Exact Structures Research Articles

Locally Coherent Exact Categories

A locally coherent exact category is a finitely accessible additive category endowed with an exact structure in which the admissible short exact sequences are the directed colimits of admissible short exact sequences of finitely presentable objects. We show that any exact structure on a small idempotent-complete additive category extends uniquely to a locally coherent exact structure on the category of ind-objects; in particular, any finitely accessible category has the unique maximal and the unique minimal locally coherent exact category structures. All locally coherent exact categories are of Grothendieck type in the sense of Št’ovíček. We also discuss the canonical embedding of a small exact category into the abelian category of additive sheaves in connection with the locally coherent exact structure on the ind-objects, and deduce two periodicity theorems as applications.

Exact coherent structures in two-dimensional turbulence identified with convolutional autoencoders

Convolutional autoencoders are used to deconstruct the changing dynamics of two-dimensional Kolmogorov flow as $Re$ is increased from weakly chaotic flow at $Re=40$ to a chaotic state dominated by a domain-filling vortex pair at $Re=400$ . ‘Latent Fourier analysis’ (Page et al., Phys. Rev. Fluids6, 2021, p. 034402) reveals a detached class of bursting dynamics at $Re=40$ which merge with the low-dissipation dynamics as $Re$ is increased to $100$ and provides an efficient representation within which to find unstable periodic orbits (UPOs) using recurrent flow analysis. Focusing on initial guesses with energy in higher latent Fourier wavenumbers allows a significant number of high-dissipation-rate UPOs associated with the bursting events to be found for the first time. At $Re=400$ , the UPOs discovered at lower $Re$ move away from the attractor, and an entirely different embedding structure is formed within the network devoid of small-scale vortices. Here latent Fourier projections identify an associated ‘large-scale’ UPO which we believe to be a finite- $Re$ continuation of a solution to the Euler equations.

Mono-ADP-ribosylation of peptides: an overview of synthetic and chemoenzymatic methodologies.

Adenosine diphosphate (ADP)-ribosylation is a ubiquitous post-translational modification that regulates vital biological processes like histone reorganization and DNA-damage repair through the modification of various amino acid residues. Due to advances in mass-spectrometry, the collection of long-known ADP-ribose (ADPr) acceptor sites, e.g. arginine, cysteine and glutamic acid, has been expanded with serine, tyrosine and histidine, among others. Well-defined ADPr-peptides are valuable tools for investigating the exact structures, mechanisms of action and interaction partners of the different flavors of this modification. This review provides a comprehensive overview of synthetic and chemoenzymatic methodologies that enabled the construction of peptides mono-ADP-ribosylated on various amino acids, and close mimetics thereof.

Quaternion-based finite-element computation of nonlinear modes and frequency responses of geometrically exact beam structures in three dimensions

Quaternion-based finite-element computation of nonlinear modes and frequency responses of geometrically exact beam structures in three dimensions

Experimental and numerical evaluation of the influence of voids on sound absorption behaviors of 3D printed continuous flax fiber reinforced PLA composites

This study aims to quantitatively analyze the effects of voids on sound absorption properties of 3D printed continuous flax fiber reinforced PLA composites (CFFRCs). Three kinds of flax yarns with different linear density were employed to prepare CFFRCs via 3D printing technology. The sound absorption performances of these composites were measured using the impedance tube based on the two-microphone transfer function method. The microstructure morphologies including cross-sections of flax yarns, voids shape and distributions of the composites were observed via ultra-depth microscope and micro-computed tomography to reconstruct the exact structures in simulation. Mercury intrusion porosimetry was applied to measure the voids dimensions of CFFRCs. The influence of voids on sound absorption mechanisms of CFFRCs were revealed based on thermoviscous acoustics theory by conducting the simulation in COMSOL software. The experimental results demonstrated that CFFRCs exhibited excellent sound absorption coefficients (close to 1) within the frequency range of 150–350 Hz and 350–550 Hz, resulting from the voids inside and between the flax yarns respectively. With the increase of linear density (diameter of the yarn), the contents of voids inside and between the flax yarns both increased. The dimensions of voids inside the flax yarns improved while those between flax yarns remained unchanged. The existence of the voids between the flax yarns resulted in a decrease in the sound absorption coefficient of CFFRCs, while more voids inside flax yarns led to the increase of the sound absorption frequency. Numerical results indicated that voids between the flax yarns contributed to a more uniform change in sound speed, reducing sound absorption performance. Whereas, voids inside the flax yarns could improve viscous friction of soundwaves due to narrow structures, enhancing sound absorption capabilities. This study is anticipated to provide a guidance for the design of integration of structure and function of 3D printed CFFRCs.

Imaging surface structure and premelting of ice Ih with atomic resolution.

Ice surfaces are closely relevant to many physical and chemical properties, such as melting, freezing, friction, gas uptake and atmospheric reaction1-8. Despite extensive experimental and theoretical investigations9-17, the exact atomic structures of ice interfaces remain elusive owing to the vulnerable hydrogen-bonding network and the complicated premelting process. Here we realize atomic-resolution imaging of the basal (0001) surface structure of hexagonal water ice (ice Ih) by using qPlus-based cryogenic atomic force microscopy with a carbonmonoxide-functionalized tip. We find that the crystalline ice-Ih surface consists of mixed Ih- and cubic (Ic)-stacking nanodomains, forming periodic superstructures. Density functional theory reveals that this reconstructed surface is stabilized over the ideal ice surface mainly by minimizing the electrostatic repulsion between dangling OH bonds. Moreover, we observe that the ice surface gradually becomes disordered with increasing temperature (above 120 Kelvin), indicating the onset of the premelting process. The surface premelting occurs from the defective boundaries between the Ih and Ic domains and can be promoted by the formation of a planar local structure. These results put an end to the longstanding debate on ice surface structures and shed light on the molecular origin of ice premelting, which may lead to a paradigm shift in the understanding of ice physics and chemistry.

Systematic evaluation of single-cell RNA-seq analyses performance based on long-read sequencing platforms

IntroductionThe rapid development of next-generation sequencing (NGS)-based single-cell RNA sequencing (scRNA-seq) allows for detecting and quantifying gene expression in a high-throughput manner, providing a powerful tool for comprehensively understanding cellular function in various biological processes. However, the NGS-based scRNA-seq only quantifies gene expression and cannot reveal the exact transcript structures (isoforms) of each gene due to the limited read length. On the other hand, the long read length of third-generation sequencing (TGS) technologies, including Oxford Nanopore Technologies (ONT) and Pacific Biosciences (PacBio), enable direct reading of intact cDNA molecules. ObjectivesBoth ONT and PacBio have been used in conjunction with scRNA-seq, but their performance in single-cell analyses has not been systematically evaluated. MethodsTo address this, we generated ONT and PacBio data from the same single-cell cDNA libraries containing different amount of cells. ResultsUsing NGS as a control, we assessed the performance of each platform in cell type identification. Additionally, the reliability in identifying novel isoforms and allele-specific gene/isoform expression by both platforms was verified, providing a systematic evaluation to design the sequencing strategies in single-cell transcriptome studies. ConclusionBeyond gene expression analysis, which the NGS-based scRNA-seq only affords, TGS-based scRNA-seq achieved gene splicing analyses, identifying novel isoforms. Attribute to higher sequencing quality of PacBio, it outperforms ONT in accuracy of novel transcripts identification and allele-specific gene/isoform expression.

Exploring chalcone-sulfonyl piperazine hybrids as anti-diabetes candidates: design, synthesis, biological evaluation, and molecular docking study.

To address the escalating rates of diabetes mellitus worldwide, there is a growing need for novel compounds. The demand for more affordable and efficient methods of managing diabetes is increasing due to the inevitable side effects associated with existing antidiabetic medications. In this present research, various chalcone-sulfonyl piperazine hybrid compounds (5a-k) were designed and synthesized to develop inhibitors against alpha-glucosidase and alpha-amylase. In addition, several spectroscopic methods, including FT-IR, 1H-NMR, 13C-NMR, and HRMS, were employed to confirm the exact structures of the synthesized derivatives. All synthesized compounds were evaluated for their ability to inhibit alpha-glucosidase and alpha-amylase in vitro using acarbose as the reference standard and they showed excellent to good inhibitory potentials. Compound 5k exhibited excellent inhibitory activity against alpha-glucosidase (IC50 = 0.31 ± 0.01 µM) and alpha-amylase (IC50 = 4.51 ± 1.15 µM), which is 27-fold more active against alpha-glucosidase and 7-fold more active against alpha-amylase compared to acarbose, which had IC50 values of 8.62 ± 1.66 µM for alpha-glucosidase and 30.97 ± 2.91 µM for alpha-amylase. It was discovered from the Lineweaver-Burk plot that 5k exhibited competitive inhibition against alpha-glucosidase. Furthermore, cytotoxicity screening assay results against human fibroblast HT1080 cells showed that all compounds had a good level of safety profile. To explore the binding interactions of the most potent compound (5k) with the active site of enzymes, molecular docking research was conducted, and the results obtained supported the experimental data.

Structure and ionic conduction enhancement mechanisms at CeO2/SrTiO3 heterointerfaces

Fluorite-perovskite heterointerfaces garner great interest for enhanced ionic conductivity for application in electronic and energy devices. However, the origin of observed enhanced ionic conductivity as well as the details of the atomic structure at these interfaces remain elusive. Here, systematic, multi-stoichiometry computational searches and experimental investigations are performed to obtain stable and exact atomic structures of interfaces between CeO2 and SrTiO3—two archetypes of the corresponding structural families. Local reconstructions take place at the interface because of mismatched lattices. TiO2 terminated SrTiO3 causes a buckled rock salt CeO interface layer to emerge. In contrast, SrO terminated SrTiO3 maintains the fluorite structure at the interface compensated by a partially occupied anion lattice. Moderate enhancement in oxygen diffusion is found along the interface by simulations, yet evidence to support further significant enhancement is lacking. Our findings demonstrate the control of interface termination as an effective pathway to achieve desired device performance.

Dynamical analysis of exact optical soliton structures of the complex nonlinear Kuralay-II equation through computational simulation

In this paper, we successfully extracted the various types of soliton solutions for the complex nonlinear Kuralay-II equation through the improved F-expansion method with symbolic computational software Mathematica. The extracted soliton solutions for the Kuralay-II equation are interesting, novel and more general such as anti-kink wave solitons, dark solitons, kink wave solitons, bright solitons, periodic wave solitons, mixed solitons in bright-dark soliton shape, peakon solitons, and solitary wave structures. The graphical structure of some extracted solutions is visualized in 2D, 3D and contour plottings with imaginary, real, and absolute values of the functions by using the numerical simulation. The proposed research will contribute to advancing our knowledge about the complex nonlinear Kuralay-II equation and demonstrating the applicability to the proposed approach to investigate other higher-order complex nonlinear equations. The successful investigation demonstrated that the proposed method is effective, simple, more powerful, efficient and can be utilized on a variety of other nonlinear equations. The explored solitary waves and optical solitons will play an important role in the investigation of nonlinear phenomena in various domains of science and engineering.

Largest exact structures and almost split sequences on hearts of twin cotorsion pairs

Abstract Hearts of cotorsion pairs on extriangulated categories are abelian categories. On the other hand, hearts of twin cotorsion pairs are not always abelian. They were shown to be semi-abelian by Liu and Nakaoka. Moreover, Hassoun and Shah proved that they are quasi-abelian under certain conditions. In this article, we first show that the heart of any twin cotorsion pair has a largest exact category structure and is always quasi-abelian. We also provide a sufficient and necessary condition for the heart of a twin cotorsion pair being abelian. Then by using the results we have got, we investigate the almost split sequences in the hearts of twin cotorsion pairs. Finally, as an application, we show that a Krull–Schmidt, Hom-finite triangulated category has a Serre functor whenever it has a cluster tilting object.

Effects of a spanwise magnetic field on the exact coherent states in a channel flow

The primary objective of this study is to examine the effect of a uniformly constant spanwise magnetic field on exact coherent states and their structures in channel flow. Exact coherent states represent nonlinear solutions to the Navier–Stokes equations, bearing significant importance in the prediction and control of flow with and without magnetic field. Despite the recent extensive research which have reported the influences of magnetic fields with respect to fluid dynamics, the specific effect of a spanwise magnetic field on the exact coherent states remain ambiguous. To investigate the influence of magnetic field on exact coherent states in channel flow, our study encompasses Reynolds numbers ranging from 3000 to 10 000, with variations in the size of computational domains. High-precision direct numerical simulations, coupled with a Fourier–Chebyshev spatial pseudospectra discretization, are employed to solve the governing equations under the assumption of low magnetic Reynolds number. Starting from laminar flow, we utilize a bisection method on the amplitude of perturbations to track the exact coherent states in the channel. In a smaller computational domain 2π × 2.4 × 2, the spanwise magnetic field expedites the self-sustaining process of exact coherent structures, accelerating the transition from streamwise vortices to streamwise streaks. In a larger computational domain, the exact coherent states are bifurcated from relative periodic orbit solutions to traveling wave solutions. Furthermore, as the spanwise computational domain expands, localization coherent structures persist and steadily propagate downstream in the channel.

Orientation Relationship of Intergrowth Al2Fe and Al5Fe2 Intermetallics Determined by Single-Crystal X-ray Diffraction

Although the Al2Fe phase has similar decagonal-like atomic arrangements as that of the orthorhombic Al5Fe2 phase, no evidence for intergrowth samples of Al2Fe and Al5Fe2 has been reported. In the present work, the co-existence of Al2Fe and Al5Fe2 phases has been discovered from the educts obtained with a nominal atomic ratio of Al:Fe of 2:1 by arc melting. First, single-crystal X-ray diffraction (SXRD) as well as scanning electron microscope (SEM) equipped with energy-dispersive X-ray spectroscopy (EDX) measurements have been utilized to determine the exact crystal structures of both phases, which are refined to be Al12.48Fe6.52 and Al5.72Fe2, respectively. Second, the orientation relationship between Al2Fe and Al5Fe2 has been directly deduced from the SXRD data sets, and the co-existence structure model has been constructed. Finally, four pairs of parallel atomic planes and their unique orientation relations have been determined from the reconstructed reciprocal-space precession images of (0kl), (h0l), and (hk0) layers. In addition, one kind of interface atomic structure model is constructed by the orientation relations between two phases, correspondingly.

Perturbations in human bile acid profiles following drug-induced liver injury investigated using semitargeted high-resolution mass spectrometry.

Acetaminophen (APAP) overdose is the leading cause of acute liver failure (ALF) in North America. To investigate the effect of drug-induced liver injury (DILI) on circulating bile acid (BA) profiles, serum from ALF patients and healthy controls were analyzed using a semitargeted high-resolution mass spectrometry approach to measure BAs in their unconjugated and amidated forms and their glucuronide and sulfate conjugates. Human serum samples from 20 healthy volunteers and 34 ALF patients were combined with deuterated BAs and extracted, prior to liquid chromatography high-resolution tandem mass spectrometry analysis. A mix of 46 standards helped assign 26 BAs in human serum by accurate mass and retention time matching. Moreover, other isomers of unconjugated and amidated BAs, as well as glucuronide and sulfate conjugates, were assigned by accurate mass filtering. In vitro incubations of standard BAs provided increased information for certain peaks of interest. A total of 275 BA metabolites, with confirmed or putative assignments, were measured in human serum samples. APAP overdose significantly influenced the levels of most BAs, promoting glycine conjugation, and, to a lesser extent, taurine conjugation. When patient outcome was considered, 11 BAs were altered significantly, including multiple sulfated species. Although many of the BAs measured did not have exact structures assigned, several putatively identified BAs of interest were further characterized using in vitro incubations. An optimized chromatographic separation tailored to BAs of ranging polarities was combined with accurate mass measurements to investigate the effect that DILI has on their complex profiles and metabolism to a much wider extent than previously possible. The analysis of complex BA profiles enabled in-depth analysis of the BA metabolism perturbations in ALF, including certain metabolites related to patient outcomes.

On the exact soliton solutions and different wave structures to the (2+1) dimensional Chaffee–Infante equation

Nonlinear phenomena observed in diverse scientific disciplines, including fluid dynamics, plasma physics, and biology, are frequently described by partial differential equations (PDEs). Among these PDEs, the Chaffee–Infante equation holds considerable importance and finds applications in various scientific and engineering domains. The focus of this research article revolves around the exploration of closed-form solitary wave solutions for this significant nonlinear evolution equation (NLEE) through the utilization of two efficient techniques. By employing rigorous analysis and computation, our study presents a wealth of soliton solutions and thoroughly investigates their physical implications by examining parameter values and constructing illustrative figures. In-depth exploration of trigonometric, hyperbolic, and rational expression solution forms enables a comprehensive understanding of the intricate dynamics exhibited by plasma behavior. Through the consideration of diverse solution possibilities, this research contributes to an enhanced comprehension of the inherent complexities within plasma systems. In this paper, we have put all the obtained solutions in the main equation and found that all the solutions are correct. This provides strong evidence for the validity of our proposed method and its ability to accurately solve the considered problem. The methods employed in this study distinguish themselves by their simplicity, reliability, and ability to generate novel solutions for nonlinear partial differential equations within the realm of mathematical physics.

A modular chemoenzymatic cascade strategy for the structure-customized assembly of ganglioside analogs

Gangliosides play vital biological regulatory roles and are associated with neurological system diseases, malignancies, and immune deficiencies. They have received extensive attention in developing targeted drugs and diagnostic markers. However, it is difficult to obtain enough structurally defined gangliosides and analogs especially at an industrial-relevant scale, which prevent exploring structure-activity relationships and identifying drug ingredients. Here, we report a highly modular chemoenzymatic cascade assembly (MOCECA) strategy for customized and large-scale synthesis of ganglioside analogs with various glycan and ceramide epitopes. We typically accessed five gangliosides with therapeutic promising and systematically prepared ten GM1 analogs with diverse ceramides. Through further process amplification, we achieved industrial production of ganglioside GM1 in the form of modular assembly at hectogram scale. Using MOCECA-synthesized GM1 analogs, we found unique ceramide modifications on GM1 could enhance the ability to promote neurite outgrowth. By comparing the structures with synthetic analogs, we further resolved the problem of contradicting descriptions for GM1 components in different pharmaceutical documents by reinterpreting the exact two-component structures of commercialized GM1 drugs. Because of its applicability and stability, the MOCECA strategy can be extended to prepare other glycosphingolipid structures, which may pave the way for developing new glycolipid drugs.

Structural evolution and electronic properties of anionic carbon-nitrogen clusters.

Carbon-doped nitrogen clusters have represented a fascinating area of materials science in recent years. However, achieving precise control of the doping level and distribution of carbon within nitrogen clusters is challenging. Advanced techniques are required to elucidate their exact structures and electronic properties. Here, we perform systematic structure searches of anionic carbon-doped nitrogen clusters by the Crystal structure AnaLYsis by Particle Swarm Optimization method combined with density-functional theory calculations. The ground state structures of CNn- (n = 4-16) clusters for each cluster size are determined. The structural evolution, photoelectron energy spectra, electronic properties, and chemical bonding modes of anionic CNn- (n = 4-16) clusters are discussed. The calculated results indicate that the two-dimensional planar geometry of the anionic CN6- cluster with the C1 symmetry exhibits robust stability. The molecular orbitals and the adaptive natural density partitioning calculations show that the high stability of the anionic CN6- cluster is attributed to the localized σ-bonding formed by the 2p orbitals of carbon and nitrogen atoms. The four delocalized π chemical bonds contribute to the stability of the anionic CN6- cluster, resulting in a stable ring geometry. The present results enrich the database of geometric structures of carbon-nitrogen clusters and provide valuable insights for the experimental synthesis and characterization of nitrogen-based clusters.

Spectroscopic inspection, DFT analysis, biological evaluation and molecular docking studies of new 2-(phenylamino)acetohydrazide hydrazone based- transition metal complexes

The binuclear Pd(II) and mononuclear Zn(II), Ru(III) and Pt(IV) chelates were synthesized based on new hydrazone ligand derived from 2-(phenylamino)acetohydrazide and 3-Acetyl-2-hydroxy-6-methyl-4H-pyran-4-one (dehydroacetic acid DHA) (H2L). Variable characterization tools were used to confirm the exact structures. Spectral data show that (H2L) ligand acts as monobasic tridentate with ONO donor form. UV–Vis absorption spectroscopy and magnetic moment measurements demonstrated that the Ru(III) and Pt(IV) chelates possess an octahedral environment while Zn(II) and Pd(II) chelates possess square planar environment. The geometry of each complex was optimized using DFT calculation. The stability of the compounds was elucidated by the TGA technique. Antimicrobial activity of the compounds was evaluated and the results showed that the complexes demonstrated superior inhibitory action to ligand and display excellent antimicrobial activities against the tested microorganisms. Zn(II) mononuclear chelate showed the greatest effect against both types of bacterial strains. Antiviral activity was evaluated against Coxsackie virus (Cox B4), Herpes simplex (HSV1) and Hepatitis AVirus(HAV). The binuclear Pd(II) chelate revealed high activity against the three studied viruses while the mononuclear Ru(III) chelate revealed similar activity against the two types only. The cytotoxicity results supported the greatest effect of Zn(II) and Pd(II) against MCF-7 type. Zn(II) chelate revealed the best result against Hep-G2 type. Finally, we can conclude that binuclear Pd(II) chelate was active against all studied disease types, while not all mononuclear chelates are active. The microbial and tumor inhibition activity was compared with the theoretical molecular docking results with the specification of the active species in the selected proteins.

Exploring regular and turbulent flow states in active nematic channel flow via Exact Coherent Structures and their invariant manifolds

Exploring regular and turbulent flow states in active nematic channel flow via Exact Coherent Structures and their invariant manifolds

On abelian subcategories of triangulated categories

The stable module category of a selfinjective algebra is triangulated, but need not have any nontrivial t-structures, and in particular, full abelian subcategories need not arise as hearts of a t-structure. The purpose of this paper is to investigate full abelian subcategories of triangulated categories whose exact structures are related, and more precisely, to explore relations between invariants of finite-dimensional selfinjective algebras and full abelian subcategories of their stable module categories.