A Mathematical Model for the Enhancement of Stress Induced Hypoglycaemia by Andtidepressant Treatment in Healthy Men using Multivariate Normal Distribution
The normal distribution is a very commonly occurring continuous probability distribution. In this paper the Multivariate Normal distribution is used for finding the mgf of the curve for the enhancement of stress induced Hypoglycaemia with consideration of the variablesProlactin, ACTH, Growth Hormone, Blood Pressure, Plasma Glucose, Plasma Renin, Epinephrine, Cortisol. These variables are treated with the drugs (citalopram and tianeptine) and the joint moment generating function for the variables in Citalopram, Tianeptineand Placebo casesare found out and are given as curves in the Mathematical Results
A Mathematical Model for the Hormonal Responses During Neurally Mediated Sync...IJRES Journal
The purpose of this study is to find a Mathematical model for the participation of central serotonergic activity in neurocardiogenic syncope by comparing cortisol and prolactin plasma levels in patients with positive and negative tilt test by using Multivariate Normal Distribution.
A Class of Polynomials Associated with Differential Operator and with a Gener...iosrjce
The object of this paper is to present several classes of linear and bilateral generating relations by
employing operational techniques, which reduces as a special case of (known or new) bilateral generating
relations.At last some of generating functions associated with stirling number of second kind are also discussed.
PROBABILITY DISTRIBUTION OF SUM OF TWO CONTINUOUS VARIABLES AND CONVOLUTIONJournal For Research
All physical subjects, involving random phenomena, something depending upon chance, naturally find their own way to theory of Statistics. Hence there arise relations between the results derived for hose random phenomena in different physical subjects and the concepts of Statistics. Convolution theorem has a variety of applications in field of Fourier transforms and many other situations, but it bears beautiful applications in field of statistics also .Here in this paper authors want to discuss some notions of Electrical Engineering in terms of convolution of some probability distributions.
Correlation measure for intuitionistic fuzzy multi setseSAT Journals
The document proposes a correlation measure for intuitionistic fuzzy multi sets (IFMS). IFMS are an extension of intuitionistic fuzzy sets that allow elements to have multiple membership and non-membership values. The document defines IFMS and reviews existing correlation measures for fuzzy and intuitionistic fuzzy sets. It then proposes a new correlation similarity measure for IFMS that is an extension of existing intuitionistic fuzzy set correlation measures. This new measure takes into account the multiple membership and non-membership values of elements in IFMS. Examples are provided to demonstrate properties of the new correlation measure.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
A System of Estimators of the Population Mean under Two-Phase Sampling in Pre...Premier Publishers
This paper deals with estimation of the population mean under two-phase sampling. Utilizing information on two-auxiliary variables, a system of estimators for estimating the finite population mean is proposed and its properties, up to the first order of approximation, are studied. As particular cases various estimators are suggested. The performance of suggested estimators is compared with some contemporary estimators of the population mean through numerical illustrations carried over the data set of some natural populations. Also, a small-scale Monte Carlo simulation is carried out for the empirical comparison.
A Mathematical Model for the Hormonal Responses During Neurally Mediated Sync...IJRES Journal
The purpose of this study is to find a Mathematical model for the participation of central serotonergic activity in neurocardiogenic syncope by comparing cortisol and prolactin plasma levels in patients with positive and negative tilt test by using Multivariate Normal Distribution.
A Class of Polynomials Associated with Differential Operator and with a Gener...iosrjce
The object of this paper is to present several classes of linear and bilateral generating relations by
employing operational techniques, which reduces as a special case of (known or new) bilateral generating
relations.At last some of generating functions associated with stirling number of second kind are also discussed.
PROBABILITY DISTRIBUTION OF SUM OF TWO CONTINUOUS VARIABLES AND CONVOLUTIONJournal For Research
All physical subjects, involving random phenomena, something depending upon chance, naturally find their own way to theory of Statistics. Hence there arise relations between the results derived for hose random phenomena in different physical subjects and the concepts of Statistics. Convolution theorem has a variety of applications in field of Fourier transforms and many other situations, but it bears beautiful applications in field of statistics also .Here in this paper authors want to discuss some notions of Electrical Engineering in terms of convolution of some probability distributions.
Correlation measure for intuitionistic fuzzy multi setseSAT Journals
The document proposes a correlation measure for intuitionistic fuzzy multi sets (IFMS). IFMS are an extension of intuitionistic fuzzy sets that allow elements to have multiple membership and non-membership values. The document defines IFMS and reviews existing correlation measures for fuzzy and intuitionistic fuzzy sets. It then proposes a new correlation similarity measure for IFMS that is an extension of existing intuitionistic fuzzy set correlation measures. This new measure takes into account the multiple membership and non-membership values of elements in IFMS. Examples are provided to demonstrate properties of the new correlation measure.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
A System of Estimators of the Population Mean under Two-Phase Sampling in Pre...Premier Publishers
This paper deals with estimation of the population mean under two-phase sampling. Utilizing information on two-auxiliary variables, a system of estimators for estimating the finite population mean is proposed and its properties, up to the first order of approximation, are studied. As particular cases various estimators are suggested. The performance of suggested estimators is compared with some contemporary estimators of the population mean through numerical illustrations carried over the data set of some natural populations. Also, a small-scale Monte Carlo simulation is carried out for the empirical comparison.
SUEC 高中 Adv Maths (Quadratic Equation in One Variable)tungwc
Sources:
Visual - various maths sites (credits to original creator)
Questions - Dong Zong's Textbook
suitable for SUEC (Maths), SPM (Maths and Add Maths) too
This document discusses different types of equations that can be reduced to quadratic form. It provides examples of each type:
1) Equations of the form ax4 - bx2 + c = 0 can be reduced to quadratic by substituting x2 = y.
2) Equations containing terms like apx + b/px can be reduced by substituting the x terms as y.
3) Reciprocal equations of the form ax2 + 1/x2 + bx + 1/x + c = 0 are reduced by substituting x - 1/x = y.
4) Exponential equations can be reduced by substituting a variable for the exponential term.
5) Equations
An alternative approach to estimation of populationAlexander Decker
This document summarizes an alternative approach to estimating population mean in two-stage sampling. It proposes ratio, product, and regression estimators when the population mean of the auxiliary variable is unknown. The estimators are defined and their mean squared errors are derived. It is shown that under certain conditions, the suggested estimators are more efficient than existing estimators. Numerical examples are provided to support the theoretical results. In summary, this paper presents new estimators for population mean in two-stage sampling that make use of auxiliary information when the auxiliary population mean is unknown.
1. This document discusses methods for solving first-order linear differential equations. It defines a first-order linear differential equation as one of the form y'+py=f(x).
2. It provides examples of solving homogeneous and non-homogeneous first-order linear differential equations. The general solutions are presented as y=Ce^-px + particular solutions.
3. Bernoulli differential equations of the form y'+py=f(x)y^n, n≠1 are introduced, which can be transformed into a first-order linear equation using a substitution. An example of solving a Bernoulli equation is shown.
The document provides examples for solving matrix equations using inverses. It introduces the concept of pre-multiplying both sides of a matrix equation AX=B by the inverse of A to solve for X. Example 1 demonstrates this process, finding the inverse of the coefficient matrix and multiplying both sides to isolate X. Example 2 shows that the inverse does not exist when the coefficient matrix is singular, meaning there may be no solution or infinite solutions depending on whether the rows of B satisfy the relationship of the rows of the singular A.
- The document discusses new special functions K_n(x) defined in terms of Legendre polynomials P_n(x).
- Recurrence relations and differential equations for the new functions K_n(x) are derived.
- Properties of Legendre polynomials such as the generating function and orthogonality are used to derive relationships between the K_n(x) functions.
This document discusses derivatives of inverse trigonometric functions and provides examples of taking their derivatives. It contains the following key points:
1. The derivatives of the main inverse trigonometric functions are given as fractions involving the term 1/(1-x^2).
2. Two examples are worked through, differentiating compositions of inverse trig functions and using trigonometric substitutions.
3. The last example proves that if y = sin^(-1)(2x/(1+x^2)), then (1+x^2)dy/dx = 2 by making a u-substitution of x = tanθ.
This document discusses applications of partial differential equations, specifically looking at the effects of convective conditions on radiative peristaltic flow of pseudoplastic nanofluid through a porous medium. It presents governing equations for the problem, including equations for stress, momentum, heat transfer and stream functions. It then uses perturbation methods and binomial expansion to simplify the equations for a small pseudoplastic fluid parameter.
∂z
∂x
= f′.
∂g
∂x
∂z
∂y
= f′.
∂g
∂y
The document discusses multi-variable functions and their derivatives. It defines partial derivatives as the slope of a multi-variable function with respect to one variable, holding the other variables constant. It provides examples of calculating partial derivatives using limits and applying rules like the product and chain rules. Formulas are given for finding the partial derivatives of a function z with respect to x and y at a specific point.
This document summarizes key concepts in number theory presented in a lecture by Dr. N. Chandramowliswaran including:
- Properties of divisibility, greatest common divisors, prime numbers, and the fundamental theorem of arithmetic.
- Definitions and properties of the Mobius function, Euler's totient function, and congruences.
- Theorems regarding congruences including the Euler-Fermat theorem and the Chinese Remainder Theorem.
- The document discusses numerical methods for solving first order differential equations, namely Picard's method and Euler's method.
- Picard's method involves iteratively replacing y with the previous approximation in the differential equation to obtain better approximations that converge to the solution.
- Euler's method approximates the solution at the next point by the current value plus the rate of change times the change in x. This provides a first order approximation to the solution.
1) The document discusses the envelope theorem and its application to optimization problems with parameters. The envelope theorem describes how optimal values of decision variables change with parameters.
2) It provides an example of optimizing a quadratic function with respect to a single parameter b, showing how the optimal values of x and y vary with b.
3) The envelope theorem can be applied to constrained and unconstrained optimization problems. It allows calculating the rate of change of the optimal objective value with respect to parameters.
Least Square Plane and Leastsquare Quadric Surface Approximation by Using Mod...IOSRJM
Now a days Surface fitting is applied all engineering and medical fields. Kamron Saniee ,2007 find a simple expression for multivariate LaGrange’s Interpolation. We derive a least square plane and least square quadric surface Approximation from a given N+1 tabular points when the function is unique. We used least square method technique. We can apply this method in surface fitting also.
Asymptotic properties of bayes factor in one way repeated measurements modelAlexander Decker
1) The document discusses asymptotic properties of Bayes factors for testing linear models in one-way repeated measurements designs.
2) It considers a linear mixed model with one within-subject factor and one between-subject factor that incorporates random effects and error terms.
3) Under certain conditions on the prior distributions and design matrix, the document identifies the analytic form of the Bayes factor and shows that it is consistent as sample size increases.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Ii m sc mathematics probability and statisticsTharini7
This document provides definitions and key properties for 27 different probability distributions and statistical concepts. Some of the distributions and concepts covered include:
- The distribution function of a random variable is a non-decreasing function.
- Parameters and formulas are provided for the normal, negative binomial, geometric, gamma, beta, exponential, and hypergeometric distributions.
- Expected values and variances are given for several continuous and discrete distributions.
- The relationship between the normal distribution and the z-score is defined.
Newborn Care: Skills workshop Glucose control and hypoglycaemiaSaide OER Africa
Newborn Care was written for healthcare workers providing special care for newborn infants in level 2 hospitals. It covers: resuscitation at birth, assessing infant size and gestational age, routine care and feeding of both normal and high-risk infants, the prevention, diagnosis and management of hypothermia, hypoglycaemia, jaundice, respiratory distress, infection, trauma, bleeding and congenital abnormalities, communication with parents
Hypoglycaemia, or low blood glucose, can cause brain damage or death in newborns. It is defined as a blood glucose level below 2.0 mmol/L. Infants at highest risk include preterm infants, underweight infants, and infants of diabetic mothers. Clinical signs of hypoglycaemia are non-specific but may include depression or overstimulation of brain function. Mild hypoglycaemia can be treated with milk feeds while severe hypoglycaemia below 1.5 mmol/L requires immediate intravenous glucose therapy. Preventing hypothermia and early feeding helps reduce the risk of hypoglycaemia.
Aspire in home study-hypo protection plan learning modulemedtronicdiab
The ASPIRE In-Home Study evaluated the effect of the MiniMed VEO pump with Low Glucose Suspend (LGS) feature compared to Sensor Augmented Pump (SAP) therapy alone on nocturnal hypoglycemia and A1c in patients experiencing nocturnal hypos. The study found that LGS significantly reduced the duration and severity of nocturnal hypos by 38% and the frequency of nocturnal hypos by 31.8%, without increasing A1c. LGS also reduced the frequency of hypos throughout the 24-hour period by 30% and the number of mild, moderate, and severe hypos, without causing rebound hyperglycemia.
An insightful presentation on issue of Hypoglycaemia in patients of Diabetes Mellitus with focus on causes, symptoms and management. Also find included experience based inputs on issue of vehicle driving and hypoglycaemia
SUEC 高中 Adv Maths (Quadratic Equation in One Variable)tungwc
Sources:
Visual - various maths sites (credits to original creator)
Questions - Dong Zong's Textbook
suitable for SUEC (Maths), SPM (Maths and Add Maths) too
This document discusses different types of equations that can be reduced to quadratic form. It provides examples of each type:
1) Equations of the form ax4 - bx2 + c = 0 can be reduced to quadratic by substituting x2 = y.
2) Equations containing terms like apx + b/px can be reduced by substituting the x terms as y.
3) Reciprocal equations of the form ax2 + 1/x2 + bx + 1/x + c = 0 are reduced by substituting x - 1/x = y.
4) Exponential equations can be reduced by substituting a variable for the exponential term.
5) Equations
An alternative approach to estimation of populationAlexander Decker
This document summarizes an alternative approach to estimating population mean in two-stage sampling. It proposes ratio, product, and regression estimators when the population mean of the auxiliary variable is unknown. The estimators are defined and their mean squared errors are derived. It is shown that under certain conditions, the suggested estimators are more efficient than existing estimators. Numerical examples are provided to support the theoretical results. In summary, this paper presents new estimators for population mean in two-stage sampling that make use of auxiliary information when the auxiliary population mean is unknown.
1. This document discusses methods for solving first-order linear differential equations. It defines a first-order linear differential equation as one of the form y'+py=f(x).
2. It provides examples of solving homogeneous and non-homogeneous first-order linear differential equations. The general solutions are presented as y=Ce^-px + particular solutions.
3. Bernoulli differential equations of the form y'+py=f(x)y^n, n≠1 are introduced, which can be transformed into a first-order linear equation using a substitution. An example of solving a Bernoulli equation is shown.
The document provides examples for solving matrix equations using inverses. It introduces the concept of pre-multiplying both sides of a matrix equation AX=B by the inverse of A to solve for X. Example 1 demonstrates this process, finding the inverse of the coefficient matrix and multiplying both sides to isolate X. Example 2 shows that the inverse does not exist when the coefficient matrix is singular, meaning there may be no solution or infinite solutions depending on whether the rows of B satisfy the relationship of the rows of the singular A.
- The document discusses new special functions K_n(x) defined in terms of Legendre polynomials P_n(x).
- Recurrence relations and differential equations for the new functions K_n(x) are derived.
- Properties of Legendre polynomials such as the generating function and orthogonality are used to derive relationships between the K_n(x) functions.
This document discusses derivatives of inverse trigonometric functions and provides examples of taking their derivatives. It contains the following key points:
1. The derivatives of the main inverse trigonometric functions are given as fractions involving the term 1/(1-x^2).
2. Two examples are worked through, differentiating compositions of inverse trig functions and using trigonometric substitutions.
3. The last example proves that if y = sin^(-1)(2x/(1+x^2)), then (1+x^2)dy/dx = 2 by making a u-substitution of x = tanθ.
This document discusses applications of partial differential equations, specifically looking at the effects of convective conditions on radiative peristaltic flow of pseudoplastic nanofluid through a porous medium. It presents governing equations for the problem, including equations for stress, momentum, heat transfer and stream functions. It then uses perturbation methods and binomial expansion to simplify the equations for a small pseudoplastic fluid parameter.
∂z
∂x
= f′.
∂g
∂x
∂z
∂y
= f′.
∂g
∂y
The document discusses multi-variable functions and their derivatives. It defines partial derivatives as the slope of a multi-variable function with respect to one variable, holding the other variables constant. It provides examples of calculating partial derivatives using limits and applying rules like the product and chain rules. Formulas are given for finding the partial derivatives of a function z with respect to x and y at a specific point.
This document summarizes key concepts in number theory presented in a lecture by Dr. N. Chandramowliswaran including:
- Properties of divisibility, greatest common divisors, prime numbers, and the fundamental theorem of arithmetic.
- Definitions and properties of the Mobius function, Euler's totient function, and congruences.
- Theorems regarding congruences including the Euler-Fermat theorem and the Chinese Remainder Theorem.
- The document discusses numerical methods for solving first order differential equations, namely Picard's method and Euler's method.
- Picard's method involves iteratively replacing y with the previous approximation in the differential equation to obtain better approximations that converge to the solution.
- Euler's method approximates the solution at the next point by the current value plus the rate of change times the change in x. This provides a first order approximation to the solution.
1) The document discusses the envelope theorem and its application to optimization problems with parameters. The envelope theorem describes how optimal values of decision variables change with parameters.
2) It provides an example of optimizing a quadratic function with respect to a single parameter b, showing how the optimal values of x and y vary with b.
3) The envelope theorem can be applied to constrained and unconstrained optimization problems. It allows calculating the rate of change of the optimal objective value with respect to parameters.
Least Square Plane and Leastsquare Quadric Surface Approximation by Using Mod...IOSRJM
Now a days Surface fitting is applied all engineering and medical fields. Kamron Saniee ,2007 find a simple expression for multivariate LaGrange’s Interpolation. We derive a least square plane and least square quadric surface Approximation from a given N+1 tabular points when the function is unique. We used least square method technique. We can apply this method in surface fitting also.
Asymptotic properties of bayes factor in one way repeated measurements modelAlexander Decker
1) The document discusses asymptotic properties of Bayes factors for testing linear models in one-way repeated measurements designs.
2) It considers a linear mixed model with one within-subject factor and one between-subject factor that incorporates random effects and error terms.
3) Under certain conditions on the prior distributions and design matrix, the document identifies the analytic form of the Bayes factor and shows that it is consistent as sample size increases.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Ii m sc mathematics probability and statisticsTharini7
This document provides definitions and key properties for 27 different probability distributions and statistical concepts. Some of the distributions and concepts covered include:
- The distribution function of a random variable is a non-decreasing function.
- Parameters and formulas are provided for the normal, negative binomial, geometric, gamma, beta, exponential, and hypergeometric distributions.
- Expected values and variances are given for several continuous and discrete distributions.
- The relationship between the normal distribution and the z-score is defined.
Newborn Care: Skills workshop Glucose control and hypoglycaemiaSaide OER Africa
Newborn Care was written for healthcare workers providing special care for newborn infants in level 2 hospitals. It covers: resuscitation at birth, assessing infant size and gestational age, routine care and feeding of both normal and high-risk infants, the prevention, diagnosis and management of hypothermia, hypoglycaemia, jaundice, respiratory distress, infection, trauma, bleeding and congenital abnormalities, communication with parents
Hypoglycaemia, or low blood glucose, can cause brain damage or death in newborns. It is defined as a blood glucose level below 2.0 mmol/L. Infants at highest risk include preterm infants, underweight infants, and infants of diabetic mothers. Clinical signs of hypoglycaemia are non-specific but may include depression or overstimulation of brain function. Mild hypoglycaemia can be treated with milk feeds while severe hypoglycaemia below 1.5 mmol/L requires immediate intravenous glucose therapy. Preventing hypothermia and early feeding helps reduce the risk of hypoglycaemia.
Aspire in home study-hypo protection plan learning modulemedtronicdiab
The ASPIRE In-Home Study evaluated the effect of the MiniMed VEO pump with Low Glucose Suspend (LGS) feature compared to Sensor Augmented Pump (SAP) therapy alone on nocturnal hypoglycemia and A1c in patients experiencing nocturnal hypos. The study found that LGS significantly reduced the duration and severity of nocturnal hypos by 38% and the frequency of nocturnal hypos by 31.8%, without increasing A1c. LGS also reduced the frequency of hypos throughout the 24-hour period by 30% and the number of mild, moderate, and severe hypos, without causing rebound hyperglycemia.
An insightful presentation on issue of Hypoglycaemia in patients of Diabetes Mellitus with focus on causes, symptoms and management. Also find included experience based inputs on issue of vehicle driving and hypoglycaemia
The document discusses various endocrine emergencies including diabetic ketoacidosis (DKA), hypoglycemia, and thyroid storm. It provides details on the causes, symptoms, diagnostic criteria and treatment approaches for each condition. DKA results from lack of insulin and needs urgent treatment including rehydration, insulin administration, and electrolyte correction. Hypoglycemia can be caused by too much insulin or too little food intake and requires glucose administration. Thyroid storm is a life-threatening exacerbation of hyperthyroidism that requires treatments to correct the hyperthyroidism and address any precipitating factors.
The document discusses various types of insulin and insulin delivery methods for managing diabetes. It describes a 37-year-old man with type 1 diabetes of 18 years whose HbA1c is consistently high at 9.0-10.5% despite different insulin regimens. It then discusses options like Glargine insulin and education programs that can help improve blood sugar control and reduce hypoglycemia for patients.
Similar to A Mathematical Model for the Enhancement of Stress Induced Hypoglycaemia by Andtidepressant Treatment in Healthy Men using Multivariate Normal Distribution
A Mathematical Model for the Hormonal Responses During Neurally Mediated Sync...irjes
The purpose of this study is to find a Mathematical model for the participation of central serotonergic activity in neurocardiogenic syncope by comparing cortisol and prolactin plasma levels in patients with positive and negative tilt test by using Multivariate Normal Distribution.
Our journal has been transition marks a significant shift in the landscape of academic publishing, aiming to provide numerous benefits to both authors and readers. Open access has the potential to democratize knowledge, enhance research impact, and foster greater collaboration within the academic community.
Uniformity of the Local Convergence of Chord Method for Generalized EquationsIOSR Journals
This document summarizes research on the uniform convergence of the Chord method for solving generalized equations. The Chord method is an iterative method for finding solutions to equations of the form y ∈ f(x) + F(x), where f is a function and F is a set-valued mapping. The authors prove that under certain conditions, including F being pseudo-Lipschitz and the derivative of f being continuous, the Chord method converges uniformly for small variations in the parameter y. They obtain this result in two different ways. The document also provides relevant definitions and preliminaries on generalized equations, set-valued mappings, and convergence properties.
Generalised Statistical Convergence For Double SequencesIOSR Journals
Recently, the concept of 𝛽-statistical Convergence was introduced considering a sequence of infinite
matrices 𝛽 = (𝑏𝑛𝑘 𝑖 ). Later, it was used to define and study 𝛽-statistical limit point, 𝛽-statistical cluster point,
𝑠𝑡𝛽 − 𝑙𝑖𝑚𝑖𝑡 inferior and 𝑠𝑡𝛽 − 𝑙𝑖𝑚𝑖𝑡 superior. In this paper we analogously define and study 2𝛽-statistical
limit, 2𝛽-statistical cluster point, 𝑠𝑡2𝛽 − 𝑙𝑖𝑚𝑖𝑡 inferior and 𝑠𝑡2𝛽 − 𝑙𝑖𝑚𝑖𝑡 superior for double sequences.
The document discusses properties of complex numbers including:
- Commutativity and associativity of addition and multiplication
- Additive and multiplicative identities and inverses
- Conjugates, modulus, and triangle inequality
- Polar form representation using modulus and argument
- Exponential form for products, quotients, and powers
- Roots of complex numbers and finding nth roots
- Representing functions of a complex variable using modulus and argument
A Probabilistic Algorithm for Computation of Polynomial Greatest Common with ...mathsjournal
- The document presents a probabilistic algorithm for computing the polynomial greatest common divisor (PGCD) with smaller factors.
- It summarizes previous work on the subresultant algorithm for computing PGCD and discusses its limitations, such as not always correctly determining the variant τ.
- The new algorithm aims to determine τ correctly in most cases when given two polynomials f(x) and g(x). It does so by adding a few steps instead of directly computing the polynomial t(x) in the relation s(x)f(x) + t(x)g(x) = r(x).
Regression analysis is a mathematical measure of the average relationship between two or more variables in terms of the original units of the data.
In regression analysis there are two types of variables. The variable whose value is influenced or is to be predicted is called dependent variable and the variable which influences the values or is used for prediction, is called independent variable.
In regression analysis independent variable is also known as regressor or predictor or explanatory variable while the dependent variable is also known as regressed or explained variable.
A Generalised Class of Unbiased Seperate Regression Type Estimator under Stra...IOSRJM
In this paper a generalized class of regression type estimators using the auxiliary information on population mean and population variance is proposed under stratified random sampling. In order to improve the performance of the proposed class of estimator, the Jack-knifed versions are also proposed. A comparative study of the proposed estimator is made with that of separate ratio estimator, separate product estimator, separate linear regression estimator and the usual stratified sample mean. It is shown that the estimators through proposed allocation always give more efficient estimators in the sense of having smaller mean square error than those obtained through Neyman Allocation
The document discusses solving simultaneous linear equations using the substitution method. It begins by explaining how to reduce a set of simultaneous linear equations into a single linear equation with one unknown. This is done by substituting one equation into the other to eliminate one of the unknowns. Three examples are then worked through step-by-step to demonstrate the substitution method. The key steps are: 1) express one unknown in terms of the other, 2) substitute this into the other equation to get a single-variable equation, 3) solve for the value of the unknown, and 4) back-substitute to find the value of the other unknown. Checking the solution involves substituting the values back into the original equations.
The document is a table of contents for a report on probability and random processes. It lists 8 topics that will be covered in the report: probability density function, properties of probability density function, properties of distribution function, normal distribution, parameters of the normal distribution, exponential distribution, central limit theorem, and distribution function of the exponential distribution.
Many Decision Problems in business and social systems can be modeled using mathematical optimization, which seeks to maximize or minimize some objective which is a function of the decisions.
Stochastic Optimization Problems are mathematical programs where some of the data incorporated into the objective or constraints are Uncertain.
whereas, Deterministic Optimization Problems are formulated with known parameters.
LINEAR DIFFERENTIAL EQUATIONSLINEAR DIFFERENTIAL EQUATIONS .pptxAlaOffice1
This document presents an overview of linear differential equations of the first order. It discusses the definition, general form, and solution methods like separation of variables and integrating factors. Some examples are provided to demonstrate how to solve first-order linear differential equations. Applications to areas like population growth, heat transfer, and electrical circuits are also mentioned. The goal is to provide an introduction to these fundamental equations and their use in mathematical modeling of real-world phenomena.
This document presents concepts related to the convergence of the Bernoulli distribution to other probability distributions. It begins with definitions of the Bernoulli distribution and introduces binomial, Poisson, and Gaussian distributions. It then presents three lemmas to be used in proofs in the next section. The lemmas cover the limiting behavior of exponential terms, factorials, and an approximation for large factorials. The document aims to directly prove convergence results, unlike most previous works that used an indirect approach via moment generating functions.
This document presents concepts related to the convergence of the Bernoulli distribution to other probability distributions. It begins with definitions of the Bernoulli distribution and introduces binomial, Poisson, and Gaussian distributions. It then presents three lemmas to be used in proofs in the next section. The lemmas cover the limiting behavior of exponential terms, factorials, and an approximation for large factorials. The document aims to directly prove convergence results, unlike most previous works that used an indirect approach via moment generating functions.
Approximate Solution of a Linear Descriptor Dynamic Control System via a non-...IOSR Journals
This document discusses approximate solutions for linear descriptor dynamic control systems using a non-classical variational approach. It begins by introducing descriptor systems and their importance in applications. It then discusses making irregular systems regular through computational algorithms. The paper focuses on consistent initial conditions and their characterization. It proposes using a non-classical variational approach to obtain approximate solutions with a high degree of accuracy and freedom of choice for the bilinear form.
This paper presents concepts of Bernoulli distribution, and how it can be used as an approximation of Binomial, Poisson, and Gaussian distributions with a different approach from earlier existing literature. Due to discrete nature of the random variable X, a more appropriate method of the principle of mathematical induction (PMI) is used as an alternative approach to limiting behavior of the binomial random variable. The study proved de Moivre–Laplace theorem (convergence of binomial distribution to Gaussian distribution) to all values of p such that p ≠ 0 and p ≠ 1 using a direct approach which opposes the popular and most widely used indirect method of moment generating function.
1) The document discusses periodic solutions for nonlinear systems of integro-differential equations with impulsive action of operators.
2) It presents a numerical-analytic method for approximating periodic solutions using uniformly convergent sequences of periodic functions.
3) The method is proved to construct a unique periodic solution that converges uniformly as m approaches infinity.
Properties of coefficient of correlationNadeem Uddin
The document discusses properties of the coefficient of correlation (r) including:
1) r always lies between -1 and 1
2) r is the geometric mean of the two regression coefficients
3) Several examples are shown calculating r from regression coefficients and comparing to Pearson's coefficient of correlation.
The document discusses matrix representations of operators and changes of basis in quantum mechanics. Some key points:
- Matrix elements of an operator are computed using a basis of kets. The expectation value of an operator is computed from its matrix elements and the state vectors.
- If two operators commute, they have the same set of eigenkets.
- A change of basis is a unitary transformation that relates two different sets of basis kets that span the same space. It establishes a link between the two basis representations.
- Linear algebra concepts like linear independence of eigenvectors and Hermitian operators having real eigenvalues are important in quantum mechanics.
1. Statistical efficiency compares two unbiased estimators by calculating their relative variance. The estimator with the lower variance is more efficient.
2. The Cramer-Rao inequality provides a lower bound (CRLB) for the variance of an unbiased estimator. It states that the variance of an estimator must be greater than or equal to the inverse of the expected information.
3. An estimator that achieves the Cramer-Rao lower bound is considered statistically efficient, as its variance reaches the theoretical minimum. In the example given, the maximum likelihood estimator of the mean of a normal distribution is shown to be efficient.
Similar to A Mathematical Model for the Enhancement of Stress Induced Hypoglycaemia by Andtidepressant Treatment in Healthy Men using Multivariate Normal Distribution (20)
Exploratory study on the use of crushed cockle shell as partial sand replacem...IJRES Journal
The increasing demand for natural river sand supply for the use in construction industry along
with the issue of environmental problem posed by the dumping of cockle shell, a by-product from cockle
business have initiated research towards producing a more environmental friendly concrete. This research
explores the potential use of cockle shell as partial sand replacement in concrete production. Cockle shell used
in this experimental work were crushed to smaller size almost similar to sand before mixed in concrete. A total
of six concrete mixtures were prepared with varying the percentages of cockle shell viz. 0%, 5%, 10%, 15%,
20% and 25%. All the specimens were subjected to continuous water curing. The compressive strength test was
conducted at 28 days in accordance to BS EN 12390. Finding shows that integration of suitable content of
crushed cockle shell of 10% as partial sand replacement able to enhance the compressive strength of concrete.
Adopting crushed cockle shell as partial sand replacement in concrete would reduce natural river sand
consumption as well as reducing the amount of cockle shell disposed as waste.
Congenital Malaria: Correlation of Umbilical Cord Plasmodium falciparum Paras...IJRES Journal
The vertical (trans-placental) transmission of the parasite Plasmodium falciparum from
pregnant mother to fetus during gestational period was investigated in a clinical research involving 43 full term
pregnant women in selected Hospitals in Jimeta Yola, Adamawa State Nigeria. During the observational study,
parasitemia was determined by light microscopic examination of umbilical and maternal peripheral blood film
for the presence of the trophozoites of Plasmodium falciparum. Correlational analysis was then carried on the
result obtained at p<0.05.><0.05) was established between maternal peripheral blood and umbilical cord
blood parasitemia with Pearson’s correlation coefficient of 0.762. Thus, in a malaria endemic area like Yola,
Adamawa State, Nigeria, with a stable transmission of parasite, there is a high probability of vertical
transmission of Plasmodium falciparum parasite from mother to fetus during gestation that can be followed by
the presentation of the symptoms of malaria by the newborn and other malaria related complications. Families
are advised to consistently sleep under appropriately treated insecticide mosquito net to avoid mosquito bite and
subsequent infestation.
Review: Nonlinear Techniques for Analysis of Heart Rate VariabilityIJRES Journal
Heart rate variability (HRV) is a measure of the balance between sympathetic mediators of heart
rate that is the effect of epinephrine and norepinephrine released from sympathetic nerve fibres acting on the
sino-atrial and atrio-ventricular nodes which increase the rate of cardiac contraction and facilitate conduction at
the atrio-ventricular node and parasympathetic mediators of heart rate that is the influence of acetylcholine
released by the parasympathetic nerve fibres acting on the sino-atrial and atrio-ventricular nodes leading to a
decrease in the heart rate and a slowing of conduction at the atrio-ventricular node. Sympathetic mediators
appear to exert their influence over longer time periods and are reflected in the low frequency power(LFP) of
the HRV spectrum (between 0.04Hz and 0.15 Hz).Vagal mediators exert their influence more quickly on the
heart and principally affect the high frequency power (HFP) of the HRV spectrum (between 0.15Hz and 0.4
Hz). Thus at any point in time the LFP:HFP ratio is a proxy for the sympatho- vagal balance. Thus HRV is a
valuable tool to investigate the sympathetic and parasympathetic function of the autonomic nervous system.
Study of HRV enhance our understanding of physiological phenomenon, the actions of medications and disease
mechanisms but large scale prospective studies are needed to determine the sensitivity, specificity and predictive
values of heart rate variability regarding death or morbidity in cardiac and non-cardiac patients. This paper
presents the linear and nonlinear to analysis the HRV.
Dynamic Modeling for Gas Phase Propylene Copolymerization in a Fluidized Bed ...IJRES Journal
The document presents a dynamic two-phase model for a fluidized bed reactor used to produce polypropylene. The model divides the reactor into an emulsion phase and bubble phase, with reaction assumed to occur in both phases. Simulation results show the temperature profile is lower than previous single-phase models due to considering both phases. Approximately 13% of the produced polymer comes from the bubble phase, demonstrating the importance of accounting for both phases.
Study and evaluation for different types of Sudanese crude oil propertiesIJRES Journal
Sudanese crude oil is regarded as one of the sweet types of crude in the world, Sulphur containing
compounds are un desirable in petroleum because they de activate the catalyst during the refining processes and
are the main source of acid rains and environmental pollution.(Mark Cullen 2001),Since it contains considerable
amount of salts and acids, it negatively impact the production facilities and transportation lines with corrosive
materials. However it suffers other problems in flow properties represented by the high viscosity and high
percentage of wax. Samples were collected after the initial and final treatment at CPF, and tested for
physical and chemical properties.wax content is in the range 23-31 weight % while asphalting content is about
0.1 weight% . Resin content is 13-7 weight % and deposits are 0.01 weight%. The carbon number distribution in
the crude is in the range 7-35 carbon atoms. The pour point vary between 39°C-42°C and the boiling point is in
the range 70 °C - 533 °C.
A Short Report on Different Wavelets and Their StructuresIJRES Journal
This article consists of basics of wavelet analysis required for understanding of and use of wavelet
theory. In this article we briefly discuss about HAAR wavelet transform their space and structures.
A Case Study on Academic Services Application Using Agile Methodology for Mob...IJRES Journal
Recently, Mobile Cloud Computing reveals many modern development areas in the Information
Technology industry. Several software engineering frameworks and methodologies have been developed to
provide solutions for deploying cloud computing resources on mobile application development. Agile
methodology is one of the most commonly used methodologies in the field. This paper presents the MCCAS a
Web and Mobile application that provide feature for the Palestinian higher education/academic institutions. An
Agile methodology was used in the development of the MCCAS but in parallel with emphasis on Cloud
computing resources deployment. Also many related issues is discussed such as how software engineering
modern methodologies (advances) influenced the development process.
Wear Analysis on Cylindrical Cam with Flexible RodIJRES Journal
Firstly, the kinetic equation of spatial cylindrical cam with flexible rod has been established. Then, an
accurate cylindrical cam mechanism model has been established based on the spatial modeling software
Solidworks. The dynamic effect of flexible rod on mechanical system was studied in detail based on the
mechanical system dynamics analytical software Adams, and Archard wear model is used to predict the wear of
the cam. We used Ansys to create finite element model of the cam link, extracted the first five order mode to
export into Adams. The simulation results show that the dynamic characteristics of spatial cylindrical cam
mechanical system with flexible rod is closed to ideal mechanism. During the cam rotate one cycle, the collision
in the linkage with a clearance occurs in some special location, others still keep a continuous contact, and the
prediction of wear loss is smaller than rigid body.
DDOS Attacks-A Stealthy Way of Implementation and DetectionIJRES Journal
Cloud Computing is a new paradigm provides various host service [paas, saas, Iaas over the internet.
According to a self-service,on-demand and pay as you use business model,the customers will obtain the cloud
resources and services.It is a virtual shared service.Cloud Computing has three basic abstraction layers System
layer(Virtual Machine abstraction of a server),Platform layer(A virtualized operating system, database and
webserver of a server and Application layer(It includes Web Applications).Denial of Service attack is an attempt
to make a machine or network resource unavailable to the intended user. In DOS a user or organization is
deprived of the services of a resource they would normally expect to have.A Successful DOS attack is a highly
noticeable event impacting the entire online user base.DOS attack is found by First Mathematical Metrical
Method (Rate Controlling,Timing Window,Worst Case and Pattern Matching)DOS attack not only affect the
Quality of the service and also affect the performance of the server. DDOS attacks are launched from Botnet-A
large Cluster of Connected device(cellphone,pc or router) infected with malware that allow remote control by an
attacker. Intruder using SIPDAS in DDOS to perform attack.SIPDAS attack strategies are detected using Heap
Space Monitoring Algorithm.
An improved fading Kalman filter in the application of BDS dynamic positioningIJRES Journal
Aiming at the poor dynamic performance and low navigation precision of traditional fading
Kalman filter in BDS dynamic positioning, an improved fading Kalman filter based on fading factor vector is
proposed. The fading factor is extended to a fading factor vector, and each element of the vector corresponds to
each state component. Based on the difference between the actual observed quantity and the predicted one, the
value of the vector is changed automatically. The memory length of different channel is changed in real time
according to the dynamic property of the corresponding state component. The actual observation data of BDS is
used to test the algorithm. The experimental results show that compared with the traditional fading Kalman filter
and the method of the third references, the positioning precision of the algorithm is improved by 46.3% and
23.6% respectively.
Positioning Error Analysis and Compensation of Differential Precision WorkbenchIJRES Journal
The document analyzes positioning errors in differential precision workbenches and proposes a compensation method. It discusses sources of error in workbench transmission systems and guides. Through theoretical analysis and experimentation, it is shown that positioning errors increase with travel distance due to factors like guideway errors. A method is developed to sample positioning at multiple points, compare values to identify errors, and implement reverse error correction through motion control cards. This allows positioning accuracy better than 15 micrometers over 150mm of travel to be achieved. The compensation method can improve precision for a range of machine tool designs.
Status of Heavy metal pollution in Mithi river: Then and NowIJRES Journal
The Mithi River runs through the heart of suburban Mumbai. Its path of flow has been severely
damaged due to industrialization and urbanization. The quality of water has been deteriorating ever since. The
Municipal and industrial effluents are discharged in unchecked amounts. The municipal discharge comprises
untreated domestic and sewage wastes whereas the industries are majorly discharge chemicals and other toxic
effluents which are responsible in increasing the metal load of the river. In the current study, the water is
analysed for heavy metals- Copper, Cadmium, Chromium, Lead and Nickel. It also includes a brief
understanding on the fluctuations that have occurred in the heavy metal pollution, through the compilation of
studies carried out in the area previously.
The Low-Temperature Radiant Floor Heating System Design and Experimental Stud...IJRES Journal
In order to analyze the temperature distribution of the low-temperature radiant floor heating system
that uses the condensing wall-hung boiler as the heat source, the heating system is designed according to a typical
house facing south in Shanghai. The experiments are carried out to study the effects of the supply water
temperature on the thermal comfort of the system. Eventually, the supply water temperature that makes people in
the room feel more comfortable is obtained. The result shows that in the condition of that the outside temperature
is 8~15℃ and the relative humidity is 30~70%RH, the temperature distribution in the room is from high to low
when the height is from bottom to top. The floor surface temperature is highest, but its uniformity is very poor.
When the heating system reaches the steady state, the air temperature of the room is uniform. When the supply
water temperature is 63℃ The room is relatively comfortable at the above experimental condition.
Experimental study on critical closing pressure of mudstone fractured reservoirsIJRES Journal
This study examines the critical closing pressure of fractures in mudstone reservoir cores from the Daqing oilfield in China. Laboratory experiments subjected fractured and unfractured mudstone cores to increasing external pressures while measuring permeability. The critical closing pressure is defined as the pressure when fractured core permeability matches unfractured permeability, indicating fracture closure. Results show fractured cores have higher permeability than unfractured cores due to fractures. Permeability generally decreases exponentially with increasing pressure. By calculating sensitivity equations relating permeability and production pressure difference, the study estimates critical closing pressures under reservoir conditions are lower than values from external pressure experiments. The study provides guidance but notes limitations in fully simulating complex in-situ stress conditions.
Correlation Analysis of Tool Wear and Cutting Sound SignalIJRES Journal
With the classic signal analysis and processing method, the cutting of the audio signal in time
domain and frequency domain analysis. We reached the following conclusions: in the time domain analysis,
cutting audio signals mean and the variance associated with tool wear state change occurred did not change
significantly, and tool wear is not high degree of correlation, and the mean-square value of the audio signal
changes in the size and tool wear the state has a good relationship.
Reduce Resources for Privacy in Mobile Cloud Computing Using Blowfish and DSA...IJRES Journal
Mobile cloud computing in light of the increasing popularity among users of mobile smart
technology which is the next indispensable that enables users to take advantage of the storage cloud computing
services. However, mobile cloud computing, the migration of information on the cloud is reliable their privacy
and security issues. Moreover, mobile cloud computing has limitations in resources such as power energy,
processor, Memory and storage. In this paper, we propose a solution to the problem of privacy with saving and
reducing resources power energy, processor and Memory. This is done through data encryption in the mobile
cloud computing by symmetric algorithm and sent to the private cloud and then the data is encrypted again and
sent to the public cloud through Asymmetric algorithm. The experimental results showed after a comparison
between encryption algorithms less time and less time to decryption are as follows: Blowfish algorithm for
symmetric and the DSA algorithm for Asymmetric. The analysis results showed a significant improvement in
reducing the resources in the period of time and power energy consumption and processor.
Resistance of Dryland Rice to Stem Borer (Scirpophaga incertulas Wlk.) Using ...IJRES Journal
Rice stem borer is one of the important pests that attack plants so as to reduce production. One way
to control pests is to use organic fertilizers that make the plant stronger and healthier. This study was conducted
to determine the effects of organic fertilizers with various doses without the use of pesticides in controlling stem
borer, Scirpophaga incertulas. Methods using split-split plot design which consists of two levels of the whole
plot factor (solid and liquid organic fertilizers), two levels of the subplot factor (conventional and industry,
Tiens and Mitraflora), and four levels of the sub-subplot factor of conventional and industry (5, 10, 15, 20
tonnes/ha), and one level of the sub-subplot factor of Tiens and Mitraflora (each 2 ml/l). Based on the results
Statistical analysis there were no significant differences among treatments and this shows that the use of organic
fertilizers that only a dose of 5 tonnes/ha is sufficient available nutrients that make plants more robust and
resistant to control stem borer, besides that can reduce production costs and friendly to the environment when
compared with using inorganic fertilizers.
A novel high-precision curvature-compensated CMOS bandgap reference without u...IJRES Journal
A novel high-precision curvature-compensated bandgap reference (BGR) without using op-amp
is presented in this paper. It is based on second-order curvature correction principle, which is a weighted sum of
two voltage curves which have opposite curvature characteristic. One voltage curve is achieved by first-order
curvature-compensated bandgap reference (FCBGR) without using op-amp and the other found by using W
function is achieved by utilizing a positive temperature coefficient (TC) exponential current and a linear
negative TC current to flow a linear resistor. The exponential current is gained by using anegative TC voltage to
control a MOSFET in sub-threshold region. In the temperature ranging from -40℃ to 125℃, experimental
results implemented with SMIC 0.18μm CMOS process demonstrate that the presented BGR can achieve a TC
as low as 2.2 ppm/℃ and power-supply rejection ratio(PSRR)is -69 dB without any filtering capacitor at 2.0 V.
While the range of the supply voltage is from 1.7 to 3.0 V, the output voltage line regulation is about1 mV/ V
and the maximum TC is 3.4 ppm/℃.
Structural aspect on carbon dioxide capture in nanotubesIJRES Journal
In this work we reported the carbon dioxide adsorption (CO2) in six different nanostructures in order
to investigate the capturing capacity of the materials at nanoscale. Here we have considered the three different
nanotubes including zinc oxide nanotube (ZnONT), silicon carbide nanotube (SiCNT) and single walled carbon
nanotube (SWCNT). Three different chiralities such as zigzag (9,0), armchair (5,5) and chiral (6,4) having
approximately same diameter are analyzed. The adsorption binding energy values under various cases are
estimated with density functional theory (DFT). We observed CO2 molecule chemisorbed on ZnONT and
SiCNT’s whereas the physisorption is predominant in CNT. To investigate the structural aspect, the tubes with
defects are studied and compared with defect free tubes. We have also analyzed the electrical properties of tubes
from HOMO, LUMO energies. Our results reveal the defected structure enhance the CO2 capture and is
predicted to be a potential candidate for environmental applications.
Thesummaryabout fuzzy control parameters selected based on brake driver inten...IJRES Journal
In this paper, the brake driving intention identification parameters based on the fuzzy control are
summarized and analyzed, the necessary parameters based on the fuzzy control of the brake driving intention
recognition are found out, and I pointed out the commonly corrupt parameters, and through the relevant
parameters , I establish the corresponding driving intention model.
HCL Notes und Domino Lizenzkostenreduzierung in der Welt von DLAUpanagenda
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-und-domino-lizenzkostenreduzierung-in-der-welt-von-dlau/
DLAU und die Lizenzen nach dem CCB- und CCX-Modell sind für viele in der HCL-Community seit letztem Jahr ein heißes Thema. Als Notes- oder Domino-Kunde haben Sie vielleicht mit unerwartet hohen Benutzerzahlen und Lizenzgebühren zu kämpfen. Sie fragen sich vielleicht, wie diese neue Art der Lizenzierung funktioniert und welchen Nutzen sie Ihnen bringt. Vor allem wollen Sie sicherlich Ihr Budget einhalten und Kosten sparen, wo immer möglich. Das verstehen wir und wir möchten Ihnen dabei helfen!
Wir erklären Ihnen, wie Sie häufige Konfigurationsprobleme lösen können, die dazu führen können, dass mehr Benutzer gezählt werden als nötig, und wie Sie überflüssige oder ungenutzte Konten identifizieren und entfernen können, um Geld zu sparen. Es gibt auch einige Ansätze, die zu unnötigen Ausgaben führen können, z. B. wenn ein Personendokument anstelle eines Mail-Ins für geteilte Mailboxen verwendet wird. Wir zeigen Ihnen solche Fälle und deren Lösungen. Und natürlich erklären wir Ihnen das neue Lizenzmodell.
Nehmen Sie an diesem Webinar teil, bei dem HCL-Ambassador Marc Thomas und Gastredner Franz Walder Ihnen diese neue Welt näherbringen. Es vermittelt Ihnen die Tools und das Know-how, um den Überblick zu bewahren. Sie werden in der Lage sein, Ihre Kosten durch eine optimierte Domino-Konfiguration zu reduzieren und auch in Zukunft gering zu halten.
Diese Themen werden behandelt
- Reduzierung der Lizenzkosten durch Auffinden und Beheben von Fehlkonfigurationen und überflüssigen Konten
- Wie funktionieren CCB- und CCX-Lizenzen wirklich?
- Verstehen des DLAU-Tools und wie man es am besten nutzt
- Tipps für häufige Problembereiche, wie z. B. Team-Postfächer, Funktions-/Testbenutzer usw.
- Praxisbeispiele und Best Practices zum sofortigen Umsetzen
Driving Business Innovation: Latest Generative AI Advancements & Success StorySafe Software
Are you ready to revolutionize how you handle data? Join us for a webinar where we’ll bring you up to speed with the latest advancements in Generative AI technology and discover how leveraging FME with tools from giants like Google Gemini, Amazon, and Microsoft OpenAI can supercharge your workflow efficiency.
During the hour, we’ll take you through:
Guest Speaker Segment with Hannah Barrington: Dive into the world of dynamic real estate marketing with Hannah, the Marketing Manager at Workspace Group. Hear firsthand how their team generates engaging descriptions for thousands of office units by integrating diverse data sources—from PDF floorplans to web pages—using FME transformers, like OpenAIVisionConnector and AnthropicVisionConnector. This use case will show you how GenAI can streamline content creation for marketing across the board.
Ollama Use Case: Learn how Scenario Specialist Dmitri Bagh has utilized Ollama within FME to input data, create custom models, and enhance security protocols. This segment will include demos to illustrate the full capabilities of FME in AI-driven processes.
Custom AI Models: Discover how to leverage FME to build personalized AI models using your data. Whether it’s populating a model with local data for added security or integrating public AI tools, find out how FME facilitates a versatile and secure approach to AI.
We’ll wrap up with a live Q&A session where you can engage with our experts on your specific use cases, and learn more about optimizing your data workflows with AI.
This webinar is ideal for professionals seeking to harness the power of AI within their data management systems while ensuring high levels of customization and security. Whether you're a novice or an expert, gain actionable insights and strategies to elevate your data processes. Join us to see how FME and AI can revolutionize how you work with data!
"Choosing proper type of scaling", Olena SyrotaFwdays
Imagine an IoT processing system that is already quite mature and production-ready and for which client coverage is growing and scaling and performance aspects are life and death questions. The system has Redis, MongoDB, and stream processing based on ksqldb. In this talk, firstly, we will analyze scaling approaches and then select the proper ones for our system.
For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/how-axelera-ai-uses-digital-compute-in-memory-to-deliver-fast-and-energy-efficient-computer-vision-a-presentation-from-axelera-ai/
Bram Verhoef, Head of Machine Learning at Axelera AI, presents the “How Axelera AI Uses Digital Compute-in-memory to Deliver Fast and Energy-efficient Computer Vision” tutorial at the May 2024 Embedded Vision Summit.
As artificial intelligence inference transitions from cloud environments to edge locations, computer vision applications achieve heightened responsiveness, reliability and privacy. This migration, however, introduces the challenge of operating within the stringent confines of resource constraints typical at the edge, including small form factors, low energy budgets and diminished memory and computational capacities. Axelera AI addresses these challenges through an innovative approach of performing digital computations within memory itself. This technique facilitates the realization of high-performance, energy-efficient and cost-effective computer vision capabilities at the thin and thick edge, extending the frontier of what is achievable with current technologies.
In this presentation, Verhoef unveils his company’s pioneering chip technology and demonstrates its capacity to deliver exceptional frames-per-second performance across a range of standard computer vision networks typical of applications in security, surveillance and the industrial sector. This shows that advanced computer vision can be accessible and efficient, even at the very edge of our technological ecosystem.
Fueling AI with Great Data with Airbyte WebinarZilliz
This talk will focus on how to collect data from a variety of sources, leveraging this data for RAG and other GenAI use cases, and finally charting your course to productionalization.
Connector Corner: Seamlessly power UiPath Apps, GenAI with prebuilt connectorsDianaGray10
Join us to learn how UiPath Apps can directly and easily interact with prebuilt connectors via Integration Service--including Salesforce, ServiceNow, Open GenAI, and more.
The best part is you can achieve this without building a custom workflow! Say goodbye to the hassle of using separate automations to call APIs. By seamlessly integrating within App Studio, you can now easily streamline your workflow, while gaining direct access to our Connector Catalog of popular applications.
We’ll discuss and demo the benefits of UiPath Apps and connectors including:
Creating a compelling user experience for any software, without the limitations of APIs.
Accelerating the app creation process, saving time and effort
Enjoying high-performance CRUD (create, read, update, delete) operations, for
seamless data management.
Speakers:
Russell Alfeche, Technology Leader, RPA at qBotic and UiPath MVP
Charlie Greenberg, host
"Frontline Battles with DDoS: Best practices and Lessons Learned", Igor IvaniukFwdays
At this talk we will discuss DDoS protection tools and best practices, discuss network architectures and what AWS has to offer. Also, we will look into one of the largest DDoS attacks on Ukrainian infrastructure that happened in February 2022. We'll see, what techniques helped to keep the web resources available for Ukrainians and how AWS improved DDoS protection for all customers based on Ukraine experience
AppSec PNW: Android and iOS Application Security with MobSFAjin Abraham
Mobile Security Framework - MobSF is a free and open source automated mobile application security testing environment designed to help security engineers, researchers, developers, and penetration testers to identify security vulnerabilities, malicious behaviours and privacy concerns in mobile applications using static and dynamic analysis. It supports all the popular mobile application binaries and source code formats built for Android and iOS devices. In addition to automated security assessment, it also offers an interactive testing environment to build and execute scenario based test/fuzz cases against the application.
This talk covers:
Using MobSF for static analysis of mobile applications.
Interactive dynamic security assessment of Android and iOS applications.
Solving Mobile app CTF challenges.
Reverse engineering and runtime analysis of Mobile malware.
How to shift left and integrate MobSF/mobsfscan SAST and DAST in your build pipeline.
Generating privacy-protected synthetic data using Secludy and MilvusZilliz
During this demo, the founders of Secludy will demonstrate how their system utilizes Milvus to store and manipulate embeddings for generating privacy-protected synthetic data. Their approach not only maintains the confidentiality of the original data but also enhances the utility and scalability of LLMs under privacy constraints. Attendees, including machine learning engineers, data scientists, and data managers, will witness first-hand how Secludy's integration with Milvus empowers organizations to harness the power of LLMs securely and efficiently.
Discover top-tier mobile app development services, offering innovative solutions for iOS and Android. Enhance your business with custom, user-friendly mobile applications.
Programming Foundation Models with DSPy - Meetup SlidesZilliz
Prompting language models is hard, while programming language models is easy. In this talk, I will discuss the state-of-the-art framework DSPy for programming foundation models with its powerful optimizers and runtime constraint system.
Essentials of Automations: Exploring Attributes & Automation ParametersSafe Software
Building automations in FME Flow can save time, money, and help businesses scale by eliminating data silos and providing data to stakeholders in real-time. One essential component to orchestrating complex automations is the use of attributes & automation parameters (both formerly known as “keys”). In fact, it’s unlikely you’ll ever build an Automation without using these components, but what exactly are they?
Attributes & automation parameters enable the automation author to pass data values from one automation component to the next. During this webinar, our FME Flow Specialists will cover leveraging the three types of these output attributes & parameters in FME Flow: Event, Custom, and Automation. As a bonus, they’ll also be making use of the Split-Merge Block functionality.
You’ll leave this webinar with a better understanding of how to maximize the potential of automations by making use of attributes & automation parameters, with the ultimate goal of setting your enterprise integration workflows up on autopilot.
Northern Engraving | Nameplate Manufacturing Process - 2024Northern Engraving
Manufacturing custom quality metal nameplates and badges involves several standard operations. Processes include sheet prep, lithography, screening, coating, punch press and inspection. All decoration is completed in the flat sheet with adhesive and tooling operations following. The possibilities for creating unique durable nameplates are endless. How will you create your brand identity? We can help!
The Microsoft 365 Migration Tutorial For Beginner.pptxoperationspcvita
This presentation will help you understand the power of Microsoft 365. However, we have mentioned every productivity app included in Office 365. Additionally, we have suggested the migration situation related to Office 365 and how we can help you.
You can also read: https://www.systoolsgroup.com/updates/office-365-tenant-to-tenant-migration-step-by-step-complete-guide/
What is an RPA CoE? Session 1 – CoE VisionDianaGray10
In the first session, we will review the organization's vision and how this has an impact on the COE Structure.
Topics covered:
• The role of a steering committee
• How do the organization’s priorities determine CoE Structure?
Speaker:
Chris Bolin, Senior Intelligent Automation Architect Anika Systems
A Mathematical Model for the Enhancement of Stress Induced Hypoglycaemia by Andtidepressant Treatment in Healthy Men using Multivariate Normal Distribution
1. International Refereed Journal of Engineering and Science (IRJES)
ISSN (Online) 2319-183X, (Print) 2319-1821
Volume 4, Issue 3 (March 2015), PP.51-58
www.irjes.com 51 | Page
A Mathematical Model for the Enhancement of Stress Induced
Hypoglycaemia by Andtidepressant Treatment in Healthy Men
using Multivariate Normal Distribution
Dr.S.Lakshmi1
, M.Goperundevi2
1
Principal, Government Arts and Science College, Peravurani – 614804, Thanjavur – District,
Tamilnadu, South India
2
Research Scholar, P.G and Research Department of Mathematics, K.N. Govt. Arts College for
Women (Autonomous), Thanjavur – 613 007, Tamilnadu, South India
Abstract:The normal distribution is a very commonly occurring continuous probability distribution. In this
paper the Multivariate Normal distribution is used for finding the mgf of the curve for the enhancement of stress
induced Hypoglycaemia with consideration of the variablesProlactin, ACTH, Growth Hormone, Blood Pressure,
Plasma Glucose, Plasma Renin, Epinephrine, Cortisol. These variables are treated with the drugs (citalopram
and tianeptine) and the joint moment generating function for the variables in Citalopram, Tianeptineand
Placebo casesare found out and are given as curves in the Mathematical Results.
Keywords: Adrenocorticotrophic Hormone (ACTH), Antidepressants, Growth Hormone(GH), Joint Moment
Generating Function, Prolactin.
I. INTRODUCTION
The aim of the present study is to verify the hypothesis that (i) treatment with antidepressants inhibits
hormone release in response to stressful stimulation in humans and (ii) drugs with opposing effects on brain
serotonin (citalopram and tianeptine) exert similar modulatory effects on neuroendocrine activation during
stress. As a stress stimulus, insulin – induced hypoglycaemia was selected because hypoglycaemia induces the
release of a wide spectrum of hormones and the insulin tolerance test is a clinically useful one to assess pituitary
function. This study shows that treatment with antidepressants in healthy men results in an augmentation of
neuroendocrine response during stress of hypoglycaemia, manifested by increased release of ACTH, growth
hormone and prolactin. Treatment with antidepressants should have induced an attenuation of the stress
response. It was not due to altered intensity of the stress stimulus, as the degree of hypoglycaemia in
antidepressant treated groups was not different from that in the control, placebo treated group. The Stress
induced changes and its mechanisms are clearly showed in /the Mathematical figures to obtain the conclusion of
the medical part.
II. MATHEMATICAL MODEL
2.1 Bivariate And Multivariate Normal Distribution:
Two random variables (X,Y) have a bivariate normal distribution 𝑁(𝜇1, 𝜇2, 𝜍1
2
, 𝜍2
2
, 𝜌) if their joint p.d.f
is 𝑓𝑋,𝑌 𝑥, 𝑦 =
1
2𝜋𝜍1 𝜍2 1−𝜌2
𝑒
−1
2 1−𝜌2
𝑥−𝜇 1
𝜍1
2
−2𝜌
𝑥−𝜇 1
𝜍1
𝑦−𝜇 2
𝜍2
+
𝑦−𝜇 2
𝜍2
2
; (2.1.1)
for all x ,y [6, 9].
The parameters 𝜇1, 𝜇2 may be any real numbers, 𝜍1 > 0, 𝜍2 > 0 ,−1 ≤ 𝜌 ≤ 1. It is convenient to rewrite (2.1.1)
in the form 𝑓𝑋,𝑌 𝑥, 𝑦 = 𝑐𝑒
−1
2
𝑄(𝑥,𝑦)
, where c =
1
2𝜋𝜍1 𝜍2 1−𝜌2
𝑎𝑛𝑑
𝑄 = 1 − 𝜌2 −1 𝑥−𝜇1
𝜍1
2
− 2𝜌
𝑥−𝜇1
𝜍1
𝑦−𝜇2
𝜍2
+
𝑦−𝜇2
𝜍2
2
; (2.1.2)
Statement:
The marginal distributions of 𝑁(𝜇1, 𝜇2, 𝜍1
2
, 𝜍2
2
, 𝜌) are normal with random variables X and Y having
density functions
𝑓𝑋 𝑥 =
1
2𝜋𝜍1
𝑒
−
(𝑥−𝜇 1)2
2𝜍1
2
, 𝑓𝑌 𝑦 =
1
2𝜋𝜍2
𝑒
−
(𝑦−𝜇 2)2
2𝜍2
2
Proof:
The expression for Q(x,y) can be rearranged as follows:
𝑄 =
1
1−𝜌2
𝑥−𝜇1
𝜍1
− 𝜌
𝑦−𝜇2
𝜍2
2
+ 1 − 𝜌2 𝑦−𝜇2
𝜍2
2
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=
(𝑥−𝑎)2
1−𝜌2 𝜍1
2 +
(𝑦−𝜇2)2
𝜍2
2 ; (2.1.3)
where 𝑎 = 𝑎 𝑦 = 𝜇1 + 𝜌
𝜍1
𝜍2
𝑦 − 𝜇2 . Hence
𝑓𝑌 𝑦 = 𝑓𝑋,𝑌 𝑥, 𝑦 𝑑𝑥 = 𝑐𝑒
−
(𝑦−𝜇 2)2
2𝜍2
2
∞
−∞
× 𝑒
−
(𝑥−𝑎)2
2 1−𝜌2 𝜍1
2
∞
−∞
𝑑𝑥 =
1
2𝜋𝜍2
𝑒
−
(𝑦−𝜇 2)2
2𝜍2
2
Where the last step makes use of the formula 𝑒
−
(𝑥−𝑎)2
2𝜍2
𝑑𝑥 = 2𝜋𝜍
∞
−∞
with σ = σ1 1 − 𝜌2
Corollaries
1. Since 𝑋~𝑁 𝜇1, 𝜍1
2
, 𝑌~𝑁(𝜇2, 𝜍2
2
) we know the meaning of four parameters involved into the
definition of the normal distribution, namely
𝐸 𝑋 = 𝜇1 , 𝑉𝑎𝑟 𝑋 = 𝜍1
2
, 𝐸 𝑌 = 𝜇2, 𝑉𝑎𝑟 𝑌 = 𝜍2
2
2. 𝑋 ∣ 𝑌 = 𝑦 is a normal variable. To verify this statement we substitute the necessary ingredients into
the formula defining the relevant conditional density
𝑓𝑋∣𝑌 𝑥 ∣∣ 𝑦 =
𝑓 𝑋,𝑌 𝑥,𝑦
𝑓 𝑌 𝑦
=
1
2𝜋 1−𝜌2 𝜍1
𝑒
−
(𝑥−𝑎 𝑦 )2
2𝜍1
2 1−𝜌2
In otherwords, 𝑋 ∣ 𝑌 = 𝑦 ~𝑁 𝑎 𝑦 . 1 − 𝜌2
𝜍1
2
.
3. 𝐸 𝑋 ∣∣ 𝑌 = 𝑦 = 𝑎 𝑦 or equivalently, 𝐸 𝑋 ∣ 𝑌 = 𝜇1 + 𝜌
𝜍1
𝜍2
𝑌 − 𝜇2 . In particular we see that
E(X∣Y) is a linear function of Y [6].
4. 𝐸 𝑋𝑌 = 𝜍1 𝜍2 𝜌 + 𝜇1 𝜇2.
Proof:
𝐸 𝑋𝑌 = 𝐸 𝐸(𝑋𝑌 ∣ 𝑌) = 𝐸 𝑌𝐸(𝑋 ∣ 𝑌) = 𝐸 𝑌(𝜇1 + 𝜌
𝜍1
𝜍2
𝑌 − 𝜇2
= 𝜇1 𝐸 𝑌 + 𝜌
𝜍1
𝜍2
𝐸 𝑌2
− 𝜇2 𝐸(𝑌) = 𝜇1 𝜇2 + 𝜌
𝜍1
𝜍2
𝐸 𝑌2
− 𝜇2
2
= 𝜇1 𝜇2 + 𝜌
𝜍1
𝜍2
𝑉𝑎𝑟 𝑌 = 𝜍1 𝜍2 𝜌 + 𝜇1 𝜇2.
5. 𝐶𝑜𝑣 𝑋, 𝑌 = 𝜍1 𝜍2 𝜌. This follows from Corollary 4 and the formula
𝐶𝑜𝑣 𝑋, 𝑌 = 𝐸 𝑋𝑌 − 𝐸 𝑋 𝐸(𝑌)
6. 𝜌 𝑋, 𝑌 = 𝜌, in words ρ is the correlation coefficient of X, Y. This is now obvious from the
definition 𝜌 𝑋, 𝑌 =
𝐶𝑜𝑣 𝑋,𝑌
𝑉𝑎𝑟 𝑋 𝑉𝑎𝑟 (𝑌)
.
Remark:
It is possible to show that the m.g.f of X, Y is
𝑀 𝑋,𝑌 𝑡1, 𝑡2 = 𝑒 𝜇1 𝑡1+𝜇2 𝑡2 +
1
2
𝜍1
2 𝑡1
2+2𝜌𝜍1 𝜍2 𝑡1 𝑡2+𝜍2
2 𝑡2
2
.
2.2 Multivariate Normal Distribution:
Using Vector and Matrix Notation:
To study the joint normal distributions of more than two random variables it is convenient to use
vectors and matrices. But let us first introduce these notations for the case of two normal random variables X1,
X2[8]. We set,
𝑋 =
𝑋1
𝑋2
, 𝑥 =
𝑥1
𝑥2
, 𝑡 =
𝑡1
𝑡2
, 𝑚 =
𝜇1
𝜇2
, 𝑉 =
𝜍1
2
𝜌𝜍1 𝜍2
𝜌𝜍1 𝜍2 𝜍2
2
Then m is the vector of means and V is the variance – covariance matrix.
Note that 𝑉 = 𝜍1
2
𝜍2
2
1 − 𝜌2
and 𝑉−1
=
1
1−𝜌2
1
𝜍1
2
−𝜌
𝜍1 𝜍2
−𝜌
𝜍1 𝜍2
1
𝜍2
2
Hence 𝑓𝑋 𝑥 =
1
2𝜋 1 2 𝑉 1 2 𝑒
−1
2
(𝑥−𝑚) 𝑇 𝑉−1 𝑥−𝑚
for all x. Also Mx t = etTm+
1
2
tTVt
; (2.2.1)
We again use matrix and vector notation, but now there are n random variables so that X, x, t and m are now n-
vectors with ith
entries𝑋𝑖, 𝑥𝑖, 𝑡𝑖, 𝑎𝑛𝑑𝜇𝑖 and V is the n x n matrix with iith
entryσi
2
and ijth
entry 𝑓𝑜𝑟𝑖 ≠ 𝑗 𝜍𝑖𝑗 .
Note that V is symmetric so that 𝑉 𝑇
= 𝑉.
The joint p.d.f is 𝑓𝑋 𝑥 =
1
2𝜋 𝑛 2 𝑉 1 2 𝑒
−1
2
(𝑥−𝑚) 𝑇 𝑉−1 𝑥−𝑚
for all x.We say that 𝑋~𝑁 𝑚, 𝑉 .
We can find the joint m.g.f quite easily.
𝑀𝑥 𝑡 = 𝐸 𝑒 𝑡 𝑇 𝑋
= …
1
2𝜋 𝑛 2 𝑉 1 2 𝑒
−1
2
(𝑥−𝑚) 𝑇 𝑉−1 𝑥−𝑚 −2𝑡 𝑇 𝑥
𝑑𝑥1
∞
−∞
∞
−∞
… 𝑑𝑥 𝑛 ;(2.2.2)
We do the equivalent of completing the square, i.e we write
(𝑥 − 𝑚) 𝑇
𝑉−1
𝑥 − 𝑚 − 2𝑡 𝑇
𝑥 = (𝑥 − 𝑚 − 𝑎) 𝑇
𝑉−1
𝑥 − 𝑚 − 𝑎 + 𝑏
for a suitable choice of the n-vector a of constants and a constant b. Then
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𝑀𝑥 𝑡 = 𝑒−𝑏 2
…
1
2𝜋 𝑛 2 𝑉 1 2 𝑒
−1
2
(𝑥−𝑚−𝑎) 𝑇 𝑉−1 𝑥−𝑚−𝑎
𝑑𝑥1
∞
−∞
∞
−∞
… 𝑑𝑥 𝑛 = 𝑒−𝑏 2
; (2.2.3)
We just need to find a andb. Expanding we have
( 𝑥 − 𝑚 − 𝑎) 𝑇
𝑉−1
𝑥 − 𝑚 − 𝑎 + 𝑏
= 𝑥 − 𝑚 𝑇
𝑉−1
𝑥 − 𝑚 − 2𝑎 𝑇
𝑉−1
𝑥 − 𝑚 + 𝑎 𝑇
𝑉−1
𝑎 + 𝑏
= 𝑥 − 𝑚 𝑇
𝑉−1
𝑥 − 𝑚 − 2𝑎 𝑇
𝑉−1
𝑥 + 2𝑎 𝑇
𝑉−1
𝑚 + 𝑎 𝑇
𝑉−1
𝑎 + 𝑏
This has equal to (𝑥 − 𝑚) 𝑇
𝑉−1
𝑥 − 𝑚 − 2𝑡 𝑇
𝑥 for all x. Hence we need 𝑎 𝑇
𝑉−1
= 𝑡 𝑇
𝑎𝑛𝑑
𝑏 = − 2𝑎 𝑇
𝑉−1
𝑚 + 𝑎 𝑇
𝑉−1
𝑎 . Hence𝑎 = 𝑉𝑡𝑎𝑛𝑑𝑏 = − 2𝑡 𝑇
𝑚 + 𝑡 𝑇
𝑉𝑡 .
Therefore 𝑀𝑥 𝑡 = 𝑒−𝑏 2
= 𝑒 𝑡 𝑇 𝑚+
1
2
𝑡 𝑇 𝑉𝑡
.
Results obtained using the m.g.f:
1. Any (non-empty) subset of multivariate normals is multivariate normal. Simply put 𝑡𝑗 = 0 for all j for
which Xj is not in the subset.
For example 𝑀 𝑋1,…..,𝑋 𝑛
𝑡1, 0, … … … . ,0 = 𝑒 𝜇1 𝑡1+
1
2
𝜍1
2 𝑡1
2
.
Hence 𝑋1~𝑁 𝜇1, 𝜍1
2
. A similar result holds for Xi. This identifies the parameters 𝜇𝑖 𝑎𝑛𝑑𝜍𝑖
2
as the mean and
variance of Xi. Also
𝑀 𝑋1
𝑡1 = 𝑀 𝑋1,𝑋2
𝑡1, 𝑡2 = 𝑀 𝑋1,𝑋2…..,𝑋 𝑛
𝑡1, 𝑡20, … … … . ,0
= 𝑒 𝜇1 𝑡1+𝜇2 𝑡2 +
1
2
𝜍1
2 𝑡1
2+2𝜍12 𝑡1 𝑡2+𝜍2
2 𝑡2
2
; (2.2.4)
Hence 𝑋1 𝑎𝑛𝑑𝑋2 have bivariate normal distribution with 𝜍12 = 𝐶𝑜𝑣(𝑋1, 𝑋2). A similar result holds for the joint
distribution of 𝑋𝑖 𝑎𝑛𝑑𝑋𝑗 𝑓𝑜𝑟𝑖 ≠ 𝑗. This identifies V as the variance – covariance matrix for 𝑋1, 𝑋2 … . . , 𝑋 𝑛 .
2. X is a vector of independent random variables iff V is diagonal (i.e. all off-diagonal entries are zero so
that 𝜍𝑖𝑗 = 0 𝑓𝑜𝑟𝑖 ≠ 𝑗).
Proof:
From the above result (result 1) if the X’s are independent then 𝑡 𝑇
𝑉𝑡 = 𝜍𝑗
2
𝑡𝑗
2𝑛
𝑗=1 and hence
𝑀 𝑋 𝑡 = 𝑒 𝑡 𝑇 𝑚+
1
2
𝑡 𝑇 𝑉𝑡
= 𝑒 𝜇 𝑗 𝑡 𝑗 +
1
2
𝜍 𝑗
2 𝑡 𝑗
2 2𝑛
𝑗 =1 = 𝑀 𝑋 𝑗
𝑡𝑗
𝑛
𝑗 =1 (2.2.5)
By the uniqueness of the joint m.g.f𝑋1, 𝑋2 … . . , 𝑋 𝑛 are independent.
3. Linearly independent linear functions of multivariate normal random variables are multivariate normal
random variables. If 𝑌 = 𝐴𝑋 + 𝑏, where A is a n x n non-singular matrix and b is a (column) n-vector of
constants, then 𝑌~𝑁(𝐴𝑚 + 𝑏, 𝐴𝑉𝐴 𝑇
).
Proof:
Use the joint m.g.f
𝑀 𝑌 𝑡 = 𝐸 𝑒 𝑡 𝑇 𝑌
= 𝐸 𝑒 𝑡 𝑇 𝐴𝑋+𝑏
= 𝑒 𝑡 𝑇 𝑏
𝐸 𝑒(𝐴 𝑇 𝑡) 𝑇 𝑋
= 𝑒 𝑡 𝑇 𝑏
𝑀 𝑋 𝐴 𝑇
𝑡
= 𝑒 𝑡 𝑇 𝑏
𝑒(𝐴 𝑇 𝑡) 𝑇 𝑚+
1
2
(𝐴 𝑇 𝑡) 𝑇 𝑉 𝐴 𝑇 𝑡
= 𝑒 𝑡 𝑇 𝐴𝑚+𝑏 +
1
2
𝑡 𝑇 𝐴𝑉𝐴 𝑇 𝑡
This is just the m.g.f for the multivariate normal distribution with vector of means Am+b and variance –
covariance matrix AVAT
. Hence, from the uniqueness of the joint m.g.f
𝑌~𝑁(𝐴𝑚 + 𝑏, 𝐴𝑉𝐴 𝑇
) . Note that from (2) a subset of the Y’s is multivariate normal.
III. APPLICATION
Stress is generally considered to be one of the factors involved in the pathogenesis of affective
disorders. Neuroendocrine activation includes profound changes in central neurotransmitter systems as well as
increased release of stress hormones, such as cortisol, catecholamines, adrenocorticotropic hormone(ACTH),
growth hormone (GH), prolactin or angiogenesis II. The relationship between antidepressants and stress is
further substantiated by their effects on stress hormone release. Acute administration of antidepressants leads to
a rise in hormone secretion, whereas prolonged treatment can be associated with inhibitory effects. Thus,
decreased levels of plasma corticosterone and ACTH were observed after chronic treatment with several
antidepressants.
The aim of the present study is to verify the hypothesis that (i) treatment with antidepressants inhibits
hormone release in response to stressful stimulation in humans and (ii) drugs with opposing effects on brain
serotonin (citalopram and tianeptine) exert similar modulatory effects on neuroendocrine activation during
stress. As a stress stimulus, insulin – induced hypoglycaemia was selected because hypoglycaemia induces the
release of a wide spectrum of hormones and the insulin tolerance test is a clinically useful to assess pituitary
function [7]. The study was designed as a randomized, double – blind, placebo – controlled trial in a total of 31
healthy male volunteers in the age group of 20 – 27 years. All treatments were given three times daily (one of
active drugs or placebo) with the main meals for 7 days. The subjects were treated with tianeptine (37.5 mg p.o
daily divided in three doses) or citalopram (20 mg p.o daily in one dose in the morning while placebo was given
at noon and evening) given in the same manner as the active drugs. Hypoglycaemia was induced by
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administration of inslulin. An appropriate dose of insulin was diluted in 5 ml of isotonic saline and injected in
to the catheter inserted in a cubital vein within 1 min. After 7 days of drug treatment, the observations started
the following morning at 07.30 h after an overnight fast.Each subject was asked to take his last dose of
treatment. An indwelling catheter was inserted into a cubital vein. The first blood sample was taken at least 30
minutes after catheter insertion and exactly 45 min after the last drug administration. Insulin was injected 60
min after the drug and blood samples were collected at 30, 45, 60 and 90 min after insulin injection.
Figure – 3.1
Decrease in plasma glucose levels induced by insulin infusion in citalopram, tianeptine or placebo
treated subjects. Statistical significance: effect of time ++p < 0.001; effect of treatment p < 0.05; post hoc
treatment tianeptinevesus citalopram #p < 0.05
As expected insulin administration induced a decrease in blood glucose, which the nadir at 30 min and
the returned towards the control levels (Fig.3.1). No significant differences in blood glucose concentrations
were found between placebo and any of the antidepressant treated groups. Insulin induced hypoglycaemia was
somewhat more prolonged in subjects treated within tianeptine compared to the values in citalopram but not
placebo treated group.
Figure – 3.2
Enhancement of systolic blood pressure response during stress of hypoglycaemia by treatment with
citalopram or tianeptine in comparison to placebo. Statistical significance: effect of time ++p < 0.001; post –
hoc test, citalopram versus placebo *p < 0.01p; tianeptine versus placebo #p < 0.01
When respect to cardiovascular responses, changes in systolic blood pressure reached statistical
significance for both time and treatment. Stress induced rise in systolic blood pressure was significantly higher
in the citalopram and tianeptine groups compared to that in subjects treated with placebo (Fig.3.2). Diastolic
blood pressure decreased in time, but no statiscally significant differences among groups were observed.
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Figure – 3.3 Figures – 3.4
Elevation of plasma ACTH and cortisol levels during stress of hypoglycaemia in subjects treated with
citalopram (cit), tianeptine (tia) or placebo (pla) for 7 days. Statistical significance: effect of time ++p<0.001;
post – hoc test (treatment), citalopram versus placebo *p<0.01; tianeptine versus placebo #P<0.01
ACTH levels increased significantly in response to insulin hypoglycaemia (Fig.–3.3). ACTH responses
were enhanced in subjects treated with both antidepressants compared to those treated with placebo. The
differences between the values in placebo versus citalopram, as well as placebo versus tianeptine – pretreated
groups, were found to be significant. The changes in cortisol levels were less pronounced in (Fig.3.4). Stress of
hypoglycaemia was associated with a similar rise in cortisol levels in the control and tianeptine – pretreated
groups. In subjects treated with citalopram, the elevation in cortisol levels was more pronounced and prolonged
compared to that in the control group.
Figure – 3.5 Figure – 3.6
Enhancement of growth hormone response during stress of hypoglycaemia by treatment with
citalopram (cit), tianeptine (tia) in comparison to placebo (pla). The rise in plasma prolactin levels was
potentiated in citalopram treated subjects only. Statistical significance: effect of time ++p<0.001; post – hoc test
(treatment), citalopram versus placebo *p<0.05, **p<0.01; tianeptine versus placebo #p<0.01.
Release of Growth Hormone induced by insulin hypoglycaemia was significantly potentiated by both
citalopram and tianeptine treatments. Significant differences were found for both time and treatment. Thus, the
rise in growth hormone release during stress was higher in subjects treated with citalopram as well as with
tianeptine compared to those treated with placebo(Fig. – 3.5) . There were no differences between the groups
treated with citalopram or tianeptine. Similarly, changes in prolactin levels showed significant differences for
both time and treatment(Fig.–3.6). However, a potentiation of stress – induced prolactin release was found in
citalopram – pretreated volunteers, while this hormone levels were similar in tianeptine and placebo treated
groups.
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Figure – 3.7 Figures – 3.8
Increase of plasma rennin activity and epinephrine levels during stress of hypoglycaemia in subjects
treated with citalopram (cit), tianeptine (tia) or placebo (pla) for 7 days. Statistical significance: effect of time
+p<0.01, ++p<0.001
Plasma Renin activity rose in response to insulin – induced hypoglycaemia in all groups. With respect
to treatment, no significant differences were observed. Concentrations of epinephrine in plasma increased
significantly in a similar manner in all treatment groups (Fig.–3.7, 3.8).
This study shows that treatment with antidepressants in healthy men results in an augmentation of
neuroendocrine response during stress of hypoglycaemia, manifested by increased release of ACTH, growth
hormone and prolactin. Treatment with antidepressants should have induced an attenuation of the stress
response. It was not due to altered intensity of the stress stimulus, as the degree of hypoglycaemia in
antidepressant treated groups was not different from that in the control, placebo treated group. Stress induced
changes as well as the mechanisms involved are affected by several factors particularly by the character of stress
stimulus [5]. Patients with major depression were found to exhibit decreased responses of ACTH or prolactin to
the stress of hypoglycaemia [4],attenuated beta – endorphin responses in Trier’s social stress test and lower
cardiovascular activation in response to a cognitive challenge [3]. A similar modulation of acute stress
responses by antidepressants in depressed patients remains to be confirmed.
Some drugs such as tianeptine, cause a reduction of serotonin availability in the brain, which is
opposite to the action of most widely used group of antidepressants acting as specific serotonin reuptake
inhibitors [1]. On the basis of the present findings showing the ability of both citalopram and tianeptine to
enhance neuroendocrine activation during stress. Single intravenous infusion of citalopram is known to increase
plasma cortisol and prolactin levels in healthy individuals. Repeated oral treatment with citalopram has no
effect on vassal hormone levels (prolactin, growth hormone, ACTH, cortisol). The same was true for tianeptine
treatment. On the other hand, neuroendocrine activation during stress was found to be potentiated by both
treatments. The actions of citalopram and tianeptine were similar.
The only exception was observed in stress – induced prolactin release, which was enhanced by
citalopram but not tianeptine administration. It should be noted that prolactin levels were not modified by
tianeptine treatment [2]. The present data further indicate that cortisol is not an optimal indicator of ACTH
release as the changes in ACTH levels were much more evident than those in cortisol secretion. However, the
observation period of 90 minutes was not long enough to reveal any possible differences in the duration of the
cortisol response, which might be induced by the drug treatments used.
The repeated antidepressant treatment in healthy men does not inhibit, but enhances neuroendocrine
activation during stress. Such effects were observed after treatment with antidepressants having opposing
actions on brain serotonin. Stress induces both protective and damaging effects on the body. It is suggested that
an enhancement of neuroendocrine activation to acute stress stimuli may be of benefit for patients with
depression, in which an attenuated stress response has been reported.
7. A Mathematical Model for the Enhancement of Stress Induced Hypoglycaemia by Andtidepressant
www.irjes.com 57 | Page
IV. MATHEMATICAL RESULTS
Figure 4.1
Moment Generating Function for the enhancement of stress induced by insulin infusion for the four
variables Prolactin, ACTH, Cortisol and Epinephrine for the Citalopram, Tianeptine and Placebo cases.
Figure 4.2
Moment Generating Function for the enhancement of stress induced by insulin infusion for the five variables
Prolactin, ACTH, Cortisol. Plasma Renin and Epinephrine for the Citalopram, Tianeptine and Placebo cases.
Figure 4.3
Moment Generating Function for the enhancement of stress induced by insulin infusion for the seven variables
Prolactin, ACTH, Cortisol. Plasma Renin, Blood Pressure, Plasma Glucose and Epinephrine for the Citalopram,
Tianeptine and Placebo cases.
V. CONCLUSION
In this paper the multivariate normal distribution is used for the treatment with depressants inhibits
hormone release in response to stressful stimulation in humans. The curves for moment generating function of
stress induced by insulin infusion for the i.) Four Variables - Prolactin, ACTH, Cortisol and Epinephrine for the
0
50
100
150
1 2 3 4
JointMoment
GeneratingFunction
Time
Citalopram
Tianeptine
Placebo
0
1000
2000
3000
4000
1 2 3 4 5
JpintMoment
GeneratingFunction
Time
Citalopram
Tianeptine
Placebo
0
50000
100000
150000
1 2 3 4 5 6 7
JointMoment
GeneratingFunction
Time
Citalopram
Tianeptine
Placebo
8. A Mathematical Model for the Enhancement of Stress Induced Hypoglycaemia by Andtidepressant
www.irjes.com 58 | Page
Citalopram, Tianeptine and Placebo cases are given in Fig.4.1. In this, the mgf of citalopram is found to be
maximum than tianeptine and placebo in the time period 30 minutes to 1 hour. ii.) Five variables Prolactin,
ACTH, Cortisol, Plasma Renin and Epinephrine for the Citalopram, Tianeptine and Placebo cases are given in
Fig.4.2. In this, the mgf of citalopram is found to be maximum than the other two cases and reach the peak
value in the time period of 45 minutes exactly. iii.) Seven variables Prolactin, ACTH, Cortisol. Plasma Renin,
Blood Pressure, Plasma Glucose and Epinephrine for the Citalopram, Tianeptine and Placebo cases are given in
Fig.4.3. In this, the mgf of citalopram is find to be maximum when compared to the mgf of tianeptine and
placebo has no more effect. Here citalopram increases in the time interval of 0 to 15 minutes and decreases
from the 15th
minute.
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