Conformal Point Research Articles

Principles of bacterial genome organization, a conformational point of view.

Bacterial chromosomes are large molecules that need to be highly compacted to fit inside the cells. Chromosome compaction must facilitate and maintain key biological processes such as gene expression and DNA transactions (replication, recombination, repair, and segregation). Chromosome and chromatin 3D-organization in bacteria has been a puzzle for decades. Chromosome conformation capture coupled to deep sequencing (Hi-C) in combination with other "omics" approaches has allowed dissection of the structural layers that shape bacterial chromosome organization, from DNA topology to global chromosome architecture. Here we review the latest findings using Hi-C and discuss the main features of bacterial genome folding.

An Observation About Conformal Points on Surfaces

AbstractWe study the existence of points on a compact oriented surface at which a symmetric bilinear two-tensor field is conformal to a Riemannian metric. We give applications to the existence of conformal points of surface diffeomorphisms and vector fields.

Tunable Quantum Criticality in Multicomponent Rydberg Arrays.

Arrays of Rydberg atoms have appeared as a remarkably rich playground to study quantum phase transitions in one dimension. One of the biggest puzzles that was brought forward in this context are chiral phase transitions out of density waves. Theoretically predicted chiral transition out of period-four phase is still pending experimental verification mainly due to extremely short interval over which this transition is realized in a single-component Rydberg array. In this Letter, we show that multicomponent Rydberg arrays with extra experimentally tunable parameters provide a mechanism to manipulate quantum critical properties without breaking translation symmetry explicitly. We consider an effective blockade model of two component Rydberg atoms. Weak and strong components obey nearest- and next-nearest-neighbor blockades correspondingly. When laser detuning is applied to either of the two components the system is in the period-3 and period-2 phases. But laser detuning applied to both components simultaneously stabilizes the period-4 phase partly bounded by the chiral transition. We show that relative ratio of the Rabi frequencies of the two components tunes the properties of the conformal Ashkin-Teller point and allows us to manipulate an extent of the chiral transition. The prospects of multicomponent Rydberg arrays in the context of critical fusion is briefly discussed.

Enhanced Structure-Based Prediction of Chiral Stationary Phases for Chromatographic Enantioseparation from 3D Molecular Conformations.

The accurate prediction of suitable chiral stationary phases (CSPs) for resolving the enantiomers of a given compound poses a significant challenge in chiral chromatography. Previous attempts at developing machine learning models for structure-based CSP prediction have primarily relied on 1D SMILES strings [the simplified molecular-input line-entry system (SMILES) is a specification in the form of a line notation for describing the structure of chemical species using short ASCII strings] or 2D graphical representations of molecular structures and have met with only limited success. In this study, we apply the recently developed 3D molecular conformation representation learning algorithm, which uses rapid conformational analysis and point clouds of atom positions in the 3D space, enabling efficient chemical structure-based machine learning. By harnessing the power of the rapid 3D molecular representation learning and a data set comprising over 300,000 chromatographic enantioseparation records sourced from the literature, our models afford notable improvements for the chemical structure-based choice of appropriate CSP for enantioseparation, paving the way for more efficient and informed decision-making in the field of chiral chromatography.

Laser surface texturing for superhydrophobic, icephobic and friction reduction functionalization

Nanometre and/or micrometer scale periodic features naturally present decorating the skin of many insects, fishes or plants have been found to give them extraordinary aesthetic, adhesion, antifouling, wear resistance, superhydrophobic or drag reduction properties. With the aim of artificially conveying the same properties to products and tools, researchers have tried to reproduce such bionic topography on the surface of a huge variety of materials using different manufacturing methods. Among the different manufacturing technologies, surface texturing based on direct laser writing using ultrashort pulses offers great flexibility in terms of geometry and size of the feature to be created. This work will focus on two specific types of functionalization of metallic as well as rubber surfaces through laser surface texturing, i.e., icephobicity and friction reduction. In the first case, different texture patterns were laser written on sheet samples of Aluminum Alloy of interest for aerospace applications. Their wettability and anti-icing properties were investigated through water contact angle experiments in different environmental conditions and steam-freezing experiments were conducted in a climate chamber. The role of the laser textured pattern geometry on the frictional performances of a rubber surface under lubricated non-conformal as well as conformal point contact has been also widely investigated. In the first case, no improvements were obtained in terms of frictional performances, ascribable to the reduced number of dimples involved in the contact area. Conversely, remarkable friction reduction was achieved in mixed and in the transition between the mixed and the elasto-hydrodinamic lubrication regime, thanks to the concurrence of several effects as micro-cavitation, wear debris trapping, and lubricant entrapping within the texture.

Soft-gluon effective coupling: perturbative results and the large-nF limit to all orders

We consider extensions of the soft-gluon effective coupling that generalize the Catani-Marchesini-Webber (CMW) coupling in the context of soft-gluon resummation beyond the next-to-leading logarithmic accuracy. Starting from the probability density of correlated soft emission in d dimensions we introduce a class of soft couplings relevant for resummed QCD calculations of hard-scattering observables. We show that at the conformal point, where the d-dimensional QCD β function vanishes, all these effective couplings are equal and they are also equal to the cusp anomalous dimension. We present explicit results in d dimensions for the soft-emission probability density and the soft couplings at the second-order in the QCD coupling αS. In d = 4 dimensions we obtain the explicit relation between the soft couplings at O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(αS3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\alpha}_{\ extrm{S}}^3 $$\\end{document}). Finally, we study the structure of the soft coupling in the large-nF limit and we present explicit expressions to all orders in perturbation theory. We also check that, at the conformal point, our large-nF results agree with the known result of the cusp anomalous dimension.

Partition functions of non-Lagrangian theories from the holomorphic anomaly

The computation of the partition function in certain quantum field theories, such as those of the Argyres-Douglas or Minahan-Nemeschansky type, is problematic due to the lack of a Lagrangian description. In this paper, we use the holomorphic anomaly equation to derive the gravitational corrections to the prepotential of such theories at rank one by deforming them from the conformal point. In the conformal limit, we find a general formula for the partition function as a sum of hypergeometric functions. We show explicit results for the round sphere and the Nekrasov-Shatashvili phases of the Ω background. The first case is relevant for the derivation of extremal correlators in flat space, whereas the second one has interesting applications for the study of anharmonic oscillators.

Nonsingular black holes from conformal symmetries

We derive the form of the metric for static, nonsingular black holes with a de Sitter core, representing a deformation of the Schwarzschild solution, by assuming that the gravitational sources describe a flow between two conformal points, at small and great distances. The resulting black-hole metric turns out to be a particular case of the Fan & Wang metric, whose parameters have been recently constrained by using the data of the S2 star orbits around the galactic center SgrA.

On a class of conformal mathcal{E} -models and their chiral Poisson algebras

In this paper, we study conformal points among the class of mathcal{E} -models. The latter are σ-models formulated in terms of a current Poisson algebra, whose Lie-theoretic definition allows for a purely algebraic description of their dynamics and their 1-loop RG-flow. We use these results to formulate a simple algebraic condition on the defining data of such a model which ensures its 1-loop conformal invariance and the decoupling of its observables into two chiral Poisson algebras, describing the classical left- and right-moving fields of the theory. In the case of so-called non-degenerate mathcal{E} -models, these chiral sectors form two current algebras and the model takes the form of a WZW theory once realised as a σ-model. The case of degenerate mathcal{E} -models, in which a subalgebra of the current algebra is gauged, is more involved: the conformal condition yields a wider class of theories, which includes gauged WZW models but also other examples, seemingly different, which however sometimes turn out to be related to gauged WZW models based on other Lie algebras. For this class, we build non-local chiral fields of parafermionic-type as well as higher-spin local ones, forming classical mathcal{W} -algebras. In particular, we find an explicit and efficient algorithm to build these local chiral fields. These results (and their potential generalisations discussed at the end of the paper) open the way for the quantisation of a large class of conformal mathcal{E} -models using the standard operator formalism of two-dimensional CFT.

Topological Fracton Quantum Phase Transitions by Tuning Exact Tensor Network States.

Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable models remains a formidable challenge. Here we employ an exact 3D quantum tensor-network approach that allows us to study a Z_{N} generalization of the prototypical X cube fracton model and its quantum phase transitions between distinct topological states via fully tractable wave function deformations. We map the (deformed) quantum states exactly to a combination of a classical lattice gauge theory and a plaquette clock model, and employ numerical techniques to calculate various entanglement order parameters. For the Z_{N} model we find a family of (weakly) first-order fracton confinement transitions that in the limit of N→∞ converge to a continuous phase transition beyond the Landau-Ginzburg-Wilson paradigm. We also discover a line of 3D conformal quantum critical points (with critical magnetic flux loop fluctuations) which, in the N→∞ limit, appears to coexist with a gapless deconfined fracton state.

Gravitational-gauge vector interaction in the Hořava–Lifshitz framework

An anisotropic model describing gravity-vector gauge coupling at all energy scales is presented. The starting point is the 4+1 dimensional non–projectable Hořava–Lifshitz gravity theory subject to a geometrical restriction. Renormalizability arguments require all possible interactions in the potential up to terms with z = 4 spatial derivatives on the geometrical tensor fields: the Riemann and Weyl tensors. The latter being necessary on a 4+1 dimensional formulation. The dimensional reduction to 3+1 dimensions gives rise to a model invariant under foliation-preserving diffeomorphisms (FDiff) and U(1) symmetry groups. The reduced theory on the kinetic conformal point (), propagates the same spectrum of the Einstein–Maxwell theory. Moreover, at low energies, on the IR point α = 0, β = 1, its field equations are exactly the Einstein–Maxwell ones in a particular gauge condition. The Minkowski ground state is stable provided several restrictions on the coupling parameters are satisfied, they are explicitly obtained. The quantum propagators of the physical degrees of freedom are obtained and after an analysis of the first and second class constraints the renormalizability by power counting is proved, provided that the aforementioned restrictions on the coupling parameters are satisfied.

Conformal and chiral phase transitions in Rydberg chains

Using density matrix renormalization group simulations on open chains, we map out the wave-vector in the incommensurate disordered phase of a realistic model of Rydberg chains with $1/r^6$ interactions, and we locate and characterize the points along the commensurate lines where the transition out of the period 3 and 4 phases is conformal. We confirm that it is 3-state Potts for the period-3 phase, and we show that it is Ashkin-Teller with $\nu\simeq 0.80$ for the period-4 phase. We further show that close to these points the transition is still continuous, but with a completely different scaling of the wave-vector, in agreement with a chiral transition. Finally, we propose to use the conformal points as benchmarks for Kibble-Zurek experiments, defining a roadmap towards a conclusive identification of the chiral universality class.

Mutagenesis and structural modeling implicate RME-8 IWN domains as conformational control points.

After endocytosis, transmembrane cargo is differentially sorted into degradative or recycling pathways. This process is facilitated by recruitment into physically distinct degradative or recycling microdomains on the limiting membrane of individual endosomes. Endosomal sorting complexes required for transport (ESCRT) mark the degradative microdomain, while the recycling domain is marked by the retromer complex and associated proteins RME-8 and SNX-1. The separation of endosomal microdomains is also controlled by RME-8 and SNX-1, at least in part via removal of degradative component HRS/HGRS-1 from the recycling microdomain. This activity is likely due to recruitment and activation of chaperone Hsc70 on the endosome by the RME-8 DNAJ domain. To better understand the mechanism of RME-8 function we performed a new phylogenetic analysis of RME-8 and identified new conserved sequence features. In a complementary approach, we performed structure-function analysis that identified the C-terminus as important for microdomain localization and likely substrate binding, while N-terminal sequences beyond the known single N-terminal PH-like domain are important for endosome recruitment. Random mutagenesis identified IWN4, and by analogy IWN3, to be important for the autoinhibitory DNAJ domain binding, with IWN3 playing a critical role in HRS uncoating activity. Combining AlphaFold structural predictions with in vivo mutation analysis of RME-8, we propose a model whereby SNX-1 and the IWN domains control the conformation of RME-8 and hence the productive exposure of the DNAJ domain. Furthermore, we propose that the activation of RME-8 is cyclical, with SNX-1 acting as an activator and a target of RME-8 uncoating activity.

On conformal points of area preserving maps and related topics

In this article we consider area preserving diffeomorphisms of planar domains, and we are interested in their conformal points, i.e., points at which the derivative is a similarity. We present some conditions that guarantee existence of conformal points for the infinitesimal problem of Hamiltonian vector fields as well as for what we call moderate symplectomorphisms of simply connected domains. We also link this problem to the Carathéodory and Loewner conjectures.

Conformation and structural features of diuron and irgarol: Insights from quantum chemistry calculations

The structure and the conformations of diuron and irgarol have been investigated from crystal structure analyses and Density Functional Theory (DFT) calculations. Significant changes in terms of conformer distribution are found according to the surroundings (gas phase or water). Irgarol appears expectedly as flexible from a conformational point of view, nine or eight conformers being identified in the isolated state and water, respectively. Natural Bond Orbital (NBO) analyses have been realised on the energetic minima to rationalise the conformational preferences. Molecular electrostatic potential calculations have been carried out to bring to light and rank the potential intermolecular interaction sites of the two biocides. The interaction potential of irgarol, essentially represented by the triazine nitrogen atoms and the NH groups, is found to be much more sensitive to the conformational preferences that the one of diuron, the N3 triazine being preferred as HB acceptor, in agreement with the crystallographic data available.

Conformational Dynamics and Mechanisms of Client Protein Integration into the Hsp90 Chaperone Controlled by Allosteric Interactions of Regulatory Switches: Perturbation-Based Network Approach for Mutational Profiling of the Hsp90 Binding and Allostery.

Understanding the allosteric mechanisms of the Hsp90 chaperone interactions with cochaperones and client protein clientele is fundamental to dissect activation and regulation of many proteins. In this work, atomistic simulations are combined with perturbation-based approaches and dynamic network modeling for a comparative mutational profiling of the Hsp90 binding and allosteric interaction networks in the three Hsp90 maturation complexes with FKBP51 and P23 cochaperones and the glucocorticoid receptor (GR) client. The conformational dynamics signatures of the Hsp90 complexes and dynamics fluctuation analysis revealed how the intrinsic plasticity of the Hsp90 dimer can be modulated by cochaperones and client proteins to stabilize the closed dimer state required at the maturation stage of the ATPase cycle. In silico deep mutational scanning of the protein residues characterized the hot spots of protein stability and binding affinity in the Hsp90 complexes, showing that binding hot spots may often coincide with the regulatory centers that modulate dynamic allostery in the Hsp90 dimer. We introduce a perturbation-based network approach for mutational scanning of allosteric residue potentials and characterize allosteric switch clusters that control mechanism of cochaperone-dependent client recognition and remodeling by the Hsp90 chaperone. The results revealed a conserved network of allosteric switches in the Hsp90 complexes that allow cochaperones and GR protein to become integrated into the Hsp90 system by anchoring to the conformational switch points in the functional Hsp90 regions. This study suggests that the Hsp90 binding and allostery may operate under a regulatory mechanism in which activation or repression of the Hsp90 activity can be pre-encoded in the allosterically regulated Hsp90 dimer motions. By binding directly to the conformational switch centers on the Hsp90, cochaperones and interacting proteins can efficiently modulate the allosteric interactions and long-range communications required for client remodeling and activation.

Emergent dark energy from unparticles

A limiting temperature of a species can cause the Universe to asymptote to it yielding a deSitter (dS) phase due to macroscopic emergent behavior. The limiting temperature is generic for theories slightly shifted from their conformal point. We demonstrate such behavior in the example of unparticles/Banks-Zaks theory. The unparticles behave like radiation at high energies reducing the Hubble tension, and a cosmological constant (CC) at low energies yielding a model that follows closely {\Lambda}CDM model but due to collective phenomenon. It is technically natural and avoids the no-dS conjecture. The model is free of the coincidence and initial conditions problems, of scalar fields and of modified gravity.

V-PCC Performance Evaluation of the First MPEG Point Codec

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Representation of 3D scenes has become increasingly important in several industries using virtual and augmented reality technologies. The point cloud format is well suited for such representations. Indeed, point clouds can be created with a simple capture process and modest processing, enabling a realtime, end-to-end point cloud distribution chain. However, point cloud compression is required to obtain data rates and file sizes that could be economically viable for the industry. Standardization is required to ensure interoperability. In 2021, the International Organization for Standardization (ISO) Moving Picture Experts Group (MPEG) plans to publish a standard for its first point cloud codec, MPEG-I Part 5: Visual Volumetric Video-based Coding (V3C) and Video-based Point Cloud Compression (V-PCC). This standard enables a world of new services and applications, including cultural heritage, telepresence, and new forms of entertainment. In this paper, we review the principal use cases targeted by the V-PCC standard. We present the architecture of the V-PCC codec and describe its main tools, by giving insights into complexity at the encoder and decoder levels and explaining profiles and conformance points in V-PCC. We then present the methodology established, as a collaboration between industry and academics, for the evaluation of the V-PCC codec performance and the methodology’s origins. This methodology was applied to the MPEG point cloud compression test model software (named TMC2) to consistently evaluate technologies proposed during the standardization process. Finally, we compare the performance of the main V-PCC tools available for lossy and lossless compression. Finally, the conclusion provides elements in favor of a near-term deployment of V-PCC in the media industry</i> .

Integrability vs. RG flow in G \xd7 G and G \xd7 G/H sigma models

We consider a class of 2d σ-models on products of group spaces that provide new examples of a close connection between integrability and stability under the RG flow. We first study the integrable G × G model derived from the affine Gaudin construction (for which the 1-loop β-functions were found in arXiv:2010.07879) and show that its condition of integrability is preserved also by the 2-loop RG flow. We then investigate the RG flow in the gauged G × G/H model, in particular the integrable T1,1 model found in arXiv:2010.05573. We also construct a new class of integrable G × G/H models in the case when the subgroup H is abelian. In the simplest case of G = SU2, H = U1 this leads to an integrable σ-model on the T1,q space (with a particular B-field). This model is also shown to be stable under the 2-loop RG flow, and we relate this property to its invariance under T-duality in an isometric U1 direction. This T1,q model may be interpreted as an integrable deformation of the GMM model (of two coupled WZW theories with generic levels) away from the conformal point.

Lifshitz point at commensurate melting of chains of Rydberg atoms

The recent investigation of chains of Rydberg atoms has brought back the problem of commensurate-incommensurate transitions into the focus of current research. In 2D classical systems, or in 1D quantum systems, the commensurate melting of a period-p phase with p larger than 4 is known to take place through an intermediate floating phase where correlations between domain walls or particles decay only as a power law, but when p is equal to 3 or 4, it has been argued by Huse and Fisher that the transition could also be direct and continuous in a non-conformal chiral universality class with a dynamical exponent larger than 1. This is only possible however if the floating phase terminates at a Lifshitz point before reaching the conformal point, a possibility debated since then. Here we argue that this is a generic feature of models where the number of particles is not conserved because the exponent of the floating phase changes along the Pokrovsky-Talapov transition and can thus reach the value at which the floating phase becomes unstable. Furthermore, we show numerically that this scenario is realized in an effective model of the period-3 phase of Rydberg chains in which hard-core bosons are created and annihilated three by three: The Luttinger liquid parameter reaches the critical value $p^2/8=9/8$ along the Pokrovsky-Talapov transition, leading to a Lifshitz point that separates the floating phase from a chiral transition. Implications beyond Rydberg atoms are briefly discussed.