Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry

We introduce the notion of algebraic higher symmetry, which generalizes higher symmetry and is beyond higher group. We show that an algebraic higher symmetry in a bosonic system in $n$-dimensional space is characterized and classified by a local fusion $n$-category. We find another way to describe algebraic higher symmetry by restricting to symmetric sub Hilbert space where symmetry transformations all become trivial. In this case, algebraic higher symmetry can be fully characterized by a non-invertible gravitational anomaly (i.e. an topological order in one higher dimension). Thus we also refer to non-invertible gravitational anomaly as categorical symmetry to stress its connection to symmetry. This provides a holographic and entanglement view of symmetries. For a system with a categorical symmetry, its gapped state must spontaneously break part (not all) of the symmetry, and the state with the full symmetry must be gapless. Using such a holographic point of view, we obtain (1) the gauging of the algebraic higher symmetry; (2) the classification of anomalies for an algebraic higher symmetry; (3) the equivalence between classes of systems, with different (potentially anomalous) algebraic higher symmetries or different sets of low energy excitations, as long as they have the same categorical symmetry; (4) the classification of gapped liquid phases for bosonic/fermionic systems with a categorical symmetry, as gapped boundaries of a topological order in one higher dimension (that corresponds to the categorical symmetry). This classification includes symmetry protected trivial (SPT) orders and symmetry enriched topological (SET) orders with an algebraic higher symmetry.Comment: 61 pages, 31 figure

Effect of graphene oxide on the thermal properties of bovine hide powders

Content: Graphene oxide (GO) is one of the most interesting nanomaterials in recent years. In order to explore its potential application in leather making process, a study on evaluating the effects of GO on the thermal stability and decomposition kinetics of bovine hide powders (HP) was performed by thermogravimetry. It was shown that the GO-doped hide powders (GO-HP) exhibit better thermal stability than those of raw hide powders. The kinetic and mechanism analysis of the decomposition stage used an integrated procedure involving model-free methods and universal master-plots method. Various methods were employed to calculate the activation energy of the fibers, including the Flynn-Wall-Ozawa (FWO), Modified Kissinger-Akahira-Sunose (MKAS) and Friedman methods. The activation energy values of GO-HP and raw hide powder were found to be 240.5 and 184.7 kJ/mol, respectively. Comparison of the experimental and theoretical master plots of various reaction mechanisms showed that when the conversion values are below 0.5, the most probable decomposition mechanism for HP and GO-HP is D1. Above 0.5, the decomposition mechanisms of HP and GO-HP are most probably described by A3 and R3 models, respectively. Take-Away: Graphene oxide (GO) doped hide powders (GO-HP) exhibit better thermal stability than those of raw hide powders. The activation energy values of GO-HP and raw hide powder were found to be 240.5 and 184.7 kJ/mol, respectively

Classification of topological phases with finite internal symmetries in all dimensions

We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approaches with an emphasis on the second approach. The first approach is to gauge the symmetry in the same dimension by adding topological excitations as it was done in the 2d case, in which the gauging process is mathematically described by the minimal modular extensions of unitary braided fusion 1-categories. This 2d result immediately generalizes to all dimensions except in 1d, which is treated with special care. The second approach is to use the 1-dimensional higher bulk of the SPT/SET order and the boundary-bulk relation. This approach also leads us to a precise mathematical description and a classification of SPT/SET orders in all dimensions. The equivalence of these two approaches, together with known physical results, provides us with many precise mathematical predictions.Comment: 41 pages, 6 figures; add more results on anomalies; final version to appear in JHE

Least squares estimation of spatial autoregressive models for large-scale social networks

Due to the rapid development of various social networks, the spatial autoregressive (SAR) model is becoming an important tool in social network analysis. However, major bottlenecks remain in analyzing largescale networks (e.g., Facebook has over 700 million active users), including computational scalability, estimation consistency, and proper network sampling. To address these challenges, we propose a novel least squares estimator (LSE) for analyzing large sparse networks based on the SAR model. Computationally, the LSE is linear in the network size, making it scalable to analysis of huge networks. In theory, the LSE is root n-consistent and asymptotically normal under certain regularity conditions. A new LSE-based network sampling technique is further developed, which can automatically adjust autocorrelation between sampled and unsampled units and hence guarantee valid statistical inferences. Moreover, we generalize the LSE approach for the classical SAR model to more complex networks associated with multiple sources of social interaction effect. Numerical results for simulated and real data are presented to illustrate performance of the LSE.National Natural Science Foundation of China [71532001, 11525101, 71332006, 11701560, 11401482]; Beijing Municipal Social Science Foundation [17GLC051]; Center for Applied Statistics, School of Statistics, Renmin University of China; Center of Statistical Research, Southwestern University of Finance and Economics; China's National Key Research Special Program [2016YFC0207700]; NSF [DMS-1309507, DMS-1418172]; NSFC [11571009]Open Access JournalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Constraints on smoothness parameter and dark energy using observational H(z)H(z) data

The universe, with large-scale homogeneity, is locally inhomogeneous, clustering into stars, galaxies and larger structures. Such property is described by the smoothness parameter $\alpha$ which is defined as the proportion of matter in the form of intergalactic medium. If we take consideration of the inhomogeneities in small scale, there should be modifications of the cosmological distances compared to a homogenous model. Dyer and Roeder developed a second-order ordinary differential equation (D-R equation) that describes the angular diameter distance-redshift relation for inhomogeneous cosmological models. Furthermore, we may obtain the D-R equation for observational $H(z)$ data (OHD). The density-parameter $\Omega_{\rm M}$, the state of dark energy $\omega$, and the smoothness-parameter $\alpha$ are constrained by a set of OHD in a spatially flat $\Lambda$CDM universe as well as a spatially flat XCDM universe. By using of $\chi^2$ minimization method we get $\alpha=0.81^{+0.19}_{-0.20}$ and $\Omega_{\rm M}=0.32^{+0.12}_{-0.06}$ at $1\sigma$ confidence level. If we assume a Gaussian prior of $\Omega_{\rm M}=0.26\pm0.1$, we get $\alpha=0.93^{+0.07}_{-0.19}$ and $\Omega_{\rm M}=0.31^{+0.06}_{-0.05}$. For XCDM model, $\alpha$ is constrained to $\alpha\geq0.80$ but $\omega$ is weakly constrained around -1, where $\omega$ describes the equation of the state of the dark energy ($p_{\rm X}=\omega\rho_{\rm X}$). We conclude that OHD constrains the smoothness parameter more effectively than the data of SNe Ia and compact radio sources.Comment: 11 pages, 12 figures, accepted for publication in Research in Astronomy and Astrophysic

Multimodal Molecular Pretraining via Modality Blending

Self-supervised learning has recently gained growing interest in molecular modeling for scientific tasks such as AI-assisted drug discovery. Current studies consider leveraging both 2D and 3D molecular structures for representation learning. However, relying on straightforward alignment strategies that treat each modality separately, these methods fail to exploit the intrinsic correlation between 2D and 3D representations that reflect the underlying structural characteristics of molecules, and only perform coarse-grained molecule-level alignment. To derive fine-grained alignment and promote structural molecule understanding, we introduce an atomic-relation level "blend-then-predict" self-supervised learning approach, MoleBLEND, which first blends atom relations represented by different modalities into one unified relation matrix for joint encoding, then recovers modality-specific information for 2D and 3D structures individually. By treating atom relationships as anchors, MoleBLEND organically aligns and integrates visually dissimilar 2D and 3D modalities of the same molecule at fine-grained atomic level, painting a more comprehensive depiction of each molecule. Extensive experiments show that MoleBLEND achieves state-of-the-art performance across major 2D/3D molecular benchmarks. We further provide theoretical insights from the perspective of mutual-information maximization, demonstrating that our method unifies contrastive, generative (cross-modality prediction) and mask-then-predict (single-modality prediction) objectives into one single cohesive framework

Primary localized histoplasmosis with lesions restricted to the mouth in a Chinese HIV-negative patient

SummaryHistoplasmosis is a deep mycosis caused by Histoplasma capsulatum, which is endemic in many areas of the world but is relatively rare in China. Although the majority of cases present as a mild to moderate flu-like disease requiring only supportive therapy, approximately 1% of patients experience more serious pulmonary and extrapulmonary disease, which can be life-threatening if diagnosis is delayed or the treatment is not initiated rapidly. Definitive diagnosis is usually made by a combination of culture, detection of the organism in tissues, measurement of antibodies, and detection of antigen. We present the case of a 51-year-old patient who presented with histoplasmosis only, with several ulcerated lesions in the oral cavity and without HIV infection, who did not show any detectable signs and symptoms of systemic disease or extra-oral manifestations. Histopathological analysis indicated a chronic inflammatory process with granulomas with yeast-like organisms. Isolation of H. capsulatum and molecular identification provided the definitive diagnosis. Treatment with oral itraconazole led to remission of the oral lesions. This is the first Chinese case report of localized histoplasmosis with lesions restricted to the mouth in an HIV-negative patient

CryoFormer: Continuous Reconstruction of 3D Structures from Cryo-EM Data using Transformer-based Neural Representations

High-resolution heterogeneous reconstruction of 3D structures of proteins and other biomolecules using cryo-electron microscopy (cryo-EM) is essential for understanding fundamental processes of life. However, it is still challenging to reconstruct the continuous motions of 3D structures from hundreds of thousands of noisy and randomly oriented 2D cryo-EM images. Existing methods based on coordinate-based neural networks show compelling results to model continuous conformations of 3D structures in the Fourier domain, but they suffer from a limited ability to model local flexible regions and lack interpretability. We propose a novel approach, cryoFormer, that utilizes a transformer-based network architecture for continuous heterogeneous cryo-EM reconstruction. We for the first time directly reconstruct continuous conformations of 3D structures using an implicit feature volume in the 3D spatial domain. A novel deformation transformer decoder further improves reconstruction quality and, more importantly, locates and robustly tackles flexible 3D regions caused by conformations. In experiments, our method outperforms current approaches on three public datasets (1 synthetic and 2 experimental) and a new synthetic dataset of PEDV spike protein. The code and new synthetic dataset will be released for better reproducibility of our results. Project page: https://cryoformer.github.io

Changes of plasma fibroblast growth factor-21 (FGF-21) in oral glucose tolerance test and effects of metformin on FGF-21 levels in type 2 diabetes mellitus

Wstęp: Badanie przeprowadzono w celu ustalenia, czy czynnik wzrostu fibroblastów-21 (FGF-21) uczestniczy w regulacji stężenia glukozy i czy zastosowanie metforminy u chorych na cukrzycę wpływa na stężenie FGF-21. Materiał i metody: Do badania włączono 43 osoby, w tym 27 chorych z nowo rozpoznaną cukrzycą typu 2 (nT2DM). U wszystkich przeprowadzono test doustnego obciążenia 75 g glukozy (OGTT). Próbki krwi pobrano w 0., 60.,120. i 180. minucie testu. Osobom z nT2DM zaproponowano udział w dalszych badaniach; zastosowano u nich metforminę w dawce 1,0 g/dobę przez tydzień. Wyniki: Zmiany stężenia FGF-21 w osoczu podczas OGTT zaobserwowano tylko w grupie chorych na nT2DM; w grupie kontrolnej stężenie FGF-21 pozostało niezmienione. Nie stwierdzono, by stężenia FGF-21 w poszczególnych punktach czasowych różniły się w zależności od płci badanych (p < 0,05). Zastosowanie metforminy u osób z nT2DM spowodowało istotne zmniejszenie stężeń glukozy i FGF-21 we wszystkich punktach czasowych OGTT oraz zmniejszenie stężenia insuliny w 60. i 180. minucie, co wskazuje na obniżenie wskaźnika HOMA-IR. Wnioski: FGF-21 nie uczestniczy w krótkoterminowej regulacji glikemii u ludzi, a zmiany jego stężenia podczas OGTT są opóźnione w T2DM. Być może FGF-21 bierze udział w metabolizowaniu metforminy, zwiększając wrażliwość na glukozę i insulinę. (Endokrynol Pol 2013; 64 (3): 220&#8211;224)Introduction: The objectives of our study were to investigate whether fibroblast growth factor-21 (FGF-21) is involved in short-term regulation of glucose and the change of FGF-21 after metformin use in diabetic subjects. Material and methods: 43 subjects were recruited in the study, including 27 new-onset type 2 diabetes patients (nT2DM). A 75 g oral glucose tolerance test (OGTT) was administered to them. Blood samples were taken at 0, 60 ,120 and 180 minute of OGTT. nT2DM subjects were invited for further investigation, metformin was administered in a dose of 1.0 g every day for 1 week. Results: Plasma FGF-21 changed significantly in the nT2DM group during the OGTT administration but not in the control group. No gender differences were observed at different time points in FGF-21 levels (p < 0.05). Administration of metformin for nT2DM resulted in a significant decrease in both glucose and FGF-21 at all OGTT times and in insulin at 60 min and 180 min, indicative of a decrease in HOMA-IR. Conclusion: FGF-21 does not seem to be involved in short-term regulation of glycaemia in human subjects, and the change in OGTT delayed in T2DM. FGF-21 may participate in the processing of metformin, improving glucose and insulin sensitivity. (Pol J Endocrinol 2013; 64 (3): 220&#8211;224