Entropic Analysis of Votes Expressed in Italian Elections between 1948 and 2018

open access articleIn Italy, the elections occur often, indeed almost every year the citizens are involved in a democratic choice for deciding leaders of different administrative entities. Sometimes the citizens are called to vote for filling more than one office in more than one administrative body. This phenomenon has occurred 35 times after 1948; it creates the peculiar condition of having the same sample of people expressing decisions on political bases at the same time. Therefore, the Italian contemporaneous ballots constitute the occasion to measure coherence and chaos in the way of expressing political opinion. In this paper, we address all the Italian elections that occurred between 1948and2018. Wecollectthenumberofvotesperpartyateachadministrativelevelandwetreateach electionasamanifestationofacomplexsystem. Then,weusetheShannonentropyandtheGiniIndex to study the degree of disorder manifested during different types of elections at the municipality level. A particular focus is devoted to the contemporaneous elections. Such cases implicate different disorder dynamics in the contemporaneous ballots, when different administrative level are involved. Furthermore, some features that characterize different entropic regimes have emerged

Entropic Analysis of Votes Expressed in Italian Elections between 1948 and 2018

In Italy, the elections occur often, indeed almost every year the citizens are involved in a democratic choice for deciding leaders of different administrative entities. Sometimes the citizens are called to vote for filling more than one office in more than one administrative body. This phenomenon has occurred 35 times after 1948; it creates the peculiar condition of having the same sample of people expressing decisions on political bases at the same time. Therefore, the Italian contemporaneous ballots constitute the occasion to measure coherence and chaos in the way of expressing political opinion. In this paper, we address all the Italian elections that occurred between 1948 and 2018. We collect the number of votes per party at each administrative level and we treat each election as a manifestation of a complex system. Then, we use the Shannon entropy and the Gini Index to study the degree of disorder manifested during different types of elections at the municipality level. A particular focus is devoted to the contemporaneous elections. Such cases implicate different disorder dynamics in the contemporaneous ballots, when different administrative level are involved. Furthermore, some features that characterize different entropic regimes have emerged

Topology Reconstruction of Dynamical Networks via Constrained Lyapunov Equations

The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using measurements obtained from the network. In this technical note we define the notion of solvability of the network reconstruction problem. Subsequently, we provide necessary and sufficient conditions under which the network reconstruction problem is solvable. Finally, using constrained Lyapunov equations, we establish novel network reconstruction algorithms, applicable to general dynamical networks. We also provide specialized algorithms for specific network dynamics, such as the well-known consensus and adjacency dynamics.Comment: 8 page

Criptomoedas: ensaios sobre eficiência, risco e contágio

Esta tese investiga três aspetos relevantes e complementares do mercado de criptomoedas, a eficiência, o risco e a incerteza, e o contágio e a integração, visando compreender de forma mais aprofundada este mercado. O primeiro ensaio avalia a eficiência informativa na forma fraca do mercado de criptomoedas, aplicando métodos que permitem captar a dependência global, de longo alcance para diferentes escalas temporais, e identificar possíveis fontes de não linearidade. Recorre-se à Informação mútua, à Detrended fluctuation analysis e aos Expoentes de Lyapunov. Os resultados evidenciam algum grau de predictabilidade nas rendibilidades das criptomoedas, não exibindo na sua generalidade características dos mercados informacionalmente eficientes, embora a Hipótese de Eficiência do Mercado não seja colocada em causa. O segundo ensaio avalia a dinâmica da volatilidade, bem como a incerteza e o risco associado ao investimento em criptomoedas. A incerteza é avaliada com recurso à entropia simbólica de Shannon, e o risco é avaliado com recurso ao Value-at-risk e Conditional Value-at-risk. O investimento em criptomoedas revela sempre possibilidade de perdas associadas, embora nem sempre a períodos de maiores níveis de incerteza correspondam períodos de maiores níveis de risco. O investimento em algumas das criptomoedas poderá proporcionar, a investidores não avessos à incerteza ou ao risco, rendibilidades mais elevadas. O terceiro ensaio avalia a integração e o contágio no mercado de criptomoedas num contexto crise de origem não financeira, explorando medidas de correlação global, com capacidade para captar não-linearidades e a dinâmica dos fluxos de informação. Recorre-se à causalidade à Granger, ao coeficiente de correlação da Detrended cross-corrrelation analysis, à Informação mútua e à Transfer entropy. Os resultados evidenciaram a complexidade e integração entre os mercados de criptomoedas, embora com níveis distintos de integração antes e durante a pandemia. Foi encontrada evidência de contágio apenas entre algumas criptomoedas, concluindo-se na generalidade a ausência de contágio; -Cryptocurrencies: Essays on efficiency, risk and contagion Abstract: This thesis investigates three relevant and complementary aspects of the cryptocurrency market, efficiency, risk and uncertainty, and contagion and integration, intending to understand this market in greater depth. The first essay evaluates the weak-form efficiency of the cryptocurrency market, applying methods that allow capturing global dependence, long-range for different time scales, and identifying possible sources of non-linearity. Mutual information, detrended fluctuation analysis and Lyapunov's exponents are applied. The results show some degree of predictability in the returns of cryptocurrencies, not revealing, in general, characteristics of informationally efficient markets. However, it does not allow to reject the efficient market hypothesis. The second essay assesses the volatility dynamics and the uncertainty and risk associated with investing in cryptocurrencies. Uncertainty is evaluated using Shannon's symbolic entropy, and risk is evaluated using Value-at-risk and Conditional Value-at-risk. Investing in cryptocurrencies always reveals the possibility of associated losses, although periods of higher levels of uncertainty do not always correspond to periods of higher levels of risk. Investing in some of the cryptocurrencies may provide investors, non-averse to uncertainty or risk, higher returns. The third essay evaluates the integration and contagion in the cryptocurrency market in a crisis context of non-financial origin, exploring global correlation measures that are able to capture non-linearities and the dynamics of information flows. Granger causality, the Detrended cross-correlation analysis correlation coefficient, Mutual information and Transfer entropy are used. The results highlighted the complexity and integration between cryptocurrency markets, albeit with different levels of integration before and during the pandemic. Evidence of contagion was found only among some cryptocurrencies, concluding, in general, the absence of contagion

Transfer Entropy between Communities in Complex Financial Networks

In this paper, we analyze information flows between communities of financial markets, represented as complex networks. Each community, typically corresponding to a business sector, represents a significant part of the financial market and the detection of interactions between communities is crucial in the analysis of risk spreading in the financial markets. We show that the transfer entropy provides a coherent description of information flows in and between communities, also capturing non-linear interactions. Particularly, we focus on information transfer of rare events—typically large drops which can spread in the network. These events can be analyzed by Rényi transfer entropy, which enables to accentuate particular types of events. We analyze transfer entropies between communities of the five largest financial markets and compare the information flows with the correlation network of each market. From the transfer entropy picture, we can also identify the non-linear interactions, which are typical in the case of extreme events. The strongest flows can be typically observed between specific types of business sectors—financial sectors is the most significant example