A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Introduces nonlinear splittings on fibre bundles for generalizing connections.
New methods for constructing submersions between different types of spaces.
Novel methods for splitting Gaussian mixtures improve uncertainty propagation in nonlinear systems.
Paper analyzes and proves convergence of a new method for solving complex PDEs.
A deep learning method solves nonlinear filtering problems efficiently.
A new numerical scheme approximates nonlinear filtering densities for noisy and partial measurements.
Develops a new parabolic equation for surfaces, proving long-time existence and convergence.
In this paper we introduce a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational graph for each of the subproblems is comparatively small, the approach can handl…
Develops formal moduli theory for splitting complex supermanifolds.
In the geometry of generic 2-plane fields on 5-manifolds, the local equivalence problem was solved by Cartan who also constructed the fundamental curvature invariant. For generic 2-plane fields or -distributions determined by a single function of the form , the vanishing condition for the curvature invar…
We show that the pluriclosed flow preserves generalized Kähler structures with the extra condition , a condition referred to as "split tangent bundle." Moreover, we show that in this in this case the flow reduces to a nonconvex fully nonlinear parabolic flow of a scalar potential function. We prove a num…
The usual Gromoll-Meyer's generalized Morse lemma near degenerate critical points on Hilbert spaces, so called splitting lemma, is stated for at least -smooth functionals. In this paper we establish a splitting theorem and a shifting theorem for a class of continuously directional differentiable functionals (lower…
We present a new method for nonlinear prediction of discrete random sequences under minimal structural assumptions. We give a mathematical construction for optimal predictors of such processes, in the form of hidden Markov models. We then describe an algorithm, CSSR (Causal-State Splitting Reconstruction), which approx…
We propose a tree regularization framework, which enables many tree models to perform feature selection efficiently. The key idea of the regularization framework is to penalize selecting a new feature for splitting when its gain (e.g. information gain) is similar to the features used in previous splits. The regularizat…
We consider a global, nonlinear version of the Whitney extension problem for manifold-valued smooth functions on closed domains , with non-smooth boundary, in possibly non-compact manifolds. Assuming is a submanifold with corners, or is compact and locally convex with rough boundary, we prove that the restrictio…
We propose a new algorithm called PLUTO for building logistic regression trees to binary response data. PLUTO can capture the nonlinear and interaction patterns in messy data by recursively partitioning the sample space. It fits a simple or a multiple linear logistic regression model in each partition. PLUTO employs th…
Novel approach for creating interpretable classifiers using bilevel optimization of split-rules in NLDTs.
We derive some consequences of the Liouville theorem for plurisubharmonic functions of L.-F. Tam and the author. The first result provides a nonlinear version of the complex splitting theorem (which splits off a factor of isometrically from the simply-connected Kähler manifold with nonnegative bisectional …
WeldNet reduces complex dynamics to simpler, manageable segments.
Study develops a method to select penalty parameters for sparse neural networks without cross-validation.
The Gromoll-Meyer's generalized Morse lemma (so called splitting lemma) near degenerate critical points on Hilbert spaces, which is one of key results in infinite dimensional Morse theory, is usually stated for at least -smooth functionals. It obstructs one using Morse theory to study most of variational problems …
The paper studies statistical properties of CART regression trees.
New theorem on flat tori stability using harmonic maps and Ricci flow.
Novel method estimates complex nonlinear systems with stochastic differential equations.
Proposes adversarial method to estimate Riesz representer.
Infinitesimal gradient boosting is a new algorithm derived from gradient boosting.
Structural equation models (SEMs) have been widely adopted for inference of causal interactions in complex networks. Recent examples include unveiling topologies of hidden causal networks over which processes such as spreading diseases, or rumors propagate. The appeal of SEMs in these settings stems from their simplici…
We study the small perturbations of the -dimensional Milne model for the Einstein-Klein-Gordon (EKG) system. We prove the nonlinear future stability, and show that the perturbed spacetimes are future causally geodesically complete. For the proof, we work within the constant mean curvature (CMC) gauge and focus on …
Develops geometric framework for dissipative field equations.
The asymptotic behavior of the stochastic gradient algorithm with a biased gradient estimator is analyzed. Relying on arguments based on the dynamic system theory (chain-recurrence) and the differential geometry (Yomdin theorem and Lojasiewicz inequality), tight bounds on the asymptotic bias of the iterates generated b…
LGB+ improves macroeconomic forecasting by combining linear and tree models.
This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this decomposition is examined in detail. In particular, the dependency of various ki…
This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fundamental geometric structures as well as their preservation along solutions can be obtained directly from the variational principle. In parti…
We investigate bi-Hamiltonian structures and mKdV hierarchies of solitonic equations generated by (semi) Riemannian metrics and curve flows of non-stretching curves. There are applied methods of the geometry of nonholonomic manifolds enabled with metric-induced nonlinear connection (N-connection) structure. On spacetim…
Optimization is at the heart of machine learning, statistics and many applied scientific disciplines. It also has a long history in physics, ranging from the minimal action principle to finding ground states of disordered systems such as spin glasses. Proximal algorithms form a class of methods that are broadly applica…
Physics-based deep learning improves fiber-optic communication efficiency.
SPlit optimizes dataset splitting for better model performance.
We consider solutions to the anti-self-dual Yang Mills (ASDYM) equations in split signature that are global on the double cover of the appropriate conformally compactified Minkowski space $\widetilde\M$. Ward's ASDYM twistor construction is adapted to this geometry by using a correspondence between points of $\widetild…
Algorithm recovers factors of rank-1 matrices from noisy measurements.
We report analytical results for the development of the viscous fingering instability in a cylindrical Hele-Shaw cell of radius a and thickness b. We derive a generalized version of Darcy's law in such cylindrical background, and find it recovers the usual Darcy's law for flow in flat, rectangular cells, with correctio…
As data collections become larger, exploratory regression analysis becomes more important but more challenging. When observations are hierarchically clustered the problem is even more challenging because model selection with mixed effect models can produce misleading results when nonlinear effects are not included into…
The paper extends keenness concept to bridge splittings and finds conditions for existence.
Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. Further it is shown that non-split structures appear in the first case as deformations of a split reduction and in the …
Study flippable Heegaard splittings in Seifert fibered spaces.
The paper uses deep neural networks to estimate and infer ATE without needing to know the dimension of the data.
New method weaves paper strips for designing curved surfaces with elasticity.
We study the self-dual Yang-Mills equations in split signature. We give a special solution, called the basic split instanton, and describe the ADHM construction in the split signature. Moreover a split version of t'Hooft ansatz is described.
Paper proposes a novel SVM method for creating survival trees.