“Experimental results show that our EA4eigCS outperforms EA4eig and is competitive when compared with state-of-the-art algorithms.”

“The proposed approach leverages the analytical solution for linear vibration of system's modes so that physical parameters of a system remain easily accessible after the training without the need for a parameter encoder in the model architecture.”

“I wanted to review the definitions of specific operations, so I summarized them.”

“Since the quality of data-driven ROMs is sensitive to the quality of the limited training data, we seek to identify training parameters for which using the associated training data results in the best possible parametric ROM.”

““Chat was there for me, calm and rational, helping me strategize, always planning.” and “I see Chat like a last-year medical student: doesn't have a license, isn't…”,”

“The paper formulates the covariant hydrodynamics equations as an intersection problem on an infinite dimensional symplectic manifold associated with spacetime.”

“The PDE-ODI principle converts a broad class of parabolic differential equations into systems of ordinary differential inequalities.”

“The paper derives explicit expressions for the joint Laplace-Stieltjes transform, probability density function, and governing differential equations of the multivariate gamma subordinator.”

“The paper demonstrates that the most general inertial transformation which further preserves the speed of light in all directions is, however, still affine linear.”

“The paper shows that the generalization error of DGFMs tends to zero as the number of neurons and the training time tend to infinity.”

“The paper develops a general convergence analysis based on a reformulation of the operators by means of a fixed-point equation, providing a list of hypotheses related to the regularization properties of the equation and the convergence of the chosen approximation techniques on suitable subspaces.”

“The paper establishes a correspondence between solutions of the Liouville equation and the Weierstrass representations of spacelike and timelike minimal surfaces.”

“The paper determines the robust optimal growth rate, constructs a worst-case admissible model, and characterizes the robust growth-optimal strategy via a solution to a certain partial differential equation (PDE).”

“The article likely details the technical aspects of the framework, its implementation, and evaluation.”

“The article focuses on the mathematical analysis of a chemotaxis-Navier-Stokes system.”

“The paper introduces the phenomenon of role reversal in the Mpemba effect, wherein changes in the system parameters invert the relaxation ordering of a given pair of initial states.”

“The introduction of the 'Darboux family' as a tool for studying r-matrices in four-dimensional indecomposable coboundary Lie bialgebras.”

“The paper successfully examines a relationship between the thermal and magnetic properties of the ferromagnetic amorphous alloy under its non-linear deformation, using the critical exponents.”

“The paper focuses on modifying the damping and shifting schemes used in the original CFFT formulation to reduce boundary errors and improve accuracy and convergence.”

“The paper derives a third-order linear differential equation for the partition function, a key result.”

“Solutions are attracted toward the unique invariant probability measure at polynomial rates of arbitrary order.”

“The paper introduces a polarization differential loss (PDL) mechanism directly into the cladding architecture.”

“The paper aims to reproduce the differential mass distribution for the D*π system in B-decays and determine the D*π scattering length.”

“Backpropagation arises as the differential of a KL projection map on a delta-lifted factorization.”

“Virtual-Eyes improves RAD-DINO slice-level AUC from 0.576 to 0.610 and patient-level AUC from 0.646 to 0.683 (mean pooling) and from 0.619 to 0.735 (max pooling), with improved calibration (Brier score 0.188 to 0.112).”

“MedKGI improves dialogue efficiency by 30% on average while maintaining state-of-the-art accuracy.”

“The paper gives sufficient criteria that guarantee the integrability for the aforementioned generalized structures, formulated in terms of properties of the associated 2-form and connection.”

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“The paper derives least squares estimators for the drift, diffusion, and jump-diffusion coefficients and establishes their asymptotic rate of convergence.”

“The SPDE-based extensions improve both point and probabilistic forecasts relative to standard benchmarks.”

“High current density up to 800 A/cm$^2$, 5 orders of on/off ratio, and low differential on-resistance of 2.6 m$Ω\cdot$cm$^2$ at the highest current density is achieved.”

“Our approach relies on nonlinear analysis, topological methods, and the theory of strongly continuous semigroups, yielding results applicable to a wide range of models.”

“The paper proposes to leverage connections between proximal operators and Hamilton-Jacobi partial differential equations (HJ PDEs) to develop novel deep learning architectures for learning the prior.”

“The paper demonstrates competitive or state-of-the-art performance across a range of time-series benchmarks.”

“NeuroSPICE's flexibility enables the simulation of emerging devices, including highly nonlinear systems such as ferroelectric memories.”

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“The paper introduces the new flexible class of intrinsic Whittle--Matérn Gaussian random fields obtained as the solution to a stochastic partial differential equation (SPDE).”

“The paper establishes the small-time global approximate controllability of the system using three scalar controls, and then studies the small-time global exact controllability to non-zero constant states.”

“The paper introduces the notion of the essential convergence rate and justifies it by proving that, under appropriate assumptions on discretization, no method obtained by discretizing an ODE can achieve a faster rate than its essential convergence rate.”

“When the noise acts on the velocity, the rescaled dynamics produce an additional Laplacian damping term, leading to a stochastic derivation of a Westervelt-type acoustic model.”

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“The paper likely presents novel constructions or classifications within the realm of differential $\mathbb Z$-graded varieties.”

“Tube formation is studied versus temperature, revealing bilamellar layers retracting and folding into tubes upon DC15PC lipids transitioning from liquid to solid phase, which is explained by lipid transfer from bilamellar to unilamellar layers.”

“The paper shows that generalized normal operators are elliptic pseudodifferential operators of order -1.”

“The article's content is highly technical and requires a strong background in mathematics, specifically differential equations and complex analysis, to fully understand.”

“PI-MFM consistently outperforms purely data-driven counterparts, especially with sparse labeled spatiotemporal points, partially observed time domains, or few labeled function pairs.”

“The paper explains the appearance of singularities of dual curves and considers applications to the Clairaut differential equation.”

“The VIE approach is a valuable methodological scaffold: It addresses SC-HDM and simpler models, but can also be adapted to more advanced ones.”

“The paper analyzes the refined limiting profiles of the principal eigenpair (λ, φ) for (0.1) as α→∞, which display the visible effect of the large advection on (λ, φ).”

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