In this paper we study infinitesimal and finite flexibility for generic semidiscrete surfaces. We prove that generic 2-ribbon semidiscrete surfaces have one degree of infinitesimal and finite flexibility. In particular we write down a system of differential equations describing isometric deformations in the case of exi…
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48 results for “semidiscrete formulation”
This paper deals with the exact calibration of semidiscretized stochastic local volatility (SLV) models to their underlying semidiscretized local volatility (LV) models. Under an SLV model, it is common to approximate the fair value of European-style options by semidiscretizing the backward Kolmogorov equation using fi…
A new method for flow matching reduces computational costs and improves performance.
problem Efficiently matching flow models to target data distributions.
method Semidiscrete formulation of optimal transport (SD-OT) using SGD and maximum inner product search (MIPS).
result Semidiscrete FM (SD-FM) outperforms batch-OT and traditional flow matching methods.
New method approximates anisotropic curve shortening flow.
problem Approximating anisotropic curve shortening flow.
method Weak formulation and finite element approximation.
result Optimal -error bound for approximation.
A discrete method approximates hyperbolic curvature flow in the plane.
problem Modeling wave phenomena in solid-liquid interfaces.
method Semidiscrete finite difference method for hyperbolic curvature flow.
result Error bounds for natural discrete norms are proven.
Existence proved for -Bass martingales with specific marginals.
problem Constructing martingales with prescribed marginals close to a reference measure.
method Geometric analysis of parametrized convex polygonal chains.
result Existence and uniqueness of -Bass martingales with finitely supported initial marginals.
In this paper we investigate the effectiveness of Alternating Direction Implicit (ADI) time discretization schemes in the numerical solution of the three-dimensional Heston-Hull-White partial differential equation, which is semidiscretized by applying finite difference schemes on nonuniform spatial grids. We consider t…
In this article, we start to recall the inversion formula for the convolution with the Box spline. The equivariant cohomology and the equivariant K-theory with respect to a compact torus G of various spaces associated to a linear action of G in a vector space M can be both described using some vector spaces of distribu…
Efficient numerical valuation of European options under the two-asset Kou jump-diffusion modelmath.NA
The paper efficiently solves a complex option valuation equation for two assets.
problem Valuation of European options under a two-asset Kou jump-diffusion model.
method Extends an efficient algorithm for a one-dimensional integral to a two-dimensional one, using operator splitting schemes for time discretization.
result The method achieves optimal computational cost and stable convergence for various operator splitting schemes.
Optimal data-driven formulations are found for learning and decision-making with historical data.
problem Designing optimal learning and decision-making formulations from historical data.
method Define a yardstick for measuring formulation quality, then construct an optimal formulation that is uniformly closer to the true cost.
result Existence of three distinct out-of-sample performance regimes with corresponding optimal formulations.
A new DR formulation improves metric learning for faster and more stable performance.
problem Learning embeddings for class separation in metric learning.
method Distance-ratio (DR) formulation for metric learning.
result DR formulation achieves improved or comparable generalization performances.
New formulations for Ricci flows without smoothness.
problem Characterize Ricci flows without smooth solutions.
method Weak formulations of super Ricci flows with saturation condition.
result Generalized formulations for singular settings.
Paper proposes a QUBO formulation that reduces binary variables in Bayesian network learning.
problem Reducing the number of binary variables in QUBO formulations for Bayesian network learning.
method Proposes a new QUBO formulation that minimizes binary variables.
result Significantly reduces the number of binary variables required for Bayesian network structure learning.
Defines a metric and form for a bundle moduli space, leading to a zero-curvature formulation.
problem Formulating a metric and form for a bundle moduli space.
method Defines an algebraic metric and closed 3-form on a subspace of the moduli of -bundles.
result Shows a zero-curvature formulation for a -model with target the moduli space.
We study ranking quantilized mean-field games to select top-performing agents.
problem Selecting top-performing agents in competitive scenarios.
method Developed two formulations: target-based and threshold-based, and provided analytic and semi-explicit solutions.
result Analytic and semi-explicit solutions for quantilized mean-field consistency conditions.
New conic quadratic formulations improve outlier detection in regression models.
problem Detecting outliers in regression models with corrupted data.
method Deriving stronger second-order conic relaxations without big-M constraints.
result Proposed formulations are significantly faster than existing methods.
The paper develops mixed-integer formulations for neural networks using partitioning.
problem Optimizing trained ReLU neural networks with balanced model size and tightness.
method Partitioning node inputs into groups, forming the convex hull via disjunctive programming.
result The proposed formulations outperform existing ones, especially with fewer partitions.
Equivalent formulations for low-rank matrix optimization are proven.
problem Low-rank matrix optimization with rank constraints.
method Established geometric landscape connections between manifold and factorization formulations.
result Equivalence between manifold and factorization formulations at FOSPs, SOSPs, and strict saddles.
A new Lagrangian formulation of the Raychaudhuri equation in non-Riemannian geometry.
problem Formulating the Raychaudhuri equation in non-Riemannian geometries.
method Established a formal connection between the expansion scalar and the cross-sectional volume of the congruence. Derived a Lagrangian and Hamiltonian formulation.
result The expansion scalar equals the fractional rate of change of volume, weighted by a scalar factor.
In this paper we introduce a new optimization formulation for sparse regression and compressed sensing, called CLOT (Combined L-One and Two), wherein the regularizer is a convex combination of the - and -norms. This formulation differs from the Elastic Net (EN) formulation, in which the regularizer is a…
We propose a parallelizable sparse inverse formulation Gaussian process (SpInGP) for temporal models. It uses a sparse precision GP formulation and sparse matrix routines to speed up the computations. Due to the state-space formulation used in the algorithm, the time complexity of the basic SpInGP is linear, and becaus…
Paper offers a dual formulation for consumption problem with multiplicative habit.
problem Optimal consumption with multiplicative habit formation.
method Dual formulation using Fenchel's Duality Theorem.
result Strong duality result linking primal and dual controls.
The paper tackles robust statistical methods using Wasserstein DRO formulations.
problem Distributional uncertainty in learning from limited samples.
method Min-max distributionally robust optimization with Wasserstein DRO formulations.
result Error bounds free from the curse of dimensionality.
Genetic algorithms are a well-known method for tackling the problem of variable selection. As they are non-parametric and can use a large variety of fitness functions, they are well-suited as a variable selection wrapper that can be applied to many different models. In almost all cases, the chromosome formulation used …
Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution equa- tions for nonequilibrium thermodynamics admit an intrinsic formulation in …
The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation for solving the optimal binning problem for a binary, continuous and multi-class target type, incorporating constraints not p…
Bayesian optimization identifies optimal alloy formulations.
problem Accelerated discovery in materials science with autonomous systems.
method Bayesian optimization over problem formulation space.
result Framework converges on optimal alloy formulations.
New formulations capture aversion to ambiguity about volatility.
problem Capturing aversion to ambiguity about unknown and time-varying volatility.
method Introduces novel preference formulations and compares them with existing models.
result Illustrates the impact of ambiguity aversion in static and dynamic models.
ROCK: A variational formulation for occupation kernel methods in Reproducing Kernel Hilbert Spacesstat.ML
ROCK method generalizes MOCK for learning dynamical systems efficiently.
problem Learning dynamical systems from data efficiently.
method Variational formulation in Reproducing Kernel Hilbert Spaces.
result ROCK method is more computationally efficient and performs better on benchmarks.
In this technical paper, we present a new formulation of higher parallel transport in strict higher gauge theory required for the rigorous construction of Wilson lines and surfaces. Our approach is based on an original notion of Lie crossed module cocycle and cocycle 1- and 2-gauge transformation with a non standard do…
Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes. In this paper, we study the problem of learning an optimal DAG from continuous observational data. We cast this problem in the f…
We introduce a new convex formulation for stable principal component pursuit (SPCP) to decompose noisy signals into low-rank and sparse representations. For numerical solutions of our SPCP formulation, we first develop a convex variational framework and then accelerate it with quasi-Newton methods. We show, via synthet…
Current pharmaceutical formulation development still strongly relies on the traditional trial-and-error approach by individual experiences of pharmaceutical scientists, which is laborious, time-consuming and costly. Recently, deep learning has been widely applied in many challenging domains because of its important cap…
Oral Disintegrating Tablets (ODTs) is a novel dosage form that can be dissolved on the tongue within 3min or less especially for geriatric and pediatric patients. Current ODT formulation studies usually rely on the personal experience of pharmaceutical experts and trial-and-error in the laboratory, which is inefficient…
The paper proves an index theorem for loop spaces of compact manifolds.
problem Defining an index theorem for loop spaces of compact manifolds.
method Formulated and proved an equivariant index theorem for non-compact manifolds with -actions, using a ring of formal power series.
result Found an appropriate form of the index theorem for loop spaces.
A geometric multisymplectic formulation of the classical BRST symmetry of constrained first-order classical field theories is described. To effect this we introduce graded analogues of the bundles and manifolds of the multisymplectic formulation of first-order field theories. The Lagrange-d'Alembert formalism is also d…
Since its inception, the modus operandi of multi-task learning (MTL) has been to minimize the task-wise mean of the empirical risks. We introduce a generalized loss-compositional paradigm for MTL that includes a spectrum of formulations as a subfamily. One endpoint of this spectrum is minimax MTL: a new MTL formulation…
Designs a robust data-driven decision-making model to handle multiple overfitting sources.
problem Overfitting in data-driven models due to statistical error, data noise, and data misspecification.
method Holistic distributionally robust optimization formulation combining Kullback-Leibler and Lévy-Prokhorov approaches.
result Guaranteed holistic protection against statistical error, data noise, and data misspecification.
The reduction of nonholonomic systems is formulated in terms of Dirac reduction. An optimal reduction method for a class of nonholonomic systems is formulated. Several examples are studied in detail.
Unified formulation bridges adversarial and nonstationary bandits.
problem Handling time-varying reward distributions in multi-armed bandit problems.
method Unified oracle that switches between adversarial and nonstationary bandit oracles based on window size.
result Optimal regret achieved with matching lower bound.
In this paper, we have proposed a deep quantum SVM formulation, and further demonstrated a quantum-clustering framework based on the quantum deep SVM formulation, deep convolutional neural networks, and quantum K-Means clustering. We have investigated the run time computational complexity of the proposed quantum deep c…
Revisits superfields and geometry, offering new formulations and interpretations.
problem Exploring the connection between superfields and geometry.
method Combining different superfield formulations, using a doubled target space, and interpreting equations of motion geometrically.
result Shows that the doubled geometry is Donaldson's deformation of the original Kähler manifold.
Joint sparsity regularization in multi-task learning has attracted much attention in recent years. The traditional convex formulation employs the group Lasso relaxation to achieve joint sparsity across tasks. Although this approach leads to a simple convex formulation, it suffers from several issues due to the loosenes…
This paper deals with the explicit design of strategy formulations to make the best strategic choices from a conventional matrix form of representing strategic choices. The explicit strategy formulation is an analytical model which is targeted to provide a mathematical strategy framework to find the best moment for str…
Abstract: Geometrically reformulates estimation theory for finite-dimensional C*-algebras.
problem Estimation theory for finite-dimensional C*-algebras.
method Geometrical formulation of estimation theory.
result Derivation of Cramer-Rao and Helstrom bounds.
Derives a primal-dual MLSVD formulation for multilinear data.
problem Efficiently decompose multilinear data for signal analysis and deep learning.
method Kernelizable primal-dual formulation of MLSVD.
result Derives a new MLSVD formulation with computational advantages.
Paper presents a new port-Hamiltonian model for vehicle manipulators.
problem Complex mechanical systems' energy flow and conservation.
method Derives port-Hamiltonian dynamics from Hamiltonian reduction theory.
result Establishes mathematical equivalence with existing formulations.
We show that the pseudo-Riemannian geometry of submanifolds can be formulated in terms of higher order multi-linear maps. In particular, we obtain a Poisson bracket formulation of almost (para-)Kähler geometry.