Study on material inhomogeneity and strain compatibility in thin elastic shells.
problem Understanding material inhomogeneity and strain compatibility in thin elastic shells.
method Developed a relationship between inhomogeneity and incompatibility measures using both 3D and 2D theories, derived intrinsic dislocation density tensors, and formulated governing equations for residual stress fields.
result Explicit forms of intrinsic dislocation density tensors characterizing inhomogeneity of dislocated Cosserat shells and simplified governing equations for residual stress fields.
A geometrical interpretation of the G-structures associated to elastic material bodies is given. In addition, characterizations of their integrability are obtained. Since the lack of integrability is a geometrical measure of the lack of homogeneity, the corresponding inhomogeneity conditions are obtained
GPR enhances materials discovery by automating parameter space exploration.
problem Automating exploration of large, high-dimensional parameter spaces in materials science.
method Gaussian process regression with inhomogeneous measurement noise and anisotropic kernels.
result Importance and benefits of tuning GPR for materials science experiments.
Study of metric anomalies in uniform elastic solids without stress.
problem Understanding metric anomalies in uniform elastic solids.
method Introducing a quasi-plastic deformation framework and deriving a general form of metric anomalies.
result Derivation of a general form of metric anomalies yielding zero stress in uniform solids.
Study reconstructs Riemannian metric from Cherenkov radiation in complex media.
problem Reconstructing internal geometry of inhomogeneous anisotropic targets.
method Mathematical model of waves in medium, including vector-valued wave operator and phase velocity.
result Riemannian metric inside a bounded region can be reconstructed from boundary measurements of Cherenkov radiation.
Study magnetic field evolution in inhomogeneous axion stars.
problem Magnetic field evolution in axion stars with spatial inhomogeneity.
method Derived new induction equation for magnetic field, analyzed CS waves interactions, and considered compact domain effects.
result Spatial inhomogeneity of pseudoscalar field significantly affects magnetic field evolution.
Study shows deformations of quaternionic Kähler manifolds are locally inhomogeneous.
problem Understanding deformations of quaternionic Kähler manifolds.
method Proved one-loop deformation of quaternionic Kähler manifolds are locally inhomogeneous.
result Full isometry group of one-loop deformations has cohomogeneity one.
We introduce a new parameter to measure the inhomogeneity of training datasets.
problem The need for non-stationary models in supervised learning.
method We introduce a new parameter, the inhomogeneity parameter, to measure the inhomogeneity of training datasets.
result A training set with a non-zero inhomogeneity parameter requires a non-stationary model for accurate predictions.
Researchers describe a specific type of submanifolds in Euclidean space.
problem Understanding inhomogeneous almost symmetric submanifolds.
method Completely describing submanifolds as unions of parallel symmetric submanifolds.
result Described inhomogeneous properly embedded almost symmetric submanifolds as unions of symmetric submanifolds.
Sharp threshold found for Frechet mean of inhomogeneous graphs.
problem Finding the Frechet mean of inhomogeneous Erdos-Renyi random graphs.
method Thresholding the expected adjacency matrix of the ensemble.
result The Frechet mean graph of inhomogeneous Erdos-Renyi random graphs exhibits a sharp threshold.
We start by a review of the chronology of mathematical results on the Dirichlet-to-Neumann map which paved the way towards the physics of transformational acoustics. We then rederive the expression for the (anisotropic) density and bulk modulus appearing in the pressure wave equation written in the transformed coordina…
We construct examples of inhomogeneous isoparametric real hypersurfaces in complex hyperbolic spaces.
Develops time-inhomogeneous polynomial processes for better model calibration and seasonality capture.
problem Calibration to market prices and seasonality in term-structure models.
method Introduces time-inhomogeneous polynomial processes with time-dependent coefficients and characterizes them using semimartingale characteristics. Alternative numerical approximations using Magnus series are explored.
result Matrix exponentials are not sufficient for computing moments in time-inhomogeneous polynomial processes, necessitating alternative numerical methods.
The paper studies inhomogeneous isoparametric hypersurfaces in pseudo-spheres.
problem Investigating inhomogeneous isoparametric hypersurfaces in pseudo-sphere.
method Construction of Clifford systems and analysis of isoparametric hypersurfaces.
result Connected isoparametric hypersurfaces of OT-FKM-type in pseudo-spheres are inhomogeneous under specific conditions.
Paper examines floating exercise boundaries for American options in time-inhomogeneous models.
problem Floating exercise boundaries in time-inhomogeneous models with negative interest rates or yields.
method Semi-analytical approach for pricing American options.
result Specialized pricing methodologies are required for models with floating exercise boundaries.
Efficiently matches random graphs with inhomogeneous edge probabilities.
problem Matching latent vertex correspondence between two correlated random graphs with inhomogeneous edge probabilities.
method Inspired by Ding et al. (2021), an efficient matching algorithm is developed with conditions on minimal average degree and minimal correlation.
result An efficient matching algorithm is obtained as long as the minimal average degree is at least Ω(log2n) and the minimal correlation is at least 1−O(log−2n). Two families of curvature inhomogeneous manifolds with constant Ricci eigenvalues are constructed.
problem Constructing curvature inhomogeneous Riemannian manifolds with constant Ricci eigenvalues.
method Derived from Einstein warped products and Riemannian Schwarzschild--Tangherlini manifold.
result Admits local isometric immersions and isometric embeddings of minimum codimension.
Unique inhomogeneous ruled hypersurface found in complex hyperbolic space.
problem Classifying ruled real hypersurfaces with constant norm.
method Analyzing nonflat complex space forms, proving existence and uniqueness.
result Existence of a unique inhomogeneous example in complex hyperbolic space.
We construct explicit global symplectic coordinates for the Calabi's inhomogeneous Kaehler-Einstein metric on tubular domains.
New hypergraph clustering method assigns different costs to hyperedge cuts.
problem Hypergraph partitioning assumes uniform costs for different hyperedge cuts.
method Inhomogeneous hypergraph partitioning assigns different costs to different hyperedge cuts.
result Inhomogeneous partitioning offers significant performance improvements in various applications.
Study optimal algorithms for recovering signals through inhomogeneous low-rank channels.
problem Recovering signals through an inhomogeneous low-rank matrix channel.
method Derive and analyze an approximate message-passing algorithm (AMP) and a spectral method.
result The AMP iteration matches the conjectured optimal computational phase transition.
In this note, we propose Bernstein's problem and De Giorgi's conjecture for spatially inhomogeneous equations, as well as De Giorgi's conjecture for system of reaction-diffusion equations.
An extension of the ambient metric construction of Fefferman-Graham to infinite order in even dimensions is described. The main ingredients are the introduction of "inhomogeneous ambient metrics" with asymptotic expansions involving the logarithm of a defining function homogeneous of degree 2, and an invariant procedur…
Study of time-inhomogeneous affine processes in finance.
problem Understanding and modeling financial processes with time-varying parameters.
method Developed a theory for time-inhomogeneous affine processes and applied it to financial market models.
result Affine processes can be modified to include real-valued processes, improving model flexibility.
Unified method detects and localizes anomalous cliques in inhomogeneous networks.
problem Detect and localize anomalous cliques in inhomogeneous networks.
method Unified method based on egonets for detection and localization.
result Unified method can detect and localize anomalous cliques in inhomogeneous networks.
This paper generalizes Moody's correlated binomial default distribution for homogeneous (exchangeable) credit portfolio, which is introduced by Witt, to the case of inhomogeneous portfolios. As inhomogeneous portfolios, we consider two cases. In the first case, we treat a portfolio whose assets have uniform default cor…
We consider a heat kernel approach for the development of stochastic pricing kernels. The kernels are constructed by positive propagators, which are driven by time-inhomogeneous Markov processes. We multiply such a propagator with a positive, time-dependent and decreasing weight function, and integrate the product over…
Unified framework for non-uniform materials evolving over time.
problem Dealing with non-uniform materials evolving over time.
method Constructing a material groupoid and material distribution.
result Unified framework for general non-uniform evolution materials.
Optimal spectral method found for inhomogeneous spiked Wigner model.
problem Structured noise in learning scenarios.
method Random matrix theory and spectral analysis.
result Optimal threshold for phase transition in block-structured Wigner model.
We construct new complete, compact, inhomogeneous Einstein metrics on S^{m+2} sphere bundles over 2n-dimensional Einstein-Kahler spaces K_{2n}, for all n \ge 1 and all m \ge 1. We also obtain complete, compact, inhomogeneous Einstein metrics on warped products of S^m with S^2 bundles over K_{2n}, for m>1. Additionally,…
Study volatility models with rough paths, focusing on large deviations and option behavior.
problem Analyzing volatility in financial markets with very rough paths.
method Introduced time-inhomogeneous stochastic volatility models with Volterra Gaussian processes.
result Obtained large deviation principles for log-price processes in super rough Gaussian models.
Paper proposes a new method for designing materials using deep learning.
problem Designing high-performance material distributions from given distributions.
method Iterative process of selecting, generating, and merging material distributions using a deep generative model.
result The method improves material performance through iterative refinement.
New method constructs deformation groupoid for inhomogeneous pseudo-differential calculus.
problem Recovering inhomogeneous pseudo-differential calculus using a deformation groupoid.
method Elementary construction of deformation groupoid for Heisenberg calculus, then generalization to arbitrary filtrations.
result Elementary construction of deformation groupoid for inhomogeneous pseudo-differential calculus.
New material groupoid theory subdivides non-uniform bodies into smoothly uniform parts and isolated points.
problem Lack of differentiability in material bodies leads to non-uniformity.
method Introducing material groupoid and material distribution to study non-uniform bodies rigorously.
result Material bodies can be subdivided into smoothly uniform parts and isolated points.
Lie groupoids and algebroids help analyze material uniformity and homogeneity.
problem Analyzing uniformity and homogeneity of material bodies.
method Associated Lie groupoids and algebroids to elastic materials, using them to characterize uniformity and homogeneity.
result Characterized uniformity and homogeneity of materials using Lie groupoids and algebroids.
A new infinite series of Einstein metrics is constructed explicitly on S^2 x S^3, and the non-trivial S^3-bundle over S^2, containing infinite numbers of inhomogeneous ones. They appear as a certain limit of a nearly extreme 5-dimensional AdS Kerr black hole. In the special case, the metrics reduce to the homogeneous E…
We show how the relation between Poisson brackets and symplectic forms can be extended to the case of inhomogeneous multivector fields and inhomogeneous differential forms (or pseudodifferential forms). In particular we arrive at a notion which is a generalization of a symplectic structure and gives rise to higher Pois…
New adaptive clustering method detects local inhomogeneity.
problem Detecting clusters in data without specifying their structure.
method Adaptive Weights Clustering (AWC) method that grows locality parameter at each step.
result AWC method can recover clusters with sharp edges or manifold structure.
We provide representations of solutions to terminal value problems of inhomogeneous Black-Scholes equations and studied such general properties as min-max estimates, gradient estimates, monotonicity and convexity of the solutions with respect to the stock price variable, which are important for financial security prici…
DECT-MULTRA improves material decomposition in CT images.
problem Noise and artifacts degrade material images in DECT imaging.
method Combines PWLS estimation with MULTRA model for efficient clustering and sparse coding.
result Superior material image quality and decomposition accuracy compared to other methods.
Proposes a new graph trend filtering model for inhomogeneous graph signals.
problem Estimating piecewise smooth signals over a graph with varying smoothness levels.
method Introduces a l2,0 norm penalized Graph Trend Filtering (GTF) model and two solution methods: spectral decomposition and simulated annealing.
result The GTF model performs better than existing approaches in denoising, support recovery, and semi-supervised classification.
MatGAN uses GAN to efficiently generate new inorganic materials.
problem Efficiently searching the vast chemical design space for new materials.
method Generative adversarial network (GAN) trained on ICSD materials database.
result 92.53% novelty and 84.5% chemically valid samples generated.
A new test for IRG models using KSD for small networks.
problem Testing goodness-of-fit for inhomogeneous random graph models.
method Kernelised Stein Discrepancy (KSD) test for IRG models.
result The test is effective for small networks and provides theoretical guarantees.
Deep learning model reconstructs material microstructures from feature representations.
problem Reconstructing complex material microstructures accurately and efficiently.
method Convolutional deep belief network for automated feature learning and dimension reduction.
result Material reconstructions preserve microstructural features and material properties.
Study quantizes energy for a specific fourth-order system in 4D.
problem Energy quantization for a fourth-order inhomogeneous system in 4D.
method Establishes angular energy quantization for the given system.
result Angular energy quantization proven for the system.
This research provides theoretical guarantees for hyperparameter estimation in complex network dynamical systems.
problem Theoretical guarantees for hyperparameter estimation in large, inhomogeneous complex network dynamical systems.
method Formulating the system's evolution in a measure transport perspective, proposing a theoretical framework for estimating hyperparameters with mean-type observations.
result A nonasymptotic bound for the deviation of hyperparameter estimates in inhomogeneous complex network dynamical systems with respect to network population size.
Predicts fracture evolution and material failure in brittle materials.
problem Predicting how fractures propagate and materials fail in brittle materials.
method Recurrent graph convolutional neural networks trained on simulation data.
result Predictions within 3% for fracture damage and 15% for time to failure.
We construct uncountably many isoparametric families of hypersurfaces in Damek-Ricci spaces. We characterize those of them that have constant principal curvatures by means of the new concept of generalized Kahler angle. It follows that, in general, these examples are inhomogeneous and have nonconstant principal curvatu…