Regular Points Research Articles

Regular points of extremal subsets in Alexandrov spaces

We define regular points of an extremal subset in an Alexandrov space and study their basic properties. We show that a neighborhood of a regular point in an extremal subset is almost isometric to an open subset in Euclidean space and that the set of regular points in an extremal subset has full measure and is dense in it. These results actually hold for strained points in an extremal subset. Applications include the volume convergence of extremal subsets under a noncollapsing convergence of Alexandrov spaces, and the existence of a cone fibration structure of a metric neighborhood of the regular part of an extremal subset. In an appendix, a deformation retraction of a metric neighborhood of a general extremal subset is constructed.

A Goodness-of-Identifiability Criterion for Parametric Statistical Models

Abstract This note sets out a goodness-of-identifiability criterion. This criterion quantifies the identifying strength of a parametric statistical model. Unlike the qualitative criterion for identifiability based only on the Fisher matrix, it applies to both regular and irregular points of the Fisher matrix. Unlike the qualitative criterion based only on the Hellinger distance, it quantifies set-identification. JEL classification numbers: C10, C50. Keywords: Parametric statistical model, Identifiability, Fisher matrix, Hellinger distance.

Affordability of essential medicines: The case of fluoride toothpaste in 78 countries.

BackgroundFluoride toothpaste (FT) has recently been included in the WHO Model List of Essential Medicines. Whereas it is essential for preventing dental caries, its current affordability around the globe remains unclear. This study aimed to analyse the affordability of FT in as many as possible countries worldwide, to capture the extent of variations in FT affordability between high-, middle- and low-income countries.MethodsA standardized protocol was developed to collect country-specific information about the characteristics of the cheapest available FT at a regular point of purchase. 82 members of the WHO Global Oral Health Network of Chief Dental Officers (CDOs), directors of WHO Collaborative Centres and other oral health experts collected data using mobile phone technology. In line with established methodologies to assess affordability, the Fluoride Toothpaste Affordability Ratio (FTAR) was calculated as the expenditure associated with the recommended annual consumption of FT relative to the daily wage of the lowest-paid unskilled government worker (FTAR >1 = unaffordable spending on fluoride toothpaste).ResultsThere are significant differences in the affordability of FT across 78 countries. FT was strongly affordable in high-income countries, relatively affordable in upper middle-income countries, and strongly unaffordable in lower middle-income and low-income countries. The affordability of FT across WHO Regions was dependent upon the economic mix of WHO Regions’ member states.ConclusionFT is still unaffordable for many people, particularly in low-income settings. Strategies to improve the universal affordability of FT should be part of health policy decisions in order to contribute to reducing dental caries as a global public health problem.

Time investments and questions raised by atrial fibrillation patients following a personalized educational follow-up strategy

Abstract Background Atrial fibrillation (AF) has a complex treatment strategy. As stated in the recent guidelines for AF management, AF management requires a holistic and multidisciplinary approach in which a personalized follow-up strategy is important to involve patients in their care. This also includes the need for an improved communication method in which patients can contact the healthcare team between in-hospital follow-up moments to easily ask questions with a low threshold. Purpose Two personalized follow-up methods for AF management (in-person and online) are currently being studied in a prospective, randomized controlled trial. The aim of this subanalysis is to evaluate time investment to answer patients' questions. Methods At three Belgian hospitals, a total of 1.038 AF patients were randomized to two groups with personalized education and follow-up, and a control group. The educational intervention focuses on four elements: improving patients' AF knowledge, improving OAC therapy adherence, encouraging self-care capabilities based on personal AF risk factors, and the reachability of an AF specialized team. Patients in the in-person group were followed personally at the hospital at regular time points, while the patients in the online group received education via an online platform. During the whole follow-up period, patients of both intervention groups could ask questions via e-mail or by phone contact. Results A total of 628 questions were raised by 275 patients (137 in-person and 138 online patients) with a mean number of 4.85±2.57 questions per patient. Patients in the online group had a trend towards asking more questions than the in-person group (2.46±2.08 vs. 2.11±1.74; p=0.061). However, there was no significant difference when looking at medical questions (online 2.12±1.80; in-person 2.16±2.42; p=0.55). In both groups, most questions were asked by phone contact (in-person: 72%; online: 51%; Fig. 1, red bars), although significantly less by the online group (p<0.001). In the in-person group, most questions were related to their study visit appointments (27.3%), symptoms (23.9%) and medication (23.2%). In the online group, most questions were related to the online platform (38.9%), symptoms (16.5%) and medication (11.2%). The research team spent on average 7.37±8.18 minutes to answer a question. There was a significant difference in duration to answer questions of the specific categories (p<0.001, Fig, 2). The top three categories on which the most time was spent were questions about symptoms (14.94±12.455 min), treatment and clinical investigations (9.29±7.9 min) and follow-up of clinical parameters (6.94±5.79 min). Conclusion A personalized educational follow-up method includes the possibility for patients to ask questions if needed. Most questions are related to AF symptoms and treatment. This indicates that a specialized AF team can be supportive in the management of AF patients. Funding Acknowledgement Type of funding sources: Public grant(s) – National budget only. Main funding source(s): The AF-EduCare study is a project supported by the Fund for Scientific Research, Flanders (T002917N).

Topological and quantum stability of low-dimensional crystalline lattices with multiple nonequivalent sublattices* *Dedicated to the memory of our close friend, fellow colleague, former student (PA) and teacher (AK) Prof. A A Kuzubov (1974–2016).

The terms of topological and quantum stabilities of low-dimensional crystalline carbon lattices with multiple non-equivalent sublattices are coined using theoretical analysis, multilevel simulations, and available experimental structural data. It is demonstrated that complex low-dimensional lattices are prone to periodicity breakdown caused by structural deformations generated by linear periodic boundary conditions (PBC). To impose PBC mandatory limitations for complex low-dimensional lattices, the topology conservation theorem (TCT) is introduced, formulated and proved. It is shown that the lack of perfect filling of planar 2D crystalline space by structural units may cause the formation of (i) structure waves of either variable or constant wavelength; (ii) nanotubes or rolls; (iii) saddle structures; (iv) aperiodic ensembles of irregular asymmetric atomic clusters. In some cases the lattice can be stabilized by aromatic resonance, correlation effects, or van-der-Waals interactions. The effect of quantum instability and periodicity breakdown of infinite structural waves is studied using quasiparticle approach. It is found that both perfect finite-sized, or stabilized structural waves can exist and can be synthesized. It is shown that for low-dimensional lattices prone to breakdown of translation invariance (TI), complete active space of normal coordinates cannot be reduced to a subspace of TI normal coordinates. As a result, constrained TI subspace structural minimization may artificially return a regular point at the potential energy surface as either a global/local minimum/maximum. It is proved that for such lattices, phonon dispersion cannot be used as solid and final proof of either stability or metastability. It is shown that ab initio molecular dynamics (MD) PBC Nosé–Hoover thermostat algorithm constrains the linear dimensions of the periodic slabs in MD box preventing their thermostated equilibration. Based on rigorous TCT analysis, a flowchart algorithm for structural analysis of low-dimensional crystals is proposed and proved to be a powerful tool for theoretical design of advanced complex nanomaterials.

Dislocation-Mediated Oxygen–Ionic Conductivity in Yttria-Stabilized Zirconia

Yttria-stabilized zirconia (YSZ) has become an indispensable solid electrolyte material in modern solid oxide fuel and electrolysis cells (SOFCs/SOECs) as well as oxygen sensors. The oxygen ionic conductivity of YSZ is among the highest known so far. For energy efficiency optimization of SOFCs and lowering the high-temperature degradation of electrodes, the oxygen ionic conductivity needs to be further enhanced. This would allow for a reduction in application temperature. Despite extensive regular point defect-doping strategies, this key issue remains unsolved. Here, we investigate the role of mechanically induced dislocations (line-defects) on electrical conductivity and oxygen transport in bulk YSZ. An advanced mechanical deformation approach is employed to generate distinctly aligned dislocation-rich and -deficient regions. The in-depth electrical characterization of these regions exhibited highly conducting effects of dislocation-induced strain inside the bulk material. Furthermore, targeted oxygen tracer diffusion experiments prove enriched oxygen incorporation within the dislocation bundles. Therefore, the potential of mechanically induced dislocations is elucidated as a design element to tune the bulk ionic transport in YSZ.

Ising-like and Fibonacci anyons from KZ-equations

In this work we present solutions to Knizhnik-Zamolodchikov (KZ) equations corresponding to conformal block wavefunctions of non-Abelian Ising-like and Fibonacci Anyons. We solve these equations around regular singular points in configuration space in terms of hypergeometric functions and derive explicit monodromy representations of the braid group action. This confirms the correct non-Abelian statistics of the solutions. One novelty of our approach is that we explicitly keep track of spin basis states and identify conformal blocks uniquely with such states at relevant points in moduli space.

Intelligent Multi-AUG Ocean Data Collection Scheme in Maritime Wireless Communication Network

The new generation of wireless networks is strengthening ocean development capabilities. The deep-sea detection ability of the offshore platform is being improved by Ocean Internet of Everything (OIoE) system formed by various equipment. This paper studies the application of a new generation of Artificial Intelligence (AI) wireless communication technology in marine monitoring platforms. The purpose is to solve the problem of high data redundancy and high energy consumption in multi-Automatic Underwater Glider (AUG) monitoring. In response to these problems, this paper proposes a matrix completion-based Sampling Points Selection joint Multi-AUG Path Planning (SPS-MAPP) scheme, which includes AUGs path planning and collection information matrix completion. In parts of AUGs path planning, the SPS-MAPP designed a multi-AUG trajectory optimization method using intermittent satellite communication. It proposes a reinforcement learning reward rule based on the idea of artificial potential field, which can effectively increase the coverage of AUGs trajectory. In parts of information processing, the SPS-MAPP proposes a 3-D matrix completion method, which searches for key nodes and edge nodes by designing regular sample points and operators to recover the entire space information. The experimental results show that the proposed SPS-MAPP scheme can effectively improve the subsea monitoring capability of multi-AUG.

Singlet and nonsinglet three-loop massive form factors

We consider Quantum Chromodynamics with external vector, axial-vector, scalar and pseudo-scalar currents and compute three-loop corrections to the corresponding vertex function taking into account massive quarks. We consider all non-singlet contributions as well as those singlet contributions where the external current couples to a massive quark loop. We apply a semi-numerical method which is based on expansions around singular and regular kinematical points. They are matched at intermediate values of the squared partonic center-of-mass energy $s$ which allows to cover the whole kinematic range for negative and positive values of $s$. Our method permits a systematic increase of the precision by varying the expansion depth and the choice of the intermediate matching points. In our current set-up we have at least seven significant digits for the finite contribution of all form factors. We present our results as a combination of series expansions and interpolation functions which allows for a straightforward use in practical applications.

Solving the nonlinear Riccati equation for the 1D plane-wave reflection response from a velocity gradient interface by a Heun to hypergeometric reduction

For 1D acoustic wave propagation in the frequency domain, the complex nonlinear Riccati differential equation describes the dependence of the plane-wave reflection response in depth, defined as the upgoing part of the wavefield divided by the downgoing part of the wavefield at that depth. In the case that the model is a velocity gradient interface expressed in terms of a smooth Heaviside function defined by the Fermi-Dirac function, the Riccati equation is shown to have an analytical solution for the reflection response. The solution accounts for all wave phenomena in the gradient zone. The solution of the Riccati equation for the reflection response is obtained by introducing the Riccati equation for the reciprocal of the reflection response which can be related to a second-order self-adjoint linear differential equation. The two latter equations obey the same radiation condition. Furthermore, a connection between the second-order linear equation and the Heun equation is obtained, both being characterized by having four regular singular points. By a change of variables, the Heun equation can be transformed into Gauss’ hypergeometric equation, whereby the solution is expressed as the sum of two linearly independent functions containing hypergeometric functions. The advantage of applying the Heun-to-hypergeometric reduction to the nonlinear Riccati equation is that solutions to the hypergeometric equation are well known. The two functions allow us to analytically determine the Riccati solution because the ratio of the linearly independent functions at infinity is constant. In contrast to the classic frequency-independent reflection coefficient from two layers in welded contact, the reflection coefficient at the surface associated with the gradient interface depends on frequency. In the limit of zero frequency, the reflection coefficient approaches the classic one. We have implemented the iterative solution of the integral form of the Riccati equation and found that the solution builds up nonlinearly to the correct solution. The model is verified by a numerical example valid for 1D wave propagation.

Midinfrared Compressed Fourier-Transform Spectroscopy with an Optical Frequency Comb

Broadband precision spectroscopy is an invaluable tool for high-fidelity species diagnostics as well as multispecies sensing in complex real-world environments. However, concurrent demands for broad spectral coverage and high spectral resolution present great challenges to both optical measurement systems and data acquisition and processing. We report methodological and experimental demonstration of a midinfrared direct optical frequency comb (OFC) spectrometer, using Fourier-transform spectroscopy (FTS) with a compressed sensing (CS) algorithm. Efficient data sampling and accurate spectral recovery are demonstrated with comb-teeth-resolving resolution of $0.0083\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ (250 MHz) over a spectral range of $300\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. The ${v}_{3}$ band of ${\mathrm{CH}}_{4}$ is measured, and validated against conventional FTS results and theoretical calculations. Studies on the effect of compression ratio show that a compressed interferogram using as few as 2% of the regular sample points can effectively recover the high-resolution broadband spectrum with an accuracy of 1.9%. The developed diagnostic system bears promising potential for accurate, real-time, multispecies sensing that is pressingly needed for studying the dynamics of complex multicomponent systems.

Adjoint pairs and unbounded normal operators

An adjoint pair is a pair of densely defined closed linear operatorsA,B on a Hilbert space such that langle Ax,yrangle = langle x,Byrangle for x in mathcal{D} (A),y in mathcal{D} (B) . We consider adjoint pairs for which 0 is a regular point for bothoperators and associate a boundary triplet to such an adjoint pair. Properextensions of the operator B are in one-to-one correspondence Tcleftrightarrow mathcal{C} to closed subspaces mathcal{C} of mathcal{N}(A^{*}) oplusmathcal{N}(B^{*}). In the case when B is formallynormal andmathcal{D}(A) =mathcal{D}(B) , the normal operators Tc are characterized.Next we assume that B has an extension to a normal operator withbounded inverse. Then the normal operators Tc are described and thecase when mathcal{N}(A^{*}) has dimension one is treated.

The Deligne–Simpson problem for connections on [formula omitted] with a maximally ramified singularity

The classical additive Deligne–Simpson problem is the existence problem for Fuchsian connections with residues at the singular points in specified adjoint orbits. Crawley-Boevey found the solution in 2003 by reinterpreting the problem in terms of quiver varieties. A more general version of this problem, solved by Hiroe, allows additional unramified irregular singularities. We apply the theory of fundamental and regular strata due to Bremer and Sage to formulate a version of the Deligne–Simpson problem in which certain ramified singularities are allowed. These allowed singular points are called toral singularities; they are singularities whose leading term with respect to a lattice chain filtration is regular semisimple. We solve this problem in the special case of connections on Gm with a maximally ramified singularity at 0 and possibly an additional regular singular point at infinity. Examples of such connections arise from Airy, Bessel, and Kloosterman differential equations. They play an important role in recent work in the geometric Langlands program. We also give a complete characterization of all such connections which are rigid, under the additional hypothesis of unipotent monodromy at infinity.

Fredholm Pfaffian $$\tau $$-Functions for Orthogonal Isospectral and Isomonodromic Systems

We extend the approach to \(\tau \)-functions as Widom constants developed by Cafasso, Gavrylenko and Lisovyy to orthogonal loop group Drinfeld–Sokolov reductions and isomonodromic deformations systems. The combinatorial expansion of the \(\tau \)-function as a sum of correlators, each expressed as products of finite determinants, follows from using multicomponent fermionic vacuum expectation values of certain dressing operators encoding the initial conditions and dependence on the time parameters. When reduced to the orthogonal case, these correlators become finite Pfaffians and the determinantal \(\tau \)-functions, both in the Drinfeld–Sokolov and isomonodromic case, become squares of \(\tau \)-functions of Pfaffian type. The results are illustrated by several examples, consisting of polynomial \(\tau \)-functions of orthogonal Drinfeld–Sokolov type and isomonodromic ones with four regular singular points.

THE NUMERICAL MESHLESS APPROACH FOR SOLVING THE 2D TIME NONLINEAR MULTI-TERM FRACTIONAL CABLE EQUATION IN COMPLEX GEOMETRIES

The cable equation plays a prominent role in biological neuron models, for instance, in spiking neuron models and electrophysiology. Thus, the current investigation scrutinizes the 2D time nonlinear multi-term fractional cable equation. By adopting a valid meshfree technique, the nonlinear multi-term time-fractional cable equations (NM-TTFCEs) that consist of government equations and their boundary conditions are transformed into the boundary value problems. For this purpose, the finite difference method is derived for temporal discretization such that the considered NM-TTFCEs can be transformed into a sequence of boundary value problems in inhomogeneous Helmholtz-type equations. The dual reciprocity method (DRM) is implemented to obtain a particular solution and the improved singular boundary method (ISBM) is employed to evaluate the homogeneous solution. Moreover, we apply the meshless method for solving two-dimensional NM-TTFCEs on regular and irregular distribution points with several computational domains. The numerical results vouch for the accuracy and high efficiency of the proposed method. Finally, we will conclude that the ISBM/DRM method can be considered a potential alternative to existing meshless strong form approaches in solving multi-term fractional equation problems with complex geometries.

Multiscale approach for tFUS neurocomputational modelling.

Among the non-invasive methods employed for brain stimulation, trans cranial Focused Ultrasound Stimulation (tFUS) is the technique with the best penetration into the tissues and spatial resolution. The development of computational models of US propagation in brain tissue can be useful for estimating the behaviour of neural cells subjected to mechanical stimulus due to US. This paper aims at studying the neural cell response of a cortical Regular Spiking point neuron model, for different values of stimulus Duty Cycle (DC). The main goal is to use a multiscale approach to couple the results obtained from a macroscale simulation on wave propagation in tissue, with neuron model described by Hodgkin-Huxley equations to study latency and firing rate of the RS model. The obtained results showed that latency and firing rate have slight variations along the propagation direction of the US beam, in the focal region under the skull model, for different stimulus DC.

Electromyographic Response of the Abdominal Muscles and Stabilizers of the Trunk to Reflex Locomotion Therapy (RLT). A Preliminary Study.

Reflex locomotion therapy (RLT) was developed by Vaclav Vojta in 1954 as a diagnostic and treatment tool. This therapy is mainly used to rehabilitate children with motor disorders and risk of cerebral palsy. It is also used for adults with neurological and motor impairment. RLT is based on specific postures and regular stimulation points through which a series of reflex responses are triggered. The neurophysiological mechanisms of this therapy have recently been discovered. This study aims to objectively evaluate muscular responses at the abdominal level after stimulation in the first phase of reflex rolling by showing, with surface electromyography analysis (sEMG), the muscular activity in trunk stabilizing muscles (rectus abdominis, external oblique, internal oblique, and serratus anterior) before, during, and after the application of RLT. A total sample of 27 healthy subjects over 18 years of age was recruited. An experimental study on a cohort was conducted. Two experimental conditions were considered: stimuli according to the Vojta protocol, and a control non-STI condition. Regarding muscular electrical activity, statistically significant differences were determined in all muscles during right-sided stimulation in the VSTI condition (p < 0.001), but not in the non-STI condition. The mean increase in muscle activity in the VSTI condition during the first stimulation ranged from 7% to 20% in the different abdominal muscles. In conclusion, an sEMG response was observed in the abdominal muscles during stimulation of the pectoral area as described in RLT, compared to stimulation of non-described areas.

Plasma and Interstitial Fluid Pharmacokinetics of Prophylactic Cefazolin in Elective Bariatric Surgery Patients.

Guidelines for surgical prophylactic dosing of cefazolin in bariatric surgery vary in terms of recommended dose. This study aimed to describe the plasma and interstitial fluid (ISF) cefazolin pharmacokinetics in patients undergoing bariatric surgery and to determine an optimum dosing regimen. Abdominal subcutaneous ISF concentrations (measured using microdialysis) and plasma samples were collected at regular time points after administration of cefazolin 2 g intravenously. Total and unbound cefazolin concentrations were assayed and then modeled using Pmetrics. Monte Carlo dosing simulations (n = 5,000) were used to define cefazolin dosing regimens able to achieve a fractional target attainment (FTA) of >95% in the ISF suitable for the MIC for Staphylococcus aureus in isolates of ≤2 mg · L-1 and for a surgical duration of 4 h. Fourteen patients were included, with a mean (standard deviation [SD]) bodyweight of 148 (35) kg and body mass index (BMI) of 48 kg · m-2. Cefazolin protein binding ranged from 14 to 36% with variable penetration into ISF of 58% ± 56%. Cefazolin was best described as a four-compartment model including nonlinear protein binding. The mean central volume of distribution in the final model was 18.2 (SD 3.31) L, and the mean clearance was 32.4 (SD 20.2) L · h-1. A standard 2-g dose achieved an FTA of >95% for all patients with BMIs ranging from 36 to 69 kg · m-2. A 2-g prophylactic cefazolin dose achieves appropriate unbound plasma and ISF concentrations in obese and morbidly obese bariatric surgery patients.

Developing an adaptive management approach to cowbird control on the Santa Clara River, California

AbstractBrood parasitism by the brown‐headed cowbird (Molothrus ater) has caused population declines for conservation‐reliant songbird species such as the federally and state endangered subspecies least Bell's vireo (Vireo bellii pusillus). Although cowbird trapping has increased vireo populations, it is costly, and may prevent the development of parasitism‐avoidance behaviors and result in high rates of non‐target species captures. Therefore, wildlife managers have a compelling interest in evaluating multiple means of cowbird control. We conducted a study between 2016 and 2018 on the Santa Clara River (SCR) in Ventura County, California, USA, to test how the removal of cowbird traps would affect cowbird parasitism of the vireo. At our control site, cowbird trapping occurred in spring using modified Australian crow (Corvus spp.) traps. At our treatment site, we stopped this method of trapping and instead used target‐netting of individual cowbirds and a very short duration trap to capture specific individual cowbirds (i.e., contingency trapping). We also tested the impact of shortening the cowbird trapping period on nest parasitism rates, and used point counts to compare cowbird densities between sites. Additionally, we compared the costs of these techniques. A shorter trapping period still resulted in a large number of cowbird captures on the control site (n = 452 captures) with no observed brood parasitism (n = 67 nests). On the treatment site, cowbird parasitism rates varied from 0% to 14% (n = 75 broods). The target‐netting method was not effective for capturing female cowbirds, probably because of their low densities. The short‐term contingency trapping method effectively removed female cowbirds in the vicinity of vulnerable vireo nests. Cowbird traps captured &gt;300 individuals of 9 different non‐target species each year on the control site, whereas target‐netting and contingency trapping resulted in only 8 captures of 4 different non‐target species. Costs of continuous trapping for 2 months versus point counts, nest monitoring, and contingency trapping were $21,100.00 versus $16,996.00, respectively. Based on these findings, we recommend that an adaptive cowbird management program to benefit songbird populations should consider using regular point counts and nest monitoring to provide data on cowbird impacts, in lieu of continued intensive trapping without monitoring. Thresholds for the density of cowbird females and the allowable level of parasitism for host species should also be established to guide an adaptive cowbird management program. Short‐term contingency trapping based on the thresholds should be considered, but restoration of native vegetation, especially in southwestern riparian areas, is also crucial and effective at limiting parasitism, and so should strongly be considered. Lastly, large numbers of non‐target species captures in cowbird traps are probably having consequential impacts to these species, and need to be monitored and minimized.

Spectral Analysis Near Regular Point of Reducibility and Representations of Coxeter Groups

Spectral Analysis Near Regular Point of Reducibility and Representations of Coxeter Groups