arXiv research

This paper constructs PH spline curves with prescribed arc lengths.

The paper proves $\Gamma$-convergence of discrete tangent-point energies to continuous energies and ropelength, with applications to biarc curves.

A new method joins two arcs with a degree of freedom.

Ph.D. thesis on complex Brunn-Minkowski theory using Hilbert bundles.

The paper studies groups with proper actions on finite products of hyperbolic spaces.

Characterizes mappings preserving Pythagorean-hodograph curves.

Adapts bandit algorithms for online survival analysis under Cox PH model.

An emended and improved version of the present paper has been archived in math-ph/0505057, and a preliminary account of its content has been published in Phys.Rev.Lett. 92, 60601, (2004). Moreover, in order to prove the relevance of topology for phase transition phenomena in a broad domain of physically interesting cas…

Vogt's theorem, concerning boundary angles of a convex arc with monotonic curvature (spiral arc), is taken as a starting point to establish basic properties of spirals. The theorem is expanded by removing requirements of convexity and curvature continuity; the cases of inflection and multiple windings are considered. P…

We discuss twistor-like interpretation of the $Sp(8)$ invariant formulation of 4d massless fields in ten dimensional Lagrangian Grassmannian $Sp(8)/P$ which is the generalized space-time in this framework. The correspondence space $\mathbf{C}$ is $SpH(8)/PH$ where $SpH(8)$ is the semidirect product of $Sp(8)$ with Heis…

PH-VAE models heavy-tailed data with flexible Phase-Type distributions.

PH-CS selects test inputs with reliability guarantees, adapting FDR to data.

Enhances graph neural networks with spectral and topological information.

Physics-informed learning framework for pH systems and EB-PBC control.

This text proposes geometrical descriptions of all variational problems invariant by conformal transformations in two variables. First a characterisation in terms of C-Finsler manifolds, a suitable generalization of Finsler manifolds, is given. Second Hamiltonian formalisms are explored, with an emphasis on Caratheodor…

Paper introduces stable vectorization for multiparameter PH using signed barcodes.

New method enhances graph neural networks using contractions and hourglass persistence.

We introduce an open source python framework named PHS - Parallel Hyperparameter Search to enable hyperparameter optimization on numerous compute instances of any arbitrary python function. This is achieved with minimal modifications inside the target function. Possible applications appear in expensive to evaluate nume…

A new method for federated survival analysis using Cox models.

Extends results of math-ph/0407067

Extends results of math-ph/0407067

Extends results of math-ph/0407067

PHLP uses persistent homology to interpret graph link prediction.

PTOPOFL uses topological descriptors to protect privacy in federated learning.

This work characterizes topological descriptors of graph products and their expressive power.

This paper has been superseded by math-ph/0102032, "Bures geometry of the three-level quantum systems. II".

We implement a market microstructure model including informed, uninformed and heuristic-driven investors, which latter behave in line with loss-aversion and mental accounting. We show that the probability of informed trading (PIN) varies significantly during 2008. In contrast, the probability of heuristic-driven tradin…

We begin a systematic study of these spaces, initially following along the lines of Eberlein's comprehensive study of the Riemannian case. In particular, we integrate the geodesic equation, discuss the structure of the isometry group, and make a study of lattices and periodic geodesics. Some major differences from the …

The present paper attempts to show an alternative approach with regards to rational Pythagorean-hodograph (PH) curves and especially more natural approach for rational PH helices (i.e. rational helices). It exploits geometric features of rational helices to obtain a simpler construction of these curves and apply this t…

Persistent homology provides a new, efficient molecular descriptor for protein dynamics.

We study a model situation in which direct limit ($\text{colim}$) and inverse limit ($\lim$) do not commute, and offer some computations of their "commutator". The homology of a separable metrizable space $X$ has two well-known approximants: $qH_n(X)$ ("Čech homology") and $pH_n(X)$ ("Čech homology with compact support…

These are notes of a talk I gave in a seminar at the University of Pennsylvania summarizing results in the Ph.D. thesis of Michael Mueter obtained under the direction of Wolfgang Meyer at the University of Muenster. His thesis on "Kruemmungserhoehende Deformationen mittels Gruppenaktionen" examines in detail curvature …

This paper is a revised version of a previously posted paper in arxiv. The authors posted it as a new submission by mistake. The latest version of the paper can be found at arXiv:math-ph/0512003v2

In precision agriculture (PA), soil sampling and testing operation is prior to planting any new crop. It is an expensive operation since there are many soil characteristics to take into account. This paper gives an overview of soil characteristics and their relationships with crop yield and soil profiling. We propose a…

We show that if $P$ is a quadratic polynomial with a fixed Cremer point and Julia set $J$, then for any monotone map $\ph:J\to A$ from $J$ onto a locally connected continuum $A$, $A$ is a single point.

LightGBM outperforms other models in predicting pH values in Georgia, USA.

Markov chain decoders improve generative models' ability to produce heavy-tailed data.

We give the complete Bott-Chern-Aeppli cohomology for compact complex 3-folds in terms of Dolbeault, Frolicher, a bi-degree DeRham-like type of cohomology, $K^{p,q}$, defined as $$ K^{p,q}=\frac{ker( \partial ) \cap ker( {\bar{\partial}}) }{im( \partial )\cap ker( {\bar{\partial}} )+im( {\bar{\partial}})\cap ker( \part…

It is known that all left-invariant pseudo-Riemannian metrics on $H_3$ are algebraic Ricci solitons. We consider generalizations of Riemannian $H$-type, namely pseudo$H$-type and $pH$-type. We study algebraic Ricci solitons of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups of both types.

Three methods solve spatial rational curves with rational arc length.

This short note contains an explicit proof of the Jacobi identity for variational Schouten bracket in $Z_2$-graded commutative setup. For the reasoning to be rigorous, it refers to the product bundle geometry of iterated variations (see arXiv:1312.1262 [math-ph]); no ad hoc regularizations occur anywhere in this theory…

These notes are the first half of the contents of the course given by the second author at the Bachelier Seminar (February 8-15-22 2008) at IHP. They also correspond to topics studied by the first author for her Ph.D.thesis.

Proved a combinatorial conjecture in machine learning.

Paper shows equivalence between MM and PH for n-D Morse functions.

A Ph.D. thesis proposes an efficient approach for optimizing aircraft eco-design with high-dimensional mixed integer variables.

We explore a model of dark matter called wave dark matter (also known as scalar field dark matter and boson stars) which has recently been motivated by a new geometric perspective by Bray. Wave dark matter describes dark matter as a scalar field which satisfies the Einstein-Klein-Gordon equations. These equations rely …

Using ideas from an article of P. Bieliavsky, M. Rooman and Ph. Spindel on BTZ black holes, I construct a family of interesting examples of quasi-Poisson actions as defined by A. Alekseev and Y. Kosmann-Schwarzbach. As an application, I obtain a genuine Poisson structure on $SL(2,R)$ which induces a Poisson structure o…

A new model avoids the PH assumption for right-censored survival data.