Unique Root Research Articles

Cubic-like Features of I–V Relations via Classical Poisson–Nernst–Planck Systems Under Relaxed Electroneutrality Boundary Conditions

We focus on higher-order matched asymptotic expansions of a one-dimensional classical Poisson–Nernst–Planck system for ionic flow through membrane channels with two oppositely charged ion species under relaxed electroneutrality boundary conditions. Of particular interest are the current–voltage (I–V) relations, which are used to characterize the two most relevant biological properties of ion channels—permeation and selectivity—experimentally. Our result shows that, up to the second order in ε=λ/r, where λ is the Debye length and r is the characteristic radius of the channel, the cubic I–V relation has either three distinct real roots or a unique real root with a multiplicity of three, which sensitively depends on the boundary layers because of the relaxation of the electroneutrality boundary conditions. This indicates more rich dynamics of ionic flows under our more realistic setups and provides a better understanding of the mechanism of ionic flows through membrane channels.

Bowen's equations for packing BS dimension of subsets for free semigroup actions

We introduce and study the relations between the packing BS dimension of an arbitrary subset and topological pressure for free semigroup actions. We show that the packing BS dimension is the unique root of the topological pressure function for semigroup actions. Also, we establish a variational principle between the packing BS dimension and the measure-theoretic BS dimension for an arbitrary non-invariant compact set of an action S .

Shifting the Paradigm in Workforce Diversity: Prioritizing an Inclusive Environment in Graduate Medical Education.

A diverse physician workforce is important to achieving the goal of health equity. Recruitment efforts are often the focus of graduate medical education (GME) workforce diversity efforts. However, to achieve the goal of workforce diversity, a foundation of inclusivity is essential to address the experiences of trainees whose race and ethnicity are underrepresented in medicine (UIM).Professional identity formation (PIF) describes the process through which trainees integrate their personal and professional identities as they learn to not only act but feel like they belong in their professional role. The concept of PIF provides a framework to consider how GME leaders can intentionally address inclusivity in training programs. The process of PIF is influenced by many factors including trainees' clinical and non-clinical experiences, their treatment by others, as well as the training program's structure, policy, and physical environment. The authors describe these factors influencing PIF, then through the lens of PIF, describe approaches that programs and institutions have taken to address inclusivity by investing in the workforce, disrupting the hidden curriculum, revisiting policies and procedures, and examining the physical environment.The authors encourage programs, institutions, and the greater GME community to leverage each learning environment's unique strengths and root out challenges to enhance inclusivity for UIM trainees.

Unique root hydraulic and mechanical properties support the resilience of grapevines adapted to the Atacama Desert.

Cortical lacunae caused by drought, especially observed in hybrids originating from Vitis rupestris, disrupt the connection between roots and soil. Yet, the physiological processes behind lacuna formation during drought and its consistency across Vitis species remain unclear. Here, we used a root pressure probe to investigate fine root hydraulic and mechanical properties, in the arid-adapted R-65 and drought-susceptible 101-14Mgt cultivars. We then performed P-V curves, root sap osmolality, and electrolyte leakage (EL) and used fluorescent light microscopy techniques. Only 101-14Mgt showed lacunae formation during drought due to its stiffer cortical tissue, unlike R-65. Lacunae resulted in a notable decline in root hydraulic conductivity during severe drought, with increased EL and root sap osmolality, indicating potential cellular damage. R-65 displayed different and xerophyte-like characteristics featuring a higher turgor loss point and decreased root capacitance, essential for maintaining root structural integrity in arid conditions. Our findings highlight lacuna formation is impacted by root tissue elasticity possibly linked to specific Vitis species favoring deeper rooting. In arid-adapted grapevines, hydraulic regulators such as reduced turgor loss point, and root capacitance could contribute to enhanced drought tolerance.

Unique root anatomy of mandibular second premolars: clinical strategies for effective disinfection and preservation of dentine structure in root canal treatment—a case report

It is difficult to predict the outcomes of non-surgical root canal treatment (NSRCT) for mandibular second premolars with multiple root canals. In these teeth, the complicated anatomy with fin(s), or a C-shape, and possible secondary canal(s) varies unpredictably. The morphology of the root canals provides shelters for bacteria to remain, regrow, and form biofilms despite the endodontic treatment. Moreover, the prevalence of mandibular second premolars with multiple canals is extremely infrequent. Therefore, the clinical management of NSRCT in such cases is not sufficiently reported. This case report introduces two cases of NSRCT for mandibular second premolars with a radicular groove and also presents the appropriate clinical strategies and techniques. Cone-beam computed tomography (CBCT) imaging was used preoperatively. After the completion of NSRCT, CBCT was reused to review the completed procedures using the Nerve Canal tool in CS 3D Imaging v3.2.9 and v3.8.7. Five canals were obturated in case 1, and four canals in case 2 along with a C-shape morphology. Analyzing the configuration of the root canals by CBCT was critical to achieve successful NSRCT because the numbers, exits, configurations, and volumes of the secondary canals were not anticipated after reviewing 2D radiographs. Based on the interpretation, the advanced protocols of NSRCT were planned: first, augmentation of chemo-mechanical cleaning, but minimizing the loss of dentine; second, the tactile examination to locate and negotiate the orifices of the secondary canals; and lastly, the optimized plan and technique for root canal filling of the complex canal systems.

Modeling the effects of strigolactone levels on maize root system architecture.

Maize is the most in-demand staple crop globally. Its production relies strongly on the use of fertilizers for the supply of nitrogen, phosphorus, and potassium, which the plant absorbs through its roots, together with water. The architecture of maize roots is determinant in modulating how the plant interacts with the microbiome and extracts nutrients and water from the soil. As such, attempts to use synthetic biology and modulate that architecture to make the plant more resilient to drought and parasitic plants are underway. These attempts often try to modulate the biosynthesis of hormones that determine root architecture and growth. Experiments are laborious and time-consuming, creating the need for simulation platforms that can integrate metabolic models and 3D root growth models and predict the effects of synthetic biology interventions on both, hormone levels and root system architectures. Here, we present an example of such a platform that is built using Mathematica. First, we develop a root model, and use it to simulate the growth of many unique 3D maize root system architectures (RSAs). Then, we couple this model to a metabolic model that simulates the biosynthesis of strigolactones, hormones that modulate root growth and development. The coupling allows us to simulate the effect of changing strigolactone levels on the architecture of the roots. We then integrate the two models in a simulation platform, where we also add the functionality to analyze the effect of strigolactone levels on root phenotype. Finally, using in silico experiments, we show that our models can reproduce both the phenotype of wild type maize, and the effect that varying strigolactone levels have on changing the architecture of maize roots.

On the balanced pantograph equation of mixed type

UDC 517.9 We consider the balanced pantograph equation (BPE) y ′ ( x ) + y ( x ) = ∑ k = 1 m p k y ( a k x ) , where a k , p k > 0 and ∑ k = 1 m p k = 1. It is known that if K = ∑ k = 1 m p k ln a k ≤ 0 then, under mild technical conditions, the BPE does not have bounded solutions that are not constant, whereas for K > 0 these solutions exist. In the present paper, we deal with a BPE of <em>mixed type</em>, i.e., a 1 < 1 < a m , and prove that, in this case, the BPE has a nonconstant solution y and that y ( x ) ∼ c x σ as x → ∞ , where c > 0 and σ is the unique positive root of the characteristic equation P ( s ) = 1 - ∑ k = 1 m p k a k - s = 0. We also show that y is unique (up to a multiplicative constant) among the solutions of the BPE that decay to zero as x → ∞ .

On the date of the epidemic peak.

Epidemiologists have used the timing of the peak of an epidemic to guide public health interventions. By determining the expected peak time, they can allocate resources effectively and implement measures such as quarantine, vaccination, and treatment at the right time to mitigate the spread of the disease. The peak time also provides valuable information for those modeling the spread of the epidemic and making predictions about its future trajectory. In this study, we analyze the time needed for an epidemic to reach its peak by presenting a straightforward analytical expression. Utilizing two epidemiological models, the first is a generalized $ SEIR $ model with two classes of latent individuals, while the second incorporates a continuous age structure for latent infections. We confirm the conjecture that the peak occurs at approximately $ T\sim(\ln N)/\lambda $, where $ N $ is the population size and $ \lambda $ is the largest eigenvalue of the linearized system in the first model or the unique positive root of the characteristic equation in the second model. Our analytical results are compared to numerical solutions and shown to be in good agreement.

Diversity and correlation analysis of different root exudates on the regulation of microbial structure and function in soil planted with Panax notoginseng.

Specific interactions between root exudates and soil microorganisms has been proposed as one of the reasons accounting for the continuous cropping obstacle (CCO) of Panax notoginseng. However, rotation of other crops on soils planted with P. notoginseng (SPP) did not show CCO, suggesting that root exudates of different crops differentially regulate soil microorganisms in SPP. Here, we investigated the microbial community structure and specific interaction mechanisms of the root exudates of the four plant species, P. notoginseng (Pn), Zea mays (Zm), Nicotiana tabacum (Nt) and Perilla frutescens (Pf), in SPP by static soil culture experiment. The results showed that the chemical diversity of root exudates varied significantly among the four plant species. Pn had the highest number of unique root exudates, followed by Nt, Zm and Pf. Terpenoids, flavonoids, alkaloids and phenolic acids were the most abundant differentially accumulated metabolites (DAMs) in Pn, Nt, Zm and Pf, respectively. However, lipids were the most abundant common DAMs among Zm Nt and Pf. Pn root exudates decreased the relative abundance of bacteria, but increased that of fungi. While specific DAMs in Pn enriched Phenylobacterium_zucineum, Sphingobium_yanoikuyae, Ophiostoma_ulmi and functional pathways of Nucleotide excision repair, Streptomycin biosynthesis, Cell cycle-Caulobacter and Glycolysis/Gluconeogenesis, it inhibited Paraburkholderia _caledonica and Ralstonia_pickettii. However, common DAMs in Zm, Nt and Pf had opposite effects. Moreover, common DAMs in Zm, Nt and Pf enriched Ralstonia_pseudosolanacearum and functional pathway of Xylene degradation; unique DAMs in Zm enriched Talaromyces_purcureogeneus, while inhibiting Fusarium_tricinctum and functional pathways of Nucleotide excision repair and Alanine, aspartate and glutamate metabolism; unique DAMs in Pf enriched Synchytrium_taraxaci. The core strains identified that interact with different root exudates will provide key clues for regulation of soil microorganisms in P. notoginseng cultivation to alleviate CCO.

Fullerenes via their counting polynomials

For a graph G with orbits O1,…,Ok, the orbit polynomial is defined as OG(x)=∑i=1kx|Oi|. In the current work, we will characterize all fullerenes concerning their pentagonal orbit polynomials (namely, the orbit polynomials for orbits of pentagons). Besides, the orbit polynomial, the orbit-entropy, the symmetry index and the unique positive root of orbit polynomial are computed for several infinite families of fullerenes. Finally, correlations between these graph measures are established to quantify their relationship.

Generalized torsion, unique root property and Baumslag–Solitar relation for knot groups

Generalized torsion, unique root property and Baumslag–Solitar relation for knot groups

Unit roots of the unit root L-functions of Kloosterman family

As a consequence of Wan's theorem about Dwork's conjecture, the unit root L-functions of the n-dimensional Kloosterman family are p-adic meromorphic. By studying the symmetric power L-functions associated to the Kloosterman family, we prove that for each 0≤j≤n, the unit root L-function coming from slope j has a unique unit root which equals 1.

The advance of underdetermined linear regression optimization based on implicit bias

The gradient descent method has the characteristics of easy realization and simple structure. The traditional gradient descent method has many advantages, especially in solving convex optimization problems. In recent years, some researchers have noticed that the gradient descent algorithm is helpful to solve the problem of underdetermined linear regression optimization. Therefore, in order to explore the specific relationship between gradient descent and under-determined linear regression optimization, this paper focuses on a case with a unique finite root loss function and discusses in detail the working principles of the natural-gradient-descent, mirror-descent, and gradient-descent in this case, and proves the auxiliary effect of gradient descent on under-determined linear regression optimization theoretically. How to use the characteristics of the gradient descent algorithm to design a suitable model, and how do we use the idea of the gradient descent algorithm to find an answer for problem of under determined linear regression optimization in the practical application will be the future research work to continue to advance.

Core Microbiome and Microbial Community Structure in Coralloid Roots of Cycas in Ex Situ Collection of Kunming Botanical Garden in China.

Endophytes are essential in plant succession and evolution, and essential for stress resistance. Coralloid root is a unique root structure found in cycads that has played a role in resisting adverse environments, yet the core taxa and microbial community of different Cycas species have not been thoroughly investigated. Using amplicon sequencing, we successfully elucidated the microbiomes present in coralloid roots of 10 Cycas species, representing all four sections of Cycas in China. We found that the endophytic bacteria in coralloid roots, i.e., Cyanobacteria, were mainly composed of Desmonostoc_PCC-7422, Nostoc_PCC-73102 and unclassified_f__Nostocaceae. Additionally, the Ascomycota fungi of Exophiala, Paraboeremia, Leptobacillium, Fusarium, Alternaria, and Diaporthe were identified as the core fungi taxa. The Ascomycota fungi of Nectriaceae, Herpotrichiellaceae, Cordycipitaceae, Helotiaceae, Diaporthaceae, Didymellaceae, Clavicipitaceae and Pleosporaceae were identified as the core family taxa in coralloid roots of four sections. High abundance but low diversity of bacterial community was detected in the coralloid roots, but no significant difference among species. The fungal community exhibited much higher complexity compared to bacteria, and diversity was noted among different species or sections. These core taxa, which were a subset of the microbiome that frequently occurred in all, or most, individuals of Cycas species, represent targets for the development of Cycas conservation.

Dynamics of the Three-Compartment Financial Bubble Model under the Mittag-Leffler Operator

This paper presents an investigation into the dynamics of the emerging three-compartment financial bubble problem using a new non-singular kernel Atangana–Baleanu derivative operator. The problem is tested for at least one solution, and a unique root is determined using an iterative Newton approximation method, providing a globally stable fractional analysis technique. Curve sketches of the globalized model are provided, considering integers and other conformable orders. Sensitivities of the fractional order and other model parameters are examined, offering insights into their impact on the system dynamics. This research contributes to understanding financial bubbles and lays the groundwork for future studies in this field.

Successful Root Canal Treatment of an Atypical Mandibular Canine with a Boomerang-shaped Root and Canal System with a Large Periapical lesion—A Case Report with 9-year Follow-up

AimThis report describes an atypical mandibular canine with a single boomerang-shaped root and root canal system with a large periapical lesion managed by root canal treatment. MethodsThe chief complaint of a 16-year-old male was acute pain and an abnormal sensation in the right mandibular canine (tooth #27). The clinical examination revealed that tooth #27 had an unusual coronal morphology. The buccal aspect of the tooth resembled that of a normal canine but was significantly broader than expected. On the lingual aspect of the crown; however, there was an unusual cusp-like structure with ridges that was slightly less prominent than the buccal incisal tip. The intraoral periapical radiographs revealed a complex root with an obvious cow horn-shaped canal mesially and distally, but with the suggestion of a root structure joining the mesial and distal extensions. A large periapical lesion was present. Computed tomography revealed the presence of a single root and canal system shaped like a boomerang. Root canal treatment was performed and the patient was followed-up for 9 years. ResultsFollowing root canal treatment, the patient had no symptoms, no mobility, no periodontal pockets, or root resorption. At 9 years, the cone beam computed tomography images confirmed that satisfactory healing of the periapical tissues had occurred. ConclusionThe mandibular right canine had a unique boomerang-shaped root and canal system. Effective shaping and cleaning of the complex canal shape plus thermoplastic root filling aided the successful healing of the periapical lesion.

On Automorphic Forms of Small Weight for Fake Projective Planes

On the projective plane there is a unique cubic root of the canonical bundle and this root is acyclic. On fake projective planes such root exists and is unique if there are no 3-torsion divisors (and usually exists, but not unique, otherwise). Earlier we conjectured that any such cubic root must be acyclic. In the present note we give two short proofs of this statement and show acyclicity of some other line bundles on the fake projective planes with at least $9$ automorphisms. Similarly to our earlier work we employ simple representation theory for non-abelian finite groups. The first proof is based on the observation that if some line bundle is non-linearizable with respect to a finite abelian group, then it should be linearized by a finite, \emph{non-abelian}, Heisenberg group. For the second proof, we also demonstrate vanishing of odd Betti numbers for a class of abelian covers, and use linearization of an auxiliary line bundle as well.

A Kullback-Leibler Divergence Variant of the Bayesian Cramér-Rao Bound

This paper proposes a Bayesian Cramér-Rao type lower bound on the minimum mean square error. The key idea is to minimize the latter subject to the constraint that the joint distribution of the input-output statistics lies in a Kullback–Leibler divergence ball centered at a Gaussian reference distribution. The bound is tight and is attained by a Gaussian distribution whose mean is identical to that of the reference distribution and whose covariance matrix is determined by a scalar parameter that can be obtained by finding the unique root of a simple function. Examples of applications in signal processing and information theory illustrate the usefulness of the proposed bound in practice.

COMPOSITION AND AMOUNT OF MARINE DEBRIS DISTRIBUTED TO MANGROVE ECOSYSTEMS IN KUPANG CITY, EAST NUSA TENGGARA, INDONESIA

The unique mangrove root system is a gathering place for small and large waste. The density of the population results in varied activities so that the waste produced in various types, quantities and sizes can be distributed to the mangrove area either through rivers or carried by the wind. The purpose of this study was to determine the type and amount of waste in the mangrove ecosystem in Kupang City. The method used is observation. Sampling was carried out by installing a transect perpendicular to the sea along 70 m at the place with the highest abundance of waste and the thickness of the mangrove reached 50-100 meters. There are 6 transects installed at the study site and each transect is divided into three zones consisting of three quadrants with a size of 30 x 10 m2. The distance between quadrants is 20 m with the first quadrant being at the first point where mangroves are found. The results of the study found that the composition of the types of waste scattered in the mangrove ecosystem of Kupang City were 88,91% plastik with a total of 15,628 pieces, cloth (4,21%) with a total of 640 pieces, other waste (3,97%) with a total of 604 pieces, cork/foam (1,18%) with a total of 148 pieces, rubber (0,57%) with a total of 86 pieces, metal (0,29%) with a total of 44 pieces, glass and ceramics (0,15%) with a total of 11 pieces, then paper and cardboard (0,05%) with a total of 7 pieces. Types of plastic waste, fabrics, others, rubber and metal have a greater amount in the first zone, cork / foam is the most in the second zone then paper and cardboard are most found in the first and third zones, while glass and ceramics are the most in zone three.

Using machine learning enabled phenotyping to characterize nodulation in three early vegetative stages in soybean.

The symbiotic relationship between soybean [Glycine max L. (Merr.)] roots and bacteria (Bradyrhizobium japonicum) lead to the development of nodules, important legume root structures where atmospheric nitrogen (N2) is fixed into bio-available ammonia (NH3) for plant growth and development. With the recent development of the Soybean Nodule Acquisition Pipeline (SNAP), nodules can more easily be quantified and evaluated for genetic diversity and growth patterns across unique soybean root system architectures. We explored six diverse soybean genotypes across three field year combinations in three early vegetative stages of development and report the unique relationships between soybean nodules in the taproot and non-taproot growth zones of diverse root system architectures of these genotypes. We found unique growth patterns in the nodules of taproots showing genotypic differences in how nodules grew in count, size, and total nodule area per genotype compared to non-taproot nodules. We propose that nodulation should be defined as a function of both nodule count and individual nodule area resulting in a total nodule area per root or growth regions of the root. We also report on the relationships between the nodules and total nitrogen in the seed at maturity, finding a strong correlation between the taproot nodules and final seed nitrogen at maturity. The applications of these findings could lead to an enhanced understanding of the plant-Bradyrhizobium relationship and exploring these relationships could lead to leveraging greater nitrogen use efficiency and nodulation carbon to nitrogen production efficiency across the soybean germplasm.