Implicit Low-Rank Riemannian Schemes for the Time Integration of Stiff Partial Differential Equations.

We propose two implicit numerical schemes for the low-rank time integration of stiff nonlinear partial differential equations. Our approach uses the preconditioned Riemannian trust-region method of Absil, Baker, and Gallivan, 2007. We demonstrate the efficiency of our method for solving the Allen-Cahn and the Fisher-KPP equations on the manifold of fixed-rank matrices. Our approach allows us to avoid the restriction on the time step typical of methods that use the fixed-point iteration to solve the inner nonlinear equations. Finally, we demonstrate the efficiency of the preconditioner on the same variational problems presented in Sutti and Vandereycken, 2021.

KPP transition fronts in a one-dimensional two-patch habitat.

This paper is concerned with the existence of transition fronts for a one-dimensional two patch model with KPP reaction terms. Density and flux conditions are imposed at the interface between the two patches. We first construct a pair of suitable super- and sub solutions by making full use of information of the leading edges of two KPP fronts and gluing them through the interface conditions. Then, an entire solution obtained thanks to a limiting argument is shown to be a transition front moving from one patch to the other one. This propagating solution admits asymptotic past and future speeds, and it connects two different fronts, each associated with one of the two patches. The paper thus provides the first example of a transition front for a KPP-type two-patch model with interface conditions.

Ascertainment of Nutrition Care Process (NCP) Implementation and Use of NCP Terminologies (NCPT) among Hospital Dietitians in the Philippines.

Background and Objective: The Nutrition Care Process (NCP) is a systematic method used by dietitians to provide high-quality nutrition care resulting in good patient outcomes. This study aimed to assess the NCP implementation and use of NCP Terminologies (NCPT) among hospital dietitians in the Philippines. Specifically, the study aimed at assessing the knowledge, perception, and practices on NCP and use of NCPT and correlate them with the dietitians' education, and professional and employment profile; and explain the barriers and facilitators of the practice of NCP and use of NCPT among hospital dietitians in the Philippines. Methods: The knowledge, perception, and practices (KPP) on NCP and NCPT of the dietitians employed in the Philippine Department of Health's licensed level 3 hospitals were determined using a validated questionnaire. Significant factors associated with the KPP were also determined. The barriers and facilitators of the practice of NCP and NCPT were determined using focus group discussion and key informant interviews of chief clinical dietitians and hospital administrators, respectively. Results: The study revealed that majority of the participants had a high level of knowledge on NCP and NCPT, positively perceived its implementation, and more than half of them implement NCP and NCPT in the hospitals. The participants' knowledge on NCP and NCPT was significantly associated with research involvement and active membership in a professional organization. While the practice of NCP and NCPT was significantly associated with having NCP-related trainings, frequency of trainings, and active membership in a professional organization. The barriers to NCP implementation were insufficient resources; lack of orientation, trainings, and support; organizational and administrative constraints; pandemic constraints; insufficient time; and lack of confidence to conduct NCP. While the facilitators of implementation were collaboration, dedication, and commitment of the healthcare team; institutionalization of NCP laws and policies; budget allocation for NCP-related activities; monitoring and consistency of NCP implementation; and work schedule. Conclusion: The findings suggest that the implementation of NCP and NCPT in the Philippines needs further support from the institution, professional organizations, and policy makers by developing strategies to cope with the barriers, and strengthen the facilitators and factors associated with practice.

Effect of the nonlinear dispersive coefficient on time-dependent variable coefficient soliton solutions of the Kolmogorov-Petrovsky-Piskunov model arising in biological and chemical science.

In this article, we study the soliton solutions with a time-dependent variable coefficient to the Kolmogorov-Petrovsky-Piskunov (KPP) model. At first, this model was used as the genetics model for the spread of an advantageous gene through a population, but it has also been used as a number of physics, biological, and chemical models. The enhanced modified simple equation technique applies to get the time-dependent variable coefficient soliton solutions from the KPP model. The obtained solutions provide diverse, exact solutions for the different functions of the time-dependent variable coefficient. For the special value of the constants, we get the kink, anti-kink shape, the interaction of kink, anti-kink, and singularities, the interaction of instanton and kink shape, instanton shape, kink, and bell interaction, anti-kink and bell interaction, kink and singular solitons, anti-kink and singular solitons, the interaction of kink and singular, and the interaction of anti-kink and singular solutions to diverse nature wave functions as time-dependent variable coefficients. The presented phenomena are clarified in three-dimension, contour, and two-dimension plots. The obtained wave patterns are powerfully exaggerated by the variable coefficient wave transformation and connected variable parameters. The effect of second-order and third-order nonlinear dispersive coefficients is also explored in 2D plots.

Cost structure in specialist mental healthcare: what are the main drivers of the most expensive episodes?

BACKGROUND: Mental disorders are one of the costliest conditions to treat in Norway, and research into the costs of specialist mental healthcare are needed. The purpose of this article is to present a cost structure and to investigate the variables that have the greatest impact on high-cost episodes. METHODS: Patient-level cost data and clinic information during 2018-2021 were analyzed (N = 180,220). Cost structure was examined using two accounting approaches. A generalized linear model was used to explain major cost drivers of the 1%, 5%, and 10% most expensive episodes, adjusting for patients' demographic characteristics [gender, age], clinical factors [length of stay (LOS), admission type, care type, diagnosis], and administrative information [number of planned consultations, first hospital visits, interval between two hospital episode]. RESULTS: One percent of episodes utilized 57% of total resources. Labor costs accounted for 87% of total costs. The more expensive an episode was, the greater the ratio of the inpatient (ward) cost was. Among the top-10%, 5%, and 1% most expensive groups, ward costs accounted for, respectively, 89%, 93%, and 99% of the total cost, whereas the overall average was 67%. Longer LOS, ambulatory services, surgical interventions, organic disorders, and schizophrenia were identified as the major cost drivers of the total cost, in general. In particular, LOS, ambulatory services, and schizophrenia were the factors that increased costs in expensive subgroups. The "first hospital visit" and "a very short hospital re-visit" were associated with a cost increase, whereas "the number of planned consultations" was associated with a cost decrease. CONCLUSIONS: The specialist mental healthcare division has a unique cost structure. Given that resources are utilized intensively at the early stage of care, improving the initial flow of hospital care can contribute to efficient resource utilization. Our study found empirical evidence that planned outpatient consultations may be associated with a reduced health care burden in the long-term.

The speed of invasion in an advancing population.

We derive rigorous estimates on the speed of invasion of an advantageous trait in a spatially advancing population in the context of a system of one-dimensional F-KPP equations. The model was introduced and studied heuristically and numerically in a paper by Venegas-Ortiz et al. (Genetics 196:497-507, 2014). In that paper, it was noted that the speed of invasion by the mutant trait is faster when the resident population is expanding in space compared to the speed when the resident population is already present everywhere. We use the Feynman-Kac representation to provide rigorous estimates that confirm these predictions.

Looking forwards and backwards: dynamics and genealogies of locally regulated populations.

We introduce a broad class of mechanistic spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial position and local population density, defined at a location to be the convolution of the point measure with a suitable non-negative integrable kernel centred on that location. We pass to three different scaling limits: an interacting superprocess, a nonlocal partial differential equation (PDE), and a classical PDE. The classical PDE is obtained both by a two-step convergence argument, in which we first scale time and population size and pass to the nonlocal PDE, and then scale the kernel that determines local population density; and in the important special case in which the limit is a reaction-diffusion equation, directly by simultaneously scaling the kernel width, timescale and population size in our individual based model. A novelty of our model is that we explicitly model a juvenile phase. The number of juveniles produced by an individual depends on local population density at the location of the parent; these juvenile offspring are thrown off in a (possibly heterogeneous, anisotropic) Gaussian distribution around the location of the parent; they then reach (instant) maturity with a probability that can depend on the local population density at the location at which they land. Although we only record mature individuals, a trace of this two-step description remains in our population models, resulting in novel limits in which the spatial dynamics are governed by a nonlinear diffusion. Using a lookdown representation, we are able to retain information about genealogies relating individuals in our population and, in the case of deterministic limiting models, we use this to deduce the backwards in time motion of the ancestral lineage of an individual sampled from the population. We observe that knowing the history of the population density is not enough to determine the motion of ancestral lineages in our model. We also investigate (and contrast) the behaviour of lineages for three different deterministic models of a population expanding its range as a travelling wave: the Fisher-KPP equation, the Allen-Cahn equation, and a porous medium equation with logistic growth.

Revisiting Fisher-KPP model to interpret the spatial spreading of invasive cell population in biology.

In this paper, the homotopy analysis method, a powerful analytical technique, is applied to obtain analytical solutions to the Fisher-KPP equation in studying the spatial spreading of invasive species in ecology and to extract the nature of the spatial spreading of invasive cell populations in biology. The effect of the proliferation rate of the model of interest on the entire population is studied. It is observed that the invasive cell or the invasive population is decreased within a short time with the minimum proliferation rate. The homotopy analysis method is found to be superior to other analytical methods, namely the Adomian decomposition method, the homotopy perturbation method, etc. because of containing an auxiliary parameter, which provides us with a convenient way to adjust and control the region of convergence of the series solution. Graphical representation of the approximate series solutions obtained by the homotopy analysis method, the Adomian decomposition method, and the Homotopy perturbation method is illustrated, which shows the superiority of the homotopy analysis method. The method is examined on several examples, which reveal the ingenuousness and the effectiveness of the method of interest.

Heterogeneous Diffusion and Nonlinear Advection in a One-Dimensional Fisher-KPP Problem.

The goal of this study is to provide an analysis of a Fisher-KPP non-linear reaction problem with a higher-order diffusion and a non-linear advection. We study the existence and uniqueness of solutions together with asymptotic solutions and positivity conditions. We show the existence of instabilities based on a shooting method approach. Afterwards, we study the existence and uniqueness of solutions as an abstract evolution of a bounded continuous single parametric (t) semigroup. Asymptotic solutions based on a Hamilton-Jacobi equation are then analyzed. Finally, the conditions required to ensure a comparison principle are explored supported by the existence of a positive maximal kernel.

Non-vanishing sharp-fronted travelling wave solutions of the Fisher-Kolmogorov model.

The Fisher-Kolmogorov-Petrovsky-Piskunov (KPP) model, and generalizations thereof, involves simple reaction-diffusion equations for biological invasion that assume individuals in the population undergo linear diffusion with diffusivity $D$, and logistic proliferation with rate $\lambda $. For the Fisher-KPP model, biologically relevant initial conditions lead to long-time travelling wave solutions that move with speed $c=2\sqrt {\lambda D}$. Despite these attractive features, there are several biological limitations of travelling wave solutions of the Fisher-KPP model. First, these travelling wave solutions do not predict a well-defined invasion front. Second, biologically relevant initial conditions lead to travelling waves that move with speed $c=2\sqrt {\lambda D}> 0$. This means that, for biologically relevant initial data, the Fisher-KPP model cannot be used to study invasion with $c \ne 2\sqrt {\lambda D}$, or retreating travelling waves with $c < 0$. Here, we reformulate the Fisher-KPP model as a moving boundary problem and show that this reformulated model alleviates the key limitations of the Fisher-KPP model. Travelling wave solutions of the moving boundary problem predict a well-defined front that can propagate with any wave speed, $-\infty < c < \infty $. Here, we establish these results using a combination of high-accuracy numerical simulations of the time-dependent partial differential equation, phase plane analysis and perturbation methods. All software required to replicate this work is available on GitHub.

Hypokalemic Periodic Paralysis: An Atypical Presentation of Non-autoimmune Hypothyroidism With Distal Renal Tubular Acidosis.

Hypokalemic periodic paralysis (hypo KPP) is a rare form of autosomal dominant channelopathy characterized by muscular weakness and paralysis caused by decreased potassium levels. Precipitating factors are a diet rich in starches and sweets, and rest after an unusual degree of exercise. Paralytic attacks are more common between the ages of 15 and 40 years. The presentation can be a total paralysis or severe quadriplegia or mild weakness in certain group of muscles. During the acute episode of weakness proximal muscles are involved initially with gradual spread to the distal muscles. Deep reflexes are decreased or absent but the cognitive functions and sensory systems are intact. The paralysis may last for few hours to several days, but recovery is usually sudden in most patients. Hypo KPP is usually associated with thyroid disorders and distal renal tubular acidosis (DRTA). Here we report a case of young female patient who presented in emergency with two days history of weakness of all four limbs. The patient also had two episodes of similar illness in the last two and half years. On examination she had decreased tone and power in all four limbs with absent deep tendon reflexes, and plantar reflexes were down going bilaterally. On initial laboratory workup, patient was diagnosed to have hypokalemic, hyperchloremic metabolic acidosis with alkaline urine secondary to hypothyroidism. Features of hypokalemia with metabolic acidosis and failure to acidify urine was consistent with DRTA. Intravenous potassium chloride and bicarbonate replacement resulted in biochemical and clinical improvement.

A Continuum Mathematical Model of Substrate-Mediated Tissue Growth.

We consider a continuum mathematical model of biological tissue formation inspired by recent experiments describing thin tissue growth in 3D-printed bioscaffolds. The continuum model, which we call the substrate model, involves a partial differential equation describing the density of tissue, [Formula: see text] that is coupled to the concentration of an immobile extracellular substrate, [Formula: see text]. Cell migration is modelled with a nonlinear diffusion term, where the diffusive flux is proportional to [Formula: see text], while a logistic growth term models cell proliferation. The extracellular substrate [Formula: see text] is produced by cells and undergoes linear decay. Preliminary numerical simulations show that this mathematical model is able to recapitulate key features of recent tissue growth experiments, including the formation of sharp fronts. To provide a deeper understanding of the model we analyse travelling wave solutions of the substrate model, showing that the model supports both sharp-fronted travelling wave solutions that move with a minimum wave speed, [Formula: see text], as well as smooth-fronted travelling wave solutions that move with a faster travelling wave speed, [Formula: see text]. We provide a geometric interpretation that explains the difference between smooth and sharp-fronted travelling wave solutions that is based on a slow manifold reduction of the desingularised three-dimensional phase space. In addition, we also develop and test a series of useful approximations that describe the shape of the travelling wave solutions in various limits. These approximations apply to both the sharp-fronted and smooth-fronted travelling wave solutions. Software to implement all calculations is available at GitHub .

A Fisher-KPP Model with a Nonlocal Weighted Free Boundary: Analysis of How Habitat Boundaries Expand, Balance or Shrink.

In this paper, we propose a novel free boundary problem to model the movement of single species with a range boundary. The spatial movement and birth/death processes of the species found within the range boundary are assumed to be governed by the classic Fisher-KPP reaction-diffusion equation, while the movement of a free boundary describing the range limit is assumed to be influenced by the weighted total population inside the range boundary and is described by an integro-differential equation. Our free boundary equation is a generalization of the classical Stefan problem that allows for nonlocal influences on the boundary movement so that range expansion and shrinkage are both possible. In this paper, we prove that the new model is well-posed and possesses steady state. We show that the spreading speed of the range boundary is smaller than that for the equivalent problem with a Stefan condition. This implies that the nonlocal effect of the weighted total population on the boundary movement slows down the spreading speed of the population. While the classical Stefan condition categorizes asymptotic behavior via a spreading-vanishing dichotomy, the new model extends this dichotomy to a spreading-balancing-vanishing trichotomy. We specifically analyze how habitat boundaries expand, balance or shrink. When the model is extended to have two free boundaries, we observe the steady state scenario, asymmetric shifts, or even boundaries moving synchronously in the same direction. These are newly discovered phenomena in the free boundary problems for animal movement.

[Genetics of complex and syndromic palmoplantar keratoderma]. / Génétique des kératodermies palmoplantaires complexes et syndromiques.

Palmoplantar keratodermas (PPK) comprise a heterogenous group of acquired and hereditary disorders marked by excessive thickening of the epidermis of palms and soles. Hereditary PPKs can be classified into 3 groups: 1) isolated non-syndromic PPKs; 2) complex non-syndromic PPKs associated with other ectodermal defects; and 3) syndromic PPKs associated with extracutaneous manifestations. All types of inheritance have been observed: autosomal dominant, autosomal recessive, X-linked recessive, and mitochondrial. Some of these disorders are restricted to geographic isolates. This review describes the different genetic causes of hereditary syndromic and complex PPKs for which the genes have been identified. The identification of pathogenic variants has consequences in terms of genetic counseling, appropriate medical care and follow-up, especially for PPKs predisposing to hearing loss, cardiomyopathies, benign tumors or carcinomas. In addition, the development of targeted therapies based on pathophysiology of disorders should allow a more effective treatment of these conditions in the near future.

Homogenization of a reaction diffusion equation can explain influenza A virus load data.

We study the influence of spatial heterogeneity on the antiviral activity of mouse embryonic fibroblasts (MEF) infected with influenza A. MEF of type Ube1L-/- are composed of two distinct sub-populations, the strong type that sustains a strong viral infection and the weak type, sustaining a weak viral load. We present new data on the virus load infection of Ube1L-/-, which have been micro-printed in a checker board pattern of different sizes of the inner squares. Surprisingly, the total viral load at one day after inoculation significantly depends on the sizes of the inner squares. We explain this observation by using a reaction diffusion model and we show that mathematical homogenization can explain the observed inhomogeneities. If the individual patches are large, then the growth rate and the carrying capacity will be the arithmetic means of the patches. For finer and finer patches the average growth rate is still the arithmetic mean, however, the carrying capacity uses the harmonic mean. While fitting the PDE to the experimental data, we also predict that a discrepancy in virus load would be unobservable after only half a day. Furthermore, we predict the viral load in different inner squares that had not been measured in our experiment and the travelling distance the virions can reach after one day.

Influence of a road on a population in an ecological niche facing climate change.

We introduce a model designed to account for the influence of a line with fast diffusion-such as a road or another transport network-on the dynamics of a population in an ecological niche.This model consists of a system of coupled reaction-diffusion equations set on domains with different dimensions (line / plane). We first show that, in a stationary climate, the presence of the line is always deleterious and can even lead the population to extinction. Next, we consider the case where the niche is subject to a displacement, representing the effect of a climate change. We find that in such case the line with fast diffusion can help the population to persist. We also study several qualitative properties of this system. The analysis is based on a notion of generalized principal eigenvalue developed and studied by the authors (2019).

Determining the optimal coefficient of the spatially periodic Fisher-KPP equation that minimizes the spreading speed.

This paper is concerned with the spatially periodic Fisher-KPP equation [Formula: see text], [Formula: see text], where d(x) and r(x) are periodic functions with period [Formula: see text]. We assume that r(x) has positive mean and [Formula: see text]. It is known that there exists a positive number [Formula: see text], called the minimal wave speed, such that a periodic traveling wave solution with average speed c exists if and only if [Formula: see text]. In the one-dimensional case, the minimal speed [Formula: see text] coincides with the "spreading speed", that is, the asymptotic speed of the propagating front of a solution with compactly supported initial data. In this paper, we study the minimizing problem for the minimal speed [Formula: see text] by varying r(x) under a certain constraint, while d(x) arbitrarily. We have been able to obtain an explicit form of the minimizing function r(x). Our result provides the first calculable example of the minimal speed for spatially periodic Fisher-KPP equations as far as the author knows.

The Fisher-KPP equation over simple graphs: varied persistence states in river networks.

In this article, we study the dynamical behaviour of a new species spreading from a location in a river network where two or three branches meet, based on the widely used Fisher-KPP advection-diffusion equation. This local river system is represented by some simple graphs with every edge a half infinite line, meeting at a single vertex. We obtain a rather complete description of the long-time dynamical behaviour for every case under consideration, which can be classified into three different types (called a trichotomy), according to the water flow speeds in the river branches, which depend crucially on the topological structure of the graph representing the local river system and on the cross section areas of the branches. The trichotomy includes two different kinds of persistence states, and the state called "persistence below carrying capacity" here appears new.

The MAP Kinase SsKpp2 Is Required for Mating/Filamentation in Sporisorium scitamineum.

In the phytopathogenic fungus Sporisorium scitamineum, sexual mating between two compatible haploid cells and the subsequent formation of dikaryotic hyphae is essential for infection. This process was shown to be commonly regulated by a mitogen-activated protein kinase (MAPK) and a cAMP/PKA signaling pathway in the corn smut fungus Ustilago maydis but remains largely unknown in S. scitamineum. In this study, we identified a conserved putative MAP kinase Kpp2 in S. scitamineum and named it as SsKpp2. The sskpp2Δ mutant displayed significant reduction in mating/filamentation, which could be partially restored by addition of cAMP or tryptophol, a quorum-sensing molecule identified in budding yeast. Transcriptional profiling showed that genes governing S. scitamineum mating or tryptophol biosynthesis were significantly differentially regulated in the sskpp2Δ mutant compared to the WT, under mating condition. Our results demonstrate that the MAP kinase SsKpp2 is required for S. scitamineum mating/filamentation likely through regulating the conserved pheromone signal transduction pathway and tryptophol production.

The CIF1 protein is a master orchestrator of trypanosome cytokinesis that recruits several cytokinesis regulators to the cytokinesis initiation site.

To proliferate, the parasitic protozoan Trypanosoma brucei undergoes binary fission in a unidirectional manner along the cell's longitudinal axis from the cell anterior toward the cell posterior. This unusual mode of cell division is controlled by a regulatory pathway composed of two evolutionarily conserved protein kinases, Polo-like kinase and Aurora B kinase, and three trypanosome-specific proteins, CIF1, CIF2, and CIF3, which act in concert at the cytokinesis initiation site located at the distal tip of the newly assembled flagellum attachment zone (FAZ). However, additional regulators that function in this cytokinesis signaling cascade remain to be identified and characterized. Using proximity biotinylation, co-immunofluorescence microscopy, and co-immunoprecipitation, we identified 52 CIF1-associated proteins and validated six CIF1-interacting proteins, including the putative protein phosphatase KPP1, the katanin p80 subunit KAT80, the cleavage furrow-localized proteins KLIF and FRW1, and the FAZ tip-localized proteins FAZ20 and FPRC. Further analyses of the functional interplay between CIF1 and its associated proteins revealed a requirement of CIF1 for localization of a set of CIF1-associated proteins, an interdependence between KPP1 and CIF1, and an essential role of katanin in the completion of cleavage furrow ingression. Together, these results suggest that CIF1 acts as a master regulator of cytokinesis in T. brucei by recruiting a cohort of cytokinesis regulatory proteins to the cytokinesis initiation site.