples of pterm linear combinations of Catalan numbers arise naturally from a related power series expansion for sin(2pα) (in odd powers of sin(α)) which itself has an interesting history. In this article some explicit results generated previously by the author (for p = 1, 2, 3) are discussed in the context of this general problem of series summation, and new evaluations made for the cases p = 4, 5 by way of further examples. A powerful hypergeometric approach is adopted which offers, from the analytical formulation developed, a means to achieve these particular evaluations and in principle many others for even greater values of p.

On the geometry of certain periodic nonhomogeneous Horadam sequences.Horadam sequences are secondorder recurrences depending on a family of four complex parameters: two initial conditions and two recurrence coefficients. The periodicity conditions, as well as the number and geometric structure of selfrepeating Horadam sequences of fixed length have been recently investigated. In this paper various geometric properties of nonhomogeneous Horadam sequences are explored, including periodicity conditions and the structure of certain periodic orbits.

On the jacobsthal, horadam and geometric mean sequencesThis paper, in considering aspects of the geometric mean sequence, offers new results connecting Jacobsthal and Horadam numbers which are established and then proved independently.

On the masked periodicity of Horadam sequences: A generatorbased approach.The Horadam sequence is a general second order linear recurrence sequence, dependent on a family of four (possibly complex) parameterstwo recurrence coe cients and two initial conditions. In this article we examine a phenomenon identi ed previously and referred to as `masked' periodicity, which links the period of a selfrepeating Horadam sequence to its initial conditions. This is presented in the context of cyclicity theory, and then extended to periodic sequences arising from recursion equations of degree three or more.

On the nonexistence of stationary solutions in bioinspired collective decision making via meanfield gameConditions for nonexistence of stationary solutions in collective decision making are investigated via discretestate continuoustime meanfield games. The study builds on a bioinspired model in honeybee swarms. The ultimate goal is to find the best alternative decision in a collective fashion. A crossinhibition signal, as the one observed in honeybee swarms, is used to capture different types of failures, including disrupted communication channels, computational errors or malevolent behaviour. The model is based on the hypotheses that players control their transition rates from one state to another to minimise a cost, under the presence of an adversarial disturbance. The cost to minimise involves a penalty on control and a congestiondependent term. As a main result, we prove that the solution obtained as the asymptotic limit of the nonstationary one can be approximated by a closed orbit trajectory. This argument is used to prove the nonexistence of stationary solution under certain conditions.

On the notion of mathematical genius: rhetoric and reality.The existential hypothesis of mathematical ‘genius’ rests irrefutably with the afﬁrmative. We can’t all be one of course—that sublime solopreneur in creativity—but we may still contribute to research as lesser mortals. This short essay attempts to explore what the notion means to both us and nonmathematicians.

On the number of complex horadam sequences with a fixed periodThe Horadam sequence is a direct generalization of the Fibonacci numbers in the complex plane, depending on a family of four complex parameters: two recurrence coefficients and two initial conditions. Here the Horadam sequences with a given period are enumerated. The result generates a new integer sequence whose representation involves some wellknown functions such as Euler's totient function φ and the number of divisors function ω.

On the phenomenon of masked periodic Horadam sequencesA recently discovered phenomenon, termed masked periodicity and observed in selfrepeating Horadam sequences using matrix based methods in a study by the authors elsewhere, is considered further here. This article continues the approach, identifying both governing parameters and particular behaviour types which fall naturally into three categories convenient for explanation and illustration.

On the ratios and geometric boundaries of complex Horadam sequences.Horadam sequences are secondorder linear recurrences in the complex plane which depend on two initial conditions and two recurrence coefficients which are complex numbers. Recently, numerous papers have been devoted to the periodicity of these sequences, as well as to generalizations and applications. In this paper we investigate aspects related to the sequence of rations of consecutive terms and geometric bounds of Horadam sequences. We also propose some directions for further study.

On the structure of periodic complex Horadam orbitsNumerous geometric patterns identified in nature, art or science can be generated from recurrent sequences, such as for example certain fractals or Fermat’s spiral. Fibonacci numbers in particular have been used to design search techniques, pseudo randomnumber generators and data structures. Complex Horadam sequences are a natural extension of Fibonacci sequence to complex numbers, involving four parameters (two initial values and two in the defining recursion), therefore successive sequence terms can be visualized in the complex plane. Here, a classification of the periodic orbits is proposed, based on divisibility relations between orders of generators (roots of the characteristic polynomial). Regular star polygons, bipartite graphs and multisymmetric patterns can be recovered for selected parameter values. Some applications are also suggested.

On two derivative sequences from scaled geometric mean sequence terms.The so called geometric mean sequence recurrence, with additional scaling variable, produces a sequence for which the general term has a known closed form. Two types of derivative sequence—comprising products of such sequence terms—are examined. In particular, the general term closed forms formulated are shown to depend strongly on a mix of three existing sequences, from which sequence growth rates are deduced and other results given.

Optimising student achievement in Collaborative PartnershipsThis presentation demonstrates an example of how to ensure that student experience is similar in collaborative partnerships to that which is experienced in the UK setting, in the context of transferring innovative Learning, Teaching and Assessment (LTA) strategies to collaborative partners which can present significant challenges caused by different academic cultures and distance.

Optimization of temporally diffuse impulses for decorrelation of multiple discrete loudspeakersTemporally diffuse impulses (TDIs) were originally developed for large arrays of distributed mode loudspeakers to achieve even radiation patterns. This initial investigation evaluates the performance of TDIs in terms of the reduction of low frequency spatial variance across an audience area when used with conventional loudspeakers. A novel variable decay windowing method is presented, allowing users control of TDI performance and perceptibility. System performance is modelled using an anechoic and an image source acoustic model. Results in the anechoic model show a mean spatial variance reduction of 42%, with a range of source material and using the optimal TDI generation methodology. Results in the image source model are more variable, suggesting that coherence of source reflections reduces static TDI effectiveness.

Optimizing computational resource management for the scientific gateways ecosystems based on the service‐oriented paradigmScience Gateways provide portals for experiments execution, regardless of the users' computational background. Nowadays its construction and performance need enhancement in terms of resource provision and task scheduling. We present the Modular Distributed Architecture to support the Protein Structure Prediction (MDAPSP), a Service‐Oriented Architecture for management and construction of Science Gateways, with resource provisioning on a heterogeneous environment. The Decision Maker, central module of MDAPSP, defines the best computational environment according to experiment parameters. The proof of concept for MDAPSP is presented in WorkflowSim, with two novel schedulers. Our results demonstrate good Quality of Service (QoS), capable of correctly distributing the workload, fair response times, providing load balance, and overall system improvement. The study case relies on PSP algorithms and the Galaxy framework, with monitoring experiments to show the bottlenecks and critical aspects.

Optimizing K2 trees: a case for validating the maturity of network of practicesOf late there has been considerable interest in the efficient and effective storage of largescale network graphs, such as those within the domains of social networks, web and virtual communities. The representation of these data graphs is a complex and challenging task and arises as a result of the inherent structural and dynamic properties of a community network, whereby naturally occurring churn can severely affect the ability to optimize the network structure. Since the organization of the network will change over time, we consider how an established method for storing large data graphs (K^2 tree) can be augmented and then utilized as an indicator of the relative maturity of a community network. Within this context, we present an algorithm and a series of experimental results upon both real and simulated networks, illustrating that the compression effectiveness reduces as the community network structure becomes more dynamic. It is for this reason we highlight a notable opportunity to explore the relevance between the K^2 tree optimization factor with the maturity level of the network community concerned.