New methods correct spectral distortions using known analyte concentrations.
problem Distorted spectral shapes from absorbing and scattering contributions.
method Modified penalized baseline correction methods that incorporate known analyte concentrations.
result Improved prediction performance on near infra-red data sets.
Proves smooth critical points of Möbius energy are analytic.
problem Analyticity of critical points of Möbius energy.
method Cauchy's method of majorants and gradient decomposition.
result Smooth critical points of Möbius energy are analytic.
Improved neural network predicts spectral functions more accurately than traditional methods.
problem Reconstructing real-time spectral functions from imaginary-time Green's functions is ill-posed and challenging.
method Feature Learning Network (FL-net) for enhanced prediction accuracy.
result FL-net achieves at least 20% improvement over traditional methods like MEM.
The paper defines wave-front singularities using explicit analytic functions.
problem Characterizing the images of wave-front singularities.
method Explicit resultant computations to construct main-analytic functions.
result Explicit formulas for main-analytic functions of wave-front singularities of types A, D, and E.
Proves time analyticity for heat and Navier-Stokes equations without decaying conditions.
problem Analyticity of solutions to heat and Navier-Stokes equations without decaying conditions.
method Real variable method and algebraic manipulation of integral kernels.
result First general pointwise time analyticity result for all dimensions.
Efficient semi-analytic methods for pricing double barrier options with time-dependent parameters.
problem Pricing and calibration of double barrier options with time-dependent parameters.
method Two approaches: General Integral transform method and Heat Potential method.
result Semi-analytic techniques are more efficient for pricing double barrier options than traditional numerical methods.
A new method for non-rigid point set registration reduces computational complexity.
problem Efficiently registering non-rigid point sets with large numbers of points.
method Structured Analytic Coherent Point Drift (Analytic-CPD) reformulates CPD for structured analytic mappings.
result Analytic-CPD reduces computational complexity by controlling the deformation model's dimensionality.
Survey visual analytics methods for detecting anomalous user behaviors.
problem Understanding and detecting anomalous user behaviors in various domains.
method Survey and classification of visual analytics methods in four categories.
result Discussion of findings and potential research directions.
Develops a semi-analytic method for auto-callable accrual notes valuation.
problem Valuation of auto-callable structures with accrual features subject to barrier conditions.
method Extends recent studies of multi-assessed binaries to time-dependent parameters, using a semi-analytic approach.
result The semi-analytic approach is more advantageous for high precision valuation compared to Monte Carlo methods.
Analyzes log canonical pairs using harmonic integrals and dbar-equation theory.
problem Establishing an analytic proof of the injectivity theorem for log canonical pairs.
method Theory of harmonic integrals and L2-method for dbar-equation.
result Analytic proof of the injectivity theorem for purely log terminal pairs.
Analyticity of critical points for O'Hara's knot energies proved.
problem Analyzing the regularity of critical points for O'Hara's knot energies.
method Cauchy's method of majorants and a Möbius energy-inspired gradient decomposition.
result Smooth critical points of O'Hara's knot energies are analytic.
The paper explores bond pricing in short rate models using numerical and analytical methods.
problem Bond pricing in short rate convergence models of interest rates.
method Numerical and analytical methods for obtaining approximate solutions to partial differential equations.
result Approximations of bond prices in short rate convergence models.
The paper generalizes a key theorem in complex geometry.
problem Complex geometry theorems and their generalizations.
method Analytical methods
result Generalization of the Kodaira embedding theorem
Visual system compares and evaluates machine learning models for clinical data predictions.
problem Challenges in comparing and evaluating different machine learning models for medical predictions.
method Developed a visual analytics system to compare and evaluate multiple models' prediction criteria and consistency.
result Demonstrated the effectiveness of the visual analytics system in assisting clinicians and researchers.
Survey of complex analytic methods in minimal surface theory.
problem Global theory of minimal surfaces in Euclidean spaces.
method Complex analytic methods including Oka theory, holomorphic sprays, and Riemann-Hilbert boundary value problem.
result New constructions and results on minimal surfaces in various contexts.
Analyzes pricing methods for American and Asian options.
problem Pricing American and Asian options accurately.
method Analytic and empirical methods based on Muldowney's theory.
result Empirical method for Asian options pricing.
Analyzes Saito vanishing theorem using L2 methods.
problem Proving the Saito vanishing theorem.
method Uses L2-methods to prove the theorem. result Analytic proof of the Saito vanishing theorem.
In this survey we review some results concerning negatively curved exotic strucutres (DIFF and PL) and its (unexpected) implications on the limitations of some analytic methods in geometry. This article is dedicated to the memory of Armand Borel.
New methods map circular discs to squares smoothly and invertibly.
problem Mapping circular discs to squares while maintaining desirable properties.
method Analytical expressions for smooth, invertible mappings with specific properties.
result Presented new mappings with conformal, equiareal, and radially-constrained properties.
We perform the first study of the tradeoff space of access methods and replication to support statistical analytics using first-order methods executed in the main memory of a Non-Uniform Memory Access (NUMA) machine. Statistical analytics systems differ from conventional SQL-analytics in the amount and types of memory …
It is shown that any irreducible analytic 1-flat G-structure as well as any analytic torsion-free affine connection with irreducibly acting holonomy group can, in principle, be contstructed by twistor methods.
Visual analytics tool detects and corrects concept drift in data streams.
problem Concept drift causes inaccurate predictions in evolving data.
method DriftVis combines drift detection and visualization.
result Visual analytics supports detection, examination, and correction of concept drift.
Surveying future location and trajectory prediction methods for moving objects.
problem Growth of positioning technologies produces large tracking datasets.
method Extensive review of 50 works on predictive analytics for moving objects.
result Proposes a novel taxonomy of predictive algorithms.
A new method uses vector embeddings to improve analytics model performance.
problem Challenges in selecting high-quality datasets for enhanced analytics performance.
method Transform datasets into vector embeddings using NumTabData2Vec, then use similarity search for model inference.
result The proposed method accurately predicts analytics outcomes and increases speedup.
Develops a method to discriminate between competing models using Gaussian process surrogates.
problem Discriminating between competing models when data is insufficient and models are non-analytical.
method Introduces Gaussian process surrogates to extend design of experiments methods to non-analytical models.
result Extends design of experiments methods to non-analytical models in a computationally efficient manner.
In this paper we present qualitative and quantitative comparison of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of the American put option paying zero dividends. First we analyze their asymptotic behavior close to expiration. In the second part of the…
New method improves safety analytics by addressing imbalanced data issues.
problem Imbalanced safety datasets lead to inaccurate predictions and management problems.
method Extended accident triangle theory and three oversampling methods.
result Robust improvements in machine learning algorithms for safety analytics.
This paper reviews marketing analytics from multiple fields.
problem Understanding marketing analytics from various academic and practical backgrounds.
method Historical overview and practical implementation advice.
result Emphasizes interdisciplinary collaboration in marketing analytics.
Proposes efficient Bayesian logistic regression for large sparse datasets.
problem Infeasibility of theoretical Bayesian methods for large sparse feature sets.
method Low complexity analytical approximations for sparse online logistic and probit regressions.
result Empirical results show superior performance compared to more complex methods.
Efficiently augments triplet data for better data analytics.
problem Lack of direct pairwise distance information for data analysis.
method Triplets augmentation to infer hidden information from existing data.
result Improves quality of kernel-based and kernel-free data analytics.
Study extends holomorphic forms on noncompact Kahler manifolds.
problem Extension of holomorphic canonical forms on noncompact Kahler manifolds.
method L2 analytic methods and L2 Hodge theory.
result Generalizes classical results to noncompact cases.
Functional-analytic method for stochastic parallel transport in bundles.
problem Stochastic parallel transport in Hermitian bundles over Riemannian manifolds.
method Purely functional-analytic construction.
result Obtained a general Feynman-Kac formula in vector bundles.
The paper defines functions that induce bounded composition operators on RKHSs with analytic positive definite functions.
problem Characterizing functions that induce bounded composition operators on RKHSs.
method Intrinsic properties of RKHSs and asymptotic properties of orthogonal polynomials.
result Only affine transforms can induce bounded composition operators in a large class of RKHSs.
FASTER platform improves public transport commuter experience with analytics.
problem Operational challenges in urban public transport systems.
method Multi-sensor fusion, prediction, and optimization techniques.
result Improved commuter experience through fine-grained situational awareness and real-time decision support.
Using Chebyshev polynomials combined with some mild combinatorics, we provide a new formula for the analytical planar limit of a random matrix model with a one-cut potential V. For potentials V(x)=x2/2−∑n≥1anxn/n, as a power series in all an, the formal Taylor expansion of the analytic planar …
Analytical formula and Newton's method compared for nonlinear Black-Scholes equations.
problem Solving nonlinear Black-Scholes parabolic equations with market illiquidity and risk factors.
method Comparison of analytical approximation formula and Newton's method.
result Accuracy and time complexity of both methods compared using market data.
Analytical method finds deeper optima in two-layer ReLU networks.
problem Training two-layer ReLU networks with analytical methods.
method Analytically finding critical points of the loss function for one layer while keeping the other fixed.
result Significantly smaller training loss values on real datasets compared to gradient descent methods.
Proves real analyticity on surfaces based on restrictions.
problem Determining analyticity on non-continuous functions on manifolds.
method Analyzes restrictions to submanifolds homeomorphic to 2-sphere.
result Analyticity on manifold follows from analytic restrictions.
A new method solves SABR and Heston equations for option pricing.
problem Solving SABR and Heston equations for option pricing.
method Semi-analytical method based on path integrals, integrating analytically one set and numerically the other using Monte-Carlo.
result Compact expressions for correlated stochastic variables, efficient for Vanilla and Asian options.
Real analytic submersion images are always real analytic.
problem Analyticity of submersion images
method Analyticity proof for Riemannian submersions
result Image of real analytic submersion is real analytic
Chebyshev polynomials improve DEM analysis and generalization.
problem Improving accuracy and efficiency of digital terrain models.
method Spectral analysis using Chebyshev polynomials for DEM treatment.
result Effective in denoising, generalizing, and computing morphometric variables.
The delta invariant of curves on rational surfaces is calculated using embedded topological and analytic methods.
problem Calculating the delta invariant of curves on rational surfaces.
method Embedded topological and analytic approaches.
result The delta invariant can be recovered with a concrete expression associated with the embedded topological type of the pair (X,C).
In this work, we have presented a simple analytical approximation scheme for generic non-linear FBSDEs. By treating the interested system as the linear decoupled FBSDE perturbed with non-linear generator and feedback terms, we have shown that it is possible to carry out a recursive approximation to an arbitrarily highe…
Stochastic volatility (SV) and local stochastic volatility (LSV) processes can be used to model the evolution of various financial variables such as FX rates, stock prices, and so on. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such processes. Many issues remain, thou…
Study index theory on Lie group homogeneous spaces using topological and analytic methods.
problem Index theory on homogeneous spaces of Lie groups.
method Topological and analytic approaches: Riemann-Roch formula and heat kernel methods.
result Local index formula representing higher indices of equivariant elliptic operators.
Review of Gerber-Shiu function for practical actuarial science.
problem Difficulty in numerical approximation and statistical inference of Gerber-Shiu function.
method Comprehensive review of formulations, surplus processes, numerical methods, and statistical inference.
result Enhanced understanding and practical guide for Gerber-Shiu function.
Heat flow method proves existence of harmonic maps.
problem Analyzing harmonic maps from surfaces coupled to potentials.
method Heat flow method
result Existence of critical points in string theory.
We develop analytical methods for nonlinear Dirac equations. Examples of such equations include Dirac-harmonic maps with curvature term and the equations describing the generalized Weierstrass representation of surfaces in three-manifolds. We provide the key analytical steps, i.e., small energy regularity and removable…