arXiv research

Corrects technical error in change of measure for HTB models.

This note corrects conditions in Proposition 3.4 and Theorem 5.2(ii) and comments on imprecisions in Propositions 4.2 and 4.4 in Fissler and Ziegel (2016).

The supplement proves the existence and properties of a dynamical system related to asset price bubbles.

Duncan and Ihrig (1993) gave a classification of the flat homogeneous spaces of metric signature (m,2), provided that a certain condition on the development image of these spaces holds. In this note we show that this condition can be dropped, so that Duncan and Ihrig's classification is in fact the full classification …

New calculus solves boundary value problems for elliptic operators.

Study investigates how machine learning models degrade over time, leading to patient safety issues.

In the previous work, the notion of the Finsleroid--Finsler space have been formulated and the necessary and sufficient conditions for the space to be of the Landsberg type have been found. In the present paper, starting with particular spray coefficients, we demonstrate how the Landsberg condition can explicitly appea…

When dealing with Heston's stochastic volatility model, the change of measure from the subjective measure P to the objective measure Q is usually investigated under the assumption that the Feller condition is satisfied. This paper closes this gap in the literature by deriving sufficient conditions for the existence of …

Study short-time existence of Ricci-DeTurck flow from rough metrics with Morrey-type integrability.

Improved surname geocoding and name supplements enhance race imputation accuracy.

Develops a new framework for estimating joint probability distributions.

In the first of these two lectures, I use a comparison to symplectic Khovanov homology to motivate the idea that the Jones polynomial and Khovanov homology of knots can be defined by counting the solutions of certain elliptic partial differential equations in 4 or 5 dimensions. The second lecture is devoted to a descri…

A standard convexity condition on the boundary of a symplectic manifold involves an induced positive contact form (and contact structure) on the boundary; the corresponding concavity condition involves an induced negative contact form. We present two methods of symplectically attaching 2-handles to convex boundaries of…

We review origins and main properties of the most important bracket operations appearing canonically in differential geometry and mathematical physics in the classical, as well as the supergeometric setting. The review is supplemented by a few new concepts and examples.

We point out a duality between steady incompressible Euler flows and solutions of the strongly coupled Faddeev-Skyrme sigma model with potential (mass) term. We supplement this result with various applications and several explicit examples.

The paper predicts Bitcoin volatility using order flow images.

This supplementary material includes three parts: some preliminary results, four examples, an experiment, three new algorithms, and all proofs of the results in the paper "Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs".

Auxiliary Tuning adapts pre-trained models for novel tasks efficiently.

Model forecasts natural gas consumption with Fourier series and feedback.

We discuss fun problems, vaguely related to notions and theorems of a course in differential geometry. This paper can be regarded as a weekend "treasure chest" supplementing the course weekday lecture notes. The problems and solutions are not original, while their relation to the course might be so.

We prove global and local upper bounds for the Hessian of log positive solutions of the heat equation on a Riemannian manifold. The metric is either fixed or evolves under the Ricci flow. These upper bounds supplement the well-known global lower bound.

In this paper, we give infinitely many non-Haken hyperbolic genus three 3-manifolds each of which has a finite cover whose induced Heegaard surface from some genus three Heegaard surface of the base manifold is reducible but can be compressed into an incompressible surface. This result supplements [CG] and extends [MMZ…

Survey of Gaussian process constraints for modeling expensive data.

As a supplement to the authors' article "Prime knots with arc index up to 11 and an upper bound of arc index for non-alternating knots", to appear in the Journal of Knot Theory and its Ramifications, we present minimal arc presentations of the prime knots up to arc index 11.

Solves open problems on curved projective varieties.

Generalizing empirical findings to new environments, settings, or populations is essential in most scientific explorations. This article treats a particular problem of generalizability, called "transportability", defined as a license to transfer information learned in experimental studies to a different population, on …

We propose an alternative approach on the existence of affine realizations for HJM interest rate models. It is applicable to a wide class of models, and simultaneously it is conceptually rather comprehensible. We also supplement some known existence results for particular volatility structures and provide further insig…

Let $E$ be a vector bundle over a suitable differential manifold $M$ and let $\wedge^p E$ denote $p$-exterior product of $E$. Given sections $ω_1,\dots,ω_k$ of $E$ and a section $η$ of $\wedge^p E$, we consider the problem if $η$ can be written in the form $η=\sum ω_i\wedgeγ_i,$ where $γ_i$ are sections of $\wedge^{p…

We formulate a kinematical extension of Double Field Theory on a $2d$-dimensional para-Hermitian manifold $(\mathcal{P},η,ω)$ where the $O(d,d)$ metric $η$ is supplemented by an almost symplectic two-form $ω$. Together $η$ and $ω$ define an almost bi-Lagrangian structure $K$ which provides a splitting of the tangent bu…

Defines basic Albanese maps for foliated Riemannian manifolds.

Autonomous reinforcement learning agents, like children, do not have access to predefined goals and reward functions. They must discover potential goals, learn their own reward functions and engage in their own learning trajectory. Children, however, benefit from exposure to language, helping to organize and mediate th…

The study examines how quantum resources enhance the complexity of quantum circuits.

CRBMs improve financial regime detection with PCD and free energy analysis.

Develops consistent approximations for composite optimization problems.

We propose a Bayesian model that predicts recovery curves based on information available before the disruptive event. A recovery curve of interest is the quantified sexual function of prostate cancer patients after prostatectomy surgery. We illustrate the utility of our model as a pre-treatment medical decision aid, pr…

The Plebański complex is a differential operator that squares to the Laplacian and is composed of two Dirac operators.

Study uses surrogate data to improve treatment effect estimation with scarce outcome data.

We consider the problem of multi-task learning in the high dimensional setting. In particular, we introduce an estimator and investigate its statistical and computational properties for the problem of multiple connected linear regressions known as Data Enrichment/Sharing. The between-tasks connections are captured by a…

This expository article introduces the topic of roots in a compact Lie group. Compared to the many other treatments of this standard topic, I intended for mine to be relatively elementary, example-driven, and free of unnecessary abstractions. Some familiarity with matrix groups and with maximal tori is assumed. This ar…

With the advent of the Internet of Things (IoT), an increasing number of energy harvesting methods are being used to supplement or supplant battery based sensors. Energy harvesting sensors need to be configured according to the application, hardware, and environmental conditions to maximize their usefulness. As of toda…

We present a constructive proof, that there exists a decomposition of the 2-skeleton of the k-dimensional cross polytope β^k into closed surfaces of genus \leq 1, each with a transitive automorphism group given by the vertex transitive Z_{2k}-action on β^k. Furthermore we show, that for each k \equiv 1,5(6) the 2-skele…

Confocal conics form an orthogonal net. Supplementing this net with one of the following: 1) the net of Cartesian coordinate lines aligned along the principal axes of conics, 2) the net of Apollonian pencils of circles whose foci coincide with the foci of conics, 3) the net of tangents to a conic of the confocal family…

This is a supplement to [arXiv:1503.03676], where an approach towards a mathematically rigorous definition of the Coulomb branch of a $3$-dimensional $\mathcal N=4$ SUSY gauge theory was proposed. We ask questions on their expected properties, especially in relation to the corresponding Higgs branch, partly motivated b…

The paper proposes a new model to analyze directed networks and accurately estimate community memberships.

Machine learning methods have had spectacular success on numerous problems. Here we show that a prominent class of learning algorithms - including Support Vector Machines (SVMs) -- have a natural interpretation in terms of ecological dynamics. We use these ideas to design new online SVM algorithms that exploit ecologic…

Fibonacci anyons are attractive for use in topological quantum computation because any unitary transformation of their state space can be approximated arbitrarily accurately by braiding. However there is no known braid that entangles two qubits without leaving the space spanned by the two qubits. In other words, there …

Graph neural network using Beltrami flow for feature and topology evolution.

Unified theory for semiparametric data fusion with individual-level data.