Conformal Change Research Articles

Nonexistence of mean curvature flow solitons with polynomial volume growth immersed in certain semi-Riemannian warped products

Abstract Our purpose is to establish nonexistence results concerning complete noncompact mean curvature flow solitons with polynomial volume growth immersed in certain semi-Riemannian warped products, under mild constraints on the warping and soliton functions. Applications to self-shrinkers in the Euclidean space, as well as to mean curvature flow solitons in other important warped product models such as the Schwarzschild and Reissner-Nordström spaces, and Robertson-Walker spacetimes such as the Einstein-de Sitter spacetime, are also given. Furthermore, we study the nonexistence of entire solutions to the mean curvature flow equation. Our approach is based on a suitable conformal change of metric jointly with a maximum principle for complete noncompact Riemannian manifolds with polynomial volume growth due to Alías et al.

On the conformal change of a Douglas space of a second kind with a class of ($\alpha, \beta $)-metric

On the conformal change of a Douglas space of a second kind with a class of ($\alpha, \beta $)-metric

Rate-dependent cochlear outer hair cell force generation: Models and parameter estimation

The outer hair cells (OHCs) of the mammalian cochlea are the mediators of an active, nonlinear electromechanical process necessary for sensitive, frequency-specific hearing. The membrane protein prestin conveys to the OHC a piezoelectric-like behavior hypothesized to actuate a high frequency, cycle-by-cycle conversion of electrical to mechanical energy to boost cochlear responses to low-level sound. This hypothesis has been debated for decades, with two key remaining issues: the influence of the rate dependence of conformal changes in prestin and the OHC transmembrane impedance. In this paper, we mainly focus on the rate dependence of the conformal change in prestin. A theoretical electromechanical model of the OHC that explicitly includes rate dependence of conformal transitions, viscoelasticity, and piezoelectricity. Using this theory, we show the influence of rate dependence and viscoelasticity on electromechanical force generation and transmembrane impedance. Furthermore, we stress the importance of using the correct mechanical boundary conditions when estimating the transmembrane capacitance. Finally, a set of experiments is described to uniquely estimate the constitutive properties of the OHC from whole-cell measurements.

Anisotropic conformal change of conic pseudo-Finsler surfaces, I*

Abstract The present work is devoted to investigate anisotropic conformal transformation of conic pseudo-Finsler surfaces $(M,F)$, that is, $ F(x,y)\longmapsto \overline{F}(x,y)=e^{\phi(x,y)}F(x,y)$, where the function $\phi(x,y)$ depends on both position $x$ and direction $y$, contrary to the ordinary (isotropic) conformal transformation which depends on position only. If $F$ is a pseudo-Finsler metric, the above transformation does not yield necessarily a pseudo-Finsler metric. Consequently, we find out necessary and sufficient condition for a (conic) pseudo-Finsler surface $(M,F)$ to be transformed to a (conic) pseudo-Finsler surface $(M,\overline{F})$ under the transformation $\overline{F}=e^{\phi(x,y)}F$. In general dimension, it is extremely difficult to find the anisotropic conformal change of the inverse metric tensor in a tensorial form. However, by using the modified Berwald frame on a Finsler surface, we obtain the change of the components of the inverse metric tensor in a tensorial form. This progress enables us to study the transformation of the Finslerian geometric objects and the geometric properties associated with the transformed Finsler function $\overline{F}$. In contrast to isotropic conformal transformation, we have a non-homothetic conformal factor $\phi(x,y)$ that preserves the geodesic spray. Also, we find out some invariant geometric objects under the anisotropic conformal change. Furthermore, we investigate a sufficient condition for $\overline{F}$ to be dually flat or/and projectively flat. Finally, we study some special cases of the conformal factor $\phi(x,y)$. Various examples are provided whenever the situation needs.

On a class of elliptic equations with critical perturbations in the hyperbolic space

We study the existence and non-existence of positive solutions for the following class of nonlinear elliptic problems in the hyperbolic space − Δ B N u − λ u = a ( x ) u p − 1 + ε u 2 ∗ − 1 in B N , u ∈ H 1 ( B N ) , where B N denotes the hyperbolic space, 2 < p < 2 ∗ : = 2 N N − 2 , if N ⩾ 3 ; 2 < p < + ∞, if N = 2, λ < ( N − 1 ) 2 4 , and 0 < a ∈ L ∞ ( B N ). We first prove the existence of a positive radially symmetric ground-state solution for a ( x ) ≡ 1. Next, we prove that for a ( x ) ⩾ 1, there exists a ground-state solution for ε small. For proof, we employ “conformal change of metric” which allows us to transform the original equation into a singular equation in a ball in R N . Then by carefully analysing the energy level using blow-up arguments, we prove the existence of a ground-state solution. Finally, the case a ( x ) ⩽ 1 is considered where we first show that there is no ground-state solution, and prove the existence of a bound-state solution (high energy solution) for ε small. We employ variational arguments in the spirit of Bahri–Li to prove the existence of high energy-bound-state solutions in the hyperbolic space.

Comparative study of physical properties of As2Se3 and (As2Se3)90Ge10 glassy alloys doped with metallic impurities

To examine the compositional and chemical effects on the glassy system, one must first understand its network structure. Alloying glassy systems cause significant conformal and configurational changes. The optical and physical parameters of As2Se3 and (As2Se3)90Ge10 glassy alloys doped with metallic impurities (X = Bi, Cd, Pb, Sb) have been evaluated. A comparison of the physical properties of glassy alloys has been made as the doping elements increase, i.e., from binary to ternary to quaternary system, and an effort has been made to correlate the optical and physical parameters. The optical density (Dop) and penetration depth (δ) have been calculated from the reported absorption coefficient (α) data. The mean coordination number (<r>) and the number of floppy modes (Mf) calculations show that the floppy regions are decreasing, and hence, the rigidity is increasing when As–Se is doped with Ge and As–Se-Ge is doped with X. The density (ρ) and packing density (PD) have also been evaluated, which are interrelated to the parameters like refractive index (n) and δ. Cohesive energy (CE), mean bond energy (<E>), and glass transition temperature (Tg) values give an insight into the stability and average crosslinking of the system with alloying. The conduction and valence band potentials have supported the optical bandgap (Egopt) values variation.

Clairaut Conformal Submersions

The aim of this paper is to introduce Clairaut conformal submersions between Riemannian manifolds. First, we find necessary and sufficient conditions for conformal submersions to be Clairaut conformal submersions. In particular, we obtain Clairaut relation for geodesics on the total manifolds of conformal submersions, and prove that Clairaut conformal submersions have constant dilation along their fibers, which are totally umbilical, with mean curvature being gradient of a function. Further, we calculate the scalar and Ricci curvatures of the vertical distributions of the total manifolds. Moreover, we find a necessary and sufficient condition for Clairaut conformal submersions to be harmonic. For a Clairaut conformal submersion we find conformal changes of the metric on its domain or image, that give a Clairaut Riemannian submersion, a Clairaut conformal submersion with totally geodesic fibers, or a harmonic Clairaut submersion. Finally, we give two non-trivial examples of Clairaut conformal submersions to illustrate the theory and present a local model of every Clairaut conformal submersion with integrable horizontal distribution.

Long-term follow-up demonstrates change in conformation shape of the focal choroidal excavation lesions

PurposeThis study aims to present long-term observation of 5 eyes with focal choroidal excavation (FCE), focusing on morphological changes in conformity of the lesion.MethodsA retrospective case series was conducted, including 5 eyes of 5 patients with FCE. The study utilized multimodal imaging including color fundus photography, optical coherence tomography (OCT), enhanced depth imaging OCT (EDI-OCT), fundus fluorescein angiography (FFA), fundus autofluorescence (FAF), red free imaging, and OCT angiography.ResultsThe mean age at diagnosis was 51 ± 10.65 years, with a mean follow-up period 37 ± 13.59 months. All cases were unilateral, with 1 presenting FCE as an isolated lesion, and one patient exhibiting 2 FCEs in one eye. The mean choroidal thickness measured by EDI-OCT was 268.2 ± 63.39 μm in the affected eye. One patient displayed choroidal thickening and pachyvessels. Of the 5 eyes, one had conforming and 4 non-conforming FCE. We observed a conversion in conformity in all patients, with 4 cases transitioning from non-conforming FCE to conforming type (3 spontaneously, 1 treatment-induced). In conforming FCE, a hyporeflective space appeared twice between neuroretina and retinal pigment epithelium with spontaneous regression.ConclusionWe observed change in shape from the conforming to non-conforming FCE and vice versa in all patients. We consider this small change in the hyporeflective space as non-pathologic and clinically insignificant.

Finsler surfaces with vanishing T-tensor

In this paper, for Finsler surfaces, we prove that the T-condition and σT-condition coincide. For higher dimensions n≥3, we illustrate by an example that the T-condition and σT-condition are not equivalent. We show that the non-homothetic conformal change of a Berwald (resp. a Landsberg) surface is Berwaldian (resp. Landsbergian) if and only if the σT-condition is satisfied. By solving the Landsberg's PDE, we classify all Finsler surfaces satisfying the T-condition, or equivalently the σT-condition. Some examples are provided and studied.

Multiple positive radial solutions for Dirichlet problem of the prescribed mean curvature spacelike equation in a Friedmann–Lemaître–Robertson–Walker spacetime

In this paper, we consider the radially symmetric spacelike solutions of a nonlinear Dirichlet problem for the prescribed mean curvature spacelike equation in a Friedmann–Lemaître–Robertson–Walker spacetime. By using a conformal change of variable, this problem can be translated an equivalent problem in the Minkowski spacetime. By using the lower and upper solution method, fixed point, a priori bounds and topological degree method, we obtain the existence, nonexistence and multiplicity of radially symmetric spacelike solutions.

Formation of Supplementary Metal-Binding Centers in Proteins under Stress Conditions.

In many proteins, supplementary metal-binding centers appear under stress conditions. They are known as aberrant or atypical sites. Physico-chemical properties of proteins are significantly changed after such metal binding, and very stable protein aggregates are formed, in which metals act as "cross-linking" agents. Supplementary metal-binding centers in proteins often arise as a result of posttranslational modifications caused by reactive oxygen and nitrogen species and reactive carbonyl compounds. New chemical groups formed as a result of these modifications can act as ligands for binding metal ions. Special attention is paid to the role of cysteine SH-groups in the formation of supplementary metal-binding centers, since these groups are the main target for the action of reactive species. Supplementary metal binding centers may also appear due to unmasking of amino acid residues when protein conformation changing. Appearance of such centers is usually considered as a pathological process. Such unilateral approach does not allow to obtain an integral view of the phenomenon, ignoring cases when formation of metal complexes with altered proteins is a way to adjust protein properties, activity, and stability under the changed redox conditions. The role of metals in protein aggregation is being studied actively, since it leads to formation of non-membranous organelles, liquid condensates, and solid conglomerates. Some proteins found in such aggregates are typical for various diseases, such as Alzheimer's and Huntington's diseases, amyotrophic lateral sclerosis, and some types of cancer.

On conformal transformations preserving the Ricci tensor in Finsler geometry

Here we obtain a classical integral formula on the conformal change of Finsler metrics. As an application, we obtain significant results depending on the sign of the Ricci scalars, for mean Landsberg surfaces and show there is no conformal transformation between two compact mean Landsberg surfaces, one of a non-positive Ricci scalar and another of a non-negative Ricci scalar, except for the case where both Ricci scalars are identically zero. Conformal transformations preserving the Ricci tensor are known as Liouville transformations. Here we show that a Liouville transformation between two compact mean Landsberg manifolds of isotropic S-curvature is homothetic. Moreover, every Liouville transformation between two compact Finsler n-manifolds of bounded mean value Cartan tensor is homothetic. These results are an extension of the results of M. Obata and S. T. Yau on Riemannian geometry and give a positive answer to a conjecture on Liouville's theorem.

Optimal control for sampling the transition path process and estimating rates

Many processes in nature such as conformal changes in biomolecules and clusters of interacting particles, genetic switches, mechanical or electromechanical oscillators with added noise, and many others are modeled using stochastic differential equations with small white noise. The study of rare transitions between metastable states in such systems is of great interest and importance. The direct simulation of rare transitions is difficult due to long waiting times. Transition path theory is a mathematical framework for the quantitative description of rare events. Its crucial component is the committor function, the solution to a boundary value problem for the backward Kolmogorov equation. The key fact exploited in this work is that the optimal controller constructed from the committor leads to the generation of transition trajectories exclusively. We prove this fact for a broad class of stochastic differential equations. Moreover, we demonstrate that the committor computed for a dimensionally reduced system and then lifted to the original phase space still allows us to construct an effective controller and estimate the transition rate with reasonable accuracy. Furthermore, we propose an all-the-way-through scheme for computing the committor via neural networks, sampling the transition trajectories, and estimating the transition rate without meshing the space. We apply the proposed methodology to four test problems: the overdamped Langevin dynamics with Mueller’s potential and the rugged Mueller potential in 10D, the noisy bistable Duffing oscillator, and Lennard-Jones-7 in 2D.

Prescribing nearly constant curvatures on balls

In this paper, we address two boundary cases of the classical Kazdan–Warner problem. More precisely, we consider the problem of prescribing the Gaussian and boundary geodesic curvature on a disk of $\mathbb {R}^2$ , and the scalar and mean curvature on a ball in higher dimensions, via a conformal change of the metric. We deal with the case of negative interior curvature and positive boundary curvature. Using a Ljapunov–Schmidt procedure, we obtain new existence results when the prescribed functions are close to constants.

Computing committors in collective variables via Mahalanobis diffusion maps

The study of rare events in molecular and atomic systems such as conformal changes and cluster rearrangements has been one of the most important research themes in chemical physics. Key challenges are associated with long waiting times rendering molecular simulations inefficient, high dimensionality impeding the use of PDE-based approaches, and the complexity or breadth of transition processes limiting the predictive power of asymptotic methods. Diffusion maps are promising algorithms to avoid or mitigate all these issues. We adapt the diffusion map with Mahalanobis kernel proposed by Singer and Coifman (2008) for the SDE describing molecular dynamics in collective variables in which the diffusion matrix is position-dependent and, unlike the case considered by Singer and Coifman, is not associated with a diffeomorphism. We offer an elementary proof showing that one can approximate the generator for this SDE discretized to a point cloud via the Mahalanobis diffusion map. We use it to calculate the committor functions in collective variables for two benchmark systems: alanine dipeptide, and Lennard-Jones-7 in 2D. For validating our committor results, we compare our committor functions to the finite-difference solution or by conducting a “committor analysis” as used by molecular dynamics practitioners. We contrast the outputs of the Mahalanobis diffusion map with those of the standard diffusion map with isotropic kernel and show that the former gives significantly more accurate estimates for the committors than the latter.

Controlling the assembly of soy β-conglycinin to fabricate heat-stable particles for high protein liquid systems.

Recently, there is a growing interest in developing protein-fortified liquid systems, which are formulated to provide special nutrient combinations to those with special dietary needs. The fabrication of heat-stable protein for protein-fortified liquid systems relies heavily on precise control of the edible protein-building process. Results suggested that heat-stable 7S protein particles (7SPPs) could be obtained by preheating at 100 °C for an extended time, whereas 7S proteins with better gelling properties were discovered after preheating at lower temperatures. According to the findings of the protein conformational and morphological characterization, the 7SPPs showed rather stable tertiary and secondary structures as well as size distributions, which might be responsible for their heat stability. Additionally, during the reheating test, suspensions of 7SPPs showed no signs of gelation and had a low viscosity even though the protein content was as high as 120 mg mL-1 . However, 7S proteins with improved gelling properties were found to show rising aggregate size, higher susceptibility and larger conformational structure changing rates upon reheating treatment. Soy β-conglycinin (7S) proteins with tunable heat stability were successfully prepared by preheating 10 mg mL-1 protein dispersions at various temperatures (80-120 °C) and durations (15-120 min). These findings provide fundamental insights for developing 7S-based protein-fortified systems. © 2023 Society of Chemical Industry.

Generalizations of the Q-prime curvature via renormalized characteristic forms

The Q-prime curvature is a local pseudo-Einstein invariant on CR manifolds defined by Case and Yang, and Hirachi. Its integral, the total Q-prime curvature, gives a non-trivial global CR invariant. On the other hand, Marugame has constructed a family of global CR invariants via renormalized characteristic forms, which contains the total Q-prime curvature. In this paper, we introduce a generalization of the Q-prime curvature for each renormalized characteristic form, and show that its integral coincides with Marugame's CR invariant. We also study generalizations of the critical CR GJMS operator and the P-prime operator, which are related to the transformation laws of our new curvatures under conformal change.

Dermatology and Venereology Consultation Pattern from Inpatient and Emergency Department in Tertiary Hospital Setting Before and During COVID-19 Pandemic.

COVID-19 pandemic has compromised healthcare services in dermatology and venereology. Given such circumstances, studies investigating the consultation pattern of related fields in hospitals were relatively scarce. The present study aimed to delineate such matter from tertiary hospital viewpoint. Details concerning referred patients from the emergency room, inpatient wards, intensive care unit, and nursery to the Department of Dermatology and Venereology, Dr. Cipto Mangunkusumo Hospital were retrospectively collected from electronic health records. Cases admitted in the 17 months span before and during COVID-19 global outbreak were included. The obtained data were presented descriptively, and Chi-squared test was performed upon attributes of interest at a significance level of 0.05. A slight increase of total consultation was found in the COVID-19 era with an initial reduction at the beginning (April-May 2020). One-time consultation was the most inquired to our department in both periods of which dermatitis was the most prevalent case and Gram staining was the most common examination. Topical antibiotics and emollient were the most prescribed medications before and during the outbreak, respectively. The conformity of initial-final decision, appropriateness of initial-final diagnosis, and consult response time were significantly different (p < 0.05) between the two groups. There were changes of the number of consultation requests in the pandemic era with statistically significant change of decision conformity, diagnoses, appropriateness, and consult response time. Although some changes appeared, the most prevalent diagnoses remained.

Liposome fusogenic enzyme-free circuit enables high-fidelity determination of single exosomal RNA

Accurate determination of single exosomal inclusions in situ presents a significant challenge due to their extremely low abundance as well sub-100 nm vesicle dimensions. Here, we created a Liposome Fusogenic Enzyme-free circuit (LIFE) approach for the high-fidelity identification of exosome-encapsulated cargoes without destroying the vesicle integrity. The probe-loaded cationic fusogenic liposome could capture and fuse with a single target exosome, enabling probes delivery and target biomolecule-initiated cascaded signal amplification in situ. Then the DNAzyme probe encountered conformal change upon exosomal microRNA activation, and generated a convex DNAzyme structure to cleave the RNA site of substrate probe. After that, the target microRNA could be released to introduce a cleavage cycle to yield amplified fluorescence readout. Therefore, trace cargoes in a single exosome could be accurately determined by elaborately controlling the ratio of introduced LIFE probe, paving the way toward the exploration of a universal sensing platform for the assessment of exosomal cargoes to facilitate early disease diagnosis and personalized treatment.

Simulation-based inference for non-parametric statistical comparison of biomolecule dynamics.

Numerous models have been developed to account for the complex properties of the random walks of biomolecules. However, when analysing experimental data, conditions are rarely met to ensure model identification. The dynamics may simultaneously be influenced by spatial and temporal heterogeneities of the environment, out-of-equilibrium fluxes and conformal changes of the tracked molecules. Recorded trajectories are often too short to reliably discern such multi-scale dynamics, which precludes unambiguous assessment of the type of random walk and its parameters. Furthermore, the motion of biomolecules may not be well described by a single, canonical random walk model. Here, we develop a two-step statistical testing scheme for comparing biomolecule dynamics observed in different experimental conditions without having to identify or make strong prior assumptions about the model generating the recorded random walks. We first train a graph neural network to perform simulation-based inference and thus learn a rich summary statistics vector describing individual trajectories. We then compare trajectories obtained in different biological conditions using a non-parametric maximum mean discrepancy (MMD) statistical test on their so-obtained summary statistics. This procedure allows us to characterise sets of random walks regardless of their generating models, without resorting to model-specific physical quantities or estimators. We first validate the relevance of our approach on numerically simulated trajectories. This demonstrates both the statistical power of the MMD test and the descriptive power of the learnt summary statistics compared to estimates of physical quantities. We then illustrate the ability of our framework to detect changes in α-synuclein dynamics at synapses in cultured cortical neurons, in response to membrane depolarisation, and show that detected differences are largely driven by increased protein mobility in the depolarised state, in agreement with previous findings. The method provides a means of interpreting the differences it detects in terms of single trajectory characteristics. Finally, we emphasise the interest of performing various comparisons to probe the heterogeneity of experimentally acquired datasets at different levels of granularity (e.g., biological replicates, fields of view, and organelles).