Computational Object-Wrapping Rope Nets

Wrapping objects using ropes is a common practice in our daily life. However, it is difficult to design and tie ropes on a 3D object with complex topology and geometry features while ensuring wrapping security and easy operation. In this article, we propose to compute a rope net that can tightly wrap around various 3D shapes. Our computed rope net not only immobilizes the object but also maintains the load balance during lifting. Based on the key observation that if every knot of the net has four adjacent curve edges, then only a single rope is needed to construct the entire net. We reformulate the rope net computation problem into a constrained curve network optimization. We propose a discrete-continuous optimization approach, where the topological constraints are satisfied in the discrete phase and the geometrical goals are achieved in the continuous stage. We also develop a hoist planning to pick anchor points so that the rope net equally distributes the load during hoisting. Furthermore, we simulate the wrapping process and use it to guide the physical rope net construction process. We demonstrate the effectiveness of our method on 3D objects with varying geometric and topological complexity. In addition, we conduct physical experiments to demonstrate the practicability of our method.

Formal derivation of the Laughlin function and its generalization for other topological phases of FQHE

Using the braid symmetry we demonstrate the derivation of the Laughlin function for the main hierarchy 1/q of FQHE in the lowest Landau level of two-dimensional electron system with a mathematical rigour. This proves that the derivation of Laughlin function unavoidably requires some topological elements and cannot be completed within a local quantum mechanics, i.e., without global topological constraints imposed. The method shows the way for the generalization of this function onto other fractions from the general quantum Hall hierarchy. A generalization of the Laughlin function is here formulated.

Controlling Toughness of Polymer-grafted Nanoparticle Composites for Impact Mitigation

Toughness in an entangled polymer network is typically controlled by the number of load-bearing topological constraints per unit volume. In this work, we demonstrate a new paradigm for controlling toughness...

Self-Localized Liquid Crystal Micro-Droplet Arrays on Chemically Patterned Surfaces

Liquid crystal (LC) micro-droplet arrays are elegant systems that have a range of applications, such as chemical and biological sensing, due to a sensitivity to changes in surface properties and strong optical activity. In this work, we utilize self-assembled monolayers (SAMs) to chemically micro-pattern surfaces with preferred regions for LC occupation. Exploiting discontinuous dewetting, dragging a drop of fluid over the patterned surfaces demonstrates a novel, high-yield method of confining LC in chemically defined regions. The broad applicability of this method is demonstrated by varying the size and LC phase of the droplets. Although the optical textures of the droplets are dictated by topological constraints, the additional SAM interface is shown to lock in inhomogeneous alignment. The surface effects are highly dependent on size, where larger droplets exhibit asymmetric director configurations in nematic droplets and highly knotted structures in cholesteric droplets.

Characterization of Almost Yamabe Solitons and Gradient Almost Yamabe Solitons with Conformal Vector Fields

In this paper, some sufficient conditions of almost Yamabe solitons are established, such that the solitons are Yamabe metrics, by which we mean metrics of constant scalar curvature. This is achieved by imposing fewer topological constraints. The properties of the conformal vector fields are exploited for the purpose of establishing various necessary criteria on the soliton vector fields of gradient almost Yamabe solitons so as to obtain Yamabe metrics.

HippUnfold: Automated hippocampal unfolding, morphometry, and subfield segmentation

The archicortical hippocampus differs, like the neocortex, in its folding patterns between individuals. Here, we present an automated and robust BIDS-App, HippUnfold, for defining and indexing subject-specific hippocampal folding in MRI, analogous to popular tools used in neocortical reconstruction. This is critical for inter-individual alignment, with topology as the basis for homology. This topological framework enables qualitatively new analyses of morphological and laminar structure in the hippocampus or hippocampal subfields, and is critical for the advancement of neuroimaging analyses at a meso- or micro-scale. HippUnfold uses state-of-the-art deep learning combined with previously developed topological constraints on hippocampal tissue. It is designed to work with commonly employed sub-millimetric MRI acquisitions, with extensibility to microscopic resolutions as well. In this paper we illustrate the power of HippUnfold in feature extraction, and its construct validity compared to several extant hippocampal subfield analysis methods.

Gompf connected sum for orbifolds and K-contact Smale–Barden manifolds

We develop the Gompf fiber connected sum operation for symplectic orbifolds. We use it to construct a symplectic 4-orbifold with b 1 = 0 {b_{1}=0} and containing symplectic surfaces of genus 1 and 2 that are disjoint and span the rational homology. This is used in turn to construct a K-contact Smale–Barden manifold with specified 2-homology that satisfies the known topological constraints with sharper estimates than the examples constructed previously. The manifold can be chosen spin or non-spin.

Analytical Method of Human Systemic and Global Circulation

The human circulatory system is one of the admirable rhythms of nature. The heart and the vasculature are constitutive structures. The vasculature consists of arterial and venous appurtenances which are arranged in an idealized network capable of enhancing circulation. The crux of this study is the representation of the cardiovascular system as a network in which electrical constraints apply. As a network, the system is amenable to graph analytic treatment; as edge-nodal parameters ensue, topological constraints apply. In virtue of cardiac auto-rhythmicity, electrical impulses are driven through the vessels to the body cells. As a rule, the vessels must elicit a modicum of resistance. This work weaponized the elements of graph theory and electrical properties of the heart in elucidating the flow mechanism associated with the cardio-vascular system. The voltage drop across the connecting vessels (idealized as wires) was carefully depicted and analyzed by the method of matrices. When the cardiac function is within physiological definition a vascular compartment may be a liability in the event of poor circulation. Therefore the knowledge of vascular resistive capacities, which this work portrayed, is a sine-qua-non to the assessment of flow integrity of the system under consideration. MSC 2010 No.: 05C21, 92C42, 92B25. Keywords: Cardiovascular, Network, Matrices, Flow, Circuit, Edges and Nodes, Wave propagation, Bifurcation.

Modeling of thermal studies on melt quenched Ge18Bi4Se78 chalcogenide

The crystallization characteristics for Ge18Bi4Se78 glass are studied in this work by means of DTA under the non-isothermal conditions. One stage endothermic glass transition and one exothermic crystallization are observed in the DTA curves. The results of topological constraints for Ge18Bi4Se78 glass show that the calculated value of glass transition temperature (Tg) is very close to that of the experimental results. The as-prepared as well as the annealed samples are examined using XRD, EDX, SEM techniques. Avrami exponent reveals the complicated stage of growth. Many models are used to estimate the activation energies for glass transition (Eg) and crystallization (Ec). The crystallization process found to be described by the Sestak- Berggren SB(M,N) model.

A Yeast-Based Screening System for Differential Identification of Poison Inhibitors and Catalytic Inhibitors of Human Topoisomerase I

Inhibition of human topoisomerase I (TOP1) by camptothecin and topotecan has been shown to reduce excessive transcription of PAMP (Pathogen-Associated Molecular Pattern) -induced genes in prior studies, preventing death from sepsis in animal models of bacterial and SARS-CoV-2 infections. The TOP1 catalytic activity likely resolves the topological constraints on DNA that encodes these genes to facilitate the transcription induction that leads to excess inflammation. The increased accumulation of TOP1 covalent complex (TOP1cc) following DNA cleavage is the basis for the anticancer efficacy of the TOP1 poison inhibitors developed for anticancer treatment. The potential cytotoxicity and mutagenicity of TOP1 targeting cancer drugs pose serious concerns for employing them as therapies in sepsis prevention. The aim of this study is to develop a novel yeast-based screening system that employs yeast strains expressing wild-type or a dominant lethal mutant recombinant human TOP1. This yeast-based screening system can identify human TOP1 poison inhibitors for anticancer efficacy as well as catalytic inhibitors that can inhibit TOP1 DNA binding or cleavage activity in steps prior to the formation of the TOP1cc. In addition to distinguishing between such TOP1 catalytic inhibitors and TOP1 poison inhibitors, results from this yeast-based screening system will also allow elimination of compounds that are likely to be cytotoxic based on their effect on yeast cell growth that is independent of recombinant human TOP1 overexpression.