arXiv research

Given a parallel calibration $φ\in Ω^p(M)$ on a Riemannian manifold $M$, I prove that the $φ$--critical submanifolds with nonzero critical value are minimal submanifolds. I also show that the $φ$--critical submanifolds are precisely the integral manifolds of a $\mathscr{C}^\infty(M)$--linear subspace $\sP \subset Ω^p(M…

Planes are the only calibrated submanifolds with flat normal bundles.

In this article, we determine the seven-dimensional almost Abelian Lie algebras which admit calibrated or parallel G_2-/G_2^*-structures. Along the way, we show that certain well-established curvature restrictions for calibrated and parallel G_2-structures are not valid in the G_2^* case. In more detail, we provide the…

We describe a family of calibrations arising naturally on a hyperkähler manifold $M$. These calibrations calibrate the holomorphic Lagrangian, holomorphic isotropic and holomorphic coisotropic subvarieties. When $M$ is an HKT (hyperkaehler with torsion) manifold with holonomy $SL(n, {\Bbb H})$, we construct another fam…

New conditions for calibrated submanifolds in Riemannian geometry.

We describe a high performance parallel implementation of a derivative pricing model, within which we introduce a new parallel method for the calibration of the industry standard SABR (stochastic-αβρ) stochastic volatility model using three strike inputs. SABR calibration involves a non-linear three dimensional minimis…

We extend the "bundle constructions" of calibrated submanifolds, due to Harvey--Lawson in the special Lagrangian case, and to Ionel--Karigiannis--Min-Oo in the cases of exceptional calibrations, by "twisting" the bundles by a special (harmonic, holomorphic, parallel) section of a complementary bundle. The existence of …

We introduce a fast model based deep learning approach for calibrationless parallel MRI reconstruction. The proposed scheme is a non-linear generalization of structured low rank (SLR) methods that self learn linear annihilation filters from the same subject. It pre-learns non-linear annihilation relations in the Fourie…

We investigate the deformation theory of a class of generalized calibrations in Riemannian manifolds for which the tangent bundle has reduced structure group U(n), SU(n), G_2 and Spin(7). For this we use the property of the associated calibration form to be parallel with respect to a metric connection which may have no…

We use AD to compute gradients for complex functionals in stochastic model calibration.

Given $(\bar{M},Ω)$ a calibrated Riemannian manifold with a parallel calibration of rank $m$, and $M^m$ an immersed orientable submanifold with parallel mean curvature $H$ we prove that if $\cos θ$ is bounded away from zero, where $θ$ is the $Ω$-angle of $M$, and if $M$ has zero Cheeger constant, then $M$ is minimal. I…

We present simple reconstruction networks for multi-coil data by extending deep cascade of CNN's and exploiting the data consistency layer. In particular, we propose two variants, where one is inspired by POCSENSE and the other is calibration-less. We show that the proposed approaches are competitive relative to the st…

Efficiently calibrates SABR/LIBOR models to real market caplets and swaptions data.

In this work, we discuss the Automatic Adjoint Differentiation (AAD) for functions of the form $G=\frac{1}{2}\sum_1^m (Ey_i-C_i)^2$, which often appear in the calibration of stochastic models. { We demonstrate that it allows a perfect SIMD\footnote{Single Input Multiple Data} parallelization and provide its relative co…

Study of interactions between functions on manifolds via submersions.

By only using spectral theory of the Laplace operator on spheres, we prove that the unit 3-dimensional sphere of a 2-dimensional complex subspace of $\mathbb{C}^3$ is a $Ω$-stable submanifold with parallel mean curvature, when $Ω$ is the Kähler calibration of rank 4 of $\mathbb{C}^3$.

A data-driven approach called CaNN (Calibration Neural Network) is proposed to calibrate financial asset price models using an Artificial Neural Network (ANN). Determining optimal values of the model parameters is formulated as training hidden neurons within a machine learning framework, based on available financial op…

A nearly parallel $G_{2}$-manifold $Y$ is a Riemannian 7-manifold whose cone $C(Y) = \mathbb{R}_{>0} \times Y$ has the holonomy group contained in ${\rm Spin(7)}$. In other words, it is a spin 7-manifold with a real Killing spinor. We have a special class of calibrated submanifolds called Cayley submanifolds in $C(Y)$.…

Improved DOA estimation with distributed sensors across multiple frequencies.

On a Riemannian manifold $\bar{M}^{m+n}$ with an $(m+1)$-calibration $Ω$, we prove that an $m$-submanifold $M$ with constant mean curvature $H$ and calibrated extended tangent space $\mathbb{R}H\oplus TM$ is a critical point of the area functional for variations that preserve the enclosed $Ω$-volume. This recovers the …

New forms calibrate minimal graphs in arbitrary dimensions.

Unified Bayesian-AI framework improves epidemiological risk prediction and uncertainty quantification.

FMP sampling improves model calibration without sharing data.

ParaMonte::Python streamlines Bayesian data analysis with fast Monte Carlo and MCMC routines.

Packed-Ensembles improve uncertainty estimation in constrained hardware.

For an element $Ψ$ in the graded vector space $Ω^*(M, TM)$ of tangent bundle valued forms on a smooth manifold $M$, a $Ψ$-submanifold is defined as a submanifold $N$ of $M$ such that $Ψ_{|N} \in Ω^*(N, TN)$. The class of $Ψ$-submanifolds encompasses calibrated submanifolds, complex submanifolds and all Lie subgroups in…

The paper studies deformations of calibrated subbundles in special holonomy manifolds.

Study quantifies geometric complexity of connections on product surfaces.

We study natural variations of the G2 structure σ_0 \in Λ^3_+ existing on the unit tangent sphere bundle SM of any oriented Riemannian 4-manifold M. We find a circle of structures for which the induced metric is the usual one, the so-called Sasaki metric, and prove how the original structure has a preferred role in the…

New methods for volatility modeling using rough paths and signatures.

We prove that an integral Cauchy-Riemann inequality holds for any pair of smooth functions $(f,h)$ on the 2-sphere $\mathbb{S}^2$, and equality holds iff $f$ and $h$ are related $λ_1$-eigenfunctions. We extend such inequality to 4-tuples of functions, only valid on the $L^2$-orthogonal complement of a suitable nonzero …

A new framework for consistent segmentation evaluation reduces operating losses.

The investigation of strings and M-theory involves the understanding of various BPS solitons which in a certain approximation can be thought of as solutions of ten- and eleven-dimensional supergravity theories. These solitons have a brane or a intersecting brane interpretation, saturate a bound and are associated with …

Structured low-rank (SLR) algorithms, which exploit annihilation relations between the Fourier samples of a signal resulting from different properties, is a powerful image reconstruction framework in several applications. This scheme relies on low-rank matrix completion to estimate the annihilation relations from the m…

The paper extends a theorem about stable minimal surfaces to higher codimensions.

We developed a novel statistical method to identify structural differences between networks characterized by structural equation models. We propose to reparameterize the model to separate the differential structures from common structures, and then design an algorithm with calibration and construction stages to identif…

This paper evaluates conformal prediction for aerial image classification in challenging environments.

We find Weitzenböck formula for the Fueter-Dirac operator which controls the infinitesimal deformations of an associative submanifold in a $7$--manifold with a $G_2$--structure. We establish a vanishing theorem to conclude rigidity under some positivity assumptions on curvature, which are particularly mild in the nearl…

Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data based on conditional mutual information combined with a local permutation scheme …

Twin-Boot integrates uncertainty estimation into optimization using parallel training of identical models.

Proposes new method for calibrating treatment effect predictors.

New method predicts binary matrix entries using empirical Bayes and low-rank structure.

Optimal engine operation during a transient driving cycle is the key to achieving greater fuel economy, engine efficiency, and reduced emissions. In order to achieve continuously optimal engine operation, engine calibration methods use a combination of static correlations obtained from dynamometer tests for steady-stat…

Proposes top-label calibration and M2B framework for multiclass to binary calibration.

Study explores calibration properties in neural architectures.

A new perfectly truthful calibration measure improves prediction reliability.

New truthful calibration errors improve model ranking in multiclass prediction.

New framework for evaluating multiclass classifier calibration.