Right inverse found for Cartan differential in rank-1 symmetric spaces.
problem Finding a right inverse for the Cartan differential in symmetric spaces.
method Integral operator approach to the Cartan differential on exact forms.
result Extension of Gauss linking integral to rank-1 symmetric spaces.
Constructs a support-preserving homotopy for differential forms with boundary decay estimates.
problem Non-uniqueness of chain homotopies in de Rham complexes with boundary decay properties.
method Constructs a specific chain homotopy with desirable support propagation and boundary decay estimates.
result Obtains a support-preserving right inverse of the divergence operator with optimal decay estimates.
We derive explicit reconstruction formulas for the attenuated geodesic X-ray transform over functions and, in the case of non-vanishing attenuation, vector fields, on a class of simple Riemannian surfaces with boundary. These formulas partly rely on new explicit approaches to construct continuous right-inverses for bac…
Proves smoothness and star-shapedness of weak IMCF solutions in hyperbolic space.
problem Analyzing weak inverse mean curvature flow in hyperbolic space.
method Inspired by Alexandrov reflection method, uses Li-Wei result.
result Proves expanding spheres as the only proper weak IMCF on hyperbolic space.
Study non-degeneracy of minimal hypersurfaces asymptotic to cones, proving Jacobi equation solvability.
problem Non-degeneracy properties of minimal hypersurfaces asymptotic to cones.
method Analysis of the Jacobi operator and construction of its right inverse.
result Proved solvability of the Jacobi equation under non-degeneracy assumptions.
On the unit sphere S in a real Hilbert space H, we derive a binary operation ⊙ such that (S,⊙) is a power-associative Kikkawa left loop with two-sided identity e0, i.e., it has the left inverse, automorphic inverse, and Al properties. The operation ⊙ is co…
The classical Van Est theory relates the smooth cohomology of Lie groups with the cohomology of the associated Lie algebra, or its relative versions. Some aspects of this theory generalize to Lie groupoids and their Lie algebroids. In this paper, continuing an idea from [18], we revisit the van Est theory using the Per…
Study evaluates ML methods for two-sample testing with right-censored data.
problem Evaluating ML methods for two-sample testing with right-censored data.
method Developed and compared several ML-based methods with classical tests.
result Proposed methods outperform classical tests in terms of statistical power.
In addition to their security properties, adversarial machine-learning attacks and defenses have political dimensions. They enable or foreclose certain options for both the subjects of the machine learning systems and for those who deploy them, creating risks for civil liberties and human rights. In this paper, we draw…
A method for online tensor dictionary learning is proposed. With the assumption of separable dictionaries, tensor contraction is used to diminish a N-way model of O(LN) into a simple matrix equation of O(NL2) with a real-time capability. To avoid numerical instability d…
We construct radial fundamental solutions for the differential form Laplacian on negatively curved symmetric spaces. At least one of these Green's functions also yields a Biot-Savart Opearator, i.e. a right inverse of the exterior differential on closed forms with image in the kernel of the codifferential. Any Biot-Sav…
This paper discusses online algorithms for inverse dynamics modelling in robotics. Several model classes including rigid body dynamics (RBD) models, data-driven models and semiparametric models (which are a combination of the previous two classes) are placed in a common framework. While model classes used in the litera…
The paper studies how surfaces evolve in a cone under a specific flow.
problem Investigating the evolution of surfaces in a cone using a special flow.
method Analyzing a fully nonlinear parabolic Neumann problem under inverse curvature flow conditions.
result The evolving surfaces converge to a piece of the round sphere under certain conditions.
Let M be a manifold, possibly with boundary. We show that the deRham differential from k-forms to exact (k+1)-forms has a continuous right inverse when both spaces are given the weak Whitney topology. This antidifferential operator is given a fairly explicit formula depending on the choice of a suitable good cover of M…
New formula for implied volatility from Black-Scholes model.
problem Computing implied volatility from Black-Scholes model.
method Analytical solution using inverse Gaussian distribution.
result Explicit formulas for implied volatility with high precision.
In this article, we will use inverse mean curvature flow to establish an optimal Sobolev-type inequality for hypersurfaces Σ with nonnegative sectional curvature in Hn. As an application, we prove the hyperbolic Alexandrov-Fenchel inequalities for hypersurfaces with nonnegative sectional curvature in $\ma…
The literature of heavy tails (typically) starts with a random walk and finds mechanisms that lead to fat tails under aggregation. We follow the inverse route and show how starting with fat tails we get to thin-tails when deriving the probability distribution of the response to a random variable. We introduce a general…
One of the key issues in the analysis of machine learning models is to identify the appropriate function space and norm for the model. This is the set of functions endowed with a quantity which can control the approximation and estimation errors by a particular machine learning model. In this paper, we address this iss…
New approach uses distributed persistence for stable, parallelizable topological analysis of large point clouds.
problem Estimating the full persistence diagram of large point clouds is expensive, unstable, and not a sufficient statistic.
method Proposes distributed persistence as a new invariant, which is perfectly parallelizable, more stable, and has a rich inverse theory.
result The map from point clouds to distributed persistence invariants is a global quasi-isometry, interpolating between purely geometric and topological invariants.
Let M be a smooth manifold equipped with a conformal structure, E[w] the space of densities with the the conformal weight w and $D_{w,w+\de}$ the space of differential operators from E[w] to E[w+δ]. Conformal quantization Q is a right inverse of the principle symbol map on Dw,w+δ such that Q is confo…
Constructs smooth integrable magnetic systems on a two-torus.
problem Creating smooth magnetic systems on a two-torus with specific properties.
method Uses Nash-Moser implicit function theorem to find zeros of an action functional.
result Characterizes Zoll magnetic systems and proves their existence.
Finite groups of RAAGs act on a contractible space without fixed points.
problem Characterizing finite subgroups of RAAG outer automorphisms.
method Analyzing the action of finite subgroups on a contractible space.
result Finite subgroups of RAAG outer automorphisms fix a point in the space.
Explicit relation found between knot torsion and TQFT signatures.
problem Relating Reidemeister torsion of two-bridge knots to TQFT signatures.
method Established an explicit relation using parabolic representations and SU2-TQFT. result Inverse sum of torsions is constant and signatures have similar asymptotic behavior.
We will give a new proof of a recent result of P.~Daskalopoulos, G.Huisken and J.R.King ([DH] and reference [7] of [DH]) on the existence of self-similar solution of the inverse mean curvature flow which is the graph of a radially symmetric solution in Rn, n≥2, of the form u(x,t)=eλtf(e−λtx) f…
The stability and robustness of compact schemes for parabolic PDEs are analyzed.
problem Stability and robustness of compact schemes for solving parabolic PDEs.
method Compact spatial discretization, Crank-Nicolson temporal discretization, eigenvalue analysis of amplification matrix.
result An upper bound on the condition number of the amplification matrix is derived, showing stability.
The paper derives new inequalities for non-convex domains and flows.
problem Inequalities for non-convex domains and flows.
method Inverse curvature flow and Alexandrov-Fenchel-type inequalities.
result New inequalities for non-convex domains and flows.
Linear ODEs are solved by geodesics in hyperbolic geometry.
problem Solving real linear second order ODEs.
method Defined a Riemannian hyperbolic geometry and showed that solutions to ODEs correspond to geodesics in this geometry.
result Local solutions to ODEs correspond to geodesics in a specific hyperbolic geometry.
This paper introduces the Inverse Gamma (IGa) stochastic volatility model with time-dependent parameters, defined by the volatility dynamics dVt=κt(θt−Vt)dt+λtVtdBt. This non-affine model is much more realistic than classical affine models like the Heston stochastic volatility model, e…
Study presents a method to induce a generalized neural network from joint group invariant functions.
problem Encoding rule of neural network internal data representation.
method Systematic method using joint group invariant function on data-parameter domain.
result Induces a generalized neural network and its inverse operator (ridgelet transform).
Investigates Künneth formula for foliated de Rham cohomology, overcoming non-Hausdorff issues.
problem Computing cohomology for foliated manifolds, especially when non-Hausdorff.
method Develops a Künneth formula for specific cases of Hausdorff foliated cohomology and finite-dimensional cohomology.
result Valid Künneth formula for certain foliated cohomology spaces, with counterexamples for others.
Causal Interaction Trees identify treatment subgroup effects in observational data.
problem Identifying subgroups with enhanced treatment effects in observational studies.
method Extending Classification and Regression Trees with subgroup-specific treatment effect estimators.
result The proposed algorithms enhance treatment effect heterogeneity in subgroups.
The paper revisits the σk-Yamabe problem and proves the existence of a conformal metric with constant σ2-scalar curvature.
problem Finding a conformal metric with constant σk-scalar curvature on closed manifolds. method Analyzing the σ2-Yamabe constant and proving its achievability under certain conditions. result The σ2-Yamabe constant is achieved by a conformal metric, solving the σ2-Yamabe problem on manifolds with positive Yamabe constant. Let M be a smooth manifold and F be a vector field on M. My article ["Smooth shifts along trajectories of flows", Topol. Appl. 130 (2003) 183-204, arXiv:math/0106199] concerning the homotopy types of the group of diffeomorphisms preserving orbits of F contains two errors. They imply that the principal statement…
A new family of momentum coefficients improves the convergence rate of accelerated algorithms.
problem Improving the convergence rate of accelerated gradient methods for strongly convex functions.
method Introducing a family of controllable momentum coefficients for forward-backward accelerated methods.
result Established a controllable $O\left(1/k^{2α}
ight)$ convergence rate for the NAG-α method. The image of a polygonal knot K under a spherical inversion of R^3 (union infinity) is a simple closed curve made of arcs of circles, having the same knot type as the mirror image of K. Suppose we reconnect the vertices of the inverted polygon with straight lines, making a new polygon. This may be a different knot type…
We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. Given multiple traded assets, the prices of which depend on multiple observable stochastic factors, we construct a large class of forward performance processes with power-utility initial data, a…
New methods improve off-policy evaluation for survival outcomes with censoring.
problem Systematic underestimation of policy performance due to censoring bias in survival outcomes.
method Proposes IPCW-IPS and IPCW-DR to handle censoring bias in survival outcomes.
result The proposed methods are unbiased and achieve double robustness.
The paper proves foliations of solutions to the minimal surface equation in exterior domains.
problem Existence and properties of foliations by solutions to the exterior Dirichlet problem for minimal surfaces.
method Analyzes a 1-parameter family of solutions to the minimal surface equation in exterior domains with specific boundary conditions.
result Foliation of the open subset in R^(n+1) by graphs of solutions, with bounds and asymptotic behavior.
The paper examines differentiability of horizons along their generators in Lorentz manifolds.
problem Analyzing the differentiability of horizons along their generators in Lorentz manifolds.
method Using a result that every mathematical horizon locally coincides with a Cauchy horizon, the paper proves conditions for differentiability of horizons.
result Horizons are either continuously differentiable or have differentiability jumping points.
Uniqueness of quasi-roots explored in right-angled Artin groups.
problem Uniqueness of quasi-roots in right-angled Artin groups.
method Introducing quasi-roots and studying their uniqueness.
result Uniqueness of quasi-roots established in right-angled Artin groups.
A new matrix concentration inequality for random products of matrices.
problem Understanding the behavior of random matrix products under bounded independent positive semidefinite matrices.
method Developed a non-asymptotic concentration inequality for the product of matrices.
result The inequality provides a bound on the deviation of the matrix product from its expected value.
The paper forecasts corporate distress using a novel MIDAS logistic regression method.
problem Forecasting corporate distress with right-censored data, high-dimensional predictors, and mixed-frequency data.
method The paper introduces a novel high-dimensional censored MIDAS logistic regression method that handles censoring through inverse probability weighting and employs a sparse-group penalty for mixed-frequency predictors.
result The method achieves accurate estimation and superior performance in predicting financial distress of Chinese-listed firms.
For a Lie group G and a vector bundle E we study those actions of the Lie group TG on E for which the action map TG×E→E is a morphism of vector bundles, and call those \emph{affine actions}. We prove that the category VectTGaff(X) of such actions over a fixed G…
Detects right-veering properties in open books using combinatorial methods.
problem Determining the right-veering property of contact structures.
method Combinatorial approach to detect left-veering arcs in open books.
result Existence of an algorithm to detect right-veering for compact surfaces.
Deep learning improves quantile regression for censored survival data.
problem Predicting nonlinear patterns in censored survival data.
method Neural network with adjusted check function for inverse censoring distribution.
result Deep learning outperforms traditional quantile regression methods in prediction accuracy.
Surveying connections between graph combinatorics and algebraic right-angled Artin groups.
problem Understanding the relationship between graph structures and algebraic properties of right-angled Artin groups.
method Analyzing the defining and extension graphs of right-angled Artin groups.
result Discovers connections to geometric group theory and complexity theory.
We introduce a notion of "quasi-right-veering" for closed braids, which plays an analogous role to "right-veering" for open books. We show that a transverse link K in a contact 3-manifold (M,ξ) is non-loose if and only if every braid representative of K with respect to every open book decomposition that supports …
Impact of projective curvature tensor in f(R,G), f(R,T) and f(R,Lm)-gravitygr-qc The study characterizes spacetime and modified gravity models using projective curvature tensor.
problem Characterizing spacetime and modified gravity models with projective curvature tensor.
method Analyzing $f\left(R,G
ight)$, $f\left(R,T
ight)$, and $f\left(R,L_{m}
ight)$-gravity models.
result Projectively flat perfect fluid spacetimes represent dark energy era and are locally isometric to Minkowski or de-Sitter spacetimes.