scholarly journals Limit theorems for hitting times of 1-dimensional generalized diffusions

1998 ◽  
Vol 152 ◽  
pp. 1-37
Author(s):  
Matsuyo Tomisaki ◽  
Makoto Yamazato
Keyword(s):  
Limit Theorems ◽  
Bessel Functions ◽  
Diffusion Processes ◽  
Hitting Times ◽  
Finite Dimensional ◽  
Independent Increments ◽  
Starting Point ◽  
Self Similar ◽  
The Mean ◽  
The One

Abstract.Limit theorems are obtained for suitably normalized hitting times of single points for 1-dimensional generalized diffusion processes as the hitting points tend to boundaries under an assumption which is slightly stronger than that the existence of limits γ + 1 of the ratio of the mean and the variance of the hitting time. Laplace transforms of limit distributions are modifications of Bessel functions. Results are classified by the one parameter {γ}, each of which is the degree of corresponding Bessel function. In case the limit distribution is degenerate to one point, by changing the normalization, we obtain convergence to the normal distribution. Regarding the starting point as a time parameter, we obtain convergence in finite dimensional distributions to self-similar processes with independent increments under slightly stronger assumption.

scholarly journals Limit theorems related to a class of operator-self-similar processes

1996 ◽  
Vol 142 ◽  
pp. 161-181 ◽  
Author(s):  
Makoto Maejima
Keyword(s):  
Stochastic Process ◽  
Linear Operator ◽  
Limit Theorems ◽  
Finite Dimensional ◽  
Self Similar

An Rd-valued (d ≥ 1) stochastic process X = {X(t)}t≥0 is said to be operator-self-similar if there exists a linear operator D on Rd such that for each c > 0where means the equality for all finite-dimensional distributions and

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

Evaluation of Road Utilisation as Space For Holding Social Ceremonies in Indigenous Residential Area of Ogbomoso, Nigeria

2018 ◽  
Vol 1 (March 2018) ◽  
Author(s):  
S.A Okanlawon ◽  
O.O Odunjo ◽  
S.A Olaniyan
Keyword(s):  
Transport Infrastructure ◽  
Noisy Environment ◽  
Policy Makers ◽  
The Core ◽  
Local Roads ◽  
Strict Enforcement ◽  
The Mean ◽  
The One ◽  
The City ◽  
The Town

This study examined Residents’ evaluation of turning transport infrastructure (road) to spaces for holding social ceremonies in the indigenous residential zone of Ogbomoso, Oyo State, Nigeria. Upon stratifying the city into the three identifiable zones, the core, otherwise known as the indigenous residential zone was isolated for study. Of the twenty (20) political wards in the two local government areas of the town, fifteen (15) wards that were located in the indigenous zone constituted the study area. Respondents were selected along one out of every three (33.3%) of the Trunk — C (local) roads being the one mostly used for the purpose in the study area. The respondents were the residents, commercial motorists, commercial motorcyclists, and celebrants. Six hundred and forty-two (642) copies of questionnaire were administered and harvested on the spot. The Mean Analysis generated from the respondents’ rating of twelve perceived hazards listed in the questionnaire were then used to determine respondents’ most highly rated perceived consequences of the practice. These were noisy environment, Blockage of drainage by waste, and Endangering the life of the sick on the way to hospital; the most highly rated reasons why the practice came into being; and level of acceptability of the practice which was found to be very unacceptable in the study area. Policy makers should therefore focus their attention on strict enforcement of the law prohibiting the practice in order to ensure more cordial relationship among the citizenry, seeing citizens’ unacceptability of the practice in the study area.

Descriptive statistics

2017 ◽  
Author(s):  
Andrew Gelman ◽  
Deborah Nolan
Keyword(s):  
Descriptive Statistics ◽  
Metabolic Rates ◽  
World Record ◽  
Linear Combinations ◽  
Record Times ◽  
Starting Point ◽  
Statistics Course ◽  
Scatter Plots ◽  
Economic Indexes ◽  
The Mean

Descriptive statistics is the typical starting point for a statistics course, and it can be tricky to teach because the material is more difficult than it first appears. The activities in this chapter focus more on the topics of data displays and transformations, rather than the mean, median, and standard deviation, which are covered easily in a textbook and on homework assignments. Specific topics include: distributions and handedness scores; extrapolation of time series and world record times for the mile run; linear combinations and economic indexes; scatter plots and exam scores; and logarithmic transformations and metabolic rates.

scholarly journals SAT0267 ROLE OF AGGRESSIVE IMMUNOSUPPRESSION ON SUBGLOTTIC STENOSIS IN GRANULOMATOSIS WITH POLYANGIITIS: RETROSPECTIVE ANALYSIS OF A MONOCENTRIC COHORT

2020 ◽  
Vol 79 (Suppl 1) ◽  
pp. 1076.1-1077
Author(s):  
L. Moroni ◽  
L. Giudice ◽  
G. A. Ramirez ◽  
S. Sartorelli ◽  
A. Cariddi ◽  
...  
Keyword(s):  
Medical Treatment ◽  
Clinical Characteristics ◽  
Granulomatosis With Polyangiitis ◽  
Balloon Catheter ◽  
Subglottic Stenosis ◽  
Damage Accrual ◽  
The Mean ◽  
The One

Background:Subglottic stenosis (SGS) is defined as airway narrowing below the vocal cords and is a common and potentially life-threatening manifestation of Granulomatosis with Polyangiitis (GPA), with an estimated prevalence of 16-23% (1). Balloon catheter dilation is effective in GPA-related SGS, but relapses are frequent. Little is known about the role of immunosuppression in this setting.Objectives:to analyse the clinical characteristics of a monocentric GPA cohort, describe phenotype differences among patients with and without SGS and investigate the role of surgical and medical treatments on relapse risk and general outcome.Methods:Biopsy-proven patients with SGS were identified by review of medical charts among a cohort of patients with GPA, classified according to the algorithm of the European Medicine Agency (2). The clinical characteristics of patients with SGS were retrospectively collected over a median follow-up time of 15.9 years and compared to those of patients without SGS.Results:Fourteen patients with SGS-GPA were identified, with a female to male ratio of 1:1 and a prevalence of 29.2% among the cohort. The mean ± SD age at GPA onset was 30.8 ± 14.4 years, with a mean time from GPA diagnosis to SGS onset of 4.7 ± 4.2 years. ANCA were positive in 78.6% (54.0% anti-PR3, 18.1% anti-MPO and 27.9% IFI only). The mean Birmingham Vasculitis Activity Score (BVAS) at onset was 10.0 ± 5.6. The main clinical manifestations associated with SGS were crusty rhinitis (100%), sinusitis (78%), pulmonary disease (72.7%), otitis/mastoiditis (50%), glomerulonephritis (42.9%), orbital pseudotumor (28.6%). Six patients (42.9%) received medical treatment only, other six (42.9%) had one to three balloon dilations and two (14.2%) underwent four or more procedures. Eight patients had no SGS relapse (maximum one dilation) and they all received immunosuppression with rituximab (RTX), cyclophosphamide (CYC) or azathioprine (AZA). All patients who received no immunosuppression, methotrexate (MTX) or mycophenolate (MMF) had at least one relapse. Patients treated with MTX or MMF had a mean relapse-free survival of 13.1 months, which was comparable to the one of patients not receiving medical treatment (40.2 months; p=NS) and shorter than the one of patients receiving CYC or RTX (153.2 months; p=0.032). CYC use also inversely correlated with the number of surgical procedures (r=-0.691, p=0.006). Compared to patients without SGS (31 consecutive patients with at least 4 years of follow-up), patients with SGS-GPA had an earlier disease onset (mean age 30.8 vs 50.4 years; p<0.001), but with lower BVAS (mean 10.0 vs 15.3; p=0.013) and showed a higher prevalence of crusty rhinitis (100% vs 67.7%; p=0.019). No difference was observed in damage accrual over time between the two groups.Conclusion:Subglottic stenosis is highly prevalent in patients with GPA and may define a milder disease subset occurring more frequently in younger patients. MTX and MMF might be insufficient to prevent SGS relapses requiring balloon dilation. Aggressive immunosuppression (CYC or RTX) might have a non-redundant role in this setting and reduce the risk of relapses.References:[1]Quinn KA, et al. Subglottic stenosis and endobronchial disease in granulomatosis with polyangiitis. Rheumatology 2019; 58 (12), 2203-2211.[2]Watts R, et al. Development and validation of a consensus methodology for the classification of the ANCA associated vasculitides and polyarteritis nodosa for epidemiological studies. Ann Rheum Dis 2007; 66: 222-7.Disclosure of Interests:Luca Moroni: None declared, Laura Giudice: None declared, Giuseppe Alvise Ramirez: None declared, Silvia Sartorelli: None declared, adriana cariddi: None declared, Angelo Carretta: None declared, Enrica Bozzolo: None declared, Lorenzo Dagna Grant/research support from: The Unit of Immunology, Rheumatology, Allergy and Rare Diseases (UnIRAR) received unresctricted research/educational grants from Abbvie, Bristol-Myers Squibb, Celgene, Janssen, Merk Sharp & Dohme, Mundipharma Pharmaceuticals, Novartis, Pfizer, Roche, Sanofi-Genzyme, and SOBI., Consultant of: Prof Lorenzo Dagna received consultation honoraria from Abbvie, Amgen, Biogen, Bristol-Myers Squibb, Celltrion, Novartis, Pfizer, Roche, Sanofi-Genzyme, and SOBI.

scholarly journals Practices of sustainability and the enactment of their natures/cultures: Ecosystem services, rights of nature, and geoengineering

2021 ◽  
pp. 053901842199894
Author(s):  
Frank Adloff ◽  
Iris Hilbrich
Keyword(s):  
Ecosystem Services ◽  
Latin American ◽  
Social Systems ◽  
The Earth ◽  
Starting Point ◽  
Knowledge Cultures ◽  
Rights Of Nature ◽  
Value Of Nature ◽  
The One ◽  
And Control

Possible trajectories of sustainability are based on different concepts of nature. The article starts out from three trajectories of sustainability (modernization, transformation and control) and reconstructs one characteristic practice for each path with its specific conceptions of nature. The notion that nature provides human societies with relevant ecosystem services is typical of the path of modernization. Nature is reified and monetarized here, with regard to its utility for human societies. Practices of transformation, in contrast, emphasize the intrinsic ethical value of nature. This becomes particularly apparent in discourses on the rights of nature, whose starting point can be found in Latin American indigenous discourses, among others. Control practices such as geoengineering are based on earth-systemic conceptions of nature, in which no distinction is made between natural and social systems. The aim is to control the earth system as a whole in order for human societies to remain viable. Practices of sustainability thus show different ontological understandings of nature (dualistic or monistic) on the one hand and (implicit) ethics and sacralizations (anthropocentric or biocentric) on the other. The three reconstructed natures/cultures have different ontological and ethical affinities and conflict with each other. They are linked to very different knowledge cultures and life-worlds, which answer very differently to the question of what is of value in a society and in nature and how these values ought to be protected.

scholarly journals Representations of hermite processes using local time of intersecting stationary stable regenerative sets

2020 ◽  
Vol 57 (4) ◽  
pp. 1234-1251
Author(s):  
Shuyang Bai
Keyword(s):  
Long Range ◽  
Local Time ◽  
Limit Theorems ◽  
Local Times ◽  
Long Range Dependence ◽  
Random Interval ◽  
Stationary Increments ◽  
Self Similar ◽  
Regenerative Sets

AbstractHermite processes are a class of self-similar processes with stationary increments. They often arise in limit theorems under long-range dependence. We derive new representations of Hermite processes with multiple Wiener–Itô integrals, whose integrands involve the local time of intersecting stationary stable regenerative sets. The proof relies on an approximation of regenerative sets and local times based on a scheme of random interval covering.

scholarly journals Two-term expansion of the ground state one-body density matrix of a mean-field Bose gas

2021 ◽  
Vol 60 (3) ◽  
Author(s):  
Phan Thành Nam ◽  
Marcin Napiórkowski
Keyword(s):  
Density Matrix ◽  
Ground State ◽  
Mean Field ◽  
Interaction Strength ◽  
Bose Gas ◽  
Body Density ◽  
The Mean ◽  
The One ◽  
Mean Field Regime ◽  
Number Of Particles

AbstractWe consider the homogeneous Bose gas on a unit torus in the mean-field regime when the interaction strength is proportional to the inverse of the particle number. In the limit when the number of particles becomes large, we derive a two-term expansion of the one-body density matrix of the ground state. The proof is based on a cubic correction to Bogoliubov’s approximation of the ground state energy and the ground state.

scholarly journals Acute bilateral foot drop with or without cauda equina syndrome—a case series

2021 ◽  
Vol 163 (4) ◽  
pp. 1191-1198
Author(s):  
Andreas K. Demetriades ◽  
Marco Mancuso-Marcello ◽  
Asfand Baig Mirza ◽  
Joseph Frantzias ◽  
David A. Bell ◽  
...  
Keyword(s):  
Cauda Equina Syndrome ◽  
Cauda Equina ◽  
Case Series ◽  
Foot Drop ◽  
Spinal Disease ◽  
Full Resolution ◽  
Degenerative Spinal Disease ◽  
The Mean ◽  
The One

Abstract Introduction Isolated acute bilateral foot drop due to degenerative spine disease is an extremely rare neurosurgical presentation, whilst the literature is rich with accounts of chronic bilateral foot drop occurring as a sequela of systemic illnesses. We present, to our knowledge, the largest case series of acute bilateral foot drop, with trauma and relevant systemic illness excluded. Methods Data from three different centres had been collected at the time of historic treatment, and records were subsequently reviewed retrospectively, documenting the clinical presentation, radiological level of compression, timing of surgery, and degree of neurological recovery. Results Seven patients are presented. The mean age at presentation was 52.1 years (range 41–66). All patients but one were male. All had a painful radiculopathic presentation. Relevant discopathy was observed from L2/3 to L5/S1, the commonest level being L3/4. Five were treated within 24 h of presentation, and two within 48 h. Three had concomitant cauda equina syndrome; of these, the first two made a full motor recovery, one by 6 weeks follow-up and the second on the same-day post-op evaluation. Overall, five out of seven cases had full resolution of their ankle dorsiflexion pareses. One patient with 1/5 power has not improved. Another with 1/5 weakness improved to normal on the one side and to 3/5 on the other. Conclusion When bilateral foot drop occurs acutely, we encourage the consideration of degenerative spinal disease. Relevant discopathy was observed from L2/3 to L5/S1; aberrant innervation may be at play. Cauda equina syndrome is not necessarily associated with acute bilateral foot drop. The prognosis seems to be pretty good with respect to recovery of the foot drop, especially if partial at presentation and if treated within 48 h.

scholarly journals Admixing Chaff with Straw Increased the Residues Collected without Compromising Machinery Efficiencies

Energies ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1766 ◽  
Author(s):  
Alessandro Suardi ◽  
Sergio Saia ◽  
Walter Stefanoni ◽  
Carina Gunnarsson ◽  
Martin Sundberg ◽  
...  
Keyword(s):  
Energy Production ◽  
Dry Weight ◽  
Global Scale ◽  
Unit Weight ◽  
Residual Biomass ◽  
Energy Needs ◽  
The Mean ◽  
Field Efficiency ◽  
The One ◽  
Staple Crop

The collection of residues from staple crop may contribute to meet EU regulations in renewable energy production without harming soil quality. At a global scale, chaff may have great potential to be used as a bioenergy source. However, chaff is not usually collected, and its loss can consist of up to one-fifth of the residual biomass harvestable. In the present work, a spreader able to manage the chaff (either spreading [SPR] on the soil aside to the straw swath or admixed [ADM] with the straw) at varying threshing conditions (with either 1 or 2 threshing rotors [1R and 2R, respectively] in the combine, which affects the mean length of the straw pieces). The fractions of the biomass available in field (grain, chaff, straw, and stubble) were measured, along with the performances of both grain harvesting and baling operations. Admixing chaff allowed for a slightly higher amount of straw fresh weight baled compared to SPR (+336 kg straw ha−1), but such result was not evident on a dry weight basis. At the one time, admixing chaff reduced the material capacity of the combine by 12.9%. Using 2R compared to 1R strongly reduced the length of the straw pieces, and increased the bale unit weight; however, it reduced the field efficiency of the grain harvesting operations by 11.9%. On average, the straw loss did not vary by the treatments applied and was 44% of the total residues available (computed excluding the stubble). In conclusion, admixing of chaff with straw is an option to increase the residues collected without compromising grain harvesting and straw baling efficiencies; in addition, it can reduce the energy needs for the bale logistics. According to the present data, improving the chaff collection can allow halving the loss of residues. However, further studies are needed to optimise both the chaff and the straw recoveries.

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