Results 41 to 50 of about 6,627,879 (323)
Learning knot invariants across dimensions
SciPost Physics, 2023 We use deep neural networks to machine learn correlations between knot invariants in various dimensions. The three-dimensional invariant of interest is the Jones polynomial $J(q)$, and the four-dimensional invariants are the Khovanov polynomial $\text ...
Jessica Craven, Mark Hughes, Vishnu Jejjala, Arjun Kar
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Exact computation for existence of a knot counterexample
Applied General Topology, 2019 Previously, numerical evidence was presented of a self-intersecting Bezier curve having the unknot for its control polygon. This numerical demonstration resolved open questions in scientic visualization, but did not provide a formal proof of self ...
K. Marinelli, T. J. Peters
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On some ternary operations in knot theory [PDF]
, 2013 We introduce a way to color the regions of a classical knot diagram using ternary operations, so that the number of colorings is a knot invariant. By choosing appropriate substitutions in the algebras that we assign to diagrams, one obtains the relations
Maciej Niebrzydowski
semanticscholar +1 more source
All‐Polyimide‐Mediated Liquid Metal Assembly on Aerogels for Breathable and Robust Electronic Skins
Advanced Materials, EarlyView.An all‐polyimide‐mediated assembly strategy resolves the fundamental conflict between physiological breathability and electromechanical robustness in wearable electronics. By integrating a polyamic acid‐encapsulated liquid metal ink onto an ultralight polyimide aerogel, imidization‐induced contraction enables low‐temperature conductive activation and ...
Haijun Zhu +18 more
wiley +1 more source
A geometric characterization of the upper bound for the span of the jones polynomial
, 2011 Let D be a link diagram with n crossings, sA and sB be its extreme states and |sAD| (respectively, |sBD|) be the number of simple closed curves that appear when smoothing D according to sA (respectively, sB). We give a general formula for the sum |sAD| +
PEDRO M. G. MANCHÓN +4 more
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Advanced Materials Technologies, EarlyView.Transducers convert physical signals into electrical and optical representations, yet each mechanism is bounded by intrinsic trade‐offs across bandwidth, sensitivity, speed, and energy. This review maps transduction mechanisms across physical scale and frequency, showing how heterogeneous integration and multiphysics co‐design transform isolated ...
Aolei Xu +8 more
wiley +1 more source
Fractional Dehn twists in knot theory and contact topology [PDF]
, 2012 Fractional Dehn twists give a measure of the difference between the relative isotopy class of a homeomorphism of a bordered surface and the Thurston representative of its free isotopy class. We show how to estimate and compute these invariants.
W. Kazez, R. Roberts
semanticscholar +1 more source
Advanced Robotics Research, EarlyView.This article introduces a soft wearable eyelid sling device incorporating a hydraulic soft artificial muscle (SAM) for achieving complete closure of an eyelid. The SAM is driven by a cam mechanism that provides a displacement profile closely matched with those of a healthy eyelid.
Patrick Pruscino +7 more
wiley +1 more source
Perspectives of differential expansion
Physics Letters B, 2020 We outline the current status of the differential expansion (DE) of colored knot polynomials i.e. of their Z–F decomposition into representation– and knot–dependent parts.
L. Bishler, A. Morozov
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An introduction to knots and knot groups [PDF]
, 1970 The purpose of this paper is to present an introduction to the theory of knots and knot groups assuming an intermediate knowledge of group theory and topology on the part of the reader.
Supulski, Gwendolyn Eva +1 more
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