arXiv research

Study bounds changes in hyperbolic 3-manifold structures after drilling short geodesics.

Drilling hyperbolic groups to simplify complex conjectures.

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 $π\cdot l$ where $l$ is the length of the g…

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 .

Bounding geodesic length variation for surface projective structures.

The paper proves drilled bundles over graphs are virtually special cubulable.

Uniform linear bounds on volume changes in 3D hyperbolic spaces.

Directional oil well drilling requires high precision of the wellbore positioning inside the productive area. However, due to specifics of engineering design, sensors that explicitly determine the type of the drilled rock are located farther than 15m from the drilling bit. As a result, the target area runaways can be d…

We present a data-driven algorithm and mathematical model for anomaly alarming at directional drilling. The algorithm is based on machine learning. It compares the real-time drilling telemetry with one corresponding to past accidents and analyses the level of similarity. The model performs a time-series comparison usin…

Effective drilling and filling bounds for hyperbolic 3-manifolds.

Machine learning improves prediction of complex geology ahead of drilling.

Veering branched surfaces help construct geodesic flows on curved surfaces.

Profinite rigidity proven for many hyperbolic manifolds.

In-plane drill rotations are impossible for smooth shells.

We prove a volume inequality for 3-manifolds having C^0 metrics "bent" along a hypersurface, and satisfying certain curvature pinching conditions. The result makes use of Perelman's work on Ricci flow and geometrization of closed 3-manifolds. Corollaries include a new proof of a conjecture of Bonahon about volumes of c…

Characterizes neutral deformation modes of minimal surfaces.

EnLSTM network improves log generation from small datasets.

During the directional drilling, a bit may sometimes go to a nonproductive rock layer due to the gap about 20m between the bit and high-fidelity rock type sensors. The only way to detect the lithotype changes in time is the usage of Measurements While Drilling (MWD) data. However, there are no general mathematical mode…

Detects project management anti-patterns using code and issue data.

New Einstein metrics found close to almost hyperbolic ones.

We introduce and study some deformations of complete finite-volume hyperbolic four-manifolds that may be interpreted as four-dimensional analogues of Thurston's hyperbolic Dehn filling. We construct in particular an analytic path of complete, finite-volume cone four-manifolds $M_t$ that interpolates between two hyperbo…

Generative adversarial network improves geosteering in fluvial reservoirs.

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 $M_i$ of $M$ and modify the boundary to make them 2-convex. We use the induced path-metric, wh…

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…

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…

3D Convolutional Neural Networks (3D-CNN) have been used for object recognition based on the voxelized shape of an object. However, interpreting the decision making process of these 3D-CNNs is still an infeasible task. In this paper, we present a unique 3D-CNN based Gradient-weighted Class Activation Mapping method (3D…

We prove that any mapping torus of a pseudo-Anosov mapping class with bounded normalized Weil-Petersson translation length contains a finite set of transverse and level closed curves, and drilling out this set of curves results in one of a finite number of cusped hyperbolic 3-manifolds. The number of manifolds in the f…

The process of exploring and exploiting Oil and Gas (O&G) generates a lot of data that can bring more efficiency to the industry. The opportunities for using data mining techniques in the "digital oil-field" remain largely unexplored or uncharted. With the high rate of data expansion, companies are scrambling to develo…

Study explores kinematics of surfaces under metric restrictions.

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{…

We extend Matveev's complexity of 3-manifolds to PL compact manifolds of arbitrary dimension, and we study its properties. The complexity of a manifold is the minimum number of vertices in a simple spine. We study how this quantity changes under the most common topological operations (handle additions, finite coverings…

Horizontal surgery on pseudo-Anosov flows yields almost equivalent flows.

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…

The main task in oil and gas exploration is to gain an understanding of the distribution and nature of rocks and fluids in the subsurface. Well logs are records of petro-physical data acquired along a borehole, providing direct information about what is in the subsurface. The data collected by logging wells can have si…

With recent progress in algorithms and the availability of massive amounts of computation power, application of machine learning techniques is becoming a hot topic in the oil and gas industry. One of the most promising aspects to apply machine learning to the upstream field is the rock facies classification in reservoi…

New method fractures hyperbolic manifolds using cone singularities.

Using PL-methods, we prove the Marden's conjecture that a hyperbolic 3-manifold $M$ with finitely generated fundamental group and with no parabolics are topologically tame. Our approach is to form an exhaustion $M_i$ of $M$ and modify the boundary to make them 2-convex. We use the induced path-metric, which makes the s…

Proposes RTL model for sentiment classification and key word detection in online reviews.

The growing capability and accessibility of machine learning has led to its application to many real-world domains and data about people. Despite the benefits algorithmic systems may bring, models can reflect, inject, or exacerbate implicit and explicit societal biases into their outputs, disadvantaging certain demogra…

In this work we perform a study of various unsupervised methods to identify mental stress in firefighter trainees based on unlabeled heart rate variability data. We collect RR interval time series data from nearly 100 firefighter trainees that participated in a drill. We explore and compare three methods in order to pe…

Deep learning speeds up pressure prediction in carbon storage reservoirs.

A half-geodesic is a closed geodesic realizing the distance between any pair of its points. All geodesics in a round sphere are half-geodesics. Conversely, this note establishes that Riemannian spheres with all geodesics closed and sufficiently many half-geodesics are round.

Study on homogeneous geodesics in sub-Riemannian geometry.

In non-compact manifolds, geodesic flowers exist.

Study on Mabuchi functional's convexity using ε-geodesics.

Geodesic graphs for special Finsler metrics on spheres are studied.

Characterizes visibility and geodesic loops in complex domains.

Conformal geodesics can't spiral in Riemannian manifolds.