Local Limit Research Articles

Size convergence of the E×B staircase pattern in flux tube simulations of ion temperature gradient-driven turbulence

The radial size convergence of the E×B staircase pattern is addressed in local gradient-driven flux tube simulations of ion temperature gradient (ITG)-driven turbulence. It is shown that a mesoscale pattern size of ∼57–76 ρ is inherent to ITG-driven turbulence with Cyclone Base Case parameters in the local limit.

Current clinical and research practices on frontotemporal dementia in Brazil: a national survey.

Frontotemporal dementia (FTD) is a frequent cause of young-onset dementia and represents a major challenge for the diagnosis and clinical management. It is essential to evaluate the difficulties faced by physicians on the diagnostic workup and on patient care. The aim of this study was to investigate the current practices and the local limits on the diagnosis and management of FTD in Brazil. We elaborated an online survey, composed of 29 questions and divided in four parts, comprising questions about existing health facilities, clinical practices related to FTD, and suggestions to increment the national research on FTD. The invitation to participate was sent by email to all neurologists affiliated to the Brazilian Academy of Neurology (n = 3658), and to all physicians who attended the XII Meeting of Researchers on Alzheimer's disease, in 2019 (n = 187). The invitation was also diffused through social media. 256 Brazilian physicians answered the questionnaire. The three most relevant disorders for the differential diagnosis of FTD were Alzheimer's disease (AD) (n = 211), bipolar disorder (n = 117) and dementia with Lewy bodies (n = 92). Most respondents (125/256) reported the difficulty in performing genetic testing as the main limit in the diagnostic of FTD. 93% and 63% of participants considered that the assessment of social cognition and AD CSF biomarkers are useful for the diagnosis of FTD, respectively. The present study may provide valuable insights for the medical education and clinical training of physicians, and to foster future research on FTD in Brazil.

Presence of Primary Care Physicians and Patients' Ability to Register: A Simulated-Patient Survey in the Paris Region.

Using the health care system fully in some countries requires patients to register with a primary care physician (PCP). Public health policies measure PCP density to maintain satisfactory local PCP supplies and limit geographic inequalities. In an exhaustive simulated-patient survey in the Paris, France region, we analyzed how well presence of PCPs was associated with patients' ability to register for care. Of 5,188 census blocks, 55.4% had at least 1 PCP; however, only 38.6% had at least 1 PCP accepting registration for office visits, and only 19.4% had at least 1 PCP accepting registration for home visits (P <.001 across the 3 indicators). Cross-block inequalities in accepting registration were steeper than those related to PCP density, indicating that this density metric offers false reassurance and is inadequate to support policy decisions.

Local limit laws for symbol statistics in bicomponent rational models

We study the local limit distribution of the number of occurrences of a symbol in words of length n generated at random in a regular language according to a rational stochastic model. We present an analysis of the main local limits when the finite state automaton defining the stochastic model consists of two primitive components. The limit distributions depend on several parameters and conditions, such as the main constants of mean value and variance of our statistics associated with the two components, and the existence of communications from the first to the second component. The convergence rate of these results is always of order O(n−1/2). For the same statistics we also prove an analogous O(n−1/2) convergence rate of the Gaussian local limit law whenever the stochastic model consists of one primitive component.

An Asymptotically Compatible Coupling Formulation for Nonlocal Interface Problems with Jumps

We introduce a mathematically rigorous formulation for a nonlocal interface problem with jumps and propose an asymptotically compatible finite element discretization for the weak form of the interface problem. After proving the well-posedness of the weak form, we demonstrate that solutions to the nonlocal interface problem converge to the corresponding local counterpart when the nonlocal data are appropriately prescribed. Several numerical tests in one and two dimensions show the applicability of our technique, its numerical convergence to exact nonlocal solutions, its convergence to the local limit when the horizons vanish, and its robustness with respect to the patch test.

Comparison of water use efficiency of sand-binding species along revegetation chronosequence in an alpine desert

Afforestation is an effective measure for ecological restoration in the desert ecosystem. The long-term water use efficiency (WUE) of leaves is an important indicator for evaluating the water adaptation strategy of sand-fixing species. However, the WUE of typical sand-fixing plants in the alpine desert and its responses to local climatic, micro-geomorphology, environmental conditions and nutrient limitations are still unclear. In this study, sand-fixing vegetation community along a revegetation chronosequence (Hippophae rhammoides planted on dunes in 1987, 2008, and 2015, respectively. H. rhammoides with the longest recovery period were defined as mature plantations, and the shortest recovery period were defined as juveniles.) at the alpine desert at the eastern shore of the Qinghai Lake were used as the research plots. Stable carbon isotope was used to evaluate species WUE. The results showed that: (1) the δ13C values of H. rhammoides showed a decreasing trend as plants grew. The seasonal δ13C variation was mainly affected by average relative humidity (MRH). (2) The δ13C in the dunes revegetated in 2008 and 2015 were significantly higher than that in 1987 at the windward slope (P < 0.05). The values of δ13C had various responses to the available soil water under the influence of topography, and soil water content was the key factor for the WUE of individuals in communities. There was a significant negative correlation between the ratio of carbon and nitrogen content in H. rhammoides leaves and WUE. The research indicated that mature plantations had adopted a more stable water use pattern than the juveniles, which provide an effective insight for ecological restoration in fragile ecological regions.

Bronchoscopic instillation of amphotericin B is a safe and effective measure to treat pulmonary mycosis.

Background and objectives: In recent years, there has been a significant increase in the prevalence of pulmonary mycosis disease, and its mortality has increased. There are very few studies on treating pulmonary mycosiss with bronchoscopic instillation of amphotericin B. This study investigated the clinical efficacy and safety of bronchoscopic instillation of amphotericin B for treating pulmonary mycosiss. Methods: This was a multi-centre, retrospective clinical study of 80 patients with pulmonary mycosiss who were treated with bronchoscopic instillation of amphotericin B. The efficacy and safety of this treatment were evaluated. Results: Eighty patients were included {51 males; mean [standard deviation (SD)] age, 46 (15.9) years}. The most common underlying cause was haematological malignancy (73.75%). The mean number of bronchoscopic instillations of amphotericin B was 2.4 (SD 1.5). In terms of treatment success, 58 (72.5%) patients achieved complete or partial changes on imaging after treatment. A total of 62 (77.5%) patients achieved complete or partial changes on imaging and/or local limitation of the mycosis infection. Seventy-six (95%) patients achieved complete or partial changes on imaging and/or local limitation of mycosis infection and/or an immunotherapy time window. The efficacy rates for treatment of Aspergillus and Mucor infections in terms of the three treatment success criteria described above were 73.81% vs. 63.64%, 80.95% vs. 72.73%, and 92.86% vs. 90.91%, respectively. Conclusion: Bronchoscopic instillation of amphotericin B is safe and effective for treatment of pulmonary mycosiss.

Scaling of the Clustering Function in Spatial Inhomogeneous Random Graphs

We consider an infinite spatial inhomogeneous random graph model with an integrable connection kernel that interpolates nicely between existing spatial random graph models. Key examples are versions of the weight-dependent random connection model, the infinite geometric inhomogeneous random graph, and the age-based random connection model. These infinite models arise as the local limit of the corresponding finite models. For these models we identify the asymptotics of the local clustering as a function of the degree of the root in different regimes in a unified way. We show that the scaling exhibits phase transitions as the interpolation parameter moves across different regimes. This allows us to draw conclusions on the geometry of a typical triangle contributing to the clustering in the different regimes.

Local limit theorems for collective risk models

A probability model known as the collective risk model is used to describe the total claim from a portfolio of insurance contracts. It is essential to non-life insurance. Let N represent the number of claims and X1,X2,… represent the amount of loss in each claim where Xj′s are independent and identically distributed. For the collective risk model, the total claim is given by SN=X1+X2+⋯+XN. Local limit theorems estimate the probability at a particular point P(SN=k). In this paper, we provide local limit theorems for SN, where N is a random variable with a binomial, Poisson and negative binomial distribution. Our results give a better rate of convergence than Berry–Esseen’s Theorem. Explicit constants of the error bounds are also given.

Coordination and divergence in community assembly processes across co-occurring microbial groups separated by cell size.

Setting the pace of life and constraining the role of members in food webs, body size can affect the structure and dynamics of communities across multiple scales of biological organization (e.g., from the individual to the ecosystem). However, its effects on shaping microbial communities, as well as underlying assembly processes, remain poorly known. Here, we analyzed microbial diversity in the largest urban lake in China and disentangled the ecological processes governing microbial eukaryotes and prokaryotes using 16S and 18S amplicon sequencing. We found that pico/nano-eukaryotes (0.22-20 μm) and micro-eukaryotes (20-200 μm) showed significant differences in terms of both community composition and assembly processes even though they were characterized by similar phylotype diversity. We also found scale dependencies whereby micro-eukaryotes were strongly governed by environmental selection at the local scale and dispersal limitation at the regional scale. Interestingly, it was the micro-eukaryotes, rather than the pico/nano-eukaryotes, that shared similar distribution and community assembly patterns with the prokaryotes. This indicated that assembly processes of eukaryotes may be coupled or decoupled from prokaryotes' assembly processes based on eukaryote cell size. While the results support the important influence of cell size, there may be other factors leading to different levels of assembly process coupling across size classes. Additional studies are needed to quantitatively parse the influence of cell size versus other factors as drivers of coordinated and divergent community assembly processes across microbial groups. Regardless of the governing mechanisms, our results show that there are clear patterns in how assembly processes are coupled across sub-communities defined by cell size. These size-structured patterns could be used to help predict shifts in microbial food webs in response to future disturbance.

Explicit conditions for the CLT and related results for non-uniformly partially expanding random dynamical systems via effective RPF rates

The purpose of this paper is to provide a first class of explicit sufficient conditions for the central limit theorem and related results in the setup of non-uniformly (partially) expanding non iid random transformations, considered as stochastic processes together with some random Gibbs measure. More precisely, we prove a central limit theorem (CLT), an almost sure invariance principle, a moderate deviations principle, Berry-Esseen type estimates and a moderate local central limit theorem for random Birkhoff sums generated by a non-uniformly partially expanding dynamical systems Tω and a random Gibbs measure μω, corresponding to a random potential ϕω with a sufficiently regular variation. In the partially expanding case the maps we consider are similar to the ones in [44], with the exception that the amount of expansion dominates the amount of contraction fiberwise and not only on the average, and with an additional regularity condition on a certain type of local variation of ϕω along inverse branches of Tω. A notable example when the maps are truly partially-expanding is the case when ϕω≡0 which corresponds to random measures of maximal entropy μω, but any potential with a sufficiently small (fiberwise) variation can be considered. Our results in the partially expanding case are new even in the uniformly random case, where all the random variables describing the maps are uniformly controlled. For properly expanding maps (as in [42,33]), the above local regularity condition allows applications also in the smooth case where the Gibbs measure is absolutely continuous with respect to the underlying volume measure and ϕω=−ln⁡JTω. For instance, we can consider certain fiberwise piecewise C2-perturbations of piecewise linear or affine maps. All of the above is achieved by first proving random, real and complex, Ruelle-Perron-Frobenius (RPF) theorems with rates that can be expressed analytically by means of certain random parameters that describe the maps (such rates will be referred to as “effective”). Using these effective rates, our conditions for the limit theorems involve some weak type of upper mixing conditions on the driving system (base map) and some integrability conditions on the norm of the random function generating the Birkhoff sums. A big part of the proof of the moderate deviations, the Berry-Esseen type estimates and the local CLT is to show how Rugh's theory [43] of complex cones contractions applies to the cones considered in [16] (and their random versions in [44]), which is new even for deterministic dynamical systems T, and in that case it yields explicit estimates on the spectral gap of appropriate deterministic complex perturbations of the transfer operator of T, as well as explicit constants in the corresponding Berry-Esseen theorem for deterministic partially expanding dynamical systems.

The Extent of the Application of English Laws in the Cameroonian Legal System

The decisive events which made the introduction of English laws possible in Cameroon were the arrival of European traders, the activities of European missionaries and the introduction of the English legal system by the British Government. The arrival of these Europeans introduced certain new practices and institutions which the traditional laws of the country, particularly customary law could not cope with. Besides, the Europeans themselves were not prepared to be bound by tribal laws since the type of society to which the law and custom was appropriate was totally different from the type of society in which they (Europeans) had been brought up. After the 1st World War, Cameroon ceased to be a German Protectorate following her defeat and was thus administered by Great Britain and France under the League of Nations Mandate and subsequently under the United Nations Trusteeship Agreement. By Article 9 of the Mandate Agreement, the laws of the administering authorities were to be transplanted into Cameroon. Article 9 thus provided the basis and officially marked the beginning of the duality of Western legal systems which the people of Cameroon have since experienced and to which they remain subject to till this day. The Foreign Jurisdiction Act, 1890 was also very important and served as the enabling statute that led to the introduction and observance of English law in Southern Cameroons. The English common law, the doctrines of equity and the statutes of general application which were in force in England on the 1st day of January 1900 were then transplanted in Anglophone Cameroon viz s. 11 of the Southern Cameroons High Court Law, 1955. However, neither the statutes in England on the 1st day of January 1900, nor common law and the doctrines of equity apply in Cameroon without limitations. They are subject to local limits and circumstances. In this 21st Century, the laws of a colonial power particularly the statutes of general application should not apply again to an independent nation like Cameroon and thus should be repealed and replaced with local legislation. The Executive and Legislature should thus ensure compliance while the Government is called upon to hasten and complete the harmonization process of the common law and the civil law in a bid to give the country a unified/uniform legal system.

Local Group dwarf galaxy detection limit in the CSST survey

ABSTRACT We predict the dwarf galaxy detection limits for the upcoming Chinese Space Station Telescope (CSST) survey that will cover 17 500 ${\rm \, deg}^{2}$ of the sky with a wide field of view of 1.1 deg2. The point-source depth reaches 26.3 mag in the g band and 25.9 mag in the i band. Constructing mock survey data based on the designed photometric bands, we estimate the recovery rate of artificial dwarf galaxies from mock point-source photometric catalogues. The detection of these artificial dwarf galaxies is strongly dependent on their distance, magnitude, and size, in agreement with searches in current surveys. We expect CSST to enable the detection of dwarf galaxies with MV = −3.0 and μ250 = 32.0 mag arcsec−2 (surface brightness limit for a system of half-light radius rh = 250 ${\rm \, pc}$) at $400 {\rm \, kpc}$, and MV = −4.9 and μ250 = 30.5 mag arcsec−2 around the Andromeda galaxy. Beyond the Local Group, the CSST survey will achieve MV = −5.8, and μ250 = 29.7 mag arcsec−2 in the distance range of 1–2 Mpc, opening up an exciting discovery space for faint field dwarf galaxies. With its optical bands, wide survey footprint, and space resolution, CSST will undoubtedly expand our knowledge of low-mass dwarf galaxies to an unprecedented volume.

Asymptotic expansions in the local limit theorem for a branching Wiener process

Consider a supercritical branching Wiener process in Rd. Let Zn(A) be the number of the nth generation particles located in a given set A⊂Rd. Under the moment condition of EX(lnX)1+λ type, the complete asymptotic expansions of Zn(A) as n tends to infinity are obtained. This result gives an alternative version of the work by Révész, Rosen and Shi (2005), hence generalizing theirs by weakening the second moment condition therein.

Push the Limit of Millimeter-wave Radar Localization

Existing device-free localization systems have achieved centimeter-level accuracy and show their potential in a wide range of applications. However, today’s radio-based solutions fail to locate the target in millimeter-level due to their limited bandwidth and sampling rate, which constrains their applications in high-accuracy demand scenarios. We find an opportunity to break the bottleneck of existing radio-based localization systems by reconstructing the accurate signal spectral peak from the discrete samples, without changing either the bandwidth or the sampling rate of the radio hardware. This study proposes milliLoc , a millimeter-level radio-based localization system. We first derive a spectral peak reconstruction algorithm to reduce the ranging error from the previous centimeter-level to millimeter-level. Then, we improve the AoA measurement accuracy by leveraging the signal amplitude information. To ensure the practicality of milliLoc , we further extend our system to handle multi-target situations. We fully implement milliLoc on a commercial mmWave radar. Experiments show that milliLoc achieves a median ranging accuracy of 5.5 mm and decreases the AoA measurement error by 31.2% compared with the baseline. Our system fulfills the accuracy requirements of most application scenarios and can be easily integrated with other existing solutions, shedding light on high-accuracy location-based applications.

Impact of Metal Accumulation on Photosynthetic Pigments, Carbon Assimilation, and Oxidative Metabolism in Mangroves Affected by the Fundāo Dam Tailings Plume

The effects of iron, manganese, zinc, copper, and lead on the chlorophyll content, carbon assimilation, and the antiradical activity of Rhizophora mangle and Laguncularia racemosa were evaluated in regions affected by the Fundão dam disruption in Brazil. The mine waste which settled and accumulated in the sediments could represent long-term contamination. It can be expected that the iron oxyhydroxides deposited in the sediments will be solubilized, leading to chronic contamination by trace metals and the accumulation of these metals in the biota. In this sense, biological indicators prove to be important tools to assess this type of damage. The different bioaccumulation of metals by the species revealed that R. mangle was more impacted by Mn and Cu and that L. racemosa showed alterations in its physiological responses in the presence of Cu, Zn, and Fe. The concentration of these metals in the leaves, with values above previous local reference limits, was associated with reductions in the chlorophyll-a and chlorophyll-b content and carbon assimilation, mainly in L. racemosa. The antiradical activity was also altered, suggesting a lower ability of both species to eliminate reactive oxygen species (ROS). A possible reason for the symptoms of oxidative stress may be due to the reduced efficiency of antioxidant defense by Cu2+ and Zn2+. In addition, the presence of Pb in the leaf tissue may be toxic to the fauna and the bioaccumulation of this metal and trace elements can be a way to transfer them into the food web by biomagnification.

Local limits of spatial inhomogeneous random graphs

AbstractConsider a set of n vertices, where each vertex has a location in $\mathbb{R}^d$ that is sampled uniformly from the unit cube in $\mathbb{R}^d$ , and a weight associated to it. Construct a random graph by placing edges independently for each vertex pair with a probability that is a function of the distance between the locations and the vertex weights.Under appropriate integrability assumptions on the edge probabilities that imply sparseness of the model, after appropriately blowing up the locations, we prove that the local limit of this random graph sequence is the (countably) infinite random graph on $\mathbb{R}^d$ with vertex locations given by a homogeneous Poisson point process, having weights which are independent and identically distributed copies of limiting vertex weights. Our set-up covers many sparse geometric random graph models from the literature, including geometric inhomogeneous random graphs (GIRGs), hyperbolic random graphs, continuum scale-free percolation, and weight-dependent random connection models.We prove that the limiting degree distribution is mixed Poisson and the typical degree sequence is uniformly integrable, and we obtain convergence results on various measures of clustering in our graphs as a consequence of local convergence. Finally, as a byproduct of our argument, we prove a doubly logarithmic lower bound on typical distances in this general setting.

Scale-up analysis of a twin-bed PSA pilot plant

Small-scale pressure swing adsorption (PSA) plants, also referred to as pilot plants, are commonly exploited for studying separation processes in favour of the development of mathematical models and scale-up strategies. The applicability of a lately presented mathematical model, which was developed based on experimental data acquired from a high-purity twin-bed N2-PSA pilot plant, is verified in this paper for the design of large-scale systems by an analysis of the mass transfer zone development at different PSA cycle times. Effects of the PSA scale-up factor, adsorber aspect ratio, packed-bed density, and flow resistances along the piping system on the process performance are studied numerically. These considerations are particularly relevant for the scale-up of bank-type PSA units as well as for skid-mounted systems fitted to local space limitations, where the standard scale-up concept of keeping the gas velocity constant often cannot be fully realised. It is demonstrated that the sensitivity of the PSA performance to studied factors increases along with the required product purity level. Therefore, recommendations for adequate dimensions of pilot plants depending on the desired gas purity level can be derived. Limitations of the gas velocity through the adsorber shall be observed to generate reliable simulation data. The agreement between experimental results obtained from an industrial-scale system on one hand, and the outcome of a dynamic simulation on the other hand, is confirmed—provided that realistic pressure profiles are generated by a proper adjustment of flow resistances along the piping.

The local limit theorem for general weighted sums of Bernoulli random variables

The local limit theorem (LLT) is one of the well-known limit theorems which can be used to estimate the probability at a particular point of a random variable. In this paper, we generalize weighted sums which are introduced by Giuliano and Weber and give the LLT with explicit error bounds.

Richter’s local limit theorem, its refinement, and related results*

We give a detailed exposition of the proof of Richter’s local limit theorem in a refined form and establish the stability of the remainder term in this theorem under small perturbations of the underlying distribution (including smoothing).We also discuss related quantitative bounds for characteristic functions and Laplace transforms.