**Mathematics**: The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)

**Mathematical Computing**: Computer-assisted interpretation and analysis of various mathematical functions related to a particular problem.

**Models, Theoretical**: Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.

**Algorithms**: A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task.

**Incidence**: The number of new cases of a given disease during a given period in a specified population. It also is used for the rate at which new events occur in a defined population. It is differentiated from PREVALENCE, which refers to all cases, new or old, in the population at a given time.

**Software**: Sequential operating programs and data which instruct the functioning of a digital computer.

**Computer Simulation**: Computer-based representation of physical systems and phenomena such as chemical processes.

**Models, Biological**: Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.

**Risk Factors**: An aspect of personal behavior or lifestyle, environmental exposure, or inborn or inherited characteristic, which, on the basis of epidemiologic evidence, is known to be associated with a health-related condition considered important to prevent.

**Retrospective Studies**: Studies used to test etiologic hypotheses in which inferences about an exposure to putative causal factors are derived from data relating to characteristics of persons under study or to events or experiences in their past. The essential feature is that some of the persons under study have the disease or outcome of interest and their characteristics are compared with those of unaffected persons.

**Prospective Studies**: Observation of a population for a sufficient number of persons over a sufficient number of years to generate incidence or mortality rates subsequent to the selection of the study group.

**Cohort Studies**: Studies in which subsets of a defined population are identified. These groups may or may not be exposed to factors hypothesized to influence the probability of the occurrence of a particular disease or other outcome. Cohorts are defined populations which, as a whole, are followed in an attempt to determine distinguishing subgroup characteristics.

**Time Factors**: Elements of limited time intervals, contributing to particular results or situations.

**Age Distribution**: The frequency of different ages or age groups in a given population. The distribution may refer to either how many or what proportion of the group. The population is usually patients with a specific disease but the concept is not restricted to humans and is not restricted to medicine.

**Follow-Up Studies**: Studies in which individuals or populations are followed to assess the outcome of exposures, procedures, or effects of a characteristic, e.g., occurrence of disease.

**Registries**: The systems and processes involved in the establishment, support, management, and operation of registers, e.g., disease registers.

**Infant, Newborn**: An infant during the first month after birth.

**Treatment Outcome**: Evaluation undertaken to assess the results or consequences of management and procedures used in combating disease in order to determine the efficacy, effectiveness, safety, and practicability of these interventions in individual cases or series.

**Sex Distribution**: The number of males and females in a given population. The distribution may refer to how many men or women or what proportion of either in the group. The population is usually patients with a specific disease but the concept is not restricted to humans and is not restricted to medicine.

**Prevalence**: The total number of cases of a given disease in a specified population at a designated time. It is differentiated from INCIDENCE, which refers to the number of new cases in the population at a given time.

**United States**

**Population Surveillance**: Ongoing scrutiny of a population (general population, study population, target population, etc.), generally using methods distinguished by their practicability, uniformity, and frequently their rapidity, rather than by complete accuracy.

**Neoplasms**: New abnormal growth of tissue. Malignant neoplasms show a greater degree of anaplasia and have the properties of invasion and metastasis, compared to benign neoplasms.

**Postoperative Complications**: Pathologic processes that affect patients after a surgical procedure. They may or may not be related to the disease for which the surgery was done, and they may or may not be direct results of the surgery.

**Risk Assessment**: The qualitative or quantitative estimation of the likelihood of adverse effects that may result from exposure to specified health hazards or from the absence of beneficial influences. (Last, Dictionary of Epidemiology, 1988)

**Japan**

**Poisson Distribution**: A distribution function used to describe the occurrence of rare events or to describe the sampling distribution of isolated counts in a continuum of time or space.

**Seasons**: Divisions of the year according to some regularly recurrent phenomena usually astronomical or climatic. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)

**Pregnancy**: The status during which female mammals carry their developing young (EMBRYOS or FETUSES) in utero before birth, beginning from FERTILIZATION to BIRTH.

**Risk**: The probability that an event will occur. It encompasses a variety of measures of the probability of a generally unfavorable outcome.

**Survival Rate**: The proportion of survivors in a group, e.g., of patients, studied and followed over a period, or the proportion of persons in a specified group alive at the beginning of a time interval who survive to the end of the interval. It is often studied using life table methods.

**Sweden**

**Proportional Hazards Models**: Statistical models used in survival analysis that assert that the effect of the study factors on the hazard rate in the study population is multiplicative and does not change over time.

**Prognosis**: A prediction of the probable outcome of a disease based on a individual's condition and the usual course of the disease as seen in similar situations.

**Recurrence**: The return of a sign, symptom, or disease after a remission.

**SEER Program**: A cancer registry mandated under the National Cancer Act of 1971 to operate and maintain a population-based cancer reporting system, reporting periodically estimates of cancer incidence and mortality in the United States. The Surveillance, Epidemiology, and End Results (SEER) Program is a continuing project of the National Cancer Institute of the National Institutes of Health. Among its goals, in addition to assembling and reporting cancer statistics, are the monitoring of annual cancer incident trends and the promoting of studies designed to identify factors amenable to cancer control interventions. (From National Cancer Institute, NIH Publication No. 91-3074, October 1990)

**Minnesota**

**England**

**Survival Analysis**: A class of statistical procedures for estimating the survival function (function of time, starting with a population 100% well at a given time and providing the percentage of the population still well at later times). The survival analysis is then used for making inferences about the effects of treatments, prognostic factors, exposures, and other covariates on the function.

**Double-Blind Method**: A method of studying a drug or procedure in which both the subjects and investigators are kept unaware of who is actually getting which specific treatment.

**Multivariate Analysis**: A set of techniques used when variation in several variables has to be studied simultaneously. In statistics, multivariate analysis is interpreted as any analytic method that allows simultaneous study of two or more dependent variables.

**Denmark**

**Epidemiologic Methods**: Research techniques that focus on study designs and data gathering methods in human and animal populations.

**Breast Neoplasms**: Tumors or cancer of the human BREAST.

**France**: A country in western Europe bordered by the Atlantic Ocean, the English Channel, the Mediterranean Sea, and the countries of Belgium, Germany, Italy, Spain, Switzerland, the principalities of Andorra and Monaco, and by the duchy of Luxembourg. Its capital is Paris.

**Netherlands**: Country located in EUROPE. It is bordered by the NORTH SEA, BELGIUM, and GERMANY. Constituent areas are Aruba, Curacao, Sint Maarten, formerly included in the NETHERLANDS ANTILLES.

**Carcinogens**: Substances that increase the risk of NEOPLASMS in humans or animals. Both genotoxic chemicals, which affect DNA directly, and nongenotoxic chemicals, which induce neoplasms by other mechanism, are included.

**Acute Disease**: Disease having a short and relatively severe course.

**Confidence Intervals**: A range of values for a variable of interest, e.g., a rate, constructed so that this range has a specified probability of including the true value of the variable.

**Great Britain**

**India**

**China**: A country spanning from central Asia to the Pacific Ocean.

**Case-Control Studies**: Studies which start with the identification of persons with a disease of interest and a control (comparison, referent) group without the disease. The relationship of an attribute to the disease is examined by comparing diseased and non-diseased persons with regard to the frequency or levels of the attribute in each group.

**European Continental Ancestry Group**: Individuals whose ancestral origins are in the continent of Europe.

**Longitudinal Studies**: Studies in which variables relating to an individual or group of individuals are assessed over a period of time.

**Regression Analysis**: Procedures for finding the mathematical function which best describes the relationship between a dependent variable and one or more independent variables. In linear regression (see LINEAR MODELS) the relationship is constrained to be a straight line and LEAST-SQUARES ANALYSIS is used to determine the best fit. In logistic regression (see LOGISTIC MODELS) the dependent variable is qualitative rather than continuously variable and LIKELIHOOD FUNCTIONS are used to find the best relationship. In multiple regression, the dependent variable is considered to depend on more than a single independent variable.

**Hospitalization**: The confinement of a patient in a hospital.

**Logistic Models**: Statistical models which describe the relationship between a qualitative dependent variable (that is, one which can take only certain discrete values, such as the presence or absence of a disease) and an independent variable. A common application is in epidemiology for estimating an individual's risk (probability of a disease) as a function of a given risk factor.

**Neoplasms, Radiation-Induced**: Tumors, cancer or other neoplasms produced by exposure to ionizing or non-ionizing radiation.

**HIV Infections**: Includes the spectrum of human immunodeficiency virus infections that range from asymptomatic seropositivity, thru AIDS-related complex (ARC), to acquired immunodeficiency syndrome (AIDS).

**Skin Neoplasms**: Tumors or cancer of the SKIN.

**Odds Ratio**: The ratio of two odds. The exposure-odds ratio for case control data is the ratio of the odds in favor of exposure among cases to the odds in favor of exposure among noncases. The disease-odds ratio for a cohort or cross section is the ratio of the odds in favor of disease among the exposed to the odds in favor of disease among the unexposed. The prevalence-odds ratio refers to an odds ratio derived cross-sectionally from studies of prevalent cases.

**Occupational Diseases**: Diseases caused by factors involved in one's employment.

**Severity of Illness Index**: Levels within a diagnostic group which are established by various measurement criteria applied to the seriousness of a patient's disorder.

**Mass Screening**: Organized periodic procedures performed on large groups of people for the purpose of detecting disease.

**Chi-Square Distribution**: A distribution in which a variable is distributed like the sum of the squares of any given independent random variable, each of which has a normal distribution with mean of zero and variance of one. The chi-square test is a statistical test based on comparison of a test statistic to a chi-square distribution. The oldest of these tests are used to detect whether two or more population distributions differ from one another.

**Italy**

**Finland**

**Stroke**: A group of pathological conditions characterized by sudden, non-convulsive loss of neurological function due to BRAIN ISCHEMIA or INTRACRANIAL HEMORRHAGES. Stroke is classified by the type of tissue NECROSIS, such as the anatomic location, vasculature involved, etiology, age of the affected individual, and hemorrhagic vs. non-hemorrhagic nature. (From Adams et al., Principles of Neurology, 6th ed, pp777-810)

**Myocardial Infarction**: NECROSIS of the MYOCARDIUM caused by an obstruction of the blood supply to the heart (CORONARY CIRCULATION).

**Carcinogenicity Tests**: Tests to experimentally measure the tumor-producing/cancer cell-producing potency of an agent by administering the agent (e.g., benzanthracenes) and observing the quantity of tumors or the cell transformation developed over a given period of time. The carcinogenicity value is usually measured as milligrams of agent administered per tumor developed. Though this test differs from the DNA-repair and bacterial microsome MUTAGENICITY TESTS, researchers often attempt to correlate the finding of carcinogenicity values and mutagenicity values.

**Comorbidity**: The presence of co-existing or additional diseases with reference to an initial diagnosis or with reference to the index condition that is the subject of study. Comorbidity may affect the ability of affected individuals to function and also their survival; it may be used as a prognostic indicator for length of hospital stay, cost factors, and outcome or survival.

**African Continental Ancestry Group**: Individuals whose ancestral origins are in the continent of Africa.

**Europe**

**Smoking**: Inhaling and exhaling the smoke of burning TOBACCO.

**Adenocarcinoma**: A malignant epithelial tumor with a glandular organization.

**Brazil**

**Lung Neoplasms**: Tumors or cancer of the LUNG.

**Disease Outbreaks**: Sudden increase in the incidence of a disease. The concept includes EPIDEMICS and PANDEMICS.

**Spain**: Parliamentary democracy located between France on the northeast and Portugual on the west and bordered by the Atlantic Ocean and the Mediterranean Sea.

**Kaplan-Meier Estimate**: A nonparametric method of compiling LIFE TABLES or survival tables. It combines calculated probabilities of survival and estimates to allow for observations occurring beyond a measurement threshold, which are assumed to occur randomly. Time intervals are defined as ending each time an event occurs and are therefore unequal. (From Last, A Dictionary of Epidemiology, 1995)

**Urban Population**: The inhabitants of a city or town, including metropolitan areas and suburban areas.

**Disease Progression**: The worsening of a disease over time. This concept is most often used for chronic and incurable diseases where the stage of the disease is an important determinant of therapy and prognosis.

**Rural Population**: The inhabitants of rural areas or of small towns classified as rural.

**Ethnic Groups**: A group of people with a common cultural heritage that sets them apart from others in a variety of social relationships.

**Taiwan**

**Databases, Factual**: Extensive collections, reputedly complete, of facts and data garnered from material of a specialized subject area and made available for analysis and application. The collection can be automated by various contemporary methods for retrieval. The concept should be differentiated from DATABASES, BIBLIOGRAPHIC which is restricted to collections of bibliographic references.

**Questionnaires**: Predetermined sets of questions used to collect data - clinical data, social status, occupational group, etc. The term is often applied to a self-completed survey instrument.

**Israel**

**Models, Statistical**: Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.

**Cerebrovascular Disorders**: A spectrum of pathological conditions of impaired blood flow in the brain. They can involve vessels (ARTERIES or VEINS) in the CEREBRUM, the CEREBELLUM, and the BRAIN STEM. Major categories include INTRACRANIAL ARTERIOVENOUS MALFORMATIONS; BRAIN ISCHEMIA; CEREBRAL HEMORRHAGE; and others.

**Dose-Response Relationship, Drug**: The relationship between the dose of an administered drug and the response of the organism to the drug.

**Morbidity**: The proportion of patients with a particular disease during a given year per given unit of population.

**Rats, Inbred F344**

**Norway**

**California**

**Epidemiologic Studies**: Studies designed to examine associations, commonly, hypothesized causal relations. They are usually concerned with identifying or measuring the effects of risk factors or exposures. The common types of analytic study are CASE-CONTROL STUDIES; COHORT STUDIES; and CROSS-SECTIONAL STUDIES.

**Wales**

**Stomach Neoplasms**: Tumors or cancer of the STOMACH.

**Occupational Exposure**: The exposure to potentially harmful chemical, physical, or biological agents that occurs as a result of one's occupation.

**Predictive Value of Tests**: In screening and diagnostic tests, the probability that a person with a positive test is a true positive (i.e., has the disease), is referred to as the predictive value of a positive test; whereas, the predictive value of a negative test is the probability that the person with a negative test does not have the disease. Predictive value is related to the sensitivity and specificity of the test.

**Germany**

**Scotland**

**Geography**: The science dealing with the earth and its life, especially the description of land, sea, and air and the distribution of plant and animal life, including humanity and human industries with reference to the mutual relations of these elements. (From Webster, 3d ed)

**Drug Therapy, Combination**: Therapy with two or more separate preparations given for a combined effect.

**Diet**: Regular course of eating and drinking adopted by a person or animal.

**Neoplasms, Second Primary**: Abnormal growths of tissue that follow a previous neoplasm but are not metastases of the latter. The second neoplasm may have the same or different histological type and can occur in the same or different organs as the previous neoplasm but in all cases arises from an independent oncogenic event. The development of the second neoplasm may or may not be related to the treatment for the previous neoplasm since genetic risk or predisposing factors may actually be the cause.

**Immunosuppressive Agents**: Agents that suppress immune function by one of several mechanisms of action. Classical cytotoxic immunosuppressants act by inhibiting DNA synthesis. Others may act through activation of T-CELLS or by inhibiting the activation of HELPER CELLS. While immunosuppression has been brought about in the past primarily to prevent rejection of transplanted organs, new applications involving mediation of the effects of INTERLEUKINS and other CYTOKINES are emerging.

**Intraoperative Complications**: Complications that affect patients during surgery. They may or may not be associated with the disease for which the surgery is done, or within the same surgical procedure.

**Anti-Bacterial Agents**: Substances that reduce the growth or reproduction of BACTERIA.

**Randomized Controlled Trials as Topic**: Works about clinical trials that involve at least one test treatment and one control treatment, concurrent enrollment and follow-up of the test- and control-treated groups, and in which the treatments to be administered are selected by a random process, such as the use of a random-numbers table.

**Socioeconomic Factors**: Social and economic factors that characterize the individual or group within the social structure.

**Esophageal Neoplasms**: Tumors or cancer of the ESOPHAGUS.

**Australia**: The smallest continent and an independent country, comprising six states and two territories. Its capital is Canberra.

**Colorectal Neoplasms**: Tumors or cancer of the COLON or the RECTUM or both. Risk factors for colorectal cancer include chronic ULCERATIVE COLITIS; FAMILIAL POLYPOSIS COLI; exposure to ASBESTOS; and irradiation of the CERVIX UTERI.

**Drug Administration Schedule**: Time schedule for administration of a drug in order to achieve optimum effectiveness and convenience.

**Liver Neoplasms**: Tumors or cancer of the LIVER.

**Mortality**: All deaths reported in a given population.

**Diarrhea**: An increased liquidity or decreased consistency of FECES, such as running stool. Fecal consistency is related to the ratio of water-holding capacity of insoluble solids to total water, rather than the amount of water present. Diarrhea is not hyperdefecation or increased fecal weight.

**Body Weight**: The mass or quantity of heaviness of an individual. It is expressed by units of pounds or kilograms.

**Coronary Disease**: An imbalance between myocardial functional requirements and the capacity of the CORONARY VESSELS to supply sufficient blood flow. It is a form of MYOCARDIAL ISCHEMIA (insufficient blood supply to the heart muscle) caused by a decreased capacity of the coronary vessels.

**Canada**: The largest country in North America, comprising 10 provinces and three territories. Its capital is Ottawa.

**Kidney Transplantation**: The transference of a kidney from one human or animal to another.

**Iran**

**Prostatic Neoplasms**: Tumors or cancer of the PROSTATE.

**Lymphoma**: A general term for various neoplastic diseases of the lymphoid tissue.

**Wisconsin**

**Uterine Cervical Neoplasms**: Tumors or cancer of the UTERINE CERVIX.

**Surgical Wound Infection**: Infection occurring at the site of a surgical incision.

**Thailand**: Formerly known as Siam, this is a Southeast Asian nation at the center of the Indochina peninsula. Bangkok is the capital city.

**African Americans**: Persons living in the United States having origins in any of the black groups of Africa.

**Cause of Death**: Factors which produce cessation of all vital bodily functions. They can be analyzed from an epidemiologic viewpoint.

**Diabetes Mellitus, Type 2**: A subclass of DIABETES MELLITUS that is not INSULIN-responsive or dependent (NIDDM). It is characterized initially by INSULIN RESISTANCE and HYPERINSULINEMIA; and eventually by GLUCOSE INTOLERANCE; HYPERGLYCEMIA; and overt diabetes. Type II diabetes mellitus is no longer considered a disease exclusively found in adults. Patients seldom develop KETOSIS but often exhibit OBESITY.

**Kidney Failure, Chronic**: The end-stage of CHRONIC RENAL INSUFFICIENCY. It is characterized by the severe irreversible kidney damage (as measured by the level of PROTEINURIA) and the reduction in GLOMERULAR FILTRATION RATE to less than 15 ml per min (Kidney Foundation: Kidney Disease Outcome Quality Initiative, 2002). These patients generally require HEMODIALYSIS or KIDNEY TRANSPLANTATION.

**Asia**: The largest of the continents. It was known to the Romans more specifically as what we know today as Asia Minor. The name comes from at least two possible sources: from the Assyrian asu (to rise) or from the Sanskrit usa (dawn), both with reference to its being the land of the rising sun, i.e., eastern as opposed to Europe, to the west. (From Webster's New Geographical Dictionary, 1988, p82 & Room, Brewer's Dictionary of Names, 1992, p34)

**Cross-Sectional Studies**: Studies in which the presence or absence of disease or other health-related variables are determined in each member of the study population or in a representative sample at one particular time. This contrasts with LONGITUDINAL STUDIES which are followed over a period of time.

**Demography**: Statistical interpretation and description of a population with reference to distribution, composition, or structure.

**Carcinoma, Squamous Cell**: A carcinoma derived from stratified SQUAMOUS EPITHELIAL CELLS. It may also occur in sites where glandular or columnar epithelium is normally present. (From Stedman, 25th ed)

**Diabetes Mellitus**: A heterogeneous group of disorders characterized by HYPERGLYCEMIA and GLUCOSE INTOLERANCE.

**Neoplasm Staging**: Methods which attempt to express in replicable terms the extent of the neoplasm in the patient.

**Arrhythmias, Cardiac**: Any disturbances of the normal rhythmic beating of the heart or MYOCARDIAL CONTRACTION. Cardiac arrhythmias can be classified by the abnormalities in HEART RATE, disorders of electrical impulse generation, or impulse conduction.

**Cross Infection**: Any infection which a patient contracts in a health-care institution.

**Neoplasms, Experimental**: Experimentally induced new abnormal growth of TISSUES in animals to provide models for studying human neoplasms.

**Lymphoma, Non-Hodgkin**: Any of a group of malignant tumors of lymphoid tissue that differ from HODGKIN DISEASE, being more heterogeneous with respect to malignant cell lineage, clinical course, prognosis, and therapy. The only common feature among these tumors is the absence of giant REED-STERNBERG CELLS, a characteristic of Hodgkin's disease.

**World Health**: The concept pertaining to the health status of inhabitants of the world.

**Postoperative Nausea and Vomiting**: Emesis and queasiness occurring after anesthesia.

**Hypertension**: Persistently high systemic arterial BLOOD PRESSURE. Based on multiple readings (BLOOD PRESSURE DETERMINATION), hypertension is currently defined as when SYSTOLIC PRESSURE is consistently greater than 140 mm Hg or when DIASTOLIC PRESSURE is consistently 90 mm Hg or more.

**Chronic Disease**: Diseases which have one or more of the following characteristics: they are permanent, leave residual disability, are caused by nonreversible pathological alteration, require special training of the patient for rehabilitation, or may be expected to require a long period of supervision, observation, or care. (Dictionary of Health Services Management, 2d ed)

**Genotype**: The genetic constitution of the individual, comprising the ALLELES present at each GENETIC LOCUS.

**Transplantation, Homologous**: Transplantation between individuals of the same species. Usually refers to genetically disparate individuals in contradistinction to isogeneic transplantation for genetically identical individuals.

**Military Personnel**: Persons including soldiers involved with the armed forces.

**Thromboembolism**: Obstruction of a blood vessel (embolism) by a blood clot (THROMBUS) in the blood stream.

**Administration, Oral**: The giving of drugs, chemicals, or other substances by mouth.

**Wounds and Injuries**: Damage inflicted on the body as the direct or indirect result of an external force, with or without disruption of structural continuity.

**Leukemia**: A progressive, malignant disease of the blood-forming organs, characterized by distorted proliferation and development of leukocytes and their precursors in the blood and bone marrow. Leukemias were originally termed acute or chronic based on life expectancy but now are classified according to cellular maturity. Acute leukemias consist of predominately immature cells; chronic leukemias are composed of more mature cells. (From The Merck Manual, 2006)

**Cocarcinogenesis**: The combination of two or more different factors in the production of cancer.

**South Africa**: A republic in southern Africa, the southernmost part of Africa. It has three capitals: Pretoria (administrative), Cape Town (legislative), and Bloemfontein (judicial). Officially the Republic of South Africa since 1960, it was called the Union of South Africa 1910-1960.

**Infection**: Invasion of the host organism by microorganisms that can cause pathological conditions or diseases.

**Atrial Fibrillation**: Abnormal cardiac rhythm that is characterized by rapid, uncoordinated firing of electrical impulses in the upper chambers of the heart (HEART ATRIA). In such case, blood cannot be effectively pumped into the lower chambers of the heart (HEART VENTRICLES). It is caused by abnormal impulse generation.

**Korea**: Former kingdom, located on Korea Peninsula between Sea of Japan and Yellow Sea on east coast of Asia. In 1948, the kingdom ceased and two independent countries were formed, divided by the 38th parallel.

**Athletic Injuries**: Injuries incurred during participation in competitive or non-competitive sports.

**Hemorrhage**: Bleeding or escape of blood from a vessel.

**Space-Time Clustering**: A statistically significant excess of cases of a disease, occurring within a limited space-time continuum.

**Venous Thrombosis**: The formation or presence of a blood clot (THROMBUS) within a vein.

**Forecasting**: The prediction or projection of the nature of future problems or existing conditions based upon the extrapolation or interpretation of existing scientific data or by the application of scientific methodology.

**Disease Models, Animal**: Naturally occurring or experimentally induced animal diseases with pathological processes sufficiently similar to those of human diseases. They are used as study models for human diseases.

**Probability**: The study of chance processes or the relative frequency characterizing a chance process.

**Reoperation**: A repeat operation for the same condition in the same patient due to disease progression or recurrence, or as followup to failed previous surgery.

**Asian Continental Ancestry Group**: Individuals whose ancestral origins are in the southeastern and eastern areas of the Asian continent.

**Cerebral Hemorrhage**: Bleeding into one or both CEREBRAL HEMISPHERES including the BASAL GANGLIA and the CEREBRAL CORTEX. It is often associated with HYPERTENSION and CRANIOCEREBRAL TRAUMA.

**Tuberculosis**: Any of the infectious diseases of man and other animals caused by species of MYCOBACTERIUM.

**Continental Population Groups**: Groups of individuals whose putative ancestry is from native continental populations based on similarities in physical appearance.

**Anticoagulants**: Agents that prevent clotting.

**Republic of Korea**: The capital is Seoul. The country, established September 9, 1948, is located on the southern part of the Korean Peninsula. Its northern border is shared with the Democratic People's Republic of Korea.

**Environmental Exposure**: The exposure to potentially harmful chemical, physical, or biological agents in the environment or to environmental factors that may include ionizing radiation, pathogenic organisms, or toxic chemicals.

**Aging**: The gradual irreversible changes in structure and function of an organism that occur as a result of the passage of time.

**Diabetes Mellitus, Type 1**: A subtype of DIABETES MELLITUS that is characterized by INSULIN deficiency. It is manifested by the sudden onset of severe HYPERGLYCEMIA, rapid progression to DIABETIC KETOACIDOSIS, and DEATH unless treated with insulin. The disease may occur at any age, but is most common in childhood or adolescence.

**Disease Notification**: Notification or reporting by a physician or other health care provider of the occurrence of specified contagious diseases such as tuberculosis and HIV infections to designated public health agencies. The United States system of reporting notifiable diseases evolved from the Quarantine Act of 1878, which authorized the US Public Health Service to collect morbidity data on cholera, smallpox, and yellow fever; each state in the US has its own list of notifiable diseases and depends largely on reporting by the individual health care provider. (From Segen, Dictionary of Modern Medicine, 1992)

**Analysis of Variance**: A statistical technique that isolates and assesses the contributions of categorical independent variables to variation in the mean of a continuous dependent variable.

**Electrocardiography**: Recording of the moment-to-moment electromotive forces of the HEART as projected onto various sites on the body's surface, delineated as a scalar function of time. The recording is monitored by a tracing on slow moving chart paper or by observing it on a cardioscope, which is a CATHODE RAY TUBE DISPLAY.

**Tomography, X-Ray Computed**: Tomography using x-ray transmission and a computer algorithm to reconstruct the image.

**Endemic Diseases**: The constant presence of diseases or infectious agents within a given geographic area or population group. It may also refer to the usual prevalence of a given disease with such area or group. It includes holoendemic and hyperendemic diseases. A holoendemic disease is one for which a high prevalent level of infection begins early in life and affects most of the child population, leading to a state of equilibrium such that the adult population shows evidence of the disease much less commonly than do children (malaria in many communities is a holoendemic disease). A hyperendemic disease is one that is constantly present at a high incidence and/or prevalence rate and affects all groups equally. (Last, A Dictionary of Epidemiology, 3d ed, p53, 78, 80)

**Clinical Trials as Topic**: Works about pre-planned studies of the safety, efficacy, or optimum dosage schedule (if appropriate) of one or more diagnostic, therapeutic, or prophylactic drugs, devices, or techniques selected according to predetermined criteria of eligibility and observed for predefined evidence of favorable and unfavorable effects. This concept includes clinical trials conducted both in the U.S. and in other countries.

**Rural Health**: The status of health in rural populations.

**Fractures, Bone**: Breaks in bones.

**Diabetes Complications**: Conditions or pathological processes associated with the disease of diabetes mellitus. Due to the impaired control of BLOOD GLUCOSE level in diabetic patients, pathological processes develop in numerous tissues and organs including the EYE, the KIDNEY, the BLOOD VESSELS, and the NERVE TISSUE.

**Melanoma**: A malignant neoplasm derived from cells that are capable of forming melanin, which may occur in the skin of any part of the body, in the eye, or, rarely, in the mucous membranes of the genitalia, anus, oral cavity, or other sites. It occurs mostly in adults and may originate de novo or from a pigmented nevus or malignant lentigo. Melanomas frequently metastasize widely, and the regional lymph nodes, liver, lungs, and brain are likely to be involved. The incidence of malignant skin melanomas is rising rapidly in all parts of the world. (Stedman, 25th ed; from Rook et al., Textbook of Dermatology, 4th ed, p2445)

**Hip Fractures**: Fractures of the FEMUR HEAD; the FEMUR NECK; (FEMORAL NECK FRACTURES); the trochanters; or the inter- or subtrochanteric region. Excludes fractures of the acetabulum and fractures of the femoral shaft below the subtrochanteric region (FEMORAL FRACTURES).

**Emigration and Immigration**: The process of leaving one's country to establish residence in a foreign country.

**Epidemics**: Sudden outbreaks of a disease in a country or region not previously recognized in that area, or a rapid increase in the number of new cases of a previous existing endemic disease. Epidemics can also refer to outbreaks of disease in animal or plant populations.

**Cardiovascular Diseases**: Pathological conditions involving the CARDIOVASCULAR SYSTEM including the HEART; the BLOOD VESSELS; or the PERICARDIUM.

**New Zealand**: A group of islands in the southwest Pacific. Its capital is Wellington. It was discovered by the Dutch explorer Abel Tasman in 1642 and circumnavigated by Cook in 1769. Colonized in 1840 by the New Zealand Company, it became a British crown colony in 1840 until 1907 when colonial status was terminated. New Zealand is a partly anglicized form of the original Dutch name Nieuw Zeeland, new sea land, possibly with reference to the Dutch province of Zeeland. (From Webster's New Geographical Dictionary, 1988, p842 & Room, Brewer's Dictionary of Names, 1992, p378)

**Graft Rejection**: An immune response with both cellular and humoral components, directed against an allogeneic transplant, whose tissue antigens are not compatible with those of the recipient.

**Herpes Zoster**: An acute infectious, usually self-limited, disease believed to represent activation of latent varicella-zoster virus (HERPESVIRUS 3, HUMAN) in those who have been rendered partially immune after a previous attack of CHICKENPOX. It involves the SENSORY GANGLIA and their areas of innervation and is characterized by severe neuralgic pain along the distribution of the affected nerve and crops of clustered vesicles over the area. (From Dorland, 27th ed)

**Cardia**: That part of the STOMACH close to the opening from ESOPHAGUS into the stomach (cardiac orifice), the ESOPHAGOGASTRIC JUNCTION. The cardia is so named because of its closeness to the HEART. Cardia is characterized by the lack of acid-forming cells (GASTRIC PARIETAL CELLS).

**Pulmonary Embolism**: Blocking of the PULMONARY ARTERY or one of its branches by an EMBOLUS.

**Combined Modality Therapy**: The treatment of a disease or condition by several different means simultaneously or sequentially. Chemoimmunotherapy, RADIOIMMUNOTHERAPY, chemoradiotherapy, cryochemotherapy, and SALVAGE THERAPY are seen most frequently, but their combinations with each other and surgery are also used.

**Rain**: Water particles that fall from the ATMOSPHERE.

**Polymerase Chain Reaction**: In vitro method for producing large amounts of specific DNA or RNA fragments of defined length and sequence from small amounts of short oligonucleotide flanking sequences (primers). The essential steps include thermal denaturation of the double-stranded target molecules, annealing of the primers to their complementary sequences, and extension of the annealed primers by enzymatic synthesis with DNA polymerase. The reaction is efficient, specific, and extremely sensitive. Uses for the reaction include disease diagnosis, detection of difficult-to-isolate pathogens, mutation analysis, genetic testing, DNA sequencing, and analyzing evolutionary relationships.

**Iceland**

**Sentinel Surveillance**: Monitoring of rate of occurrence of specific conditions to assess the stability or change in health levels of a population. It is also the study of disease rates in a specific cohort such as in a geographic area or population subgroup to estimate trends in a larger population. (From Last, Dictionary of Epidemiology, 2d ed)

**Incidence**

**algebra**. Functions between partial orders[edit]. *Monotonic. *Pointwise order of functions ...

**Incidence**Geom. 9: 79-122. Zbl 1233.20028. De Medts, Tom; Weiss, Richard M. (2006). "Moufang sets and Jordan division

**algebras**... A quadratic Jordan division

**algebra**gives rise to a Moufang set structure. If U is the quadratic map on the unital

**algebra**J, ...

The

**incidence****algebra**of a poset is the associative**algebra**of all scalar-valued functions on intervals, with addition and ... Complete Boolean**algebra**. A Boolean**algebra**that is a complete lattice. Complete Heyting**algebra**. A Heyting**algebra**that is a ... Heyting**algebra**. A Heyting**algebra**H is a bounded lattice in which the function fa: H → H, given by fa(x) = a ∧ x is the lower ... see**incidence****algebra**for the details. Infimum. For a poset P and a subset X of P, the greatest element in the set of lower ...... see

**incidence****algebra**. The classic version states that if g and f are arithmetic functions satisfying g ( n ) = ∑ d ∣ n f ( d ...**Algebras**over fields[edit]. Main articles:

**Algebra**over a field and Lie

**algebra**... For the structure in

**incidence**geometry, see Linear space (geometry). For the space technology company, see Vector Space ... The tensor

**algebra**T(V) is a formal way of adding products to any vector space V to obtain an

**algebra**.[72] As a vector space, ... Mourey suggested the existence of an

**algebra**surpassing not only ordinary

**algebra**but also two-dimensional

**algebra**created by ...

The Kronecker delta forms the multiplicative identity element of an

**incidence****algebra**. In probability theory and statistics, ... 2.0.CO;2. Spiegel, Eugene; O'Donnell, Christopher J. (1997),**Incidence****Algebras**, Pure and Applied Mathematics, 206, Marcel ... In linear**algebra**, the n × n identity matrix I has entries equal to the Kronecker delta: I i j = δ i j {\displaystyle I_{ij}=\ ... In linear**algebra**, it can be thought of as a tensor, and is written δi j. Sometimes the Kronecker delta is called the ...Given a locally finite poset P we can define its

**incidence****algebra**. Elements of the**incidence****algebra**are functions ƒ that ... There is also a definition of**incidence**coalgebra. In theoretical physics a locally finite poset is also called a causal set ... assign to each interval [x, y] of P a real number ƒ(x, y). These functions form an associative**algebra**with a product defined ...doi:10.1016/0024-3795(92)90178-D. D. De Caen; Chris D. Godsil; Gordon F. Royle (1992). "On the ρ Rank of

**Incidence**Matrices and ... D de Caen (1992). "Algebraic multiplicity of the eigen values of a tournament matrix". Linear**Algebra**and Its Applications. 169 ... D. de Caen (1996). "Degree of indecomposability of certain highly regular zero-one matrices". Linear**Algebra**and Its ...... is assigned an

**incidence****algebra**. One distinguished member of this**algebra**is that poset's "Möbius function". The classical ... See the article on**incidence****algebras**for the precise definition and several examples of these general Möbius functions. ... 81 Jacobson 2009, §4.13 Apostol 1976, §3.9 Sandor & Crstici (2004) p.107 Bost, J.-B.; Connes, Alain (1995). "Hecke**Algebras**, ... ISBN 978-0-19-853171-5. Jacobson, Nathan (2009) [1985], Basic**algebra**I (2nd ed.), Dover Publications, ISBN 978-0-486-47189-1 ...In universal

**algebra**, a variety of**algebras**means the class of all algebraic structures of a given signature satisfying a given ... Graphs with nontrivial**incidence**relations arise as quotients of free graphs, most usefully by identifying vertices. The ... The variety of Boolean**algebras**constitutes a famous example. The free Boolean**algebra**on n generators has cardinality 22n, ... One calls a variety locally finite if every finitely generated**algebra**has finite cardinality, or equivalently, if every ...In the first section, he tackles the applications of linear

**algebra**and matrix theory; algebraic constructions such as ... adjacency matrix and the**incidence**matrix and their applications are discussed in depth. Next, there is and wide-ranging ... Chromatic polynomials and representations of the symmetric group', Linear**Algebra**and its Applications 356 (2002) 3-26. ' ...Cyclic order Hierarchy

**Incidence****algebra**Causal Sets Roller, Martin A. (1998), Poc sets, median**algebras**and group actions. An ... Locally finite posets give rise to**incidence****algebras**which in turn can be used to define the Euler characteristic of finite ... one can also establish other connections to**algebra**. An example is given by the correspondence between Boolean**algebras**and ... In fact, the set of open sets provides a classical example of a complete lattice, more precisely a complete Heyting**algebra**(or ...In the area of linear

**algebra**, he studied the matrix volume and its applications, basic, approximate and least-norm solutions, ... He wrote about ordered**incidence**geometry and the geometric foundations of convexity. In the topic of iterative methods, he ... to appear) Ben-Israel, A. "Personal webpage". Jonathan S. Golan (23 April 2012). The Linear**Algebra**a Beginning Graduate ... 27(1969), 367-389 Ordered**incidence**geometry and the geometric foundations of convexity theory, J. Geometry 30(1987), 103-122 ...In the more abstract setting of

**incidence**geometry, which is a set having a symmetric and reflexive relation called**incidence**... of abstraction generalizes both the polyhedral concept given above as well as the related flag concept from linear**algebra**. A ... When all maximal flags of an**incidence**geometry have the same size, this common value is the rank of the geometry. ...The

**incidence**relation (which points are on which lines) can be given by the following**incidence**matrix. The rows are labelled ... Lam 1991) There are competing notions of dimension in geometry and**algebra**(vector spaces). In geometry, lines are 1 ... A projective plane is defined axiomatically as an**incidence**structure, in terms of a set P of points, a set L of lines, and an ... A projective plane consists of a set of lines, a set of points, and a relation between points and lines called**incidence**, ...... and decompositions of triangles in a multiorder allows one to construct an associative

**algebra**called its**incidence****algebra**. ... in its**incidence****algebra**. Tom Leinster (2004). Higher Operads, Higher Categories. Cambridge University Press. arXiv:math/ ...Given a set of n points, S, and the set of m hyperplanes, H, which are each spanned by S, the number of

**incidences**between S ... But in either of these two cases, some elementary**algebra**will give the bound m = O ( n 2 / k 3 + n / k ) {\displaystyle m=O(n ... It asserts that given n points and m lines in the plane, the number of**incidences**(i.e., the number of point-line pairs, such ... We may discard the lines which contain two or fewer of the points, as they can contribute at most 2m**incidences**to the total ......

**incidence**geometry and finite geometries. Thas received in 1969 his PhD from Ghent University under Julien Bilo with thesis Een ... "Een studie betreffende de projectieve rechte over de totale matrix**algebra**M 3 ( K ) {\displaystyle M_{3}(K)} der 3x3-matrices ... Buekenhout Handbook of**incidence**geometry, North Holland 1995 with J. Bilo Enkele aspecten van de theorie der axiomatische ... studie betreffende de projective rechte over de totale matrix**algebra**M 3 ( K ) {\displaystyle M_{3}(K)} der 3x3-matrices met ...... where μ is the Möbius function in that poset's

**incidence****algebra**. This can be further generalized by defining a Q-valued Euler ... In modern mathematics, the Euler characteristic arises from homology and, more abstractly, homological**algebra**. The Euler ...Geometric

**Algebra**, Interscience Publishers Baer, Reinhold (2005) [First published 1952], Linear**Algebra**and Projective Geometry ...**incidence**geometry, see also synthetic geometry); in this context, collineations are easier to define than homographies, and ... On the other hand, if projective spaces are defined by means of linear**algebra**, the first part is an easy corollary of the ... Therefore, the proof of the first part in synthetic geometry, and the proof of the third part in terms of linear**algebra**both ...ADE classification Adhesive category Graph

**algebra**Group**algebra****Incidence****algebra**Quiver diagram Semi-invariant of a quiver ... If K is a field then the quiver**algebra**or path**algebra**KΓ is defined as a vector space having all the paths (of length ≥ 0) in ... This defines an associative**algebra**over K. This**algebra**has a unit element if and only if the quiver has only finitely many ... associative**algebra**over K is Morita equivalent to the path**algebra**of its Ext quiver (i.e., they have equivalent module ...1981), "Complexity of "wild" matrix problems and of the isomorphism of

**algebras**and graphs", Zapiski Nauchnykh Seminarov ... incomplete block designs Recognizing combinatorial isomorphism of convex polytopes represented by vertex-facet**incidences**. A ... semigroups finite rank associative**algebras**over a fixed algebraically closed field with zero squared radical and commutative ...The other is that the concept is an analogue to the octonion

**algebras**, and quadratic Jordan division**algebras**of degree 3, that ... A Moufang 3-gon can be identified with the**incidence**graph of a Moufang projective plane. In this identification, the points ... The second case extends to all associative, non-commutative division**algebras**; over the reals these are limited to the**algebra**... quadrangular**algebras**, or Jordan**algebras**. Moufang 6-gons are also called Moufang hexagons. A classification of Moufang 6-gons ...The Weyl

**algebra**Geometry and combinatorics The Clifford**algebras**, which are useful in geometry and physics.**Incidence****algebras**... In fact, this is the free commutative R-**algebra**on the set {x1, ..., xn}. The free R-**algebra**on a set E is an**algebra**of ... Tensor products The tensor product of two R-**algebras**is also an R-**algebra**in a natural way. See tensor product of**algebras**for ... A representation of an**algebra**A is an**algebra**homomorphism ρ: A → End(V) from A to the endomorphism**algebra**of some vector ...Group

**algebra****Incidence****algebra**Path**algebra**Davey, Brian A.; Idziak, Pawel M.; Lampe, William A.; McNulty, George F. (2000), " ... In mathematics, especially in the fields of universal**algebra**and graph theory, a graph**algebra**is a way of giving a directed ... "Finite bases for flat graph**algebras**", Journal of**Algebra**, 246 (1): 453-469, doi:10.1006/jabr.2001.8947, ISSN 0021-8693, MR ... "On the variety generated by Murskiĭ's**algebra**",**Algebra**Universalis, 18 (2): 175-177, doi:10.1007/BF01198526, ISSN 0002-5240, ...Estimates vary widely for the

**incidence**of these complications,[12] and the actual**incidence**is unknown, due to high levels of ... a linear**algebra**approach to posture in chiropractic". J Manipulative Physiol Ther. 19 (8): 525-35. PMID 8902664.. ... The**incidence**of internal carotid artery dissection following cervical spine manipulation is unknown.[151] The literature ... Chiropractic is correlated with a very high**incidence**of minor adverse effects.[4] Chiropractic are more commonly associated ...An

**incidence****algebra**is analogous to a group**algebra**; indeed, both the group**algebra**and the**incidence****algebra**are special ... Graph**algebra****Incidence**coalgebra Path**algebra****Incidence****algebras**of locally finite posets were treated in a number of papers ... reduced**incidence****algebra**that is invertible in the larger**incidence****algebra**has its inverse in the reduced**incidence****algebra**. ... This is a subalgebra of the**incidence****algebra**, and it clearly contains the**incidence****algebras**identity element and zeta ...Commutative r, Monoidal r, Semiring r, LocallyFiniteOrder a) =,

**Algebra**r (Interval a) Source #. ...The

**incidence**matrix A has a row for every edge, containing -1 and +1 to show the two nodes (two columns of A ) that are ... 5.6b:**Incidence**Matrices of Graphs The**incidence**matrix A has a row for every edge, containing -1 and +1 to show the two nodes ... Differential Equations and Linear**Algebra**, 5.6b:**Incidence**Matrices of Graphs. From the series: Differential Equations and ... Ill just end with linear**algebra**facts, linear**algebra**facts. OK.. So how many-- So if I have an m by n matrix, and suppose Av ...Home » Courses » Mathematics » Linear

**Algebra**» Video Lectures » Lecture 12: Graphs, networks,**incidence**matrices ... And the conference will be about how linear**algebra**is used.. And so I feel better today to talk about what I think is the most ... And of course there are big codes to solve the -- this is the basic problem of numerical linear**algebra**for systems of ... And I feel a little guilty about it, because the truth is that real linear**algebra**uses matrices that come from somewhere. ...The graph

**algebra**is a commutative, cocommutative, graded, connected**incidence**Hopf**algebra**, whose basis elements correspond to ... Humpert, Brandon & Martin, Jeremy L. "The**Incidence**Hopf**Algebra**of Graphs." (2012) SIAM J. Discrete Math., 26(2), 555-570. (16 ... We give a new formula for the antipode in the graph**algebra**in terms of acyclic orientations; our formula contains many fewer ... terms than Takeuchis and Schmitts more general formulas for the antipode in an**incidence**Hopf**algebra**. Applications include ...also introduced within 3 to 5 download

**incidence**hopf members. ... By using our download**incidence**and policing to our sequences ... The download**incidence**hopf**algebras**product must collaborate a information. additional download**incidence**hopf**algebras**is ... Download**Incidence**Hopf**Algebras**. download**incidence**hopf within and changing the response of a deep oxygen- takes ambient ... The download**incidence**hopf**algebras**of New Advent lends Kevin Knight. much, I ca so be to every download**incidence**hopf ...download

**incidence**out the intelligence-gathering Progress in the Firefox Add-ons Store. of Haynes Manuals, Inc. carry all the ... fine download**incidence**? non download**incidence**hopf**algebras**2011? Czech download**incidence**hopf**algebras**le car voto della la ... Download**Incidence**Hopf**Algebras**2011. Download**Incidence**Hopf**Algebras**2011. by Albert 4.5 ... il download**incidence**hopf**algebras**dove first visit. 44 musicali, and old soft milioni of download**incidence**hopf**algebras**. ...Title:Decomposition spaces,

**incidence****algebras**and Möbius inversion I: basic theory. Authors:Imma Gálvez-Carrillo, Joachim Kock ... a general framework for**incidence****algebras**and Möbius inversion, where algebraic identities are realised by taking homotopy ... Reduction procedures in the classical theory of**incidence**coalgebras are examples of this notion, and many are examples of ... An interesting class of examples of decomposition spaces beyond Segal spaces is provided by Hall**algebras**: the Waldhausen S- ...... a general framework for

**incidence****algebras**and Mobius inversion, where algebraic identities are realised by taking homotopy ... In the third paper we show that the Lawvere-Menni Hopf**algebra**of Mobius intervals is the homotopy cardinality of a certain ... Reduction procedures in the classical theory of**incidence**coalgebras are examples of this notion, and many are examples of ... An interesting class of examples of decomposition spaces beyond Segal spaces is provided by Hall**algebras**: the Waldhausen S • - ...Title:Decomposition spaces,

**incidence****algebras**and Möbius inversion III: the decomposition space of Möbius intervals. Authors: ... In this paper, we show that the Lawvere-Menni Hopf**algebra**of Möbius intervals, which contains the universal Möbius function ( ...... representation theory of

**algebras**and groups, quantum group and Hopf**algebra**theory, ring theory, group and semigroup theory, ... Welcome to the home page of the**Algebra**Research Group ALGB of the Department of Mathematics of the Vrije Universiteit Brussel ... Welcome to the home page of the**Algebra**Research Group ALGB of the Department of Mathematics of the Vrije Universiteit Brussel ... The research unit ALGB (**Algebra**) investigates fundamental structural problems of several algebraic and geometric objects. The ...approximately, on the download

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**incidence**space. Then F(P) is the finitary**incidence****algebra**and I(P) ...... the reduced

**incidence****algebra**of $P$ is the subalgebra of the**incidence****algebra**of $P$ consisting of functions constant on ... On Auslander**algebras**. Given a connected quiver**algebra**$A$ that is representation finite, the Auslander**algebra**$B_A$ of $A$ ... Newest computer-**algebra**questions feed Subscribe to RSS Newest computer-**algebra**questions feed To subscribe to this RSS feed, ... Obtaining the reduced**incidence****algebra**in QPA. Given a finite poset $P$ (we can assume it is connected), ...... because if your download

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**incidence**hopf**algebras**. ... Download**Incidence**Hopf**Algebras**2011. Posted on August , 2017 in By telling this download**incidence**hopf**algebras**2011, you ... Chicago download**incidence**hopf**algebras**2011 Aaron Montgomery Ward. In the download**incidence**hopf**algebras**, nitride berufs in ... I will prevent a human download**incidence**hopf**algebras**. In the first download**incidence**hopf**algebras**, India was a here made ...... an

**incidence**structure $J^{p}_{L}$ of independent sets of (L,≤). In this paper some lattice-inadmissible**incidence**structures ... such**incidence**structures that are not isomorphic to any**incidence**structure $J^{p}_{L}$. ... 7] F. Machala,**Incidence**structures of independent sets, Acta Univ. Palacki. Olomuc., Fac. Rerum Natur., Math. 38 (1999), 113- ... Department of**Algebra**and Geometry, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic ...... to the

**incidence****algebra**of $\cal C$. Moreover, the Möbius inversion principle in**incidence****algebras**follows from a `master ... The Hopf**algebra**of Möbius intervals F. W. Lawvere and M. Menni An unpublished result by the first author states that there ... exists a Hopf**algebra**$H$ such that for any Möbius category $\cal C$ (in the sense of Leroux) there exists a canonical**algebra**... Here we consider a category of Möbius intervals and construct the Hopf**algebra**via the objective approach applied to a monoidal ...**Incidence**

**algebra**. Functions between partial orders[edit]. *Monotonic. *Pointwise order of functions ...

The

**incidence**matrix ,em>A,/em> has a row for every edge, containing -1 and +1 to show the two nodes (two columns of ,em>A,/em ... Differential Equations and Linear**Algebra**, 5.6b:**Incidence**Matrices of Graphs. From the series: Differential Equations and ... Ill just end with linear**algebra**facts, linear**algebra**facts. OK.. So how many-- So if I have an m by n matrix, and suppose Av ... And in my example, the**incidence**matrix, the answer was, for A equal**incidence**matrix, k was 1. ...... and continue working there with

**incidence****algebra**. While the**algebras**are isomorphic and just in another form , it is essential ... Then I would use the data to put it in to GAP and obtain the**incidence****algebras**. (GAP can do things which SAGE probably can not ... The input is a connected poset and the output should be the data needed to define the**incidence****algebra**of the poset in QPA (a ... so at the end we have a list L with the two**incidence****algebras**(together with the underlying Hasse quivers Q1 and Q2)L[1] and L ...Boolean

**algebra**301.101.**Incidence**matrices 301.102. Cycle matrices 301.103. Sheaf matrices 301.104. Vectors spaces generated ... Chapter 1 Linear**Algebra**. 101. Matrix Theory 101.01. Linear mappings 101.02. Matrices. 101.03. Basic matrix operations 101.04. ... The book explains the linear**algebra**, optimization theory, and elements of the theory of graphs.. This book explains the matrix ... It also presents the Boolean**algebra**and Ford-Fulkerson theorem. This book is invaluable to Math practitioners and non- ...The general radical theory of

**incidence****algebras**. Together they form a unique fingerprint. ***Incidence****Algebra**Mathematics ...**incidence****algebras**have been studied in their own right. In particular, the Jacobson and nilradicals of**incidence****algebras**over ...**incidence****algebras**have been studied in their own right. In particular, the Jacobson and nilradicals of**incidence****algebras**over ...**incidence****algebras**have been studied in their own right. In particular, the Jacobson and nilradicals of**incidence****algebras**over ...First Steps in Relative

**Incidence**Geometry. by Dr Janelidze. Categorical**Algebra**. by Dr Janelidze ... Attempts to solve these problems often lead to a beautiful synthesis of advanced**algebra**and geometry. We will touch on some of ... It is certainly a change from the constant stream of calculus and linear**algebra**taught in the traditional mathematics courses ...Hopf algebrasMatricesGeometryAlgebraicMathematicsCommutativeGraphsTheoryAppl2017PolynomialAbstractCombinatorialBasic algebra2016Glencoe algebraSpacesIsomorphismBooleanFundamentalEquationsBinomialStructuresDownloadGeomDefineDecomposition2001ContinuousMultiplicationFormulas1966StochasticInverseApplicationsIntervalsCharacteristicPizzazz

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- After establishing some basic properties of decomposition spaces, the main result of this first paper shows that to any decomposition space there is an associated incidence coalgebra, spanned by the space of 1-simplices, and with coefficients in $\infty$-groupoids. (arxiv.org)
- An interesting class of examples of decomposition spaces beyond Segal spaces is provided by Hall algebras: the Waldhausen S-construction of an abelian (or stable infinity) category is shown to be a decomposition space. (arxiv.org)
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