Computation and visualization of ideal knot shapes

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We examine the connection of two graph parameters, the size of a minimum feedback arcs set and the acyclic disconnection. A feedback arc set of a directed graph is a subset of arcs such that after deletion the graph becomes acyclic. The acyclic disconnecti ...

Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem. Spectral algorithms ...

We investigate the failure mechanism of stopper knots, with a particular focus on the figure -8 knot as a representative example. Stopper knots are widely used in climbing, sailing, racket stringing, and sewing to maintain tension in ropes, strings, or thr ...

Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...

We introduce and derive the Fourier -enhanced 3D electrostatic field solver of the gyrokinetic full -f PIC code PICLS. The solver makes use of a Fourier representation in one periodic direction of the domain to make the solving of the system easily paralle ...

The Schottky monitors of the Large Hadron Collider (LHC) can be used for non-invasive beam diagnostics to estimate various bunch characteristics, such as tune, chromaticity, bunch profile or synchrotron frequency distribution. However, collective effects, ...

We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...

This article focuses on spectral methods for recovering communities in temporal networks. In the case of fixed communities, spectral clustering on the simple time-aggregated graph (i.e., the weighted graph formed by the sum of the interactions over all tem ...

We propose a statistically optimal approach to construct data-driven decisions for stochastic optimization problems. Fundamentally, a data-driven decision is simply a function that maps the available training data to a feasible action. It can always be exp ...

Zoning reform is a crucial tool for cities to adapt to contemporary challenges. However, its implementation remains challenging. Property owners, with a vested interest in the value of their neighborhoods, are sensitive to local developments and the potent ...

Computer simulations are often used as support material for science education, as they can engage students through inquiry-based learning, promote their active interaction in the experimentation phase, and help them visualize abstract concepts. For instanc ...

Sample efficiency is a fundamental challenge in de novo molecular design. Ideally, molecular generative models should learn to satisfy a desired objective under minimal calls to oracles (computational property predictors). This problem becomes more apparen ...

In light of the challenges posed by climate change and the goals of the Paris Agreement, electricity generation is shifting to a more renewable and decentralized pattern, while the operation of systems like buildings is increasingly electrified. This calls ...

In this thesis, we study the mechanics of tight physical knots. Knots are omnipresent in surgery, climbing, and sailing, with disastrous consequences when the filament or the rope fails to perform its function. Even if the importance of mechanical analysis ...

We present an algorithmic approach to discover, study, and design multistable elastic knots. Elastic knots are physical realizations of closed curves embedded in 3-space. When endowed with the material thickness and bending resistance of a physical wire, t ...

Knots are the weakest link in surgical sutures, serving as mechanical ligatures between filaments. Exceeding their safe operational limits can cause fatal complications. The empirical nature of present guidelines calls for a predictive understanding of the ...

This thesis is a study of the global well-posedness of the Cauchy problems for half-wave maps from the Minkowski space of dimension n+1 to the 2-dimensional sphere and the hyperbolic plane. The work is mainly based on the results from Krieger-Sire 17' in ...

Graph machine learning offers a powerful framework with natural applications in scientific fields such as chemistry, biology and material sciences. By representing data as a graph, we encode the prior knowledge that the data is composed of a set of entiti ...

We propose ordering-based approaches for learning the maximal ancestral graph (MAG) of a structural equation model (SEM) up to its Markov equivalence class (MEC) in the presence of unobserved variables. Existing ordering-based methods in the literature rec ...

We study experiment design for unique identification of the causal graph of a system where the graph may contain cycles. The presence of cycles in the structure introduces major challenges for experiment design as, unlike acyclic graphs, learning the skele ...

Computation and visualization of ideal knot shapes

Chattez avec Graph Search

The connection of the acyclic disconnection and feedback arc sets - On an open problem of Figueroa et al

The Power of Two Matrices in Spectral Algorithms for Community Recovery

Capsizing due to friction-induced twist in the failure of stopper knots

BENIGN LANDSCAPES OF LOW-DIMENSIONAL RELAXATIONS FOR ORTHOGONAL SYNCHRONIZATION ON GENERAL GRAPHS

Verification of the Fourier-enhanced 3D finite element Poisson solver of the gyrokinetic full-f code PICLS

Impact of beam-coupling impedance on the Schottky spectrum of bunched beam

Non-planarity of Markoff graphs mod p

Recovering Static and Time-Varying Communities Using Persistent Edges

A Pareto Dominance Principle for Data-Driven Optimization

Spatial Modeling for Building Design Evaluation: from Visual Landscape Quality Assessment to Devaluation Risk Estimation

Teacher-Mediated and Student-Led Interaction with a Physics Simulation: Effects on the Learning Experience

Augmented Memory: Sample-Efficient Generative Molecular Design with Reinforcement Learning

Quantifying the Unknown: Data-Driven Approaches and Applications in Energy Systems

Mechanics of Physical Knots: From Filaments in Contact to Surgical Suturing

Computational Exploration of Multistable Elastic Knots

The strength of surgical knots involves a critical interplay between friction and elastoplasticity

Well-posedness Issues For the Half-Wave Maps Equation With Hyperbolic And Spherical Targets

Equivariant Neural Architectures for Representing and Generating Graphs

Novel Ordering-based Approaches for Causal Structure Learning in the Presence of Unobserved Variables

A Unified Experiment Design Approach for Cyclic and Acyclic Causal Models