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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.

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.

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.

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.

It is known that the probability is not a conserved quantity in the stock market, given the fact that it corresponds to an open system. In this paper we analyze the flow of probability in this system by expressing the ideal Black-Scholes equation in the Hamiltonian form. We then analyze how the non-conservation of probability affects the stability of the prices of the Stocks. Finally, we find the conditions under which the probability might be conserved in the market, challenging in this way the non-Hermitian nature of the Black-Scholes Hamiltonian.

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.

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.

In this chapter, a mathematical model explaining generically the propagation of a pandemic is proposed, helping in this way to identify the fundamental parameters related to the outbreak in general. Three free parameters for the pandemic are identified, which can be finally reduced to only two independent parameters. The model is inspired in the concept of spontaneous symmetry breaking, used normally in quantum field theory, and it provides the possibility of analyzing the complex data of the pandemic in a compact way. Data from 12 different countries are considered and the results presented. The application of nonlinear quantum physics equations to model epidemiologic time series is an innovative and promising approach.

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.

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 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.

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.

Following the World Health Organization proclaims a pandemic due to a disease that originated in China and advances rapidly across the globe, studies to predict the behavior of epidemics have become increasingly popular, mainly related to COVID-19. The critical point of these studies is to discuss the disease's behavior and the progression of the virus's natural course. However, the prediction of the actual number of infected people has proved to be a difficult task, due to a wide range of factors, such as mass testing, social isolation, underreporting of cases, among others. Therefore, the objective of this work is to understand the behavior of COVID-19 in the state of Ceará to forecast the total number of infected people and to aid in government decisions to control the outbreak of the virus and minimize social impacts and economics caused by the pandemic. So, to understand the behavior of COVID-19, this work discusses some forecast techniques using machine learning, logistic regression, filters, and epidemiologic models. Also, this work brings a new approach to the problem, bringing together data from Ceará with those from China, generating a hybrid dataset, and providing promising results. Finally, this work still compares the different approaches and techniques presented, opening opportunities for future discussions on the topic. The study obtains predictions with R2 score of 0.99 to short-term predictions and 0.93 to long-term predictions.

The use of computational tools for medical image processing are promising tools to effectively detect COVID-19 as an alternative to expensive and time-consuming RT-PCR tests. For this specific task, CXR (Chest X-Ray) and CCT (Chest CT Scans) are the most common examinations to support diagnosis through radiology analysis. With these images, it is possible to support diagnosis and determine the disease’s severity stage. Computerized COVID-19 quantification and evaluation require an efficient segmentation process. Essential tasks for automatic segmentation tools are precisely identifying the lungs, lobes, bronchopulmonary segments, and infected regions or lesions. Segmented areas can provide handcrafted or self-learned diagnostic criteria for various applications. This Chapter presents different techniques applied for Chest CT Scans segmentation, considering the state of the art of UNet networks to segment COVID-19 CT scans and a segmentation experiment for network evaluation. Along 200 epochs, a dice coefficient of 0.83 was obtained.

COVID-19 is a respiratory disorder caused by CoronaVirus and SARS (SARS-CoV2). WHO declared COVID-19 a global pandemic in March 2020 and several nations’ healthcare systems were on the verge of collapsing. With that, became crucial to screen COVID-19-positive patients to maximize limited resources. NAATs and antigen tests are utilized to diagnose COVID-19 infections. NAATs reliably detect SARS-CoV-2 and seldom produce false-negative results. Because of its specificity and sensitivity, RT-PCR can be considered the gold standard for COVID-19 diagnosis. This test’s complex gear is pricey and time-consuming, using skilled specialists to collect throat or nasal mucus samples. These tests require laboratory facilities and a machine for detection and analysis. Deep learning networks have been used for feature extraction and classification of Chest CT-Scan images and as an innovative detection approach in clinical practice. Because of COVID-19 CT scans’ medical characteristics, the lesions are widely spread and display a range of local aspects. Using deep learning to diagnose directly is difficult. In COVID-19, a Transformer and Convolutional Neural Network module are presented to extract local and global information from CT images. This chapter explains transfer learning, considering VGG-16 network, in CT examinations and compares convolutional networks with Vision Transformers (ViT). Vit usage increased VGG-16 network F1-score to 0.94.