Mathematics, Volume 14, Issue 16

Physics-informed neural networks (PINNs) approximate partial differential equations (PDEs) by enforcing governing equations and boundary conditions during training, but their accuracy depends on how collocation points are distributed and updated. We...

We consider the classical one-dimensional focusing nonlinear Schrödinger equation (NLS). We give a brief overview of the techniques used to solve it since its formulation. Then we present various results obtained by the author in recent years. F...

The Hyperbolic Sombor index $HSO\left(G\right)$ of a graph $G=\left(V\right(G),E(G\left)\right)$ is proposed as a new vertex-degree-based topological index. In this paper, we investigate the mathematical properties of this novel vertex-degree-based topological index for general graphs....

Outpatient care facilities combine high patient turnover, repeated short contacts, accompanying persons, clinically vulnerable subgroups, and healthcare-worker movement across functional zones. This study develops a synthetic dynamic contact-network...

Estimating conditional average treatment effects (CATEs) in high-dimensional causal inference problems remains challenging because complex nonlinear relationships, heterogeneous feature distributions, and dependence among covariates can limit the eff...

The classical Ingleton inequality is known to hold for entropic points under specific exact conditional independence constraints. Recently, Matveev and Romashchenko (2026) investigated the stability of these implications, quantifying the extent to wh...

Testing multinormality in two-level structural equation models (SEMs) presents a fundamental challenge because observations from the same level-2 unit are correlated, violating the independence assumption required by classical normality tests. In thi...

This paper studies how hidden, stochastic continuation of informed participation shapes price discovery in a two-period Kyle-type market. Hidden participation separates two analytical questions that coincide in the standard Gaussian-linear model. Con...

Uniform algorithmic stability is a classical route to non-vacuous generalization bounds, yet existing analyses typically track the forward optimization trajectory on adjacent training sets. This paper develops a different construction of the same sta...

Multi-modal image fusion integrates complementary information from different modalities to generate a unified representation that is informative for human perception and beneficial to downstream vision tasks. However, existing methods often inefficie...

This study applies a prespecified dynamic MFDFA workflow across pandemic, geopolitical-conflict, and tariff-policy regimes for ten non-stable, long-history cryptoassets selected ex post from the 23 July 2026 market-cap ranking. The common sample comp...

As the market of perishable goods in China continues to expand, reducing quality loss during transportation has become an urgent issue for the industry. Multimodal transport, as a key approach to optimizing the transportation structure and lowering l...

This paper studies codimension-one transverse bifurcations of several classes of simple robust homoclinic cycles in group-symmetric systems on ${\mathbb{R}}^5$. The analysis follows a complete classification induced by the representation of the symmetric group. Su...

Innovation can strengthen industrial resilience, but in interconnected networks, it may also create financial fragility. This paper develops a coupled nonlinear multiplex-network model in which financial distress and effective knowledge evolve on ris...

This paper develops a stylized continuous-time framework for open-end fund investment in which state-dependent fund flows, passive benchmarking, and strategic manager–investor interaction are modeled jointly. The contribution is not a new Stack...

The Grey Wolf Optimizer (GWO) is a popular metaheuristic, yet it often suffers from premature convergence and rapid diversity loss in complex, high-dimensional, or highly constrained optimization problems. This paper introduces HAGWO, a novel Hierarc...

Nonlinear mixed-effects models (NLMMs) provide a flexible framework for modeling repeated-measures trajectories. However, how best to forecast future observations, especially at ages well beyond those represented in the data, remains relatively under...

For national statistics offices (NSOs), data sharing is essential for the production of official statistics, yet it must comply with stringent confidentiality and governance mandates. Blockchain technology has emerged as a promising means to enable t...

The Anatolian Caracal Optimization Algorithm (ACOA), a swarm-based optimization approach inspired by nature, approximately describes the characteristic hunting strategy of the Anatolian caracal, shaped by its superior auditory–visual perception...

The study of graph connectedness is a central topic in graph theory, with $\mathcal{CF}$-connectedness being a specialized property of interest. A simple graph is $\mathcal{CF}$-connected if it is connected and, in each of its optimal drawings, any two of its distinct verti...

The Special Issue is focused on object detection and recognition, a central task in almost all applications of computer vision, showing the capability of novel mathematical algorithms, architectures and methods to improve the performance in this task...

Predicting molecular bioactivity in low-data regimes remains a central challenge in computational drug discovery, where labeled compounds for specialized tasks are scarce while related datasets are abundant. Here, we propose FerrGAT, a graph attentio...

To address challenges associated with high-dimensional coordination and strict physical constraints in fixed-base space manipulator tool transfer under zero gravity, this paper proposes a preference-conditioned safe reinforcement learning algorithm,...

Classical approaches often treat interaction as engineered product terms or as emergent patterns in flexible models, offering little control over how synergy or antagonism arises. We take a quantum-inspired view: following the Born rule (probability...

The study of galactic dynamics remains fragmented across three competing paradigms—Dark Matter ($\Lambda CDM$), Modified Newtonian Dynamics (MOND), and Yukawa-type modifications. This work relies on Enhanced Newtonian Dynamics (END), a parameter-...

To address dimensional reduction for continuous single-label and multi-label data, this paper proposes an improved variable precision rough set method based on maximal consistent blocks. We formulate dimensional reduction as an attribute reduction pr...

In this paper, we consider the groups of linear operators that preserve idempotent matrices over the binary Boolean algebra. We prove that this set forms an automorphism group under composition and determine its exact algebraic structure as a direct...

Let $\Gamma$ be a graph of order n with m edges, and let $A_{ag}(\Gamma )$ denote its arithmetic–geometric matrix. The eigenvalues of $A_{ag}(\Gamma )$ are referred to as the arithmetic–geometric eigenvalues of $\Gamma$. The sum of the absolute value...

This paper investigates the controller design problem for switched systems with input delays. A predictor-based switched controller is proposed to compensate for the effect of input delays. By introducing an appropriate transformation, the switched s...

This paper presents a numerical method for solving transient one-dimensional heat conduction problems in multilayer slabs with temperature-dependent thermal conductivities. The governing nonlinear partial differential equations are formulated separat...

Using reliability assessment methods to calculate failure probability for a product is of vital importance in the design process of the product. The active learning reliability method combining Kriging and Monte Carlo simulation (AK-MCS) is a famous...

This paper studies short-horizon trajectory forecasting through a coordinate-conditioned multiscale architecture, termed AeroMixer. The framework combines segment-wise local Cartesian re-representation, multiscale decomposition, bidirectional trend m...

Human surveys in a variety of disciplines experience challenges such as social desirability bias, confidentiality distrust by the respondents, and errors in measurement. All these factors may significantly reduce the quality of the data. To handle th...

In this paper, a controlled Picard semi-analytical technique is improved for a branch of nonlinear fractional stochastic delay differential equations since the nonlinear terms always prevent the establishment of closed-form solutions. The proposed ap...

Recently, multi-view learning techniques based on non-negative matrix factorization (NMF) have demonstrated remarkable efficacy in clustering multi-source data. However, existing methods often overlook the intrinsic similarity between views, and conv...

This paper investigates the energy-efficient hybrid flow shop scheduling problem considering deteriorating maintenance and transportation times (EHFSP-DMT), which is an NP-hard combinatorial optimization problem in complex manufacturing systems. To f...

This study investigates the fixed-time quasi-consensus and quasi-containment control for multi-agent systems (MASs) under non-periodic unknown denial-of-service (DoS) attacks. Most available strategies fail to construct fixed-time observers and feasi...

Constructing scalable, non-degenerate, and intensity-tunable high-dimensional hyperchaotic maps is a key challenge for chaotic cryptography. Existing n-dimensional real-valued chaotic systems frequently suffer from dynamical degradation, limited adju...

This paper addresses the finite-time global Mittag-Leffler projective synchronization problem for a class of uncertain fractional-order delayed neural networks with heterogeneous fractional orders, parameter uncertainties, and multiple time delays. A...

Graph-based nonnegative matrix factorization (GNMF) has been widely used for dimensionality reduction and data clustering because it can preserve the intrinsic geometric structure of data. However, many existing GNMF-based methods still rely on full...

This paper develops a pointwise distributional theory for linear wavelet density and regression estimation from randomly right-censored observations exhibiting stationary ergodic dependence. In contrast to the prevailing literature, which typically r...

Knowledge graph completion (KGC) commonly relies on embedding models trained with observed triples. Multi-hop paths provide additional evidence, but rule-derived triples differ in reliability and should not receive equal training weight. We study how...

This work examines a new methodology for the nonlinear electrohydrodynamic interfacial stability of dielectric viscoelastic liquids to enhance the predictive accuracy of microfluidic and biological applications. It tackles the intricacies of nonlinea...

Four-dimensional chaotic systems have garnered significant attention due to their complex nonlinear dynamics, high-dimensional complexity, and wide range of applications in science and engineering. This paper proposes and investigates a novel four-di...

Event-level segmentation of small-scale unmanned aerial vehicles (UAVs) is challenging because target-generated events are sparse and are easily mixed with background motion and sensor noise. This study extends EV-SpSegNet with Adaptive Temporal Real...

Interval censoring commonly arises in clinical trials, screening studies, and longitudinal medical investigations in which event status is assessed only at scheduled examination times. Rank-based procedures provide flexible tools for comparing interv...

Closed-loop regulation of the bispectral index (BIS) during propofol–remifentanil co-administration is challenging because of nonlinear drug interactions, patient variability, model uncertainty, external disturbances, and infusion constraints....

In this paper, we introduce a hybrid inertial algorithm for solving variational inequality problems and split common fixed point problems in real Hilbert spaces. The proposed method combines inertial and viscosity techniques within a unified framewor...

Transportation networks are subject to multiple sources of uncertainty, ranging from stochastic fluctuations in demand and travel times to epistemic indeterminacy in infrastructure condition, disruption risk, and user behavior. A diverse body of math...

We study an infinite-horizon consumption, portfolio, and job-choice problem in which an investor may move costlessly and reversibly among N income–leisure regimes. Job i provides constant labor income $Y_i$ and leisure $L_i$, with higher-income jobs...