A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study evaluates feature selection methods for emotion recognition in resource-constrained settings.
Energy-efficient DL inference for IoT devices reduces power consumption and improves performance.
Unintentional falls can cause severe injuries and even death, especially if no immediate assistance is given. The aim of Fall Detection Systems (FDSs) is to detect an occurring fall. This information can be used to trigger the necessary assistance in case of injury. This can be done by using either ambient-based sensor…
AutoTune learns wireless identifiers for facial recognition in real-world settings.
The paper presents a novel, principled approach to train recurrent neural networks from the Reservoir Computing family that are robust to missing part of the input features at prediction time. By building on the ensembling properties of Dropout regularization, we propose a methodology, named DropIn, which efficiently t…
Extends Weyl geometry from conformal to Weyl manifolds using ambient metrics.
We prove existence and uniqueness of weighted ambient metric for manifolds with density.
Extended solitons show constant curvature on compact manifolds.
For a conformal manifold we introduce the notion of an ambient connection, an affine connection on an ambient manifold of the conformal manifold, possibly with torsion, and with conditions relating it to the conformal structure. The purpose of this construction is to realise the normal conformal tractor holonomy as aff…
This paper studies the relation between two notions of holonomy on a conformal manifold. The first is the conformal holonomy, defined to be the holonomy of the normal tractor connection. The second is the holonomy of the Fefferman-Graham ambient metric of the conformal manifold. It is shown that the infinitesimal confo…
DVAO predicts volumetric ambient occlusion for real-time volume rendering.
Proves existence and uniqueness of weighted metrics for smooth spaces.
AI learns market manipulation through simulation, suggesting regulation.
We present three large classes of examples of conformal structures for which the equations for the Fefferman-Graham ambient metric to be Ricci-flat are linear PDEs, which we solve explicitly. These explicit solutions enable us to discuss the holonomy of the corresponding ambient metrics. Our examples include conformal …
In this paper we relate the Fefferman-Graham ambient metric construction for conformal manifolds to the approach to conformal geometry via the canonical Cartan connection. We show that from any ambient metric that satisfies a weakening of the usual normalisation condition, one can construct the conformal standard tract…
The paper characterizes ambient metrics using conformal completion and null infinity properties.
Mathematical framework using Riemannian geometry for intelligence and consciousness.
An extension of the ambient metric construction of Fefferman-Graham to infinite order in even dimensions is described. The main ingredients are the introduction of "inhomogeneous ambient metrics" with asymptotic expansions involving the logarithm of a defining function homogeneous of degree 2, and an invariant procedur…
The conformal Fefferman-Graham ambient metric construction is one of the most fundamental constructions in conformal geometry. It embeds a manifold with a conformal structure into a pseudo-Riemannian manifold whose Ricci tensor vanishes up to a certain order along the original manifold. Despite the general existence re…
Artificial intelligence has impacted many aspects of human life. This paper studies the impact of artificial intelligence on economic theory. In particular we study the impact of artificial intelligence on the theory of bounded rationality, efficient market hypothesis and prospect theory.
New property: polygons have a fixed dimension regardless of ambient space dimensions.
The (Fefferman-Graham) ambient obstruction tensor is a conformally invariant symmetric trace-free 2-tensor on even-dimensional Riemannian and pseudo-Riemannian manifolds. The conformal deformation complex is a differential complex related to infinitesimal deformations of conformal structure. We construct a conformally …
We present conformal structures in signature (3,2) for which the holonomy of the Fefferman-Graham ambient metric is equal to the non-compact exceptional Lie group G_{2(2)}. We write down the resulting 8-parameter family of G_{2(2)}-metrics in dimension seven explicitly in an appropriately chosen coordinate system on th…
Curve shortening flow shrinks curves to points under certain conditions.
Uniform convergence of isotopies implies ambient isotopy, aiding knot equivalence.
We give simple conditions on an ambient manifold that are necessary and sufficient for isoperimetric inequalities (for submanifolds) to hold.
The paper proposes a test for trading intelligence similar to the Turing Test.
Given an -dimensional manifold with an affine connection , we show that the associated Patterson-Walker metric on admits a global and explicit Fefferman-Graham ambient metric. This provides a new and large class of conformal structures which are generically not conformally Einstein but for which th…
We study deformations of free boundary constant mean curvature (CMC) hypersurfaces whose Jacobi operator is degenerate due to symmetries of the ambient space. The value of the mean curvature and the ambient metric are allowed to vary simultaneously, provided that the infinitesimal ambient symmetries change smoothly. We…
It is shown that any transverse invariant measure of a foliated space can be considered as a measure on the ambient space.
We study piecewise linear co-dimension two embeddings of closed oriented manifolds in Euclidean space, and show that any such embedding can always be isotoped to be a closed braid as long as the ambient dimension is at most five, extending results of Alexander (in ambient dimension three), and Viro and independently Ka…
This thesis explores emergent intelligence in disordered systems like spin glasses and neural networks.
Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite order ambient lift for conformal densities in the case in which harmonic extension …
Generative adversarial models are powerful tools to model structure in complex distributions for a variety of tasks. Current techniques for learning generative models require an access to samples which have high quality, and advanced generative models are applied to generate samples from noisy training data through amb…
This paper provides details of the construction, properties and some applications of the ambient metric associated to a conformal class of metrics on a smooth manifold. Existence and uniqueness of formal expansions defining such metrics are considered. Equivalence with the expansions of associated Poincare metrics is e…
Generative models use Riemannian manifolds to improve latent space interpretation.
Researchers study solitons on homogeneous manifolds, proving properties of specific types of solitons.
Researchers create a family of conformally covariant operators.
Extends submanifold theorem to general spaces.
The paper extends knot contact homology to tangles and proves a gluing formula.
This brief note highlights some basic concepts required toward understanding the evolution of machine learning and deep learning models. The note starts with an overview of artificial intelligence and its relationship to biological neuron that ultimately led to the evolution of todays intelligent models.
We provide an explicit formula for the Fefferman-Graham-ambient metric of an -dimensional conformal -wave in those cases where it exists. In even dimensions we calculate the obstruction explicitly. Furthermore, we describe all 4-dimensional -waves that are Bach-flat, and give a large class of Bach-flat examp…
We provide a self-contained treatment of set-theoretic subsolutions to flow by mean curvature, or, more generally, to flow by mean curvature plus an ambient vector field. The ambient space can be any smooth Riemannian manifold. Most importantly, we show that if two such set-theoretic subsolutions are initially disjoint…
We give a geometric derivation of Branson's Q-curvature in terms of the ambient metric associated with conformal structures; it naturally follows from the ambient metric construction of conformally invariant operators and can be applied to a large class of invariant operators. This procedure can be also applied to CR g…
These notes are based on my lectures at IMA summer program "Symmetries and Overdetermined Systems of Partial Differential Equations." Here I try to explain basic ideas of the ambient metric construction by studying the Szego kernel of the sphere.
It is shown that the variational derivative of the integral of Branson's Q-curvature is the ambient obstruction tensor of Fefferman-Graham. A classification of irreducible conformally invariant tensors modulo quadratic and higher degree terms in curvature is established.
Study surfaces in 4-manifolds with cyclic fundamental group.
Novel model detects communities in noisy multilayer networks.