3D-CNN method visualizes localized geometric features for manufacturability analysis.
problem Interpreting 3D-CNN decisions for complex geometries.
method 3D-CNN with surface normals, 3D-GradCAM for feature visualization.
result Identifies critical local features for manufacturability.
3D convolutional neural networks (3D-CNN) have been used for object recognition based on the voxelized shape of an object. In this paper, we present a 3D-CNN based method to learn distinct local geometric features of interest within an object. In this context, the voxelized representation may not be sufficient to captu…
In this paper we try to establish a connection between a three-dimensional Lotka--Volterra dynamical system and two-dimensional topological surgery. There are many physical phenomena exhibiting two-dimensional topological surgery through a `hole drilling' process. By our connection, such phenomena may be modelled mathe…
Machine learning identifies rock type at drilling bit, reducing error from 13.5% to 9%
problem Precision drilling requires rock type identification at the drilling bit, but sensors are far away.
method Machine learning and data mining on sensors readings, comparing various algorithms.
result Real-time rock type classification error reduced from 13.5% to 9%
The paper proves drilled bundles over graphs are virtually special cubulable.
problem Proving drilled bundles over graphs are virtually special cubulable.
method Starting with a Gromov-hyperbolic surface bundle, drilling out essential curves, and using relative hyperbolicity and Wise's theorem.
result Proves drilled bundles over graphs are virtually special cubulable.
Machine learning detects drilling anomalies, reducing accidents and costs.
problem Detecting and preventing accidents during directional drilling.
method Time-series comparison using machine learning and Gradient Boosting classification.
result The model detects half of the anomalies with about 0.53 false alarms per day.
Drilling hyperbolic groups to simplify complex conjectures.
problem Proving the Cannon Conjecture for hyperbolic groups with 2-sphere boundary.
method Defining drilling of hyperbolic groups and proving it preserves relative hyperbolicity.
result Reduction of the Cannon Conjecture to a more tractable relative version.
Uniform linear bounds on volume changes in 3D hyperbolic spaces.
problem Volume variation in hyperbolic 3-manifolds.
method Uniform linear bounds proof for drilling and filling operations.
result Uniform linear bounds on volume variation proved.
Study bounds changes in hyperbolic 3-manifold structures after drilling short geodesics.
problem Bounding changes in complex projective structures after drilling short geodesics.
method Analyzes L2-bounds on changes in conformally compact hyperbolic 3-manifolds. result Change is bounded by a universal constant times the square root of the length of the drilled geodesics.
In this paper we define a new state sum based on the regions defined by tangles on a surface which is an oriented closed surface with a finite number of open holes drilled. From this state sum we obtain an invariant of regular isotopy for the tangles named u-invariant. The values of the u-invariant are in $\mathbb{…
Machine learning improves prediction of complex geology ahead of drilling.
problem Predicting complex geology during drilling in real-time.
method Generative Adversarial Network (GAN) and Forward Deep Neural Network (FDNN) for real-time geological uncertainty reduction.
result Real-time estimates of complex geological uncertainty achieved.
In this paper we observe that 2-dimensional 0-surgery occurs in natural processes, such as tornado formation and other phenomena reminiscent of hole drilling. Inspired by such phenomena, we introduce new theoretical concepts which enhance the formal definition of 2-dimensional 0-surgery with the observed dynamics. To d…
Profinite rigidity proven for many hyperbolic manifolds.
problem Profinite rigidity of hyperbolic manifolds.
method Geometric topology and bubble-drilling construction.
result Profinite rigidity of many cusped hyperbolic manifolds.
In-plane drill rotations are impossible for smooth shells.
problem In-plane drill rotations on smooth shells are impossible.
method Analyzing the differential geometry of surfaces and isometries.
result Any isometry that coincides with the given surface at a portion of the boundary is the identity.
In this paper we investigate how the volume of hyperbolic manifolds increases under the process of removing a curve, that is, Dehn drilling. If the curve we remove is a geodesic we are able to show that for a certain family of manifolds the volume increase is bounded above by π⋅l where l is the length of the g…
New method detects rock type changes in real-time during drilling.
problem Detecting rock type changes in time during directional drilling.
method Combines machine learning and change detection procedures.
result Significant reduction in change detection delay and false positives.
Characterizes neutral deformation modes of minimal surfaces.
problem Understanding the energy content of deformation modes of minimal surfaces.
method Analyzes the energy content of stretching, drilling, and bending modes of minimal surfaces.
result All isometries of a minimal surface are globally neutral and give rise to soft elasticity.
Topological surgery is a mathematical technique used for creating new manifolds out of known ones. We observe that it occurs in natural phenomena where a sphere of dimension 0 or 1 is selected, forces are applied and the manifold in which they occur changes type. For example, 1-dimensional surgery happens during chromo…
EnLSTM network improves log generation from small datasets.
problem Generating well logs from small datasets with high accuracy.
method Combining ENN and C-LSTM networks with perturbation methods.
result 34% reduction in mean-square-error compared to existing models.
Detects project management anti-patterns using code and issue data.
problem Detecting project management anti-patterns requires expert judgment and is expensive.
method Convert descriptions to detectable metrics, quantify deviations, and optimize patterns.
result Automatic calibration enhances pattern detection and severity assessment.
New Einstein metrics found close to almost hyperbolic ones.
problem Finding Einstein metrics near almost hyperbolic ones.
method Extending Tian's work, using C2,α-topology. result Existence of Einstein metrics close to almost hyperbolic ones.
Generative adversarial network improves geosteering in fluvial reservoirs.
problem Improving geosteering in complex reservoirs with high uncertainties.
method Generative adversarial deep neural network (GAN) trained to model fluvial successions.
result Reduces uncertainty and correctly predicts geological features up to 500 meters ahead of drill-bit.
Effective drilling and filling bounds for hyperbolic 3-manifolds.
problem Understanding changes in metrics and geodesics during Dehn fillings of hyperbolic 3-manifolds.
method Combining tools from Kleinian group theory to transfer results from finite-volume to infinite-volume manifolds.
result Effective bilipschitz and complex length bounds quantifying filling theorems.
Given a hyperbolic 3-manifold M containing an embedded closed geodesic, we estimate the volume of a complete hyperbolic metric on the complement of the geodesic in terms of the geometry of M. As a corollary, we show that the smallest volume orientable hyperbolic 3-manifold has volume >.32 .
We supply a proof of the fact that a hyperbolic 3-manifold M with finitely generated fundamental group and with no parabolics is topologically tame. This proves the Marden's conjecture. Our approach is to form an exhaustion Mi of M and modify the boundary to make them 2-convex. We use the induced path-metric, wh…
Using black-hole inequalities and the increase of the horizon's areas, we show that there are arbitrarily small electro-vacuum perturbations of the standard initial data of the extreme Reissner-Nordstrom black-hole that, (by contradiction), cannot decay in time into any extreme Kerr-Newman black-hole. This proves the e…
Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five year…
Uniqueness theorem for extremal charged black holes in de Sitter space.
problem Proving uniqueness of extremal charged black holes in de Sitter space.
method Analyzing Einstein-Maxwell theory with a positive cosmological constant.
result Local isometry to extremal Reissner-Nordström-de Sitter black hole or its near-horizon geometry.
We study some aspects of spherical symmetric dyonic non-supersymmetric black holes in 4dN=1 supergravity coupled to chiral and vector multiplets on Kähler-Ricci solitons. Then, we have a family of dyonic non-supersymmetric black holes deformed with respect to the flow parameter related to the Kähler-Ricci soliton…
Proof of reverse isoperimetric inequality for black holes.
problem Reverse isoperimetric inequality for black holes in Einstein gravity.
method Geometric-analytic approach.
result Reversal of the usual isoperimetric inequality is explained by curved backgrounds governed by Einstein's equations.
This paper describes the black hole threshold in a moduli space of spherically symmetric spacetimes.
problem Understanding the black hole threshold in a moduli space of spherically symmetric spacetimes.
method Complete description and analysis of the black hole threshold in the moduli space M. result The black hole threshold is the extremal leaf of a C1 foliation of the moduli space, separating black hole solutions from non-collapsing solutions. The geometry of five-dimensional Kerr black holes is discussed based on geodesics and Weyl curvatures. Kerr-Star space, Star-Kerr space and Kruskal space are naturally introduced by using special null geodesics. We show that the geodesics of AdS Kerr black hole are integrable, which generalizes the result of Frolov and…
New construction of self-dual black holes using quadrics.
problem Hidden features of self-dual black holes obscured by twistor theory.
method Holomorphic quadrics in dual twistor space.
result Directly encoded geometry of self-dual black holes in quadrics.
Bounding geodesic length variation for surface projective structures.
problem Understanding how geodesic lengths change under projective structure variations.
method Bounding the derivative of complex length in terms of the Schwarzian norm.
result Application to cone-manifold deformations of hyperbolic 3-manifolds.
Researchers create black holes isometric to extremal Reissner-Nordström.
problem Third law of black hole thermodynamics.
method Novel Ck characteristic gluing procedure and scalar field pulses. result Definitive disproof of the third law of black hole thermodynamics.
Introduces holed cone structures to generalize cone structures on 3-manifolds.
problem Generalizing cone structures to 3-manifolds with irreducible holonomy representations.
method Introduces holed cone structures and considers their deformation space.
result The deformation space of holed cone structures is a covering space of the character variety.
Topology connects to black holes and wormholes.
problem Understanding topological changes in 3D space.
method Direct connection via surgery.
result New insights into black hole and wormhole formation.
Adds charged black holes to de Sitter space.
problem Gluing charged black holes into de Sitter space.
method Extends Hintz's result to Einstein-Maxwell system with positive cosmological constant, using Reissner-Nordström or Kerr--Newman--de Sitter black holes.
result Determines conditions for gluing black holes into de Sitter space.
Achieved all-orders worldline action for Kerr black hole.
problem Calculating effective action for Kerr black hole.
method Twistor particle theory.
result All-orders worldline effective action for Kerr black hole.
Extreme black holes with $\SU(2)$ symmetry have a specific near horizon geometry.
problem Understanding the near horizon geometry of extreme black holes with $\SU(2)$ symmetry.
method Analyzing the near horizon geometry of 5D extreme black holes with $\SU(2)$ symmetry.
result The near horizon geometry of these black holes must be that of a Berger sphere.
Study of waves on Reissner-Nordström-AdS black holes, proving uniform boundedness and continuity.
problem Analyzing waves on black holes in AdS spacetimes, focusing on uniform boundedness and continuity.
method Initial data on a spacelike hypersurface, Dirichlet boundary conditions at infinity, proving uniform boundedness and continuity.
result Uniform boundedness and continuity of waves at the Cauchy horizon on Reissner-Nordström-AdS black holes.
RG-2 flow reveals horizons in noncompact black hole metrics.
problem Understanding the evolution of black hole metrics under RG-2 flow.
method Adapted proofs for asymptotically flat case, analyzed horizons and monotonicity of entanglement entropy.
result Entanglement entropy is monotonic under RG-2 flow, related to horizon appearance.
New black hole models with both null and spacelike singularities.
problem Understanding singularities in black hole spacetimes.
method Developed a new spacelike-characteristic gluing method to construct black hole spacetimes.
result First examples of black holes with coexisting null and spacelike singularities.
Black holes offer insights into machine learning's loss landscapes.
problem Understanding the loss landscape in machine learning.
method Comparing machine learning loss landscapes to black hole entropy.
result Black holes provide an infinite family of potential landscapes with known minima.
Deep neural network predicts black hole merger remnants with high accuracy.
problem Estimating the properties of black hole merger remnants.
method Trained on a dataset of binary black hole simulations, a deep neural network predicts mass and spin with high precision.
result The network predicts remnant black hole mass and spin with errors less than 0.04% and 0.3% respectively, and reduces errors in precessing cases to half.
Study proves inequality linking black hole properties and angular momentum.
problem Establishing a Penrose-type inequality for black holes with 3-sphere horizons.
method Analyzing biaxially symmetric, maximal, asymptotically flat initial data sets for the Einstein equations.
result Equality holds only for stationary Myers-Perry black holes.
A key result in four dimensional black hole physics, since the early 1970s, is Hawking's topology theorem asserting that the cross-sections of an "apparent horizon", separating the black hole region from the rest of the spacetime, are topologically two-spheres. Later, during the 1990s, by applying a variant of Hawking'…
New definitions of null infinity extend black hole theory to generalized plane waves.
problem Extend black hole theory to generalized plane waves with non-standard null infinity.
method New definitions of null infinity and black hole regions in terms of causal boundaries.
result Closed trapped surfaces are inside black hole regions if null infinity is regular and null convergence condition is obeyed.