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Department of Statistics
 Mu Sigma Rho National Statistics Honor Society - FSU Chapter

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 Colloquium Series
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 Colloquia December 2, 2011, 10:05 am Dr. Ji Zhu November 18, 2011, 10:05 am Dr. Kshitij Khare November 8, 2011, 11:00 am Dr. Bertrand Clark, Professor of Statistics, Dept of Medicine and Dept of Epidemiology and Public Health Center for Computational Science Miller School of Medicine - Univ of Miami November 4, 2011, 10:05 am Dr. Giray Okten October 28, 2011, 10:05 am Dr. Howard Bondell October 21, 2011, 10:05 am Dr. Jinfeng Zhang October 14, 2011, 10:05 am Dr. Yiyuan She October 7, 2011, 10:05 am Dr. Jonathan H. Dennis September 30, 2011, 10:05 am Dr. Hui Zou September 23, 2011, 10:10 am Dr. Robert Clickner September 16, 2011, 10:10 am Dr. Adrian Barbu September 2, 2011, 10:10 am Dr. Victor Patrangenaru August 25, 2011, 2:00 pm Rommel Bain August 23, 2011, 9:30 am Jihyung Shin August 15, 2011, 9:30 am Wei Liu August 3, 2011, 9:30 am Sentibaleng Ncube July 29, 2011, 10:00 am Emilola Abayomi July 28, 2011, 10:00 am Felicia Williams June 9, 2011, 10:00 am Lindsey Bell June 7, 2011, 10:00 am Greg Miller June 2, 2011, 10:00 am Robert Holden May 31, 2011, 1:00 pm Jennifer Geis May 26, 2011, 10:00 am Leif Ellingson May 19, 2011, 1:00 pm Jianchang Lin May 19, 2011, 10:00 am Daniel Osborne May 16, 2011, 9:30 am Tamika Royal-Thomas May 2, 2011, 11:00 am Yinfeng Tao April 29, 2011, 10:00 am Paul Hill March 25, 2011, 2:00 pm Yu Gu March 24, 2011, 3:35 pm Vernon Lawhern March 16, 2011, 9:30 am Anqi Tang February 25, 2011, 10:10 am Wei Wu February 18, 2011, 10:10 am Adrian Barbu February 11, 2011, 10:10 am Feng Zhao January 28, 2011, 10:10 am Anuj Srivastava January 21, 2011, 10:10 am Jim Berger of Duke University

 December 2, 2011 Speaker: Dr. Ji Zhu Title: Joint Estimation of Multiple Graphical Models When: December 2, 2011 10:05 am Where: OSB 110 Abstract: Gaussian graphical models explore dependence relationships between random variables, through estimation of the corresponding inverse covariance matrices. In this paper we develop an estimator for such models appropriate for data from several graphical models that share the same variables and some of the dependence structure. In this setting, estimating a single graphical model would mask the underlying heterogeneity, while estimating separate models for each category does not take advantage of the common structure. We propose a method which jointly estimates the graphical models corresponding to the different categories present in the data, aiming to preserve the common structure, while allowing for differences between the categories. This is achieved through a hierarchical penalty that targets the removal of common zeros in the inverse covariance matrices across categories. We establish the asymptotic consistency and sparsity of the proposed estimator in the high-dimensional case, and illustrate its superior performance on a number of simulated networks. An application to learning semantic connections between terms from webpages collected from computer science departments is also included. This is joint work with Jian Guo, Elizaveta Levina, and George Michailidis. Back To Top

 November 18, 2011 Speaker: Dr. Kshitij Khare Title: Cholesky based estimation in graphical models. When: November 18, 2011 10:05 am Where: OSB 110 Abstract: We consider the problem of sparse covariance estimation in high dimensional settings using graphical models. These models can be represented in terms of a graph, where the nodes represent random variables and edges represent their interactions. When the random variables are jointly Gaussian distributed, the lack of edges in such graphs can be interpreted as conditional and/or marginal independencies between these variables. We present a computationally efficient approach for high dimensional sparse covariance estimation in graphical models based on the Cholesky decomposition of the covariance matrix or its inverse. The proposed method is illustrated on both simulated and real data. Back To Top

 November 8, 2011 Speaker: Dr. Bertrand Clark, Professor of Statistics, Dept of Medicine and Dept of Epidemiology and Public Health Center for Computational Science Miller School of Medicine - Univ of Miami Title: Clustering Stability: Impossibility and Possibility When: November 8, 2011 11:00 am Where: 499 DSL (Dirac Science Library) Abstract: In the first part of this talk we present a theorem that gives conditions under which high dimensional clustering is unstable. Specifically, for any fixed sample size, clustering becomes impossible (in a squared error sense) as the dimension increases unless the separation among the clusters is large enough in the sense that coordinatewise differences do not decrease too quickly with $D$, the dimension of the data points. We also show that clustering impossibility occurs with a theoretical rate of ${\cal{O}}(\sqrt{D})$. In the second part of this talk we present a Bayesian method for assessing clustering stability. Roughly, the idea is to evaluate the probability that the distances between points and cluster centers can be re-ordered by random factors. The method seems to be consistent for choosing the number of clusters and we argue that it accurately reflects what we mean by the stability of a clustering. This work is ongoing research and hence comments and discussion are particularly welcome. Back To Top

 November 4, 2011 Speaker: Dr. Giray Okten Title: Putting randomness back in quasi-Monte Carlo When: November 4, 2011 10:05 am Where: OSB 110 Abstract: Abstract: The quasi-Monte Carlo method is often described as the deterministic version of the Monte Carlo method. It was developed in the last few decades, and its main advantage over Monte Carlo is faster convergence, at least asymptotically, and deterministic error bounds. In quasi-Monte Carlo one uses the so called low-discrepancy sequences to sample from a function, somewhat similar to the way pseudorandom numbers are used in Monte Carlo. Some mathematicians have even suggested avoiding the use of pseudorandom numbers altogether in favor of low-discrepancy sequences, since the former does not have a "rigorous" definition. Despite having certain advantages, the quasi-Monte Carlo method has also some drawbacks. In this talk I will give a survey of hybrid methods: these are methods that bring randomness back in quasi-Monte Carlo, in order bring together the best features of Monte Carlo and quasi-Monte Carlo. Back To Top

 October 28, 2011 Speaker: Dr. Howard Bondell Title: Efficient Robust Estimation via Two-Stage Generalized Empirical Likelihood When: October 28, 2011 10:05 am Where: OSB 110 Abstract: The triumvirate of outlier resistance, distributional robustness, and efficiency in both small and large samples, constitute the Holy Grail of robust statistics. We show that a two-stage procedure based on an initial robust estimate of scale followed by an application of generalized empirical likelihood comes very close to attaining that goal. The resulting estimators are able to attain full asymptotic efficiency at the Normal distribution, while simulations point to the ability to maintain this efficiency down to small sample sizes. Additionally, the estimators are shown to have the maximum attainable finite-sample replacement breakdown point, and thus remain stable in the presence of heavy-tailed distributions and outliers. Although previous proposals with full asymptotic efficiency exist in the literature, their finite sample efficiency can often be low. The method is discussed in detail for linear regression, but can be naturally extended to other areas, such as multivariate estimation of location and covariance. Back To Top

 October 21, 2011 Speaker: Dr. Jinfeng Zhang Title: Integrated Bio-entity Network: A System for Biological Knowledge Discovery When: October 21, 2011 10:05 am Where: OSB 110 Abstract: A significant part of our biological knowledge is centered on relationships between biological entities (bio-entities) such as proteins, genes, small molecules, pathways, gene ontology (GO) terms and diseases. Accumulated at an increasing speed, the information on bio-entity relationships is archived in different forms at scattered places. Most of such information is buried in scientific literature as unstructured text. Organizing heterogeneous information in a structured form not only facilitates study of biological systems using integrative approaches, but also allows discovery of new knowledge in an automatic and systematic way. In this study, we performed a large scale integration of bio-entity relationship information from both databases containing manually annotated, structured information and automatic information extraction of unstructured text in scientific literature. The relationship information is organized in a graph data structure, named integrated bio-entity network (IBN), where the vertices are the bio-entities and edges represent their relationships. Uncertainties associated with each edge in IBN are quantified by the probabilities inferred using statistical machine learning methods. Under this framework, probabilistic-based graph theoretic algorithms can be designed to perform various knowledge discovery tasks. We designed breadth-first search with pruning (BFSP) and most probable path (MPP) algorithms to automatically generate hypothesesthe indirect relationships with high probabilities in the network. We show that IBN can be used to generate plausible hypotheses, which not only help to better understand the complex interactions in biological systems, but also provide guidance for experimental designs. Back To Top

 October 14, 2011 Speaker: Dr. Yiyuan She Title: Predictive Learning Though Joint Variable Selection and Rank Reduction for High-dimensional Data When: October 14, 2011 10:05 am Where: OSB 110 Abstract: The talk discusses joint variable and rank selection for supervised dimension reduction in predictive learning. When the number of responses and/or that of the predictors exceed the sample size, one has to consider shrinkage methods for estimation and prediction. We propose to apply sparsity and reduced rank techniques jointly to attain simultaneous feature selection and feature extraction. A class of estimators are introduced are based on novel penalties that impose both row and rank restrictions on the coefficient matrix. We prove that these estimators adapt to the unknown matrix sparsity and have fast rates of convergence than LASSO and reduced rank regression. A computation algorithm is developed and applied to real world applications in machine learning, cognitive neuroscience and macroeconometrics forecasting. Back To Top

 September 30, 2011 Speaker: Dr. Hui Zou Title: Some Results on Large Bandable Covariance Matrix Estimation When: September 30, 2011 10:05 am Where: OSB 110 Abstract: Covariance matrix is fundamental to many multivariate analysis techniques. In the era of high-dimensional data, estimating large covariance matrices is practically important and theoretically interesting. The first part of my talk concerns a general minimax theorem on the optimal estimation of large bandable covariance matrices. This result is a generalization of the minimax theorem obtained in Cai et al. (2010). The general minimax theorem reveals some new interesting phenomena. For example, for certain parameter spaces there is a tapering estimator that simultaneously attains the minimax optimal rates of convergence under both Frobenius and Spectral norms. For the same parameter spaces it is even possible to achieve adaptive minimax optimal estimation under the spectral norm with NP dimensions. In the second part of the talk, I will address the issue of selecting the right tapering parameter. We propose a SURE tuning method based on the Stein's Unbiased Risk Estimation theory. An extensive empirical study shows that SURE tuning is often comparable to the oracle tuning and outperforms CV. Back To Top

 September 23, 2011 Speaker: Dr. Robert Clickner Title: Applications of Statistics to Environmental, Health and Housing Research When: September 23, 2011 10:10 am Where: OSB 110 Abstract: The United States government and other governments collect and analyze data to inform public policy and programs. Generally, studies to collect and analyze data consist of one or more of the following components: research design, statistical design, methods development, implementation or data collection, data analysis, and report writing. All of these need statistics to help ensure the validity of the findings and the public policies and programs that may result. This is a review of the applications and use of statistical methods in environmental, health and housing studies, drawn on my personal experiences and those of my colleagues. Topics include the design and implementation of population-based housing and environmental studies; modeling of industrial effluents; analyses of the contributions of environmental contaminants to human body burden and health effects in the face of measurement errors, confounding variables and other data issues; and the presentation of the findings. Back To Top

 September 16, 2011 Speaker: Dr. Adrian Barbu Title: Hierarchical Object Parsing from Noisy Point Clouds When: September 16, 2011 10:10 am Where: OSB 110 Abstract: Object parsing and segmentation from point clouds are challenging tasks because the relevant data is available only as thin structures along object boundaries or other object features and is corrupted by large amounts of noise. One way to handle this kind of data is by employing shape models that can accurately follow the object boundaries. Popular models such as Active Shape and Active Appearance models lack the necessary flexibility for this task. While more flexible models such as Recursive Compositional Models have been proposed, this paper builds on the Active Shape models and makes three contributions. First, it presents a flexible, mid-entropy, hierarchical generative model of object shape and appearance in images. The input data is explained by an object parsing layer, which is a deformation of a hidden PCA shape model with Gaussian prior. Second, it presents a novel efficient inference algorithm that uses a set of informed data-driven proposals to initialize local searches for the hidden variables. Third, it applies the proposed model and algorithm to object parsing from point clouds such as edge detection images, obtaining state of the art parsing errors on two standard datasets without using any intensity information. Back To Top

 September 2, 2011 Speaker: Dr. Victor Patrangenaru Title: Object Data Analysis When: September 2, 2011 10:10 am Where: 110 OSB Abstract: Analysis of Object Data is the more traditional name for Data Analysis on Sample Spaces with a Manifold Stratification. It includes Multivariate Analysis, Directional Data Analysis, Projective Shape Analysis as well as classical Shape Analysis, Diffusion Tensor Imaging, Functional Data Analysis, Analysis of Phylogenetic Trees Data; pretty much any non-categorical statistical problem can be formulated as object data analysis problem. Much of the standard nonparametric methodology extends from the multivariate case, in the generic case when the Frechet mean of a random object (r.o.) is at a regular point. In practice there are situations when a r.o. has a mean located on the singular part of the stratified sample space, and the manifold CLT based technique break down. Our initial goal is to understand the asymptotic behavior of the estimators of the Frechet mean of an arbitrary random object, and to develop nonparametric methodologies and fast inference techniques in applications. Back To Top

 August 25, 2011 Speaker: Rommel Bain Title: Monte Carlo Likelihood Estimation for Conditional Autoregressive Models with Application to Sparse Spatiotemporal Data When: August 25, 2011 2:00 pm Where: 108 OSB Abstract: Spatiotemporal modeling is increasingly used in a diverse array of fields, such as ecology, epidemiology, health care research, transportation, economics, and other areas where data arise from a spatiotemporal process. Often analyses of spatiotemporal models are fraught with problems such as missing data and computational complexity. In this paper, a Monte Carlo likelihood (MCL) method is introduced for the analysis of sparse spatiotemporal temporal data (monthly mean zooplankton biomass) collected on a spatiotemporal lattice by the California Cooperative Oceanic Fisheries Investigations (CalCOFI) and assumed to follow a log-normal distribution. A conditional autoregressive (CAR) model is used to allow for spatiotemporal dependencies between nearest neighbor sites on the spatiotemporal lattice. Typically, CAR model likelihood inference is quite complicated because of the intractability of the CAR models normalizing constant. Monte Carlo likelihood estimation provides an approximation for intractable likelihood functions. We illustrate MCL parameter estimation by computing log normalized monthly mean (small) zooplankton displacement volume in ml/1000m3 to describe zooplankton seasonal variations for the CalCOFI time series. Back To Top

 August 23, 2011 Speaker: Jihyung Shin Title: Mixed-effects and mixed-distribution models for count data with applications to educational research data When: August 23, 2011 9:30 am Where: 108 OSB Abstract: This research is motivated by an analysis of reading and vocabulary data collected by Florida Center for Reading Research. We are interested in modeling the outcome of reading ability of kindergarten children aged between 5 and 7. With consents of both parents and teacher, data was collected from 461 students of number of letters with correct pronunciation in sixty seconds time period. The test has been conducted three times over the academic year, Fall, Winter and Spring. The data showed excessive zero scores on the test. In this dissertation, we examine zero-inflated Poisson (ZIP) regression models and mixed-e ffects and mixed-distribution models (MEMD) proposed by Lambert(1992) and Tooze(2002) respectively. The MEMD model is extended to Poisson count data in longitudinal setting. The maximum likelihood estimation is obtained through standard statistical software package. The application result is also shown. Back To Top

 August 15, 2011 Speaker: Wei Liu Title: A RIEMANNIAN FRAMEWORK FOR ANNOTATED CURVES ANALYSIS When: August 15, 2011 9:30 am Where: 108 OSB Abstract: We propose a Riemannian framework for shape analysis of annotated curves, curves that have certain attributes defined along them, in addition to their geometries. These attributes may be in form of vector-valued functions, discrete landmarks, or symbolic labels, and provide auxiliary information along the curves. The resulting shape analysis, that is comparing, matching, and deforming, is naturally influenced by the auxiliary functions. Our idea is to construct curves in higher dimensions using both geometric and auxiliary coordinates, and analyze shapes of these curves. The difficulty comes from the need for removing different groups from different components: the shape is invariant to rigid-motion, global scale and re-parameterization while the auxiliary component is usually invariant only to the re-parameterization. Thus, the removal of some transformations (rigid motion and global scale) is restricted only to the geometric coordinates, while the re-parameterization group is removed for all coordinates. We demonstrate this framework using a number of experiments. Back To Top

 August 3, 2011 Speaker: Sentibaleng Ncube Title: A Novel Riemannian Metric for Analyzing Spherical Functions with Applications to HARDI Data When: August 3, 2011 9:30 am Where: 108 OSB Abstract: We propose a novel Riemannian framework for analyzing orientation distribution functions (ODFs), or their probability density functions (PDFs), in HARDI data sets for use in comparing, interpolating, averaging, and denoising PDFs. This is accomplished by separating shape and orientation features of PDFs, and then analyzing them separately under their own Riemannian metrics. We formulate the action of the rotation group on the space of PDFs, and define the shape space as the quotient space of PDFs modulo the rotations. In other words, any two PDFs are compared in: (1) shape by rotationally aligning one PDF to another, using the Fisher-Rao distance on the aligned PDFs, and (2) orientation by comparing their rotation matrices. This idea improves upon the results from using the Fisher-Rao metric in analyzing PDFs directly, a technique that is being used increasingly, and leads to geodesic interpolations that are biologically feasible. This framework leads to definitions and efficient computations for the Karcher mean that provide tools for improved interpolation and denoising. We demonstrate these ideas, using an experimental setup involving several PDFs. Back To Top

 July 29, 2011 Speaker: Emilola Abayomi Title: The Relationship of Body Weight to Blood Pressure in Diverse Populations When: July 29, 2011 10:00 am Where: 108 OSB Abstract: High blood pressure is a major determinant of risk for Coronary Heart Disease (CHD) and stroke, leading causes of death in the industrialized world. A myriad of pharmacological treatments for elevated blood pressure, defined as a blood pressure greater than 140/90mmHg, are available and have at least partially resulted in large reductions in the incidence of CHD and stroke in the U.S. over the last 50 years. The factors that may increase blood pressure levels are not well understood, but body fat is thought to be a major determinant of blood pressure level. Obesity is measured through various methods (skinfolds, waist-to-hip ratio, bioelectrical impedance analysis (BIA), etc.), but the most commonly used measure is body mass index, ?. Although the relationship between level of blood pressure and BMI has been extensively reported, several questions remain: Is there a significant relationship between blood pressure and body mass index in all populations? Is the relationship between body mass and blood pressure linear? How does the relationship vary in different populations? Do characteristics such as race and gender explain heterogeneity that maybe present amongst the relationship in diverse populations? How does the relationship of other measures of body fat (skinfolds, waist-to-hip ratio, etc.) compare to the relationships found for BMI in diverse populations? To examine these questions we will conduct a meta-analysis based on person-level data from almost 30 observational studies from around the world. Back To Top

 July 28, 2011 Speaker: Felicia Williams Title: The Relationship of Diabetes and Coronary Heart Disease Mortality: a meta- analysis based on person level data When: July 28, 2011 10:00 am Where: 108 OSB Abstract: Studies have suggested that diabetes is a stronger risk factor for coronary heart disease (CHD) in women than in men. We present a meta-analysis of person-level data from diverse populations to examine this issue. Our data comes from 18 studies in which diabetes, CHD mortality and potential confounders were available and a minimum of 75 CHD deaths occurred. These studies followed up 69,308 men and 74,735 women aged 42 to 73 years on average from the US, Denmark, Iceland, Norway and the UK. Individual study prevalence rates of diabetes mellitus (mostly self-reported) at baseline ranged between less than 1\% in the youngest cohort and 15.7% (males) and 11.1% (females) in the NHLBI Cardiovascular Health Study (CHS) of the elderly. CHD death rates varied between 2% and 20%. Hazard ratios (HR) associated with baseline diabetes, adjusted for age only, varied between 1.06 and 5.12 (males) and between 1.42 and 10.87 (females). Hazard ratios (HR) associated with baseline diabetes, adjusted for age, serum cholesterol level , systolic blood pressure, and cigarette smoking status varied between 1.10 and 6.69 (males) and between 1.25 and 9.01 (females). The male fixed-effect estimated HR of fatal CHD in diabetic versus non-diabetic participants after adjustment for the major risk factors was 2.40 (95% CI 2.11-2.73) whereas the corresponding HR for females was 2.89 (2.50-3.34). These estimates differed only slightly from unadjusted ones obtained from the same data [males: 2.43 (2.14, 2.75) p-value>0.25 and females: 2.91 (2.52, 3.35) p-value>0.25]. They agree closely with estimates (odds ratios of 2.3 for males and 2.9 for females) obtained in a recent meta-analysis of 8 studies of both fatal and nonfatal CHD but based on literature-based data. There are insufficient data to suggest that there is a difference in the models that adjust for additional major CHD risk factors and the models that are unadjusted. Back To Top

 June 9, 2011 Speaker: Lindsey Bell Title: A STATISTICAL APPROACH FOR INFORMATION EXTRACTION OF BIOLOGICAL RELATIONSHIPS When: June 9, 2011 10:00 am Where: HCB 207 Abstract: Vast amounts of biomedical information are stored in scienti c literature, easily accessed through publicly available databases. Relationships among biomedical terms constitute a major part of our biological knowledge. Acquiring such structured information from unstructured literature can be done through human annotation, but is time and resource consuming. As this content continues to rapidly grow, the popularity and importance of text mining for obtaining information from unstructured text becomes increasingly evident. Text mining has four major components. First relevant articles are identi ed through information retrieval (IR), next important concepts and terms are agged using entity recognition(ER), and then facts concerning these entities are extracted from the literature in a process called information extraction(IE). Finally, text mining takes these elements and seeks to synthesize new information from the literature. Our goal is information extraction from unstructured literature concerning biological entities. To do this, we use the structure of triplets where each triplet contains two biological entities and one interaction word. The biological entities may include terms such as protein names, disease names, genes, and small-molecules. Interaction words describe the relationship between the biological terms. Under this framework we aim to combine the strengths of three classi ers in an ensemble approach. The three classi ers we consider are Bayesian Networks, Support Vector Machines, and mixture of logistic models de ned by interaction word. The three classi ers and ensemble approach are evaluated on three benchmark corpora and one corpus that is introduced in this study. The evaluation includes cross validation and cross-corpus validation to replicate an application scenario. The three classi ers are unique and we nd that performance of individual classi ers varies depending on the corpus. Therefore, an ensemble of classi ers removes the need to choose one classi er and provides optimal performance. Back To Top

 June 7, 2011 Speaker: Greg Miller Title: INVESTIGATING THE USE OF MORTALITY DATA AS A SURROGATE FOR MORBIDITY DATA When: June 7, 2011 10:00 am Where: Bel 001 Abstract: We are interested in dierences between risk models based on Coronary Heart Disease (CHD) incidence, or morbidity, compared to risk models based on CHD death. Risk models based on morbidity have been developed based on the Framingham Heart Study, while the European SCORE project developed a risk model for CHD death. Our goal is to determine whether those two developed models dier in treatment decisions concerning patient heart health. We begin by reviewing recent metrics in surrogate variables and prognostic model performance. We then conduct bootstrap hypotheses tests between two Cox proportional hazards models using Framingham data, one with incidence as a response, and one with death as a response, and nd that the coecients dier for the age covariate, but no signicant dierence for other risk factors. To understand how surrogacy can be applied to our case, where the surrogate variable is nested within the true variable of interest, we examine models based on a composite event compared to models based on singleton events. We also conduct a simulation, simulating times to a CHD incidence and time from CHD incidence to CHD death, censoring at 25 years to emulate the end of a study. We compare a Cox model with death response with a Cox model based on incidence using bootstrapped condence intervals, and nd that age and systolic blood pressure have dierences with their covariates. We continue the simulation by using Net Reclassication Index (NRI) to evaluate the treatment decision performance of the two models, and that the two models do not perform signicantly different in correctly classifying events, if the decisions are based on the risk ranks of the individuals. As long as the relative order of patients' risks is preserved across dierent risk models, treatment decisions based on classifying an upper specied percent as high risk will not be signicantly different. We conclude the dissertation with statements about future methods of approaching our question. Back To Top

 June 2, 2011 Speaker: Robert Holden Title: Failure Time Regression Models for Thinned Point Processes When: June 2, 2011 10:00 am Where: BEL 006 Abstract: In survival analysis, data on the time until a speci c criterion event occurs are analyzed, often with regard to the eff ects of various predictors. In the classic applications, the criterion event is in some sense a terminal event, e.g., death of a person or failure of a machine or machine component. In these situations, the analysis requires assumptions only about the distribution of waiting times until the criterion event occurs and the nature of the eff ects of the predictors on that distribution. Suppose that the criterion event isn't a terminal event that can only occur once, but is a repeatable event. The sequence of events forms a stochastic point process. Further suppose that only some of the events are detected (observed); the detected events form a thinned point process. Any failure time model based on the data will be based not on the time until the first occurrence, but on the time until the fi rst detected occurrence of the event. I will consider the implications of this for survival regression models. Such models will have little meaning unless the regression parameters are independent of the detection probability, or, more generally, the thinning mechanism. I will show that the e ffect of thinning on regression parameters depends on the combination of the type of regression model and the type of point process that generates the events. For some combinations, the eff ect of a predictor will be the same for time to the rst event and the time to the fi rst detected event. For other combinations, the regression eff ect will be changed as a result of the incomplete detection. Back To Top

 May 31, 2011 Speaker: Jennifer Geis Title: A WEIGHTED APPROACH TO RANK SELECTION WITH A DATA-ADAPTIVE METHOD TO CANONICAL CORRELATION ANALYSIS When: May 31, 2011 1:00 pm Where: BEL 007 Abstract: Back To Top

 May 26, 2011 Speaker: Leif Ellingson Title: STATISTICAL SHAPE ANALYSIS ON MANIFOLDS WITH APPLICATIONS TO PLANAR CONTOURS AND STRUCTURAL PROTEOMICS When: May 26, 2011 10:00 am Where: 006 BEL Abstract: The technological advances in recent years have produced a wealth of intricate digital imaging data that is analyzed effectively using the principles of shape analysis. Such data often lies on either high-dimensional or infinite-dimensional manifolds. With computing power also now strong enough to handle this data, it is necessary to develop theoretically-sound methodology to perform the analysis in a computationally efficient manner. In this dissertation, we propose approaches of doing so for planar contours and the three-dimensional atomic structures of protein binding sites. First, we adapt Kendallfs definition of direct similarity shapes of finite planar configurations to shapes of planar contours under certain regularity conditions and utilize Ziezoldfs nonparametric view of FrLechet mean shapes. The space of direct similarity shapes of regular planar contours is embedded in a space of Hilbert-Schmidt operators in order to obtain the Veronese-Whitney extrinsic mean shape. For computations, it is necessary to use discrete approximations of both the contours and the embedding. For cases when landmarks are not provided, we propose an automated, randomized landmark selection procedure that is useful for contour matching within a population and is consistent with the underlying asymptotic theory. For inference on the extrinsic mean direct similarity shape, we consider a one-sample neighborhood hypothesis test and the use of nonparametric bootstrap to approximate confidence regions. Bandulasiri et al (2008) suggested using exrinsic reflection size-and-shape analysis to study the relationship between the structure and function of protein binding sites. In order to obtain meaningful results for this approach, it is necessary to identify the atoms common to a group of binding sites with similar functions and obtain proper correspondences for these atoms. We explore this problem in depth and propose an algorithm for simultaneously finding the common atoms and their respective correspondences based upon the Iterative Closest Point algorithm. For a benchmark data set, our classification results compare favorably with those of leading established methods. Finally, we discuss current directions in the field of statistics on manifolds, including a computational comparison of intrinsic and extrinsic analysis for various applications and a brief introduction of sample spaces with manifold stratification. Back To Top

 May 19, 2011 Speaker: Jianchang Lin Title: Semiparametric Bayesian survival analysis via transform-both-sides model When: May 19, 2011 1:00 pm Where: BEL 007 Abstract: We propose a new semiparametric survival model with a log-linear median regression function as an useful alternative to the popular Cox's (1972) models and linear transformation models (Cheng et al., 1995). Compared to existing semiparametric models, our models have many practical advantages, including the interpretation of regression parameters via median, ability to incorporate heteroscedasticity, the ease of prior elicitation and computation of Bayesian estimators. Our Bayesian estimation method is also extended to multivariate survival model with symmetric random effects distribution. Our multivariate survival model has same covariate effects on marginal (population average) as well as conditional (given random effects) median survival time. Our other aim is to develop a Bayesian simultaneous variable selection and estimation of median regression for skewed response variable. Our hierarchical Bayesian model can incorporates advantages of Lasso penalty albeit for skewed and heteroscedastic response variable. Some preliminary simulation studies have been conducted to compare the performance of proposed model and existing frequentist median lasso. Considering the estimation bias and Mean squared error, our proposed model performs as good as and, in some scenarios, better than competing frequentist estimators. We illustrate our approaches and model diagnostics via reanalysis of some real life clinical studies including a small-cell lung cancer study and a retinopathy study. Back To Top

 May 19, 2011 Speaker: Daniel Osborne Title: Nonparametric Data Analysis on Manifolds with an Application in Medical Imaging When: May 19, 2011 10:00 am Where: 006 BEL Abstract: Over the past fifteen years, there has been a rapid development in Nonparametric Statistical Analysis on Shape Manifolds applied to Medical Imaging. For surgery planning, a more appropriate approach is to take into account the size as well when analyzing the CT scan data. In this context, one performs a nonparametric analysis on the 3D data retrieved from CT scans of healthy young adults, on the Size-and-Reflection Shape Space of k-ads in general position in 3D. This work, as part of larger project on planning reconstructive surgery in severe skull injuries, includes preprocessing and post-processing steps of CT images. The preprocessing step, consists of the extraction the boundary of the bone structure from the CT slices while the post-processing steps consists of 3D reconstruction of the virtual skull from these bone extractions and smoothing. Next we present preliminary results for the Schoenbergs sample mean Size-and-Reflection Shape of k-ads in general position in R^3 for the human skull based on these virtual reconstructions. The bootstrap distribution of the Schoenberg sample means 3D Size-and-Reflection Shape for a selected group of anatomic landmarks and pseudo-landmarks, are computed for 500 bootstrap resamples of the original 20 skulls represented by the 3 by k configurations, when k=9. Finally, we report a confidence region for the Schoenberg mean configuration. Back To Top

 May 16, 2011 Speaker: Tamika Royal-Thomas Title: Interrelating of Longitudinal Processes: An Empirical Example When: May 16, 2011 9:30 am Where: 207 HCB Abstract: The Barker Hypothesis states that maternal and in utero' attributes during pregnancy affects a child's cardiovascular health throughout life. We present an analysis of a unique longitudinal dataset from Jamaica that consists of three longitudinal processes: (i) Maternal longitudinal process- Blood pressure and anthropometric measurements at seven time-points on the mother during pregnancy. (ii)In Utero measurements - Ultrasound measurements of the fetus taken at six time-points during pregnancy. (iii)Birth to present process - Children's anthropometric and blood pressure measurements at 24 time-points from birth to 14 years. A comprehensive analysis of the interrelationship of these three longitudinal processes is presented using joint modeling for multivariate longitudinal profiles. We propose a new methodology of examining child's cardiovascular risk by extending a current view of likelihood estimation. Joint modeling of multivariate longitudinal profiles is done and the extension of the traditional likelihood method is utilized in this paper and compared to the maximum likelihood estimates. Our main goal is to examine whether the process in mothers predicts fetal development which in turn predicts the future cardiovascular health of the children. One of the difficulties with in utero' and early childhood data is that certain variables are highly correlated and so using dimension reduction techniques are quite applicable in this scenario. Principal component analysis (PCA) is utilized in creating a smaller dimension of uncorrelated data which is then utilized in a longitudinal analysis setting. These principal components are then utilized in an optimal linear mixed model for longitudinal data which indicates that in utero and early childhood attributes predicts the future cardiovascular health of the children. This thesis has added a body of knowledge to developmental origins of adult diseases and has supplied some significant results while utilizing a rich diversity of statistical methodologies. Back To Top

 May 2, 2011 Speaker: Yinfeng Tao Title: Title: "The frequentist properties and general performance of Bayesian Confidence Intervals for the survival function." When: May 2, 2011 11:00 am Where: 108 OSB Abstract: Estimation of a survival function is a very important topic insurvival analysis with contributions from many authors. We consider estimation of confidence intervals for the survival function based on right censored or interval-censored survival data. In the right-censored case, almost all confidence intervals are based in some way on the Kaplan-Meier estimator first proposed by Kaplan and Meier (1958) and widely used As the nonparametric estimator in the presence of right-censored data. For interval-censored data, the Turnbull estimator (Turnbull(1974)) plays a similar role. For a class of Bayesian models involving mixtures of Dirichlet priors, Doss and Huffer (2003) suggested several simulation techniques to approximate the posterior distribution of the survival function byusing Markov chain Monte Carlo or sequential importance sampling. These techniques can lead to point estimates and probability intervalsfor the survival function at arbitrary time points for both the right-censored and interval-censored cases. The main objective of this thesis is to examine the frequentist properties and general performance of the Bayesian probability intervals when the prior is non-informative. Simulation studies willbe used to compare these Bayesian probability intervals based on Doss & Huffer's approach with other published methods for obtainingpointwise confidence intervals for the survival function. Similarcomparisons will be carried out for confidence intervals for quantilesof the survival function. Also we describe an approach for constructing simultaneous confidence bands for the survival function which will be investigated in future work. Back To Top

 April 29, 2011 Speaker: Paul Hill Title: Bootstrap Prediction Bands for Non-Parametric Function Signals in a Complex System When: April 29, 2011 10:00 am Where: 307 HCB Abstract: Methods employed in the construction of prediction bands for continuous curves require a different approach to those used for a data point. In many cases, the underlying function is unknown and thus a distribution-free approach which preserves sufficient coverage for the signal in its entirety is necessary in the signal analysis. Three methods for the formation of (1-?)100% prediction bands are presented and their performances are compared through the coverage probabilities obtained. These techniques are applied to constructing prediction bands for spring discharge in a successful manner giving good coverage in each case. Spring discharge measured over time can be considered as a continuous signal and the ability to predict the future signals of spring discharge is useful for monitoring flow and other issues related to the spring. There has been common use of the gamma distribution in the simulation of rainfall. Bootstrapping the rainfall in the proposed manner, allows for adequately creating new samples over different periods of time as well as specific rain events such as hurricanes or drought. This non-parametric approach to the input rainfall augurs well for the non-parametric nature of the output signal. Back To Top

 March 25, 2011 Speaker: Yu Gu Title: New Semiparametric Methods for Recurrent Events Data" and here is the abstract. When: March 25, 2011 2:00 pm Where: HCB 210 Abstract: Recurrent events data are rising in all areas of biomedical research. We present a model for recurrent events data with the same link for the intensity and mean functions. Simple interpretations of the covariate effects on both the intensity and mean functions lead to a better understanding of the covariate effects on the recurrent events process. We use partial likelihood and empirical Bayes methods for inference and provide theoretical justifications and as well as relationships between these methods. We also show the asymptotic properties of the empirical Bayes estimators. We illustrate the computational convenience and implementation of our methods with the analysis of a heart transplant study. We also propose an additive regression model and associated empirical Bayes method for the risk of a new event given the history of the recurrent events. Both the cumulative mean and rate functions have closed form expressions for our model. Our inference method for the simiparametric model is based on maximizing a finite dimensional integrated likelihood obtained by integrating over the nonparametric cumulative baseline hazard function. Our method can accommodate time-varying covariates and is easier to implement computationally instead of iterative algorithm based full Bayes methods. The asymptotic properties of our estimates give the large-sample justifications from a frequentist stand point. We apply our method on a study of heart transplant patients to illustrate the computational convenience and other advantages of our method. Back To Top

 March 24, 2011 Speaker: Vernon Lawhern Title: "Statistical Modeling and Applications of Neural Spike Trains" When: March 24, 2011 3:35 pm Where: 110 OSB Abstract: Understanding how spike trains encode information is a principle question in the study of neural activity. Recent advances in biotechnology have given researchers the ability to record neural activity on a wide scale, allowing researchers to perform detailed analyses that may have been impossible just a few years ago. Here we present several frameworks for the statistical modeling of neural spike trains. We first develop a Generalized Linear Model (GLM) framework that incorporates the effects of hidden states in the modeling of neural activity in the primate motor cortex. We then develop a state-space model that incorporates target information in the modeling framework. In both cases, significant improvements in model fitting and decoding accuracy were observed. Finally, in joint work with Dr. Contreras and Dr. Nikonov from the Psychology Department, we study taste coding and discrimination in the gustatory system by using information-theoretic tools such as Mutual Information, and by using a recently-developed spike train metric to study the clustering performance from recordings of proximate neurons. Back To Top

 March 16, 2011 Speaker: Anqi Tang Title: A CLASS OF MIXED-DISTRIBUTION MODELS WITH APPLICATIONS IN FINANCIAL DATA ANALYSIS When: March 16, 2011 9:30 am Where: 499 DSL Abstract: Statisticians often encounter data in the form of a combination of discrete and continuous outcomes. A special case is zero-inflated longitudinal data where the response variable has a large portion of zeros. These data exhibit correlation because observations are obtained on the same subjects over time. In this dissertation, we propose a two-part mixed distribution model to model zero-inflated longitudinal data. The first part of the model is a logistic regression model that models the probability of nonzero response; the other part is a linear model that models the mean response given that the outcomes are not zeros. Random effects with AR(1) covariance structure are introduced into the both parts of the model to allow serial correlation and subject specific effect. Estimating the two-part model is challenging because of high dimensional integration necessary to obtain the maximum likelihood estimates. We propose a Monte Carlo EM algorithm for estimating the maximum likelihood estimates of parameters. Through simulation study, we demonstrate the good performance of the MCEM method in parameter and standard error estimation. To illustrate, we apply the two-part model with correlated random effects and the model with autoregressive random effects to executive compensation data to investigate potential determinants of CEO stock option grants. Back To Top

 February 25, 2011 Speaker: Wei Wu Title: When: February 25, 2011 10:10 am Where: Abstract: Back To Top

 February 18, 2011 Speaker: Adrian Barbu Title: Automatic Detection and Segmentation of Lymph Nodes from CT Data When: February 18, 2011 10:10 am Where: 108 OSB Abstract: Lymph nodes are assessed routinely in clinical practice and their size is followed throughout radiation or chemotherapy to monitor the effectiveness of cancer treatment. This work presents a robust learning-based method for automatic detection of solid lymph nodes from CT data, with the following contributions. First, it presents a learning based approach to solid lymph node detection that relies on Marginal Space Learning to achieve great speedup with virtually no loss in accuracy. Second, it presents an efficient segmentation method for solid lymph nodes. Third, it introduces two new sets of features that are effective for LN detection, one that self-aligns to high gradients and another set obtained from the segmentation result. The method is evaluated on large datasets obtaining better than state of the art results, with a running time of 5-40 seconds per volume. An added benefit of the method is the capability to detect and segment conglomerated lymph nodes. Back To Top

 February 11, 2011 Speaker: Feng Zhao Title: Bayesian portfolio optimization with time-varying factor models When: February 11, 2011 10:10 am Where: 108 OSB Abstract: We develop a modeling framework to simultaneously evaluate various types of predictability in stock returns, including stocks' sensitivity (\betas") to systematic risk factors, stocks' abnormal returns unexplained by risk factors (\alphas"), and returns of risk factors in excess of the risk-free rate (\risk premia"). Both Back To Top

 January 28, 2011 Speaker: Anuj Srivastava Title: Statistical Modeling of Elastic Functions When: January 28, 2011 10:10 am Where: 108 OSB Abstract: Motivated by the well-known problem of finding spurts in Berkeley growth data, we are interested in modeling functions that allow some warping in the time domains. Such warping is useful in improving the matching of peaks and valleys across functions and results in models that better preserve structures in the original data. The challenge is to develop a principled approach that can automatically warp a given set functions to result in an optimal alignment. The aligned functions are said to represent the "y-variability" and the warping functions used to align them form the "x-variability" of the data. I will start by summarizing the main ideas used in the past literature (e.g. Kneip and Gasser, Annals, 1992; Ramsay and Li, JRSSB, 1998; Kneip and Ramsay, JASA 2008; Liu and Mueller, JASA, 2004) and what I view as their limitations. Then, I will describe our approach for (1) aligning, comparing and modeling functions and (2) modeling the warping functions. This framework is based on the use of the Fisher-Rao Riemannian metric that provides a proper distance for comparing time-warped functional data. These distances are then used to define Karcher means and the individual functions are optimally warped to align them to the Karcher means to extract the y variability. Principal component analysis and stochastic modeling of these constituents x and y in their respective spaces leads to the desired modeling of functional variation. These ideas are demonstrated using both simulated and real data from different application domains: the Berkeley growth study, handwritten signature curves, and neuroscience spike trains. (Collaborators: Wei Wu, Sebastian Kurtek, Eric Klassen, and J. Steve Marron (UNC, Chapel Hill)) Back To Top

 January 21, 2011 Speaker: Jim Berger of Duke University Title: "I don't know where I'm gonna go when the volcano blows" When: January 21, 2011 10:10 am Where: 108 OSB Abstract: wrote Jimmy Buffet. Great song line, but usually it's too late to go when the volcano blows; one has to know when to go before the volcano blows. The problem of risk assessment for rare natural hazards -- such as volcanic pyroclastic flows -- is addressed, and illustrated with the Soufriere Hills Volcano on the island of Montserrat. Assessment is approached through a combination of mathematical computer modeling, statistical modeling of geophysical data, and extreme-event probability computation. A mathematical computer model of the natural hazard is used to provide the needed extrapolation to unseen parts of the hazard space. Statistical modeling of the available geophysical data is needed to determine the initializing distribution for exercising the computer model. In dealing with rare events, direct simulations involving the computer model are prohibitively expensive, so computation of the risk probabilities requires a combination of adaptive design of computer model approximations (emulators) and rare event simulation. Back To Top
 Google Maps Email: webmaster@stat.fsu.edu Office: 214 OSB 117 N. Woodward Ave. P.O. Box 3064330 Tallahassee, FL32306-4330 Phone: (850) 644-3218 Fax: (850) 644-5271Admissions Inquiries: info@stat.fsu.edu


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# tomcat-users mailing list archives

##### Site index · List index
Message view
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From Manfred Steurer <manfred.steu...@gamed.com>
Subject Re: tomcat base vs. home
Date Tue, 02 Aug 2005 15:13:28 GMT
I don't know VSS, but using CVS I would do a new checkout to the H:
drive, so Tomcat and VSS would use the same location and there is no
extra config to do.
- Manfred

Sternbergh, Cornell wrote:

>Sorry for the basic stuff here guys...  I'm a bit under the gun and
>haven't found the answer in an admittedly cursory search, so I thought
>I'd ask those who know all (that's you ;-)
>
>I've eclipse (3.0) with sysdeo's plugin for tomcat, and tomcat (4.1).
>In eclipse/window/preferences/tomcat there's a text box for "Tomcat
>home", currently h:\tomcat.  Under tomcat, in advanced, there's a text
>box for "Tomcat base", also h:\tomcat.
>
>Is Tomcat home the place tomcat looks for its stuff and Tomcat base
>where it looks for applications?  And then where would the HTML/JSP
>pages go?
>
>
>Now, with my limited understanding of this stuff, there's a directory
>with the java stuff in it, for the application server, a directory for
>the HTML and JSP stuff, for the http server, and a directory for the
>libraries used to actually run the application server.
>
>When I'd worked with Visual Age for Java, we had the source code in, for
>example, C:\project\ etc. and the HTML/JSPs in C:\Program
>Files\IBM\...\DEFAULT_HOST\ProjectApp\ etc.  I'm guessing that VAJ's
>libraries were also in C:\Program Files\IBM etc.
>
>In support of that, we also have Visual Source Safe pointing to the same
>directories, as it contains the Java/HTML/JSP and conf and prop and etc
>files.
>
>I'd put Eclipse and Tomcat on C:\tomcat, and had to move it to a network
>drive, H:\tomcat. (because of the zips and McAfee)
>
>But, I need to get tomcat to get the Java, HTML and JSPs from the same
>place that VSS is pointed at, i.e. back at C:\project and C:\program
>files\ibm\etc.  (so as to minimize my straying from the standard ;-)
>
>So what do I set to c:\project and what do I set to C;\program
>files\ibm\ etc.?
>
>Thanks
>
>Thank you
>R. Cornell Sternbergh
>PennDOT/BIS
>APRASTeam
>(717) 787-6760
>rsternberg@state.pa.us
>
>
>---------------------------------------------------------------------
>To unsubscribe, e-mail: tomcat-user-unsubscribe@jakarta.apache.org

format: plain


text:
# complex analysis

#### fredrick08

$$\displaystyle I=\int^{2\pi}_{0}\frac{cos(3\theta)}{5-4\cos(\theta)}d\theta$$

$$\displaystyle z=e^{i\theta},\frac{dz}{d\theta}=i\\e^{i\theta}=i\\z\Rightarrow\\d\theta=\frac{dz}{i\\z}$$

$$\displaystyle I=\oint_{C_{1}(0)}\frac{z^{3}+z^{-3}}{2\\i(-2z^{2}+5z-2)}dz$$

factorizing gives

$$\displaystyle I=\oint_{C_{1}(0)}\frac{z^{3}+z^{-3}}{2\\i(z-2)(z-\frac{1}{2})}dz$$

now from here.. i need to do $$\displaystyle 2\pi\\i*\sum\\Res\\|_{z}$$ but everytime i do it, i get dumb answers, im pretty sure the answer is $$\displaystyle \frac{\pi}{12}$$

please can anyone help me.. i may have done something stupid

#### fredrick08

I think the residues are at z=0,1/2 and 2... but not sure... and the contour only encloses z=0 and 1/2

#### Drexel28

MHF Hall of Honor
$$\displaystyle I=\int^{2\pi}_{0}\frac{cos(3\theta)}{5-4\cos(\theta)}d\theta$$
Rewrite it as $$\displaystyle iI=\int_0^{2\pi}\frac{\left(e^{i\theta}\right)^2}{5-4\frac{e^{i\theta}+\frac{1}{e^{i\theta}}}{2}}e^{i\theta}d\theta$$ but this is clearly $$\displaystyle \underset{|z|=1}{\oint}\frac{z^2}{5-2(z+\frac{1}{z})}dz=\underset{|z|=1}{\oint}\frac{-z^3}{2(z-2)(z-\tfrac{1}{2})}$$. But, clearly $$\displaystyle f(z)=\frac{-z^3}{2(z-2)}$$ is analytic on $$\displaystyle \mathbb{D}$$ and so Cauchy's integral formula tells us that $$\displaystyle iI=2\pi i\frac{-(\tfrac{1}{2})^3}{2(\tfrac{1}{2}-2)}=\frac{\pi i}{12}\implies I=\frac{\pi}{12}$$

.

#### fredrick08

ok yes, that makes perfect sense... but could please do it by residue theorem, coz thats how we are meant to atm.. srry but also.... how did u get the -z^3 on top.... where does the z^-3 go?

because i know that $$\displaystyle z^{3}+z^{-3}=\frac{z^{6}+1}{z^{3}}$$ can that work at all?

#### Drexel28

MHF Hall of Honor
ok yes, that makes perfect sense... but could please do it by residue theorem, coz thats how we are meant to atm
.........

Ok, well let $$\displaystyle f(z)$$ be as above and note that by it's analyticity that $$\displaystyle f(z)=\sum_{n=0}^{\infty}\frac{f^{(n)}(\tfrac{1}{2})(z-\tfrac{1}{2})^n}{n!}$$ and so $$\displaystyle \frac{f(z)}{z-\tfrac{1}{2}}=\frac{f(\tfrac{1}{2})}{z-\tfrac{1}{2}}+\frac{1}{2}f'(\tfrac{1}{2})(z-\tfrac{1}{2})+\cdots$$ and so $$\displaystyle \underset{z=\tfrac{1}{2}}{\text{Res}}\text{ }\frac{f(z)}{z-\tfrac{1}{2}}=f(\tfrac{1}{2})$$..........

#### Drexel28

MHF Hall of Honor
-z^3 on top.... where does the z^-3 go?
$$\displaystyle \frac{z^2}{5-2(z+\tfrac{1}{z})}=\frac{z^3}{5z-2(z^2+1)}=\frac{z^3}{-2z^2+5z-2}=\frac{-z^3}{2z^2-5z+2}$$

#### fredrick08

$$\displaystyle \frac{z^2}{5-2(z+\tfrac{1}{z})}=\frac{z^3}{5z-2(z^2+1)}=\frac{z^3}{-2z^2+5z-2}=\frac{-z^3}{2z^2-5z+2}$$
srry i dont understand how u went from

$$\displaystyle \int^{2\pi}_{0}\frac{cos(3\theta)}{5-4\cos(\theta)}d\theta$$

$$\displaystyle iI=\int_0^{2\pi}\frac{\left(e^{i\theta}\right)^2}{5-4\frac{e^{i\theta}+\frac{1}{e^{i\theta}}}{2}}e^{i\theta}d\theta$$

how can u change cos(3theta) which is 1/2(z^3+z^-3) to z^2???

[/COLOR][/FONT][/COLOR]
[/FONT][/COLOR]

[/FONT][/COLOR]

#### Drexel28

MHF Hall of Honor
srry i dont understand how u went from

$$\displaystyle \int^{2\pi}_{0}\frac{cos(3\theta)}{5-4\cos(\theta)}d\theta$$

$$\displaystyle iI=\int_0^{2\pi}\frac{\left(e^{i\theta}\right)^2}{5-4\frac{e^{i\theta}+\frac{1}{e^{i\theta}}}{2}}e^{i\theta}d\theta$$

how can u change cos(3theta) which is 1/2(z^3+z^-3) to z^2???

[/COLOR][/FONT][/COLOR]
[/FONT][/COLOR]

[/FONT][/COLOR]
Oops, forgot to explain that. I'm kinda used to just writing stuff. I'll let you explain, think about $$\displaystyle \int_0^{2\pi}\frac{e^{3i\theta}}{5-4\cos(\theta)}d\theta$$ and how that relates to the real part of the residue? It just happens that the real part of the residue is the entire residue and so I just omitted it. My sloppy mistake

fredrick08

#### fredrick08

Oops, forgot to explain that. I'm kinda used to just writing stuff. I'll let you explain, think about

$$\displaystyle \int_0^{2\pi}\frac{e^{3i\theta}}{5-4\cos(\theta)}d\theta$$

and how that relates to the real part of the residue? It just happens that the real part of the residue is the entire residue and so I just omitted it. My sloppy mistake
srry i dont know what you mean by real part of residue??

are u saying that $$\displaystyle \cos(3\theta)=\frac{1}{2}(z^{3}+z^{-3})=z^{3}$$????

na i definately dont understand that... and is that how it became z^2.. because u brought i out the front then cancelled the z form i*z?

#### Drexel28

MHF Hall of Honor
srry i dont know what you mean by real part of residue??

are u saying that $$\displaystyle \cos(3\theta)=\frac{1}{2}(z^{3}+z^{-3})=z^{3}$$????

na i definately dont understand that... and is that how it became z^2.. because u brought i out the front then cancelled the z form i*z?
Ok, well I'll just say it then.

$$\displaystyle \cos(3\theta)=\text{Re }e^{3i\theta}$$...so?


text:
# Search for heavy resonances decaying to a top quark and a bottom quark in the lepton+jets final state in proton–proton collisions at 13 TeV

CMS Collaboration,; Canelli, Florencia; Kilminster, Benjamin; Aarestad, Thea; Caminada, Lea; de Cosa, Annapaoloa; Del Burgo, Riccardo; Donato, Silvio; Galloni, Camilla; Hinzmann, Andreas; Hreus, Tomas; Ngadiuba, Jennifer; Pinna, Deborah; Rauco, Giorgia; Robmann, Peter; Salerno, Daniel; Schweiger, Korbinian; Seitz, Claudia; Takahashi, Yuta; Zucchetta, Alberto; et al, (2018). Search for heavy resonances decaying to a top quark and a bottom quark in the lepton+jets final state in proton–proton collisions at 13 TeV. Physics Letters B, B777:39-63.

## Abstract

A search is presented for narrow heavy resonances decaying to a top quark and a bottom quark using data collected by the CMS experiment at $\sqrt{s}$ = 13TeV in 2016. The data set analyzed corresponds to an integrated luminosity of 35.9 $fb^{−1}$ . Final states that include a single lepton (e, μ), multiple jets, and missing transverse momentum are analyzed. No evidence is found for the production of a W′ boson, and the production of right-handed W′ bosons is excluded at 95% confidence level for masses up to 3.6TeV depending on the scenario considered. Exclusion limits for W′ bosons are also presented as a function of their coupling strength to left- and right-handed fermions. These limits on a W′ boson decaying via a top and a bottom quark are the most stringent published to date.

## Abstract

A search is presented for narrow heavy resonances decaying to a top quark and a bottom quark using data collected by the CMS experiment at $\sqrt{s}$ = 13TeV in 2016. The data set analyzed corresponds to an integrated luminosity of 35.9 $fb^{−1}$ . Final states that include a single lepton (e, μ), multiple jets, and missing transverse momentum are analyzed. No evidence is found for the production of a W′ boson, and the production of right-handed W′ bosons is excluded at 95% confidence level for masses up to 3.6TeV depending on the scenario considered. Exclusion limits for W′ bosons are also presented as a function of their coupling strength to left- and right-handed fermions. These limits on a W′ boson decaying via a top and a bottom quark are the most stringent published to date.

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## Additional indexing

Item Type: Journal Article, refereed, original work 07 Faculty of Science > Physics Institute 530 Physics Nuclear and High Energy Physics English 2018 08 Feb 2018 16:53 13 Oct 2019 05:47 Elsevier 0370-2693 Gold Publisher DOI. An embargo period may apply. https://doi.org/10.1016/j.physletb.2017.12.006 : FunderH2020: Grant ID675440: Project TitleAMVA4NewPhysics - Advanced Multi-Variate Analysis for New Physics Searches at the LHC

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text:
# Why does a strong acid have a weak conjugate base, whereas a weak acid has a relatively strong conjugate base?

Jan 1, 2016

Because a strong acid necessarily implies a weak conjugate base, and a strong base implies a weak conjugate acid.

#### Explanation:

For strong acids, the following equilibrium lies strongly to the right:

$H A + {H}_{2} O r i g h t \le f t h a r p \infty n s {H}_{3} {O}^{+} + {A}^{-}$

This implies that the conjugate BASE of $H A$, ${A}^{-}$ does not compete strongly for the proton. For weaker acids, say hydrogen fluoride, the $H - F$ is strong so that ${F}^{-}$ is moderately basic. A solution of sodium fluoride in water would be slightly basic because the basic fluroide would abstract a proton from water to give back the parent acid:

${F}^{-} + {H}_{2} O r i g h t \le f t h a r p \infty n s H F + H {O}^{-}$

A little time and effort taken to understand these definitions and equilibria will be very useful (and I mean you should consult your text). Good luck.


text:
# Change of basis matrix for $B_2\{(1,-1,0),(1,0,-1)\}$ to $B_1\{(0,1,-1),(1,1,-2)\}$

Change of basis matrix for $B_2\{a_1=(1,-1,0),a_2=(1,0,-1)\}$ to $B_1\{b_1=(0,1,-1),b_2=(1,1,-2)\}$, where $B_{1,2}$ are bases of $V=\{(x,y,z)|x+y+z=0\}$.

I haven't practiced that for a very long time and the definitions are a rather formal, total and loaded. I think I got the idea right, but I think I should have it checked:

I know that $b_1=-a_1+a_2,b_2=-a_1+2a_2$. Hence, for $P=\begin{pmatrix}-1&-1\\1&2\\ \end{pmatrix}$, $[b_1]_{B_1}=P[b_1]_{B_2}$ and the same goes for $b_2$. How do I arrive at the requested matrix from here? What about the standard basis? Is $B_2$ the standard basis here? I am confused, and could use some help.

• Basis in R3? Dim R3=3 , no two... – Martín Vacas Vignolo Mar 8 '16 at 15:19
• I tried to do that, but I get non-invertible matrices... – Meitar Abarbanel Mar 8 '16 at 15:20
• B1 and B2 aren't basis... – Martín Vacas Vignolo Mar 8 '16 at 15:21
• I have been remiss in stating they are bases of a subspace V. Which is $\{x+y+z=0\}$, sorry. – Meitar Abarbanel Mar 8 '16 at 15:23
• Duplicate of math.stackexchange.com/q/1688392/265466 – amd Mar 8 '16 at 19:15

The confusion may go as follows: the vector space $V$ is basically 2 dimensional and if we do as usual $a_1 = \pmatrix{1 \\ 0}$, $a_2 = \pmatrix{0 \\ 1}$ then the matrix $P$ maps this basis to the basis $b_1 = \pmatrix{-1 \\ 1}$, $b_2 = \pmatrix{-1 \\ 2}$. So yes, $P$ is the correct change-of-base matrix in these terms, but it is NOT the matrix that maps $\pmatrix{1 \\ -1 \\ 0} \mapsto \pmatrix{0 \\ 1 \\ -1}$ and $\pmatrix{1 \\ 0 \\ -1} \mapsto \pmatrix{1 \\ 1 \\ 2}$, as obviously, that matrix needs to be $3 \times 3$.

To find the $3 \times 3$ matrix, try this: note that $V$ is set of vectors orthogonal to $\pmatrix{1 \\ 1 \\ 1}$, with the standard Euclid inner product. Start with a general $3 \times 3$ matrix having 9 unknown coefficients and the require it to map $a_1$ to $b_1$, $a_2$ to $b_2$ and to leave $\pmatrix{1 \\ 1 \\ 1}$ invariant. Unless I am wrong, such matrix would change the basis of $V$, leaving the orthogonal subspace in $\mathbb{R}^3$ invariant.

• Thank you Martin. Can you explain what is the importance of leaving $(1,1,1)$ invariant? How does one know to look at that? – Meitar Abarbanel Mar 9 '16 at 0:57
• Well, basically you need to describe a transformation of 3 (linearly independent) vectors to obtain a unique linear mapping, that is the practical reason. I am not sure whether mapping it to $0$ vector or some other multiple of itself would work for you - it quite depends on what you want to do. E.g. mapping the vector to $0$ would, trivially, yield a noninvertible transformation. – Martin Plávala Mar 9 '16 at 8:18


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Main> Essay Writing Help> Solve logarithm problems online

# Solve logarithm problems online

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Logarithm Equations - IntMath For example, ‘$\,\ln(3x-1) = 5\,$’ is a logarithmic equation, since there is a variable $\,x\,$ inside the logarithm.
The logarithm laws that we met earlier are particularly useful for solving equations that involve exponents. Example 1. Solve the equation 3^x= 12.7.

Logarithm Equation Calculator - Calculator Soup Like other online College Algebra courses, course material also examines arithmetic and geometric sequences and discusses linear equations and inequalities.
Solve Exponential Equations for Exponents using X = logB / logA. Will calculate the value of the exponent. Free online calculators for exponents, math.

Solving Logarithmic Equations - Maple Programming Help - Maplesoft Informally speaking, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
Solving Logarithmic Equations Basic que for Solving Logarithms If an equation with logarithms can be solved using algebraic ques, then those.

Solving Logarithmic Equations - YouTube The P versus NP problem is a major unsolved problem in computer science.
From Thinkwell's College Algebra Chapter 6 Exponential and Logarithmic Functions, Subchapter 6.4 Exponential and Logarithmic Equations.

Natural Logarithm -- from Wolfram MathWorld With these lessons, algebra will no longer be a mystery reserved for the selected few.
The notation is used in physics and engineering to denote the natural logarithm, while mathematicians commonly use the notation. In this work, denotes a.

Online Calculator [email protected] However, ‘$x\log 3 = 5$’ is not a logarithmic equation, since there is no variable The IUSC method for solving logarithmic equations may introduce extraneous solutions. Here are examples of logarithmic equations solvable by IUSC (and each is solved below): to yield equivalent equations.
Online Calculators are useful tools for doing calculations related to Math, Physics, Chemistry etc. We offer multiple online calculators with steps and explanation.

How To Solve Logarithmic Equations. Video Tutorial and Practice. The population of the earth is growing at approximately 1.3% per year.
How To solve logarithmic equations-step by step video tutorial, plus more practice problems. General method for solving this type log on one side, Rewrite the logarithm as. Interactive simulation the most controversial math riddle ever!

Sometimes, however, this is not possible—and you must remain aware that you may have lost or added a solution.
In this tutorial we will be looking at logarithmic functions. If you understand that A LOG IS ANOTHER WAY TO WRITE AN EXPONENT, it will help you tremendously when you.

Solve Logarithmic Equations - Detailed Solutions The precise statement of the P versus NP problem was introduced in 1971 by Stephen Cook in his seminal paper "The complexity of theorem proving procedures" It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US

Algebra Help - Online Math Learning The underlying issues were first discussed in the 1950s, in letters from John Nash to the National Security Agency, and from Kurt Gödel to John von Neumann. Algebra Help - Lessons, examples, practice questions and other resources in algebra for learning and teaching algebra, How to solve equations and inequalities, How to.

Free Calculus Tutorials and Problems - An overview of algebra word problems (includes ) covers the common types of word problems in hh school and college prep math and the various ques for solving them. Interactive and analytical tutorials and problems with detailed solutions are presented.

Logarithm Equations - IntMath For example, ‘$\,\ln(3x-1) = 5\,$’ is a logarithmic equation, since there is a variable $\,x\,$ inside the logarithm. The logarithm laws that we met earlier are particularly useful for solving equations that involve exponents. Example 1. Solve the equation 3^x= 12.7.

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Algebra Help - Online Math Learning The underlying issues were first discussed in the 1950s, in letters from John Nash to the National Security Agency, and from Kurt Gödel to John von Neumann. Algebra Help - Lessons, examples, practice questions and other resources in algebra for learning and teaching algebra, How to solve equations and inequalities, How to.

Free Calculus Tutorials and Problems - An overview of algebra word problems (includes ) covers the common types of word problems in hh school and college prep math and the various ques for solving them. Interactive and analytical tutorials and problems with detailed solutions are presented.

Logarithm Equations - IntMath For example, ‘$\,\ln(3x-1) = 5\,$’ is a logarithmic equation, since there is a variable $\,x\,$ inside the logarithm. The logarithm laws that we met earlier are particularly useful for solving equations that involve exponents. Example 1. Solve the equation 3^x= 12.7.

Logarithm Equation Calculator - Calculator Soup Like other online College Algebra courses, course material also examines arithmetic and geometric sequences and discusses linear equations and inequalities. Solve Exponential Equations for Exponents using X = logB / logA. Will calculate the value of the exponent. Free online calculators for exponents, math.

Solving Logarithmic Equations - Maple Programming Help - Maplesoft Informally speaking, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. Solving Logarithmic Equations Basic que for Solving Logarithms If an equation with logarithms can be solved using algebraic ques, then those.

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Algebra Help - Online Math Learning The underlying issues were first discussed in the 1950s, in letters from John Nash to the National Security Agency, and from Kurt Gödel to John von Neumann. Algebra Help - Lessons, examples, practice questions and other resources in algebra for learning and teaching algebra, How to solve equations and inequalities, How to.

Free Calculus Tutorials and Problems - An overview of algebra word problems (includes ) covers the common types of word problems in hh school and college prep math and the various ques for solving them. Interactive and analytical tutorials and problems with detailed solutions are presented.

Logarithm Equations - IntMath For example, ‘$\,\ln(3x-1) = 5\,$’ is a logarithmic equation, since there is a variable $\,x\,$ inside the logarithm. The logarithm laws that we met earlier are particularly useful for solving equations that involve exponents. Example 1. Solve the equation 3^x= 12.7.

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Algebra Help - Online Math Learning The underlying issues were first discussed in the 1950s, in letters from John Nash to the National Security Agency, and from Kurt Gödel to John von Neumann.
Algebra Help - Lessons, examples, practice questions and other resources in algebra for learning and teaching algebra, How to solve equations and inequalities, How to.

Free Calculus Tutorials and Problems - An overview of algebra word problems (includes ) covers the common types of word problems in hh school and college prep math and the various ques for solving them.
Interactive and analytical tutorials and problems with detailed solutions are presented.

Logarithm Equations - IntMath For example, ‘$\,\ln(3x-1) = 5\,$’ is a logarithmic equation, since there is a variable $\,x\,$ inside the logarithm.
The logarithm laws that we met earlier are particularly useful for solving equations that involve exponents. Example 1. Solve the equation 3^x= 12.7.

Logarithm Equation Calculator - Calculator Soup Like other online College Algebra courses, course material also examines arithmetic and geometric sequences and discusses linear equations and inequalities.
Solve Exponential Equations for Exponents using X = logB / logA. Will calculate the value of the exponent. Free online calculators for exponents, math.

Solving Logarithmic Equations - Maple Programming Help - Maplesoft Informally speaking, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
Solving Logarithmic Equations Basic que for Solving Logarithms If an equation with logarithms can be solved using algebraic ques, then those.

Solving Logarithmic Equations - YouTube The P versus NP problem is a major unsolved problem in computer science.
From Thinkwell's College Algebra Chapter 6 Exponential and Logarithmic Functions, Subchapter 6.4 Exponential and Logarithmic Equations.

Natural Logarithm -- from Wolfram MathWorld With these lessons, algebra will no longer be a mystery reserved for the selected few.
The notation is used in physics and engineering to denote the natural logarithm, while mathematicians commonly use the notation. In this work, denotes a.

||

Algebra Help - Online Math Learning The underlying issues were first discussed in the 1950s, in letters from John Nash to the National Security Agency, and from Kurt Gödel to John von Neumann. Algebra Help - Lessons, examples, practice questions and other resources in algebra for learning and teaching algebra, How to solve equations and inequalities, How to.

Free Calculus Tutorials and Problems - An overview of algebra word problems (includes ) covers the common types of word problems in hh school and college prep math and the various ques for solving them. Interactive and analytical tutorials and problems with detailed solutions are presented.

Logarithm Equations - IntMath For example, ‘$\,\ln(3x-1) = 5\,$’ is a logarithmic equation, since there is a variable $\,x\,$ inside the logarithm. The logarithm laws that we met earlier are particularly useful for solving equations that involve exponents. Example 1. Solve the equation 3^x= 12.7.

Logarithm Equation Calculator - Calculator Soup Like other online College Algebra courses, course material also examines arithmetic and geometric sequences and discusses linear equations and inequalities. Solve Exponential Equations for Exponents using X = logB / logA. Will calculate the value of the exponent. Free online calculators for exponents, math.

Solving Logarithmic Equations - Maple Programming Help - Maplesoft Informally speaking, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. Solving Logarithmic Equations Basic que for Solving Logarithms If an equation with logarithms can be solved using algebraic ques, then those.

Solving Logarithmic Equations - YouTube The P versus NP problem is a major unsolved problem in computer science. From Thinkwell's College Algebra Chapter 6 Exponential and Logarithmic Functions, Subchapter 6.4 Exponential and Logarithmic Equations.

Natural Logarithm -- from Wolfram MathWorld With these lessons, algebra will no longer be a mystery reserved for the selected few. The notation is used in physics and engineering to denote the natural logarithm, while mathematicians commonly use the notation. In this work, denotes a.

Online Calculator [email protected] However, ‘$x\log 3 = 5$’ is not a logarithmic equation, since there is no variable The IUSC method for solving logarithmic equations may introduce extraneous solutions. Here are examples of logarithmic equations solvable by IUSC (and each is solved below): to yield equivalent equations. Online Calculators are useful tools for doing calculations related to Math, Physics, Chemistry etc. We offer multiple online calculators with steps and explanation.

How To Solve Logarithmic Equations. Video Tutorial and Practice. The population of the earth is growing at approximately 1.3% per year. How To solve logarithmic equations-step by step video tutorial, plus more practice problems. General method for solving this type log on one side, Rewrite the logarithm as. Interactive simulation the most controversial math riddle ever!

Sometimes, however, this is not possible—and you must remain aware that you may have lost or added a solution. In this tutorial we will be looking at logarithmic functions. If you understand that A LOG IS ANOTHER WAY TO WRITE AN EXPONENT, it will help you tremendously when you.

Solve Logarithmic Equations - Detailed Solutions The precise statement of the P versus NP problem was introduced in 1971 by Stephen Cook in his seminal paper "The complexity of theorem proving procedures" It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US$1,000,000 prize for the first correct solution. Solve logarithmic; examples with detailed solutions including some challenging questions. Solving Logarithmic Equations - Tree of Math Free Algebra Worksheets are available to provide practice on some of the following topics, for example solving of equations. Online precalculus course, logarithmic equations. Extraneous solutions can occur when solving logarithmic equations, so be careful! IXL - Solve logarithmic equations I Algebra 2 practice In mathematics, the logarithm is the inverse operation to exponentiation. Fun math practice! Improve your ss with free problems in 'Solve logarithmic equations I' and thousands of other practice lessons. Logarithm Calculator logx Calculator - Students perform operations on real numbers and polynomials, and simplify algebraic, rational, and radical expressions. Logarithm calculator online. Calculate logarithm of a number to any base. Logarithm Laws by Intmath - Interactive This College Algebra online course provides students with a working knowledge of college-level algebra and its applications, emphasizing methods for solving linear and quadratic equations, word problems, and polynomial, rational, and radical equations and applications. The Logarithm Laws. by M. Bourne. Since a logarithm is simply an exponent which is just being written down on the line, we expect the logarithm laws to work the. || Algebra Help - Online Math Learning The underlying issues were first discussed in the 1950s, in letters from John Nash to the National Security Agency, and from Kurt Gödel to John von Neumann. Algebra Help - Lessons, examples, practice questions and other resources in algebra for learning and teaching algebra, How to solve equations and inequalities, How to. Free Calculus Tutorials and Problems - An overview of algebra word problems (includes ) covers the common types of word problems in hh school and college prep math and the various ques for solving them. Interactive and analytical tutorials and problems with detailed solutions are presented. Logarithm Equations - IntMath For example, ‘$\,\ln(3x-1) = 5\,$’ is a logarithmic equation, since there is a variable$\,x\,$inside the logarithm. The logarithm laws that we met earlier are particularly useful for solving equations that involve exponents. Example 1. Solve the equation 3^x= 12.7. Logarithm Equation Calculator - Calculator Soup Like other online College Algebra courses, course material also examines arithmetic and geometric sequences and discusses linear equations and inequalities. Solve Exponential Equations for Exponents using X = logB / logA. Will calculate the value of the exponent. Free online calculators for exponents, math. Solving Logarithmic Equations - Maple Programming Help - Maplesoft Informally speaking, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. Solving Logarithmic Equations Basic que for Solving Logarithms If an equation with logarithms can be solved using algebraic ques, then those. Solving Logarithmic Equations - YouTube The P versus NP problem is a major unsolved problem in computer science. From Thinkwell's College Algebra Chapter 6 Exponential and Logarithmic Functions, Subchapter 6.4 Exponential and Logarithmic Equations. Natural Logarithm -- from Wolfram MathWorld With these lessons, algebra will no longer be a mystery reserved for the selected few. The notation is used in physics and engineering to denote the natural logarithm, while mathematicians commonly use the notation. In this work, denotes a. || Algebra Help - Online Math Learning The underlying issues were first discussed in the 1950s, in letters from John Nash to the National Security Agency, and from Kurt Gödel to John von Neumann. Algebra Help - Lessons, examples, practice questions and other resources in algebra for learning and teaching algebra, How to solve equations and inequalities, How to. Free Calculus Tutorials and Problems - An overview of algebra word problems (includes ) covers the common types of word problems in hh school and college prep math and the various ques for solving them. Interactive and analytical tutorials and problems with detailed solutions are presented. Logarithm Equations - IntMath For example, ‘$\,\ln(3x-1) = 5\,$’ is a logarithmic equation, since there is a variable$\,x\,$inside the logarithm. The logarithm laws that we met earlier are particularly useful for solving equations that involve exponents. Example 1. Solve the equation 3^x= 12.7. Logarithm Equation Calculator - Calculator Soup Like other online College Algebra courses, course material also examines arithmetic and geometric sequences and discusses linear equations and inequalities. Solve Exponential Equations for Exponents using X = logB / logA. Will calculate the value of the exponent. Free online calculators for exponents, math. Solving Logarithmic Equations - Maple Programming Help - Maplesoft Informally speaking, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. Solving Logarithmic Equations Basic que for Solving Logarithms If an equation with logarithms can be solved using algebraic ques, then those. Solving Logarithmic Equations - YouTube The P versus NP problem is a major unsolved problem in computer science. From Thinkwell's College Algebra Chapter 6 Exponential and Logarithmic Functions, Subchapter 6.4 Exponential and Logarithmic Equations. Natural Logarithm -- from Wolfram MathWorld With these lessons, algebra will no longer be a mystery reserved for the selected few. The notation is used in physics and engineering to denote the natural logarithm, while mathematicians commonly use the notation. In this work, denotes a. Online Calculator [email protected] However, ‘$x\log 3 = 5$’ is not a logarithmic equation, since there is no variable The IUSC method for solving logarithmic equations may introduce extraneous solutions. Here are examples of logarithmic equations solvable by IUSC (and each is solved below): to yield equivalent equations. Online Calculators are useful tools for doing calculations related to Math, Physics, Chemistry etc. We offer multiple online calculators with steps and explanation. How To Solve Logarithmic Equations. Video Tutorial and Practice. The population of the earth is growing at approximately 1.3% per year. How To solve logarithmic equations-step by step video tutorial, plus more practice problems. General method for solving this type log on one side, Rewrite the logarithm as. Interactive simulation the most controversial math riddle ever! Sometimes, however, this is not possible—and you must remain aware that you may have lost or added a solution. In this tutorial we will be looking at logarithmic functions. If you understand that A LOG IS ANOTHER WAY TO WRITE AN EXPONENT, it will help you tremendously when you. Solve Logarithmic Equations - Detailed Solutions The precise statement of the P versus NP problem was introduced in 1971 by Stephen Cook in his seminal paper "The complexity of theorem proving procedures" It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US$1,000,000 prize for the first correct solution.
Solve logarithmic; examples with detailed solutions including some challenging questions.

Solving Logarithmic Equations - Tree of Math Free Algebra Worksheets are available to provide practice on some of the following topics, for example solving of equations.
Online precalculus course, logarithmic equations. Extraneous solutions can occur when solving logarithmic equations, so be careful!

IXL - Solve logarithmic equations I Algebra 2 practice In mathematics, the logarithm is the inverse operation to exponentiation.
Fun math practice! Improve your ss with free problems in 'Solve logarithmic equations I' and thousands of other practice lessons.

• Free Calculus Tutorials and Problems -
• Logarithm Equations - IntMath
• Logarithm Equation Calculator - Calculator Soup
• ||

An overview of algebra word problems (includes ) covers the common types of word problems in hh school and college prep math and the various ques for solving them. For example, ‘$\,\ln(3x-1) = 5\,$’ is a logarithmic equation, since there is a variable $\,x\,$ inside the logarithm. Like other online College Algebra courses, course material also examines arithmetic and geometric sequences and discusses linear equations and inequalities.

## Solve logarithm problems online

Informally speaking, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. The P versus NP problem is a major unsolved problem in computer science.

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• With these lessons, algebra will no longer be a mystery reserved for the selected few.

### Solve logarithm problems online

#### Solve logarithm problems online

However, ‘$x\log 3 = 5$’ is not a logarithmic equation, since there is no variable The IUSC method for solving logarithmic equations may introduce extraneous solutions. Here are examples of logarithmic equations solvable by IUSC (and each is solved below): to yield equivalent equations. The population of the earth is growing at approximately 1.3% per year.

Sometimes, however, this is not possible—and you must remain aware that you may have lost or added a solution. YOUTH IN NAZI GERMANY ESSAY The precise statement of the P versus NP problem was introduced in 1971 by Stephen Cook in his seminal paper "The complexity of theorem proving procedures" It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US\$1,000,000 prize for the first correct solution.

,000,000 prize for the first correct solution.
Solve logarithmic; examples with detailed solutions including some challenging questions.

Solving Logarithmic Equations - Tree of Math Free Algebra Worksheets are available to provide practice on some of the following topics, for example solving of equations.
Online precalculus course, logarithmic equations. Extraneous solutions can occur when solving logarithmic equations, so be careful!

IXL - Solve logarithmic equations I Algebra 2 practice In mathematics, the logarithm is the inverse operation to exponentiation.
Fun math practice! Improve your ss with free problems in 'Solve logarithmic equations I' and thousands of other practice lessons.

• Free Calculus Tutorials and Problems -
• Logarithm Equations - IntMath
• Logarithm Equation Calculator - Calculator Soup

• Solve logarithm problems online:

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