scholarly journals The speed of a random walk excited by its recent history

2016 ◽  
Vol 48 (1) ◽  
pp. 215-234 ◽  
Author(s):  
Ross G. Pinsky
Keyword(s):  
Random Walk ◽  
Finite Number ◽  
Threshold Level ◽  
Recent History ◽  
Threshold Levels ◽  
One Step ◽  
The Right ◽  
Positive Integers

Abstract Let N and M be positive integers satisfying 1≤ M≤ N, and let 0< p0 < p1 < 1. Define a process {Xn}n=0∞ on ℤ as follows. At each step, the process jumps either one step to the right or one step to the left, according to the following mechanism. For the first N steps, the process behaves like a random walk that jumps to the right with probability p0 and to the left with probability 1-p0. At subsequent steps the jump mechanism is defined as follows: if at least M out of the N most recent jumps were to the right, then the probability of jumping to the right is p1; however, if fewer than M out of the N most recent jumps were to the right then the probability of jumping to the right is p0. We calculate the speed of the process. Then we let N→ ∞ and M/N→ r∈[0,1], and calculate the limiting speed. More generally, we consider the above questions for a random walk with a finite number l of threshold levels, (Mi,pi) i=1l, above the pre-threshold level p0, as well as for one model with l=N such thresholds.

Cardiopulmonary resuscitation in the mouse

2002 ◽  
Vol 93 (4) ◽  
pp. 1222-1226 ◽  
Author(s):  
Lei Song ◽  
Max Harry Weil ◽  
Wanchun Tang ◽  
Shijie Sun ◽  
Tommaso Pellis
Keyword(s):  
Cardiac Arrest ◽  
Cardiopulmonary Resuscitation ◽  
Cardiopulmonary Arrest ◽  
Threshold Level ◽  
Aortic Pressure ◽  
Coronary Perfusion Pressure ◽  
Coronary Perfusion ◽  
Successful Resuscitation ◽  
Threshold Levels ◽  
The Right

We sought to develop a model of cardiac arrest and resuscitation on mice that would be comparable to that of large mammals and would allow for more fundamental investigations on cardiopulmonary arrest and cardiac resuscitation. A model of cardiopulmonary resuscitation previously developed by our group on rats was adapted to anesthetized, mechanically ventilated adult male Institute of Cancer Research mice that weighed 46 ± 3 g. The trachea was intubated through the mouth, and end-tidal Pco 2(Pet CO2 ) was measured with a microcapnometer. Catheters were advanced into the aorta and into the right atrium, and coronary perfusion pressure (CPP) was computed. A 1.5-mA alternating current was delivered to the right ventricular endocardium, which produced ventricular fibrillation or a pulseless rhythm. Precordial compression was begun 4 min later. Ten sequential studies were performed, during which five animals were successfully resuscitated and five failed resuscitation efforts. Successful resuscitation was contingent on the restoration of threshold levels of CPP and Pet CO2 during chest compression. As in rats, swine, and human patients, threshold levels of mean aortic pressure, CPP, and Pet CO2 were critical determinates of resuscitability in this murine model of threshold level of cardiac arrest and resuscitation.

scholarly journals A note on the random walk model arising in double diffusion

1982 ◽  
Vol 24 (2) ◽  
pp. 121-129 ◽  
Author(s):  
L. H. Liyanage ◽  
J. M. Hill ◽  
C. M. Gulati
Keyword(s):  
Random Walk ◽  
Probability Distribution ◽  
Diffusion Model ◽  
General Result ◽  
Generating Functions ◽  
Double Diffusion ◽  
Horizontal Position ◽  
Special Cases ◽  
One Step ◽  
The Right

AbstractThe discrete random walk problem for the unrestricted particle formulated in the double diffusion model given in Hill [2] is solved explicitly. In this model it is assumed that a particle moves along two distinct horizontal paths, say the upper path I and lower path 2. For i = 1, 2, when the particle is in path i, it can move at each jump in one of four possible ways, one step to the right with probability pi, one step to the left with probability qi, remains in the same position with probability ri, or exchanges paths but remains in the same horizontal position with probability si (pi + qi + ri + si = 1). Using generating functions, the probability distribution of the position of an unrestricted particle is derived. Finally some special cases are discussed to illustrate the general result.

Three-Component [1+1+1] Cyclopropanation with Ruthenium(II)

2018 ◽  
Author(s):  
Tanner C. Jankins ◽  
Robert R. Fayzullin ◽  
Eugene Khaskin
Keyword(s):  
Quaternary Carbon ◽  
Poor Control ◽  
One Step ◽  
Synthetic Routes ◽  
Mechanistic Investigations ◽  
Chiral Centers ◽  
Metal Catalyzed ◽  
The Right ◽  
Substituted Cyclopropanes

We report a one-step, Ru(II)-catalyzed cyclopropanation reaction that is conceptually different from the previously reported protocols that include Corey-Chaykovsky, Simmons-Smith, and metal catalyzed carbene attack on olefins. Under the current protocol, various alcohols are transformed into sulfone substituted cyclopropanes with excellent isolated yields and diastereoselectivities. This new reaction forms highly congested cyclopropane products with three new C–C bonds, three or two new chiral centers and one new quaternary carbon center. 22 examples of isolated substrates are given. Previously reported synthetic routes for similar substrates are all multi-step, linear routes that proceed with overall low yields and poor control of stereochemistry. Experimental mechanistic investigations suggest initial metal-catalyzed dehydrogenation of the alcohol substrate and catalyst independent stepwise attack of two equivalents of sulfone on the aldehyde under basic conditions. While the Ru(II) is only responsible for the initial dehydrogenation step, the rate of aldehyde formation is crucial to maintaining the right balance of intermediates needed to afford the cyclopropane product.

One-step random-walk process of nanoparticles in cement-based materials

2021 ◽  
Vol 28 (6) ◽  
pp. 1679-1691
Author(s):  
Ali Bahari ◽  
Aref Sadeghi-Nik ◽  
Elena Cerro-Prada ◽  
Adel Sadeghi-Nik ◽  
Mandana Roodbari ◽  
...  
Keyword(s):  
Random Walk ◽  
Random Walk Process ◽  
Cement Based Materials ◽  
One Step

scholarly journals Current Trends in Random Walks on Random Lattices

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1148
Author(s):  
Jewgeni H. Dshalalow ◽  
Ryan T. White
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Real Time ◽  
Real Space ◽  
Historical Background ◽  
Escape Time ◽  
The Real ◽  
Current Trends ◽  
One Step ◽  
Time Position

In a classical random walk model, a walker moves through a deterministic d-dimensional integer lattice in one step at a time, without drifting in any direction. In a more advanced setting, a walker randomly moves over a randomly configured (non equidistant) lattice jumping a random number of steps. In some further variants, there is a limited access walker’s moves. That is, the walker’s movements are not available in real time. Instead, the observations are limited to some random epochs resulting in a delayed information about the real-time position of the walker, its escape time, and location outside a bounded subset of the real space. In this case we target the virtual first passage (or escape) time. Thus, unlike standard random walk problems, rather than crossing the boundary, we deal with the walker’s escape location arbitrarily distant from the boundary. In this paper, we give a short historical background on random walk, discuss various directions in the development of random walk theory, and survey most of our results obtained in the last 25–30 years, including the very recent ones dated 2020–21. Among different applications of such random walks, we discuss stock markets, stochastic networks, games, and queueing.

scholarly journals Surgical treatment for common hepatic aneurysm. Original one-step technique

Open Medicine ◽  
2020 ◽  
Vol 15 (1) ◽  
pp. 898-904
Author(s):  
Bruno Amato ◽  
Renato Patrone ◽  
Gennaro Quarto ◽  
Rita Compagna ◽  
Roberto Cirocchi ◽  
...  
Keyword(s):  
Surgical Treatment ◽  
Hepatic Artery ◽  
Distal Part ◽  
Intraoperative Ultrasound ◽  
Section Area ◽  
One Step ◽  
A New Technique ◽  
Open Surgical Treatment ◽  
The Right ◽  
Vascular Stapler

AbstractIntroductionHepatic artery aneurysms are rare, and their treatment represents a challenge for the surgeons.Materials and methodsA new technique is presented for common hepatic artery (CHA) aneurysm: it requires minimal vascular surgical dissection and only one linear vascular stapler is applied at the bottom of aneurysm. Aneurysm exclusion is easily obtained, which allowed retrograde thrombosis. Liver blood supply is ensured to the right and left hepatic artery, through the gastroduodenal artery, and can be previously monitored, with temporary clamping of the section area, by visual control, enzyme evaluation and intraoperative ultrasound examination. We reported an open surgical treatment, with simultaneous removal of hepatic and adrenal metastases, secondary to colon cancer.ResultsThe duration of vascular surgery was 30 min and did not involve complications. Postoperative controls confirmed the efficacy of the procedure.DiscussionThis original technique can be added to the various open and endovascular techniques so far described for the treatment of a CHA aneurysm. It is advisable as open surgery, mostly in case of associated pathologies.ConclusionsThe authors believe that this “one shot” technique by vascular staple of the distal part of CHA is minimally invasive and effective to obtain the exclusion of the aneurysm.

Mandatory desexing of dogs: one step in the right direction to reduce the risk of dog bite? A systematic review

2017 ◽  
Vol 23 (3) ◽  
pp. 212-218 ◽  
Author(s):  
Katina D'Onise ◽  
Susan Hazel ◽  
Charles Caraguel
Keyword(s):  
Systematic Review ◽  
Dog Bite ◽  
One Step ◽  
The Right

Single-shelf library-type Markov chains with infinitely many books

1977 ◽  
Vol 14 (02) ◽  
pp. 298-308 ◽  
Author(s):  
Peter R. Nelson
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Transition Probabilities ◽  
Natural Order ◽  
Order Book ◽  
Exit Boundary ◽  
One Step ◽  
Step Transition ◽  
The Right ◽  
Positive Recurrent

In a single-shelf library having infinitely many books B 1 , B 2 , …, the probability of selecting each book is assumed known. Books are removed one at a time and replaced in position k prior to the next removal. Books are moved either to the right or the left as is necessary to vacate position k. Those arrangements of books where after some finite position all the books are in natural order (book i occupies position i) are considered as states in an infinite Markov chain. When k &gt; 1, we show that the chain can never be positive recurrent. When k = 1, we find the limits of ratios of one-step transition probabilities; and when k = 1 and the chain is transient, we find the Martin exit boundary.

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