Stable Pairs Research Articles

The 3d twisted index and wall-crossing

We study the twisted index of 3d \mathcal{N}=2𝒩=2 supersymmetric gauge theories on S^1 \times \SigmaS1×Σ in the presence of a real FI parameter deformation. This parameter induces a 1d FI parameter for the effective supersymmetric quantum mechanics on S^1S1. Using supersymmetric localisation, the twisted index can be expressed as a contour integral. We show that the contour prescription is modified in the presence of the 1d FI parameter, leading to wall-crossing phenomena for the twisted index. In particular, we derive a general wall-crossing formula for abelian gauge theories. We also examine the origin of wall-crossing as change of stability condition in the algebro-geometric interpretation of the twisted index. These ideas are illustrated for abelian theories with \mathcal{N}=4𝒩=4 supersymmetry and in a non-abelian example that reproduces wall-crossing phenomena associated to moduli spaces of stable pairs.

High C1 selectivity in alkaline ethanol oxidation reaction over stable Lewis pairs of Pd-MxC@CNT (M = W, Mo and Cr)

Pd-based catalysts have been widely studied as electrocatalysts for ethanol oxidation reaction (EOR) because of their higher oxygenophilic properties. However, there are still some disadvantages such as low activity, poor stability and poor selectivity, which hinder the development of EOR. Herein, a method through strong metal-support interaction (SMSI) and heterostructure of Pd-MxC@CNT (M = W, Mo and Cr) to construct a stable Lewis acid-base pair is proposed. Pd-W2C@CNT nanomaterial showed the highest mass activity (13.9 A mgPd−1), C1 selectivity (74.15%) and stability, better than Pd Black (3.5 A mgPd−1, 7.2%) and Pd@CNT (4.1 A mgPd−1, 7.6%). Ex situ and in situ electrochemical experiments reveal that the introduction of W2C became a stable electron donor for Pd, increasing the electron density of Pd atoms and forming a stable Lewis acidity Pd atoms to weaken the adsorption of intermediates. Reducing the electron density of W2C and forming a stable Lewis basicity W2C to provide sufficient OH adspecies for the reaction, thereby increasing the selectivity of the C1 pathway. Furthermore, the Pd-MxC@CNT synthesized by this method also exhibited excellent EOR activity, stability and C1 selectivity and glycerol oxidation reaction (GOR) performance.

On the stability analysis of gear pairs with tooth profile modification

This paper deals with the stability of loaded gear pairs, considering the effects of tooth profile modification. An analytical method to predict the stability of gear pairs has been developed by transforming their equations of motion to a form similar to the Mathieu equation and employing Floquet theory. The variation of (spur gear pair) teeth meshing stiffness due to tooth profile modification has been introduced, for different amounts of transmitted torque. Stability charts are obtained for different gear pairs, as well as undamped and damped conditions. The simulation results have shown that during operation, the examined gear pairs may cross regimes of unstable behaviour, thus contributing to aggressive oscillations of the gearbox. A holistic transmission design must take the above potential effects into consideration when predicting the durability of machine elements, such as gears and bearings.

Numerical Computations of Non-Newtonian Fluid Flow in Hexagonal Cavity With a Square Obstacle: A Hybrid Mesh–Based Study

Thermal flow phenomena in a double lid–driven enclosure have many potential applications in numerous engineering domains. The present article theoretically investigates the heat transfer analysis of power-law fluid in a hexagonal cavity embedded with a square obstacle. The upper and lower lid walls of the cavity are considered heated along with the walls of the centered embedded square, while the rest of the cavity walls are thermally insulated. In addition, the horizontal lid walls of the cavity are uniformly moving in opposite horizontal directions. The mathematical modeling of the nonlinear fluid has been developed considering the continuity, momentum, and energy equations subjected to the appropriate boundary conditions. Due to the nonlinearity of the governing partial differential equations and of the viscosity models, we use the numerical scheme based on the finite element method The stable finite element pair (ℙ2/ℙ1) has been selected for the discretization purpose. The discretized nonlinear system is solved with the Newton method in conjunction with a direct linear solver in the inner iterations. The thermal flow features are exposed via streamlines and temperature contours for a set of governing parameters such as Reynolds number (Re), Prandtl number (Pr), and Grashof number (Gr) along with the power-law index (n). The values of local and average Nusselt numbers are calculated for the involved parameters. It is noted that the square obstacle has a strong impact for the formulation of streamlines and isotherms. Moreover, the power-law index has a strong impact on the values of the average Nusselt number and kinetic energy. The kinetic energy of the system increases with an increasing value of Gr and n, while Reynolds number has opposite effects on kinetic energy.

A proof of the Donaldson–Thomas crepant resolution conjecture

We prove the crepant resolution conjecture for Donaldson–Thomas invariants of hard Lefschetz 3-Calabi–Yau (CY3) orbifolds, formulated by Bryan–Cadman–Young, interpreting the statement as an equality of rational functions. In order to do so, we show that the generating series of stable pair invariants on any CY3 orbifold is the expansion of a rational function. As a corollary, we deduce a symmetry of this function induced by the derived dualising functor. Our methods also yield a proof of the orbifold DT/PT correspondence for multi-regular curve classes on hard Lefschetz CY3 orbifolds.

A Qualitative Signature to Identify TERT Promoter Mutant High-Risk Tumors in Low-Grade Gliomas.

Background: Telomerase reverse transcriptase promoter (TERT-p) mutation has been frequently found, but associated with contrary prognosis, in both low-grade gliomas and glioblastomas. For the low-grade gliomas (Grades II-III), TERT-p mutant patients have a better prognosis than the wildtype patients, whereas for the GBMs (Grade IV), TERT-p mutation is related to a poor prognosis. We hypothesize that there exist high-risk patients in LGGs who share GBM-like molecular features, including TERT-p mutation, and need more intensive treatment than other LGGs. A molecular signature is needed to identify these high-risk patients for an accurate and timely treatment. Methods: Using the within-sample relative expression orderings of gene pairs, we identified the gene pairs with significantly stable REOs, respectively, in both the TERT-p mutant LGGs and GBMs but with opposite directions in the two groups. These reversely stable gene pairs were used as the molecular signature to stratify the LGGs into high-risk and low-risk groups. Results: A signature consisting of 21 gene pairs was developed, which can classify LGGs into two groups with significantly different overall survival. The high-risk group has a similar genetic mutation profile and a similar survival profile as GBMs, and these high-risk tumors may progress to a more malignant state. Conclusion: The 21 gene-pair signature based on REOs is capable of identifying high-risk patients in LGGs and guiding the clinical choice for appropriate and timely intervention.

Microscopic Insights Into the Formation of Methanesulfonic Acid–Methylamine–Ammonia Particles Under Acid-Rich Conditions

Understanding the microscopic mechanisms of new particle formation under acid-rich conditions is of significance in atmospheric science. Using quantum chemistry calculations, we investigated the microscopic formation mechanism of methanesulfonic acid (MSA)–methylamine (MA)–ammonia (NH3) clusters. We focused on the binary (MSA)2n-(MA)n and ternary (MSA)3n-(MA)n-(NH3)n, (n = 1–4) systems which contain more acid than base molecules. We found that the lowest-energy isomers in each system possess considerable thermodynamic and dynamic stabilities. In studied cluster structures, all bases are protonated, and they form stable ion pairs with MSA, which contribute to the charge transfer and the stability of clusters. MA and NH3 have a synergistic effect on NPF under acid-rich conditions, and the role of NH3 becomes more remarkable as cluster size increases. The excess of MSA molecules does not only enhance the stability of clusters, but provides potential sites for further growth.

Double-Headed 2'-Deoxynucleotides That Hybridize to DNA and RNA Targets via Normal and Reverse Watson-Crick Base Pairs.

Through the use of modified nucleotides, synthetic nucleic acids have found several fields of application within biotechnology and in the pharmaceutical industry. We have previously introduced nucleotides with an additional functional nucleobase linked to C2' of arabinonucleotides (BX). These double-headed nucleotides fit neatly into DNA·DNA duplexes, where they can replace the corresponding natural dinucleotides and thus condense the molecular information. Here, we introduce a 2'-deoxy version of the BX design with inversion of the C2' stereochemistry (dSBX) with the aim of obtaining improved RNA recognition. Specifically, dSBX analogues with cytosine or isocytosine attached to C2' of 2'-deoxyuridine (dSUC and dSUiC) were synthesized and evaluated in duplexes. Whereas the dSBX design did not outperform the BX design in terms of mimicking dinucleotides in nucleic acid duplexes, it was able to engage in reverse Watson-Crick pairing using its 2'-base. This was evident from the ability of the dSUC cytosine to form stable mis-matching base pairs with opposite cytosines identified as hemiprotonated C·C+ pairs. Furthermore, specific base-pairing with guanine was only observed for the isocytosine-bearing dSUiC monomer. Very stable duplexes were obtained with dSUC/iC monomers in each strand indicating that fully modified double-headed nucleic acid sequences could be based on the dSBX design.

Emergence and structure of decentralised trade networks around dark web marketplaces

Dark web marketplaces (DWMs) are online platforms that facilitate illicit trade among millions of users generating billions of dollars in annual revenue. Recently, two interview-based studies have suggested that DWMs may also promote the emergence of direct user-to-user (U2U) trading relationships. Here, we carefully investigate and quantify the scale of U2U trading around DWMs by analysing 31 million Bitcoin transactions among users of 40 DWMs between June 2011 and Jan 2021. We find that half of the DWM users trade through U2U pairs generating a total trading volume greater than DWMs themselves. We then show that hundreds of thousands of DWM users form stable trading pairs that are persistent over time. Users in such stable pairs turn out to be the ones with the largest trading volume on DWMs. Then, we show that new U2U pairs often form while both users are active on the same DWM, suggesting the marketplace may serve as a catalyst for new direct trading relationships. Finally, we reveal that stable U2U pairs tend to survive DWM closures and that they were not affected by COVID-19, indicating that their trading activity is resilient to external shocks. Our work unveils sophisticated patterns of trade emerging in the dark web and highlights the importance of investigating user behaviour beyond the immediate buyer-seller network on a single marketplace.

Rank-one sheaves and stable pairs on surfaces

Finite Quot schemes were used by Bertram, Johnson, and the first author to study Le Potier's strange duality conjecture on del Pezzo surfaces when one of the moduli spaces is the Hilbert scheme of points. In order to rigorously enumerate the finite Quot scheme, we study the moduli space of limit stable pairs in which the target has rank one on a smooth complex projective surface. We obtain an embedding of this moduli space into a smooth space that induces a perfect obstruction theory. This obstruction theory yields a virtual fundamental class that can be computed explicitly. Because the moduli space coincides with the Quot scheme when they have dimension 0, this makes the desired count of the finite Quot scheme in Bertram et al. rigorous. As another application, we obtain a universality result for tautological integrals on the moduli space of stable pairs.

The Type IV Pilus of Plasmid TP114 Displays Adhesins Conferring Conjugation Specificity and Is Important for DNA Transfer in the Mouse Gut Microbiota.

ABSTRACTType IV pili (T4P) are common bacterial surface appendages involved in different biological processes such as adherence, motility, competence, pathogenesis, and conjugation. In this work, we describe the T4P of TP114, an IncI2 enterobacterial conjugative plasmid recently shown to disseminate at high rates in the mouse intestinal tract. This pilus is composed of the major PilS and minor PilV pilins that are both important for conjugation in broth and in the gut microbiota but not on a solid support. The PilV-coding sequence is part of a shufflon and can bear different C-terminal domains. The shufflon is a multiple DNA inversion system containing many DNA cassettes flanked by recombination sites that are recognized by a shufflon-specific tyrosine recombinase (shufflase) promoting the recombination between DNA segments. The different PilV variants act as adhesins that can modify the affinity for different recipient bacteria. Eight PilV variants were identified in TP114, including one that has not been described in other shufflons. All PilV variants allowed conjugative transfer with different recipient Escherichia coli strains. We conclude that the T4P carried by TP114 plays a major role in mating pair stabilization in broth as well as in the gut microbiota and that the shufflon acts as a biological switch modifying the conjugative host range specificity.IMPORTANCE Conjugative plasmids are involved in horizontal gene transfer in the gut microbiota, which constitutes an important antibiotic resistance gene reservoir. However, the molecular mechanisms used by conjugative plasmids to select recipient bacteria and transfer at high rates in the mouse gut microbiota remain poorly characterized. We studied the type IV pilus carried by TP114 and demonstrated that the minor pilin PilV acts as an adhesin that can efficiently select target cells for conjugative transfer. Moreover, the pilV gene can be rapidly modified by a shufflon, hence modulating the nature of the recipient bacteria during conjugation. Our study highlights the role of mating pair stabilization for conjugation in broth as well as in the gut microbiome and explains how the host spectrum of a plasmid can be expanded simply by remodeling the PilV adhesin.

The zinc-finger transcription factor LSL-1 is a major regulator of the germline transcriptional program in Caenorhabditis elegans.

Specific gene transcriptional programs are required to ensure the proper proliferation and differentiation processes underlying the production of specialized cells during development. Gene activity is mainly regulated by the concerted action of transcription factors and chromatin proteins. In the nematode Caenorhabditis elegans, mechanisms that silence improper transcriptional programs in germline and somatic cells have been well studied, however, how are tissue-specific sets of genes turned on is less known. LSL-1 is herein defined as a novel crucial transcriptional regulator of germline genes in C. elegans. LSL-1 is first detected in the P4 blastomere and remains present at all stages of germline development, from primordial germ cell proliferation to the end of meiotic prophase. lsl-1 loss-of-function mutants exhibit many defects including meiotic prophase progression delay, a high level of germline apoptosis, and production of almost no functional gametes. Transcriptomic analysis and ChIP-seq data show that LSL-1 binds to promoters and acts as a transcriptional activator of germline genes involved in various processes, including homologous chromosome pairing, recombination, and genome stability. Furthermore, we show that LSL-1 functions by antagonizing the action of the heterochromatin proteins HPL-2/HP1 and LET-418/Mi2 known to be involved in the repression of germline genes in somatic cells. Based on our results, we propose LSL-1 to be a major regulator of the germline transcriptional program during development.

Virasoro conjecture for the stable pairs descendent theory of simply connected 3-folds (with applications to the Hilbert scheme of points of a surface).

This paper concerns the recent Virasoro conjecture for the theory of stable pairs on a 3‐fold proposed by Oblomkov, Okounkov, Pandharipande, and the author. Here we extend the conjecture to 3‐folds with non‐(p,p)‐cohomology and we prove it in two specializations. For the first specialization, we let S be a surface with H1(S)=0 and consider the moduli space Pn(S×P1,n[P1]), which happens to be isomorphic to the Hilbert scheme S[n] of n points on S. The Virasoro constraints for stable pairs, in this case, can be formulated entirely in terms of descendents in the Hilbert scheme of points. The two main ingredients of the proof are the toric case and the existence of universal formulas for integrals of descendents on S[n]. The second specialization consists in taking the 3‐fold X to be a cubic and the curve class β to be the line class. In this case we compute the full theory of stable pairs using the geometry of the Fano variety of lines.

Selective and stable base pairing by alkynylated nucleosides featuring a spatially-separated recognition interface

Unnatural base pairs (UBPs) which exhibit a selectivity against pairing with canonical nucleobases provide a powerful tool for the development of nucleic acid-based technologies. As an alternative strategy to the conventional UBP designs, which involve utility of different recognition modes at the Watson–Crick interface, we now report that the exclusive base pairing can be achieved through the spatial separation of recognition units. The design concept was demonstrated with the alkynylated purine (NPu, OPu) and pyridazine (NPz, OPz) nucleosides endowed with nucleobase-like 2-aminopyrimidine or 2-pyridone (‘pseudo-nucleobases’) on their major groove side. These alkynylated purines and pyridazines exhibited exclusive and stable pairing properties by the formation of complementary hydrogen bonds between the pseudo-nucleobases in the DNA major groove as revealed by comprehensive Tm measurements, 2D-NMR analyses, and MD simulations. Moreover, the alkynylated purine-pyridazine pairs enabled dramatic stabilization of the DNA duplex upon consecutive incorporation while maintaining a high sequence-specificity. The present study showcases the separation of the recognition interface as a promising strategy for developing new types of UBPs.

The refined determination of the ion pair lifetimes in ionic liquids

Assessing lifetimes of liquid’s local structures could bring impactful output. For example, the key transport properties of ionic liquids are governed by local structure dynamics to a large extent. Due to long-range Coulomb interactions, these systems show pronounced charge ordering. In this case, the local structure breaking rate could be described in terms of cation–anion pair lifetimes. Conventional pair lifetime analysis relies on geometrical criterion, defining the maximum distance from cation to anion in pair. In this study, we argue towards additional restriction to ensure pair stability. Based on vibrational properties, we introduce lower boundary for pair lifetime to exclude false pair recognition in the case of collision-like interaction. Also, we put forward a computational algorithm which allows obtaining both mean lifetime and lifetime distribution. The calculations of mean pair lifetimes in molten alkali halides support our reasoning.

Numerical investigation of the formation and stability of homogeneous pairs of soft particles in inertial microfluidics.

We investigate the formation and stability of a pair of identical soft capsules in channel flow under mild inertia. We employ a combination of the lattice Boltzmann, finite element and immersed boundary methods to simulate the elastic particles in flow. Validation tests show excellent agreement with numerical results obtained by other research groups. Our results reveal new trajectory types that have not been observed for pairs of rigid particles. While particle softness increases the likelihood of a stable pair forming, the pair stability is determined by the lateral position of the particles. A key finding is that stabilisation of the axial distance occurs after lateral migration of the particles. During the later phase of pair formation, particles undergo damped oscillations that are independent of initial conditions. These damped oscillations are driven by a strong hydrodynamic coupling of the particle dynamics, particle inertia and viscous dissipation. While the frequency and damping coefficient of the oscillations depend on particle softness, the pair formation time is largely determined by the initial particle positions: the time to form a stable pair grows exponentially with the initial axial distance. Our results demonstrate that particle softness has a strong impact on the behaviour of particle pairs. The findings could have significant ramifications for microfluidic applications where a constant and reliable axial distance between particles is required, such as flow cytometry.

Cosection localization and vanishing for virtual fundamental classes of d-manifolds

We establish cosection localization and vanishing results for virtual fundamental classes of derived manifolds, combining the theory of derived differential geometry by Joyce with the theory of cosection localization by Kiem-Li. As an application, we show that the stable pair invariants of hyperkähler fourfolds, defined by Cao-Maulik-Toda, are zero.

Kineto-Mechanistic Investigation of Effect of Macromolecular Crowding on the Breathing of DNA Bubble.

Macromolecular crowding along with hydrogen bonding or stacking interactions and hydration reportedly has enormous repercussions on elementary biochemical processes, such as the folding of proteins or nucleic acids involving the stability of DNA base pairing. By using the mismatch-induced DNA bubble as a mesoscopic model, the complex interplay of macromolecular crowding on the dynamical fluctuations at the bubble region within the thermodynamic limit has been monitored using single-molecule fluorescence resonance energy transfer (sm-FRET). These single-molecule experimental results have been further corroborated using physical models such as "scaled particle theory" (SPT) and "Gaussian cloud model" (GCM), to predict the biological activity of DNA. The two-state fluctuation of the DNA bubble has been visualized as a function of the nature, size, and concentration of the crowder. The influence of crowders on the DNA conformation has been investigated with the help of the m-factor, the eccentricity, and the kinetic and thermodynamic parameters without any prior assumption. The clear effect of crowding on the dynamics of such a simple biomolecular system emphasizes the power of single-molecule methods and the dependency of the radius of gyration of the co-solute as well as the preferential interaction with the crowder on the distinct conformational states adopted by the bubble. This study provides an idea and hypothesizes the preferential propensity of the DNA bubble to adopt a conformation with the single-stranded domains being far apart, independent of the crowder size, that may be beneficial for efficient recognition by proteins for an uninterrupted procession of the biological process of the central dogma.

A Review on Recent Progress in the Integrated Green Hydrogen Production Processes

The thermochemical water-splitting method is a promising technology for efficiently converting renewable thermal energy sources into green hydrogen. This technique is primarily based on recirculating an active material, capable of experiencing multiple reduction-oxidation (redox) steps through an integrated cycle to convert water into separate streams of hydrogen and oxygen. The thermochemical cycles are divided into two main categories according to their operating temperatures, namely low-temperature cycles (<1100 °C) and high-temperature cycles (<1100 °C). The copper chlorine cycle offers relatively higher efficiency and lower costs for hydrogen production among the low-temperature processes. In contrast, the zinc oxide and ferrite cycles show great potential for developing large-scale high-temperature cycles. Although, several challenges, such as energy storage capacity, durability, cost-effectiveness, etc., should be addressed before scaling up these technologies into commercial plants for hydrogen production. This review critically examines various aspects of the most promising thermochemical water-splitting cycles, with a particular focus on their capabilities to produce green hydrogen with high performance, redox pairs stability, and the technology maturity and readiness for commercial use.

Shape multistability in flexible tubular crystals through interactions of mobile dislocations

We study avenues to shape multistability and shape morphing in flexible crystalline membranes of cylindrical topology, enabled by glide mobility of dislocations. Using computational modeling, we obtain states of mechanical equilibrium presenting a wide variety of tubular crystal deformation geometries, due to an interplay of effective defect interactions with out-of-tangent-plane deformations that reorient the tube axis. Importantly, this interplay often stabilizes defect configurations quite distinct from those predicted for a two-dimensional crystal confined to the surface of a rigid cylinder. We find that relative and absolute stability of competing states depend strongly on control parameters such as bending rigidity, applied stress, and spontaneous curvature. Using stable dislocation pair arrangements as building blocks, we demonstrate that targeted macroscopic three-dimensional conformations of thin crystalline tubes can be programmed by imposing certain sparse patterns of defects. Our findings reveal a broad design space for controllable and reconfigurable colloidal tube geometries, with potential relevance also to architected carbon nanotubes and microtubules.