Maminirina Franck Ramaharo

Maminirina Franck Ramaharo

Just a lifelong learner

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My integer sequences in OEIS

18 minute read

Published:

I have submitted few sequences to the OEIS, most of which are connected to my work on applying the Kauffman bracket polynomial to knot shadows.

portfolio

Menger Sponge Project

Published:

This is also part of the Origami Fractal Project we carried out in 2014, which I am especially proud of.

publications

A state enumeration of the foil knot

Published in arXiv e-Print archive, 2017

We split the crossings of the foil knot and enumerate the resulting states with a generating polynomial. Unexpectedly, the number of such states which consist of two components are given by the lazy caterer’s sequence. This sequence describes the maximum number of planar regions that is obtained with a given number of straight lines. We then establish a bijection between this partition of the plane and the concerned foil splits sequence.

Recommended citation: Franck Ramaharo and Fanja Rakotondrajao (2017), "A state enumeration of the foil knot", arXiv e-Print archive, arXiv:1712.04026 [math.CO].
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Enumerating the states of the twist knot

Published in arXiv e-Print archive, 2017

We enumerate the state diagrams of the twist knot shadow which consist of the disjoint union of two trivial knots. The result coincides with the maximal number of regions into which the plane is divided by a given number of circles. We then establish a bijection between the state enumeration and this particular partition of the plane by means of binary words.

Recommended citation: Franck Ramaharo (2017), "Enumerating the states of the twist knot", arXiv e-Print archive, arXiv:1712.06543 [math.CO].
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An approximate Jerusalem square whose side equals a Pell number

Published in arXiv e-Print archive, 2018

We take advantage of the properties of the Pell numbers to construct an integer version of the Jerusalem square fractal.

Recommended citation: Franck Ramaharo (2018), "An approximate Jerusalem square whose side equals a Pell number", arXiv e-Print archive, arXiv:1801.00466 [math.CO].
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Statistics on some classes of knot shadows

Published in arXiv e-Print archive, 2018

The present paper is concerned with the enumeration of the state diagrams for some classes of knot shadows endowed with the usual connected sum operation. We focus on shadows that are recursively generated by knot shadows with up to 3 crossings, and for which the enumeration problem is solved with the help of generating polynomials.

Recommended citation: Franck Ramaharo (2018), "Statistics on some classes of knot shadows", arXiv e-Print archive, arXiv:1802.07701 [math.CO].
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A generating polynomial for the pretzel knot

Published in arXiv e-Print archive, 2018

We collect statistics which consist of the coefficients in the expansion of the generating polynomials that count the Kauffman states associated with certain classes of pretzel knots having n tangles, of r half-twists respectively.

Recommended citation: Franck Ramaharo (2018), "A generating polynomial for the pretzel knot", arXiv e-Print archive, arXiv:1805.10680 [math.CO].
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A one-variable bracket polynomial for some Turk’s head knots

Published in arXiv e-Print archive, 2018

We compute the Kauffman bracket polynomial of the three-lead Turk’s head, the chain sinnet and the figure-eight chain shadow diagrams. Each of these knots can in fact be constructed by repeatedly concatenating the same 3-tangle, respectively, then taking the closure. The bracket is then evaluated by expressing the state diagrams of the concerned 3-tangle by means of the Kauffman monoid diagram’s elements.

Recommended citation: Franck Ramaharo (2018), "A one-variable bracket polynomial for some Turk's head knots", arXiv e-Print archive, arXiv:1807.05256 [math.CO].
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Note on sequences A123192, A137396 and A300453

Published in arXiv e-Print archive, 2019

We give the connection between three polynomials that generate triangles in The On-Line Encyclopedia of Integer Sequences (A123192, A137396 and A300453). We show that they are related with the bracket polynomial for the (2,n)-torus knot.

Recommended citation: Franck Ramaharo (2018), "Note on sequences A123192, A137396 and A300453", arXiv e-Print archive, arXiv:1911.04528 [math.CO].
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A bracket polynomial for 2-tangle shadows

Published in arXiv e-Print archive, 2020

We compute the Kauffman bracket polynomial of the numerator and denominator closures of A + A + … + A ( A is repeated n times), where A is a 2-tangle shadow that has at most 4 crossings.

Recommended citation: Franck Ramaharo (2020), "A bracket polynomial for 2-tangle shadows", arXiv e-Print archive, arXiv:2002.06672 [math.CO].
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A simplified macroeconomic framework

Published in MPRA Paper, 2020

We propose a scenario for computing the real gross domestic product in a macroeconomic framework. The scenario is designed upon simple assumptions while ensuring basic algebraic relationships between the four usual macroeconomic accounts.

Recommended citation: Franck Ramaharo (2020). "A simplified macroeconomic framework", MPRA Paper, No. 102086, University Library of Munich, Germany.
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A simple macroeconomic framework for Madagascar

Published in MPRA Paper, 2022

I present a simple model of macroeconomic accounting framework for the economy of Madagascar. The model is an identity-based framework that inherits the characteristics of the World Bank’s Revised Minimum Standard Model and the International Monetary Fund’s financial programming. Such models are mostly used for designing the macroeconomic framework of the budget laws of Madagascar.

Recommended citation: Franck Ramaharo (2022). "A simple macroeconomic framework for Madagascar", MPRA Paper, No. 112114, University Library of Munich, Germany.
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The 2019 Merged model for Madagascar

Published in MPRA Paper, 2022

This document gives the specification of the Merged model for Madagascar. The model is initialized and calibrated based on a 2019 social accounting matrix framework and an auxiliary set of 2018-2019 macroeconomic data.

Recommended citation: Franck Ramaharo (2022). "The 2019 Merged model for Madagascar", MPRA Paper, No. 115226, University Library of Munich, Germany.
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Principal component regression analysis of electricity consumption factors in Madagascar

Published in MPRA Paper, 2023

We carry out principal component regression analysis on a dataset consisting of selected relevant economic and energy indicators in order to identify the main driving factors impacting the electricity consumption in Madagascar. Our results show that in accordance with the country’s current energy profile, factors related with rural electrification have the most influence on electricity consumption in Madagascar.

Recommended citation: Franck Ramaharo and Njakanasandratra Rajaonarison (2023). "Principal component regression analysis of electricity consumption factors in Madagascar", MPRA Paper, No. 116142, University Library of Munich, Germany.
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Les modèles macroéconomiques en usage à Madagascar

Published in HAL Open Science, 2023

La modélisation économique joue un rôle crucial dans un pays car elle permet de mieux comprendre les interactions complexes entre les variables économiques et d’anticiper les impacts des décisions économiques au moyen des outils d’analyse et de prévision. Dans la présente note, nous recensons particulièrement les modèles macroéconomiques en usage à Madagascar et qui ont été internalisés au sein des départements ministériels en charge de l’Économie depuis les années 90. Les résultats obtenus révèlent que Madagascar dispose d’un éventail d’outils informatisés de modélisation, n’ayant pas nécessairement été pérennes, qui ont servis à surveiller son économie. Nous comptons des modèles comptables et quasi-comptables, des modèles d’équilibre général calculable (MEGC), des modèles d’équilibre général dynamique et stochastique (DSGE), des modèles économétriques appliquées aux prévisions immédiates et des modèles d’apprentissage automatique (Machine Learning). Cette note représente aussi un effort pour dévoiler les documents détaillant les spécificités techniques des modèles macroéconomiques malagasy dont la plupart sont depuis longtemps tombée dans l’oubli.

Recommended citation: Franck Ramaharo, Yves Razanajatovo and Emanuella Aljaona (2023), "Les modèles macroéconomiques en usage à Madagascar", HAL Open Science, hal-04174445, Centre pour la Communication Scientifique Directe.
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Determinants of renewable energy consumption in Madagascar: Evidence from feature selection algorithms

Published in Social Science Open Access Repository (SSOAR), 2023

The aim of this note is to identify the factors influencing renewable energy consumption in Madagascar. We tested 12 features covering macroeconomic, financial, social, and environmental aspects, including economic growth, domestic investment, foreign direct investment, financial development, industrial development, inflation, income distribution, trade openness, exchange rate, tourism development, environmental quality, and urbanization. To assess their significance, we assumed a linear relationship between renewable energy consumption and these features over the 1990-2021 period. Next, we applied different machine learning feature selection algorithms classified as filter-based (relative importance for linear regression, correlation method), embedded (LASSO), and wrapper-based (best subset regression, stepwise regression, recursive feature elimination, iterative predictor weighting partial least squares, Boruta, simulated annealing, and genetic algorithms) methods. Our analysis revealed that the five most influential drivers stem from macroeconomic aspects. We found that domestic investment, foreign direct investment, and inflation positively contribute to the adoption of renewable energy sources. On the other hand, industrial development and trade openness negatively affect renewable energy consumption in Madagascar.

Recommended citation: Franck Ramaharo and Fitiavana Randriamifidy (2023). "Determinants of renewable energy consumption in Madagascar: Evidence from feature selection algorithms", Social Science Open Access Repository, No. 90206, GESIS Leibniz Institute for the Social Sciences .
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The impact of energy demand on economic growth: A new empirical evidence for Madagascar

Published in Cambridge Open Engage, 2024

This study investigates the impact of energy demand on Madagascar’s economic growth from 2007Q1 to 2022Q4. Drawing upon a rich dataset from Malagasy sources, we applied the ARDL bounds testing approach and found cointegration among the series. We found that, in the long run, electricity and petroleum consumption have positive significant effects on economic growth, while energy imports and global prices have negative significant effects. We further applied Granger-causality test based on Error Correction Model to examine causal relationships. The results revealed that in the short run, there are unidirectional causal effects running from electricity consumption, energy imports, and global prices to economic growth. The test also revealed that both energy demand and global prices have a long-run causal effect on economic growth. Our findings confirms that Madagascar is an energy-dependent economy, and provide valuable insights for policymakers to design effective energy policies that promote economic growth and energy security.

Recommended citation: Franck Ramaharo, Yves Razanajatovo, Fabienne Ravelomanantsoa, Melodia Ramarosandratana, and Emanuella Aljaona (2024), "The impact of energy demand on economic growth: A new empirical evidence for Madagascar", Cambridge Open Engage, Cambridge University Press.
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Nowcasting Madagascar’s real GDP using machine learning algorithms

Published in AfricArXiv Preprints, 2024

We investigate the predictive power of different machine learning algorithms to nowcast Madagascar’s gross domestic product (GDP). We trained popular regression models, including linear regularized regression (Ridge, Lasso, Elastic-net), dimensionality reduction model (principal component regression), k-nearest neighbors algorithm (k-NN regression), support vector regression (linear SVR), and tree-based ensemble models (Random forest and XGBoost regressions), on 10 Malagasy quarterly macroeconomic leading indicators over the period 2007Q1-2022Q4, and we used simple econometric models as a benchmark. We measured the nowcast accuracy of each model by calculating the root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). Our findings reveal that the Ensemble Model, formed by aggregating individual predictions, consistently outperforms traditional econometric models. We conclude that machine learning models can deliver more accurate and timely nowcasts of Malagasy economic performance and provide policymakers with additional guidance for data-driven decision making.

Recommended citation: Franck Ramaharo and Gerzhino Rasolofomanana (2023), "Nowcasting Madagascar's real GDP using machine learning algorithms", AfricArXiv Preprints, No. vpuac, Center for Open Science.
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The macroeconomic determinants of renewable energy consumption in Madagascar: Evidence from an Autoregressive Distributed Lag modeling approach

Published in AfricArXiv Preprints, 2024

We investigate the macroeconomic determinants of renewable energy consumption in Madagascar, using annual data from 1990 to 2021 and the ARDL bounds testing approach. Our results reveal that, in the long run, domestic investment, financial development, trade openness and foreign direct investment have a significant and positive impact on renewable energy consumption. Conversely, increased economic growth, industrial development, income distribution, and carbon emissions lead to a reduction in renewable energy consumption. Therefore, to achieve its ambitious goal of generating 85% of its energy from renewable sources by 2030, the government must carefully monitor and continually analyze these interconnected macroeconomic factors. This will enable effective tailoring of policies and interventions, paving the way for a successful transition to clean and renewable energy.

Recommended citation: Franck Ramaharo and Yves Razanajatovo (2024), "The macroeconomic determinants of renewable energy consumption in Madagascar: Evidence from an Autoregressive Distributed Lag modeling approach", AfricArXiv Preprints, No. dfk2c, Center for Open Science.
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LMDI decomposition and macroeconomic drivers of electricity intensity in Madagascar

Published in SocArXiv Papers, 2024

This study employs the Logarithmic Mean Divisia Index (LMDI) decomposition method to analyze the drivers of overall electricity intensity in Madagascar over the period 2007-2022. The decomposition results reveal that the residential sector is the primary driver of overall electricity intensity, followed by the service and industry sectors. Notably, the industry sector has contributed to a decrease in intensity. Furthermore, the results indicate that the intensity effect has had a significant impact on increasing overall electricity intensity, whereas the structure effect has played a role in reducing total intensity. Building on these findings, we investigate the impact of key macroeconomic factors on the observed electricity intensity trend using the Auto Regressive Distributed Lag (ARDL) bounds testing approach with quarterly data over the same study period. The ARDL cointegrating approach estimation results reveal a long-run association between financial development, foreign direct investment, industry development, consumer energy inflation, and trade openness. Moreover, the long-run coefficients, which are further supported by the Dynamic Ordinary Least Squares (DOLS) estimates, indicate that financial development and trade openness have a positive and significant impact on electricity intensity in Madagascar, while foreign direct investment, industry development, and consumer energy inflation have a negative and significant impact, suggesting that these factors contribute to electricity efficiency. The Toda-Yamamoto non-causality approach uncovers unidirectional causal relationships, specifically from financial development, industrial development, and consumer energy inflation to electricity intensity, as well as from electricity intensity to foreign direct investment. These causal directions are further corroborated by the forecast-error variance decomposition, providing strong evidence for these relationships. These findings provide valuable insights for policymakers and stakeholders in Madagascar’s energy sector, highlighting the importance of promoting energy efficiency initiatives.

Recommended citation: Franck Ramaharo (2024), "LMDI decomposition and macroeconomic drivers of electricity intensity in Madagascar", SocArXiv Papers, No. gc5qe, Center for Open Science.
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Does economic growth drive energy consumption in Madagascar? Fresh empirical evidence

Published in Social Science Open Access Repository (SSOAR), 2024

This study uses quarterly data spanning from 2007 to 2022 to examine the long-run relationship and causal nexus between economic growth and energy consumption in Madagascar, disaggregating energy consumption into electricity and petroleum consumption, as well as considering total energy consumption, while accounting for the impact of energy imports and energy prices within an econometric framework. Using the Bayer-Hanck cointegration test, we found evidence of positive long-run relationships between the variables of interest. Furthermore, we estimated the long-run elasticities using three complementary approaches: the Fully Modified Ordinary Least Squares (FMOLS), Dynamic Ordinary Least Squares (DOLS), and Canonical Cointegrating Regression (CCR) estimators. The empirical findings indicate that economic growth, energy imports, and energy prices have a positive and statistically significant impact on energy consumption in Madagascar. Additionally, we employed the Toda-Yamamoto approach to Granger non-causality test and the Breitung-Candelon frequency-domain test to investigate the causal relationships among the variables. Notably, our results reveal a unidirectional long-run Granger-causality flowing from economic growth to electricity consumption, thereby providing support for the conservation hypothesis. Furthermore, the time-domain causality test reveals a neutral relationship between economic growth and petroleum consumption, as well as total energy consumption, which is consistent with the neutrality hypothesis. However, the Breitung-Candelon test uncovers a more nuanced dynamic, with total energy consumption found to Granger-cause economic growth in both the long and medium run, thereby supporting the growth hypothesis. Notably, the causal linkage is strengthened when the test is not conditioned on energy prices and energy imports, and petroleum consumption is also found to cause economic growth in this bivariate framework. Conversely, electricity and economic growth become neutral to each other. Our findings highlight the intricate interplay between economic growth and energy consumption, underscoring the critical roles of energy imports and prices in this dynamic.

Recommended citation: Franck Ramaharo (2024), "Does economic growth drive energy consumption in Madagascar? Fresh empirical evidence", Social Science Open Access Repository, No. 96544, GESIS Leibniz Institute for the Social Sciences.
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talks

teaching

Teaching experience 1

Undergraduate course, University 1, Department, 2014

This is a description of a teaching experience. You can use markdown like any other post.

Teaching experience 2

Workshop, University 1, Department, 2015

This is a description of a teaching experience. You can use markdown like any other post.