On the current enhancement at the edge of a crack in a lattice of resistors

1998 ◽  
Vol 30 (2) ◽  
pp. 342-364 ◽  
Author(s):  
Howard M. Taylor ◽  
Dennis E. Sweitzer
Keyword(s):  
Random Walk ◽  
Vertical Direction ◽  
Potential Gradient ◽  
Domain Of Attraction ◽  
Lattice Points ◽  
Fourier Methods ◽  
The North ◽  
The Mean ◽  
Mean Time ◽  
Cauchy Process

Consider a network whose nodes are the integer lattice points and whose arcs are fuses of 1Ω resistance. Remove a horizontal segment ofNadjacent vertical arcs, forming a ‘crack’ of lengthN. Subject the network to a uniform potential gradient ofvvolts per arc in the north-south (or vertical) direction and measure the current in one of the two vertical arcs at the ends of the crack. We write this current in the forme(N)v, and calle(N) thecurrent enhancement.We show that the enhancement grows at a rate that is the order of the square root of the crack length. Our method is to identify the enhancement with the mean time to exit an interval for a certain integer valued random walk, and then to use some of the well-known Fourier methods for studying random walk. Our random walk has no mean or higher moments and is in the domain of attraction of the Cauchy law. We provide a good approximation to the enhancement using the explicitly known mean time to exit an interval for a Cauchy process. Weak convergence arguments together with an estimate of a recurrence probability enable us to show that the current in an intact fuse, that is in the interior of a crack of lengthN, grows p roportionally withN/logN.

On the current enhancement at the edge of a crack in a lattice of resistors

1998 ◽  
Vol 30 (02) ◽  
pp. 342-364 ◽  
Author(s):  
Howard M. Taylor ◽  
Dennis E. Sweitzer
Keyword(s):  
Random Walk ◽  
Vertical Direction ◽  
Potential Gradient ◽  
Domain Of Attraction ◽  
Lattice Points ◽  
Fourier Methods ◽  
The North ◽  
The Mean ◽  
Mean Time ◽  
Cauchy Process

Consider a network whose nodes are the integer lattice points and whose arcs are fuses of 1Ω resistance. Remove a horizontal segment ofNadjacent vertical arcs, forming a ‘crack’ of lengthN. Subject the network to a uniform potential gradient ofvvolts per arc in the north-south (or vertical) direction and measure the current in one of the two vertical arcs at the ends of the crack. We write this current in the forme(N)v, and calle(N) thecurrent enhancement.We show that the enhancement grows at a rate that is the order of the square root of the crack length. Our method is to identify the enhancement with the mean time to exit an interval for a certain integer valued random walk, and then to use some of the well-known Fourier methods for studying random walk. Our random walk has no mean or higher moments and is in the domain of attraction of the Cauchy law. We provide a good approximation to the enhancement using the explicitly known mean time to exit an interval for a Cauchy process. Weak convergence arguments together with an estimate of a recurrence probability enable us to show that the current in an intact fuse, that is in the interior of a crack of lengthN, grows p roportionally withN/logN.

On the absorption probabilities and mean time for absorption for discrete Markov chains

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nikolaos Halidias
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Markov Chains ◽  
Generating Function ◽  
Discrete Time ◽  
Probability Generating Function ◽  
The Mean ◽  
Mean Time ◽  
Absorption Probabilities

Abstract In this note we study the probability and the mean time for absorption for discrete time Markov chains. In particular, we are interested in estimating the mean time for absorption when absorption is not certain and connect it with some other known results. Computing a suitable probability generating function, we are able to estimate the mean time for absorption when absorption is not certain giving some applications concerning the random walk. Furthermore, we investigate the probability for a Markov chain to reach a set A before reach B generalizing this result for a sequence of sets A 1 , A 2 , … , A k {A_{1},A_{2},\dots,A_{k}} .

Phocanema decipiens (Nematoda: Anisakinae): experimental infections in marine copepods

1982 ◽  
Vol 60 (4) ◽  
pp. 502-509 ◽  
Author(s):  
Gary McClelland
Keyword(s):  
Gravid Female ◽  
Mature Female ◽  
Cyclopoid Copepod ◽  
Calanoid Copepods ◽  
North West ◽  
The North ◽  
The Family ◽  
The Mean ◽  
Mean Time ◽  
Marine Copepods

Gravid female Phocanema decipiens were recovered from the stomachs of freshly killed harbour (Phoca vitulina) and grey seals (Halichoerus grypus). Ova dissected from the nematodes were incubated in seawater and the mean time to hatch varied from 8 days at 20 °C to 52 days at 5 °C. Posthatch survival of ensheathed larvae in seawater varied from 48 h at 20 °C to 140 days at 5 °C. Fifteen species of copepods collected from the North West Arm, Halifax, N.S., were exposed to freshly hatched larvae of P. decipiens. Exsheathed larvae of the parasite were subsequently detected in the haemocoel of 12 harpacticoid species including Danielsennia typica, Tisbe furcata, Ameira longipes, Enhydrosoma curticauda, and various undescribed species of the genera Halectinosoma, Tisbe, Alteutha, and Phyllothallestris and the family Diosaccidae. Phocanema decipiens also occurred in a cyclopoid copepod (Paracyclopina sp.) but calanoid copepods (Eurytemora sp. and Pseudocalanus sp.) did not become infected. The heaviest infections occurred in mature female copepods and prevalence and intensity of infection varied with host species. Adult male copepods and fifth copepodite females were lightly infected. Infected copepods survived for 3–7 days at 15 °C, 10–15 days at 10 °C, and 20–35 days at 5 °C. During the course of infection, larval P. decipiens grew an average of 60% and maximum of 130% in length but underwent little or no morphological change.

scholarly journals Anthropometric and clinical profiles of post-bariatric patients submitted to procedures in plastic surgery

2018 ◽  
Vol 45 (2) ◽  
Author(s):  
SIMONE CORRÊA ROSA ◽  
JEFFERSON LESSA SOARES DE MACEDO ◽  
LUIZ AUGUSTO CASULARI ◽  
LUCAS RIBEIRO CANEDO ◽  
JOÃO VITOR ALMEIDA MARQUES
Keyword(s):  
Postoperative Complications ◽  
Plastic Surgery ◽  
Analytical Study ◽  
The North ◽  
Bariatric Patients ◽  
Clinical Profiles ◽  
The Mean ◽  
Epidemiological Profile ◽  
Mean Time

ABSTRACT Objective: to evaluate the profile of patients submitted to post-bariatric plastic surgery at the North Wing Regional Hospital, Brasília, DF. Methods: we conducted a prospective, descriptive and analytical study of patients submitted to Roux-en-Y gastroplasty, and subsequently to plastic surgery, from January 2011 to December 2016. We assessed body mass index before gastroplasty and after surgery plastic surgery, postoperative complications and comorbidities. Results: we studied 139 patients (130 women and nine men), with a mean age of 41 years, who underwent 233 operations. The mean BMI at the time of plastic surgery was 27.44kg/m2. The mean weight loss was 47.02kg and the mean maximum BMI was 45.17kg/m2. The mean time between bariatric surgery and plastic surgery was 42 months. The most important co-morbidities before plastic surgery were arterial hypertension (11.5%), arthropathy (5.4%), diabetes mellitus (5%) and metabolic syndrome (4.3%) (p<0.01). Of the 139 patients operated on, 76.97% underwent abdominoplasty followed by mammoplasty (42.46%), rhytidoplasty (17.27%) and brachioplasty (13.67%). Fourteen (13.08%) patients underwent herniorrhaphy combined with abdominoplasty. We performed anchor abdominoplasty in 19.42%. The rate of postoperative complications was 26.65%. Conclusion: the epidemiological profile of post-bariatric patients who underwent plastic surgery was similar to that reported in the literature, except for the low rate of associated surgeries and postoperative complications. Plastic surgery in post-bariatric patients has led to an improvement in the quality of life in most of these patients.

Comparison of the BBL mycobacteria growth indicator tube, the BACTEC 12B, and solid media for the isolation of Mycobacterium bovis

2017 ◽  
Vol 29 (4) ◽  
pp. 508-512 ◽  
Author(s):  
Gary F. Yates ◽  
Marian Price-Carter ◽  
Kirstie Bland ◽  
Maree A. Joyce ◽  
Farina Khan ◽  
...  
Keyword(s):  
New Zealand ◽  
Mycobacterium Bovis ◽  
Tandem Repeats ◽  
Variable Number ◽  
Tissue Samples ◽  
The North ◽  
Indicator Tube ◽  
The Mean ◽  
Mean Time ◽  
Growth Indicator

We compared different methods for their ability to isolate Mycobacterium bovis from tissue samples from animals with lesions resembling bovine tuberculosis. In the first trial, M. bovis was isolated from 86 of 200 tissue samples that were cultured using 2 liquid media, BACTEC 12B and BBL mycobacteria growth indicator tube (MGIT), and a solid medium, Middlebrook 7H11 supplemented with pyruvate (7H11P). M. bovis was isolated from 2 samples with MGIT but not BACTEC 12B. M. bovis was isolated from 9 samples with BACTEC but not MGIT; these 9 samples came from the North Canterbury/Marlborough region of New Zealand. The proportion of tissues from which M. bovis was isolated with BACTEC 12B or MGIT and the mean time for isolation was different for samples from the North Canterbury/Marlborough region but not the rest of New Zealand. In the second trial, M. bovis was isolated from 401 of 1,033 tissues that were cultured using MGIT, Middlebrook 7H9 broth, or solid 7H11P. The proportion of isolates of M. bovis and the mean time for their isolation with MGIT was different for the North Canterbury/Marlborough and the rest of New Zealand. The reason for this difference was not determined but may be related to the genotypes present in this region. Genotyping using variable number tandem repeats (VNTRs) of 197 isolates of M. bovis revealed that the 44 isolates from North Canterbury/Marlborough were represented by 2 closely related VNTR types that were not found in 153 isolates from the remainder of New Zealand.

scholarly journals XVIII. On the fossil Elk of Ireland

1825 ◽  
Vol 115 ◽  
pp. 429-435
Keyword(s):  
Royal College ◽  
The West ◽  
The North ◽  
Royal Dublin Society ◽  
The Earth ◽  
History Of ◽  
The Subject ◽  
The Mean ◽  
Additional Value ◽  
Mean Time

Notwithstanding the frequent occurrence of the remains of the gigantic elk in Ireland, it is remarkable that precise accounts should not have been kept of all the peculiar cir­cumstances under which they occur entombed in its super­ficial strata. To obtain an opportunity of examining these relations had long been my desire; and as fortunately, dur­ing my avocations last autumn in the north of Ireland, a discovery came to my knowledge that seemed likely to throw light on the subject, I proceeded to its investigation, intending, should the results be found deserving of attention, to place them on record. These results have proved the more interesting, as they apparently lead to the conclusion, that this magnificent animal lived in the countries in which its remains are now found, at a period of time which, in the history of the earth, can be considered only as modern. I had advanced thus far when I became apprized of an analogous discovery made last year in the west of Ireland by the Rev. W . Wray Maunsell, Archdeacon of Limerick; which is not only confirmative of my own experience, but has the additional value of embracing particulars not hitherto noticed by any other observer. Mr. Maunseli's researches, elucidated by the able assistance of Mr. John Hart, Member of the Royal College of Surgeons, have been communicated from time to time to the Royal Dublin Society in the form of letters, and have been entered upon their minutes; and, it is to be hoped, that a distinct publication on the subject may hereafter appear, illustrated by a description of the splendid specimen of the skeleton of the animal now deposited by the liberality of the Reverend Archdeacon in the museum of that Society. In the mean time I propose, after giving a concise account of my own inquiries, to refer briefly to the more prominent points in Mr. Maunseli's discoveries, in as far as they bear immediately on the question of the ancient or modern origin of those remains.

Mortal random walks on a family of treelike regular fractals with a deep trap

2020 ◽  
Vol 34 (06) ◽  
pp. 2050031
Author(s):  
Zikai Wu ◽  
Guangyao Xu
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Network Models ◽  
Deep Trap ◽  
Initial Position ◽  
Single Step ◽  
The Mean ◽  
Walk Dimension ◽  
Mean Time ◽  
Temporal Factor

Due to the ubiquitous occurrence of evanescence in many physical, chemical and biological scenarios, mortal random walks that incorporate evanescence explicitly have drawn more and more attention. It has been a hot topic to study mortal random walks on distinct network models. In this paper, we study mortal random walks on T fractal and a family of treelike regular fractals with a trap located at central node (i.e., innermost node). First, with self-similar setting composed of T fractal, initial position of the walker and location of trap, the total trapping probability of the mortal walker reduces to a function of walker’s single-step survival parameter [Formula: see text]. In more detail, the total trapping probability is expressed by the [Formula: see text]th iteration of map (scaling function) of [Formula: see text]. Based on the map, the analytical expression of total trapping probability’s dominant behavior, the mean time to trapping (MFPT) and temporal factor are obtained, which are related to random walk dimension. Last, we extend the analysis to a family of treelike regular fractals. On them, the total trapping probability is still expressed as the [Formula: see text]th iteration of the map scaling [Formula: see text]. Accordingly, dominant behavior of total trapping probability, MFPT and temporal factor are determined analytically. Both analytical results obtained on T fractal and more general treelike regular fractals show that the mean time to trapping and desired random walk dimension can be obtained by tuning the survival probability parameter [Formula: see text]. In summary, the work advances the understanding of mortal random walks on more general deterministic networks.

Predicting Daily Maintenance Dose of Fluindione, an Oral Anticoagulant Drug

1996 ◽  
Vol 75 (05) ◽  
pp. 731-733 ◽  
Author(s):  
V Cazaux ◽  
B Gauthier ◽  
A Elias ◽  
D Lefebvre ◽  
J Tredez ◽  
...  
Keyword(s):  
Effective Dose ◽  
Maintenance Dose ◽  
Successive Approximations ◽  
Hemorrhagic Complication ◽  
Simple Method ◽  
Individual Variations ◽  
Anticoagulant Drug ◽  
The Mean ◽  
Mean Time ◽  
Daily Maintenance Dose

SummaryDue to large inter-individual variations, the dose of vitamin K antagonist required to target the desired hypocoagulability is hardly predictible for a given patient, and the time needed to reach therapeutic equilibrium may be excessively long. This work reports on a simple method for predicting the daily maintenance dose of fluindione after the third intake. In a first step, 37 patients were delivered 20 mg of fluindione once a day, at 6 p.m. for 3 consecutive days. On the morning of the 4th day an INR was performed. During the following days the dose was adjusted to target an INR between 2 and 3. There was a good correlation (r = 0.83, p<0.001) between the INR performed on the morning of day 4 and the daily maintenance dose determined later by successive approximations. This allowed us to write a decisional algorithm to predict the effective maintenance dose of fluindione from the INR performed on day 4. The usefulness and the safety of this approach was tested in a second prospective study on 46 patients receiving fluindione according to the same initial scheme. The predicted dose was compared to the effective dose soon after having reached the equilibrium, then 30 and 90 days after. To within 5 mg (one quarter of a tablet), the predicted dose was the effective dose in 98%, 86% and 81% of the patients at the 3 times respectively. The mean time needed to reach the therapeutic equilibrium was reduced from 13 days in the first study to 6 days in the second study. No hemorrhagic complication occurred. Thus the strategy formerly developed to predict the daily maintenance dose of warfarin from the prothrombin time ratio or the thrombotest performed 3 days after starting the treatment may also be applied to fluindione and the INR measurement.

Retrospective analysis of mortality within 30 days of systemic anticancer therapy and comparison with a previous audit at an Australian Regional Cancer Centre

2021 ◽  
pp. 107815522110160
Author(s):  
Bernadatte Zimbwa ◽  
Peter J Gilbar ◽  
Mark R Davis ◽  
Srinivas Kondalsamy-Chennakesavan
Keyword(s):  
Checkpoint Inhibitors ◽  
Anticancer Therapy ◽  
Mortality Rates ◽  
Feedback Process ◽  
Time To Death ◽  
Cancer Centre ◽  
Haematology Patients ◽  
The Mean ◽  
Regional Cancer Centre ◽  
Mean Time

Purpose To retrospectively determine the rate of death occurring within 14 and 30 days of systemic anticancer therapy (SACT), compare this against a previous audit and benchmark results against other cancer centres. Secondly, to determine if the introduction of immune checkpoint inhibitors (ICI), not available at the time of the initial audit, impacted mortality rates. Method All adult solid tumour and haematology patients receiving SACT at an Australian Regional Cancer Centre (RCC) between January 2016 and July 2020 were included. Results Over a 55-month period, 1709 patients received SACT. Patients dying within 14 and 30 days of SACT were 3.3% and 7.0% respectively and is slightly higher than our previous study which was 1.89% and 5.6%. Mean time to death was 15.5 days. Males accounted for 63.9% of patients and the mean age was 66.8 years. 46.2% of the 119 patients dying in the 30 days post SACT started a new line of treatment during that time. Of 98 patients receiving ICI, 22.5% died within 30 days of commencement. Disease progression was the most common cause of death (79%). The most common place of death was the RCC (38.7%). Conclusion The rate of death observed in our re-audit compares favourably with our previous audit and is still at the lower end of that seen in published studies in Australia and internationally. Cases of patients dying within 30 days of SACT should be regularly reviewed to maintain awareness of this benchmark of quality assurance and provide a feedback process for clinicians.

Vitamin D Level Stability in Dystrophinopathy Patients on Vitamin D Supplementation

2021 ◽  
pp. 1-7
Author(s):  
Naomi Vather-Wu ◽  
Matthew D. Krasowski ◽  
Katherine D. Mathews ◽  
Amal Shibli-Rahhal
Keyword(s):  
Vitamin D ◽  
Retrospective Cohort ◽  
Vitamin D Supplementation ◽  
Hydroxyvitamin D ◽  
Frequent Monitoring ◽  
25 Hydroxyvitamin D ◽  
The Mean ◽  
Stable Maintenance ◽  
Mean Time

Background: Expert guidelines recommend annual monitoring of 25-hydroxyvitamin D (25-OHD) and maintaining 25-OHD ≥30 ng/ml in patients with dystrophinopathies. Objective: We hypothesized that 25-OHD remains stable and requires less frequent monitoring in patients taking stable maintenance doses of vitamin D. Methods: We performed a retrospective cohort study, using the electronic health record to identify 26 patients with dystrophinopathies with a baseline 25-OHD ≥30 ng/mL and at least one additional 25-OHD measurement. These patients had received a stable dose of vitamin D for ≥3 months prior to their baseline 25-OHD measurement and throughout follow-up. The main outcome measured was the mean duration time the subjects spent with a 25-OHD ≥30 ng/mL. Results: Only 19% of patients dropped their 25-OHD to <  30 ng/ml, with a mean time to drop of 33 months and a median nadir 25-OHD of 28 ng/mL. Conclusions: These results suggest that measurement of 25-OHD every 2–2.5 years may be sufficient in patients with a baseline 25-OHD ≥30 ng/mL and who are on a stable maintenance dose of vitamin D. Other patients may require more frequent assessments.

Sign in / Sign up

Export Citation Format

Share Document