1,721,005 research outputs found
Ordering of nested square roots of 2 according to the Gray code
No full textIn this paper, we discuss some relations between zeros of Lucas–Lehmer polynomials and the Gray code. We study nested square roots of 2 applying a “binary code” that associates bits 0 and 1 to “plus” and “minus” signs in the nested form. This gives the possibility to obtain an ordering for the zeros of Lucas–Lehmer polynomials, which take the form of nested square roots of 2
Time Scale Separation, Normal Modes and Quasi-Steady State Approximations in Enzyme Kinetics
No full textThe mathematical treatment of enzyme kinetics, based on quasi-steady state
approximations, relies on the separation of two dierent time scales, related
to a fast transient phase and a slow phase, where the reactants can be
approximately considered in a quasi equilibrium. Several authors have determined
sucient and necessary conditions for the separation of the two
time scales in a single reaction, in the framework of the so-called standard
quasi-steady state approximation (sQSSA). In the Nineties a new type of
quasi-steady state approximation, called total (tQSSA), has been proposed;
it is valid in a very large range of parameters and initial conditions, much
larger with respect to the standard QSSA. As the classical QSSA, the tQSSA
can be interpreted as the leading term of an asymptotic expansion in terms of
a suitable parameter. Starting from some papers by Palsson and coauthors
in Eighties, we link the tQSSA to the normal modes of the system of nonlinear
EDOs governing the reactions, aiming at determining a general rule
allowing the detection of sucient conditions guaranteeing the separation of
time scales in more general reactions and, consequently, the determination
of the appropriate parameters for the corresponding asymptotic expansions
Exploring cryptocurrency price dynamics and predictability with ordinal networks
No full textOrdinal networks represent an innovative and versatile approach for time series analysis, enabling the transformation of data sequences into complex networks based on the relative order of values. This method provides a fresh perspective on uncovering the internal structure of the data, allowing the identification of recurring patterns and predictability dynamics. In our study, we employ ordinal networks and permutation entropy to analyze the predictability and evolving dynamics of four cryptocurrencies: Bitcoin, Ethereum, Litecoin, and Dogecoin. By leveraging this methodology, we investigate the temporal relationships and ordinal transitions that characterize the price fluctuations and volatility of each cryptocurrency, offering deeper insights into their dynamic complexity and predictive potential in cryptocurrency markets
Mathematical Model for the Output Signal's Energy of an Ideal DAC in the Presence of Clock Jitter
No full text
Studying the impact of fluctuations, spikes and rare events in time series through a wavelet entropy predictability measure
No full textData has become one of the most crucial sources of human life. In particular, the ability to predict the future through data is a widely studied topic. In finance, as an instance, increased volatility, fluctuations, low-frequency events, and rare events negatively affect the predictability of data, thus increasing the level of risk. As a consequence, the inability to make accurate predictions on future events increases the uncertainty and variability of a given scenario, indicating a consequent increase in risk. In this paper, we analyze data predictability introducing a new measure based on entropy and the wavelet transform. In particular, we show that the data are less predictable than one might expect due to the mentioned fluctuations and low-frequency events. Furthermore, we apply our tool to real data, in particular to time series of commodities. As a result, thanks to this new measure, we can observe that the price time series under analysis exhibit a significant level of unpredictability due to increased volatility, fluctuations, and the influence of low-frequency events
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