Physics Maths Engineering
The initial-boundary and the inverse coefficient problems for the semilinear hyperbolic equation with strong damping are considered in this study. The conditions for the existence and uniqueness of solutions in Sobolev spaces to these problems have been established. The inverse problem involves determining the unknown time-dependent parameter in the right-hand side function of the equation using a...
Posted 5 months ago
Physics Maths Engineering
The article "Regression with Ordered Predictors via Ordinal Smoothing Splines" by Nathaniel E. Helwig addresses the challenges of incorporating ordered categorical predictors into regression models. Traditional regression frameworks often treat ordinal predictors as either nominal (unordered) or continuous variables, which can be theoretically and computationally undesirable. This study propose...
Posted 5 months ago
Physics Maths Engineering
The article "A Tree-Based Multiscale Regression Method" by Haiyan Cai and Qingtang Jiang introduces a novel regression technique designed to effectively handle high-dimensional data. This method adapts to the intrinsic lower-dimensional structure of the data, mitigating the challenges posed by the "curse of dimensionality." It also offers smoother estimates in regions where the regression funct...
Posted 5 months ago
Physics Maths Engineering
We introduce the Tensor-Based Multivariate Optimization (TeMPO) framework for use in nonlinear optimization problems commonly encountered in signal processing, machine learning, and artificial intelligence. Within our framework, we model nonlinear relations by a multivariate polynomial that can be represented by low-rank symmetric tensors (multi-indexed arrays), making a compromise between model g...
Posted 5 months ago
Physics Maths Engineering
The authors proved three theorems about the exact solutions of a generalized or interacting Black–Scholes equation that explicitly includes arbitrage bubbles. These arbitrage bubbles can be characterized by an arbitrage number AN. The first theorem states that if AN = 0, then the solution at maturity of the interacting equation is identical to the solution of the free Black–Scholes equation wi...
Posted 5 months ago
Physics Maths Engineering
Physics-Informed Neural Networks (PINN) emerged as a powerful tool for solving scientific computing problems, ranging from the solution of Partial Differential Equations to data assimilation tasks. One of the advantages of using PINN is to leverage the usage of Machine Learning computational frameworks relying on the combined usage of CPUs and co-processors, such as accelerators, to achiev...
Posted 5 months ago
Physics Maths Engineering
An unprecedented amount of access to data, “big data (or high dimensional data),” cloud computing, and innovative technology have increased applications of artificial intelligence in finance and numerous other industries. Machine learning is used in process automation, security, underwriting and credit scoring, algorithmic trading and robo-advisory. In fact, machine learning AI applications ar...
Posted 5 months ago
Physics Maths Engineering
Dealing with massive data is a challenging task for machine learning. An important aspect of machine learning is function approximation. In the context of massive data, some of the commonly used tools for this purpose are sparsity, divide-and-conquer, and distributed learning. In this paper, we develop a very general theory of approximation by networks, which we have called eignets, to achieve loc...
Posted 5 months ago
Physics Maths Engineering
This article explores the application of a new portfolio optimization approach called Mean-ETL (Mean-Expected Tail Loss). This method combines traditional mean return and the risk measure of expected tail loss to create more balanced portfolios that account for both returns and risks, particularly in the context of financial markets.
The study demonstrates the practical implementation of Mean-E...
Posted 5 months ago
This article investigates the formation and elimination of dendritic spines—small protrusions on neurons that facilitate synaptic connections.
The authors employ a mathematical model based on the Ricker population model, commonly used in ecology to describe population dynamics. This model incorporates "immigration" through filopodia-type transient spines, suggesting that these transient s...
Posted 5 months ago
