The study uses Gaussian mixture models to estimate pipe wall thickness from partial scans.
problem Estimating remaining wall thickness of critical water mains in non-destructive evaluation.
method Developed a robotic vehicle for pipe inspections. Used Gaussian Processes and Gaussian Mixture Models to infer RWT at unseen sections.
result Gaussian mixture models effectively capture the probability of RWT values in inspected data.
The paper develops models to predict the remaining useful life of water pipes.
problem Predicting the remaining useful life of deteriorating water pipes.
method Artificial Neural Networks (ANNs) and Adaptive Neuro-fuzzy Inference System (ANFIS) applied to field data.
result Models accurately predict the reduction of remaining useful life due to pipe deterioration.
Paper solves Serrin problem for ring-shaped domains, showing velocity has finitely many maxima.
problem Characterizing rotationally symmetric solutions to a specific PDE on a ring-shaped domain.
method Introduced new arguments in the spirit of comparison geometry to overcome the lack of monotonicity.
result Simplest conditions are not sufficient; rotational symmetry requires finitely many maxima.
Distributed training of deep nets is an important technique to address some of the present day computing challenges like memory consumption and computational demands. Classical distributed approaches, synchronous or asynchronous, are based on the parameter server architecture, i.e., worker nodes compute gradients which…
Predict water pipe failures using machine learning and survival analysis.
problem Difficulty in accessing water pipes for maintenance.
method Classical and modern classifiers for short-term prediction, survival analysis for long-term forecast, and oversampling technique for imbalanced data.
result Identifies important risk factors for water pipe failures.
Random forest model predicts sewer pipe deterioration with high accuracy.
problem Challenges in predicting and scheduling sewer pipe inspections.
method Random forest classification model for sewer pipe condition prediction.
result Model achieved excellent AUC of 0.81 in a case study for City of LA.
Modof-pipe optimizes molecules by modifying a single site, outperforming state-of-the-art methods.
problem Improving drug candidates' properties through chemical modification.
method Deep generative model Modof over molecular graphs for molecule optimization.
result Modof-pipe achieves significant improvements in octanol-water partition coefficient and molecule similarity constraints.
Study surfaces in Half-Pipe space and vector fields on hyperbolic plane.
problem Mapping surfaces in Half-Pipe space to vector fields on hyperbolic plane.
method Use harmonic Lagrangian vector fields and infinitesimal Douady-Earle extension.
result Prove existence and uniqueness of harmonic Lagrangian extensions with Zygmund conditions.
We detail our ongoing work in Flint, Michigan to detect pipes made of lead and other hazardous metals. After elevated levels of lead were detected in residents' drinking water, followed by an increase in blood lead levels in area children, the state and federal governments directed over $125 million to replace water se…
A new deep metric learning method for defect classification in threaded pipe connections.
problem Defect classification in threaded pipe connections with limited and imbalanced multichannel functional data.
method COMPILED approach based on deep metric learning for imbalanced, multichannel, and partially observed functional data.
result Superior accuracy compared to existing benchmarks in a real-world case study.
We investigate the mapping class group of an orientable ω-bounded surface. Such a surface splits, by Nyikos's Bagpipe Theorem, into a union of a bag (a compact surface with boundary) and finitely many long pipes. The subgroup consisting of classes of homeomorphisms fixing the boundary of the bag is a normal subgroup …
New theory of distributions on spaces with singular submanifolds.
problem Defining distributions on spaces with singular submanifolds.
method Construction of thick distributions, operations, and special distributions.
result Clarified connection between thick and classical distributions.
Path-connectivity of thick laminations on high-genus surfaces.
problem Path-connectivity of thick laminations on high-genus surfaces.
method Teichmüller ray analysis and subshift of finite type construction.
result Path-connectedness of the Morse boundary of the mapping class group.
RL research overhypes potential but lacks deployable solutions.
problem Current RL research overhypes potential and lacks deployable solutions.
method Identifies and critiques current RL research practices.
result Current RL research direction is unlikely to lead to practical, economically viable solutions.
Let M be a finite volume oriented Riemannian manifold of dimension n≥3 and curvature in [−b2,−1], with thick-thin decomposition M=M(thick)∪M(thin). Denote by λk(M(thick)) the k-th eigenvalue for the Laplacian on M(thick), with Neumann boundary conditdions. We show that λk(M(thick))/3≤λk(M)…
What length of rope (of given diameter) is required to tie a particular knot? To answer this question, we define some new notions of thickness for a space curve, one based on Gromov's distortion, and another generalizing the thickness of Litherland, Simon et al. We prove a basic inequality between these thickness measu…
New examples show limits of physical link isotopies.
problem Limits of physical link isotopies in thick and thickly embedded links.
method Construction of specific examples of thick and thickly embedded links.
result Explicit examples of links that cannot be split through thick homotopies.
A knot's thickness is measured by its β invariant, a new numerical invariant.
problem Measuring the thickness of knots.
method Introduced a new invariant β(K) and proved an inequality between β(K) and knot Floer thickness.
result All Montesinos knots have thickness at most one.
The first algorithm for sampling the space of thick equilateral knots, as a function of thickness, will be described. This algorithm is based on previous algorithms of applying random reflections. To prove the existence of the algorithm, we describe a method for turning any knot into the regular planar polygon using on…
Method estimates section thickness and XY anisotropy in ssEM images.
problem Accurate 3D reconstructions require precise section thickness and XY anisotropy estimates.
method Non-parametric Bayesian regression of image statistics.
result Method has lower estimation error compared to existing methods.
Algorithm computes knot Floer complex for knots of thickness one.
problem Computing knot Floer complexes for knots of thickness one.
method Developed and implemented an algorithm for knots of thickness one.
result Algorithm can compute full knot Floer complex for knots of thickness one.
For right-angled Coxeter groups WΓ, we obtain a condition on Γ that is necessary and sufficient to ensure that WΓ is thick and thus not relatively hyperbolic. We show that Coxeter groups which are not thick all admit canonical minimal relatively hyperbolic structures; further, we show that in such a structure, …
We describe some problems, observations, and conjectures concerning thickness and packing density of knots and links in $\sp^3$ and R3. We prove the thickness of a nontrivial knot or link in $\sp^3$ is no more than 4π, the thickness of a Hopf link. We also give arguments and evidence supporting the conject…
New examples of gordian unlinks show different rope geometries.
problem Tackling the existence of non-trivial unknots with prescribed length and thickness.
method Provided the first examples of gordian unlinks with thickness in [1,2).
result Thinner normal tubes lead to different rope geometries.
We show that thick morphisms (or microformal morphisms) between smooth (super)manifolds, introduced by us before, are classical limits of `quantum thick morphisms' defined here as particular oscillatory integral operators on functions.
Study uses neural networks to predict wall quantities in turbulent flows.
problem Predicting wall quantities in turbulent open channel flows.
method Training convolutional neural networks (FCN) and a proposed R-Net architecture to predict wall-shear-stress and wall pressure.
result R-Net architecture performs better and predicts wall quantities with around 10% error.
Thick morphisms link quantum mechanics and supermanifolds.
problem Understanding the relationship between quantum mechanics and supermanifolds.
method Introducing and analyzing thick morphisms of supermanifolds.
result Quantum thick morphisms provide a spinor representation.
The paper explores new algebraic structures and morphisms in graded settings.
problem Understanding new algebraic structures and morphisms in graded settings.
method Introducing and analyzing L∞-, P∞-, and S∞-algebras, and thick morphisms in a Z2imesZ-graded context. result Shifted S∞-thick morphisms induce L∞-morphisms of shifted S∞-structures. We show that the diameter of the skinning map of an acylindrical hyperbolic 3-manifold M is bounded on thick Teichmueller geodesic rays by a constant depending only on the thickness of the ray and the topological type of the boundary of M.
The paper introduces boundary thickness as a measure for improving model robustness.
problem Improving the robustness of machine learning models to adversarial and non-adversarial corruptions.
method Introducing boundary thickness as a measure and showing how various procedures can increase it.
result Thicker decision boundaries lead to improved robustness against adversarial and out-of-distribution transforms.
This paper studies the interplay between the N=2 gauge theories in three and four dimensions that have a geometric description in terms of twisted compactification of the six-dimensional (2,0) SCFT. Our main goal is to construct the three-dimensional domain walls associated to any three-dimensional cobordism. We find t…
New G2-holonomy manifolds from 5d N=1 theories domain walls.
problem Geometrizing domain walls in 5d N=1 theories.
method Constructing 7-manifolds by fibering a Calabi-Yau over a real line.
result 7-manifolds with G2-holonomy from domain walls in 5d theories. We introduce a new quasi-isometry invariant of 2-dimensional right-angled Coxeter groups, the hypergraph index, that partitions these groups into infinitely many quasi-isometry classes, each containing infinitely many groups. Furthermore, the hypergraph index of any right-angled Coxeter group can be directly computed f…
The paper proves a theorem about earthquake extensions of vector fields on circles.
problem Proving a theorem about earthquake extensions of vector fields on circles.
method Using the geometry of the dual of Minkowski three-space and Half-pipe three-geometry.
result A generalization of Kerckhoff's and Gardiner's infinitesimal earthquake theorems to a broader setting.
New proof shows knot Floer thickness limits bad domains in diagrams.
problem Understanding knot thickness and dealternating number.
method Modified Stipsicz-Szabo approach using Kauffman states.
result Knot Floer thickness is a lower bound on dealternating number.
We show that a complete hyperbolic n-manifold has a geodesic triangulation such that the tetrahedra contained in the thick part are L-bilipschitz diffeomorphic to the standard Euclidean n-simplex, for some constant L depending only on the dimension and the constant used to define the thick-thin decomposition of M.
Study connects Morse theory with cluster variables for wall-crossing in Cerf diagrams.
problem Understanding wall-crossing in Cerf theory.
method Relates Bruhat numbers in real Morse theory to cluster variables in braid varieties.
result Provides wall-crossing coordinates in Cerf diagrams.
We explain how to adapt a construction of M. Sageev's to construct a proper action on a CAT(0) cube complex starting from a proper action on a wall space, and use this to deduce that if G is a group containing an amenable subgroup H of super-polynomial growth and G acts properly on a space with walls then there are arb…
Study on reducing surgeries on knots, developing thickness and genus bounds.
problem Understanding reducible surgeries on knots in S3. method Developed thickness bounds for L-space knots and lower bounds on slice genus; used d-invariants and mapping cone formula from Heegaard Floer homology. result Provided new upper bounds on reducing slopes for fibered, hyperbolic slice knots and on multiple reducing slopes for slice knots; verified the Cabling Conjecture for thin knots.
We show the existence of a thick thin decomposition of the domain of a pseudo holomorphic curve with boundary. The geometry of the thick part is bounded uniformly in the energy. Furthermore, in the thick part, there is a uniform bound on the differential which is exponential in the energy. The thin part consists of ann…
We prove that thick groups (and more generally thick graphs) have trivial Floyd boundary. This shows a wide class of finitely generated groups that are non-relatively hyperbolic have trivial Floyd boundary. In addition to giving new examples, our result provides a common proof and framework for many of the known result…
Neural network predicts turbulence near-wall regions efficiently.
problem Reducing computational cost in turbulent flow simulations.
method Fully-convolutional neural network trained on DNS data.
result FCN predicts velocity fluctuations at y+=50 with less than 20% error. We introduce the notion of connection thickness of spheres in a Cayley graph, related to dead-ends and their retreat depth. It was well-known that connection thickness is bounded for finitely presented one-ended groups. We compute that for natural generating sets of lamplighter groups on a line or on a tree, connection…
Farrell and Hsiang noticed that the geometric surgery groups defined By Wall, Chapter 9, do not have the naturality Wall claims for them. They were able to fix the problem by augmenting Wall's definitions to keep track of a line bundle. The definition of geometric Wall groups involves homology with local coefficients a…
A graphical calculus for microformal morphisms simplifies complex operations in classical and quantum physics.
problem Simplifying operations in classical and quantum microformal morphisms.
method Developed a graphical calculus inspired by Cattaneo-Dherin-Felder's work on formal symplectic groupoids, extended to quantum thick morphisms.
result Infinite series can be written as sums over bipartite trees for both classical and quantum thick morphisms.
The index theorem connects anomalies on a domain wall to global integrals.
problem Relating anomalies on a domain wall to global integrals.
method Formulated and proved an analog of the Atiyah-Patodi-Singer theorem.
result The index is expressed through global chiral and parity anomalies.
Convolutional networks predict turbulence from wall quantities.
problem Predicting turbulence fields from wall-shear-stress components and wall pressure.
method Two CNN models: FCN and FCN-POD, trained on DNS data.
result FCN and FCN-POD models outperform EPOD in predicting turbulence fields.
Classifies divergence and thickness in right-angled Coxeter groups.
problem Characterizing the divergence and thickness of right-angled Coxeter groups.
method Completely classifies divergence functions and proves conditions for thickness using the hypergraph index.
result Exact divergence functions of RACGs can be computed from their defining graphs.