arXiv subjects
Publications and source records attributed to Rafael Moreira.
We present a quaternionic proof that the quadratic form $t^2+2x^2+5y^2+10z^2$ represents all positive integers, and that the form $t^2+x^2+7y^2+7z^2$ represents all natural numbers which are neither equal to $3 \cdot 7^\ell$ nor equal to $6 \cdot 7^\ell$, for any $\ell \in \mathbb{N}_0$. To do this we introduce a technique that may be useful for other purposes, and that we call "metaconjugation".
Social turbulence can affect people financial decisions, causing changes in spending and saving. During a global turbulence as significant as the COVID-19 pandemic, such changes are inevitable. Here we examine how the effects of COVID-19 on various jurisdictions influenced the global price of Bitcoin. We hypothesize that lock downs and expectations of economic recession erode people trust in fiat (government-issued) currencies, thus elevating cryptocurrencies. Hence, we expect to identify a causal relation between the turbulence caused by the pandemic, demand for Bitcoin, and ultimately its price. To test the hypothesis, we merged datasets of Bitcoin prices and COVID-19 cases and deaths. We also engineered extra features and applied statistical and machine learning (ML) models. We applied a Random Forest model (RF) to identify and rank the feature importance, and ran a Long Short-Term Memory (LSTM) model on Bitcoin prices data set twice: with and without accounting for COVID-19 related features. We find that adding COVID-19 data into the LSTM model improved prediction of Bitcoin prices.