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The information paradox suggests that the black hole loses information when it emits radiation. In this way, the spectrum of radiation corresponds to a mixed (non-pure) quantum state even if the internal state generating the black hole is expected to be pure in essence. In this paper we propose an argument solving this paradox by developing an understanding of the process by which spontaneous symmetry breaks when a black hole selects one of the many possible ground states and emits radiation as a consequence of it. Here, the particle operator number is the order parameter. This mechanism explains the connection between the density matrix, corresponding to the pure state describing the black hole state, and the density matrix describing the spectrum of radiation (mixed quantum state). From this perspective, we can recover black hole information from the superposition principle, applied to the different possible order parameters (particle number operators).

The cosmological constant is normally introduced as an additional term entering the Einstein–Hilbert (EH) action. In this letter, we demonstrate that, instead, it appears naturally from the standard EH action as an invariant term emerging from spacetime symmetries. We then demonstrate that the same constraint emerging from this invariant suppresses the short wavelength modes and it favors the long wavelength ones. In this way, inside the proposed formulation, the observed value for the vacuum energy density is obtained naturally from the zero-point quantum fluctuations.

The mutual information method has demonstrated to be very useful for deriving the potential order parameter of a system. Although the method suggests some constraints which help to define this quantity, there is still some freedom in the definition. The method then results inefficient for cases where we have order parameters with a large number of constants in the expansion, which happens when we have many degenerate vacuums. Here, we introduce some additional constraints based on the existence of broken symmetries, which help us to reduce the arbitrariness in the definitions of the order parameter in the proposed mutual information method.

We demonstrate that black hole evaporation can be modeled as a process where one symmetry of the system is spontaneously broken continuously. We then identify three free parameters of the system. The sign of one of the free parameters governs whether the particles emitted by the black hole are fermions or bosons. The present model explains why the black hole evaporation process is so universal. Interestingly, this universality emerges naturally inside certain modifications of gravity.

The Revenue Management (RM) problem in airlines for a fixed capacity, single resource and two classes has been solved before by using a standard formalism. In this paper we propose a model for RM by using the semi-classical approach of the Quantum Harmonic Oscillator. We then extend the model to include external factors affecting the people’s decisions, particularly those where collective decisions emerge.

It has been claimed in \cite1, that the idea proposed in \cite2 has certain mistakes based on arguments of energy conditions and others. Additionally, some of the key arguments of the paper are criticized. Here we demonstrate that the results obtained in \cite2 are correct and that there is no violation of any energy condition. The statements claimed in \cite1 are based on three things: 1). Misinterpretation of the metric solution. 2). Language issues related to the physical quantities obtained in \cite1, where the authors make wrong interpretations about certain results over the geometry proposed in \cite2. 3). Non-rigorous evaluations of the vacuum condition defined via the result over the Ricci tensor R_\mu\nu=0.

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.

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.

The spontaneous symmetry breaking phenomena applied to Quantum Finance considers that the martingale state in the stock market corresponds to a ground (vacuum) state if we express the financial equations in the Hamiltonian form. The original analysis for this phenomena completely ignores the kinetic terms in the neighborhood of the minimal of the potential terms. This is correct in most of the cases. However, when we deal with the martingale condition, it comes out that the kinetic terms can also behave as potential terms and then reproduce a shift on the effective location of the vacuum (martingale). In this paper, we analyze the effective symmetry breaking patterns and the connected vacuum degeneracy for these special circumstances. Within the same scenario, we analyze the connection between the flow of information and the multiplicity of martingale states, providing in this way powerful tools for analyzing the dynamic of the stock markets.