Problem definition: A key challenge in supervised learning is data scarcity, which can cause prediction models to overfit to the training data and perform poorly out of sample. A contemporary approach to combat overfitting is offered by distributionally robust problem formulations that consider all data-generating distributions close to the empirical distribution derived from historical samples, where “closeness” is determined by the Wasserstein distance. Although such formulations show significant promise in prediction tasks where all input features are continuous, they scale exponentially when discrete features are present. Methodology/results: We demonstrate that distributionally robust mixed-feature classification and regression problems can indeed be solved in polynomial time. Our proof relies on classical ellipsoid method-based solution schemes that do not scale well in practice. To overcome this limitation, we develop a practically efficient (yet, in the worst case, exponential-time) cutting-plane-based algorithm that admits a polynomial-time separation oracle, despite the presence of exponentially many constraints. We compare our method against alternative techniques both theoretically and empirically on standard benchmark instances. Managerial implications: Data-driven operations management problems often involve prediction models with discrete features. We develop and analyze distributionally robust prediction models that faithfully account for the presence of discrete features, and we demonstrate that our models can significantly outperform existing methods that are agnostic to the presence of discrete features both theoretically and on standard benchmark instances. Funding: This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) [Grant EP/W003317/1]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0738 .

Abstract This paper investigates a cognitive consumer-resource model incorporating memory-dependent perception dynamics, modeled through a reaction-diffusion-advection system. We rigorously demonstrate the global existence and boundedness of classical solutions in spatial dimensions $ n \le 3 $ for arbitrary parameter values. For $ n > 3 $, solutions remain globally bounded under sufficiently small values of the perceptual sensitivity parameter $ \chi $. By employing Lyapunov functionals and parabolic regularity theory, we prove the global asymptotic stability of two equilibria: the constant coexistence steady state and the consumer-free constant steady state. For the constant coexistence steady state, solutions demonstrate exponential convergence under spectral gap constraints, whereas the consumer-free constant steady state exhibits algebraic decay. The analysis highlights how memory-driven taxis, mediated by $ \chi $, critically regulate system dynamics. This work bridges cognitive mechanisms and ecological models, providing explicit quantitative thresholds for stability in spatially structured environments.

Abstract In this paper, using the ensemble-averaged theory, we define the thermodynamic free energy of Einstein-Gauss-Bonnet (EGB) black holes in anti-de Sitter (AdS) spacetime. This approach derives the gravitational partition function by incorporating non-saddle geometries besides the classical solutions. Unlike the sharp transition points seen in free energy calculated via saddle-point approximation, the ensemble-averaged free energy plotted against temperature shows a smoother behavior, suggesting that black hole phase transitions may be viewed as a small-$G_N$ (Newton’s gravitational constant) limit of the ensemble theory. This is similar to the behavior of black hole solutions in Einstein’s gravity theory in AdS spacetime. We have obtained an expression for the quantum-corrected free energy for EGB-AdS black holes, and in the six-dimensional case, we observe a well-defined local minimum after the transition temperature which was absent in the earlier analysis of the classical free energy landscape. Furthermore, we expand the ensemble-averaged free energy in powers of $G_N$ to identify non-classical contributions. Our findings indicate that the similarities in the thermodynamic behavior between five-dimensional EGB-AdS and Reissner-Nordström-AdS (RN-AdS) black holes, as well as between six-dimensional EGB-AdS and Schwarzschild-AdS black holes, extend beyond the classical regime.

ABSTRACT This paper is devoted to the study of the asymptotic dynamics in the fractional parabolic‐elliptic Keller‐Segel system on with time‐space dependent logistic source. In [36], among others, we established a theory on the global existence, uniqueness, pointwise and uniform persistence of classical solutions to this fractional Keller‐Segel system. In this paper, we prove the existence, uniqueness, and stability of strictly positive entire solutions of this system. In summary, the results of our paper extend some of the results obtained earlier in [36].

In a half-space, for hyperbolic equations with translation operators in lower-order derivatives acting in all coordinate directions, a multiparameter family of solutions is constructed in explicit form using integral transforms. A theorem is proved stating that the obtained solutions are classical provided that the real part of the symbol of the differential–difference operator is positive.

This paper deals with the global boundedness of a classical solution to a chemotaxis-consumption model with signal-dependent sensitivity. Specifically, this paper focuses on studying the existence and boundedness of a classical solution in the absence of a logistic source term when n = 2 n=2 and the chemotaxis sensitivity function χ ( v ) = χ v k ( 1 ≤ k ≤ 2 ) \chi (v)=\chi v^{k} (1\leq k\leq 2) . Due to the absence of the logistic source term, obtaining the necessary gradient estimates for global existence seems difficult because of the strongly coupled structure. To this end, we propose new energy functionals to address this difficulty.

A bstract We consider general k = −1 FLRW covariant quantum spacetimes $$ {\mathcal{M}}^{3,1}\times \mathcal{K} $$ M 3 , 1 × K with fuzzy extra dimensions $$ \mathcal{K} $$ K as classical solutions of the IKKT matrix model. The coupled equations of motion are recast in terms of conservation laws, which allow to determine the evolution of spacetime in a transparent way. We show that $$ \mathcal{K} $$ K is stabilized as a classical solution in the presence of a large R charge, corresponding to internal angular momentum. This provides a mechanism to maintain a large hierarchy between UV and IR scales. We also argue that the evolution of spacetime is determined by a balance between classical and quantum effects, leading to a cosmic scale factor a ( t ) ~ t and constant dilaton at late times. On such a background, the undeformed IKKT model leads to a higher-spin gauge theory including gravity.

In this paper, we consider the following chemotaxis system with signal-dependent motility and indirect signal consumption: { u t = Δ ( D ( u ) ϕ ( v ) ) + ρu ( 1 − u l − 1 ) , ( x , t ) ∈ Ω × ( 0 , ∞ ) , v t = Δ v − vw , ( x , t ) ∈ Ω × ( 0 , ∞ ) , w t = − δw + u , ( x , t ) ∈ Ω × ( 0 , ∞ ) , under the smooth bounded domain Ω ⊂ R 2 with homogeneous Neumann boundary conditions, where the nonlinearities D ( u ) = ( u + 1 ) m with m>0 and the motility function ϕ satisfies the condition: ϕ ∈ C 3 ( ( 0 , ∞ ) ) is positive on [ 0 , ∞ ) . It is proved that the system possesses a unique global classical solution that is uniformly bounded. Moreover, if 0 $ ]]> ρ > 0 , the asymptotic behavior of the solution is discussed.

Orthotropic materials are increasingly employed in advanced thermal systems due to their direction-dependent heat transfer characteristics. Accurate numerical modeling of heat conduction in such media remains challenging, particularly for 3D geometries with nonlinear boundary conditions and internal heat generation. In this study, conventional boundary element method (BEM) and isogeometric boundary element method (IGABEM) formulations are developed and compared for steady-state orthotropic heat conduction problems. A coordinate transformation is adopted to map the anisotropic governing equation onto an equivalent isotropic form, enabling the use of classical Laplace fundamental solutions. Volumetric heat generation is incorporated via the radial integration method (RIM), preserving the boundary-only discretization, while nonlinear Robin boundary conditions are treated using variable condensation and a Newton–Raphson iterative scheme. The performance of both methods is evaluated using a hollow ellipsoidal benchmark problem with available analytical solutions. The results demonstrate that IGABEM provides higher accuracy and smoother convergence than conventional BEM, particularly for higher-order discretizations, which is owing to its exact geometric representation and higher continuity. Although IGABEM involves additional computational overhead due to NURBS evaluations, both methods exhibit similar quadratic scaling with respect to the degrees of freedom.

Abstract This study presents a nonlinear thermo‐mechanical framework for analyzing stress and deformation in shaft‐mounted rotating disks made of transversely isotropic materials with radially graded density. The model incorporates the combined effects of centrifugal forces, external radial traction, axial constraint, and a steady‐state thermal gradient. Utilizing Seth's transition theory, closed‐form analytical solutions are derived for radial displacement, radial stress, and hoop stress under axisymmetric conditions. The formulation is validated against classical isotropic solutions and finite element simulations, showing excellent agreement with deviations below 2%. Parametric studies reveal that positive density gradation (e.g., m = 2) reduces peak hoop stress by ∼14% and radial displacement by ∼12%, while negative gradation (e.g., m = −0.5) increases them by ∼9% and ∼8%, respectively. Axial loading significantly amplifies stress concentrations, particularly at the bore, and thermal gradients further elevate stress levels and advance the onset of yielding. It is conclusively shown that yielding initiates at the inner bore, with the critical angular velocity reduced by ∼15% under combined thermo‐mechanical loading. The proposed analytical model provides a robust tool for the design and optimization of advanced rotating components in aerospace, energy storage, and hydromechatronic systems.

Coupling micro-flow liquid chromatography with Q-Orbitrap high-resolution mass spectrometry for greener, comprehensive pesticide residue analysis in fruits and vegetables.

ABSTRACT As more individuals use public cloud networks for data storage and handling, providing the security, integrity, and confidentiality of private data becomes essential. Classical encryption solutions are unable to address the growing threats and large‐scale data processing required in such environments. Therefore, a Blockchain‐Based Framework for Secure Cloud Data Encryption Using Heterogeneous Bi‐Directional Recurrent Neural Network (BCF‐SCDE‐HBDRNN) is proposed in this paper. The input data is gathered from the IDS 2018 Intrusion CSVs Dataset. Initially, the data is encrypted using the Martino Homomorphic Encryption Algorithm (MHEA) for data security. The data is then secured using the Fair Proof‐of‐Reputation Consensus Algorithm (FPoR) based on blockchain technology for secure data storage. A Multi‐Agent Cubature Kalman Optimizer (MACKO) is employed for optimal key management. Finally, Heterogeneous Bi‐Directional Recurrent Neural Networks (HBDRNN) are used for threat detection such as normal and attack. Experimental evaluation demonstrates that the proposed framework enhances encryption efficiency, strengthens key management, and provides highly reliable threat detection compared to existing methods. The overall results highlight the framework's effectiveness as a robust and scalable solution for secure cloud data protection.

Time periodicity of global classical solution to radially symmetric unsteady flows with nonzero angular velocity in an annulus

A quantization of Lie–Poisson algebras is studied. Classical solutions of the mass-deformed Ishibashi–Kawai–Kitazawa–Tsuchiya matrix model can be constructed from semisimple Lie algebras whose dimension matches the number of matrices in the model. We consider the geometry described by the classical solutions of the Lie algebras in the limit where the mass vanishes and the matrix size tends to infinity. Lie–Poisson varieties are regarded as such geometric objects. We provide a quantization called “weak matrix regularization” of Lie–Poisson algebras (linear Poisson algebras) on the algebraic varieties defined by their Casimir polynomials. This quantization is a generalization of matrix regularization, and neither faithfulness of the map nor the correspondence between integration and trace in the commutative limit is required. Casimir polynomials correspond with Casimir operators of the Lie algebra by the quantization. This quantization is a generalization of the method for constructing the fuzzy sphere. In order to define the weak matrix regularization of the quotient space by the ideal generated by the Casimir polynomials, we take a fixed reduced Gröbner basis of the ideal. The Gröbner basis determines remainders of polynomials. The operation of replacing these remainders with representation matrices of a Lie algebra roughly corresponds to a weak matrix regularization. As concrete examples, we construct weak matrix regularization for su(2) and su(3). In the case of su(3), we not only construct weak matrix regularization for the quadratic Casimir polynomial, but also construct weak matrix regularization for the cubic Casimir polynomial.

We investigate solvent-mediated nucleation and crystallization of poly(ethylene terephthalate) (PET) from trifluoroacetic acid (TFA) solutions upon gradual addition of water, a poor solvent for PET. The system undergoes liquid–liquid phase separation, formation of PET-rich domains, and growth of nanoparticles, interpreted within classical nucleation theory and polymer solution thermodynamics, where solvent composition controls the balance between bulk free-energy gain and interfacial free-energy cost. On this conventional basis, we introduce a strictly heuristic analogy between surface-energy-dominated PET nucleation and entropy–area concepts from black-hole thermodynamics. In this view, increasing water content drives the system from a homogeneous, high-entropy solution to an aggregated state and the PET–solution interface is used metaphorically as a “soft-matter event horizon” beyond which individual chain conformations become experimentally inaccessible. Inspired by Bekenstein’s area law, we explore a simple toy model in which an effective entropy-like measure is postulated to scale with aggregate surface area, without claiming experimental verification of entropy–area scaling in PET or literal applicability of gravitational bounds. Thus, the work provides an experimentally grounded study of PET nucleation, augmented by a cross-disciplinary, metaphorical framework for discussing boundary-dominated thermodynamics.

Abstract In the present paper, we consider the inverse problem for the polyharmonic heat equation, aiming to recover a space/time heat source F along with the temperature distribution u ⁢ ( x , t ) {u(x,t)} . The problem is governed by the higher-order heat equation ( ∂ t + ( - Δ ) l ) ⁢ u = F {(\partial_{t}+(-\Delta)^{l})u=F} in a finite cylindrical domain Ω × ( 0 , T ] {\Omega\times(0,T]} within the half-space ℝ d × [ 0 , + ∞ ) {\mathbb{R}^{d}\times[0,+\infty)} , where l , d ≥ 1 {l,d\geq 1} . This is done through utilizing the values of u and its normal derivatives up to order l - 1 {l-1} on a given lateral surface of the cylinder, as well as the initial value and time-averaged data (or time observation measurement) for space-dependent source and space-averaged data (energy/mass measurement) for time-dependent source. We determine that the integer k = [ d 4 ⁢ l ] + 2 {k=[\frac{d}{4l}]+2} is admissible for the required degree of data regularity. The well-posedness of the classical solution to the inverse problem are established by employing the method of series expansion in terms of eigenfunctions for the Dirichlet poly-Laplacian. Weyl-type eigenvalue inequalities play a key role in our derivations.

We analyze the physical properties of an analytical, nonsingular quantum-corrected black hole solution recently derived in a minisuperspace model for unimodular gravity under the assumption of unitarity in unimodular time. We show that the metric corrections compared to the classical Schwarzschild solutions only depend on a single new parameter, corresponding to a minimal radius where a black hole-white hole transition occurs. While these corrections substantially alter the structure of the spacetime near this minimal radius, they fall off rapidly toward infinity, and we show in various examples how physical properties of the exterior spacetime are very close to those of the Schwarzschild solution. We derive the maximal analytic extension of the initial solution, which corresponds to an infinite sequence of Kruskal spacetimes connected via black-to-white hole transitions, and compare with some other proposals for nonsingular black hole metrics. The metric violates the achronal averaged null energy condition, which indicates that we are capturing physics beyond the semiclassical approximation. Finally, we include some thoughts on how to go beyond the simple eternal black hole-white hole model presented here.

In an open bounded real interval, this manuscript studies the evolution system \begin{cases} u_{ttt}+\alpha u_{tt} = \big(\gamma(\Theta)u_{xt}\big)_x + \big(\hat{\gamma}(\Theta)u_x\big)_x, \\ \Theta_t = D\Theta_{xx} + \Gamma(\Theta)u_{xt}^2, \end{cases} which arises as a model for the generation of heat during propagation of acoustic waves in a standard linear solid. A statement in local existence and uniqueness of classical solutions is derived for arbitrary $D>0$ and $\alpha\ge0$, for sufficiently smooth $\gamma,\hat{\gamma}$ and $\Gamma$ with $\gamma>0,\hat{\gamma}>0$ and $\Gamma\ge0$ on $[0,\infty)$, and for all suitably regular initial data of arbitrary size.

This paper presents the design and development of a comprehensive standalone application for geotechnical engineering, built entirely using Python. Unlike conventional commercial platforms or numerical packages, the application focuses on providing transparent, reproducible, and analytically grounded tools for core geotechnical challenges. This article aims to present the topic in a straightforward and easy-to-understand manner. The application includes different independent modules that cover critical areas of soil and rock mechanics, foundation engineering, tunnel lining design, slope stability, and ground improvement. All modules are based on classical solutions, derived from principles such as Rankine’s and Coulomb’s earth pressure theories, Terzaghi’s bearing capacity equations, consolidation and elastic settlement theory, the Hoek–Brown rock failure criterion, etc. The software leverages Python’s scientific libraries for data operations, interpolation, plotting, regression, and features a graphical user interface (GUI) built by Tkinter for interactive input and visualization. By adopting a modular architecture, each analytical solution can be accessed, maintained, and extended independently, promoting both scalability and usability. The program has been validated against standard geotechnical design examples and empirical relationships, showing excellent agreement. It serves both educational and professional purposes.

Abstract We develop and apply the Batalin–Fradkin–Vilkovisky (BFV) formalism for the covariant quantization of generic off-diagonal solutions of the Einstein equations in general relativity (GR). In the classical regime, such nonholonomic configurations are formulated entirely within GR and are characterized by nonlinear symmetries of generating functions, running cosmological constants, integration functions, and effective matter sources. These constructions are further extended to quantum gravity (QG) models involving effective local Lorentz symmetry violations and anisotropic scaling, as realized in Hořva–Lifshitz (HL)-type theories. The classical geometric framework is formulated on Lorentz manifolds endowed with nonholonomic 2+2 and 3+1 splitting structures and subsequently generalized to quantum configurations determined by HL-type generating functions. The 2+2 dyadic splitting, incorporating connection distortions, provides a systematic method for constructing exact and parametric classical and quantum solutions described by generating functions and effective sources depending on all spacetime coordinates, physical constants, and anisotropic scaling or deformation parameters. The complementary 3+1 splitting allows for a consistent implementation of the BFV quantization procedure. We demonstrate the renormalizability of off-diagonal quantum HL-type deformations of GR. The resulting classical and quantum nonholonomic BFV models represent viable candidates for asymptotically free theories of gravity and may provide a mechanism for resolving unitarity issues in QG. In appropriate classical limits, the framework reproduces physically relevant off-diagonal GR solutions with or without locally anisotropic scaling, offering potential applications to nonlinear classical and quantum phenomena in accelerating cosmology and dark energy and dark matter physics.