Complexification of the Exceptional Jordan Algebra and Its Application to Particle Physics

Recent papers contributed revitalizing the study of the exceptional Jordan algebra $\mathfrak{h}_{3}(\mathbb{O})$ in its relations with the true Standard Model gauge group $\mathrm{G}_{SM}$. The absence of complex representations of $\mathrm{F}_{4}$ does not allow $\Aut\left(\mathfrak{h}_{3}(\mathbb{O})\right)$ to be a candidate for any Grand Unified Theories, but the automorphisms of the complexification of this algebra, i.e., $\mathfrak{h}_{3}^{\mathbb{C}}(\mathbb{O})$, are isomorphic to the compact form of $\mathrm{E}_{6}$ and similar constructions lead to the gauge group of the minimal left-right symmetric extension of the Standard Model.

NUMERICAL EXPERIMENTS FOR NONLINEAR BURGER’S PROBLEM

The article contains the results of computational experiments for the non-homogeneous Burger’s problem and finding its solution by using the non-classical variational-Cole-Hopf transformation approach. On using exact linearization via Cole-Hopf transformation, as well as the application of the non-classical variational approach, then the non-homogeneous Burger’s problem has been solved. The solution which is obtained by this approach is in a compact form so that the original nonlinear solution is easy to be approximated. The accuracy of this method is dependent on the types of selected basis and its number.

Scalar Induced Gravitational Waves Review

We provide a review on the state-of-the-art of gravitational waves induced by primordial fluctuations, so-called induced gravitational waves. We present the intuitive physics behind induced gravitational waves and we revisit and unify the general analytical formulation. We then present general formulas in a compact form, ready to be applied. This review places emphasis on the open possibility that the primordial universe experienced a different expansion history than the often assumed radiation dominated cosmology. We hope that anyone interested in the topic will become aware of current advances in the cosmology of induced gravitational waves, as well as becoming familiar with the calculations behind.

The mechanism of complex formation between calmodulin and voltage gated calcium channels revealed by molecular dynamics

Calmodulin, a ubiquitous eukaryotic calcium sensor responsible for the regulation of many fundamental cellular processes, is a highly flexible protein and exhibits an unusually wide range of conformations. Furthermore, CaM is known to interact with more than 300 cellular targets. Molecular dynamics (MD) simulation trajectories suggest that EF-hand loops show different magnitudes of flexibility. Therefore, the four EF-hand motifs have different affinities for Ca2+ ions, which enables CaM to function on wide range of Ca2+ ion concentrations. EF-hand loops are 2–3 times more flexible in apo CaM whereas least flexible in Ca2+/CaM-IQ motif complexes. We report a unique intermediate conformation of Ca2+/CaM while transitioning from extended to compact form. We also report the complex formation process between Ca2+/CaM and IQ CaM-binding motifs. Our results showed how IQ motif recognise its binding site on the CaM and how CaM transforms from extended to compact form upon binding to IQ motif.

Discovering and Summarizing Relationships Between Chemicals, Genes, Proteins, and Diseases in PubChem

The literature knowledge panels developed and implemented in PubChem are described. These help to uncover and summarize important relationships between chemicals, genes, proteins, and diseases by analyzing co-occurrences of terms in biomedical literature abstracts. Named entities in PubMed records are matched with chemical names in PubChem, disease names in Medical Subject Headings (MeSH), and gene/protein names in popular gene/protein information resources, and the most closely related entities are identified using statistical analysis and relevance-based sampling. Knowledge panels for the co-occurrence of chemical, disease, and gene/protein entities are included in PubChem Compound, Protein, and Gene pages, summarizing these in a compact form. Statistical methods for removing redundancy and estimating relevance scores are discussed, along with benefits and pitfalls of relying on automated (i.e., not human-curated) methods operating on data from multiple heterogeneous sources.

Noether-Wald charges in six-dimensional Critical Gravity

It has been recently shown that there is a particular combination of conformal invariants in six dimensions which accepts a generic Einstein space as a solution. The Lagrangian of this Conformal Gravity theory — originally found by Lu, Pang and Pope (LPP) — can be conveniently rewritten in terms of products and covariant derivatives of the Weyl tensor. This allows one to derive the corresponding Noether prepotential and Noether-Wald charges in a compact form. Based on this expression, we calculate the Noether-Wald charges of six-dimensional Critical Gravity at the bicritical point, which is defined by the difference of the actions for Einstein-AdS gravity and the LPP Conformal Gravity. When considering Einstein manifolds, we show the vanishing of the Noether prepotential of Critical Gravity explicitly, which implies the triviality of the Noether-Wald charges. This result shows the equivalence between Einstein-AdS gravity and Conformal Gravity within its Einstein sector not only at the level of the action but also at the level of the charges.

The chiral ring of gauge theories in eight dimensions

We study the non-perturbative corrections generated by exotic instantons in U(N) gauge theories in eight and four dimensions. As it was shown previously, the eight-dimensional prepotential can be resummed using a plethystic formula showing only a dependence from the center of mass and from a U(1) gauge factor. On the contrary, chiral correlators in eight and four dimensions display a non-trivial dependence from the full gauge group. Furthermore the resolvent, the generating function for the eight and four dimensional correlators, can be written in a compact form both in the eight and four dimensional cases.

The Challenge of the Urban Compact Form: Three-Dimensional Index Construction and Urban Land Surface Temperature Impacts

Cities are growing higher and denser, and understanding and constructing the compact city form is of great importance to optimize sustainable urbanization. The two-dimensional (2D) urban compact form has been widely studied by previous researchers, while the driving mechanism of three-dimensional (3D) compact morphology, which reflects the reality of the urban environment has seldom been developed. In this study, land surface temperature (LST) was retrieved by using the mono-window algorithm method based on Landsat 8 images of Xiamen in South China, which were acquired respectively on 14 April, 15 August, 2 October, and 21 December in 2017, and 11 March in 2018. We then aimed to explore the driving mechanism of the 3D compact form on the urban heat environment (UHE) based on our developed 3D Compactness Index (VCI) and remote sensing, as well as Geo-Detector techniques. The results show that the 3D compact form can positively effect UHE better than individual urban form construction elements, as can the combination of the 2D compact form with building height. Individually, building density had a greater effect on UHE than that of building height. At the same time, an integration of building density and height showed an enhanced inter-effect on UHE. Moreover, we explore the temporal and spatial UHE heterogeneity with regards to 3D compact form across different seasons. We also investigate the UHE impacts discrepancy caused by different 3D compactness categories. This shows that increasing the 3D compactness of an urban community from 0.016 to 0.323 would increase the heat accumulation, which was, in terms of satellite derived LST, by 1.35 °C, suggesting that higher compact forms strengthen UHE. This study highlights the challenge of the urban 3D compact form in respect of its UHE impact. The related evaluation in this study would help shed light on urban form optimization.

Shulin packages axonemal outer dynein arms for ciliary targeting

The main force generators in eukaryotic cilia and flagella are axonemal outer dynein arms (ODAs). During ciliogenesis, these ~1.8-megadalton complexes are assembled in the cytoplasm and targeted to cilia by an unknown mechanism. Here, we used the ciliateTetrahymenato identify two factors (Q22YU3 and Q22MS1) that bind ODAs in the cytoplasm and are required for ODA delivery to cilia. Q22YU3, which we named Shulin, locked the ODA motor domains into a closed conformation and inhibited motor activity. Cryo–electron microscopy revealed how Shulin stabilized this compact form of ODAs by binding to the dynein tails. Our findings provide a molecular explanation for how newly assembled dyneins are packaged for delivery to the cilia.