Correction: Iriarte et al. A Unimodal/Bimodal Skew/Symmetric Distribution Generated from Lambert’s Transformation. Symmetry 2021, 13, 269

In the original article [...]

Filiform projections of the vestibular mucosa: What’s your diagnosis?

29-year-old recently married woman was reffered by her gynecologist to our dermatology department for suspected vulvar condyloma acuminatum. She had no history of any extramarital sexual contacts and her partner was free of any clinical features of genital HPV infections. She was anxious about the origin of her lesions and the risk of her husband’s contamination. She reported burning sensation, irritation and vulvar pain. On clinical examination soft digitate mucous colored papules with a smooth surface were noted at the vulvar vestibule. These papillomatous projections were pearly, uniformly arranged and had separate bases (Fig. 1). Dermatoscopy demonstrated regular and linear pinkish projections arranged in a symmetric distribution. Irregular linear vascular channels were observed (Fig. 2). Figure 1: Clinical aspect: multiple skin-colored filiform and soft projections. Figure 2: Dermatoscopy showing regular and linear pinkish projections arranged in a symmetric distribution. WHAT’S YOUR DIAGNOSIS? ANSWER: Vestibular Papillomatosis Vestibular papillomatosis (VP) is a normal variant of the female genital mucosa [1,2]. It is first described in 1981 by Altemeyer and named pseudocondylomata of the vulva [3]. VP is frequently misdiagnosed as condyloma acuminatum and presents a source of anxiety in patients, aggressive investigations and inappropriate treatment [2]. This entity is most often asymptomatic, but it can be accompanied, as our case, by a feeling of burning, pain or dyspareunia. To avoid the misdiagnosis of VP as genital warts, Moyal-Barranco et al. had proposed five clinical parameters [4]. Unlike condyloma acuminatum, VP is formed by regular, soft and pink-colored papillae arising from a separate base. It is also characterized by the lack of circumscribed whitening on 5% acetic acid application. Dermoscopy can help to differentiate these two conditions by allowing a better identification of these clinical parameters. Linear vessels may sometimes be observed in the transparent core of the finger-like projections [5]. On the other hand, dermoscopy of condyloma acuminatum shows irregular whitish projections with tapering end that arise from a common base and comprise conglomerate vessel. Based on these clinical criteria and the dermoscopic aspect, biopsies will be unnecessary to confirm the diagnosis of VP.

Three-Phase Symmetric Distribution Network Fast Dynamic Reconfiguration Based on Timing-Constrained Hierarchical Clustering Algorithm

This paper develops a novel dynamic three-phase symmetric distribution network reconfiguration (DNR) approach based on hierarchical clustering with timing constraints, which can divide the time period according to the time-varying symmetric load demand and symmetric distributed generations (DGs) output condition for a given time interval. The significance of the proposed technique is that by approximating the cluster center as the load status and DGs output status of the corresponding period, in this way, the intractable dynamic reconfiguration problem can be recast as multiple single-stage static three-phase symmetric DNR problems, which can effectively reduce the complexity of the three-phase symmetric dynamic reconfiguration. Furthermore, an improved fireworks algorithm considering heuristic rules (H-IFWA) is proposed and investigated to efficiently manage each single-stage static three-phase symmetric DNR problem. In order to avoid trapping into a local optimum or to facilitate the computational performance, the power moment method and the coding method based on heuristic rules are employed to reduce the solution space. The effectiveness of the proposed H-IFWA is validated on the IEEE 33, 119-bus system and a practical-scale Taiwan power company (TPC) 84-bus test system with DGs.

Half-leaf width symmetric distribution reveals buffering strategy of Cunninghamia lanceolata

Background Leaf length and width could be a functioning relationship naturally as plant designs. Single-vein leaves have the simplest symmetrical distribution and structural design, which means that fast-growing single-vein species could interpret the scheme more efficiently. The distribution of leaf length and width can be modulated for better adaptation, providing an informative perspective on the various operational strategies in an emergency, while this mechanism is less clear. Here we selected six age groups of Cunninghamia lanceolata pure forests, including saplings, juveniles, mature, and old-growth trees. We pioneered a tapering model to describe half-leaf symmetric distribution with mathematical approximation based on every measured leaf along developmental sequence, and evaluated the ratio of leaf basal part length to total length (called tipping leaf length ratio). Results The tipping leaf length ratio varied among different tree ages. That means the changes of tipping leaf length ratio and leaf shape are a significant but less-noticed reflection of trees tradeoff strategies at different growth stages. For instance, there exhibited relatively low ratio during sapling and juvenile, then increased with increasing age, showing the highest value in their maturity, and finally decreased on mature to old-growth transition. The tipping leaf length ratio serves as a cost-benefit ratio, thus the subtle changes in the leaf symmetrical distribution within individuals reveal buffering strategy, indicating the selection for efficient design of growth and hydraulic in their developmental sequences. Conclusions Our model provides a physical explanation of varied signatures for tree operations in hydraulic buffering through growth stages, and the buffering strategy revealed from leaf distribution morphologically provides evidence on the regulation mechanism of leaf biomechanics, hydraulics and physiologies. Our insight contributes greatly to plant trait modeling, policy and management, and will be of interest to some scientists and policy makers who are involved in climate change, ecology and environment protection, as well as forest ecology and management.

Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i. e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out.

Can a More Variable Species Win Interspecific Competition?

An individual-based approach is used to describe population dynamics. Two kinds of models have been constructed with different distributions illustrating individual variability. In both models, the growth rate of an individual and its final body weight at the end of the growth period, which determines the number of offspring, are functions of the amount of resources assimilated by an individual. In the model with a symmetric distribution, the half saturation constant in the Michaelis–Menten function describing the relationship between the growth of individuals and the amount of resources has a normal distribution. In the model with an asymmetric distribution, resources are not equally partitioned among individuals. The individual who acquired more resources in the past, will acquire more resources in the future. A single population comprising identical individuals has a very short extinction time. If individuals differ in the amount of food assimilated, this time significantly increases irrespectively of the type of model describing population dynamics. Individuals of two populations of competing species use common resources. For larger differences in individual variability, the more variable species will have a longer extinction time and will exclude less variable species. Both populations can also coexist when their variabilities are equal or even when they are slightly different, in the latter case under the condition of high variability of both species. These conclusions have a deterministic nature in the case of the model with the asymmetric distribution—repeated simulations give the same results. In the case of the model with the symmetric distribution, these conclusions are of a statistical nature—if we repeat the simulation many times, then the more variable species will have a longer extinction time more frequently, but some results will happen (although less often) when the less variable species has a longer extinction time. Additionally, in the model with the asymmetric distribution, the result of competition will depend on the way of the introduction of variability into the model. If the higher variability is due to an increase in the proportion of individuals with a low assimilation of resources, it can produce a longer extinction time of the less variable species.