On the structure of periodic complex Horadam orbits

Journal article


Bagdasar, Ovidiu, Larcombe, Peter J. and Anjum, Ashiq 2016. On the structure of periodic complex Horadam orbits. Carpathian Journal of Mathematics..
AuthorsBagdasar, Ovidiu, Larcombe, Peter J. and Anjum, Ashiq
Abstract

Numerous 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 random-number 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.

Numerous 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 random-number 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.

KeywordsDiscrete mathematics; Applied mathematics
Year2016
JournalCarpathian Journal of Mathematics.
PublisherNorth University of Baia Mare (Romania)
ISSN1584-2851
1843-4401
Web address (URL)http://hdl.handle.net/10545/620860
http://creativecommons.org/licenses/by/4.0/
hdl:10545/620860
Publication dates16 Jan 2016
Publication process dates
Deposited16 Nov 2016, 13:28
ContributorsUniversity of Derby
File
File Access Level
Open
File
File Access Level
Open
File
Permalink -

https://repository.derby.ac.uk/item/937yv/on-the-structure-of-periodic-complex-horadam-orbits

Download files

  • 31
    total views
  • 2
    total downloads
  • 2
    views this month
  • 0
    downloads this month

Export as

Related outputs

On a Hilbert-type integral inequality in the whole plane with the equivalent forms
B. C. Yang, D. Andrica, Bagdasar, O. and M. Th. Rassias 2023. On a Hilbert-type integral inequality in the whole plane with the equivalent forms. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. (57), pp. 1-16. https://doi.org/10.1007/s13398-023-01388-9
Mobility Analysis during the 2020 Pandemic in a Touristic city: the Case of Cagliari
Ferrara, Enrico, Uras, Marco, Atzori, Luigi, Bagdasar, Ovidiu and Liotta, Antonio 2021. Mobility Analysis during the 2020 Pandemic in a Touristic city: the Case of Cagliari. IEEE. https://doi.org/10.1109/ieeeconf49204.2021.9604867
Relations Between Entropy and Accuracy Trends in Complex Artificial Neural Networks
Cavallaro, Lucia, Grassia, Marco, Fiumara, Giacomo, Mangioni, Giuseppe, De Meo, Pasquale, Carchiolo, Vincenza, Bagdasar, Ovidiu and Liotta, Antonio 2022. Relations Between Entropy and Accuracy Trends in Complex Artificial Neural Networks. in: Complex Networks & Their Applications X Springer.
Embedded Data Imputation for Environmental Intelligent Sensing: A Case Study
Erhan, Laura, Di Mauro, Mario, Anjum, Ashiq, Bagdasar, Ovidiu, Song, Wei and Liotta, Antonio 2021. Embedded Data Imputation for Environmental Intelligent Sensing: A Case Study. Sensors. 21 (23), p. 7774. https://doi.org/10.3390/s21237774
An equivalent property of a Hilbert-type integral inequality and its applications
Bagdasar, O., Andrica, D., Yang, B. and Rassias, M.Th. 2022. An equivalent property of a Hilbert-type integral inequality and its applications. Applicable Analysis and Discrete Mathematics. Volume 16 (2), pp. 548-563. https://doi.org/10.2298/AADM220514025Y
On the Dynamic Geometry of Kasner Quadrilaterals with Complex Parameter
Bagdasar, O. and Andrica, D. 2022. On the Dynamic Geometry of Kasner Quadrilaterals with Complex Parameter. Mathematics. 10 (18). https://doi.org/10.3390/math10183334
Reflections On What Mathematics Is and Isn't: Halmos, Keyser, and Others
Larcombe, P. 2022. Reflections On What Mathematics Is and Isn't: Halmos, Keyser, and Others. Palestine Journal of Mathematics. 11 (3), pp. 664-699.
Mathematician? Feeling Old? A Discussion
Larcombe, P. 2022. Mathematician? Feeling Old? A Discussion. Palestine Journal of Mathematics. 11, pp. 19-36.
A unified graph model based on molecular data binning for disease subtyping
Hassan Zada, M., Yuan, B, Khan, W., Anjum, A., Reiff-Marganiec, S. and Saleem, R. 2022. A unified graph model based on molecular data binning for disease subtyping. Journal of Biomedical Informatics. pp. 1-24. https://doi.org/10.1016/j.jbi.2022.104187
Social network analysis: the use of graph distances to compare artificial and criminal networks
Ficara, Annamaria, Curreri, Francesco, Cavallaro, Lucia, De Meo, Pasquale, Fiumara, Giacomo, Bagdasar, Ovidiu and Liotta, Antonio 2021. Social network analysis: the use of graph distances to compare artificial and criminal networks. Journal of Smart Environments and Green Computing. https://doi.org/10.20517/jsegc.2021.08
Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games
Drăgan, Vasile, Ivanov, Ivan Ganchev, Popa, Ioan-Lucian and Bagdasar, Ovidiu 2021. Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games. Mathematics. 9 (21), p. 2713. https://doi.org/10.3390/math9212713
A mixed-integer linear programming formulation for the modular layout of three-dimensional connected systems
O’Neill, Sam, Wrigley, Paul and Bagdasar, Ovidiu 2021. A mixed-integer linear programming formulation for the modular layout of three-dimensional connected systems. Mathematics and Computers in Simulation. https://doi.org/10.1016/j.matcom.2021.09.019
Mixed Time-Delayed Nonlinear Multi-agent Dynamic Systems for Asymptotic Stability and Non-fragile Synchronization Criteria
Arockia, Stephen, Raja, R, Alzabut, J, Zhu, Quanxin, Niezabitowski, M and Bagdasar, Ovidiu 2021. Mixed Time-Delayed Nonlinear Multi-agent Dynamic Systems for Asymptotic Stability and Non-fragile Synchronization Criteria. Neural Processing Letters. https://doi.org/10.1007/s11063-021-10619-2
Criminal networks analysis in missing data scenarios through graph distances
Ficara, Annamaria, Cavallaro, Lucia, Curreri, Francesco, Fiumara, Giacomo, De Meo, Pasquale, Bagdasar, Ovidiu, Song, Wei and Liotta, Antonio 2021. Criminal networks analysis in missing data scenarios through graph distances. PLos ONE. 16 (8), p. e0255067. https://doi.org/10.1371/journal.pone.0255067
Internet of Planets (IoP): A New Era of the Internet
Kang, Byungseok, Malute, Francis, Bagdasar, Ovidiu and Hong, Choongseon 2021. Internet of Planets (IoP): A New Era of the Internet. IT Professional. 23 (3), pp. 76-81. https://doi.org/10.1109/mitp.2021.3068763
On Generalized Lucas Pseudoprimality of Level k
Andrica, Dorin and Bagdasar, Ovidiu 2021. On Generalized Lucas Pseudoprimality of Level k. Mathematics. 9 (8), p. 838. https://doi.org/10.3390/math9080838
On k-partitions of multisets with equal sums
Andrica, Dorin and Bagdasar, Ovidiu 2021. On k-partitions of multisets with equal sums. The Ramanujan Journal. 55 (2), pp. 421-435. https://doi.org/10.1007/s11139-021-00418-7
Graph and Network Theory for the Analysis of Criminal Networks
Cavallaro, Lucia, Bagdasar, Ovidiu, De Meo, Pasquale, Fumara, Giacomo and Liotta, Antonio 2021. Graph and Network Theory for the Analysis of Criminal Networks. in: Springer, Cham.
An LMI Approach-Based Mathematical Model to Control Aedes aegypti Mosquitoes Population via Biological Control
Dianavinnarasi, J., Raja, R., Alzabut, J., Niezabitowski, M., Selvam, G. and Bagdasar, O. 2021. An LMI Approach-Based Mathematical Model to Control Aedes aegypti Mosquitoes Population via Biological Control. Mathematical Problems in Engineering. 2021, pp. 1-18. https://doi.org/10.1155/2021/5565949
Controlling Wolbachia transmission and invasion dynamics among aedes aegypti population via impulsive control strategy
Dianavinnarasi, Joseph, Raja, Ramachandran, Alzabut, Jehad, Niezabitowski, Michał and Bagdasar, Ovidiu 2021. Controlling Wolbachia transmission and invasion dynamics among aedes aegypti population via impulsive control strategy. Symmetry. 13 (3), p. 434. https://doi.org/10.3390/sym13030434
Application of caputo–fabrizio operator to suppress the aedes aegypti mosquitoes via wolbachia: an LMI approach
Dianavinnarasi, J., Raja, R., Alzabut, J., Cao, J., Niezabitowski, M. and Bagdasar, O. 2021. Application of caputo–fabrizio operator to suppress the aedes aegypti mosquitoes via wolbachia: an LMI approach. Mathematics and Computers in Simulation. https://doi.org/10.1016/j.matcom.2021.02.002
Pseudoprimality related to the generalized Lucas sequences
Andrica, Dorin and Bagdasar, Ovidiu 2021. Pseudoprimality related to the generalized Lucas sequences. Mathematics and Computers in Simulation. https://doi.org/10.1016/j.matcom.2021.03.003
Large-scale Data Integration Using Graph Probabilistic Dependencies (GPDs)
Zada, Muhammad Sadiq Hassan, Yuan, Bo, Anjum, Ashiq, Azad, Muhammad Ajmal, Khan, Wajahat Ali and Reiff-Marganiec, Stephan 2020. Large-scale Data Integration Using Graph Probabilistic Dependencies (GPDs). IEEE. https://doi.org/10.1109/bdcat50828.2020.00028
Explaining probabilistic Artificial Intelligence (AI) models by discretizing Deep Neural Networks
Saleem, Rabia, Yuan, Bo, Kurugollu, Fatih and Anjum, Ashiq 2020. Explaining probabilistic Artificial Intelligence (AI) models by discretizing Deep Neural Networks. IEEE. https://doi.org/10.1109/ucc48980.2020.00070
On some new arithmetic properties of the generalized Lucas sequences
Andrica, Dorin and Bagdasar, Ovidiu 2021. On some new arithmetic properties of the generalized Lucas sequences. Mediterranean Journal of Mathematics. 18 (2). https://doi.org/10.1007/s00009-020-01653-w
The number of partitions of a set and Superelliptic Diophantine equations
Andrica, Dorin, Bagdasar, Ovidiu and Ţurcaş, George Cătălin 2020. The number of partitions of a set and Superelliptic Diophantine equations. in: Springer Optimization and Its Applications Springer.
On 'Two Cultures' and Tackling the 'Writing Versus Mathematics' Dichotomy
Larcombe, P. 2021. On 'Two Cultures' and Tackling the 'Writing Versus Mathematics' Dichotomy. Palestine Journal of Mathematics. 10 (2), pp. 480-486.
Write, and Write Well - Speak, and Speak Well: The Gospel According to Halmos and Rota
Larcombe, P. 2021. Write, and Write Well - Speak, and Speak Well: The Gospel According to Halmos and Rota. Palestine Journal of Mathematics. 10 (1), pp. 86-101.
Intelligent price alert system for digital assets - cryptocurrencies
Chhem, Sronglong, Anjum, Ashiq and Arshad, Bilal 2019. Intelligent price alert system for digital assets - cryptocurrencies. ACM Press. https://doi.org/10.1145/3368235.3368874
Smart anomaly detection in sensor systems: A multi-perspective review
Erhan, L., Ndubuaku, M., Di Mauro, M., Song, W., Chen, M., Fortino, G., Bagdasar, Ovidiu and Liotta, A. 2020. Smart anomaly detection in sensor systems: A multi-perspective review. Information Fusion. 67, pp. 64-79. https://doi.org/10.1016/j.inffus.2020.10.001
Congestion prediction for smart sustainable cities using IoT and machine learning approaches
Majumdar, Sharmila, Subhani, Moeez M., Roullier, Benjamin, Anjum, Ashiq and Zhu, Rongbo 2020. Congestion prediction for smart sustainable cities using IoT and machine learning approaches. Sustainable Cities and Society. 64, p. 102500. https://doi.org/10.1016/j.scs.2020.102500
WiFi probes sniffing: an artificial intelligence based approach for MAC addresses de-randomization
Uras, Marco, Cossu, Raimondo, Ferrara, Enrico, Bagdasar, Ovidiu, Liotta, Antonio and Atzori, Luigi 2020. WiFi probes sniffing: an artificial intelligence based approach for MAC addresses de-randomization. IEEE. https://doi.org/10.1109/camad50429.2020.9209257
Recurrent sequences: Key results, applications, and problems
Andrica, Dorin and Bagdasar, Ovidiu 2020. Recurrent sequences: Key results, applications, and problems. Springer International Publishing.
CloudIoT-based Jukebox Platform: a music player for mobile users in Café
Kang, Byungseok, Lee, Joohyun, Bagdasar, Ovidiu and Choo, Hyunseung 2020. CloudIoT-based Jukebox Platform: a music player for mobile users in Café. Journal of Internet Technology. https://doi.org/10.3966/160792642020092105012
DETN: delay-efficient tolerant network for internet of planet
Kang, Byungseok, Malute, Francis, Bagdasar, Ovidiu and Hyunseung, Choo 2020. DETN: delay-efficient tolerant network for internet of planet. IEEE Sensors Journal. https://doi.org/10.1109/JSEN.2020.3020585
Artificial neural networks training acceleration through network science strategies
Cavallaro, Lucia, Bagdasar, Ovidiu, De Meo, Pasquale, Fiumara, Giacomo and Liotta, Antonio 2020. Artificial neural networks training acceleration through network science strategies. Soft Computing. https://doi.org/10.1007/s00500-020-05302-y
Stability of discrete-time fractional-order time-delayed neural networks in complex field
Pratap, Anbalagan, Raja, Ramachandran, Cao, Jinde, Huang, Chuangxia, Niezabitowski, Michal and Bagdasar, Ovidiu 2020. Stability of discrete-time fractional-order time-delayed neural networks in complex field. Mathematical Methods in the Applied Sciences. https://doi.org/10.1002/mma.6745
Disrupting resilient criminal networks through data analysis: The case of Sicilian Mafia
Cavallaro, Lucia, Ficara, Annamaria, De Meo, Pasquale, Fiumara, Giacomo, Catanese, Salvatore, Bagdasar, Ovidiu, Song, Wei and Liotta, Antonio 2020. Disrupting resilient criminal networks through data analysis: The case of Sicilian Mafia. PLos ONE. 15 (8), p. e0236476. https://doi.org/10.1371/journal.pone.0236476
Multi-weighted complex structure on fractional order coupled neural networks with linear coupling delay: a robust synchronization problem
Pratap, A., Raja, R., Agarwal, Ravi. P., Cao, J. and Bagdasar, Ovidiu 2020. Multi-weighted complex structure on fractional order coupled neural networks with linear coupling delay: a robust synchronization problem. Neural Processing Letters. https://doi.org/10.1007/s11063-019-10188-5
A deep reinforcement learning based homeostatic system for unmanned position control
Manning, Warren, Anjum, Ashiq, Bower, Craig and Dassanayake, Priyanthi 2019. A deep reinforcement learning based homeostatic system for unmanned position control. Association for Computing Machinery.
Traffic assignment: on the interplay between optimization and equilibrium problems
Bagdasar, Ovidiu, Popovici, Nicolae and Berry, Stuart 2020. Traffic assignment: on the interplay between optimization and equilibrium problems. Optimization. https://doi.org/10.1080/02331934.2019.1711082
A novel delay-dependent asymptotic stability conditions for differential and Riemann-Liouville fractional differential neutral systems with constant delays and nonlinear perturbation
Chartbupapan, Watcharin, Bagdasar, Ovidiu and Mukdasai, Kanit 2020. A novel delay-dependent asymptotic stability conditions for differential and Riemann-Liouville fractional differential neutral systems with constant delays and nonlinear perturbation. Mathematics. 8 (1), p. 82. https://doi.org/10.3390/math8010082
Intelligent data fusion algorithm based on hybrid delay-aware adaptive clustering in wireless sensor networks
Liu, Xiaozhu, Zhu, Rongbo, Anjum, Ashiq, Wang, Jun, Zhang, Hao and Ma, Maode 2019. Intelligent data fusion algorithm based on hybrid delay-aware adaptive clustering in wireless sensor networks. Future Generation Computer Systems. 104, pp. 1-14. https://doi.org/10.1016/j.future.2019.10.001
Fog computing-based approximate spatial keyword queries with numeric attributes in IoV
Li, Yanhong, Zhu, Rongbo, Mao, Shiwen and Anjum, Ashiq 2020. Fog computing-based approximate spatial keyword queries with numeric attributes in IoV. IEEE Internet of Things. https://doi.org/10.1109/jiot.2020.2965730
A cascade learning approach for automated detection of locomotive speed sensor using imbalanced data in ITS
Li, Bo, Zhou, Sisi, Cheng, Lifang, Zhu, Rongbo, Hu, Tao, Anjum, Ashiq, He, Zheng and Zou, Yongkai 2019. A cascade learning approach for automated detection of locomotive speed sensor using imbalanced data in ITS. IEEE Access. 7, pp. 90851-90862. https://doi.org/10.1109/access.2019.2928224
Exploring network embedding for efficient message routing in opportunistic mobile social networks
Yuan, Bo, Anjum, Ashiq, Panneerselvam, J. and Liu, Lu 2020. Exploring network embedding for efficient message routing in opportunistic mobile social networks. IEEE. https://doi.org/10.1109/ICDMW.2019.00077
Efficient resampling for fraud detection during anonymised credit card transactions with unbalanced datasets
Mrozek, Petr, Panneerselvam, J. and Bagdasar, Ovidiu 2020. Efficient resampling for fraud detection during anonymised credit card transactions with unbalanced datasets. IEEE. https://doi.org/10.1109/ucc48980.2020.00067
Graph data modelling for genomic variants
Anjum, Ashiq and Aizad, Sanna 2019. Graph data modelling for genomic variants.
Remarks on a family of complex polynomials
Andrica, Dorin and Bagdasar, Ovidiu 2019. Remarks on a family of complex polynomials. Applicable Analysis and Discrete Mathematics. https://doi.org/10.2298/aadm180827022a
Multiclass disease predictions based on integrated clinical and genomics datasets
Anjum, Ashiq and Subhani, Moeez 2019. Multiclass disease predictions based on integrated clinical and genomics datasets. IARIA.
GORTS: genetic algorithm based on one-by-one revision of two sides for dynamic travelling salesman problems
Xu, Xiaolong, Yuan, Hao, Matthew, Peter, Ray, Jeffrey, Bagdasar, Ovidiu and Trovati, Marcello 2019. GORTS: genetic algorithm based on one-by-one revision of two sides for dynamic travelling salesman problems. Soft Computing. https://doi.org/10.1007/s00500-019-04335-2
Improved Kalman filter based differentially private streaming data release in cognitive computing.
Wang, Jun, Luo, Jing, Liu, Xiaozhu, Li, Yongkai, Liu, Shubo, Zhu, Rongbo and Anjum, Ashiq 2019. Improved Kalman filter based differentially private streaming data release in cognitive computing. Future Generation Computer Systems. https://doi.org/10.1016/j.future.2019.03.050
Intelligent augmented keyword search on spatial entities in real-life internet of vehicles
Li, Yanhong, Wang, Meng, Du, Xiaokun, Feng, Yuhe, Luo, Changyin, Tian, Shasha, Anjum, Ashiq and Zhu, Rongbo 2018. Intelligent augmented keyword search on spatial entities in real-life internet of vehicles. Future Generation Computer Systems. 94, pp. 697-711. https://doi.org/10.1016/j.future.2018.12.051
Language model-based automatic prefix abbreviation expansion method for biomedical big data analysis
Anjum, Ashiq 2019. Language model-based automatic prefix abbreviation expansion method for biomedical big data analysis. Future Generation Computer Systems. https://doi.org/10.1016/j.future.2019.01.016
Machine-learning-based side-channel evaluation of elliptic-curve cryptographic FPGA processor.
Mukhtar, Naila, Mehrabi, Mohamad, Kong, Yinan and Anjum, Ashiq 2018. Machine-learning-based side-channel evaluation of elliptic-curve cryptographic FPGA processor. Applied Sciences. 9 (1), p. 64. https://doi.org/10.3390/app9010064
Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations
Pratap, A., Raja, R., Cao, J., Lim, C.P. and Bagdasar, Ovidiu 2019. Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations. Applied Mathematics and Computation. 359, pp. 241-260. https://doi.org/10.1016/j.amc.2019.04.062
A new formula for the coefficients of Gaussian polynomials
Bagdasar, Ovidiu and Andrica, Dorin 2019. A new formula for the coefficients of Gaussian polynomials. Analele Stiintifice ale Universitatii Ovidius Constanta.
Global projective lag synchronization of fractional order memristor based BAM neural networks with mixed time varying delays
Pratap, A., Raja, R., Sowmiya, C., Bagdasar, Ovidiu, Jinde, Cao and Rajchakit, G. 2019. Global projective lag synchronization of fractional order memristor based BAM neural networks with mixed time varying delays. Asian Journal of Control.
Mathematicians can also write, right?
Larcombe, Peter J 2019. Mathematicians can also write, right? Mathematics Today.
Mittag-Leffler state estimator design and synchronization analysis for fractional order BAM neural networks with time delays
Pratap, A., Dianavinnarasi, J., Raja, R., Rajchakit, G., Cao, J. and Bagdasar, Ovidiu 2019. Mittag-Leffler state estimator design and synchronization analysis for fractional order BAM neural networks with time delays. International Journal of Adaptive Control and Signal Processing. https://doi.org/10.1002/acs.2983
On some results concerning the polygonal polynomials.
Andrica, Dorin and Bagdasar, Ovidiu 2019. On some results concerning the polygonal polynomials. Carpathian Journal of Mathematics..
A generating function approach to the automated evaluation of sums of exponentiated multiples of generalized Catalan number linear combinations.
Larcombe, Peter J. and O'Neill, Sam T. 2018. A generating function approach to the automated evaluation of sums of exponentiated multiples of generalized Catalan number linear combinations. Fibonacci Quarterly.
Assessing Domain Specificity in the Measurement of Mathematics Calculation Anxiety
Hunt, Thomas E., Bagdasar, Ovidiu, Sheffield, David and Schofield, M. 2019. Assessing Domain Specificity in the Measurement of Mathematics Calculation Anxiety. Education Research International. 2019, pp. 1-7. https://doi.org/10.1155/2019/7412193
New proofs of linear recurrence identities for terms of the Horadam sequence.
Larcombe, Peter J. and Fennessey, Eric J. 2019. New proofs of linear recurrence identities for terms of the Horadam sequence. Palestine Journal of Mathematics.
On the notion of mathematical genius: rhetoric and reality.
Larcombe, Peter J. 2019. On the notion of mathematical genius: rhetoric and reality. Palestine Journal of Mathematics.
On generalised multi-index non-linear recursion identities for terms of the Horadam sequence.
Larcombe, Peter J. and Fennessey, Eric J. 2019. On generalised multi-index non-linear recursion identities for terms of the Horadam sequence. Palestine Journal of Mathematics.
A note on two rational invariants for a particular 2 x 2 matrix.
Larcombe, Peter J. and Fennessey, Eric J. 2018. A note on two rational invariants for a particular 2 x 2 matrix. Palestine Journal of Mathematics.
A new non-linear recurrence identity class for Horadam sequence terms.
Larcombe, Peter J. and Fennessey, Eric J. 2018. A new non-linear recurrence identity class for Horadam sequence terms. Palestine Journal of Mathematics.
On two derivative sequences from scaled geometric mean sequence terms.
Larcombe, Peter J., Rabago, Julius, F. T. and Fennessey, Eric J. 2018. On two derivative sequences from scaled geometric mean sequence terms. Palestine Journal of Mathematics.
A new tri-diagonal matrix invariance property.
Larcombe, Peter J. and Fennessey, Eric J. 2017. A new tri-diagonal matrix invariance property. Palestine Journal of Mathematics.
A few thoughts on the aesthetics of mathematics in research and teaching.
Larcombe, Peter J. 2018. A few thoughts on the aesthetics of mathematics in research and teaching. Palestine Journal of Mathematics.
On an arithmetic triangle of numbers arising from inverses of analytic functions.
Bagdasaryan, Armen G. and Bagdasar, Ovidiu 2018. On an arithmetic triangle of numbers arising from inverses of analytic functions. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2018.11.003
On some new arithmetic functions involving prime divisors and perfect powers.
Bagdasar, Ovidiu and Tatt, Ralph-Joseph 2018. On some new arithmetic functions involving prime divisors and perfect powers. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2018.11.002
Some remarks on 3-partitions of multisets.
Andrica, Dorin and Bagdasar, Ovidiu 2018. Some remarks on 3-partitions of multisets. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2018.11.001
Providing traceability for neuroimaging analyses.
McClatchey, Richard, Branson, Andrew, Anjum, Ashiq, Bloodsworth, Peter, Habib, Irfan, Munir, Kamran, Shamdasani, Jetendr and Soomro, Kamran 2013. Providing traceability for neuroimaging analyses. International Journal of Medical Informatics.
CMS workflow execution using intelligent job scheduling and data access strategies.
Hasham, Khawar, Delgado Peris, Antonio, Anjum, Ashiq, Evans, Dave, Gowdy, Stephen, Hernandez, José M., Huedo, Eduardo, Hufnagel, Dirk, van Lingen, Frank, McClatchey, Richard and Metson, Simon 2011. CMS workflow execution using intelligent job scheduling and data access strategies. IEEE Transactions on Nuclear Science. https://doi.org/10.1109/TNS.2011.2146276
Context-aware service utilisation in the clouds and energy conservation.
Kiani, Saad Liaquat, Anjum, Ashiq, Antonopoulos, Nick and Knappmeyer, Michael 2012. Context-aware service utilisation in the clouds and energy conservation. Journal of Ambient Intelligence and Humanized Computing. https://doi.org/10.1007/s12652-012-0131-1
Traffic assignment: methods and simulations for an alternative formulation of the fixed demand problem
Bagdasar, Ovidiu, Berry, Stuart, O’Neill, Sam, Popovici, Nicolae and Raja, Ramachandran 2018. Traffic assignment: methods and simulations for an alternative formulation of the fixed demand problem. Mathematics and Computers in Simulation. https://doi.org/10.1016/j.matcom.2018.08.004
On some results concerning generalized arithmetic triangles.
Bagdasaryan, Armen G. and Bagdasar, Ovidiu 2018. On some results concerning generalized arithmetic triangles. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2018.05.012
On the ratios and geometric boundaries of complex Horadam sequences.
Bagdasar, Ovidiu, Hedderwick, Eve and Popa, Ioan-Lucian 2018. On the ratios and geometric boundaries of complex Horadam sequences. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2018.05.011
ENDM Proceedings for TREPAM'17: Preface
Bagdasar, Ovidiu and Popa, Ioan-Lucian 2018. ENDM Proceedings for TREPAM'17: Preface. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2018.05.001
Exploiting in-memory systems for gnomic data analysis.
Shah, Zeeshan Ali, El-Kalioby, Mohamed, Faquih, Tariq, Shokrof, Moustafa, Subhani, Shazia, Alnakhli, Yasser, Aljafar, Hussain, Anjum, Ashiq and Abouelhoda, Mohamed 2018. Exploiting in-memory systems for gnomic data analysis. Springer. https://doi.org/10.1007/978-3-319-78723-7_35
Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses.
Pratap, A., Raja, R., Sowmiya, C., Bagdasar, Ovidiu, Cao, Jinde and Rajchakit, Grienggrai 2018. Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses. Neural Networks. https://doi.org/10.1016/j.neunet.2018.03.012
Unifying local-global type properties in vector optimization.
Bagdasar, Ovidiu and Popovici, Nicolae 2018. Unifying local-global type properties in vector optimization. Journal of Global Optimization. https://doi.org/10.1007/s10898-018-0656-8
Local maximizers of generalized convex vector-valued functions.
Bagdasar, Ovidiu and Popovici, Nicolae 2017. Local maximizers of generalized convex vector-valued functions. Journal of Nonlinear and Convex Analysis.
Case studies: Using heuristics.
Lowndes, Val, Bagdasar, Ovidiu and Berry, Stuart 2017. Case studies: Using heuristics. in: Springer.
Further use of heuristic methods.
Lowndes, Val, Berry, Stuart, Parkes, Chris, Bagdasar, Ovidiu and Popovici, Nicolae 2017. Further use of heuristic methods. in: Springer.
Characterizations of generalized exponential trichotomies for linear discrete-time systems.
Popa, Ioan-Lucian, Ceauşu, Traian and Bagdasar, Ovidiu 2016. Characterizations of generalized exponential trichotomies for linear discrete-time systems. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2016.11.010
On the geometry of certain periodic non-homogeneous Horadam sequences.
Bagdasar, Ovidiu and Popa, Ioan-Lucian 2016. On the geometry of certain periodic non-homogeneous Horadam sequences. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2016.11.002
A closed form formulation for the general term of a scaled triple power product recurrence sequence.
Larcombe, Peter J. and Fennessey, Eric J. 2017. A closed form formulation for the general term of a scaled triple power product recurrence sequence. Fibonacci Quarterly.
New results and conjectures on 2-partitions of multisets.
Bagdasar, Ovidiu and Andrica, Dorin 2017. New results and conjectures on 2-partitions of multisets. Proceedings of the 7th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO). https://doi.org/10.1109/ICMSAO.2017.7934928
Opinions, opinions, opinions ...
Larcombe, Peter J. 2017. Opinions, opinions, opinions ... Mathematics Today.
Mathematics as a mirror of painting.
Larcombe, Peter J. 2017. Mathematics as a mirror of painting. Mathematics Today.
Horadam sequences: A survey update and extension.
Larcombe, Peter J. 2017. Horadam sequences: A survey update and extension. Bulletin of the Institute of Combinatorics and its Applications (ICA).
On sequence-based closed form entries for an exponentiated general $2 \times 2$ matrix: A re-formulation and an application.
Larcombe, Peter J. and Fennessey, Eric J. 2017. On sequence-based closed form entries for an exponentiated general $2 \times 2$ matrix: A re-formulation and an application. Bulletin of the Institute of Combinatorics and its Applications (ICA).
On the masked periodicity of Horadam sequences: A generator-based approach.
Bagdasar, Ovidiu and Larcombe, Peter J. 2017. On the masked periodicity of Horadam sequences: A generator-based approach. Fibonacci Quarterly.
Cloud-based video analytics using convolutional neural networks.
Yaseen, M., Anjum, Ashiq, Farid, Mohsen and Antonopoulos, Nick 2018. Cloud-based video analytics using convolutional neural networks. Software Practice and Experience. https://doi.org/10.1002/spe.2636
Deep learning hyper-parameter optimization for video analytics in clouds.
Yaseen, M., Anjum, Ashiq, Rana, Omer and Antonopoulos, Nikolaos 2018. Deep learning hyper-parameter optimization for video analytics in clouds. IEEE Transactions on Systems, Man, and Cybernetics. https://doi.org/10.1109/TSMC.2018.2840341
Edge enhanced deep learning system for large-scale video stream analytics.
Ali, Muhammad, Anjum, Ashiq, Yaseen, M. Usman, Zamani, A. Reza, Balouek-Thomert, Daniel, Rana, Omer and Parashar, Manish 2018. Edge enhanced deep learning system for large-scale video stream analytics. IEEE. https://doi.org/10.1109/CFEC.2018.8358733
Qualitative case study methodology: Automatic design and correction of ceramic colors.
Bagdasar, Ovidiu, Birlutiu, Adriana, Chen, Minsi and Popa, Ioan-Lucian 2017. Qualitative case study methodology: Automatic design and correction of ceramic colors. IEEE. https://doi.org/10.1109/ICSTCC.2017.8107118
Representing variant calling format as directed acyclic graphs to enable the use of cloud computing for efficient and cost effective genome analysis
Aizad, Sanna, Anjum, Ashiq and Sakellariou, Rizos 2017. Representing variant calling format as directed acyclic graphs to enable the use of cloud computing for efficient and cost effective genome analysis. IEEE. https://doi.org/10.1109/CCGRID.2017.116
Blockchain standards for compliance and trust
Anjum, Ashiq, Sporny, Manu and Sill, Alan 2017. Blockchain standards for compliance and trust. IEEE Cloud Computing. https://doi.org/10.1109/MCC.2017.3791019
Big data analytics in healthcare: A cloud based framework for generating insights
Anjum, Ashiq, Aizad, Sanna, Arshad, Bilal, Subhani, Moeez, Davies-Tagg, Dominic, Abdullah, Tariq and Antonopoulos, Nikolaos 2017. Big data analytics in healthcare: A cloud based framework for generating insights. in: Springer.
Clinical and genomics data integration using meta-dimensional approach
Subhani, Moeez, Anjum, Ashiq, Koop, Andreas and Antonopoulos, Nikolaos 2016. Clinical and genomics data integration using meta-dimensional approach. Association for Computing Machinery. https://doi.org/10.1145/2996890.3007896
Deadline constrained video analysis via in-transit computational environments
Zamani, Ali Reza, Zou, Mengsong, Diaz-Montes, Javier, Petri, Ioan, Rana, Omer, Anjum, Ashiq and Parashar, Manish 2017. Deadline constrained video analysis via in-transit computational environments. IEEE Transactions on Services Computing. https://doi.org/10.1109/TSC.2017.2653116
Data Intensive and Network Aware (DIANA) grid scheduling
McClatchey, Richard, Anjum, Ashiq, Stockinger, Heinz, Ali, Arshad, Willers, Ian and Thomas, Michael 2007. Data Intensive and Network Aware (DIANA) grid scheduling. Journal of Grid Computing. https://doi.org/10.1007/s10723-006-9059-z
Intelligent grid enabled services for neuroimaging analysis
McClatchey, Richard, Habib, Irfan, Anjum, Ashiq, Munir, Kamran, Branson, Andrew, Bloodsworth, Peter and Kiani, Saad Liaquat 2013. Intelligent grid enabled services for neuroimaging analysis. Neurocomputing. https://doi.org/10.1016/j.neucom.2013.01.042
Cloud-based scalable object detection and classification in video streams
Yaseen, M., Anjum, Ashiq, Rana, Omer and Hill, Richard 2017. Cloud-based scalable object detection and classification in video streams. Future Generation Computer Systems. https://doi.org/10.1016/j.future.2017.02.003
Modeling and analysis of a deep learning pipeline for cloud based video analytics.
Yaseen, M., Anjum, Ashiq and Antonopoulos, Nikolaos 2017. Modeling and analysis of a deep learning pipeline for cloud based video analytics. https://doi.org/10.1145/3148055.3148081
Conditions governing cross-family member equality in a particular class of polynomial families
Larcombe, Peter J. and Fennessey, Eric J. 2014. Conditions governing cross-family member equality in a particular class of polynomial families. Fibonacci Quarterly.
On certain series expansions of the sine function: Catalan numbers and convergence
Larcombe, Peter J., O'Neill, Sam T. and Fennessey, Eric J. 2014. On certain series expansions of the sine function: Catalan numbers and convergence. Fibonacci Quarterly.
Traffic monitoring using video analytics in clouds
Abdullah, Tariq, Anjum, Ashiq, Tariq, M. Fahim, Baltaci, Yusuf and Antonopoulos, Nikolaos 2014. Traffic monitoring using video analytics in clouds. IEEE. https://doi.org/10.1109/UCC.2014.12
On the number of complex horadam sequences with a fixed period
Bagdasar, Ovidiu and Larcombe, Peter J. 2013. On the number of complex horadam sequences with a fixed period. Fibonacci Quarterly.
On the characterization of periodic complex Horadam sequences
Bagdasar, Ovidiu and Larcombe, Peter J. 2013. On the characterization of periodic complex Horadam sequences. Fibonacci Quarterly.
Big-Data analytics and cloud computing: Theory, algorithms and applications
Hill, Richard, Trovati, Marcello, Liu, Lu, Anjum, Ashiq and Zhu, Shao Ying 2015. Big-Data analytics and cloud computing: Theory, algorithms and applications. Springer.
On a result of Bunder involving Horadam sequences: A proof and generalization
Larcombe, Peter J. and Bagdasar, Ovidiu 2013. On a result of Bunder involving Horadam sequences: A proof and generalization. Fibonacci Quarterly.
On a result of Bunder involving horadam sequences: A new proof
Larcombe, Peter J., Bagdasar, Ovidiu and Fennessey, Eric J. 2014. On a result of Bunder involving horadam sequences: A new proof. Fibonacci Quarterly.
Influence discovery in semantic networks: An initial approach
Trovati, Marcello and Bagdasar, Ovidiu 2014. Influence discovery in semantic networks: An initial approach. IEEE. https://doi.org/10.1109/UKSim.2014.48
Complementary iInequalities involving the Stolarsky Mean
Bagdasar, Ovidiu 2010. Complementary iInequalities involving the Stolarsky Mean. Journal of Inequalities and Applications. https://doi.org/10.1155/2010/492570
Concise computer mathematics: tutorials on theory and problems
Bagdasar, Ovidiu 2013. Concise computer mathematics: tutorials on theory and problems. Springer.
On the characterization of periodic generalized Horadam sequences
Bagdasar, Ovidiu and Larcombe, Peter J. 2014. On the characterization of periodic generalized Horadam sequences. Journal of Difference Equations and Applications. https://doi.org/10.1080/10236198.2014.891022
Local maximum points of explicitly quasiconvex functions
Bagdasar, Ovidiu and Popovici, Nicolae 2014. Local maximum points of explicitly quasiconvex functions. Optimization Letters. https://doi.org/10.1007/s11590-014-0781-3
A Horadam-based pseudo-random number generator
Bagdasar, Ovidiu and Chen, Minsi 2014. A Horadam-based pseudo-random number generator. IEEE. https://doi.org/10.1109/UKSim.2014.55
Alwyn Francis Horadam, 1923-2016: A personal tribute to the man and his sequence
Larcombe, Peter J. 2016. Alwyn Francis Horadam, 1923-2016: A personal tribute to the man and his sequence. Bulletin of the Institute of Combinatorics and its Applications (ICA).
A scaled power product recurrence examined using matrix methods
Larcombe, Peter J. and Fennessey, Eric J. 2016. A scaled power product recurrence examined using matrix methods. Bulletin of the Institute of Combinatorics and its Applications (ICA).
On the evaluation of sums of exponentiated multiples of generalized Catalan number linear combinations using a hypergeometric approach
Larcombe, Peter J. 2016. On the evaluation of sums of exponentiated multiples of generalized Catalan number linear combinations using a hypergeometric approach. Fibonacci Quarterly.
On a scaled balanced-power product recurrence
Larcombe, Peter J. and Fennessey, Eric J. 2016. On a scaled balanced-power product recurrence. Fibonacci Quarterly.
A short monograph on exposition and the emotive nature of research and publishing
Larcombe, Peter J. 2016. A short monograph on exposition and the emotive nature of research and publishing. Mathematics Today.
A polynomial based construction of periodic Horadam sequences
Larcombe, Peter J. and Fennessey, Eric J. 2016. A polynomial based construction of periodic Horadam sequences. Utilitas Mathematica.
A new formulation of a result by McLaughlin for an arbitrary dimension 2 matrix power
Larcombe, Peter J. 2016. A new formulation of a result by McLaughlin for an arbitrary dimension 2 matrix power. Bulletin of the Institute of Combinatorics and its Applications (ICA).
On the jacobsthal, horadam and geometric mean sequences
Larcombe, Peter J. and Rabago, Julius, F. T. 2016. On the jacobsthal, horadam and geometric mean sequences. Bulletin of the Institute of Combinatorics and its Applications (ICA).
A note on the invariance of the general $2 \times 2$ matrix anti-diagonals ratio with increasing matrix power: Four proofs
Larcombe, Peter J. 2015. A note on the invariance of the general $2 \times 2$ matrix anti-diagonals ratio with increasing matrix power: Four proofs. Fibonacci Quarterly.
Closed form evaluations of some series comprising sums of exponentiated multiples of two-term and three-term Catalan number linear combinations
Larcombe, Peter J. 2015. Closed form evaluations of some series comprising sums of exponentiated multiples of two-term and three-term Catalan number linear combinations. Fibonacci Quarterly.
Closed form evaluations of some series involving Catalan numbers
Larcombe, Peter J. 2014. Closed form evaluations of some series involving Catalan numbers. Bulletin of the Institute of Combinatorics and its Applications (ICA).
A condition for anti-diagonals product invariance across powers of $2 \times 2$ matrix sets characterizing a particular class of polynomial families
Larcombe, Peter J. and Fennessey, Eric J. 2015. A condition for anti-diagonals product invariance across powers of $2 \times 2$ matrix sets characterizing a particular class of polynomial families. Fibonacci Quarterly.
On the phenomenon of masked periodic Horadam sequences
Larcombe, Peter J. and Fennessey, Eric J. 2015. On the phenomenon of masked periodic Horadam sequences. Utilitas Mathematica.
On horadam sequence periodicity: A new approach
Larcombe, Peter J. and Fennessey, Eric J. 2015. On horadam sequence periodicity: A new approach. Bulletin of the Institute of Combinatorics and its Applications (ICA).
A non-linear identity for a particular class of polynomial families
Larcombe, Peter J. and Fennessey, Eric J. 2014. A non-linear identity for a particular class of polynomial families. Fibonacci Quarterly.
On cyclicity and density of some Catalan polynomial sequences
Larcombe, Peter J. and Fennessey, Eric J. 2014. On cyclicity and density of some Catalan polynomial sequences. Bulletin of the Institute of Combinatorics and its Applications (ICA).
Some factorisation and divisibility properties of Catalan polynomials
Jarvis, Frazer A., Larcombe, Peter J. and Fennessey, Eric J. 2014. Some factorisation and divisibility properties of Catalan polynomials. Bulletin of the Institute of Combinatorics and its Applications (ICA).
Generalised Catalan polynomials and their properties
Larcombe, Peter J., Jarvis, Frazer A. and Fennessey, Eric J. 2014. Generalised Catalan polynomials and their properties. Bulletin of the Institute of Combinatorics and its Applications (ICA).
The Asymptotic Form of the Sum $\sum_{i=0}^{n} i^{p} { n+i \choose i }$: Two Proofs
Larcombe, Peter J., Kirschenhofer, Peter and Fennessey, Eric J. 2014. The Asymptotic Form of the Sum $\sum_{i=0}^{n} i^{p} { n+i \choose i }$: Two Proofs. Utilitas Mathematica.
A cloud resource management model for the creation and orchestration of social communities
Ikram, Ahsan, Anjum, Ashiq and Bessis, Nik 2015. A cloud resource management model for the creation and orchestration of social communities. Simulation Modelling Practice and Theory. https://doi.org/10.1016/j.simpat.2014.05.003
Federated broker system for pervasive context provisioning
Kiani, Saad Liaquat, Anjum, Ashiq, Knappmeyer, Michael, Bessis, Nik and Antonopoulos, Nikolaos 2013. Federated broker system for pervasive context provisioning. Journal of Systems and Software. https://doi.org/10.1016/j.jss.2012.11.050
Adapting scientific workflow structures using multi-objective optimization strategies
Habib, Irfan, Anjum, Ashiq, Mcclatchey, Richard and Rana, Omer 2013. Adapting scientific workflow structures using multi-objective optimization strategies. ACM Transactions on Autonomous and Adaptive Systems. https://doi.org/10.1145/2451248.2451252
Video stream analysis in clouds: An object detection and classification framework for high performance video analytics
Anjum, Ashiq, Abdullah, Tariq, Tariq, M. Fahim, Baltaci, Yusuf and Antonopoulos, Nikolaos 2016. Video stream analysis in clouds: An object detection and classification framework for high performance video analytics. IEEE Transactions on Cloud Computing. https://doi.org/10.1109/TCC.2016.2517653
Towards cloud based big data analytics for smart future cities
Khan, Zaheer, Anjum, Ashiq, Tahir, Muhammad Atif and Soomro, Kamran Ahmed 2015. Towards cloud based big data analytics for smart future cities. Journal of Cloud Computing. https://doi.org/10.1186/s13677-015-0026-8
Spatial frequency based video stream analysis for object classification and recognition in clouds
Yaseen, M., Anjum, Ashiq and Antonopoulos, Nikolaos 2016. Spatial frequency based video stream analysis for object classification and recognition in clouds. IEEE.
High performance video processing in cloud data centres
Yaseen, M., Zafar, Muhammad Sarim, Anjum, Ashiq and Hill, Richard 2016. High performance video processing in cloud data centres. IEEE. https://doi.org/10.1109/SOSE.2016.56
On some functions involving the lcm and gcd of integer tuples
Bagdasar, Ovidiu 2014. On some functions involving the lcm and gcd of integer tuples. Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics. https://doi.org/10.5937/SPSUNP1402091B
An Inter-Cloud Meta-Scheduling (ICMS) simulation framework: architecture and evaluation
Sotiriadis, Stelios, Bessis, Nik, Anjum, Ashiq and Buyya, Rajkumar 2015. An Inter-Cloud Meta-Scheduling (ICMS) simulation framework: architecture and evaluation. IEEE Transactions on Services Computing. https://doi.org/10.1109/TSC.2015.2399312
Glueing grids and clouds together: a service-oriented approach
Anjum, Ashiq, Hill, Richard, McClatchey, Richard, Bessis, Nik and Branson, Andrew 2012. Glueing grids and clouds together: a service-oriented approach. International Journal of Web and Grid Services. https://doi.org/10.1504/IJWGS.2012.049169
Energy conservation in mobile devices and applications: a case for context parsing, processing and distribution in clouds
Kiani, Saad Liaquat, Anjum, Ashiq, Bessis, Nik, Hill, Richard and Knappmeyer, Michael 2013. Energy conservation in mobile devices and applications: a case for context parsing, processing and distribution in clouds. Mobile Information Systems.
Approaching the Internet of things (IoT): a modelling, analysis and abstraction framework
Ikram, Ahsan, Anjum, Ashiq, Hill, Richard, Antonopoulos, Nikolaos, Liu, Lu and Sotiriadis, Stelios 2013. Approaching the Internet of things (IoT): a modelling, analysis and abstraction framework. Concurrency and Computation: Practice and Experience. https://doi.org/10.1002/cpe.3131
Performance simulation of a context provisioning middleware based on empirical measurements
Reetz, Eike Steffen, Knappmeyer, Michael, Kiani, Saad Liaquat, Anjum, Ashiq, Bessis, Nik and Tönjes, Ralf 2012. Performance simulation of a context provisioning middleware based on empirical measurements. https://doi.org/10.1016/j.simpat.2012.03.002
Dot-base62x: building a compact and user-friendly text representation scheme of ipv6 addresses for cloud computing
Liu, Zhenxing, Liu, Lu, Hardy, J., Anjum, Ashiq, Hill, Richard and Antonopoulos, Nikolaos 2012. Dot-base62x: building a compact and user-friendly text representation scheme of ipv6 addresses for cloud computing. Journal of Cloud Computing: Advances, Systems and Applications. https://doi.org/10.1186/2192-113X-1-3