Search Results (45)

Immersive technologies offer promising advancements in medical education, particularly in procedural skill acquisition. However, their implementation often lacks a foundation in learning theories. This study investigates the application of the split-attention principle, a multimedia learning guideline, in the design of knot-tying procedural content using a mixed reality (MR) technology, specifically Microsoft HoloLens 2. A total of 26 participants took part in a between-group design experiment comparing integrated and split-source formats for learning arthroscopic knots, with the performance and the cognitive load assessed. The initial hypotheses were not confirmed, as results did not show significant differences in performance during recall, nor in extraneous and germane cognitive load. However, the findings on intrinsic cognitive load highlight the complexity of participant engagement and the cognitive demands of procedural learning. To better capture the split-attention effect, future research should address the high element interactivity in MR representations. The study provides some foundation for designing procedural simulation training that considers both learners’ needs and cognitive processes in highly immersive environments. It contributes to the ongoing exploration of instructional design in MR-based medical education, emphasizing both the potential and challenges of multimedia learning principles in advanced technological contexts. Full article

In this paper, we extend the theory of planar pseudo knots to the theories of annular and toroidal pseudo knots. Pseudo knots are defined as equivalence classes under Reidemeister-like moves of knot diagrams characterized by crossings with undefined over/under information. In the theories of annular and toroidal pseudo knots, we introduce their respective lifts to the solid and the thickened torus. Then, we interlink these theories by representing annular and toroidal pseudo knots as planar $\mathrm{O}$-mixed and $\mathrm{H}$-mixed pseudo links. We also explore the inclusion relations between planar, annular and toroidal pseudo knots, as well as of $\mathrm{O}$-mixed and $\mathrm{H}$-mixed pseudo links. Finally, we extend the planar weighted resolution set to annular and toroidal pseudo knots, defining new invariants for classifying pseudo knots and links in the solid and in the thickened torus. Full article

In this study, a novel cambered snow removal device is designed to achieve automatic snow removal in large curved areas, such as the south roof of a Chinese solar greenhouse. The theory of structural parameters and shear force is ambiguous. People are not based on the greenhouse structure parameters for the selection of snow removal devices. Therefore, the quantitative relationship between the structure of the greenhouse span and the number of scissor arm-length knots is analysed, and the relationship between the material strength and application distance is determined. This study’s objectives are (1) to establish a theoretical model of scissor arm motion and (2) to analyse the force distribution of the scissor arm using multi-body dynamics. The results show that the scissor arm of a round-arch greenhouse has fewer sections but a larger arm length, whereas the scissor arm of a traditional solar greenhouse has more sections but a smaller arm length. Based on the shear force of the scissor structure, the optimised wall thickness reduces the force of the node by 17%. Full article

Representations of braid group $B_n$ on $n\ge 2$ strands by automorphisms of a free group of rank n go back to Artin. In 1991, Kauffman introduced a theory of virtual braids, virtual knots, and links. The virtual braid group $V{B}_n$ on $n\ge 2$ strands is an extension of the classical braid group $B_n$ by the symmetric group $S_n$. In this paper, we consider flat virtual braid groups $FV{B}_n$ on $n\ge 2$ strands and construct a family of representations of $FV{B}_n$ by automorphisms of free groups of rank $2n$. It has been established that these representations do not preserve the forbidden relations between classical and virtual generators. We investigated some algebraic properties of the constructed representations. In particular, we established conditions of faithfulness in case $n=2$ and proved that the kernel contains a free group of rank two for $n\ge 3$. Full article

The breeding ecology of birds is the cornerstone of bird life-history theory, and breeding success directly affects the survival and development of populations. We studied the breeding ecology of a secondary cavity-nesting bird, the chestnut-vented nuthatch Sitta nagaensis, in southwestern China from March to June in 2020, 2021, and 2022. In total, 16 nests in nest boxes and 19 nests in natural cavities were studied. The nesting habitat was mainly Pinus yunnanensis forest (68.4%), and the nest trees were mainly P. yunnanensis and pear Pyrus spp. Cavities made by woodpeckers and knot holes were used as nest sites, and the nuthatches plastered the hole entrance with mud. The nesting material was mainly pine bark. The clutch size was 3.47 ± 0.56 (range 2–4, n = 30), with an incubation period of 16.06 ± 0.91 days (range 15–19 days, n = 18). The nestling period was 20.88 ± 1.90 days (range 18–23 days, n = 23), and both parents fed the nestlings. Full article

Although electrons (fermions)and photons (bosons) produce the same interference patterns in the two-slit experiments, known in optics for photons since the 17th Century, the description of these patterns for electrons and photons thus far was markedly different. Photons are spin one, relativistic and massless particles while electrons are spin half massive particles producing the same interference patterns irrespective to their speed. Experiments with other massive particles demonstrate the same kind of interference patterns. In spite of these differences, in the early 1930s of the 20th Century, the isomorphism between the source-free Maxwell and Dirac equations was established. In this work, we were permitted replace the Born probabilistic interpretation of quantum mechanics with the optical. In 1925, Rainich combined source-free Maxwell equations with Einstein’s equations for gravity. His results were rediscovered in the late 1950s by Misner and Wheeler, who introduced the word "geometrodynamics” as a description of the unified field theory of gravity and electromagnetism. An absence of sources remained a problem in this unified theory until Ranada’s work of the late 1980s. However, his results required the existence of null electromagnetic fields. These were absent in Rainich–Misner–Wheeler’s geometrodynamics. They were added to it in the 1960s by Geroch. Ranada’s solutions of source-free Maxwell’s equations came out as knots and links. In this work, we establish that, due to their topology, these knots/links acquire masses and charges. They live on the Dupin cyclides—the invariants of Lie sphere geometry. Symmetries of Minkowski space-time also belong to this geometry. Using these symmetries, Varlamov recently demonstrated group-theoretically that the experimentally known mass spectrum for all mesons and baryons is obtainable with one formula, containing electron mass as an input. In this work, using some facts from polymer physics and differential geometry, a new proof of the knotty nature of the electron is established. The obtained result perfectly blends with the description of a rotating and charged black hole. Full article

While it is well established that articulations of identity must always be contextualized within time and place, only when we consider how bodies move through, touch, and are touched by physical, cognitive, and even imaginary spaces do we arrive at dynamic and intersectional expressions of identity. Using two divergent visual culture case studies, this essay first applies Setha Low’s theory of embodied spaces to understand the intersection and interconnection between body, space, and culture, and how the concept of belongingness is knotted with material and representational indicators of space at the Yad Vashem Holocaust History Museum in Israel. Marianne Hirsch’s ideas about the Holocaust and affiliative postmemory are also considered to further understand how Jewish bodies inherit their identifies and sense of belonging. To test how embodied spaces and affiliative postmemory or collective memory implicitly operate to help shape and articulate expressions of Jewish identities, the focus then shifts to a consideration of the eight-decade career of New York jazz musician and visual artist, Bill Wurtzel. The clever combination of “schtick and sechel” in Wurtzel’s artistic practice, activated by his movement through the Jewish spaces of his youth such as the Catskills, and through his interaction with Jewish design great, Lou Dorfsman, underscore how Jewish belonging and identity are forged at the intersection of physical and tactile “embodied spaces,” where the internal meets the external and human consciousness and experience converge. Full article

Based on the advantages of the silicone graphene composite thermal insulation board, it was used to replace traditional plywood in the external wall formwork system, and the active embedded steel wire knot form in silicone graphene composite thermal insulation structure integrated system was designed. Firstly, the theoretical model of steel wire drawing resistance was established by theoretical analysis method, and the rationality of the theoretical model was verified by combining relevant experimental data. The relationship between multiple variables and steel wire pull-out resistance was analyzed. Then, combined with the theory of wind pressure strength of the exterior wall of a building structure, the layout form and the corresponding number of embedded steel wires of thermal insulation board under different building heights were analyzed. Finally, the silicone graphene composite thermal insulation board and ordinary plywood were compared and analyzed from the force of perspective of external wall formwork. The results showed that the pull-out resistance of steel wire was directly proportional to the diameter of steel wire, embedded depth, and embedded deflection angle. With the increase of building height, the number of steel wires to be arranged also increased. When the thickness of the silicone graphene composite thermal insulation board is not less than 80 mm, the anti-deformation effect is close to that of the ordinary plywood, which can meet the construction requirements of the external wall formwork. It can ensure the energy conservation and thermal insulation of the external wall, integrate the building’s exterior wall and thermal insulation structure of the building, and achieve the purpose of exemption from formwork removal. Full article

Manipulating cloth-like deformable objects (CDOs) is a long-standing problem in the robotics community. CDOs are flexible (non-rigid) objects that do not show a detectable level of compression strength while two points on the article are pushed towards each other and include objects such as ropes (1D), fabrics (2D) and bags (3D). In general, CDOs’ many degrees of freedom (DoF) introduce severe self-occlusion and complex state–action dynamics as significant obstacles to perception and manipulation systems. These challenges exacerbate existing issues of modern robotic control methods such as imitation learning (IL) and reinforcement learning (RL). This review focuses on the application details of data-driven control methods on four major task families in this domain: cloth shaping, knot tying/untying, dressing and bag manipulation. Furthermore, we identify specific inductive biases in these four domains that present challenges for more general IL and RL algorithms. Full article

The Kronecker algebra $\mathcal{K}$ is the path algebra induced by the quiver with two parallel arrows, one source and one sink (i.e., a quiver with two vertices and two arrows going in the same direction). Modules over $\mathcal{K}$ are said to be Kronecker modules. The classification of these modules can be obtained by solving a well-known tame matrix problem. Such a classification deals with solving systems of differential equations of the form $Ax=B{x}^{\prime }$, where A and B are $m\times n$, $\mathbb{F}$-matrices with $\mathbb{F}$ an algebraically closed field. On the other hand, researching the Yang–Baxter equation (YBE) is a topic of great interest in several science fields. It has allowed advances in physics, knot theory, quantum computing, cryptography, quantum groups, non-associative algebras, Hopf algebras, etc. It is worth noting that giving a complete classification of the YBE solutions is still an open problem. This paper proves that some indecomposable modules over $\mathcal{K}$ called pre-injective Kronecker modules give rise to some algebraic structures called skew braces which allow the solutions of the YBE. Since preprojective Kronecker modules categorize some integer sequences via some appropriated snake graphs, we prove that such modules are automatic and that they induce the automatic sequences of continued fractions. Full article

Currently, researching the Yang–Baxter equation (YBE) is a subject of great interest among scientists of diverse areas in mathematics and other sciences. One of the fundamental open problems is to find all of its solutions. The investigation deals with developing theories such as knot theory, Hopf algebras, quandles, Lie and Jordan (super) algebras, and quantum computing. One of the most successful techniques to obtain solutions of the YBE was given by Rump, who introduced an algebraic structure called the brace, which allows giving non-degenerate involutive set-theoretical solutions. This paper introduces Brauer configuration algebras, which, after appropriate specializations, give rise to braces associated with Thompson’s group F. The dimensions of these algebras and their centers are also given. Full article

We recently proposed that topological quantum computing might be based on $SL(2,\mathbb{C})$ representations of the fundamental group ${\pi }_1(S^3\backslash K)$ for the complement of a link K in the three-sphere. The restriction to links whose associated $SL(2,\mathbb{C})$ character variety $\mathcal{V}$ contains a Fricke surface ${\kappa }_d=xyz-x^2-y^2-z^2+d$ is desirable due to the connection of Fricke spaces to elementary topology. Taking K as the Hopf link $L2a1$, one of the three arithmetic two-bridge links (the Whitehead link $5_1^2$, the Berge link $6_2^2$ or the double-eight link $6_3^2$) or the link $7_3^2$, the $\mathcal{V}$ for those links contains the reducible component ${\kappa }_4$, the so-called Cayley cubic. In addition, the $\mathcal{V}$ for the latter two links contains the irreducible component ${\kappa }_3$, or ${\kappa }_2$, respectively. Taking $\rho$ to be a representation with character ${\kappa }_d$ ($d<4$), with $\left|x\right|,\left|y\right|,\left|z\right|\le 2$, then $\rho \left({\pi }_1\right)$ fixes a unique point in the hyperbolic space ${\mathcal{H}}_3$ and is a conjugate to a $SU\left(2\right)$ representation (a qubit). Even though details on the physical implementation remain open, more generally, we show that topological quantum computing may be developed from the point of view of three-bridge links, the topology of the four-punctured sphere and Painlevé VI equation. The 0-surgery on the three circles of the Borromean rings L6a4 is taken as an example. Full article

The massive amount of available neurodata suggests the existence of a mathematical backbone underlying neuronal oscillatory activities. For example, geometric constraints are powerful enough to define cellular distribution and drive the embryonal development of the central nervous system. We aim to elucidate whether underrated notions from geometry, topology, group theory and category theory can assess neuronal issues and provide experimentally testable hypotheses. The Monge’s theorem might contribute to our visual ability of depth perception and the brain connectome can be tackled in terms of tunnelling nanotubes. The multisynaptic ascending fibers connecting the peripheral receptors to the neocortical areas can be assessed in terms of knot theory/braid groups. Presheaves from category theory permit the tackling of nervous phase spaces in terms of the theory of infinity categories, highlighting an approach based on equivalence rather than equality. Further, the physical concepts of soft-matter polymers and nematic colloids might shed new light on neurulation in mammalian embryos. Hidden, unexpected multidisciplinary relationships can be found when mathematics copes with neural phenomena, leading to novel answers for everlasting neuroscientific questions. For instance, our framework leads to the conjecture that the development of the nervous system might be correlated with the occurrence of local thermal changes in embryo–fetal tissues. Full article

The Tutte polynomial is an isomorphism invariant of graphs that generalizes the chromatic and the flow polynomials. This two-variable polynomial with integral coefficients is known to carry important information about the properties of the graph. It has been used to prove long-standing conjectures in knot theory. Furthermore, it is related to the Potts and Ising models in statistical physics. The purpose of this paper is to study the interaction between the Tutte polynomial and graph symmetries. More precisely, we prove that if the automorphism group of the graph G contains an element of prime order p, then the coefficients of the Tutte polynomial of G satisfy certain necessary conditions. Full article

The sustainability problem of many intangible cultural heritage (ICH) products stems from the shrinking of the core practitioner group, which is also the case for bamboo basketry craft. We believe that the problem in bamboo basketry originated in the lack of labor division between design and manufacturing, which prevents professional designers from entering this industry and results in the absence of several key stakeholders related to innovation and R&D. The lack of labor division is due to the technical difficulties associated with expressing the design concepts. The complexity of basket weaving structures makes it difficult to communicate between designer and manufacturer without precise expression tools, thus binding design and manufacturing into an integrated role. Guided by the user innovation theory, our team studied the design technology of bamboo basketry and developed a series of aiding tools, including the modeling of basic over–under structures and free weaving structures, automatic mapping techniques from 2D to 3D and several frequently used weaving skills, such as connecting, wrapping, plaiting and knotting. This technology enables designers to quickly design and express weaving structures with full details in digital models rather than to make samples. The application of the software shows that the technology considerably improved the designer interest and confidence. This technical solution makes designers, rather than programmers, able to do the development work, which also helps to create a sustainable ecological environment of technological research, also avoiding the difficulties associated with attracting business investment for such niche demands in the starting stage. Our practice shows that the sustainability of ICH products and the sustainability of the industry are closely related and that solving the latter supports the former. Full article