We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that embedded projective variety, known as its maximum likeliho...
This paper proposes a new notion of smoothness of algebras, termed differential smoothness, that combines the existence of a top form in a differential calculus over an algebra together with a strong version of the Poincaré duality realized as an is...
Monocular depth estimation has been increasingly adopted in robotics and autonomous driving for its ability to infer scene geometry from a single camera. In self-supervised monocular depth estimation frameworks, the network jointly generates and expl...
The width of a convex curve in the plane is the minimal distance between a pair of parallel supporting lines of the curve. In this paper we study the width of nodal lines of eigenfunctions of the Laplacian on the standard flat torus. We prove a varie...
In this paper we show that there is a well defined modified dbar-Neumann problem for a spin_c manifold with a strictly pseudoconvex boundary (in the contact geometry sense). We show that the index of the associated boundary value problem can be com...
The use of GNSS in the railway sector has been postulated on the notion of a Virtual Balise (VB). The VB-based positioning system works by setting a VB point on the railway track and determining the passage of the VB point using the position solution...
Here, we present the World Trade Atlas 1870-2013, a collection of annual world trade maps in which distance combines economic size and the different dimensions that affect international trade beyond mere geography. Trade distances, which are based on...
Computing the Delaunay triangulation (DT) of a given point set in $\mathbb{R}^D$ is one of the fundamental operations in computational geometry. Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm that merges two partial tr...
Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision and pattern...
Chain-of-Thought (CoT) prompting significantly improves reasoning in Large Language Models, yet the temporal dynamics of the underlying representation geometry remain poorly understood. We investigate these dynamics by applying Manifold Capacity Theo...
In this study, we analyze how changes in the geometry of a potential energy surface in terms of depth and flatness can affect the reaction dynamics. We formulate depth and flatness in the context of one and two degree-of-freedom (DOF) Hamiltonian nor...
The magneto-optical response of monolayer transition metal dichalcogenides (TMDs), including excitonic effects, is studied using a nanoribbon geometry. We compute the diagonal optical conductivity and the Hall conductivity. Comparing the excitonic op...
We consider semitransparent pistons in the presence of extra dimensions. It is shown that the piston is always attracted to the closest wall irrespective of details of the geometry and topology of the extra dimensions and of the cross section of the...
A review on topological strings and the geometry of the space of two dimensional theories. (Lectures given by C. Gomez at the Enrico Fermi Summer School, Varenna, July 1994)...
In this work, we experimentally investigate the frequency limit of Hall effect sensor designs based on a 2 dimensional electron gas (2DEG) gallium arsenide/aluminum gallium arsenide (GaAs/AlGaAs) heterostructure. The frequency limit is measured and c...
We study cubical sets without degeneracies, which we call square sets. These sets arise naturally in a number of settings and they have a beautiful intrinsic geometry; in particular a square set C has an infinite family of associated square sets J^...
Really clear math lessons (pre-algebra, algebra, precalculus), cool math games, online graphing calculators, geometry art, fractals, polyhedra, parents and teachers areas too.
An important open question in G$_{2}$ geometry concerns whether or not a compact seven-manifold can support an exact G$_{2}$-Structure. Given the significance of this question we initiate a study of exact G$_{2}$-Structures on compact manifolds. We f...
We give a description of the boundary of a complex of free factors that is analogous to E. Klarreich's description of the boundary of a curve complex. The argument uses the geometry of folding paths developed by Bestvina and Feighn as well as structu...
We find that the frequency spectra of layered phononic and photonic composites admit a universal struc- ture, independent of the geometry of the periodic-cell and the specific physical properties. We show that this representation extends to highly de...
Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. In an accompanying paper I, we analyzed this theory and summarized it in nine equations. We now...
In this contribution to FQXi's essay contest 2018, I suggest that it is sometimes a step forward to reverse our intuition on "what is fundamental", a move that is somewhat reminiscent of the idea of noncommutative geometry. I argue that some foundati...
Revealing hidden geometry and topology in noisy data sets is a challenging task. Elastic principal graph is a computationally efficient and flexible data approximator based on embedding a graph into the data space and minimizing the energy functional...
We introduce the \emph{parameter-geometrization} to the Hitchin system, a paradigm embedding deformation parameters into geometry via the coupled Hitchin-He equations on a surface with boundary. A boundary term couples a second Higgs field $ψ$, reco...
The paper deals with associating the optimal machining strategy to a given pocket geometry, within the context of High-Speed Machining (HSM) of aeronautical pockets. First we define different classes of pocket features according to geometrical crit...
Gravitational waves can be gravitationally lensed by massive objects along their path. Depending on the lens mass and the lens--source geometry, this can lead to the observation of a single distorted signal or multiple repeated events with the same f...
Despite the recent success of face image generation with GANs, conditional hair editing remains challenging due to the under-explored complexity of its geometry and appearance. In this paper, we present MichiGAN (Multi-Input-Conditioned Hair Image GA...
In this article, the extensional flow and viscosity and the converging-diverging geometry were examined as the basis of the peculiar viscoelastic behavior in porous media. The modified Bautista-Manero model, which successfully describes shearthinni...
A banana manifold is a Calabi-Yau threefold fibered by Abelian surfaces whose singular fibers contain banana configurations: three rational curves meeting each other in two points. A nano-manifold is a Calabi-Yau threefold $X$ with very small Hodge n...
Learn about 'frontal angle,' its meaning in various fields, and its applications. Understand the significance of the frontal angle in disciplines like anatomy, geometry, and engineering.
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Archived from the original on 2020-05-17. "Poisson Geometry Home Page". www.lpthe.jussieu.fr. Retrieved 2020-01-30. "The André Lichneriwicz prize to Henrique
1088/1751-8113/44/48/483001. ISSN 1751-8113. "Effective temperatures" (PDF). www.lpthe.jussieu.fr. Kurchan, Jorge; Laloux, Laurent (1996-05-07). "Phase space geometry