III. On the proof of the law of errors of observations

1869 ◽  
Vol 17 ◽  
pp. 406-407
Keyword(s):  
Mathematical Proof ◽  
Present Writer ◽  
Joint Operation ◽  
General Proof ◽  
Sources Of Error ◽  
History Of ◽  
The Mean ◽  
The Law ◽  
Elementary Manner

The object of this Paper is to give the mathematical proof, in its most general form, of the law of single errors of observations, on the hypothesis that each error in practice arises from the joint operation of a large number of independent sources of error, each of which, did it exist alone, would occasion errors of extremely small amount as compared generally with those actually produced by all the sources combined. This proof is contained in a process given for a different object, namely, Poisson’s generalization of Laplace’s investigation of the law of the mean results of a large number of observations, to be found in the Connaissance des Temps’ for 1827, and also in his 'Recherches sur la Probabilité des Jugements ’ it is also re­produced in Mr. Todhunter’s able History of the Theory of Probability.’ It is not therefore pretended that any new results are arrived at in the present Paper. Considering, however, the importance and celebrity of the question, and the refined and difficult character of Poisson’s analysis, it will not probably be deemed superfluous to show how the same law may be demonstrated with equal generality, in a much more simple and elementary manner. The difficulty of the general proof seems indeed to have been so extensively felt, that several attempts have been made to simplify it. However, so far as the present writer is aware, no proof has been given, except Poisson’s, which is not open to grave objection, as based upon unjustifiable assumptions, or as unduly limiting, the generality of the in­vestigation.

scholarly journals IX. On the proof of the law of errors of observations

1870 ◽  
Vol 160 ◽  
pp. 175-187 ◽  
Keyword(s):  
Mathematical Proof ◽  
Joint Operation ◽  
Method Of Least Squares ◽  
Full Generality ◽  
Exponential Law ◽  
History Of ◽  
The Mean ◽  
The Law ◽  
Source Of Error ◽  
Correct Estimate

1. So much has been published upon the Theory of Errors, that some apology seems to be required from a new writer who does not profess to have arrived at any results which were unknown to his predecessors. Nevertheless, so great, as is well known, are the difficulties of the theory, whether we seek to form a correct estimate of the principles on which it rests, or to follow the subtle mathematical analysis which has been found indispensable in reasoning upon them, that any contribution which tends to simplify the processes, without weakening their logical exactness, will probably be considered of some value. My object in this paper is to give the mathematical proof, in its most general form, of the law of single errors of observations, on the hypothesis that an error in practice arises from the joint operation of a large number of independent sources of error, each of which, did it exist alone, would produce errors of extremely small amount as compared generally with those arising from all the other sources combined. Now this proof is contained in a process given for a different object, namely, Poisson’s generalization of Laplace’s investigation of the law of the mean results of a large number of observations, to be found in his ‘Recherches sur la Probabilité des jugements,’ and which is reproduced in Mr.Todhunter’s valuable ‘History of the Theory of Probability.’ It is obvious that we should altogether restrict the generality of the proof, confining it merely to a few artificial and conventional cases, if we were to suppose each source of error to give positive and negative errors with equal facility, or to assume the law of error (even supposing it unknown) to be the same for all the sources. None of the processes, therefore, contained in the 4th chapter of the ‘Théorie Analytique des Probabilités’ are of sufficient generality for our purpose, though some writers have so employed them ; nor will the method apply here which Leslie Ellis has given in his memoir “On the Method of Least Squares” (Camb. Phil. Trans. 1844), based upon Fourier’s theorem, on account of the assumption of equal facility for positive and negative errors. The proof which follows will be found, I think, of full generality,—the only cases excluded being incompatible with the existence of the exponential law (see art. 7), and at the same time greatly simpler than Poisson’s, dispensing with his refined and difficult analysis.

Revisiting the Natural History of Chronic Scaphoid Nonunions: A Retrospective Study of 20 Cases

2021 ◽  
Author(s):  
J. Terrence Jose Jerome
Keyword(s):  
Retrospective Study ◽  
Natural History ◽  
Functional Outcome ◽  
Grip Strength ◽  
Scaphoid Nonunion ◽  
Proximal Pole ◽  
Degenerative Arthritis ◽  
Level Of Evidence ◽  
History Of ◽  
The Mean

Abstract Background The natural history of scaphoid nonunion is the development of degenerative arthritis. A lot of information is still unclear about this progression. The purpose of this study is to analyze patients with scaphoid nonunions who had not received any kind of treatment and to assess the functional outcome. Materials and Methods This is a retrospective study that analyzed the patients with chronic scaphoid nonunions between 2009 and 2019. None of the patients received any treatment. The age at the time of injury, examination, pattern of fracture, types of scaphoid nonunion, symptoms, and duration of nonunion were noted. Diagnosis was confirmed by radiographs, computed tomography (CT) scan, and magnetic resonance imaging (MRI). Scapholunate and radiolunate angles were recorded. Pain score, modified mayo wrist score, grip strength, range of movement, and the functional outcome of these scaphoid nonunions were analyzed. A statistical correlation between the scaphoid nonunion presentations and the functional outcome was assessed. Results The mean age of the patients was 62 years (range: 35–82 years.). There were 17 male and 3 female patients. There were 9 waist and 11 proximal pole scaphoid nonunions. The mean duration of scaphoid nonunion was 34 years (range: 10–62 years). None of the patients had avascular necrosis (AVN) of the proximal scaphoid. The age at examination, gender, side of injury, fracture pattern (waist/proximal pole), fracture displacement ≤ 1 mm or > 1 mm, nonunion duration, and radiographic arthritic parameters had no significant impact on the functional outcome. Conclusions Untreated chronic scaphoid nonunion leads to the development of degenerative arthritis over a period of years, which is still unpredictable. Most of the patients become aware of the nonunion following a precedent injury or other reasons. Most of the patients have fair/good functional outcome despite reduced range of movements and grip strength. Many do not favor surgical intervention in the course of nonunion. Chronic nonunions open a lot of unanswered questions. Clinical relevance There have been numerous studies on the treatment aspects of scaphoid nonunion, with little knowledge about certain people with nonunion who did not have any kind of treatment. The demographics, clinical findings, and radiological parameters do confirm the progression of these nonunion to arthritis, but most of them had fair-to-good outcome throughout their life. It opens our thinking about the real need of treatment in such nonunions and raises numerous questions about the disease. Level of evidence This is a Level IV study.

نظام التوثيق وأثره في إدارة الأصول الوقفية في دولة الإمارات العربية المتحدة: نماذج من إمارة الشارقة (Documentation System and its Impact on Endowment Managements in United Arabic Emirates: The Study of Emirate of Sharjah)

2019 ◽  
Vol 16 (2) ◽  
pp. 166-193
Author(s):  
مها بنت منصور الصائغ
Keyword(s):  
Human Life ◽  
Documentation System ◽  
The People ◽  
Endowment Management ◽  
Long Time ◽  
History Of ◽  
The Law

شهد تاريخ الأمة الإسلامية حضارة ونهضة عالمية في جميع مجالات الحياة الإنسانية، ومما كان له كبير الأثر في ذلك هو الأوقاف التي بدأت مع سيد البشرية محمد صلى الله عليه وسلم واستمرت بتنوع وشمولية إلى عصرنا الحالي؛ ولكن ما تعرضت إليه الأوقاف من إهمال وإقصاء وضياع يرجع لأسباب عديدة من أهمها غياب التوثيق الوقفي. تقوم الدراسة على تتبع مفهوم الوقف والتوثيق، والوقف في الإمارات العربية المتحدة ول سيما في إمارة الشارقة. توصلت الدراسة إلى نتائج منها: أن الأوقاف قائمة منذ زمن بعيد، وأن رغبة الواقف بالوقف وإقدامه عليها لم ينقصها سوى وثيقة، وأنه لا وثائق لها ولا مستندات، كما أن العرض الموجز لنشأة دائرة الأوقاف بالشارقة وسعيها لإحياء سنة الوقف ونشر ثقافته نراه يتضح شيئاً فشيئاً من خلال تفعيل مواد القانون والبحث حول الأنسب والأصح لحماية الأوقاف، ولم يكن هذا الاهتمام بالوقف إلا انعكاساً لتوجه الواقفين وتماشياً لرؤية الحكام وامتثالاً لنهج خير الأنام ورغبة في تكافل الأرواح وحباً للسلام. الكلمات المفتاحيّة: الوقف، التوثيق، المقارنة، الشارقة. Abstract The history of Islamic nation has witnessed a global civilization and it has had a great impact in all areas of human life, including the endowments that began with the master of humankind; Muhammad S.A.W. and it was continuing in diversity and comprehensively until our epoch. However, there are some problems related to endowment management such as negligence, exclusion and loss that due to many reasons. Among the most important reasons is the absence of endowment documentations. Therefore, the study aims to discuss the concept of endowment and documentation, as well as the endowment in United Arabic Emirates, especially in the Emirate of Sharjah. The study concluded that the practice of endowment has been existed for a long time, yet there are in need of endowment documentations. This study also found that the information related to the establishment of institution of endowment in Sharjah and its role has   spread widely to the people through the enforcement of the law and the implementation of the research related to the practice of endowment in order to sustain them in a good way. This documentation system was only a reflection of what has  stated in Shariah laws regarding the practice of endowment among the donors, so that it will be in line with the approach of good intentions and love of peace. Keywords: Endowment, Documentation, Comparison, Sharjah.   

Reading Max Weber's Sociology of Law

2020 ◽  
Author(s):  
Hubert Treiber
Keyword(s):  
Sociology Of Law ◽  
Important Work ◽  
Research Setting ◽  
Stages Of Development ◽  
History Of ◽  
History Of Law ◽  
The Law ◽  
Comprehensive Study

More than a simple guide through a complicated text, this book serves both as an introduction and as a distillation of more than thirty years of reading and reflection on Max Weber's scholarship. It is a solid and comprehensive study of Weber and his main concepts. It also provides commentary in a manner informed both historically and sociologically. Drawing on recent research in the history of law, the book also presents and critiques the process by which the law was rationalized and which Weber divided into four ideal-typical stages of development. It contextualizes Weber's work in the light of current research, setting out to amend misinterpretations and misunderstandings that have prevailed from Weber's original texts. Ultimately, this volume is an important work in its own right and critical for any student of the sociology of law.

Reorganization of the Governmental Structure of Roumania

1931 ◽  
Vol 25 (3) ◽  
pp. 700-703
Author(s):  
Joseph S. Roucek
Keyword(s):  
Central Administration ◽  
World War ◽  
Liberal Party ◽  
Old Kingdom ◽  
The Balkans ◽  
History Of ◽  
The Will ◽  
The Law ◽  
Self Rule ◽  
The University

The law for the reorganization of central administration and the law on local administration (July 20, 1929) sponsored by the National Peasant government of Roumania have recently been put into effect. Both measures were drafted by Professors Negulescu, of the University of Bucharest, and Alexianu, of the University of Cernauţi. Their adoption comprises one of the most thorough governmental reforms in the history of the Balkans.The structure of the Roumanian government was, until very recently, almost completely copied from the French system. Roumania was a typical example of a unitary organization. The whole power of government was centralized in Bucharest. Practically all powers of local government were derived from the central authority, and were enlarged and contracted at the will of Bucharest. The whole system lent itself admirably to the domination of the National Liberal party, guided up to 1927 by Ion I. C. Brǎtianu, and after his death by his brother, Vintilǎ I. C. Brǎtianu, who died last year.Since the strength of the National Peasant party, which assumed the reins in 1928, lies largely in the provinces acquired at the close of the World War, a decentralization of government was to be expected. The bitter resentment of Maniu and his associates toward the over-centralization which favored the policies of the Bratianus forced the recent overhauling of the governmental structure, tending toward federalism—a form which takes cognizance of the differences of the past and present between the old kingdom and the new provinces and attempts to extend democratic features of self-rule to the electorate. At the same time, it attempts to secure bureaucratic expertness.

Elevation of pulse pressure in middle age is associated with the risk of dementia: data from a population-based cohort

2020 ◽  
Vol 41 (Supplement_2) ◽  
Author(s):  
D Kim ◽  
H Jung ◽  
P.S Yang ◽  
H.T Yu ◽  
T.H Kim ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Pulse Pressure ◽  
Middle Age ◽  
Population Based ◽  
Entire Cohort ◽  
Incident Dementia ◽  
Increased Risk ◽  
Diagnosis Of Dementia ◽  
History Of ◽  
The Mean

Abstract Aims Pulse pressure (PP) is a well-known risk factor for cardiovascular disease. However, the association between the PP and dementia is not well identified. This study aimed to determine the effect of PP on the risk of dementia development in different age subgroups using a longitudinal, population-based, and stroke-free cohort from the general population. Methods The association of PP with the development of incident dementia was assessed from January 1, 2005, to December 31, 2013, in 433,154 participants without a history of dementia or stroke from the Korea National Health Insurance Service-Health Screening cohort. The diagnosis of dementia was defined using the 10th revision of the International Classification of Disease codes. Results The mean age of the cohort was 55.7±9.2 years, 45.7% were women. Hypertension was 23.6%. The mean systolic and diastolic blood pressure of the entire cohort were 125.9±16.6 and 78.4±10.7 mmHg, respectively. Mean PP was 47.5±10.9 mmHg. In the middle-age group (40 to 50 year-old), increasing of 10 mmHg of PP was associated with incident dementia after adjusting mean blood pressure and clinical variables with a hazard ratio (HR) of 1.21 (95% confidence interval [CI]: 1.19–1.23, p<0.001). The association was still significant even after censoring for stroke (HR: 1.16, 95% CI: 1.08–1.22, p<0.001). In the older population, elevation of PP was not associated with dementia development (HR: 0.98, 95% CI: 0.95–1.01, p=0.247) Conclusion PP was associated with increased risk of dementia only in middle-aged population beyond that of mean arterial pressure. Funding Acknowledgement Type of funding source: None

scholarly journals SAT0462 ASSESSMENT OF BONE MINERAL DENSITY IN INFLAMMATORY BOWEL DISEASE

2020 ◽  
Vol 79 (Suppl 1) ◽  
pp. 1188.1-1188
Author(s):  
C. Daldoul ◽  
N. El Amri ◽  
K. Baccouche ◽  
H. Zeglaoui ◽  
E. Bouajina
Keyword(s):  
Bone Mineral Density ◽  
Inflammatory Bowel Disease ◽  
Bone Mineral ◽  
Bowel Disease ◽  
Mineral Density ◽  
Femoral Site ◽  
Significant Difference ◽  
History Of ◽  
Inflammatory Bowel ◽  
The Mean

Background:Inflammatory bowel disease (IBD), including ulcerative colitis (UC) and Crohn’s disease (CD), is considered as a risk factor of low bone mineral density (BMD). In fact, the prevalence of osteoporosis ranges from 17% to 41% in IBD patients. The possible contributing factors may include malabsorption, glucocorticoid treatment and coexisting comorbiditiesObjectives:The purpose of our work was to determine the frequency and the determinants of osteoporosis in patients with IBD and to assess whether there is a difference in BMD status between UC and CD.Methods:This is a retrospective study, over a period of 5 years (from January 2014 to December 2018) and including patients followed for IBD who had a measurement of BMD by DEXA. Clinical, anthropometric and densitometric data (BMD at the femoral and vertebral site) were recorded. The WHO criteria for the definition of osteoporosis and osteopenia were applied.Results:One hundred and five patients were collected; among them 45 were men and 60 were women. The average age was 45.89 years old. The average body mass index (BMI) was 25.81 kg/m2 [16.44-44.15]. CD and UC were diagnosed in respectively 57.1% and 42.9%. A personal history of fragility fracture was noted in 4.8%. Hypothyroidism was associated in one case. Early menopause was recorded in 7.6%. 46.8% patients were treated with corticosteroids. The mean BMD at the vertebral site was 1.023 g/cm3 [0.569-1.489 g/cm3]. Mean BMD at the femoral site was 0.920g/cm3 [0.553-1.286g / cm3]. The mean T-score at the femoral site and the vertebral site were -1.04 SD and -1.27 SD, respectively. Osteoporosis was found in 25.7% and osteopenia in 37.1%. Osteoporosis among CD and UC patients was found in respectively 63% and 37%. The age of the osteoporotic patients was significantly higher compared to those who were not osteoporotic (52.23 vs 43.67 years, p = 0.01). We found a significantly higher percentage of osteoporosis among men compared to women (35.6% vs 18.3%, p=0.046). The BMI was significantly lower in the osteoporotic patients (23.87 vs 26.48 kg/m2, p=0.035) and we found a significant correlation between BMI and BMD at the femoral site (p=0.01). No increase in the frequency of osteoporosis was noted in patients treated with corticosteroids (27.9% vs 21.6%, p=0.479). Comparing the UC and CD patients, no difference was found in baseline characteristics, use of steroids or history of fracture. No statistically significant difference was found between UC and CD patients for osteoporosis(p=0.478), BMD at the femoral site (p=0.529) and at the vertebral site (p=0.568).Conclusion:Osteoporosis was found in 25.7% of IBD patients without any difference between CD and UC. This decline does not seem to be related to the treatment with corticosteroids but rather to the disease itself. Hence the interest of an early screening of this silent disease.Disclosure of Interests:None declared

scholarly journals Patterns of Sequelae in Women with a History of Localized Breast Cancer: Results from the French VICAN Survey

Cancers ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 1161
Author(s):  
Lidia Delrieu ◽  
Liacine Bouaoun ◽  
Douae El Fatouhi ◽  
Elise Dumas ◽  
Anne-Deborah Bouhnik ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Latent Class ◽  
Early Stage ◽  
Current Analysis ◽  
Functional Pain ◽  
Cognitive Sequelae ◽  
History Of ◽  
The Mean ◽  
Study Participants ◽  
Changes Over Time

Breast cancer (BC) remains complex for women both physically and psychologically. The objectives of this study were to (1) assess the evolution of the main sequelae and treatment two and five years after diagnosis in women with early-stage breast cancer, (2) explore patterns of sequelae associated with given sociodemographic, clinical, and lifestyle factors. The current analysis was based on 654 localized BC patients enrolled in the French nationwide longitudinal survey “vie après cancer” VICAN (January–June 2010). Information about study participants was collected at enrollment, two and five years after diagnosis. Changes over time of the main sequelae were analyzed and latent class analysis was performed to identify patterns of sequelae related to BC five years after diagnosis. The mean age (±SD) of study participants at inclusion was 49.7 (±10.5) years old. Six main classes of sequelae were identified two years and five years post-diagnosis (functional, pain, esthetic, fatigue, psychological, and gynecological). A significant decrease was observed for fatigue (p = 0.03) and an increase in cognitive sequelae was reported (p = 0.03). Two latent classes were identified—functional and esthetic patterns. Substantial sequelae remain up to five years after BC diagnosis. Changes in patient care pathways are needed to identify BC patients at a high risk.

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