1) The document presents a mathematical model for analyzing the effects of oxytocin on inflammatory hormone levels in men. It analyzes likelihood functions for hormone levels when LPS (bacterial endotoxin) and oxytocin are administered.
2) The model is applied to data from a study of 10 healthy men who received placebo, oxytocin, LPS, or LPS+oxytocin. Oxytocin treatment reduced the endotoxin-induced increases in ACTH, cortisol, and procalcitonin levels, suggesting oxytocin decreases neuroendocrine and cytokine activation caused by endotoxin.
3) In vitro testing also showed oxytocin directly reduced LPS-induced cytokine release from human immune cells,
A Moment Inequality for Overall Decreasing Life Class of Life Distributions w...inventionjournals
:A moment inequality is derived for the system whose life distribution is in an overall decreasing life (ODL) class of life distributions. A new nonparametric test statistic for testing exponentiality against ODL is investigated based on this inequality. The asymptotic normality of the proposed statistic is presented. Pitman's asymptotic efficiency, power and critical values of this test are calculated to assess the performance of the test. Real examples are given to elucidate the use of the proposed test statistic in the reliability analysis. Wealso proposed a test for testing exponentiality versus ODL for right censored data and the power estimates of this test are also simulated for censored data for some commonly used distributions in reliability. Finally, real data are used as an example for practical problems.
adaptive comprehensive learning bacterial foraging optimization and its appli...Amir Shokri
adaptive comprehensive learning bacterial foraging optimization and its application on vehicle routing problem with time windows
amirsh.nll@gmail.com
seaman university - Msc. Artificial intelligence
Discrete time prey predator model with generalized holling type interactionZac Darcy
We have introduced a discrete time prey-predator model with Generalized Holling type interaction. Stability nature of the fixed points of the model are determined analytically. Phase diagrams are drawn after solving the system numerically. Bifurcation analysis is done with respect to various parameters of the system. It is shown that for modeling of non-chaotic prey predator ecological systems with Generalized Holling type interaction may be more useful for better prediction and analysis.
Artificial bee colony (ABC) algorithm is a well known and one of the latest swarm intelligence based techniques. This method is a population based meta-heuristic algorithm used for numerical optimization. It is based on the intelligent behavior of honey bees. Artificial Bee Colony algorithm is one of the most popular techniques that are used in optimization problems. Artificial Bee Colony algorithm has some major advantages over other heuristic methods. To utilize its good feature a number of researchers combined ABC algorithm with other methods, and generate some new hybrid methods. This paper provides comparative analysis of hybrid differential Artificial Bee Colony algorithm with hybrid ABC – SPSO, Genetic algorithm and Independent rough set approach based on some parameters like technique, dimension, methodology etc. KEYWORDS
ANTI-SYNCHRONIZATION OF HYPERCHAOTIC BAO AND HYPERCHAOTIC XU SYSTEMS VIA ACTI...IJCSEIT Journal
This paper investigates the anti-synchronization of identical hyperchaotic Bao systems (Bao and Liu,
2008), identical hyperchaotic Xu systems (Xu, Cai and Zheng, 2009) and non-identical hyperchaotic Bao
and hyperchaotic Xu systems. Active nonlinear control has been deployed for the anti- synchronization of
the hyperchaotic systems addressed in this paper and the main results have been established using
Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active
nonlinear control method is very effective and convenient to achieve anti-synchronization of identical and
non-identical hyperchaotic Bao and hyperchaotic Xu systems. Numerical simulations have been provided to
validate and demonstrate the effectiveness of the anti-synchronization results for the hyperchaotic Cao and
hyperchaotic Xu systems.
A Moment Inequality for Overall Decreasing Life Class of Life Distributions w...inventionjournals
:A moment inequality is derived for the system whose life distribution is in an overall decreasing life (ODL) class of life distributions. A new nonparametric test statistic for testing exponentiality against ODL is investigated based on this inequality. The asymptotic normality of the proposed statistic is presented. Pitman's asymptotic efficiency, power and critical values of this test are calculated to assess the performance of the test. Real examples are given to elucidate the use of the proposed test statistic in the reliability analysis. Wealso proposed a test for testing exponentiality versus ODL for right censored data and the power estimates of this test are also simulated for censored data for some commonly used distributions in reliability. Finally, real data are used as an example for practical problems.
adaptive comprehensive learning bacterial foraging optimization and its appli...Amir Shokri
adaptive comprehensive learning bacterial foraging optimization and its application on vehicle routing problem with time windows
amirsh.nll@gmail.com
seaman university - Msc. Artificial intelligence
Discrete time prey predator model with generalized holling type interactionZac Darcy
We have introduced a discrete time prey-predator model with Generalized Holling type interaction. Stability nature of the fixed points of the model are determined analytically. Phase diagrams are drawn after solving the system numerically. Bifurcation analysis is done with respect to various parameters of the system. It is shown that for modeling of non-chaotic prey predator ecological systems with Generalized Holling type interaction may be more useful for better prediction and analysis.
Artificial bee colony (ABC) algorithm is a well known and one of the latest swarm intelligence based techniques. This method is a population based meta-heuristic algorithm used for numerical optimization. It is based on the intelligent behavior of honey bees. Artificial Bee Colony algorithm is one of the most popular techniques that are used in optimization problems. Artificial Bee Colony algorithm has some major advantages over other heuristic methods. To utilize its good feature a number of researchers combined ABC algorithm with other methods, and generate some new hybrid methods. This paper provides comparative analysis of hybrid differential Artificial Bee Colony algorithm with hybrid ABC – SPSO, Genetic algorithm and Independent rough set approach based on some parameters like technique, dimension, methodology etc. KEYWORDS
ANTI-SYNCHRONIZATION OF HYPERCHAOTIC BAO AND HYPERCHAOTIC XU SYSTEMS VIA ACTI...IJCSEIT Journal
This paper investigates the anti-synchronization of identical hyperchaotic Bao systems (Bao and Liu,
2008), identical hyperchaotic Xu systems (Xu, Cai and Zheng, 2009) and non-identical hyperchaotic Bao
and hyperchaotic Xu systems. Active nonlinear control has been deployed for the anti- synchronization of
the hyperchaotic systems addressed in this paper and the main results have been established using
Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active
nonlinear control method is very effective and convenient to achieve anti-synchronization of identical and
non-identical hyperchaotic Bao and hyperchaotic Xu systems. Numerical simulations have been provided to
validate and demonstrate the effectiveness of the anti-synchronization results for the hyperchaotic Cao and
hyperchaotic Xu systems.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Use Proportional Hazards Regression Method To Analyze The Survival of Patient...Waqas Tariq
The Kaplan Meier method is used to analyze data based on the survival time. In this paper used Kaplan Meier procedure and Cox regression with these objectives. The objectives are finding the percentage of survival at any time of interest, comparing the survival time of two studied groups and examining the effect of continuous covariates with the relationship between an event and possible explanatory variables. The variables (Age, Gender, Weight, Drinking, Smoking, District, Employer, Blood Group) are used to study the survival patients with cancer stomach. The data in this study taken from Hiwa/Hospital in Sualamaniyah governorate during the period of (48) months starting from (1/1/2010) to (31/12/2013) .After Appling the Cox model and achieve the hypothesis we estimated the parameters of the model by using (Partial Likelihood) method and then test the variables by using (Wald test) the result show that the variables age and weight are influential at the survival of time.
Matching Weights to Simultaneously Compare Three Treatment Groups: a Simulati...Kazuki Yoshida
Presentation at the Epidemiology Congress of Americas 2016.
https://epiresearch.org/2016-meeting/submitted-abstract-sessions/pharmacoepidemiology-estimation-of-treatment/
Paper: http://journals.lww.com/epidem/Abstract/publishahead/Matching_weights_to_simultaneously_compare_three.98901.aspx (email me at kazukiyoshida@mail.harvard.edu)
Simulation code: https://github.com/kaz-yos/mw
Tutorial: http://rpubs.com/kaz_yos/matching-weights
Computational Pool-Testing with Retesting StrategyWaqas Tariq
Pool testing is a cost effective procedure for identifying defective items in a large population. It also improves the efficiency of the testing procedure when imperfect tests are employed. This study develops computational pool-testing strategy based on a proposed pool testing with re-testing strategy. Statistical moments based on this applied design have been generated. With advent of computers in 1980‘s, pool-testing with re-testing strategy under discussion is handled in the context of computational statistics. From this study, it has been established that re-testing reduces misclassifications significantly as compared to Dorfman procedure although re-testing comes with a cost i.e. increase in the number of tests. Re-testing considered improves the sensitivity and specificity of the testing scheme.
Bayesian inference for mixed-effects models driven by SDEs and other stochast...Umberto Picchini
An important, and well studied, class of stochastic models is given by stochastic differential equations (SDEs). In this talk, we consider Bayesian inference based on measurements from several individuals, to provide inference at the "population level" using mixed-effects modelling. We consider the case where dynamics are expressed via SDEs or other stochastic (Markovian) models. Stochastic differential equation mixed-effects models (SDEMEMs) are flexible hierarchical models that account for (i) the intrinsic random variability in the latent states dynamics, as well as (ii) the variability between individuals, and also (iii) account for measurement error. This flexibility gives rise to methodological and computational difficulties.
Fully Bayesian inference for nonlinear SDEMEMs is complicated by the typical intractability of the observed data likelihood which motivates the use of sampling-based approaches such as Markov chain Monte Carlo. A Gibbs sampler is proposed to target the marginal posterior of all parameters of interest. The algorithm is made computationally efficient through careful use of blocking strategies, particle filters (sequential Monte Carlo) and correlated pseudo-marginal approaches. The resulting methodology is is flexible, general and is able to deal with a large class of nonlinear SDEMEMs [1]. In a more recent work [2], we also explored ways to make inference even more scalable to an increasing number of individuals, while also dealing with state-space models driven by other stochastic dynamic models than SDEs, eg Markov jump processes and nonlinear solvers typically used in systems biology.
[1] S. Wiqvist, A. Golightly, AT McLean, U. Picchini (2020). Efficient inference for stochastic differential mixed-effects models using correlated particle pseudo-marginal algorithms, CSDA, https://doi.org/10.1016/j.csda.2020.107151
[2] S. Persson, N. Welkenhuysen, S. Shashkova, S. Wiqvist, P. Reith, G. W. Schmidt, U. Picchini, M. Cvijovic (2021). PEPSDI: Scalable and flexible inference framework for stochastic dynamic single-cell models, bioRxiv doi:10.1101/2021.07.01.450748.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
We provide an overview of some recent developments in machine learning tools for dynamic treatment regime discovery in precision medicine. The first development is a new off-policy reinforcement learning tool for continual learning in mobile health to enable patients with type 1 diabetes to exercise safely. The second development is a new inverse reinforcement learning tools which enables use of observational data to learn how clinicians balance competing priorities for treating depression and mania in patients with bipolar disorder. Both practical and technical challenges are discussed.
Discretization of a Mathematical Model for Tumor-Immune System Interaction wi...mathsjournal
The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor and immune cells. The model consists of differential equations with piecewise constant arguments and based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is obtained a system of difference equations from the system of differential equations. In order to get local and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a consequence of Neimark-Sacker bifurcation.
DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WI...mathsjournal
The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor
and immune cells. The model consists of differential equations with piecewise constant arguments and
based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is
obtained a system of difference equations from the system of differential equations. In order to get local
and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion
and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a
consequence of Neimark-Sacker bifurcation.
DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WI...mathsjournal
The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor
and immune cells. The model consists of differential equations with piecewise constant arguments and
based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is
obtained a system of difference equations from the system of differential equations. In order to get local
and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion
and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a
consequence of Neimark-Sacker bifurcation.
DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WI...mathsjournal
The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor and immune cells. The model consists of differential equations with piecewise constant arguments and based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is obtained a system of difference equations from the system of differential equations. In order to get local and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a consequence of Neimark-Sacker bifurcation.
DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WI...mathsjournal
The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor
and immune cells. The model consists of differential equations with piecewise constant arguments and
based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is
obtained a system of difference equations from the system of differential equations. In order to get local
and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion
and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a
consequence of Neimark-Sacker bifurcation.
DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WI...mathsjournal
The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor
and immune cells. The model consists of differential equations with piecewise constant arguments and
based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is
obtained a system of difference equations from the system of differential equations. In order to get local
and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion
and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a
consequence of Neimark-Sacker bifurcation.
DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WI...mathsjournal
The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor
and immune cells. The model consists of differential equations with piecewise constant arguments and
based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is
obtained a system of difference equations from the system of differential equations. In order to get local
and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion
and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a
consequence of Neimark-Sacker bifurcation.
DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WI...mathsjournal
The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor
and immune cells. The model consists of differential equations with piecewise constant arguments and
based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is
obtained a system of difference equations from the system of differential equations. In order to get local
and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion
and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a
consequence of Neimark-Sacker bifurcation.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Use Proportional Hazards Regression Method To Analyze The Survival of Patient...Waqas Tariq
The Kaplan Meier method is used to analyze data based on the survival time. In this paper used Kaplan Meier procedure and Cox regression with these objectives. The objectives are finding the percentage of survival at any time of interest, comparing the survival time of two studied groups and examining the effect of continuous covariates with the relationship between an event and possible explanatory variables. The variables (Age, Gender, Weight, Drinking, Smoking, District, Employer, Blood Group) are used to study the survival patients with cancer stomach. The data in this study taken from Hiwa/Hospital in Sualamaniyah governorate during the period of (48) months starting from (1/1/2010) to (31/12/2013) .After Appling the Cox model and achieve the hypothesis we estimated the parameters of the model by using (Partial Likelihood) method and then test the variables by using (Wald test) the result show that the variables age and weight are influential at the survival of time.
Matching Weights to Simultaneously Compare Three Treatment Groups: a Simulati...Kazuki Yoshida
Presentation at the Epidemiology Congress of Americas 2016.
https://epiresearch.org/2016-meeting/submitted-abstract-sessions/pharmacoepidemiology-estimation-of-treatment/
Paper: http://journals.lww.com/epidem/Abstract/publishahead/Matching_weights_to_simultaneously_compare_three.98901.aspx (email me at kazukiyoshida@mail.harvard.edu)
Simulation code: https://github.com/kaz-yos/mw
Tutorial: http://rpubs.com/kaz_yos/matching-weights
Computational Pool-Testing with Retesting StrategyWaqas Tariq
Pool testing is a cost effective procedure for identifying defective items in a large population. It also improves the efficiency of the testing procedure when imperfect tests are employed. This study develops computational pool-testing strategy based on a proposed pool testing with re-testing strategy. Statistical moments based on this applied design have been generated. With advent of computers in 1980‘s, pool-testing with re-testing strategy under discussion is handled in the context of computational statistics. From this study, it has been established that re-testing reduces misclassifications significantly as compared to Dorfman procedure although re-testing comes with a cost i.e. increase in the number of tests. Re-testing considered improves the sensitivity and specificity of the testing scheme.
Bayesian inference for mixed-effects models driven by SDEs and other stochast...Umberto Picchini
An important, and well studied, class of stochastic models is given by stochastic differential equations (SDEs). In this talk, we consider Bayesian inference based on measurements from several individuals, to provide inference at the "population level" using mixed-effects modelling. We consider the case where dynamics are expressed via SDEs or other stochastic (Markovian) models. Stochastic differential equation mixed-effects models (SDEMEMs) are flexible hierarchical models that account for (i) the intrinsic random variability in the latent states dynamics, as well as (ii) the variability between individuals, and also (iii) account for measurement error. This flexibility gives rise to methodological and computational difficulties.
Fully Bayesian inference for nonlinear SDEMEMs is complicated by the typical intractability of the observed data likelihood which motivates the use of sampling-based approaches such as Markov chain Monte Carlo. A Gibbs sampler is proposed to target the marginal posterior of all parameters of interest. The algorithm is made computationally efficient through careful use of blocking strategies, particle filters (sequential Monte Carlo) and correlated pseudo-marginal approaches. The resulting methodology is is flexible, general and is able to deal with a large class of nonlinear SDEMEMs [1]. In a more recent work [2], we also explored ways to make inference even more scalable to an increasing number of individuals, while also dealing with state-space models driven by other stochastic dynamic models than SDEs, eg Markov jump processes and nonlinear solvers typically used in systems biology.
[1] S. Wiqvist, A. Golightly, AT McLean, U. Picchini (2020). Efficient inference for stochastic differential mixed-effects models using correlated particle pseudo-marginal algorithms, CSDA, https://doi.org/10.1016/j.csda.2020.107151
[2] S. Persson, N. Welkenhuysen, S. Shashkova, S. Wiqvist, P. Reith, G. W. Schmidt, U. Picchini, M. Cvijovic (2021). PEPSDI: Scalable and flexible inference framework for stochastic dynamic single-cell models, bioRxiv doi:10.1101/2021.07.01.450748.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
We provide an overview of some recent developments in machine learning tools for dynamic treatment regime discovery in precision medicine. The first development is a new off-policy reinforcement learning tool for continual learning in mobile health to enable patients with type 1 diabetes to exercise safely. The second development is a new inverse reinforcement learning tools which enables use of observational data to learn how clinicians balance competing priorities for treating depression and mania in patients with bipolar disorder. Both practical and technical challenges are discussed.
Discretization of a Mathematical Model for Tumor-Immune System Interaction wi...mathsjournal
The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor and immune cells. The model consists of differential equations with piecewise constant arguments and based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is obtained a system of difference equations from the system of differential equations. In order to get local and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a consequence of Neimark-Sacker bifurcation.
DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WI...mathsjournal
The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor
and immune cells. The model consists of differential equations with piecewise constant arguments and
based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is
obtained a system of difference equations from the system of differential equations. In order to get local
and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion
and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a
consequence of Neimark-Sacker bifurcation.
DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WI...mathsjournal
The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor
and immune cells. The model consists of differential equations with piecewise constant arguments and
based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is
obtained a system of difference equations from the system of differential equations. In order to get local
and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion
and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a
consequence of Neimark-Sacker bifurcation.
DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WI...mathsjournal
The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor and immune cells. The model consists of differential equations with piecewise constant arguments and based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is obtained a system of difference equations from the system of differential equations. In order to get local and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a consequence of Neimark-Sacker bifurcation.
DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WI...mathsjournal
The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor
and immune cells. The model consists of differential equations with piecewise constant arguments and
based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is
obtained a system of difference equations from the system of differential equations. In order to get local
and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion
and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a
consequence of Neimark-Sacker bifurcation.
DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WI...mathsjournal
The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor
and immune cells. The model consists of differential equations with piecewise constant arguments and
based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is
obtained a system of difference equations from the system of differential equations. In order to get local
and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion
and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a
consequence of Neimark-Sacker bifurcation.
DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WI...mathsjournal
The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor
and immune cells. The model consists of differential equations with piecewise constant arguments and
based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is
obtained a system of difference equations from the system of differential equations. In order to get local
and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion
and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a
consequence of Neimark-Sacker bifurcation.
DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WI...mathsjournal
The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor
and immune cells. The model consists of differential equations with piecewise constant arguments and
based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is
obtained a system of difference equations from the system of differential equations. In order to get local
and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion
and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a
consequence of Neimark-Sacker bifurcation.
Let's dive deeper into the world of ODC! Ricardo Alves (OutSystems) will join us to tell all about the new Data Fabric. After that, Sezen de Bruijn (OutSystems) will get into the details on how to best design a sturdy architecture within ODC.
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
Accelerate your Kubernetes clusters with Varnish CachingThijs Feryn
A presentation about the usage and availability of Varnish on Kubernetes. This talk explores the capabilities of Varnish caching and shows how to use the Varnish Helm chart to deploy it to Kubernetes.
This presentation was delivered at K8SUG Singapore. See https://feryn.eu/presentations/accelerate-your-kubernetes-clusters-with-varnish-caching-k8sug-singapore-28-2024 for more details.
PHP Frameworks: I want to break free (IPC Berlin 2024)Ralf Eggert
In this presentation, we examine the challenges and limitations of relying too heavily on PHP frameworks in web development. We discuss the history of PHP and its frameworks to understand how this dependence has evolved. The focus will be on providing concrete tips and strategies to reduce reliance on these frameworks, based on real-world examples and practical considerations. The goal is to equip developers with the skills and knowledge to create more flexible and future-proof web applications. We'll explore the importance of maintaining autonomy in a rapidly changing tech landscape and how to make informed decisions in PHP development.
This talk is aimed at encouraging a more independent approach to using PHP frameworks, moving towards a more flexible and future-proof approach to PHP development.
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
"Impact of front-end architecture on development cost", Viktor TurskyiFwdays
I have heard many times that architecture is not important for the front-end. Also, many times I have seen how developers implement features on the front-end just following the standard rules for a framework and think that this is enough to successfully launch the project, and then the project fails. How to prevent this and what approach to choose? I have launched dozens of complex projects and during the talk we will analyze which approaches have worked for me and which have not.
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
Slack (or Teams) Automation for Bonterra Impact Management (fka Social Soluti...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on the notifications, alerts, and approval requests using Slack for Bonterra Impact Management. The solutions covered in this webinar can also be deployed for Microsoft Teams.
Interested in deploying notification automations for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
Dev Dives: Train smarter, not harder – active learning and UiPath LLMs for do...UiPathCommunity
💥 Speed, accuracy, and scaling – discover the superpowers of GenAI in action with UiPath Document Understanding and Communications Mining™:
See how to accelerate model training and optimize model performance with active learning
Learn about the latest enhancements to out-of-the-box document processing – with little to no training required
Get an exclusive demo of the new family of UiPath LLMs – GenAI models specialized for processing different types of documents and messages
This is a hands-on session specifically designed for automation developers and AI enthusiasts seeking to enhance their knowledge in leveraging the latest intelligent document processing capabilities offered by UiPath.
Speakers:
👨🏫 Andras Palfi, Senior Product Manager, UiPath
👩🏫 Lenka Dulovicova, Product Program Manager, UiPath
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
Knowledge engineering: from people to machines and back
A041030106
1. IOSR Journal of Engineering (IOSRJEN) www.iosrjen.org
ISSN (e): 2250-3021, ISSN (p): 2278-8719
Vol. 04, Issue 10 (October. 2014), ||V3|| PP 01-06
International organization of Scientific Research 1 | P a g e
Mathematical model for Oxytocin alleviates the neuroendocrine in healthy men S.Lakshmi* and M.Gayathri** *Principal, Government Arts & Science College, Peravurani – 614804, Thanjavur – Dt, Tamilnadu. **Research Scholar, P.G and Research Department of Mathematics, K.N. Govt. Arts College for Women (Autonomous), Thanjavur – 613007, Tamilnadu. Abstract: - Maximum Likelihood Estimation is by far the most popular method of parameter estimation and is an indispensable tool for many statistical modeling techniques, in particular in non-linear modeling with non- normal data. The purpose of this paper is to provide a good conceptual explanation of the method with illustrative examples. In application part by using normal distribution the likelihood functions for inflammatory hormone levels in response to endotoxin and plasma concentration oxytocin, ACTH, cortisol, and procalcitonin are obtained. These functions show a clear picture for all the above parameters when LPS+Oxytocin is administered to the inflammatory cases and compared with the medical conclusion. Keywords: Normal distribution, density function, oxytocin. Mathematical subject classification: 60GXX, 62HXX, 62PXX. 1.Mathematical model:
I. INTRODUCTION
In the psychological sciences, uncover general laws and principles that govern the behavior under investigation. As these principles are not directly observable, they are formulated in terms of hypotheses. In mathematical modeling, such hypotheses about the structure and inner working of the behavioral process of interest are stated in terms of mathematical functions called models. The goal of modeling is to deduce the form of the underlying process by testing the viability of such models. Once a model is specified with its parameters, data have been collected with specific norms. There are two generally accepted methods of parameter estimation. They are least-squares estimation (LSE) and maximum likelihood estimation (MLE). The former is well known to us as many of the familiar concepts such as linear regression, the sum of squares error, the proportion variance accounted[2] , and the root mean squared deviation are tied to the method. On the other hand, MLE is not widely recognized among modelers in psychology[3], though it is, by far, the most commonly used method of parameter estimation[7]. LSE might be useful for obtaining a descriptive measure for the purpose of summarizing observed data[9], but MLE is more suitable for statistical inference such as model comparison LSE has no basis for constructing confidence intervals or testing hypotheses. 1.2.Maximum Likelihood Estimation The likelihood Function Let X1,……Xn be an i.i.d sample with probability density function (p.d.f) f(xi;θ), where θ is a (k×1) vector of parameters that characterize f(xi;θ)[8]. For example, if Xi~ N(μ,휎2) then f(xi,θ) = (2π휎2)-1/2exp(- 12휎2( xi -μ)2) and θ = (μ,휎2 )ʹ. Then joint density of the sample is, by independence, equal to the product of the marginal densities f(x1,……..xn;θ) = f(x1;θ)……..f(xn;θ) = 푓푛푖 =1(xi,θ). The joint density is an n dimensional function of the data x1……..,xn given the parameter vector θ. The joint density satisfies f(x1,............xn;θ) ≥ 0 ∫…….∫ f(x1…………xn;θ) = 1. The likelihood function is defined as the joint density treated as a functions of the parameters θ : L(θ/x1,……..,xn) = f(x1,………xn;θ) = 푓푛푖 =1(xi,θ). Notice that the likelihood function is a k dimensional function of θ given the data x1,…..xn. It is important to keep in mind that the likelihood function, being a function of θ and not the data, is not a proper p.d.f .It is always positive but ∫……..∫ L(θ/x1……..xn)dθ1………dθk ≠ 1. To simplify notation, let the vector X = (x1,……..xn) denote the observed sample. Then the joint p.d.f and likelihood function may be expressed as f(X;θ) and L(θ/X).
2. Mathematical model for Oxytocin alleviates the neuroendocrine in healthy men
International organization of Scientific Research 2 | P a g e
Example 1 Bernoulli Sampling Let Xi ̴ Bernoulli(θ). That is, Xi = 1 with probability θ and Xi = 0 with probability 1 – θ where 0 ≤ θ ≤ 1. The p.d.f for Xi is xi f(xi;θ) = 휃푥푖 (1−휃)1−푥푖, xi = 0,1 Let X1,…..Xn be an iid sample with Xi ̴ Bernoulli(θ).The joint density/ likelihood function is given by f(x;θ) = L(θ/x) = 휃푥푖푛푖 =1(1−휃)1−푥푖 = 휃 푥푖 푛푖 =1(1−휃)푛− 푥푖 푛푖 =1 For a given value of θ and observed sample x, f(x,θ) gives the probability of observing the sample. For example, suppose n=5 and x = (0,…..,0). Now some values of θ are more likely to have generated this sample than others. In particular, it is more likely that θ is close to zero than one. To see this, note that the likelihood function for this sample is L(θ/(0,…….,0)) = (1-θ)5 The likelihood function has a clear maximum at θ = 0. That is, θ = 0 is the value of θ that makes the observed sample x = (0,……,0) most likely (highest probability) Similarly, suppose x = (1,……..,1). Then the likelihood function is L(θ/(1,……,1)) = θ5 Now the likelihood function has a maximum at θ = 1. Example 2 Normal Sampling Let X1,……….,Xn be an iid sample with Xi ̴ N(μ,휎2). The pdf for Xi is f(xi;θ) = (2π휎2)-1/2exp (- 12휎2 (xi-μ)2), - ∞<휇<∞, 휎2>0, -∞<푥<∞ so that θ = (μ,휎2)ʹ. The likelihood function is given by L(θ/x) = (푛푖 =12π휎2)-1/2exp (- 12휎2 (xi-μ)2), = (2π휎2)-n/2exp (- 12휎2 (푥푛푖 =1i-μ)2) Suppose 휎2 = 1. Then L(θ/x) = L(μ/x) = (2휋)-n/2exp(- 12 (푥푛푖 =1i-μ)2) Now (푥푛푖 =1i-μ)2 = (푥푛푖 =1i - 푥 +푥 -μ)2 = [(푥푛푖 =1i-푥 )2 + 2(xi-푥 )(x-휇 ) + (푥 -μ)2] = (푥푛푖 =1i-푥 )2 + n(푥 -μ)2 So that L(μ/x) = (2π)-n/2exp( - 12 [ (푛푖 =1xi-푥 )2 + n(푥 -μ)2] ) Since both (xi-푥 )2 and (푥 -μ)2 are positive it is clear that L(μ/x) is maximized at μ =푥 .
II. APPLICATION
Oxytocin is a hormone and neurotransmitter found to have anti- inflammatory functions in rodents. Ten healthy men received , in a randomized, placebo controlled crossover design, placebo, oxytocin, LPS, and LPS+oxytocin. Oxytocin treatment resultedin a transient or prolonged reduction of endotoxin-induced increase in plasma ACTH, Cortisol, prolactionin.Oxytocin decreases the neuroendocrine and cytokine activation caused by bacterial endotoxin in men. Possibly due to the pathway. Oxytocin –deficient mice exhibit increased stress response associated with a significant hyperactivation of the HPA axis[6]. Here we present a randomized, placebo-controlled, crossover trial, conducted to test the effect of continuous intravenous oxytocin infusion on LPS-induced systemic inflammation in 10 healthy men. In addition, we investigated whether oxytocin directly affects the LPS-induced cytokine release from peripheral blood mononuclear cells (PBMCs) of healthy human donors in vitro. 2.1.Hormone and cytokine measurement. Blood samples were immediately cooled and centrifuged for 10 min at 3.000 rpm, 4ºC, and plasma aliquots were immediately frozen at -20ºC. Plasma oxytocin and ACTH were measured using commercial RIA kits Procalcitonin (PCT) was measured using the BRAHMS Procalcitonin Sensitive LIA kit[5]. All samples taken over the 4 study days for each individual subject were analyzed at the same time and in duplicates. Cell isolation and culture. PBMCs were isolated from acid citrate dextrose buffy coats of healthy donors. CD14_ monocytes were obtained by magnetic cell sorting using anti-CD14-conjugated magnetic microbeads CD14_ monocytes (2 ± 106) or PBMCs (106 cells/ml) were cultured in human serum albumin-containing X- Vivo 10 medium in 12-well plates for 2, 4, and 24 h. Different concentrations of oxytocin (Sigma) or vehicle control (0.1% water) were added to the cells 30 min before adding LPS.
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International organization of Scientific Research 3 | P a g e
2.2. Hormone Response Administration of oxytocin elevated within 10 min plasma oxytocin levels (P = 0.021), which reached peak values at time point 60 min (P <0.001) (Fig. 2.2 A). Circulating oxytocin then began to decline 10 min after the infusion was stopped, but remained significantly elevated until time point 120 min (P < 0.001) (Fig. 2.2.A). Plasma concentrations of ACTH (Fig. 2.2.B) and cortisol (Fig. 2.2.C) remained unchanged during oxytocin treatment, but increased after the LPS bolus (P = 0.027 for ACTH at 120 min and P = 0.043 for cortisol at 90 min when comparing LPS vs. placebo). A significantly reduced increase in plasma ACTH was observed at time point 120 min: 36.1 ± 5.9 pg/ml in the LPS ± oxytocin group vs.69.6 ± 14.8 pg/ml in the LPS group (P = 0.019) (Fig. 2.2.B). The LPS-induced increase in plasma cortisol was also alleviated in the LPS ±oxytocin group at time points 90 min (P = 0.03) and 120 min (P = 0.01) (Fig. 2.2.C). To further evaluate the impact of oxytocin on the severity of endotoxinemia, measured the plasma concentrations of PCT, a diagnostic and prognostic biomarker in sepsis [10] Oxytocin significantly reduced the LPS-induced increase in PCT, which presented significant differences at the 240th min (0.178 ± 0.05 ng/ml on LPS days compared with 0.072 ± 0.01 ng/ml on LPS ± oxytocin days, P = 0.043), at the 300th min (P = 0.033), and at the 360th min (P = 0.035) (Fig. 2.3). Consideration the possibility that repeated injections of endotoxin itself may result in an altered immune response, inducing resistance or tolerance in humans. Therefore, the subjects received the four treatments in a randomized order. In addition, we compared the changes in plasma ACTH, cortisol, and PCT between volunteers randomized to receive LPS before the application of LPS ± oxytocin (n = 5) and volunteers randomized to receive LPS ±oxytocin before the administration of LPS (n = 5). Results were similar to those obtained from all volunteers being treated with LPS vs. all volunteers having received LPS ±oxytocin.
Figure 2.2. Hormone levels in response to endotoxin and oxytocin. Plasma concentrations are shown of oxytocin (A), ACTH (B),and cortisol (C) in response to placebo, oxytocin (1pmol kg -1 min-1 during 90 min. 1=- 10 to 80 min). LPS (2ng/kg iv. i =0 h), and LPS+oxytocin values are means ± SE.
4. Mathematical model for Oxytocin alleviates the neuroendocrine in healthy men
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Figure 2.3.Procalcitonin (PCT) levels in response to endotoxin and oxytocin. Plasma PCT concentrations are shown after placebo or LPS administration (2ng/kg iv. i=0 h), in the presence or absence of oxytocin infusion (t= -10 to 80 min). Values are means ± SE. First, the study population included only healthy men, and we have no data on the role of oxytocin on the LPS-induced endocrine and cytokine activation in women[1]. Second, as this is the first study coadministrating LPS and oxytocin in humans, we took care to use the smallest oxytocin dose needed to achieve elevated oxytocin concentrations during the first 120 min after LPS administration. Nevertheless, the achieved maximal concentrations of 160–180 pg/ml are clearly supraphysiological. Third, LPS administration is only an experimental and self-limiting model of infection and inflammation. In summary, this study demonstrates that pharmacological doses of oxytocin attenuate the endocrine and cytokine activation following bacterial endotoxin administration in humans. Oxytocin appears to modulate innate host defense mechanisms, thereby eventually reducing an LPS-induced overshooting immune response. Mathematical Results
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The figure (3.1),A. indicates that the likelyhood function for oxytocin (pg/ml) is suddenly decreased when LPS+oxytocin is administered. In both the cases the curves are continuous and decreased monotonically with the time axis. Similarly we have obtained the curves for the likelyhood functions for all other categories like ACTH, Cortisol, PCT (if we compare LPS administration cases). These results can be compared with the medical conclusions. This study demonstrates that pharmacological doses of oxytocin attenuate the endocrine and cytokine activation following endotoxin administration in humans. Oxytocin appears to modulate innate host defense mechanism, thereby eventually reducing an LPS induced overshooting immune response. CONCLUSION Maximum Likelihood Estimation is by far the most popular method of parameter estimation and is an indispensable tool for many statistical modeling techniques, in particular in non-linear modeling with non- normal data[4]. The purpose of this paper is to provide a good conceptual explanation of the method with illustrative examples. In application part by using normal distribution the likelihood functions for inflammatory hormone levels in response to endotoxin and plasma concentration oxytocin, ACTH, cortisol, and procalcitonin[10] are obtained. These functions show a clear picture for all the above parameters when LPS+Oxytocin is administered to the inflammatory cases and compared with the medical conclusion. This study demonstrates that pharcological doses of oxytocin attenuate the endocrine and cytokine activation following endotoxin administration in humans. Oxytocin appears to modulate innate host defense mechanism, thereby eventually reducing an LPS induced overshooting immune response. The figure (3.1),A. indicates that the likelyhood function for oxytocin (pg/ml) is suddenly decreased when LPS+oxytocin is administered. In both the cases the curves are continuous and decreased monotonically with the time axis. Similarly we have obtained the curves for the likelyhood functions for all other categories like ACTH, Cortisol, PCT (if we compare LPS administration cases). REFERENCES
[1] Amico JA, Mantella RC, Wollmer RR, Li X. Anxiety and stress responses in female oxytocin deficient mice. J Neuroendocrinol 16:319–324, 2004
[2] Bain L.J., Statistical Analysis of Reliability and life testing models ,Marcel Dekker, New York, 1978
[3] Cohen, A.C.,Jr., Tables for Maximum likelihood estimates; singly truncated and single censored s samples, Technometrices, 3:535-541(1961).
[4] Consul PC, Shenton LR, Some interesting properties of Lagrangian distributions. Comm. Stat. Theor. Meth: 2, 3, 263 – 272, 1973.
[5] Jensen JU, Heslet L, Jensen TH, Espersen K, Steffensen P, Tvede M Procalcitonin increase in early identification of critically ill patients at high risk of mortality. Crit Care Med 34: 2596– 2602, 2006.
[6] Kiriyama Y, Nomura Y, Tokumitsu Y. Calcitonin gene expression induced by lipopolysaccharide in the rat pituitary. Am J Physiol Endocrinol Metab 282: E1380–E1384, 2002.
[7] Lakshmi S, Gayathri M, Mathematical model for roles of Genital stumilation, intracerebral Oxytocin release. American Journal of pure and applied mathematics. Vol 2, No 2, July-December 2013, 93-98.
[8] Le Cam, Lucien; Lo Yang, Grace (2000). Asymptotics in Statistics: Some Basic Concepts (second ed.). Springer. ISBN 0-387-95036-2.
[9] Pfanzagl, Johann (1994). Parametric statistical theory. with the assistance of R. Hamböker. Berlin, DE: Walter de Gruyter. pp. 207–208.ISBN 3-11-013863-8
[10] Uzzan B, Cohen R, Nicolas P, Cucherat M, Perret GY. Procalcitonin as a diagnostic test for Med sepsis in critically ill adults and after surgery or trauma: a systematic review and meta-analysis. Crit Care34: 1996–2003, 2006.