scholarly journals The inspection paradox in stochastic resetting

2021 ◽  
Author(s):  
Arnab Pal ◽  
Sarah Kostinski ◽  
Shlomi Reuveni
Keyword(s):  
Probability Theory ◽  
Travel Time ◽  
Random Processes ◽  
Random Time ◽  
Bus Stop ◽  
The Subject ◽  
The Mean ◽  
Mean Time

Abstract The remaining travel time of a plane shortens with every minute that passes from its departure, and a flame diminishes a candle with every second it burns. Such everyday occurrences bias us to think that processes which have already begun will end before those which have just started. Yet, the inspection paradox teaches us that the converse can also happen when randomness is at play. The paradox comes from probability theory, where it is often illustrated by measuring how long passengers wait upon arriving at a bus stop at a random time. Interestingly, such passengers may on average wait longer than the mean time between bus arrivals – a counter-intuitive result, since one expects to wait less when coming some time after the previous bus departed. In this viewpoint, we review the inspection paradox and its origins. The insight gained is then used to explain why, in some situations, stochastic resetting expedites the completion of random processes. Importantly, this is done with elementary mathematical tools which help develop a probabilistic intuition for stochastic resetting and how it works. This viewpoint can thus be used as an accessible introduction to the subject.

Approximating Transition Probabilities and Mean Occupation Times in Continuous-Time Markov Chains

1987 ◽  
Vol 1 (3) ◽  
pp. 251-264 ◽  
Author(s):  
Sheldon M. Ross
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Transition Probabilities ◽  
Random Time ◽  
Occupation Times ◽  
New Approach ◽  
Continuous Time Markov Chains ◽  
The Mean ◽  
Mean Time

In this paper we propose a new approach for estimating the transition probabilities and mean occupation times of continuous-time Markov chains. Our approach is to approximate the probability of being in a state (or the mean time already spent in a state) at time t by the probability of being in that state (or the mean time already spent in that state) at a random time that is gamma distributed with mean t.

scholarly journals Art. V.—Topography of Nineveh, illustrative of the Maps of the chief cities of Assyria; and the general Geography of the country intermediate between the Tigris and the Upper Zab

1854 ◽  
Vol 15 ◽  
pp. 297-396 ◽  
Author(s):  
Felix Jones
Keyword(s):  
The Public ◽  
The Subject ◽  
The Mean ◽  
Mean Time ◽  
Insight Into ◽  
Of Greece

Within the last decade of years, the museums of France and England have been enriched by numerous monuments of Assyrian art, that clearly show the soil from which they were obtained was peopled by a race who, to its warlike habits, added many of the refinements of civilized life. The researches of Botta and Layard—so far as lapidary tablets are capable of conveying the economy of a nation—hare familiarised us in some measure with the public rites and ceremonies of the Assyrians, as well as given an insight into their more domestic concerns; and the pens of these travellers have further elucidated the subject in a manner of which the praise of the public is guarantee to the ability displayed, while the monuments themselves, as patents of their energy, remain in the capitals of Europe, until, in the course of time, they share in the fate of their Assyrian predecessors. Profoundly indifferent, however, to such an event, our savans are in the mean time labouring to unravel the mystic characters engraved on the records so lately revealed to ua; and such is the progress made, that we may shortly expect to be as cognizant of the deeds of the “stouthearted king and the glory of his high looks,” as we are conversant with the celebrities of Greece or Rome. The only desideratum wanting, it appears, to complete the picture of Assyria, is a faithful sketch of her aspect in desolation, when she is “empty, and void, and waste; when flocks lie down in the midst of her; and when her rivers are opened, and her palace is dissolved.” This we have endeavoured to supply in the three maps of the vestiges of Assyria, made from actual survey of the spot. Topography, however, is a dry subject, and we enter upon it with diffidence and reluctance.

scholarly journals Art. II.—Letters to the Secretary of the Royal Asiatic Society

1841 ◽  
Vol 6 (11) ◽  
pp. 11-41
Author(s):  
W. Morley ◽  
Duncan Forbes
Keyword(s):  
The Public ◽  
French Government ◽  
Asiatic Society ◽  
The Press ◽  
The Subject ◽  
The Mean ◽  
Mean Time ◽  
Royal Asiatic Society

Whilst I was engaged last year in making a catalogue of the Oriental MSS. comprised in the libraries of the Society and the Oriental Translation Committee, I met with the historical MS. which is the subject of the following letter. I, at that time, applied to the Council of the Society for permission to forward a description of the MS. to M. Quatremere, who is employed in editing the only portion of the work hitherto known, in the hope that he would represent the matter to the French Government, and cause our MS. to be published in the “Collection Orientale,” as a sequel to his “Histoire des Mongols.” The council acceded to my request, and I accordingly wrote to M. Quatremère on the subject, but whether on account of my letter not having reached its destination or from the press of business, he has not as yet returned any answer to my communication. In the mean time, I think it desirable that the existence of this important volume should be made known to the public, and I have accordingly drawn up the following account of the MS. for insertion in the Journal of the Society.

scholarly journals VII. Outlines of experiments and inquiries respecting sound and light. By Thomas Young, M. D. F. R. S. In a letter to Edward Whitaker Gray, M. D. Sec. R. S

1800 ◽  
Vol 90 ◽  
pp. 106-150 ◽  
Keyword(s):  
Royal Society ◽  
Velocity Of Sound ◽  
Human Voice ◽  
The Subject ◽  
The Mean ◽  
Elastic Fluids ◽  
Musical Sounds ◽  
Mean Time

Dear Sir, It has long been my intention to lay before the Royal Society a few observations on the subject of sound; and I have endea­voured to collect as much information, and to make as many experiments, connected with this inquiry, as circumstances enabled me to do; but, the further I have proceeded, the more widely the prospect of what lay before me has been extended; and, as I find that the investigation, in all its magnitude, will occupy the leisure hours of some years, or perhaps of a life, I am determined, in the mean time, lest any unforeseen circumstances should prevent my continuing the pursuit, to submit to the Society some conclusions which I have already formed from the results of various experiments. Their subjects are, I. The measurement of the quantity of air discharged through an aperture. II. The determination of the direction and velocity of a stream of air proceeding from an orifice. III. Ocular evidence of the nature of sound. IV. The velocity of sound. V. Sonorous cavities. VI. The degree of divergence of sound. VII. The decay of sound. VIII. The harmonic sounds of pipes. IX. The vibrations of different elastic fluids. X. The analogy between light and sound. XI. The coalescence of musical sounds. XII. The frequency of vibrations constituting a given note. XIII. The vibrations of chords. XIV. The vibrations of rods and plates. XV. The human voice. XVI. The temperament of musical intervals.

scholarly journals VIII. Experiments and observations on the influence of the nerves of the eighth pair on the secretions of the stomach. By B. C. Brodie, Esq. F. R. S. Communicated by the Society for the promotion of animal chemistry

1814 ◽  
Vol 104 ◽  
pp. 102-106 ◽  
Keyword(s):  
Nervous System ◽  
The Other ◽  
Direct Experiment ◽  
The Subject ◽  
The Mean ◽  
Mean Time ◽  
Circulation Of The Blood ◽  
The Brain ◽  
Positive Results ◽  
The Way

In a paper formerly communicated to this Society by Sir Everard Home, and since published in the Philosophical Transactions for the year 1809, some facts were stated which render it probable that the various animal secretions are dependent on the influence of the nervous system, and this opinion seemed to derive support from some physiological experiments which were afterwards instituted by myself, and in which it was observed, that after the functions of the brain had been destroyed, although the action of the heart continued, and the circulation of the blood was maintained as under ordinary circumstances, the secreting organs invariably ceased to perform their office. It has been attempted by former physiologists to determine how far the nerves are necessary to secretion, but there are considerable obstacles in the way of this inquiry, and no observations, that have been hitherto made, appear to throw a great deal of light on the subject. The only method, which can be devised, of ascertaining by direct experiment, whether the nerves are really necessary to secretion, is that of dividing the nervous branches by which the glands are supplied. But this, with respect to the greater number of the glands, is an experiment impossible to perform; and, with respect to others, can not be executed without so much disturbance and injury to the other parts, as must render it extremely difficult to arrive at any positive results. Perhaps in future investigations, some circumstances may arise, which will enable us to determine more satisfactorily this important physiological question. In the mean time, as the labours of physiologists have hitherto contributed so little to this purpose, any facts that tend to its elucidation may deserve to be recorded, and I am therefore induced to lay before the Society the following experiments, which afford one example of a secretion being dependent on the influence of the nerves.

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.

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.

Applying Circle Game to Enhance Students’ Speaking Skill

2020 ◽  
Vol 7 (2) ◽  
pp. 119
Author(s):  
Putri Denaya Side Ayu ◽  
Heri Hidayatullah ◽  
Sri Ariani
Keyword(s):  
Action Research ◽  
Learning Process ◽  
Active Involvement ◽  
Post Test ◽  
Speaking Skill ◽  
The Subject ◽  
The Mean ◽  
Classroom Action Research ◽  
Speaking Skills

This Collaborative Classroom Action Research aimed at enhancing students’ speaking skill through the application of Circle Game. It was conducted in one cycle consisting of two meetings. The subject was the seventh of C class of SMPN 2 Alas Barat consisting of 22 students. The types of data were qualitative (acquiring observation during the learning process) and quantitative (speaking tests). The results qualitatively showed that the implementation of Circle Game enhanced the students’ speaking skills. Such improvement could be seen from their enthusiasm, their interesting feeling in various materials presented by the teacher, their active involvement. In the quantitative findings, the result also showed a higher value of the mean score of the post-test (77.34) rather than the pre-test (75.75). In conclusion, the use of Circle Game can improve students’ speaking skill.

UPAYA MENINGKATKAN HASIL BELAJAR IPA MELALUI PENGGUNAAN VIDEO PEMBELAJARAN BAGI SISWA KELAS IV DI SDN 187/IV KOTA JAMBI

2015 ◽  
Vol 8 (2) ◽  
pp. 93
Author(s):  
Juniar Siregar
Keyword(s):  
Action Research ◽  
Research Method ◽  
Research Report ◽  
The Third ◽  
The Media ◽  
The Subject ◽  
The Mean ◽  
Classroom Action Research

This study presents a research report on improving students’ Learning results on IPA through Video. The objective was to find out whether students’ learning result improved when they are taught by using Video. It was conducted using classroom action research method. The subject of the study was the Grade IV students of SDN 187/IV Kota Jambi which is located on Jln. Adi Sucipto RT 05 Kecamatan Jambi Selatan, and the number of the students were 21 persons. The instruments used were test. In analyzing the data, the mean of the students’ score for the on fisrt sycle was 65,4 (42,85%) and the mean on cycle two was 68,5 (37,15%) and the mean of the third cycle was 81,4 (100%). Then it can be concluded that the use of video on learning IPA can improve the students’ learning result. It is suggested that teachers should use video as one of the media to improve students’ learning result on IPA.Keywords : IPA, students’ learning result, video

THE USE OF COMMUNITY LANGUAGE LEARNINGMETHOD TO IMPROVE STUDENTS’ SPEAKING ACHIEVEMENT

2015 ◽  
Vol 4 (1) ◽  
Author(s):  
Eko Widoyo Putro ◽  
Berlin Sibarani
Keyword(s):  
Language Learning ◽  
Secondary Data ◽  
Primary Data ◽  
Second Grade ◽  
Learning Method ◽  
Field Notes ◽  
The Subject ◽  
The Mean ◽  
Method Improvement ◽  
Community Language

This study is aimed at improving the second grade of students’ speakingachievement by using Community Language Learning (CLL) Method. Theresearch was conducted by applying classroom action research. The subject of this study was second grade of Private Senior High School (Sekolah Menengah Atas Swasta) of Dwi Tunggal Tanjung Morawa which consisted of 31 students. To collect the data, the instruments used were primary data (SpeakingTest) and secondary data (interview sheet, observation sheet, field notes). It can be seen from the score in test I, test II and test III. In the Test I, the mean of the students’score was (64.77), in the Test II was (71.35), and the mean of the students’ score of the Test III was (80.90). Based on the interview, and observation sheet, it shows that the expression and excitement of the students got improved as well. It was found that teaching of speaking by using Community Language Learningcould significantly improve students’ speaking achievement.Key Words: Community Language Learning, Method, Improvement, Speaking Achievement

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