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Stretchable devices have gained increasing interest in recent years, particularly in the field of wearable electronics. Among them, fiber‐type devices with high mechanical conformability hold great potential to enable next‐generation wearable and interactive applications with their special structure and high compatibility with the well‐established textile industries. In this study, a hydrogel fiber providing large moisture retention and high mechanical compliance is fabricated, with which a new approach to enable highly stretchable electromechanical sensors based on knot structures is developed. Comparative analysis with common orthogonal textile structures reveal the superior performance of sensors based on ionotronic knots. Stress sensors with the double overhand knot exhibit ≈four times greater variation in capacitance than those with orthogonal structures, and sensors with the clove hitch knot exhibit a fast response time of 57 ms. Based on the characteristics of different knots, a sensor matrix based on clove hitch knots to map the pressure distribution, and a wearable mole code generator based on reef knots to recognize and encode wrist motions are developed. These applications demonstrate the excellent performance of knot‐architecture sensors and their great potential in the fields of smart fabrics and human–machine interactions. [ABSTRACT FROM AUTHOR]

We study and characterize the topology of connectivity circuits observed in natively folded protein structures whose coordinates are deposited in the Protein Data Bank (PDB). Polypeptide chains of some proteins naturally fold into unique knotted configurations. Another kind of nontrivial topology of polypeptide chains is observed when, in addition to covalent bonds connecting consecutive amino acids in polypeptide chains, one also considers disulfide and ionic bonds between non‐consecutive amino acids. Bonds between non‐consecutive amino acids introduce bifurcation points into connectivity circuits defined by bonds between consecutive and nonconsecutive amino acids in analyzed proteins. Circuits with bifurcation points can form θ‐curves with various topologies. We catalog here the observed topologies of θ‐curves passing through bridges between consecutive and non‐consecutive amino acids in studied proteins. [ABSTRACT FROM AUTHOR]

The use of 2,5‐diformylpyrrole in self‐assembly reactions with diamines and Zn(II)/Cd(II) salts allowed the preparation of [2]catenane, trefoil knot, and Borromean rings. The intrinsically dynamic nature of the diiminopyrrole motif rendered all of the formed assemblies intramolecularly flexible. The presence of diiminopyrrole revealed new coordination motifs and influenced the host–guest chemistry of the systems, as illustrated by hexafluorophosphate encapsulation by Borromean rings. [ABSTRACT FROM AUTHOR]

The N‐terminal half of the giant cytoskeletal protein obscurin is comprised of more than 50 Ig‐like domains, arranged in tandem. Domains 18–51 are connected to each other through short 5‐residue linkers, and this arrangement has been previously shown to form a semi‐flexible rod in solution. Domains 1–18 generally have slightly longer ~7 residue interdomain linkers, and the multidomain structure and motion conferred by this kind of linker is understudied. Here, we use NMR, SAXS, and MD to show that these longer linkers are associated with significantly more domain/domain flexibility, with the resulting multidomain structure being moderately compact. Further examination of the relationship between interdomain flexibility and linker length shows there is a 5 residue "sweet spot" linker length that results in dual‐domain systems being extended, and conversely that both longer or shorter linkers result in a less extended structure. This detailed knowledge of the obscurin N terminus structure and flexibility allowed for mathematical modeling of domains 1–18, which suggests that this region likely forms tangles if left alone in solution. Given how infrequently protein tangles occur in nature, and given the pathological outcomes that occur when tangles do arise, our data suggest that obscurin is likely either significantly scaffolded or else externally extended in the cell. [ABSTRACT FROM AUTHOR]

Inspired by Dunitz's treatment of the geometry and flexibility of cyclohexane, we describe some ways in which hexagons and octahedra can become self‐entangled and linked. Connections to topics such as flexibility of frameworks, tensegrity structures, and Borromean rings are indicated. [ABSTRACT FROM AUTHOR]

Families of 1‐ and 2‐periodic knots and weavings that have isogonal (vertex‐transitive) piecewise‐linear embeddings are described. In these structures there is just one thread, or multiple threads with parallel or collinear axes. The principal structures are a large family of 1‐periodic knots and related multi‐thread infinite links, knitting patterns and chain‐link weaving. The relevance to synthetic chemistry is described in terms of targets for designed synthesis such as mechanically interlocked polymers. [ABSTRACT FROM AUTHOR]

Mechanically Interlocked Molecules (MIMs), such as catenanes, knots, and rotaxanes, are a class of molecules that possess mechanical bonds. These bonds constitute an entanglement in space between components of the MIMs that cannot be separated without breaking a participating covalent bond. Although it is possible to synthesize chiral MIMs with covalent stereogenic centers, this new bond opens up the possibilities of axial, planar and helical chirality, as well as topologically chiral compounds. A growing number of chiral MIMs have been investigated and employed in numerous applications, ranging from sensing to catalysis. While the investigation of the properties of MIMs is highly developed, it is also essential to study their chiroptical properties. In this review, we focus on the chiroptical properties of chiral MIMs. We discuss their electronic circular dichroism (ECD) since these properties have been analyzed in some detail in relation to their structures and stereochemistry. Although only a few examples have been described to date, we discuss the encouraging circularly polarized luminescence (CPL) properties of MIMs. The review also includes a recent study of vibrational circular dichroism (VCD) in mechanically planar chiral rotaxanes suggesting that this technique is a promising tool for analyzing the structures of MIMs. The study of the chiroptical properties of MIMs can have a large impact on their use in materials science or as catalysts. One of the key advantage of chiral MIMs is that they provide a means of generating efficient chiroptical switches that have a bright future in the context of multiple applications. [ABSTRACT FROM AUTHOR]

This article describes the simplest members of an infinite family of knots and links that have achiral piecewise‐linear embeddings in which linear segments (sticks) meet at corners. The structures described are all corner‐ and stick‐2‐transitive – the smallest possible for achiral knots. [ABSTRACT FROM AUTHOR]

Mathematical knots and links are described as piecewise linear – straight, non‐intersecting sticks meeting at corners. Isogonal structures have all corners related by symmetry ('vertex'‐transitive). Corner‐ and stick‐transitive structures are termed regular. No regular knots are found. Regular links are cubic or icosahedral and a complete account of these (36 in number) is given, including optimal (thickest‐stick) embeddings. Stick 2‐transitive isogonal structures are again cubic and icosahedral and also encompass the infinite family of torus knots and links. The major types of these structures are identified and reported with optimal embeddings. The relevance of this work to materials chemistry and biochemistry is noted. [ABSTRACT FROM AUTHOR]

The valuable luminescence, magnetic, and catalytic properties of lanthanide cations are beginning to be exploited in conjunction with structurally exotic mechanically interlocked molecules (MIMs) such as rotaxanes, catenanes and knots. This Minireview provides an account of this rapidly developing research area commencing with the use of lanthanides in extended MIM-containing frameworks. Then, attention turns to discrete lanthanide-containing pseudorotaxanes, followed by fully interlocked rotaxanes, catenanes and knots – where lanthanides have not only been incorporated into MIM architectures but have also been used to template formation of the interlocked structure. Particular focus is paid to examples where the lanthanide MIMs have been put to useful applications, in what is still a relatively youthful avenue of research in both lanthanide coordination chemistry and the chemistry of mechanically interlocked molecules. [ABSTRACT FROM AUTHOR]

Key Clinical Message Nasogastric tubes (NGT) are extensively used and generally harmless, yet loop formation and malpositioning are often reported especially when using thin NGT for enteral feeding which placed blindly; therefore, diligent follow-up of NGT is required with confirmation of right placement, changing it to PEG if long use of NGT needed. [ABSTRACT FROM AUTHOR]

ABSTRACT In wooden boards, knots and the resulting fibre deviations in their vicinities are mainly responsible for qualitative downgrading of timber elements. Thus, the development of reliable numerical simulation tools for the determination of effective strength and stiffness properties of timber elements and, in a next step, for the development and evaluation of grading criteria is highly desirable. Due to the complexity of such tools, a comprehensive validation is required. Within this work, the suitability of full-field deformation measurements for four-point bending tests on wooden boards with knots is evaluated first. Next, the test series is used to validate a previously developed three-dimensional numerical simulation tool, which combines a geometrical model for the grain course and a micromechanical model for a density and moisture dependent characterisation of the clear-wood material. The digital image correlation technique proved to be capable to reproduce the strain fields in the vicinity of knots under bending load. Moreover, a very good correlation between numerical and experimental results was obtained. [ABSTRACT FROM AUTHOR]

* Premise of the study: Leaf form and development are controlled genetically. The ARP genes encode MYB transcription factors that interact with Class 1 KNOX genes in a regulatory module that controls meristem-leaf determinations and is highly conserved in plants. ARP loss of function alleles and subsequent KNOX1 overexpression cause many unusual leaf phenotypes including loss or partial loss of the ability to produce a lamina and production of "knots" on leaf blades. CRISPA (CRI) is the ARP gene in pea, and a number of its mutant alleles are known. * Methods: We made morphological and anatomical evaluations of cri-1 mutant plants while controlling for genetic background and for heteroblastic effects, and we used aldehyde fixation and resin preparations for anatomical analysis. Further, we compared gene expression in WT and cri-1 shoot tips and HOP1/PsKN1 and CRI expression in other leaf mutants. * Key results: The cri-1 plants had more extensive abnormalities in the proximal than in the distal regions of the leaf, including ectopic stipules, narrow leaflets, and shortened petioles with excessive adaxial expansion. "Knots" were morphologically and anatomically variable but consisted of vascularized out-pocketing of the adaxial leaflet surface. HOP1/PsKN1 and UNI mRNA levels were higher in cri-1 shoot tips, and some auxin-regulated genes were lower. Low LE expression suggests that the GA level is high in cri-1 shoot tips. * Conclusions: The CRISPA gene of pea suppresses KNOX1 genes and UNI and functions to (1) maintain proximal-distal regions in their appropriate positions, (2) restrict excessive adaxial cell proliferation, and (3) promote laminar expansion. [ABSTRACT FROM AUTHOR]

Using spline functions (segmented polynomials) in regression models requires the knowledge of the location of the knots. Knots are the points at which independent linear segments are connected. Optimal positions of knots for linear splines of different orders were determined in this study for different scenarios, using existing estimates of covariance functions and an optimization algorithm. The traits considered were test-day milk, fat and protein yields, and somatic cell score (SCS) in the first three lactations of Canadian Holsteins. Two ranges of days in milk (from 5 to 305 and from 5 to 365) were taken into account. In addition, four different populations of Holstein cows, from Australia, Canada, Italy and New Zealand, were examined with respect to first lactation (305 days) milk only. The estimates of genetic and permanent environmental covariance functions were based on single- and multiple-trait test-day models, with Legendre polynomials of order 4 as random regressions. A differential evolution algorithm was applied to find the best location of knots for splines of orders 4 to 7 and the criterion for optimization was the goodness-of-fit of the spline covariance function. Results indicated that the optimal position of knots for linear splines differed between genetic and permanent environmental effects, as well as between traits and lactations. Different populations also exhibited different patterns of optimal knot locations. With linear splines, different positions of knots should therefore be used for different effects and traits in random regression test-day models when analysing milk production traits. [ABSTRACT FROM AUTHOR]

We study a semiparametric generalized additive coefficient model (GACM), in which linear predictors in the conventional generalized linear models are generalized to unknown functions depending on certain covariates, and approximate the non-parametric functions by using polynomial spline. The asymptotic expansion with optimal rates of convergence for the estimators of the non-parametric part is established. Semiparametric generalized likelihood ratio test is also proposed to check if a non-parametric coefficient can be simplified as a parametric one. A conditional bootstrap version is suggested to approximate the distribution of the test under the null hypothesis. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed methods. We further apply the proposed model and methods to a data set from a human visceral Leishmaniasis study conducted in Brazil from 1994 to 1997. Numerical results outperform the traditional generalized linear model and the proposed GACM is preferable. [ABSTRACT FROM AUTHOR]

To compare the weights of commonly used extracorporeal slip knots. The weights of seven commonly used types of extracorporeal slip knots and an intracorporeally tied flat square knot were compared. In each arm of the study, 17 knots were tied around a 5-mm jig using a laparoscopic trainer. Knots were weighed using microscales. A laboratory experiment. Weight of knot loops in milligrams. The heaviest ligature was the modified Roeder knot. The Western knot utilized less suture material than all the other knots studied. The flat square knot utilized less suture material than all the slip knots with the exception of the Western ligature. As other studies have correlated suture mass with the incidence of wound infection, a ligature with a low weight should be chosen in preference to the modified Roeder knot where possible. [ABSTRACT FROM AUTHOR]

To compare the tensile strengths of commonly used extracorporeal slipknots when tied with poliglecaprone and polydioxanone. The tensile strength of seven extracorporeal slip knots and the flat square knot were tested using a tensiometer. Knots were tied in random order with 2/0 poliglecaprone and polydioxanone. The study was designed to demonstrate a 5-newton difference in knot strength with 95% confidence at 80% power. Five knots were studied in each arm of the experiment. A laboratory experiment. Force required to break or cause slippage of knots. Knots tied with polydioxanone had a marginal yet significantly stronger tensile strength of 2.3 N (95% CI 0.1–0.75 N, P = 0.0332). The Tayside, Blood, Hutchon and Western knots had lower tensile strengths than the flat square knot in both poliglecaprone and polydioxanone. The modified Roeder knot was also stronger than the other ligatures when tied in poliglecaprone and more secure than the Western and Tayside knots when tied in polydioxanone. Slip knots tied in poliglecaprone are marginally less strong than those tied in polydioxanone. No extracorporeally tied slip knot is stronger than the modified Roeder knot. [ABSTRACT FROM AUTHOR]

The energy minimization problem associated to uniform, isotropic, linearly elastic rods leads to a geometric variational problem for the rod centreline, whose solutions include closed, knotted curves. We give a complete description of the space of closed and quasiperiodic solutions. The quasiperiodic curves are parametrized by a two-dimensional disc. The closed curves arise as a countable collection of one-parameter families, connecting the $m$-fold covered circle to the $n$-fold covered circle for any relatively prime $m$ and $n$. Each family contains exactly one self-intersecting curve, one elastic curve, and one closed curve of constant torsion. Two torus knot types are represented in each family, and all torus knots are represented by elastic rod centrelines. 1991 Mathematics Subject Classification: primary 53A04, 73C02; secondary 57M25. [ABSTRACT FROM AUTHOR]

We describe a new method for modelling braids and certain classes of knots and links, and how they may be visualized. The method uses generalized cylinders built around a bicubic spline centre line. We also show how multi-stranded, recursive, hawser laid ropes can be modelled using related techniques. [ABSTRACT FROM AUTHOR]