An algorithm for multi

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An algorithm for multi

Cancer progression is associated with genomic instability and an accumulation of gains and losses of DNA. The growing variety of tools for measuring genomic copy numbers, including various types of array-CGH, SNP arrays and high-throughput sequencing, calls for a coherent framework offering unified and consistent handling of single- and multi-track segmentation problems.

In addition, there is a demand for highly computationally efficient segmentation algorithms, due to the emergence of very high density scans of copy number. A comprehensive Bioconductor package for copy number analysis is presented. The package offers a unified framework for single sample, multi-sample and multi-track segmentation and is based on statistically sound penalized least squares principles.

Conditional on the number of breakpoints, the estimates are optimal in the least squares sense. A novel and computationally highly efficient algorithm is proposed that utilizes vector-based operations in R. Three case studies are presented. The R package copynumber is a software suite for segmentation of single- and multi-track copy number data using algorithms based on coherent least squares principles. In cancer, the path from normal to malignant cell involves multiple genomic alterations including losses and gains of genomic DNA.

A long series of studies have demonstrated the biological and clinical relevance of studying such genomic alterations see, e. After proper normalization and transformation of the raw signal intensities obtained from such technologies, the next step is usually to perform segmentation to identify regions of constant copy number. Many segmentation algorithms are designed to analyse samples individually see, e.

Multiplication algorithm

Joint handling of multiple samples is computationally and conceptually challenging, see e. Most systematic approaches for this problem are based on individual segmentation of each sample followed by post-processing to combine results across samples see, e. Recently, the emergence of new technologies have pushed the limit of genomic resolution, opening new vistas for studying very short aberrations, including aberrations affecting only part of a gene or gene regulatory sites in the DNA.

A major challenge raised by these novel technologies is the steadily growing length of the data tracks, which drastically increases the demand for computationally efficient algorithms.

The occurrence of extreme observations outliers of biological or technical origin pose an additional challenge, as most segmentation methods are substantially affected by such observations.

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Picard et al. Their approach assumes that the user either supplies the desired number of segments or leaves to the method to automatically determine this number.

In this paper, we describe a related approach. In particular, the proposed method utilizes penalized least squares regression to determine a piecewise constant fit to the data. Given the number of breakpoints, the solution will be optimal in terms of least squares error. To achieve high processing efficiency, dynamic programming is used see [ 24 ].

To further increase computational efficiency, a novel vector based algorithm is proposed, and even further speed optimization is obtained through heuristics. A central aim of the present work has been to provide methodology and high-performance algorithms for solving single- and multiple-track problems within a statistically and computationally unified framework.

Multiclass classification

All proposed algorithms are embedded in a comprehensive software suite for copy number segmentation and visualization, available as the Bioconductor package copynumber.

Main features of the package include:. The copynumber package provides functionality for many of the tasks typically encountered in copy number analysis: data preprocessing tools, segmentation methods for various analysis scenarios, and visualization tools. Allele-frequencies may also be specified for the segmentation of SNP-array data. It is strongly recommended to detect and appropriately modify extreme observations outliers prior to segmentation, as these can have a substantial negative effect on the analysis.

For this purpose, a specially designed Winsorization method is included in the software package. A missing-value imputation method appropriate for copy number data is also available.

An overview of the copynumber package. Depending on the aim of the analysis, the input will be copy number data and possibly allele frequencies from one or more experiments. Preprocessing tools are available for outlier handling and missing data imputation, and three different methods handle single sample, multi-sample and allele-specific segmentation.

Several options are also available for the graphical visualization of data and segmentation results. Segmentation methods for three different scenarios single sample, multi-sample and allele-specific segmentation are implemented in the package. All these methods are referred to as Piecewise Constant Fitting PCF algorithms and seek to minimize a penalized least squares criterion.In machine learningmulticlass or multinomial classification is the problem of classifying instances into one of three or more classes classifying instances into one of two classes is called binary classification.

While many classification algorithms notably multinomial logistic regression naturally permit the use of more than two classes, some are by nature binary algorithms; these can, however, be turned into multinomial classifiers by a variety of strategies.

Multiclass classification should not be confused with multi-label classificationwhere multiple labels are to be predicted for each instance. The existing multi-class classification techniques can be categorized into i transformation to binary ii extension from binary and iii hierarchical classification. This section discusses strategies for reducing the problem of multiclass classification to multiple binary classification problems.

It can be categorized into one vs rest and one vs one. The techniques developed based on reducing the multi-class problem into multiple binary problems can also be called problem transformation techniques. This strategy requires the base classifiers to produce a real-valued confidence score for its decision, rather than just a class label; discrete class labels alone can lead to ambiguities, where multiple classes are predicted for a single sample. In pseudocode, the training algorithm for an OvR learner constructed from a binary classification learner L is as follows:.

Making decisions means applying all classifiers to an unseen sample x and predicting the label k for which the corresponding classifier reports the highest confidence score:. Although this strategy is popular, it is a heuristic that suffers from several problems. Firstly, the scale of the confidence values may differ between the binary classifiers. Second, even if the class distribution is balanced in the training set, the binary classification learners see unbalanced distributions because typically the set of negatives they see is much larger than the set of positives.

In the one-vs. Like OvR, OvO suffers from ambiguities in that some regions of its input space may receive the same number of votes. This section discusses strategies of extending the existing binary classifiers to solve multi-class classification problems. Several algorithms have been developed based on neural networksdecision treesk-nearest neighborsnaive Bayessupport vector machines and extreme learning machines to address multi-class classification problems.

These types of techniques can also be called algorithm adaptation techniques. Multiclass perceptrons provide a natural extension to the multi-class problem. Instead of just having one neuron in the output layer, with binary output, one could have N binary neurons leading to multi-class classification.

In practice, the last layer of a neural network is usually a softmax function layer, which is the algebraic simplification of N logistic classifiers, normalized per class by the sum of the N-1 other logistic classifiers.

Extreme learning machines ELM is a special case of single hidden layer feed-forward neural networks SLFNs where in the input weights and the hidden node biases can be chosen at random. Many variants and developments are made to the ELM for multiclass classification. To classify an unknown example, the distance from that example to every other training example is measured.

The k smallest distances are identified, and the most represented class by these k nearest neighbours is considered the output class label. Naive Bayes is a successful classifier based upon the principle of maximum a posteriori MAP.

This approach is naturally extensible to the case of having more than two classes, and was shown to perform well in spite of the underlying simplifying assumption of conditional independence. Decision tree learning is a powerful classification technique. The tree tries to infer a split of the training data based on the values of the available features to produce a good generalization. The algorithm can naturally handle binary or multiclass classification problems. The leaf nodes can refer to any of the K classes concerned.

Support vector machines are based upon the idea of maximizing the margin i. The basic SVM supports only binary classification, but extensions have been proposed to handle the multiclass classification case as well. In these extensions, additional parameters and constraints are added to the optimization problem to handle the separation of the different classes. Hierarchical classification tackles the multi-class classification problem by dividing the output space i.A multiplication algorithm is an algorithm or method to multiply two numbers.

Depending on the size of the numbers, different algorithms are used. Efficient multiplication algorithms have existed since the advent of the decimal system. The grid method or box method is an introductory method for multiple-digit multiplication that is often taught to pupils at primary school or elementary school.

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It has been a standard part of the national primary school mathematics curriculum in England and Wales since the late s. Both factors are broken up "partitioned" into their hundreds, tens and units parts, and the products of the parts are then calculated explicitly in a relatively simple multiplication-only stage, before these contributions are then totalled to give the final answer in a separate addition stage.

This calculation approach though not necessarily with the explicit grid arrangement is also known as the partial products algorithm. Its essence is the calculation of the simple multiplications separately, with all addition being left to the final gathering-up stage. The grid method can in principle be applied to factors of any size, although the number of sub-products becomes cumbersome as the number of digits increases.

Nevertheless, it is seen as a usefully explicit method to introduce the idea of multiple-digit multiplications; and, in an age when most multiplication calculations are done using a calculator or a spreadsheet, it may in practice be the only multiplication algorithm that some students will ever need.

If a positional numeral system is used, a natural way of multiplying numbers is taught in schools as long multiplicationsometimes called grade-school multiplicationsometimes called Standard Algorithm : multiply the multiplicand by each digit of the multiplier and then add up all the properly shifted results.

It requires memorization of the multiplication table for single digits. This is the usual algorithm for multiplying larger numbers by hand in base Computers initially used a very similar shift and add algorithm in base 2, but modern processors have optimized circuitry for fast multiplications using more efficient algorithms, at the price of a more complex hardware realization. A person doing long multiplication on paper will write down all the products and then add them together; an abacus -user will sum the products as soon as each one is computed.

This example uses long multiplication to multiply 23, multiplicand by 5, multiplier and arrives at , for the result product. Below pseudocode describes the process of above multiplication.

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It keeps only one row to maintain the sum which finally becomes the result. Let n be the total number of digits in the two input numbers in base D. However, in certain applications, the entire result need not be kept in memory and instead the digits of the result can be streamed out as they are computed for example, to system console or file. The method is based on the observation that each digit of the result can be computed from right to left with only knowing the carry from the previous step.

Thus both these values can be stored in O log n digits. Some chips implement long multiplication, in hardware or in microcodefor various integer and floating-point word sizes. In arbitrary-precision arithmeticit is common to use long multiplication with the base set to 2 wwhere w is the number of bits in a word, for multiplying relatively small numbers.The novel coronavirus Sars-CoV-2 pandemic has spread rapidly, from December to the end of March, to countries, and there have been over 3, cases identified and overdeaths.

For a proportion of hospitalized patients, death can occur within a few days, mainly for adult respiratory distress syndrome or multi-organ dysfunction syndrome.

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In these patients, clinical signs and symptoms, as well as laboratory abnormalities, suggest a cytokine storm syndrome in response to the viral infection. No current targeted treatment is yet available for COVID, an unknown disease up to 2 months ago, which challenges doctors and researchers to find new drugs or reallocate other treatments for these patients.

Since the beginning of the COVID outbreak, a growing body of information on diagnostic and therapeutic strategies has emerged, mainly based on preliminary experience on retrospective studies or small case series. Antivirals, antimalarials, corticosteroids, biotechnological and small molecules, convalescent plasma and anticoagulants are among the drugs proposed for the treatment or in tested for COVID Given the complexity of this new condition, a multidisciplinary management seems to be the best approach.

Sharing and integrating knowledge between specialists, to evaluate the correct timing and setting of every treatment, could greatly benefit our patients. We reviewed the literature, combining it with our experiences and our specialist knowledge, to propose a management algorithm, correlating the clinical features with laboratory and imaging findings to establish the right timing for each treatment.

Abstract The novel coronavirus Sars-CoV-2 pandemic has spread rapidly, from December to the end of March, to countries, and there have been over 3, cases identified and overdeaths. Publication types Review. Substances Antiviral Agents.January 15, feature. Researchers at the SRM Institute of Science and Technology in India have recently developed a decentralized trajectory generation algorithm for multi-agent systems.

Their algorithm, presented in a paper pre-published on arXivcan generate collision-free trajectories for robots when provided with an initial state and desired end pose.

As the world is moving toward autonomous cars, I suggested developing a decentralized algorithm for autonomous vehicles to navigate intersections. Multi- robot systems involve a number of robotic agents or autonomous vehicles collaborating on a variety of tasks. These systems could have interesting applications in a number of areas, including transportation, entertainment, security and space exploration. When several robots are working together on a given task, their trajectories require careful planning to make sure that the robots do not collide with one another and that their dynamic limits are not violated.

So far, most approaches for trajectory generation have been centralized, which means that they generate trajectories beforehand and then transmit them to individual robots. While centralized approaches work well in known environments and with a limited number of robots, they are very difficult to apply on a larger scale.

In recent years, therefore, researchers have been working on decentralized approaches that can continuously re-plan trajectories, responding to unexpected changes or obstacles in the environment. The team of researchers at SRM Institute developed a new decentralized algorithm for trajectory generation of multi-agent systems. Their approach follows a two step process, generating collision-free convex regions that a robot will be constrained in, by predicting other robots' positions.

The first is the Identification of the environment, which includes map generation for the self and trajectory prediction for others in the environment to identify the ego's from the point of view of the vehicle of interest safe region," Govind Aadithya R, one of the researchers who carried out the study, Told TechXplore.

To ensure that the ego is moving along the specified path, the states are tracked using a trajectory tracker. Govind and his colleagues employed a simple method for obstacle detection, using local shape-based maps to formulate safe regions for individual agents. Based on this data, their algorithm predicts trajectories for other robots and incorporates these into the model to avoid collisions by re-sizing the regions in which a robot can navigate without colliding.

This implies that for conservative maneuvers, the obstacle representations based on simple geometry suffice but for dynamic and aggressive maneuvers that utilize full space, complex geometries are a necessity. The researchers evaluated their approach in simulations on the Gazebo platform, using ROS with flat aerial robots and non-holonomic wheeled robots; in both intersection-like and unstructured environments.

Their algorithm was able to effectively generate smooth trajectories in constrained environments, avoiding collisions between robots. Your feedback will go directly to Tech Xplore editors. Thank you for taking your time to send in your valued opinion to Science X editors. You can be assured our editors closely monitor every feedback sent and will take appropriate actions.

an algorithm for multi

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an algorithm for multi

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By using our site, you acknowledge that you have read and understand our Privacy Policy and Terms of Use. Home Robotics Home Computer Sciences. Snapshots while the robots are navigating across different unknown environments using the algorithm proposed in this work.A nonlinear programming problem forms an important part of any problem in engineering and frequently appears in the real world applications.

Traditionally, optimization techniques have been classified into two classes: direct search and indirect search techniques. Since derivative information is not used, the direct search methods slowly converge to an optimal solution whereas the indirect search methods converge faster to an optimal solution. However, for efficient implementation of the traditional techniques, the variables and objective function need to be continuous.

Furthermore, the success of these methods depends up on the quality of the starting point. In many optimization problems, discontinuous, vast multimodal, and noisy search spaces need to be considered. As a result, we have witnessed a very rapid growth of the metaheuristic algorithms for handling complex nonlinear optimization problems in recent years. As an alternative to the conventional optimization techniques, the metaheuristic optimization techniques have been used to obtain global or near-global optimum solutions.

Many metaheuristic algorithms such as, genetic algorithm GA Deep,particle swarm optimization PSO He,; Xu,; Lu, Jagatheesan,differential evolution Becerra,;Draa,joint operations algorithm Sun,ant colony optimization Rizk-Allah,quantum particle swarm optimization Soliman,bee colony swarm optimization Hassanien,flower pollination search algorithm Emary, and grey wolf optimization Emary, Anti-lion Optimization Algorithm Yamany et al.

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Free Content. More Information. Rizk-Allah, R. In Hassanien, A. IGI Global. Rizk-Allah, Rizk M. Available In. DOI: Abstract This chapter presents a hybrid optimization algorithm namely FOA-FA for solving single and multi-objective optimization problems. The proposed algorithm integrates the benefits of the fruit fly optimization algorithm FOA and the firefly algorithm FA to avoid the entrapment in the local optima and the premature convergence of the population.This is a complete lesson with explanations and exercises about the standard algorithm of multiplication multiplying in columnsmeant for fourth grade.

First, the lesson explains step-by-step how to multiply a two-digit number by a single-digit number, then has exercises on that. Next, the lesson shows how to multiply how to multiply a three or four-digit number, and has lots of exercises on that. However, in the standard way the adding is done at the same time as multiplying.

Place 2 in the ones place, but write the tens digit 1 above the tens column as a little memory note. You are regrouping or carrying. Then multiply the tens, adding the 1 ten that regrouped. Note that 25 tens means ! Multiply using both methods: the standard one and the easy one. Also, write number sentences additions, subtractions, multiplications on the empty lines.

Write 2 in the ones place and regroup the 3 tens to the tens column. Then multiply the tens, adding the 3 regrouped tens. Then multiply the hundreds, adding the regrouped hundred. Write 2 in the hundreds place, and regroup the 3 thousands.

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Solve the word problems. The school also has 24 teachers. This old video of mine below also also explains how to teach the multiplication algorithm. At first, the video goes through the partial products algorithm multiplying in partsand then explains the standard multiplication algorith as in the lesson on this page.

A self-teaching worktext for 4th grade that covers multiplying by whole tens and hundreds, multi-digit multiplication in columns, order of operations, word problems, scales problems, and money problems. Learn more and see the free samples!

See more topical Math Mammoth books. The Standard Multiplication Algorithm This is a complete lesson with explanations and exercises about the standard algorithm of multiplication multiplying in columnsmeant for fourth grade.

The standard algorithm of multiplication is based on the principle that you already know: multiplying in parts partial products : simply multiply ones and tens separately, and add.

an algorithm for multi

Math Mammoth Multiplication 2. Math Lessons menu. Hint: it has to do with a "recipe" that many math lessons follow. The do's and don'ts of teaching problem solving in math Advice on how you can teach problem solving in elementary, middle, and high school math. How to set up algebraic equations to match word problems Students often have problems setting up an equation for a word problem in algebra.

This article explains some of those relationships. Seven reasons behind math anxiety and how to prevent it Mental math "mathemagic" with Arthur Benjamin video Keeping math skills sharp in the summer Geometric vanish puzzles Science resources Short reviews of the various science resources and curricula I have used with my own children.

Guess and check. With a 3- or 4-digit number you have to regroup many times. Multiply the ones first. Then the tens. Multiply the hundreds. The school has students.

Hint: Guess and check.


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