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In the paper carried out by Wenjun et al. [Phys. Rev. A 95, 032124 (2017)], a generalization of the James effective dynamics theory based on a first version of the James method was presented. However, we contend that this is not a very rigorous way of deriving the effective third-order expansion for an interaction Hamiltonian with harmonic time-dependence. In fact, here we show that the third-order Hamiltonian obtained by Wenjun et al. is not Hermitian for general situations when we consider time dependence. Its non-Hermitian nature arises from the foundation of the theory itself. In this comment paper, the most general expression of the effective Hamiltonian expanded up to third order is obtained. Our derived effective Hamiltonian is Hermitian even in situations where we have time dependence.

We review some general aspects about the Black–Scholes equation, which is used for predicting the fair price of an option inside the stock market. Our analysis includes the symmetry properties of the equation and its solutions. We use the Hamiltonian formulation for this purpose. Taking into account that the volatility inside the Black–Scholes equation is a parameter, we then introduce the Merton–Garman equation, where the volatility is stochastic, and then it can be perceived as a field. We then show how the Black–Scholes equation and the Merton–Garman one are locally equivalent by imposing a gauge symmetry under changes in the prices over the Black–Scholes equation. This demonstrates that the stochastic volatility emerges naturally from symmetry arguments. Finally, we analyze the role of the volatility on the decisions taken by the holders of the options when they use the solution of the Black–Scholes equation as a tool for making investment decisions.

In any physical system, when we move from short to large scales, new spacetime symmetries emerge which help us to simplify the dynamics of the system. In this letter we demonstrate that certain variations on the symmetries of general relativity at large scales generate the effects equivalent to dark matter ones. In particular, we reproduce the Tully-Fisher law, consistent with the predictions proposed by MOND. Additionally, we demonstrate that the dark matter effects derived in this way are consistent with the predictions suggested by MOND, without modifying gravity.

By using the Hamiltonian formulation, we demonstrate that the Merton-Garman equation emerges naturally from the Black-Scholes equation after imposing invariance (symmetry) under local (gauge) transformations over changes in the stock price. This is the case because imposing gauge symmetry implies the appearance of an additional field, which corresponds to the stochastic volatility. The gauge symmetry then imposes some constraints over the free parameters of the Merton-Garman Hamiltonian. Finally, we analyze how the stochastic volatility gets massive dynamically via Higgs mechanism.

We are delighted to present this special issue editorial for Neural Computing and Applications special issue on LatinX in AI research. This special issue brings together a collection of articles that explore machine learning and artificial intelligence research from various perspectives, aiming to provide a comprehensive and in-depth understanding of what LatinX researchers are working on in the field. In this editorial, we will introduce the overarching theme of the special issue, highlight the significance of the selected papers, and offer insights into the contributions made by the authors. The LatinX in AI organization was launched in 2018, with leaders from organizations in Artificial Intelligence, Education, Research, Engineering, and Social Impact with a purpose to together create a group that would be focused on “Creating Opportunity for LatinX in AI.” The main goal is to increase the representation of LatinX professionals in the AI industry. LatinX in AI Org and programs are volunteer-run and fiscally sponsored by the Accel AI Institute, 501(c)3 Non-Profit.

The Black-Scholes equation is famous for predicting values for the prices of Options inside the stock market scenario. However, it has the limitation of depending on the estimated value for the volatility. On the other hand, several Machine learning techniques have been employed for predicting the values of the same quantity. In this paper we analyze some fundamental properties of the Black-Scholes equation and we then propose a way to train its free-parameters, the volatility in particular. This with the purpose of using this parameter as the fundamental one to be learned by a Machine Learning system and then improve the predictions in the stock market.

By using the Hamiltonian formulation, we demonstrate that the Merton-Garman equation emerges naturally from the Black-Scholes equation after imposing invariance (symmetry) under local (gauge) transformations over changes in the stock price. This is the case because imposing gauge symmetry implies the appearance of an additional field, which corresponds to the stochastic volatility. The gauge symmetry then imposes some constraints over the free-parameters of the Merton-Garman Hamiltonian. Finally, we analyze how the stochastic volatility gets massive dynamically via Higgs mechanism.

We prove the consistency of the different approaches for deriving the black hole radiation for the spherically symmetric case inside the theory of Massive Gravity. By comparing the results obtained by using the Bogoliubov transformations with those obtained by using the Path Integral formulation, we find that in both cases, the presence of the extra-degrees of freedom creates the effect of extra-particles creation due to the distortions on the definitions of time defined by the different observers at large scales. This, however, does not mean extra-particle creation at the horizon level. Instead, the apparent additional particles perceived at large scales emerge from how distant observers define their time coordinate, which is distorted due to the existence of extra-degrees of freedom.

By using both, the weak-value formulation as well as the standard probabilistic approach, we analyze the Hardy's experiment introducing a complex and dimensionless parameter ($\epsilon$) which eliminates the assumption of complete annihilation when both, the electron and the positron departing from a common origin, cross the intersection point $P$. We then find that the paradox does not exist for all the possible values taken by the parameter. The apparent paradox only appears when $\epsilon=1$; however, even in this case we can interpret this result as a natural consequence of the fact that the particles can cross the point $P$, but at different times due to a natural consequence of the energy-time uncertainty principle.