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In the theory of finite type Vassiliev knot invariants, the universal sl 2 weight system maps the chord diagrams to polynomials in a single variable with integer coefficients. In this paper, we define a family of polynomials that generalize the Kreweras triangle (known to refine the normalized median Genocchi numbers), and we show how it appears in this weight system.

For centuries, Kurds have been carrying out activities aimed at obtaining their own state. Due to the cooperation of Turkey, Iraq, Iran and Syria, it was impossible in the twentieth century. As a result of Operation Desert Storm, a Kurdish enclave was created in the north of Iraq, which over the years developed and allowed for real dreams of recognized independence, at least for some of the Kurds living in the Middle East. A&er the overthrow of Saddam Hussein and the withdrawal of US troops from Iraq in 2011, there was a political vacuum in which we observe the weakening of the Iraqi state, the outbreak of the Arab Spring and the emergence of the Islamic State, which also had direct consequences for the Kurds. The weakness of the central government in Baghdad, the need to fight the Kurdish army against IS fighters raised the importance of arguments for the proclamation of an independent Kurdish state in the Middle East, or maybe even two, including the possible division of Syria.

Aspergillus niger F22 producing oxalic acid (OA) as a nematicidal component is currently used as a microbial nematicide. OA is known to induce systemic resistance in plant diseases caused by fungi, bacteria, and viruses, but the induced resistance of OA has not yet been elucidated in plant diseases caused by root-knot nematodes (RKNs). In this study, we investigated the functional mechanism of induced resistance of A. niger F22 formulation (Nemafree, 20% SC) and OA in tomato plant RKN disease caused by Meloidogyne incognita and analyzed their effectiveness against the disease. Foliar spray and soil drench treatments of Nemafree and OA were effective in the management of M. incognita in tomato plant in-pot experiments. When Nemafree and OA were applied 4 days before inoculation of M. incognita eggs, the treatments of Nemafree (4,000-fold dilution) and OA (0.22 mM) reduced root gall formation by more than 50%. The soil drench treatment also effectively suppressed RKN disease in field experiments. Moreover, the treatments of Nemafree and OA enhanced the transcriptional expression of pathogenesis-related 1 gene, plant proteinase inhibitor-II, and polyphenol oxidase genes and improved the production of total phenols, flavonoids, and lignin in the tomato plants infected with M. incognita. These results demonstrate that RKN diseases can be effectively controlled by induced resistance even at low concentrations of Nemafree or OA. Accordingly, our study provides evidence for more economical and efficient application strategies of microbial nematicides that control RKNs under field conditions.

Native interactions are crucial for folding, and non-native interactions appear to be critical for efficiently knotting proteins. Therefore, it is important to understand both their roles in the folding of knotted proteins. It has been proposed that non-native interactions drive the correct order of contact formation, which is essential to avoid backtracking and efficiently self-tie. In this study we ask if non-native interactions are strictly necessary to tangle a protein, or if the correct order of contact formation can be assured by a specific set of native, but otherwise heterogeneous, interactions. In order to address this problem we conducted extensive Monte Carlo simulations of lattice models of proteinlike sequences designed to fold into a pre-selected knotted conformation embedding a trefoil knot. We were able to identify a specific set of heterogeneous native interactions that drives efficient knotting, and is able to fold the protein when combined with the remaining native interactions modeled as homogeneous. This specific set of heterogeneous native interactions is strictly enough to efficiently self-tie. A distinctive feature of these native interactions is that they do not backtrack, because their energies ensure the correct order of contact formation. Furthermore, they stabilize a knotted intermediate state, which is enroute to the native structure. Our results thus show that - at least in the context of the adopted model - non-native interactions are not necessary to knot a protein. However, when they are taken into account into protein energetics it is possible to find specific, non-local non-native interactions that operate as a scaffold that assists the knotting step.

A simple, high molecular weight DNA extraction and long read genomic sequencing library preparation from individual root-knot nematodes (RKN). This protocol successfully sequences juvenile stage 2 (j2) RKN individuals, which are less than 500 µm long, and therefore the protocol is applicable for other meiofauna. DNA extraction follows a highly modified Mu-DNA: Tissue protocol (Sellers et al., 2018) using a solid phase reversible immobilization (SPRI) magnetic bead capture method, adapted from Rohland and Reich, (2012). Library preparation follows Oxford Nanopore Technologies' Rapid PCR Barcoding Kit (SQK-RPB004), modified for extremely low input DNA template and converted for Flongle flow cell sequencing. The method is capable of generating sufficient reads for successful taxonomic assignment from juvenile stage 2 (j2) to adult individuals using our bioinformatics workflow available at: https://github.com/Graham-Sellers/RKN_genomic_taxonomic_assignment. Rohland N, Reich D (2012) Cost-effective, high-throughput DNA sequencing libraries for multiplexed target capture. Genome research 22:939–946. Sellers GS, Di Muri C, Gómez A, Hänfling B (2018) Mu-DNA: a modular universal DNA extraction method adaptable for a wide range of sample types. Metabarcoding and Metagenomics 2:e24556. (dx.doi.org/10.17504/protocols.io.qn9dvh6)

We use Langevin dynamics simulations to model, at atomistic resolution, how various natively–knotted proteins are unfolded in repeated allosteric translocating cycles of the ClpY ATPase. We consider proteins representative of different topologies, from the simplest knot (trefoil 31), to the three–twist 52 knot, to the most complex stevedore, 61, knot. We harness the atomistic detail of the simulations to address aspects that have so far remained largely unexplored, such as sequence–dependent effects on the ruggedness of the landscape traversed during knot sliding. Our simulations reveal the combined effect on translocation of the knotted protein structure, i.e. backbone topology and geometry, and primary sequence, i.e. side chain size and interactions, and show that the latter can even dominate translocation hindrance. In addition, we observe that, due to the interplay between the knotted topology and intramolecular contacts, the transmission of tension along the peptide chain occurs very differently from homopolymers. Finally, by considering native and non–native interactions, we examine how the disruption or formation of such contacts can affect the translocation processivity and concomitantly create multiple unfolding pathways with very different activation barriers.

The present field experiment was conducted to determine the efficacy of consortium of different bio-agents viz., Psuedomonas fluorescens + Trichoderma harzianum + Bacillus megatherium, organic amendments viz., neem cake, poultry manure and nematicides viz., carbosulfan, carbofuran and fluensulfone for the management of M. graminicola under direct-seeded condition during kharif 2019-20 at the University of Agricultural and Horticultural Sciences, Shivamogga. The results revealed that all the treatments were significantly superior over the untreated check with respect to plant growth parameters and nematode population. However, the plots treated with fluensulfone at 3g/plot was found to be the best treatment as it recorded highest plant height (78.87 cm), root length (18.90 cm) with lowest RKI (2.0), maximum grain yield (36.87 q/ha) and least nematode population (199.00/200g soil) followed by the consortium of bioagents P. fluorescens + T. harzianum + B. megatherium at 20g/m2, carbofuran 3G at 9.9g/ m2, carbosulfan 25 EC at 0.1%, neem cake at 100g/m2 and poultry manure at 100g/m2 respectively.

One of the most mysterious aspects of Saito’s theory of Hodge modules are the Hodge and weight filtrations that accompany the pushforward of a Hodge module under an open embedding. In this paper we consider the open embedding in a product of complementary Grassmannians given by pairs of transverse subspaces. The push-forward of the structure sheaf under this open embedding is an important Hodge module from the viewpoint of geometric representation theory and homological knot invariants. We compute the associated graded of this push-forward with respect to the induced Hodge filtration as well as the resulting weight filtration. The main tool is a categorical $${\mathfrak {sl}}_2$$ action on the category of $${\mathcal {D}}_h$$ -modules on Grassmannians. Along the way we also clarify the interaction of kernels for $${\mathcal {D}}_h$$ -modules with the associated graded functor. Both of these results may be of independent interest.

Introduction. Teaching surgical skills has historically been a hands-on activity, with instructors and learners in close physical proximity. This paradigm was disrupted by the COVID-19 pandemic, requiring innovative solutions to surmount the challenges of teaching surgical skills remotely. In this work, we describe our institution’s path and early results of developing an interactive remote surgical skills course for medical students in the surgical clerkship. Methods. 31 third-year medical students were distributed a set of surgical equipment and 3D printed phone dock. Each participant completed a baseline questionnaire and underwent 3 structured interactive remote sessions on surgical instruments, knot tying, and suturing techniques. Students were instructed on sharing their first-person viewpoint and received real-time feedback on their knot tying and suturing techniques from the course instructor. Pre- and post-session surveys were conducted and analyzed. Results. All students were able to complete the remote surgical skills course successfully, as defined by visually demonstrating successful two-handed knot and simple suture techniques. Students’ aggregate confidence score in their knot tying ability (pretest mean 7.9, SD 0.7 vs posttest mean 9.7, SD 0.9, t-statistic −2.3, P = .03) and suturing ability (pretest mean 8.0, SD 1.3 vs posttest mean 13.8, SD 0.9 t-statistic −5.5, P < .001) significantly improved after the intervention. Qualitative feedback from the students underscored the utility of the first-person perspective for teaching surgical technique. Conclusion. This study demonstrates that remote teaching of knot tying and simple suturing to medical students can be effectively implemented using a remote learning curriculum that was well received by the learners.

The knotting of biomolecules impacts their function, and enables them to carry out new tasks. Likewise, complex topologies underpin the operation of many synthetic molecular machines. The ability to generate and control more complex knotted architectures is essential to endow these machines with more advanced functions. Here we report the synthesis of a molecular knot with eight crossing points, consisting of a single organic loop woven about six templating metal centres, via one-pot self-assembly from a simple pair of dialdehyde and diamine subcomponents and a single metal salt. The structure and topology of the knot were established by NMR spectroscopy, mass spectrometry and X-ray crystallography. Upon demetallation, the purely organic strand relaxes into a symmetric conformation, whilst retaining the topology of the original knot. This knot is topologically chiral, and may be synthesised diastereoselectively through the use of an enantiopure diamine building block.

In previous work of the first and third authors, we proposed a conjecture that the Kauffman bracket skein module of any knot in $S^3$ carries a natural action of the rank 1 double affine Hecke algebra $SH_{q,t_1, t_2}$ depending on 3 parameters $q, t_1, t_2$. As a consequence, for a knot $K$ satisfying this conjecture, we defined a three-variable polynomial invariant $J^K_n(q,t_1,t_2)$ generalizing the classical colored Jones polynomials $J^K_n(q)$. In this paper, we give explicit formulas and provide a quantum group interpretation for the generalized Jones polynomials $J^K_n(q,t_1,t_2)$. Our formulas generalize the so-called cyclotomic expansion of the classical Jones polynomials constructed by K.\ Habiro: as in the classical case, they imply the integrality of $J^K_n(q,t_1,t_2)$ and, in fact, make sense for an arbitrary knot $K$ independent of whether or not it satisfies our earlier conjecture. When one of the Hecke deformation parameters is set to be 1, we show that the coefficients of the (generalized) cyclotomic expansion of $J^K_n(q,t_1)$ are determined by Macdonald orthogonal polynomials of type $A_1$., Comment: 23 pages, minor corrections in v2

Sjogren syndrome (SS) is a systemic autoimmune disease typically characterized by inflammatory involvement of the exocrine glands1. The association of SS with an increased risk of cardiovascular disease (CVD) including manifestations such as stroke and myocardial infarction has been demonstrated by numerous previous studies1. Bringing classical CVD risk factors under control through appropriate therapeutic interventions has traditionally been the primary approach that has been reiterated in most practice guidelines regarding the prevention of CVD in patients with SS2. Yet, it would appear that these measures are not adequate by themselves to halt progression to CVD in these patients, as demonstrated by previous epidemiologic evidence3. It would thus appear that more mechanisms that are as of yet unaccounted for play an important role in this context. This complex conundrum is reminiscent of the ancient Greek legend of the “Gordian knot,” a knot tied by Gordius, the king of Phrygia, rumored to be impossible to untie except … Address correspondence to Prof. Dr. S.I. Mavrogeni, Onassis Cardiac Surgery Center, Leof. Andrea Siggrou 356, Kallithea 17674, Athens, Greece. Email: sophie.mavrogeni{at}gmail.com.

More than half a century of investigations on the chemical and isotopic compositions and on geochronological data of the Cenozoic magmatic rocks in the Alps and the transition to the Apennine will be summarized. The Alps itself are dominated by a calc-alkaline series between ~42 and 30 Ma, which we summarized as Periadriatic magmatism. This magmatism includes also eroded volcanic parts and several dykes in the Southern Alps and Tyrol. In addition, Sesia Zone magmatic rocks are characterized by ultrapotassic, shoshonitic and calc-alkaline rocks between 33 and 30 Ma. Two other magmatic provinces are located in between the Alps and the Apennine: (1) Veneto volcanic province (=VVP; nephelinites, basanites and alkali basalts between 52 and 30 Ma); (2) Mortara volcano (~28 Ma). Another group is the Esterél magmatic province, which is located in the Alps and their direct foreland, but are not related to Alpine geodynamics. These are basalts, andesites and dacites with mantle signature developed between 40 and 20 Ma. In the hanging plate of the early Apennine geometry, some minor volcanic activity is preserved in Sardinia. The major volume of Apennine magmatism itself (Elba etc.) is Late Miocene-Pleistocene in age and is related to roll back dynamics of the Apennine.The Eocene/Oligocene Periadriatic magmatism of the Alps requires significant melt production in the crust combined with some ACF processes. This is possible by infiltration of fluids in the mantle wedge and the lower crust and a change of P-T conditions in the mantle. Their calc-alkaline character is related to Na-dominated input in the mantle and crust, which is commonly inferred to result from subduction of oceanic units. Ultrapotassic melts in the Sesia-unit most likely result from infiltration of K-dominated fluids, related to dehydration of continental material. The dynamics of Apennine and possible related forearc extension would allow an extensional related magmatism in the Esterél. This magmatism overlap in time with Alpine magmatism, and require a small-scale mantle dynamic due to the development of two slabs. In addition, the VVP and the Mortara volcano are located on the non deformed continental fragment of Adria between the Alps and Apennine. This area is characterized by overfilled basins and local magmatism inside the Adriatic continental plate.The sometimes minor preserved volumes, but well constrain timing of magmatic rocks at the interaction between Alps and Apennine give insights in the lower crust/mantle dynamics at Oligocene/Early Miocene times. These interpretations may differ from models based on upper crustal tectonics, due to the decoupling between upper crust and lower crust/mantle.

Background The closure of high-tension incisions without any assistance can be difficult and challenging for surgeons. A common practice is to fix the first knot with a clamp and then tie a reverse locking knot; however, this practice has certain disadvantages. The aim of this study was to introduce a novel and efficient surgical knotting technique with various advantages. Methods The two knotting methods used in this study were the absorbable braided suture where the first suture was fixed with a clamp (with assistance) and the SH-9Hospital knotting technique (without assistance) applied on the smooth surface of a cylinder. Mechanical testing was performed using a universal material testing machine. The load-elongation curve and ultimate tensile load (UTL) were recorded. Results The mean knotting time was 36.40±1.50 s (range, 32-41 s) and 24.80±1.16 s (range, 21-28 s) in the clamp and SH-9Hosptial groups, respectively. The mean UTL was 120.8±10.14 N (range, 81.11-136.55 N)and 126.5±6.29 N (range, 104.88-139.56 N) in the clamp and SH-9Hospital groups, respectively. The knot strength of the SH-9Hospital technique was not inferior to traditional clinical practice. Conclusions The SH-9Hospital knotting technique was a secure, convenient, and efficient method for high-tension closure.

Arthroscopic knot tying is a crucial component for a successful arthroscopic shoulder surgery. Knot tying should not be difficult to master or time consuming to perform. This study describes a new sliding locking knot for arthroscopic shoulder surgery and we named it Banarji knot, in the name of the author. It is a low profile, non-bulky, and double locking knot, which makes it a more secure knot.

We present ALMA $^{12}$CO (2-1), $^{13}$CO (2-1), C$^{18}$O (2-1) molecular line observations of a very young proto-brown dwarf system, ISO-OPH 200. We have conducted physical+chemical modelling of the complex internal structure for this system using the core collapse simulations for brown dwarf formation. The model at an age of $\sim$6000 yr can provide a good fit to the observed kinematics, spectra, and reproduce the complex structures seen in the moment maps. Results from modelling indicate that $^{12}$CO emission is tracing an extended ($\sim$1000 au) molecular outflow and a bright shock knot, $^{13}$CO is tracing the outer ($\sim$1000 au) envelope/pseudo-disc, and C$^{18}$O is tracing the inner ($\sim$500 au) pseudo-disc. The source size of $\sim$8.6 au measured in the 873$\mu$m image is comparable to the inner Keplerian disc size predicted by the model. A 3D model structure of ISO-OPH 200 suggests that this system is viewed partially through a wide outflow cavity resulting in a direct view of the outflow and a partial view of the envelope/pseudo-disc. We have argued that ISO-OPH 200 has been mis-classified as a Class Flat object due to the unusual orientation. The various signatures of this system, notably, the young $\sim$616 yr outflow dynamical age and high outflow rate ($\sim$1$\times$10$^{-7}$ M$_{\odot}$ yr$^{-1}$), silicate absorption in the 10$\mu$m mid-infrared spectrum, pristine ISM-like dust in the envelope/disc, comparable sizes of the extended envelope and outflow, indicate that ISO-OPH 200 is an early Class 0 stage system formed in a star-like mechanism via gravitational collapse of a very low-mass core., Comment: Accepted in MNRAS

The psychology of chess players has called the attention of several researchers for more than a century. There is a notable lack of scientific works with a plausible hypothesis about Bobby Fischer´s paranoid psychosis and its relationship with his prodigious performance. In this brief theoretical work, a new conceptual model is proposed to explain the psychosis of American chess player Bobby Fischer. Based on the pioneering work of psychoanalysts, we introduce the concept of sinthome, taken from the Lacanian topology of the Borromean knot, with its three registers: Real, symbolic and imaginary [RSI], and its fourth stabilizer knot at the breaking of the symbolic. Here we call it chess-sinthome to designate the antipsychotic role fulfilled the ultra-competitive chess, in life and in the minds of some great players. This category of chess sinthome that was brought to our analysis by lacanian theory could be presented as a new second-generation paradigm to explain Bobby Fischer´s psychosis, after the pioneering works were already studied. The ability to predict its clinical appearance in the near future shall be a fascinating perspective.

Aim: Loosing of cerclage wire is a common problem in the fixation of fractures and alternative techniques are required to provide more strength cable systems. The aim of this study was to evaluate the benefit of an additional knot to the cable system to increase durability and strength of wire

We consider the Witten-Reshetikhin-Turaev invariants or Chern-Simons partition function at or around roots of unity $q=e^{2\pi i \frac{1}{K}}$ with rational level $K=\frac{r}{s}$ where $r$ and $s$ are coprime integers. From the exact expression for the $G=SU(2)$ Witten-Reshetikhin-Turaev invariants of Seifert manifolds at other roots of unity obtained by Lawrence and Rozansky, we provide an expected form of the structure of the Witten-Reshetikhin-Turaev invariants in terms of the homological blocks at other roots of unity. Also, we discuss the asymptotic expansion of knot invariants around roots of unity where we take a limit different from the standard limit in the volume conjecture., Comment: 22 pages, v2 minor revisions, version to appear in JHEP

Legumes form two types of root organs in response to signals from microbes, namely, nodules and root galls. In the field, these interactions occur concurrently and often interact with each other. The outcomes of these interactions vary and can depend on natural variation in rhizobia and nematode populations in the soil as well as abiotic conditions. While rhizobia are symbionts that contribute fixed nitrogen to their hosts, parasitic root-knot nematodes (RKN) cause galls as feeding structures that consume plant resources without a contribution to the plant. Yet, the two interactions share similarities, including rhizosphere signaling, repression of host defense responses, activation of host cell division, and differentiation, nutrient exchange, and alteration of root architecture. Rhizobia activate changes in defense and development through Nod factor signaling, with additional functions of effector proteins and exopolysaccharides. RKN inject large numbers of protein effectors into plant cells that directly suppress immune signaling and manipulate developmental pathways. This review examines the molecular control of legume interactions with rhizobia and RKN to elucidate shared and distinct mechanisms of these root-microbe interactions. Many of the molecular pathways targeted by both organisms overlap, yet recent discoveries have singled out differences in the spatial control of expression of developmental regulators that may have enabled activation of cortical cell division during nodulation in legumes. The interaction of legumes with symbionts and parasites highlights the importance of a comprehensive view of root-microbe interactions for future crop management and breeding strategies.[Formula: see text] Copyright © 2021 The Author(s). This is an open access article distributed under the CC BY-NC-ND 4.0 International license .

Taut-line hitch, a type of ropework used in outdoor activities, was adopted to tie the artificial chordae during mitral valve repair for degenerative mitral insufficiency. This knot-tying technique facilitated artificial chordae length determination during surgery. Nineteen patients with degenerative mitral insufficiency were successfully treated using this technique.

This chapter develops the tensions inherent in Synge’s early works towards an understanding of his formal innovation, asserting the ‘time pressure’ of his one-act plays as a dimension of his response to modernity. Synge’s drafts for various articles, particularly ‘The Old and New in Ireland’, and an article on social change in Wicklow, combine with his notes on Herbert Spencer and evolutionary theory to show a writer deeply conscious of modernization and literature’s responsiveness to modernity. Contributing to and drawing on new work on the spatial and temporal dimensions of modernism, this chapter shows that the structures and plots and Synge’s one-act plays Riders to the Sea and The Shadow of the Glen are rooted in a battle of temporalities. By comparing the timescales of Synge’s one-act plays to those of his Revivalist contemporaries, this chapter shows that his reading in sociology, philosophy, and evolutionary science, alongside his experiences in the modernizing ‘Congested Districts’ of Ireland, fundamentally affected his literary output. Fractured communal relations are figured as fractures in the time frames of the drama, and the overlapping of temporalities and levels of modernization find their correlatives in the constant and unresolved competition for dominance from any one conception of time. These plays, far from being isolated from the concerns of modernization, or from reverting to a solely romanticized vision of the peasantry, in fact register a sense of formal instability as a result of their fraught and multiple conceptions of time and space.

This chapter discusses the Casson invariant of a closed three-manifold for a knot in a closed three-manifold. This is a chord diagram version of the method noted in the end of by Lickorish. It also discusses the extension of the construction of the Casson invariant from the universal Vassiliev-Kontsevich invariant by adding the 3T relation and some natural relations. The semi-simple quotient of this representation is isomorphic to a disjoint union of two copies of the natural representation of SL(2, Z). The contribution from the extension of SL(2, Z) appears in the Levi part of this representation, and this part seems to contain information for the Casson invariant. The Kirby moves correspond to Kirby’s handle slide move, where any component can be changed only along a thin line component since the thick line component is a knot and is not applied the surgery.

The quality of vesicourethral anastomosis (VUA) in laparoscopic radical prostatectomy (LRP) is associated with complications that could significantly affect quality of life.To compare different types of sutures (Chlosta's versus Van Velthoven versus V-Loc), used for VUA in LRP in terms of complication rates and continence recovery.Patients who underwent LRP between 2014 and 2018 in a tertiary center were enrolled in the study. Data were extracted from medical records. Urinary continence was assessed at 3, 6, 12 and 18 months after LRP. Propensity score weighted regression models were used to estimate the effect of sutures on outcomes.A sample of 504 patients was analyzed, of which 109 patients underwent Chlosta's suture VUA, 117 patients had Van Velthoven suture VUA, and 278 patients had V-Loc VUA. Median time of anastomosis was 13 (IQR - interquartile range: 10-16) min using Chlosta's suture, 28 (IQR: 24-30) using Van-Velthoven suture and 12 (IQR: 11-16) min using V-Loc suture (p0.001). There were no significant differences between groups concerning complications and urinary continence at 12 and 18 months after surgery. The time of urinary continence recovery was on average 19 days (95% CI: 5-33) and 31 days (95% CI: 16-45) shorter during 1 year of observation when the V-Loc suture was used compared to the Van-Velthoven and Chlosta's suture, respectively.The study showed comparable results considering urinary continence recovery at 12 and 18 months after LRP in all VUA groups. Van Velthoven VUA was more time-consuming and continence recovery was faster in the V-Loc group.

A Kakeya set $\mathcal{K}$ in an affine plane of order $q$ is the point set covered by a set $\mathcal{L}$ of $q+1$ pairwise non-parallel lines. Large Kakeya sets were studied by Dover and Mellinger; in [6] they showed that Kakeya sets with size at least $q^2-3q+9$ contain a large knot (a point of $\mathcal{K}$ lying on many lines of $\mathcal{L}$). In this paper, we improve on this result by showing that Kakeya set of size at least $\approx q^2-q\sqrt{q}+\frac{3}{2}q$ contain a large knot. Furthermore, we obtain a sharp result for planes of square order containing a Baer subplane., To appear in Advances in Geometry

With the continuous popularization of digital technology, the digital and intelligent working mode has been realized in the field of clothing design. Designers combine the traditional design elements with modern product design by using digital technology, and integrate the traditional cultural connotation into the product. Chinese Knot Button as a representative of China’s traditional art, its modeling unique, the traditional modeling elements and popular elements combined, the use of digital virtual technology to present the design effect, can better grasp the product design of the appearance of the orientation. The main methods of integrating Chinese Knot Button modeling art into product design by using digital software technology include: extracting Chinese Knot Button modeling features, using deconstructive design techniques, and using digital software for design output; Analyze the process of simulation design with PS design software.

The entanglement entropy of many quantum systems is difficult to compute in general. They are obtained as a limiting case of the R\'enyi entropy of index $m$, which captures the higher moments of the reduced density matrix. In this work, we study pure bipartite states associated with $S^3$ complements of a two-component link which is a connected sum of a knot $\mathcal{K}$ and the Hopf link. For this class of links, the Chern-Simons theory provides the necessary setting to visualise the $m$-moment of the reduced density matrix as a three-manifold invariant $Z(M_{\mathcal{K}_m})$, which is the partition function of $M_{\mathcal{K}_m}$. Here $M_{\mathcal{K}_m}$ is a closed 3-manifold associated with the knot $\mathcal K_m$, where $\mathcal K_m$ is a connected sum of $m$-copies of $\mathcal{K}$ (i.e., $\mathcal{K}\#\mathcal{K}\ldots\#\mathcal{K}$) which mimics the well-known replica method. We analyse the partition functions $Z(M_{\mathcal{K}_m})$ for SU(2) and SO(3) gauge groups, in the limit of the large Chern-Simons coupling $k$. For SU(2) group, we show that $Z(M_{\mathcal{K}_m})$ can grow at most polynomially in $k$. On the contrary, we conjecture that $Z(M_{\mathcal{K}_m})$ for SO(3) group shows an exponential growth in $k$, where the leading term of $\ln Z(M_{\mathcal{K}_m})$ is the hyperbolic volume of the knot complement $S^3\backslash \mathcal{K}_m$. We further propose that the R\'enyi entropies associated with SO(3) group converge to a finite value in the large $k$ limit. We present some examples to validate our conjecture and proposal., Comment: 38 pages, 24 figures & 15 tables; v2: Introduction & Conclusion modified, new subsection added in section 3, three new references added; matches published version

It is a common presumption that our modern risk societies are faced with a plethora of visible and invisible enemies. Balancing freedom and security in this globalised (legal) world has indeed turned into nothing less than an attempt at untying a Gordian knot. Against this background, the proportionality of measures of crime prevention and repression is unquestionably an issue of utmost importance, which basic research and legal policy are urgently called to address.

Root-knot nematodes of the genus Meloidogyne represent one of the most damaging and agricultural important group of plant-parasitic nematodes. These nematodes are obligate sedentary endoparasites infecting most species of higher plants and have a cosmopolitan distribution. Annual worldwide economic losses due to nematode infection of crops have been estimated at several hundred billion US dollars. This book is the first complete illustrated compendium of root-knot nematode species and contains 98 species descriptions with comprehensive diagnoses, information on biology, plant-hosts, pathogenicity, symptoms, distribution and biochemical and molecular diagnostics. It also includes introductions into morphology, biology, biogeography, genomics, phylogeny and host-parasite relationships of root-knot nematodes.

KNOT is one of the 32 candidates in the second round of NIST’s lightweight cryptography standardization process. The KNOT family consists of bit-slice lightweight Authenticated Encryption with Associated Data (AEAD) and hashing algorithms. In this paper, we evaluate the security for the initialization phase of two members of the KNOT-AEAD family by differential-linear cryptanalysis.

We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. We focus on capsules and vesicles, whose discretization is particularly challenging due to the higher-order derivatives that appear in their formulations. In two-dimensional settings, we employ cubic B-splines with periodic knot vectors to obtain discretizations of closed curves with C^2 inter-element continuity. In three-dimensional settings, we use analysis-suitable bi-cubic T-splines to obtain discretizations of closed surfaces with at least C^1 inter-element continuity. Large spurious changes of the fluid volume inside closed co-dimension one solids is a well-known issue for IB methods. The DCIB method results in volume changes orders of magnitude lower than conventional IB methods. This is a byproduct of discretizing the velocity-pressure pair with divergence-conforming B-splines, which lead to negligible incompressibility errors at the Eulerian level. The higher inter-element continuity of divergence-conforming B-splines is also crucial to avoid the quadrature/interpolation errors of IB methods becoming the dominant discretization error. Benchmark and application problems of vesicle and capsule dynamics are solved, including mesh-independence studies and comparisons with other numerical methods., For supplementary movies go to https://www.andrew.cmu.edu/user/hugocp/research.html

We give a corrected statement of the theorem of Gurjar and Miyanishi, which classifies smooth affine surfaces of Kodaira dimension zero, whose coordinate ring is factorial and has trivial units. Denote the class of such surfaces by $\mathcal{S}_{0}$. An infinite series of surfaces in $\mathcal{S}_{0}$, not listed by Gurjar and Miyanishi, was recently obtained by Freudenburg, Kojima and Nagamine as affine modifications of the plane. We complete their list to a series containing arbitrarily high-dimensional families of pairwise non-isomorphic surfaces in $\mathcal{S}_{0}$. Moreover, we classify them up to a diffeomorphism, showing that each occurs as an interior of a 4-manifold whose boundary is an exceptional surgery on a 2-bridge knot. In particular, we show that $\mathcal{S}_{0}$ contains countably many pairwise non-homeomorphic surfaces., Comment: 21 pages, 16 figures

For a generic $n$-qubit system, local invariants under the action of $SL(2,\mathbb{C})^{\otimes n}$ characterize non-local properties of entanglement. In general, such properties are not immediately apparent and hard to construct. Here we consider certain two-qubit Yang-Baxter operators, which we dub of the `X-type', and show that their eigenvalues completely determine the non-local properties of the system. Moreover, we apply the Turaev procedure to these operators and obtain their associated link/knot polynomials. We also compute their entangling power and compare it with that of a generic two-qubit operator., 43 pages, Published version

The presents chapter describes the main texts of reference for the movie. These include: the Leopold and Loeb case; the development of the aftermath events with particular attention to the mass-media representation of the murder and the trial; and Patrick Hamilton’s theatre play Rope (the actual direct inspiration for Hitchcock’s film). In addition to the latter, I will include some other texts that ap-peared between the play and the movie, namely a radio broadcast of the play and, more importantly, a TV adaptation of it – this having a minor role in Hitch-cock’s technical construction of his film. The goal of this chapter is first and foremost that of providing an adequate historical background for the movie, but it will also suggest important theoretical insights that will eventually developed in Chap. 3: elements of continuity and discontinuity between the play and the film; dynamics of the re-elaboration of the real events; political and ethical ques-tions and some more.

This chapter is an introduction to the book and an illustration of its theoretical background. I will introduce the main research goals, by employing a methodo-logical framework which stems from semiotics, communication studies and cul-tural studies, and which I have developed in Martinelli 2020. I will also offer gen-eral information about the movie Rope, as well as a reflection on its significance within the development of Alfred Hitchcock’s career. Finally, I will discuss the novelties introduced in the monograph, both contents- and methodology-wise.

We give simple homological conditions for a rational homology 3-sphere Y to have infinite order in the rational homology cobordism group, and for a collection of rational homology spheres to be linearly independent. These translate immediately to statements about knot concordance when Y is the branched double cover of a knot, recovering some results of Livingston and Naik. The statements depend only on the homology groups of the 3-manifolds, but are proven through an analysis of correction terms and their behavior under connected sums., 12 pages. To appear in J. Inst. Math. Jussieu

The trace of the -framed surgery on a knot in is a 4-manifold homotopy equivalent to the 2-sphere. We characterise when a generator of the second homotopy group of such a manifold can be realised by a locally flat embedded -sphere whose complement has abelian fundamental group. Our characterisation is in terms of classical and computable -dimensional knot invariants. For each, this provides conditions that imply a knot is topologically -shake slice, directly analogous to the result of Freedman and Quinn that a knot with trivial Alexander polynomial is topologically slice., Compositio Mathematica, 157 (10), ISSN:0010-437X, ISSN:1570-5846

Background Amyotrophic lateral sclerosis (ALS) is a universally fatal neurodegenerative disease. ALS is determined by gene-environment interactions and improved understanding of these interactions may lead to effective personalised medicine. The role of physical exercise in the development of ALS is currently controversial. Methods First, we dissected the exercise-ALS relationship in a series of two-sample Mendelian randomisation (MR) experiments. Next we tested for enrichment of ALS genetic risk within exercise-associated transcriptome changes. Finally, we applied a validated physical activity questionnaire in a small cohort of genetically selected ALS patients. Findings We present MR evidence supporting a causal relationship between genetic liability to frequent and strenuous leisure-time exercise and ALS using a liberal instrument (multiplicative random effects IVW, p=0.01). Transcriptomic analysis revealed that genes with altered expression in response to acute exercise are enriched with known ALS risk genes (permutation test, p=0.013) including C9ORF72, and with ALS-associated rare variants of uncertain significance. Questionnaire evidence revealed that age of onset is inversely proportional to historical physical activity for C9ORF72-ALS (Cox proportional hazards model, Wald test p=0.007, likelihood ratio test p=0.01, concordance=74%) but not for non-C9ORF72-ALS. Variability in average physical activity was lower in C9ORF72-ALS compared to both non-C9ORF72-ALS (F-test, p=0.002) and neurologically normal controls (F-test, p=0.049) which is consistent with a homogeneous effect of physical activity in all C9ORF72-ALS patients. Interpretation Our MR approach suggests a positive causal relationship between ALS and physical exercise. Exercise is likely to cause motor neuron injury only in patients with a risk-genotype. Consistent with this we have shown that ALS risk genes are activated in response to exercise. In particular, we propose that G4C2-repeat expansion of C9ORF72 predisposes to exercise-induced ALS. Funding We acknowledge support from the Wellcome Trust (JCK, 216596/Z/19/Z), NIHR (PJS, NF-SI-0617-10077; IS-BRC-1215-20017) and NIH (MPS, CEGS 5P50HG00773504, 1P50HL083800, 1R01HL101388, 1R01-HL122939, S10OD025212, P30DK116074, and UM1HG009442).

This personal philosophical reflection on outdoor learning invites consideration of wider horizons of possibility around the constructs of when and where we learn in relation to phronesis, practical wisdom, and notions of kairos and topos. The work aspires to re-infuse the three back into broader educational aims through practices of local learning outdoors. The treatise applies a pragmatic methodology, formed by tracing bearings based on field data gathered from life experiences, and uses triangulation techniques to bind the tracings, via the method of story-mapping, into a woven place-binding knot map. The work imagines phronesis as leadership that may be developed at school through time spent adventuring and learning in local outdoor contexts. Local outdoors is positioned as a pragmatic means of engaging in useful learning, defined as learning for health and wellbeing, relationships with more-than-humans, and experiences. The resultant place-binding knot map, while messy, may offer insights for learners, educators, and scholars around phronesis, kairos, and topos in learning, leadership, and local outdoors.