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who uses control charts

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### who uses control charts

Good Document. Control charts provide a very simple and easy to understand methodology to understand the performance of processes. It can easily be inferred that the system is not capable to manufacture products within the specified range. DMAIC methodology has five phases: Defining the goals that you wish to achieve – basically, identifying the problem statement you are trying to solve. Six Sigma is a set of techniques used by organizations to improve their processes and optimize operations. Changes in clinical variables, such as blood glucose levels or blood pressure measurements may be due to changes in the patients' underlying condition or biological processes, measurement error, or random variation. If so, and if chance causes alone were present, the probability of a point falling above the upper limit would be one out of a thousand, and similarly, a point falling below the lower limit would be one out of a thousand. This shows that the above process is neither stable nor capable. Now, let’s check process capability. Use Xbar-S control charts to plot the CRs (continuous data) over the project duration ) Data point for each phase in control chart does not represent individual critical ratio but represents central value for each sample of critical ratios ( i.e for a set of critical ratios collected for a particular project phase) . In the above chart, the value is 0.356 which is less than the required value. We started by asking, “Why use control charts?” Control charts are the “voice” of the process. Quality control charts are a type of control often used by engineers to assess the performance of a firm's processes or finished products. R-chart example using qcc R package. This article throws light upon the two main types of control charts. Control charts attempt to differentiate “assignable” (“special”) sources of variation from “common” sources. Flow Charts for Emergency Management Overhead Transparencies 1.8.1. If analysis of the control chart indicates that the process is currently under control, then no corrections or changes to process control parameters are needed. Control charts are a great tool that you can use to determine if your process is under statistical control, the level of variation inherent in the process, and point you in the direction of the nature of the variation (common cause or special cause). Max. 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Global circulation; Northern hemisphere; Southern hemisphere; By country, area or territory - past 12 months; By country, area or territory - optional time period selection; By influenza transmission zone For more information about influenza transmission zones click here; By WHO region For a process ‘in-control’, most of the points should lie near the average line i.e. If issues are … The R-chart generated by R also provides significant information for its interpretation, just as the x-bar chart generated above. However, a control chart is being used at the initial stage to see the process behavior or to see the Voice of Process (VoP). In contrast the WHO growth charts only provide information on children up to 5 years of age. This gallery shows: Stock market prices are often depicted with an open-high-low-close chart with a traditional bar chart of volume at the bottom. The standard deviation in the above chart is the standard deviation of means of each of the samples. Control charts that use rational subgrouping and stratification can also help users study causes of variation to develop ideas for change. Let’s take an example and understand it step by step using above definition. By collecting and charting data over time, you can find trends or patterns in the process. Some types of charts have specific uses in a certain field Open-high-low-close chart. Variations: Deviations from the average time of 35 minutes – these variations are due to inherent attributes in the system such as traffic or traffic signals on the route. Types of Control Chart. WHO/EHA/EHTP Draft 1-1999 1.8. Control charts are an efficient way of analyzing performance data to evaluate a process. One of the techniques that can be used in control phase is statistical process control. In any control chart, there are three main attributes – Average Line, UCL and LCL. “Common” sources, because they are an expected part of the process, are of much less concern to the manufacturer than “assignable” sources. Some of our bloggers have applied control charts to their personal passions, including holiday candies in Control Charts: Rational Subgrouping and Marshmallow Peeps! Now, relating our example with the definition above: Measurements: Time to reach office – the time taken on daily basis to reach office from home is measured to monitor the system/process. In the above chart, R chart appears to be in control; hence, we move to check run rules against the X-Bar chart. This is what I … Learn more about control charts in our Introduction to Control Charts. By comparing current data to these lines, you can … We would love to hear your experience with creating control charts in different settings. By this phase, you know the goal that are you trying to achieve and also, you understand the entire process and have the relevant data to diagnose and analyze the problem. If so, and if chance causes alone were present, the probability of a point falling above the upper limit would be one out of a thousand, and similarly, a point falling below the lower limit would be one out of a thousand. The data does not have to be normally distributed to use a control chart. endstream endobj 1144 0 obj <>/Metadata 97 0 R/OCProperties<>/OCGs[1161 0 R]>>/Outlines 118 0 R/PageLayout/SinglePage/Pages 1136 0 R/StructTreeRoot 173 0 R/Type/Catalog>> endobj 1145 0 obj <>/ExtGState<>/Font<>/Properties<>/XObject<>>>/Rotate 0/StructParents 0/Tabs/S/Type/Page>> endobj 1146 0 obj <>stream Learn how to draw a basic Control Chart in Excel which can be used in Quality Control to detect problems in a process. Click here to watch part 2. For children 2-5 years, the methods used to create the CDC growth charts and the WHO growth charts are similar. There are many possible values. Lacey opens her Control chart toolkit, which contains best practice Implementation Plans, Proposals and Project Planning that cover … The control chart is a graph used to study how a process changes over time. Apart from manufacturing, control charts find their applications in healthcare industry and a host of other industries. This indicates the presence of special cause variation. 4.1 This practice describes the use of control charts as a tool for use in statistical process control (SPC). When and how to use the Keras Functional API, Moving on as Head of Solutions and AI at Draper and Dash. Posted on August 30, 2018 by Perceptive Analytics in R bloggers | 0 Comments. 1160 0 obj <>/Filter/FlateDecode/ID[<2EF5C2177E2E604097171133B756E5BF>]/Index[1143 32]/Info 1142 0 R/Length 96/Prev 758817/Root 1144 0 R/Size 1175/Type/XRef/W[1 3 1]>>stream A downloadable template and instructions for this tool are available in IHI's free QI Essentials Toolkit. You leave for office from your home every day at 9:00 AM. To use QI Macros Control Chart Wizard . SPC for Excel Software. Just select your data: Then select the Control Chart Wizard from the QI Macros menu: The Control Chart Wizard will analyze your data and select the right control chart for you: If it's trying to choose between a p chart and a u chart, it will ask this question: Answer "yes" for a u chart and "no" for a p chart. These charts will reveal the variations between sample observations. Control Charts in Seconds FREE 30-day Trial × Email * Name * Company. Although the answer can become deep and complex, here are some simple recommendations. Let us understand further uses of control charts and what more information can be extracted from these charts. You have implemented new processes and now, you have to ensure that any deviations in the optimized processes are corrected before they result in any defects. 0 Candlestick chart. Qt Charts module provides a set of easy to use chart components. Landslide … Example Control Chart with invalid outliers removed (note the smaller scale for 'Elapsed Time') Tip 2: Remove triage casualties. Thanks so much for reading our publication. Thank you for the valuable document. Like (0) Former Member. In this case, you would want to use a P chart. Develop the control charts by specifying the X-axis and Y-axis. Control charts use probability expressed as control limits to help you determine whether an observed process measure would be expected to occur (in control) or not expected to occur, given normal process variation. Let us understand further uses of control charts and what more information can be extracted from these charts. The biggest challenge is how to select the best and the most effective type of chart for your task. Category: Chart. Once the control charts have been set up, you start plotting the new control values that are being collected as part of your routine work. Excessive Variation: Accident – these are events which leads to variations in the processes, leading to defects in the outputs or delayed processes. Instead, it should be a complete fact-based and data-driven exercise to identify the root cause. For a cholesterol method, two different commercial control products have been selected that have concentrations near the important medical decision levels of 200 mg/dL and 240 mg/dL identified by the National Cholesterol Education Program (NCEP) guidelines for test interpretation. Data are plotted in time order. You can use control charts to: Demonstrate whether your process is stable and consistent over time. The types are: 1. In a Control Chart, you generally want to track the issues that are resolved as 'Fixed'. Understanding the ‘As-Is’ state of the process. Range Control Charts • Control Charts for Duplicate Sample Data – Used when impossible to use same QC over time – Two samples of a batch are analyzed in duplicate • % difference plotted • Absolute difference plotted – After 10-20 points collected calculate mean range of duplicates – Tables (Youden) for determining % that should fall above/below 50% line. and bicycling in The Problem With P-Charts: Out-of-control Cycle LaneYs!. Using control charts is a continuous activity, ongoing over time.”. First decide what type of data you're dealing with. A control chart always has a central line for the average, an upper line for the upper control limit, and a lower line for the lower control limit. There are eight rules which are helpful in identifying if there are certain patterns or special causes of variation in the observations. By process capability, we can check if control limits and specification limits are in sync with each other. Monitori… Control Charts Evaluate Process Performance Over Time. Control Charts for Attributes. The individuals and moving range (I-MR) chart is one of the most commonly used control charts for continuous data; it is applicable when one data point is collected at each point in time. Control charts offer power in analysis of a process especially when using rational subgrouping. Benefits the Control chart toolkit has for you with this Control chart specific Use Case: Meet Lacey Gopinathan, Principal Consultant in Computer Software, Greater Los Angeles Area. If you're measuring the number of defects per unit, you have count data, which you would display using a U chart. The data collected in the process can be used for improvement in the subsequent of follow-up projects. www.world-class-quality.com Control Chart Factors Page 2 of 3. At the heart of Six Sigma lies the core strategies to improve the quality of processes by identifying and removing the causes leading to defects and variability in product quality and business processes. I can use a control chart to do the following: To determine the average amount; To determine the spread about the average; To determine if the process is in control (only common cause variation, see Jan 2004 e-zine on the website) To show the result of improvement efforts; Once you have established an objective, the next step is to select the type of control chart to use. Control charts, also known as Shewhart charts or process-behavior charts, are a statistical process control tool used to determine if a manufacturing or business process is in a state of control. What actions to take based on control charts? These five measurements for one-piece forms one sample or one sub-group. A bar on the org chart represents a project in the portfolio, rather than a task. If yes can you please guide on this. Average line is the mean of all the observations taken in the process. Example Control Chart with invalid outliers removed (note the smaller scale for 'Elapsed Time') Tip 2: Remove triage casualties. Pre-control charts have limited use as an improvement tool. R – Risk and Compliance Survey: we need your help! The CDC growth charts can be used continuously from ages 2-19. To generate Control charts, Does Sampling procedure must ? In the same way, engineers must take a special look to points beyond the control limits and to violating runs in order to identify and assign causes attributed to changes on the system that led the process to be out-of-control. If you're measuring the number of defects per unit, you have count data, which you would display using a U chart. FREE QI Macros 30-Day Trial . There is a variation of 5 minutes less or more because of slight traffic or you get all the traffic signals red on your way. Of course, we're just scratching the surface here -- there's a lot more to finding the right control chart for each individual situation than we … In other words, they provide a great way to monitor any sort of process you have in place so you can learn … I have had a couple of requests for help during my live training classes and online training classes on how to build a Six Sigma Control Chart. 5. A control chart (also referred to as Shew hart chart) is a tool which plots data regarding a specific process. h�b�',�@(� Configure your Control Chart to use this Quick Filter. In the above plot, red lines indicate the target value, the lower and upper specified range. Apart from manufacturing, control charts find their applications in healthcare industry and a host of other industries. By this, we can see how is the process behaving over the period of time. WHO's primary role is to direct international health within the United Nations' system and to lead partners in global health responses. Six Sigma uses empirical and statistical quality management methods to carry out operational improvement and excellence projects in organizations. Six Sigma was popularized by manufacturing organizations and Jack Welch, former CEO of GE, was one of advocators of Six Sigma. Accordingly, you choose the control chart and control objective. You can also use statuses (new, in progress, completed), as well as baselines, to represent delays. We can also call it as process behavior chart. It reduces the need for inspection – the need for inspection arises only when the process behavior is significantly different from the usual behavior. If the R chart appears to be in control, then we check the run rules against the X-Bar chart. These lines are determined from historical data. When they were first introduced, there were seven basic types of control charts, divided into two categories: variable and attribute. In particular, analyzing ARL's for CUSUM control charts shows that they are better than Shewhart control charts when it is desired to detect shifts in the mean that are 2 sigma or less. It uses the Qt Graphics View Framework, therefore charts can be easily integrated to modern user interfaces. These three values are determined by the process. The X bar S chart to be used when rationally collect measurements in subgroup size is more than 10. Most Xbar data is symmetrical assuming the subgroup size is large enough. This chart is a graph which is used to study process changes over time. Zone A, followed by Zone B and Zone C. Very few points should lie close to control limits and none of the points should fall beyond the control limits. Phone. Scatter charts have similar points with line charts since they both use vertical and horizontal axes to show different data points, but scatter types can also show the degree of difference in one variable to the other, which is known as correlation. – Kyle Dopp, First Choice Solutions. This article was contributed by Perceptive Analytics. Once you have developed control charts, you need to monitor the processes and check for any special or excessive variations which may lead to defects in the processes. In the above chart, one of the points lie outside the UCL which implies that the process is out of control. Which system will provide the data to monitor? The independent variable also called the control parameter, that systematically increases, or decreases is plotted along the horizontal or x-axis. Control Charts This chapter discusses a set of methods for monitoring process characteristics over time called control charts and places these tools in the wider perspective of quality improvement. A common question is "Which control chart should I use?" With x-axes that are time based, the chart shows a history of the … The R-chart generated by R also provides significant information for its interpretation, just as the x-bar chart generated above. When the data is assumed to be normally distributed. Kagi chart. You can use control charts to: Demonstrate whether your process is stable and consistent over time. In R chart, we look for all rules that we have mentioned above. Use the high-level, org chart to oversee a whole portfolio of projects. Control chart selection. {\displaystyle {\bar {X}}} and R chart is a type of scheme, popularly known as control chart, used to monitor the mean and range of a normally distributed variables simultaneously, when samples are collected at regular intervals from a business or industrial process.. Search for: Latest; Popular; How To Use Control Charts In Manufacturing. Floods and Health, Flow Chart 1.8.5. Configure your Control Chart to use this Quick Filter. Select and use the following control charts in various situations: X¯ – R, X¯ – s, individual and moving range (ImR), attribute charts (p, np, c, u), short-run SPC and moving average. Max level of stock a business can or wants to hold ; Example chart: 800 units; Re-order level. Sparkline . Getting Started. In this stage, everyone involved in the project understands his/her role and responsibilities. Also, for a capable process, value of Cpk should be greater than or equal to 1.33. Rational subgrouping also reduces the potential of false positives; it is not possible with pre-control charts. They can be central to process … Here is a quick view of all of these types. A stable process is one that includes only common-cause variation and does not have any out-of-control points. 1143 0 obj <> endobj While there are a few charts that are used very frequently, a wide range of options is available, and selecting the right chart can make the difference … Control charts are a great tool to monitor your processes overtime. If changes have been made to the process, control charts can help in understanding the impact of those changes on desired results. Drought and Health Response, Flow Chart 1.8.4. The main use of scatter charts is to draw the values of two series or variables and compare them over time or any other parameter. Six Sigma project teams use control charts to analyze data for special causes, and to understand the amount of variation in a process due to common cause variation. July 15, 2016 at 7:11 am. Monitoring systems need to be able to detect material changes in the clinical variable (i.e. Control charts provide a very simple and easy to understand methodology to understand the performance of processes. The materials were analyzed once per day for a period of twenty days. From these data, the means and standard deviations were calculated to be: The purpose of a control chart is to set upper and lower bounds of acceptable performance given normal variation. This wheel contains the medical eligibility criteria for starting use of contraceptive methods, based on Medical Eligibility Criteria for Contraceptive Use, 5th edition (2015), one of WHO’s evidence-based guidelines.It guides family planning providers in recommending safe and effective contraception methods for women with medical conditions or medically-relevant characteristics. Control chart is the primary statistical process control tool used to monitor the performance of processes and ensure that they are operating within the permissible limits. You have to think of new ways using techniques such as design of experiments and set up pilot projects to test the idea. %%EOF I am sure after going through this article, you will be able to use and create control charts in multiple other cases in your work. Control charts are most commonly used to monitor whether a process is stable and is under control. The most basic type of control chart, the individuals chart, i… It is often used to monitor the variables data but the performance of the Flow Charts for Emergency Management Panafrican Emergency Training Centre, Addis Ababa, July 1998. Nor would the use of a bar chart be a good choice for identifying trends and assignables causes that’s aren’t single movements beyond the control limits (something … With QI Macros You'll Never Struggle with Choosing the Right Control Chart Again For each of the rings manufactured, measurement of the diameter is taken 5 times and captured to examine the within piece variability. Now I am not professing to be a Six Sigma black belt, but I do know how to write DAX and I do know how to use Power BI. This chart shows the variations within the samples. UCL and LCL are upper control limit and lower control limit, respectively. One of the first things you learn in statistics is that when it comes to data, there's no one-size-fits-all approach. A control chart is a statistical tool that is used to chart data points over time and zeros in on points that are outside of the normal range (outliers). The steps in how to construct a c control chart were covered. 1174 0 obj <>stream Our client roster includes Fortune 500 and NYSE listed companies in the USA and India. This way you can easily see variation. So here goes. Earthquake and Disaster Response, Flow Chart 1.8.3. Leave a Reply Cancel reply. Robert Lloyd, IHI Vice President, uses his trusty whiteboard to demonstrate key improvement methods and tools. Why control charts "work" The control limits as pictured in the graph might be 0.001 probability limits. Of course, we're just scratching the surface here -- there's a lot more to finding the right control chart for each individual situation than we can fit in a simple blog post. Process capability will help us in identifying whether our system is capable to meeting the specified requirements. R chart gives an idea about the spread (dispersion) of the observations. Control charts are measuring process variation or VOP. X chart given an idea of the central tendency of the observations. There are different control charts based on the data you have, continuous or variable (height, weight, density, cost, temperature, age) and attribute (number of defective parts produced). The idea is that, for a stable testing process, the new control measurements should show the same distribution as the past control measurements. With this information they can make the right decision about how to implement process improvements, whether that involves addressing the process itself or dealing with external factors that affect process performance. Variable data takes on a measurable, numeric value. The control chart is necessary for project management as it provides the project manager as well as the stakeholders the ability to determine points which they can implement corrective actions to prevent further problems. After all, control charts are the heart of statistical process control (SPC). 1st Qu. �4a �6�7A����,)�Dr���{��mFL�,l]�T �3�m� ��@ Use google.visualization.ChartWrapper and google.visualization.ControlWrapper to define charts and controls respectively. According to Wikipedia, “The data from measurements of variations at points on the process map is monitored using control charts. The time series chapter, Chapter 14, deals more generally with changes in a variable over time. Median      Mean   3rd Qu. Copyright © 2020 | MH Corporate basic by MH Themes, Click here if you're looking to post or find an R/data-science job, Introducing our new book, Tidy Modeling with R, How to Explore Data: {DataExplorer} Package, R – Sorting a data frame by the contents of a column, Whose dream is this? Best Regards. Like (0) Waqar … She decides to design and use Control chart outputs to increase profitability. It is measured by process capability index Cpk. Using rnorm function in R, let’s create the measurement values. To get the most useful and reliable information from your analysis, you need to select the type of method that best suits the type of data you have.The same is true with control charts. 25 data points out of 100 have a value of 50. A stable process is one that includes only common-cause variation and does not have any out-of-control points. Also called: Shewhart chart, statistical process control chart. The zones tests require some symmetry about the average, but basically, you should not worry about normality. In the control chart, the performance of these processes is monitored visually to identify any anomalies or variations from the usual behavior. I am sure you must have heard of Six Sigma quality standard or Six Sigma experts. Let’s understand what are control charts and how are they used in process improvement. You then estimate that the probability of getting an event with a value of 50 is 25 out of 100, or 25 percent. R-chart example using qcc R package. The following decision tree can be used to identify which is the correct quality control chart to use based on the given data: Quality Control Charts Decision Tree. You know your process and will know if a control chart is signalling a special case most likely. Following steps present the step-by-step approach to implement a control chart: Answer to this question will come from the DMAIC process while implementing the entire project methodology. In this phase, make sure that your biases don’t lead you to results. If our process i… h�bbdb>"��H� ��LڂE$A$W4X� Although in Six Sigma study, we usually read Control chart in the Control phase. Now, you are aware about the entire process and cause behind the problems. We hope you find it informative and useful. For every control chart, there are control limits or decision limits set which define the normal behavior of the process. July 14, 2016 at 4:53 pm. … A capability analysis is only valid when performed on a stable process. FluNet - CHARTS Influenza virus detections. One needs to understand these types clearly to use the right chart for the data. Any movement outside those limits indicate variation in the process and needs to be corrected to prevent further damage. Why not use a control chart?Using a control chart on a data set is an efficient way to identify data sets that are out of control. A run chart is a line graph of data plotted over time. Since this article talks about control charts, we will focus on DMAIC project methodology of which control charts is a part of. Disasters and Health, General Flow Chart 1.8.2. Type # 1. For example, if an improvement team theorizes that there are particular times of day when problems occur, they can subgroup the data on the applicable control chart time of day to evaluate this theory. Keep sharing. The mission of WHO prequalification is to work in close cooperation with national regulatory agencies and other partner organizations to make quality priority medical products available for those who urgently need them. In this case, you would want to use a P chart. Example Control Chart with invalid outliers. What is a Control Chart? Why control charts "work" The control limits as pictured in the graph might be 0.001 probability limits. There should be clarity on ‘Why is the project being undertaken?’. In a Control Chart, you generally want to track the issues that are resolved as 'Fixed'. A Control Chart is also known as the Shewhart chart since it was introduced by Walter A Shewhart. If you want to choose the most suitable chart type, generally, you should consider the total number of variables, data points, and the time period of your data. Control Charts for Variables 2. There are different types of Control charts based on the data that we use. Like (0) Dipeshkumar Bhavsar . The main components of a control chart are: Average Line –The average value of the data set. 0.0342775 0.1627947 0.2212205 0.2131489 0.2644740 0.3919933, Group sample size:  5Number of groups:  25Center of group statistics:  0.2131489Standard deviation:  0.09163753  Control limits: LCL       UCL   0 0.4506969. Having trouble viewing this video? Understanding, monitoring and controlling variation in clinical variables is an integral part of clinical practice [1]. Control charts have long been used in manufacturing, stock trading algorithms, and process improvement methodologies like Six Sigma and Total Quality Management (TQM). But, what is Six Sigma? D&D’s Data Science Platform (DSP) – making healthcare analytics easier, High School Swimming State-Off Tournament Championship California (1) vs. Texas (2), Learning Data Science with RStudio Cloud: A Student’s Perspective, Risk Scoring in Digital Contact Tracing Apps, Junior Data Scientist / Quantitative economist, Data Scientist – CGIAR Excellence in Agronomy (Ref No: DDG-R4D/DS/1/CG/EA/06/20), Data Analytics Auditor, Future of Audit Lead @ London or Newcastle, python-bloggers.com (python/data-science news), Python Musings #4: Why you shouldn’t use Google Forms for getting Data- Simulating Spam Attacks with Selenium, Building a Chatbot with Google DialogFlow, LanguageTool: Grammar and Spell Checker in Python, Click here to close (This popup will not appear again), > qq = qcc(obs, type = “xbar”, nsigmas = 3), > obs[18,]         V1       V2       V3      V4       V5, > process.capability(qq, spec.limits = c(1.4,1.6)). Qt Charts can be used as QWidgets, QGraphicsWidget, or QML types. In the same way, engineers must take a special look to points beyond the control limits and to violating runs in order to identify and assign causes attributed to changes on the system that led the process to be out-of-control. (Apply) The IASSC Six Sigma Black Belt BOK lists knowledge of I-MR charts under it’s control phase. Summary Chart of U.S. Medical Eligibility Criteria for Contraceptive Use. The I-MR control chart is actually two charts used in tandem (Figure 7). Candlestick charts are another type of bar chart used to describe price movements of an equity over time. SPC Training. Normally the most popular types of charts are: column charts, bar charts, pie charts, doughnut charts, line charts, area charts, scatter charts, spider and radar charts, gauges and finally comparison charts. World Health Organization Prequalification . Rule 1: One or more points beyond the control limits, Rule 2: 8 out of 9 points on the same side of the center line (Average line), Rule 3: 6 consecutive points increasing or decreasing (monotonic), Rule 4: 14 consecutive points are alternating up and down, Rule 5: 2 out of 3 consecutive points in Zone C or beyond, Rule 6: 4 out of 5 consecutive points in Zone B or beyond, Rule 7: 15 consecutive points are in Zone A, Rule 8: 8 consecutive points on either side of the Average line but not in Zone A. The 'percent completed' for each project is a key metric here. Why use CDC growth charts for children 2 years and older in the U.S.? X-axis can have either time or sample sequence; while, the Y-axis can have individual values or deviations. If any of the above rules is violated, then R chart is out of control and we don’t need to evaluate further. An example of a traditional stock control chart is shown below: The key parts of the stock control chart are: Maximum level. To use a c control chart, the opportunity for defects to occur must be large, but the actual number that occur must be small. These limits define the control or decision limits within which a process should always fall for efficient and optimized operations. DMAIC methodology is used for projects aimed at improving existing business processes; while, DMADV is used for projects which aims at creating new processes. Control charts were developed by Shewhart (2) 3 in the 1920s and are still in wide use today. The control chart and histogram macros in QI Macros alone have saved me hours of work and allowed me to present data to management in a format that is meaningful. However, they can show you how the process is running. This is a good place to start our discussion. CONTROL CHARTS FOR VARIABLES As the name indicates, these charts will use variable data of a process. Statistical process control can be used to monitor the processes and ensure that the desired quality level is maintained. ��5�L�\ �X��!�*>)�DK�oR�I�Y�de}�Y�P��d�/Ã"��OA:�O髜�g��9�{&H w;���=̍�@�1x2o=~���d�h(���/�1YAd�:PE� � �1���q'�0���Ƈ��\$��bIp�a�a�efd��%����0�̕]��'|�c�niם\y&����,��eTf����0n}U ���N ��m�Hs10�3��Y �d�I�!�� f�Ӝ Users can easily create impressive graphs by selecting one of the charts themes. Correlations can be positive, negative, or equals to zero. endstream endobj startxref Summary of group statistics:     Min. Now, we have understood the control charts, attributes, applications and associated rules, let’s try to implement a small example in R. Let’s assume that there is a company which manufactures cylindrical piston rings. !�ѻ����r���)qN� Find out how he uses Control Charts to Keep Blood Sugar in Check. Can we use control charts in case of Qualitative characteristics. Read the transcript. Basically, each typ… %PDF-1.5 %���� detect a signal) from background noise to support appropriate clinical decision-making [1]. For a process where all the values lie within the control limits and there is no specific pattern in the values, the process is said to be “in-control.”. Because they do not use control limits, run charts cannot tell you if a process is stable. A process is Perceptive Analytics is a marketing analytics company and it also provides Tableau Consulting, data analytics, business intelligence and reporting services to e-commerce, retail, healthcare and pharmaceutical industries. Common sources: Slight traffic or traffic signals on the route – these are usually part of the processes and are of much less concern while driving to office. In this phase, you need to find out ways or methodologies to work on the problem and improve the current processes. For the following example, we will be focusing on quality control charts for continuous data for when the sample size is greater than 10. x-bar chart . X-Chart and R-Chart… Six Sigma projects follow methodologies which are called as DMAIC and DMADV. Together they monitor the process average as well as process variation. Many thanks. Jul 06, 2018 jag. Summing up everything, control charts are graphical techniques to monitor the performance of a process over time. SPC Consulting. Control charts have many uses; they can be used in manufacturing to test if machinery are producing products within specifications… Use of Control Charts. There are only a few (usually two) discrete values. Quick Links. The average time it takes you to reach office is 35 minutes; while in most of the cases it takes 30 to 40 minutes for you to reach office. For instance, in the case we have taken, our client wanted piston rings with target diameter of 1.5 cm with a variation of +/- 0.1 cm. Create Control And Chart Instances. Wrap-up: Why use control charts? Use X Bar S Control Charts When: The sampling procedure is same for each sample and is carried out consistently. A capability analysis is only valid when performed on a stable process. Define as many instances you need for each control and chart that will be part of the dashboard. Invented by Walter A. Shewhart while he was working for Bell Labs in the ’20s, control charts have been used in a variety of industries as part of a process improvement methodology.Shewhart understood that, no matter how well a process was designed, there will always be variation within that process—and the effect can become negative if the variation keeps you from meeting deadlines or quotas. Attribute data consists of categories. Control charts, ushered in by Walter Shewhart in 1928, continue to provide real-time benefits in today’s modern factories. Visit our home page. Before understanding the types, one should know about the concept of ‘Rational subgrouping’. Based on the goal defined in the ‘Define’ phase, you understand the process in detail and collect relevant data which is to be used in subsequent phases. Therefore the use of control chart becomes very vital in Process control. Jyothirmayee Thondamallu, Chaitanya Sagar and Saneesh Veetil contributed to this article. If we were to look at the sample 18, we see that the values in sample 18 are usually higher than values in other samples. Ordering Information . In statistics, Control charts are the tools in control processes to determine whether a manufacturing process or a business process is in a controlled statistical state. Example Control Chart with invalid outliers. • A control chart of case two’s time-to-process data showed the benefit in seeking a root cause for the detected process change (between batch’s 12 and 13); taking action on the identified root cause was the catalyst to improvement. The data is plotted in a timely order. This would not be considered an acceptable method of creating control limits for an x bar chart. Control Charts (Part 1) The science of improvement on a whiteboard! The dependant or measured variable is plotted along the Y-axis. �����ʄ}f��R�����gM��E���d+p*��5�ՄɆɈqs#��_�0�xwRwC�! Identifying the systems that will provide the data based on which control charts will be prepared and monitored. Verify that your process is stable before you perform a capability analysis. Verify that your process is stable before you perform a capability analysis. A popular method of implementing stock control is through the use of inventory (stock) control charts and algorithms that automate the process. Run charts reduce manufacturing s work zontec where are control charts how to use control charts improve manufacturing quality control chart tutorials and exles control chart rules process ility ysis. Post navigation ← Vision Test Snellen Chart. However, on one fine day you leave from your home and you reach office in 60 minutes because there was an accident on the way and the entire traffic was diverted which caused additional delay of around 20 minutes. Or equals to zero over the period of twenty days LCL are upper limit... The usual behavior focus on DMAIC project methodology of which control chart ( also referred to Shew... Sure you must have heard of Six Sigma uses empirical and statistical quality management methods to out... Can find trends or patterns in the clinical variable ( i.e wants to hold ; chart. 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Children 2-5 years, the performance of processes then we check the run rules against the x-bar.! Lists knowledge of I-MR charts under it ’ s control charts? ” control charts are commonly... They can show you how the process WHO growth charts for Emergency management Panafrican Emergency Training,! Getting an event with a traditional stock control chart outputs to increase profitability older in the above chart, process. And attribute chart given an idea about the entire process and will know a... Example and understand it step by step using above definition charts have use! How a process should always fall for efficient and optimized operations can help in understanding the types, one the. Its interpretation, just as the name indicates, these charts will be prepared monitored! The I-MR control chart with invalid outliers removed ( note the smaller scale for 'Elapsed time ). Or wants to hold ; example chart: 800 units ; Re-order level dealing! Is a key metric here key improvement methods and tools, value of the things! When using rational subgrouping x-axis and Y-axis before understanding the impact of changes... Analyzed once per day for a period of time an Open-high-low-close chart with outliers! On ‘ Why is the process behavior chart and will know if a process tool for in! And data-driven exercise to identify the root cause variations from the usual behavior some! Methods to carry out operational improvement and excellence projects in organizations methodology of which control charts, Sampling... On DMAIC project methodology of which control charts points out of 100 have a value of the.! Name indicates, these charts will reveal the variations between sample observations data of a firm processes! There were seven basic types of control charts and algorithms that automate the process ’ create... To results for: Latest ; popular ; how to use the chart! Count data, which you would display using a U chart a measurable, numeric.! Select the best and the WHO growth charts are graphical techniques to monitor the process to represent delays level... Ways using techniques such as design of experiments and set up pilot projects test. Of stock a business can or wants to hold ; example chart: 800 units ; Re-order level 'Elapsed. Data based on the data is symmetrical assuming the subgroup size is large.... To hold ; example chart: 800 units ; Re-order level detect problems in a control is! Things you learn in statistics is that when it comes to data, which you would using! Quality control charts is a key metric here that are resolved as 'Fixed ' standard deviation in process. Systems that will be prepared and monitored and will know if a control chart with invalid outliers removed note. Being undertaken? ’ or decreases is plotted along the horizontal or x-axis this shows that probability... 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Sigma is a key metric here, ushered in by Walter Shewhart in 1928 continue... Will provide the data that we use of follow-up projects average as well as behavior... If control limits as pictured in the control charts offer power in analysis of a firm 's or... Chart components variation to develop ideas for change improvement and excellence projects in.! One should know about the average line i.e qcc R package desired quality level is maintained methodologies work... Are a type of chart for your task select the best and the WHO growth and! Idea of the points lie outside the UCL which implies that the quality! Within piece variability understand these types the above chart, we have understood control! And tools variation to develop ideas for change that your process is stable before you perform a analysis... Under control 9:00 am everyone involved in the above plot, red lines indicate the target value, the of... Sigma Black Belt BOK lists knowledge of I-MR charts under it ’ s the! 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Free 30-day Trial × Email * name * Company Trial × Email name... Systems that will be part of clinical practice [ 1 ] process map is monitored using control charts what! Process control can be used in control phase comparing current data to evaluate a changes! Understanding, monitoring and controlling variation in clinical variables is an integral part of the dashboard needs! Data is symmetrical assuming the subgroup size is more than 10 idea about the spread ( )... To represent delays the problem and improve the current processes still in wide use today improvement tool 9:00! Patterns in the process is stable Thondamallu, Chaitanya Sagar and Saneesh Veetil contributed to article... Clinical decision-making [ 1 ] rather than a task control phase portfolio of projects have to of... Chart becomes very vital in process improvement in different settings 3 who uses control charts the process I use?, we for... Y-Axis can have individual values or deviations or equal to 1.33 tandem ( Figure 7 ) provides... Using qcc R package, chapter 14, deals more who uses control charts with changes in a is... Average, but basically, you can use control charts in Seconds FREE 30-day ×! Improvement on a stable process ( also referred to as Shew hart chart ) is a Quick view of the. Data based on which control charts  work '' the control chart should I use? by organizations to their. 'S primary role is to direct international health within the United Nations ' system and to lead in! Manufacturing organizations and Jack Welch, former CEO of GE, was of...


text:
Getting error when initializing a set of Stocks with Bull and Bear variables

Hello all,

I am new to Python and working with financial information.

Basically, I am trying to set up Trailing Stops for a list of stocks. The idea is that when the stock goes up, the Stop Loss will adjust with the price (I would like to make it so that the Stop Loss would be 10% behind the Current Price)

If the code had to exit, the idea was to use Moving Averages to determine the best time to get back in.

The problem is that when I add the code:

    # initialize BEAR and BULL flags
for i, stock in enumerate(context.stocks):
context.stocks[i].stop_price_bull = 0
context.stocks[i].stop_price_bear = 0
context.dayCount += 1

under the "initialize" block, I get the following error:

AttributeError: 'zipline.assets._assets.Equity' object has no
attribute 'stop_price_bull' USER ALGORITHM:17, in initialize
context.stocks[i].stop_price_bull = 0

How can I solve this problem?

TIA

format: plain


text:
## How to accurately link a parallel configuration with dummy?

Typically: "How do I... ", "How can I... " questions
coppelia
Posts: 7973
Joined: 14 Dec 2012, 00:25

### Re: How to accurately link a parallel configuration with dummy?

Please post your model in the neutral configuration. In that case also, if we make the IK for that mechanism, do you agree if we use it as a example V-REP scene on our website and/or software?

Cheers

gloria7@scuthahaha
Posts: 10
Joined: 15 Oct 2017, 10:01

### Re: How to accurately link a parallel configuration with dummy?

I am really happy to hear that you want to help me with our model~ I have noticed the importance that sometimes the common method to calculate inverse kinematic would not works as the configuration has some special geometric feature. Here is the link of our STL model and the thesis paper script with the inverse kinematic and Jacobian matrix you may need.
stl file:
PDF:
and here is some picture to define the angle and coordinate of the model
As for the use as example or put it into your software, I think it's good for other user, for I have notice there are many parallel configuration problems are not solved. But the model is designed by our laboratory originally and my supervisor want to publish some paper with this configuration. I think its a interesting configuration and if you want to use it, please let me known and make the statement with our laboratory.
My email is

Code: Select all

believegloria@gmail.com
,you can contact me in anytime. I will gave you the information of my laboratory and my supervisor, or other information of our model and questions that I don't express clearly.

cheers
Gloria
18.5.11

gloria7@scuthahaha
Posts: 10
Joined: 15 Oct 2017, 10:01

### Re: How to accurately link a parallel configuration with dummy?

and nowadays, I have started to write the inverse kinematic solution with Lua, If I have any improvement, I will let you known it in the first time : )

coppelia


text:
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# Open Physics

### formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

IMPACT FACTOR 2018: 1.005

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Volume 16, Issue 1

# A note on the transmission feasibility problem in networks

Wei Gao
/ Yunqing Zhang
/ Yaojun Chen
Published Online: 2018-12-31 | DOI: https://doi.org/10.1515/phys-2018-0110

## Abstract

In the networking designing phase, the network needs to be built according to certain indicators to ensure that the network has the ideal functions and can work smoothly. From a modeling perspective, each site in the network is represented by a vertex, channels between sites are represented by edges, and thus the entire network can be denoted as a graph. Problems in the network can be transformed into corresponding graph problems. In particular, the feasibility of data transmission can be transformed into the existence of fractional factors in network graph. This note gives an independent set neighborhood union condition for the existence of fractional factors in a special setting, and shows that the neighborhood union condition is sharp.

PACS: 02.10.Ox; 07.05.Mh

## 1 Introduction

In the initial stage of network designing, scientists pre-conceive what requirements the built network needs to meet, and then plan the structure of the network as needed, including the distribution of the sites and the channels between the sites. In mathematical modelling, each site is represented by a vertex, and the channel connecting the two sites is represented by an edge. The direction of the edge is defined according to the direction of information flow between the two sites, and the undirected edge implies two-directional flow between the two sites. As a result, problems in the network, in particular problems in the network designing phase, can be described by the problems in a network graph. In the design of the transmission network, we always require the network as a whole to achieve the pre-conceived transmission requirements, especially when some channels are not working properly due to failure or being under attacked for some unexpected reasons, the entire network is unobstructed. The problem of the transmission of data packets within a certain range within the network is equivalent to the existence of the fractional factor, from the graph theory point of view. In addition, the smooth procedure transmission under the condition that some channels that can’t are not work is equivalent to the fractional deleted graph problem in graph theory. That is, after deleting given number of edges, the fractional factor still exists.

In this note, we discuss the theoretical problem from graph theory point of view, and consider each network as a simple graph (loopless, finite multiple edges). Let G be a graph with vertex set V(G) and edge set E(G). Some fundamental notations are listed as follows (set S ⊆ V(G)):

• dG(x): degree of vertex x in G. For simply, we write it as d(x);

• NG(x) (in short, N (x)): neighborhood of x in G;

• NG[x]: NG(x) ∪ {x};

• G[S]: subgraph of G which is induced by S;

• GS: G[V(G) \ S];

• δ(G): minimum degree G;

• n: order of graph, i.e., n = |V(G)|;

• a matching M of G: a subset of E(G) such that no two elements are adjacent;

• eG(S, T) (here S and T are vertex-disjoint subsets of G): |{e = xy|x ∈ S, y ∈ T}|.

The terminologies used in this paper but undefined here can be referred to Bondy and Murty [1].

Assume that g and f are two integer-valued functions on V(G) satisfy 0 ≤ g(x) ≤ f (x) for any x ∈ V(G). A fractional (g, f )-factor is a function h that assigns a number in [0,1] to each edge of a graph G a number in [0,1], so that $g\left(x\right)\le \sum _{e\in E\left(x\right)}h\left(e\right)\le f\left(x\right)$for each vertex x. A fractional (g, f )-factor is called a fractional [a, b]-factor if g(x) = a and f (x) = b for any x ∈ V(G). Moreover, a fractional (g, f )factor is called a fractional f -factor if g(x) = f (x) for all x ∈ V(G).

Anstee [2] determined the necessary and sufficient condition for the existence of a fractional (g, f )-factor which is manifested as follows.

#### Theorem 1

(Anstee [2]) Let G be a graph, and let g, f : V(G) → {0, 1, 2, · · · } be two functions with g(x) ≤ f (x) for each x ∈ V(G). Then G has a fractional (g, f )-factor if, and only if,

$f(S)+dG−S(T)−g(T)≥0$

for any S ⊆ V(G) and T = {x : x ∈ V(G) − S, dGS(x) ≤ g(x)}.

Let S ⊆ V(G), M be a matching, T = {x : x ∈ V(G) − S, dGS(x) ≤ g(x)}, D = V(G)\(S∪T), EG(T) = {e : e = xy ∈ E(G), x, y ∈ T}, E′ = M ∩ EG(T), E′′ = M ∩ EG(T, D) and βG(S, T, M) = 2|E| + |E′′|. Li et al. [3] derived a necessary and sufficient condition for a graph to have a fractional (g, f )-factor excluding a given matching M (i.e., h(e) = 0 for any edge in M).

#### Theorem 2

(Li et al. [3]) Let G be a graph, g, f : V(G) → {0, 1, 2, · · · } be two functions with g(x) ≤ f (x) for each x ∈ V(G), and M be a matching of G. Then G has a fractional (g, f )-factor excluding M if, and only if,

$f(S)+dG−S(T)−g(T)≥βG(S,T,M)$

for any S ⊆ V(G) and T = {x : x ∈ V(G) − S, dGS(x) ≤ g(x)}.

In recent years, the problem of fractional factor has raised attention in both graph theory and computer networks. Gao et al. [4], [5], [6] and [7] studied the relationship between toughness (or isolated toughness) and the existence of fractional factor in different settings. Gao et al. [8] and [9] determined several independent set conditions for a graph with fractional factors. Furthermore, neighborhood conditions for the existence of fractional factors in special settings were researched in Gao et al. [10], [11] and [12]. More results on fractional factors can be referred to Zhou et al. [13], [14], [15], [16], [17], and [18], Khellat and Khormizi [19], Lokesha et al. [20], and Pandey and Jaboob [21].

A matching is called m-matching if it contains m edges. The aim of this note is to study the relationship between independent set neighborhood union characteristics and the existence of fractional factors in a special setting where a m-matching is deleted from G. In computer networks, neighborhood union reflects the degree of density in networks, and independent set neighborhood union reflects the distribution of the dominant set in networks. The main contribution in our work is stated in the following theorem.

#### Theorem 3

Let G be a noncomplete graph of order n. Let a, b, m, Δ and i be nonnegative integers with i ≥ 2, 2 ≤ abΔ. Let g, f be two integer-valued functions defined on V(G) such that ag(x) ≤ f (x) − ΔbΔ for each x ∈ V(G). Let e be an edge of G, and M be an m-matching of G satisfying e ∈ M. If $\delta \left(G\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\ge \text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{\left(i-1\right)\left(b-\Delta \right)\left(b+2\right)+1}{a+\Delta }\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\text{\hspace{0.17em}}1,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}n\ge$$\frac{\left(a+b\right)\left(i\left(a+b+1\right)+2m-2\right)+2}{a+\Delta },$and

$|NG(x1)∪NG(x2)∪⋯∪NG(xi)| ≥ (b−Δ)n+2a+b + i$

for any independent subset {x1, x2, · · · , xi} of V(G), then G has a fractional (g, f )-factor containing e and excluding M.

If m = 1 in Theorem 3, then we get the following corollary.

#### Corollary 1

Let G be a noncomplete graph of order n. Let a, b, m, Δ and i be nonnegative integers with i ≥ 2, 2 ≤ abΔ. Let g, f be two integer-valued functions defined on V(G), such that ag(x) ≤ f (x) − ΔbΔ for each x ∈ V(G). Let e1 and e2 be two distinct edges of G. If $\delta \left(G\right)\ge \frac{\left(i-1\right)\left(b-\Delta \right)\left(b+2\right)+1}{a+\Delta }\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\text{\hspace{0.17em}}1,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}n\ge \frac{\left(a+b\right)\left(i\left(a+b+1\right)\right)+2}{a+\Delta },$and

$|NG(x1)∪NG(x2)∪⋯∪NG(xi)| ≥ (b−Δ)n+2a+b + i$

for any independent subset {x1, x2, · · · , xi} of V(G), then G has a fractional (g, f )-factor containing e1 and excluding e2.

If we set Δ = 0 in Theorem 3, then the following corollary is obtained.

#### Corollary 2

Let G be a noncomplete graph of order n. Let a, b, m and i be nonnegative integers with i ≥ 2,2 ≤ ab. Let g, f be two integer-valued functions defined on V(G), such that ag(x) ≤ f (x) ≤ b for each x ∈ V(G). Let e be an edge of G and M be an m-matching of G satisfying e ̸∈ M. If $\delta \left(G\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\ge \text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{\left(i-1\right)b\left(b+2\right)+1}{a}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\text{\hspace{0.17em}}1,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}n\text{\hspace{0.17em}}\text{\hspace{0.17em}}\ge \text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{\left(a+b\right)\left(i\left(a+b+1\right)+2m-2\right)+2}{a},$and

$|NG(x1)∪NG(x2)∪⋯∪NG(xi)| ≥ bn+2a+b + i$

for any independent subset {x1, x2, · · · , xi} of V(G), then G has a fractional (g, f )-factor containing e and excluding M.

If g(x) = f (x) for any x ∈ V(G) in Corollary 2, then we yield the following conclusion.

#### Corollary 3

Let G be a noncomplete graph of order n. Let a, b, m and i be nonnegative integers with i ≥ 2,2 ≤ ab. Let f be an integer-valued function defined on V(G), such that af (x) ≤ b for each x ∈ V(G). Let e be an edge of G and M be an m-matching of G satisfying e ̸∈ M. If δ(G) ≥ $\frac{\left(i-1\right)b\left(b+2\right)+1}{a}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\text{\hspace{0.17em}}1,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}n\text{\hspace{0.17em}}\text{\hspace{0.17em}}\ge \text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{\left(a+b\right)\left(i\left(a+b+1\right)+2m-2\right)+2}{a},$and

$|NG(x1)∪NG(x2)∪⋯∪NG(xi)| ≥ bn+2a+b + i$

for any independent subset {x1, x2, · · · , xi} of V(G), then G has a fractional f -factor containing e and excluding M.

Let

$ε(S, T)={ 2, S is not an independent set 1, S is an independent set and eG(S, V(G)\(S∪T)) ≥ 1, or there is an edge e=uv joining S and T such that dG−S(v)=g(v) for v∈T 0, otherwise.$

To prove Theorem 3, we need the following result.

#### Theorem 4

(Li et al. [22]) Let G be a graph, and let g, f : V(G) N ∪ {0} be two functions such that g(x) ≤ f (x) for every x ∈ V(G). Then G has a fractional (g, f )-factor containing any given edge e if, and only if,

$f(S)+dG−S(T)−g(T) ≥ ε(S, T)$

for any vertex subset S of G and T = {x : x ∈ V(G) − S, dGS(x) ≤ g(x)}.

## 2 Proof of Theorem 3

Let H = GM, and we have V(H) = V(G) and δ(H) ≥ δ(G)−1. It is enough to show that H has a fractional (g, f )factor including e. In what follows, we use the counterevidence method to prove this result. Assume that H does’t have the desired fractional factor. Then in terms of Theorem 4, there exists a subset S ⊆ V(H) that satisfies

$f(S)+dH−S(T)−g(T) ≤ ε(S, T)−1$(1)

where T = {x : x ∈ V(H)−S, dHS(x) ≤ g(x)}. If T = , then dHS(T) − g(T) = 0 and by (1) we infer ε(S, T) − 1 ≥ f (S) ≥ (a + Δ)|S| ≥ 2|S|ε(S, T), a contradiction. Thus, we have T.

Set D = V(G) − S ∪ T and EG(T) = {e : e = xy ∈ E(G), x, y ∈ T}. Since M is an m-matching, we deduce

$dH−S(T)=dG−M−S(T)= dG−S(T)−(2|M∩EG(T)|+|M∩EG(T, D)|)≥ dG−S(T)−min{2m, |T|}.$(2)

Now, we discuss the following three cases according to the value of |S|.

Case 1. |S| = 0.

In this case, we have ε(S, T) = 0 and $\delta \left(H\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\ge \text{\hspace{0.17em}}\text{\hspace{0.17em}}\delta \left(G\right)-1\ge \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{\left(i-1\right)\left(b-\Delta \right)\left(b+2\right)+1}{a}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}>b-\Delta .$By means of (1), we yield

$−1 ≥ f(S)+dH−S(T)−g(T)= dH(T)−g(T)=∑x∈T(dH(x)−g(x)) ≥ ∑x∈T(δ(H)−(b−Δ)) ≥ 0,$

Case 2. |S| = 1.

In this case, we have ε(S, T) ≤ 1 and $\delta \left(G\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\ge \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{\left(i-1\right)\left(b-\Delta \right)\left(b+2\right)+1}{a}\text{\hspace{0.17em}}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\text{\hspace{0.17em}}1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}>\text{\hspace{0.17em}}\text{\hspace{0.17em}}b-\Delta +1.$In view of the integrity of δ(G), we have δ(G) ≥ bΔ + 2. In light of (1) and (2), we derive

$0 ≥ ε(S, T)−1 ≥f(S)+dH−S(T)−g(T)≥ f(S)+dG−S(T)−min{|T|, 2m}−g(T)≥ f(S)+dG−S(T)−|T|−g(T)≥ f(S)+dG(T)−2|T|−g(T)≥ f(S)+δ(G)|T|−2|T|−g(T)≥ (a+Δ)|S|+(b−Δ+2)|T|−2|T|−(b−Δ)|T|= (a+Δ)|S|=a+Δ ≥ 2,$

Case 3. |S| ≥ 2.

Note that ε(S, T) ≤ 2 and T. Let d1 = min{dGS(x) : x ∈ T} and choose x1 ∈ T such that dGS(x1) = d1. If TNT[x1] ≠, let d2 = min{dGS(x) : x ∈ TNT[x1]} and choose x2 ∈ TNT[x1] such that dGS(x2) = d2. Continue this step, if z ≥ 2 and $T\\left({\cup }_{j=1}^{z-1}{N}_{T}\left[{x}_{j}\right]\right)\ne \overline{)0},$let

$dz=min{dG−S(x)|x∈T\(∪j=1z−1NT[xj])},$

and select ${x}_{z}\in T\\left({\cup }_{j=1}^{z-1}{N}_{T}\left[{x}_{j}\right]\right)$with dGS(xz) = dz. Thus, we construct a sequence 0 ≤ d1d2 ≤ ·· ·≤ dπbΔ + 1 and an independent set {x1, x2, · · · , xπ}⊆ T.

Now, we the next lemma which is similar to Lemma 5 in Gao et al. [8].

#### Lemma 1

In the above conditions, we have

$|T| ≥ { (i−1)(b+2), if dG−S(x)=1 for any x∈T, (i−1)(b+2)+1, otherwise.$

Proof. Note that |S| + d1 = |S| + dGS(x1)≥ dG(x1)≥ δ(G). We verify that

$|S| ≥ δ(G)−d1≥ (i−1)(b−Δ)(b+2)+1a+Δ+1−d1.$(3)

Firstly, we justify that $|T|\text{\hspace{0.17em}}\text{\hspace{0.17em}}\ge \text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(i=1\right)\left(b+2\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{if}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{d}_{G-S}\left(x\right)=1$for any x ∈ T. In this case, we get d1 = 1.

Assume that |T| ≤ (i − 1)(b + 2) − 1. By means of (2), (3), d1 = 1 and i ≥ 2, we yield

$f(S)+dH−S(T)−g(T)≥f(S)+dG−S(T)−min{|T|,2m}−g(T)≥f(S)+dG−S(T)−|T|−g(T)≥(a+Δ)|S|+|T|−|T|−(b−Δ)|T|=(a+Δ)|S|−(b−Δ)|T|≥(a+Δ)((i−1)(b−Δ)(b+2)+1a+Δ+1−d1)−(b−Δ)((i−1)(b+2)−1)=(a+Δ)(i−1)(b−Δ)(b+2)+1a+Δ−(b−Δ)((i−1)(b+2)−1)=b−Δ+1>a≥2≥ε(S,T),$

which contradicts (1). Therefore, the first part of Lemma 1 is established.

Next, we check that |T| ≥ (i − 1)(b + 2) + 1 in the rest cases. Assume that |T| ≤ (i − 1)(b + 2) in this case, and the discussion can be divided into three situations in terms of the value of d1.

Case 1. d1 = 0.

In view of (1), (3) and d1 = 0, we yield

$ε(S,T)−1≥f(S)+dH−S(T)−g(T)≥f(S)−g(T)≥(a+Δ)|S|−(b−Δ)|T|≥(a+Δ)((i−1)(b−Δ)(b+2)+1a+Δ+1−d1)−(b−Δ)(i−1)(b+2)=a+Δ+1>a≥2≥ε(S,T),$

Case 2. d1 = 1.

Following from (1), (3), d1 = 1 and ε(S, T) ≤ 2, we get

$1≥ε(S,T)−1≥f(S)+dH−S(T)−g(T)≥f(S)−g(T)≥(a+Δ)|S|−(b−Δ)|T|≥(a+Δ)((i−1)(b−Δ)(b+2)+1a+Δ+1−d1)−(b−Δ)(i−1)(b+2)=1.$

It implies that all the “≥” should be “=”, and it further reveals that dHS(T) = 0, i.e., dHS(x) = 0 for each x ∈ T.

Since d1 = 1, we confirm that dGS(x) = 1 for each x ∈ T which contradicts the assumption that there exist x ∈ T satisfying dGS(x) ≠1.

Case 3. 2 ≤ d1bΔ + 1.

Using (1), (2), (3), i ≥ 2 and2 ≤ d1bΔ+1, we derive

$ε(S,T)−1≥f(S)+dH−S(T)−g(T)≥f(S)+dG−S(T)−min{|T|,2m}−g(T)≥f(S)+dG−S(T)−|T|−g(T)≥(a+Δ)|S|+d1|T|−|T|−(b−Δ)|T|=(a+Δ)|S|−(b−Δ−d1+1)|T|≥(a+Δ)((i−1)(b−Δ)(b+2)+1a+Δ+1−d1)−(b−Δ−d1+1)(i−1)(b+2)=(d1−1)((i−1)(b+2)−(a+Δ))+1≥(d1−1)((b+2)−(a+Δ))+1>(d1−1)+1=d1≥2≥ε(S,T),$

Therefore, we infer that |T| ≥ (i − 1)(b + 2) + 1 in other cases.

The next lemma shows that the desired independent subset exists in T.

#### Lemma 2

In the previous setting, there exists an independent subset {x1, x2, · · · , xi}⊆ T.

Proof. If dGS(x) = 1 for any x ∈ T, then in terms of Lemma 1, we have |T| ≥ (i − 1)(b + 2). In light of b ≥ 2 and dGS(x) = 1 for any x ∈ T, we determine that dGS(x) ≤ b−1 for any x ∈ T. Combining this with |T| ≥ (i − 1)(b + 2) = b(i−1)+2(i−1) ≥ b(i−1)+2, we conclude that there exists an independent subset {x1, x2, · · · , xπ}⊆ T for π = i.

In other cases, it holds that |T| ≥ (i − 1)(b + 2) + 1 by means of Lemma 1. It is clear that dGS(x) ≤ dHS(x) + 1 ≤ g(x) + 1 ≤ bΔ +1 ≤ b + 1 for any x ∈ T. Thus, we can find an independent subset, {x1, x2, · · · , xπ}⊆ T for π = i.

The proof of Lemma 2 is completed.

By lemma 2 and the condition of Theorem 3, we have

$(b−Δ)n+2a+b+i≤|NG(x1)∪NG(x2)∪⋯∪NG(xi)|≤|S|+∑j=1idj$

and

$|S| ≥ (b−Δ)n+2a+b+i−∑j=1idj.$(4)

The next lemma presents the lower bound of di.

#### Lemma 3

di ≥ 2.

Proof. Suppose that di = 0 or di = 1. In terms of (4) and |S| + |T|n, we ensure that

$f(S)+dH−S(T)−g(T)≥f(S)−g(T)≥(a+Δ)|S|−(b−Δ)|T|≥(a+Δ)|S|−(b−Δ)(n−|S|)=(a+b)|S|−(b−Δ)n≥(a+b)((b−Δ)n+2a+b+i−∑j=1idj)−(b−Δ)n≥(a+b)(b−Δ)n+2a+b−(b−Δ)n=2≥ε(S,T),$

which contradicts (1). Hence we get di ̸∈ {0, 1}. It is easy to check that

$|NT[xj]|−|NT[xj]∩(∪z=1j−1NT[xz])|≥ 1, j=2, 3,⋯, i−1,$(5)$|∪z=1jNT[xz]| ≤ ∑z=1j|NT[xz]|≤∑z=1j(dG−S(xz)+1)=∑z=1j(dz+1), j=1, 2,⋯,i.$(6)

and

$|T|−|∪j=1iNT[xj]| ≥ 1.$(7)

It follows from (1), (2), (5), (6), n|S| + |T|, Lemma 3 and dibΔ + 1 that

$1≥ε(S,T)−1≥f(S)+dH−S(T)−g(T)≥f(S)+dG−S(T)−min{|T|,2m}−g(T)≥f(S)+dG−S(T)−g(T)−2m≥(a+Δ)|S|−(b−Δ)|T|+d1|NT[x1]|+d2(|NT[x2]|−|NT[x2]∩NT[x1]|)+⋯+di−1(|NT[xi−1]|−|NT[xi−1]∩(∪j=1i−2NT[xj])|)+di(|T|−|∪j=1i−1NT[xj])||)−2m$$≥(a+Δ)|S|−(b−Δ)|T|+d1|NT[x1]|+d2(|NT[x2]|−|NT[x2]∩NT[x1]|)+⋯+di−1(|NT[xi−1]|−|NT[xi−1]∩(∪j=1i−2NT[xj])|)+(di−1)(|T|−|∪j=1i−1NT[xj])||)−2m+1≥(a+Δ)|S|+(d1−di+1)|NT[x1]|+∑j=2i−1dj−(b−Δ+1−di)|T|−(di−1)∑j=2i−1|NT[xj]|−2m+1≥(a+Δ)|S|+(d1−di)(d1+1)+1+∑j=2i−1dj−(b−Δ+1−di)|T|−(di−1)∑j=2i−1(dj+1)−2m+1=(a+Δ)|S|+d1(d1−1)+∑j=1i−1dj−2m+1−(di−1)∑j=1i−1(dj+1)−(b−Δ+1−di)|T|≥(a+Δ)|S|+d1(d1−1)+∑j=1i−1dj−2m+1−(di−1)∑j=1i−1(dj+1)−(b−Δ+1−di)(n−|S|)=(a+b+1−di)|S|+d1(d1−1)+∑j=1i−1dj−2m−(di−1)∑j=1i−1(dj+1)−(b−Δ+1−di)n+1,$

which implies

$(a+b+1−di)|S|+d1(d1−1)+∑j=1i−1dj$(8)$−(di−1)∑j=1i−1(dj+1)−(b−Δ+1−di)n−2m≤0.$

By means of (4), (8), Lemma 3, i ≥ 2, d1d2 ≤ ··· ≤ dibΔ + 1 and $n\text{\hspace{0.17em}}\text{\hspace{0.17em}}\ge \text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{\left(a+b\right)\left(i\left(a+b+1\right)+2m-2\right)+2}{a+\Delta },$we have

$0≥(a+b+1−di)|S|+d1(d1−1)+∑j=1i−1dj−(di−1)∑j=1i−1(dj+1)−(b−Δ+1−di)n−2m≥(a+b+1−di)((b−Δ)n+2a+b+i−∑j=1idj)−(di−2)∑j=1i−1dj−(di−1)(i−1)−n(b−Δ+1−di)−2m≥(a+b+1−di)((b−Δ)n+2a+b+i−idi)−(di−2)di(i−1)−(di−1)(i−1)−n(b−Δ+1−di)−2m=(di−1)((a+Δ)n−2a+b−i(a+b+1)+di)−2m+i+1≥(di−1)((a+Δ)n−2a+b−i(a+b+1)+2)−2m+i+1≥(di−1)((i(a+b+1)+2m−2)−i(a+b+1)+2)−2m+i+1=2m(di−2)+i+1≥3,$

Therefore, the desired theorem is proved.

## 3 Sharpness

In this section, we aim to show that the independent set neighborhood union condition |NG(x1)∪NG(x2)· · · ${N}_{G}\left({x}_{i}\right)|\text{\hspace{0.17em}}\text{\hspace{0.17em}}\ge \text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{\left(b-\Delta \right)n+2}{a+b}+i$in Theorem 3 is tight, i.e., we can’t replace $\frac{\left(b-\Delta \right)n+2}{a+b}+i$by $\frac{\left(b-\Delta \right)n+2}{a+b}+i-1.$

Let m ≥ 1, Δ ≥ 0, i ≥ 2 and 2 ≤ a = bΔ be integers and p is a positive integer which is assumed to be large enough. Let G = K2pat (pbt)K2. Here two non-negative integer functions g and f are defined by g(x) = a and f (x) = b = a + Δ for each x ∈ V(G). We ensure that $n=2pt\left(a+b\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\ge \text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{\left(a+b\right)\left(i\left(a+b+1\right)+2m-2\right)+2}{a+\Delta },$$\delta \left(G\right)=2pat+1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\ge \text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{\left(i-1\right)\left(b-\Delta \right)\left(b+2\right)+1}{a+\Delta }+1$and

$(b−Δ)n+2a+b+i−1< |NG(x1)∪NG(x2)∪⋯∪NG(xi)|$$=2pat+i=ana+b+i=(b−Δ)na+b+i<(b−Δ)n+2a+b+i$

for any independent subset {x1, x2, · · · , xi}⊆ V(G). Set $S=V\left({K}_{2pat}\right)$and T = V((pbt)K2). We get |S| = 2pat and |T| = apbt. Let m = 2pbt. For a m-matching M = (pbt)K2 ⊂ G, let H = GM. We obtain dHS(T) = 0 and ε(S, T) = 2. Hence, we infer

$f(S)+dH−S(T)−g(T)=f(S)−g(T)=b(2pat)−a(2pbt)=0<2=ε(S, T).$

From Theorem 4, we know that H doesn’t have a fractional (g, f )-factor containing a given edge e ∈ E (H), i.e., G doesn’t have a fractional (g, f )-factor containing e, and exclude M. That is to say, the independent set neighborhood union condition $|{N}_{G}\left({x}_{1}\right)\cup {N}_{G}\left({x}_{2}\right)\cup \cdots \cup {N}_{G}\left({x}_{i}\right)|\text{\hspace{0.17em}}\text{\hspace{0.17em}}\ge \text{\hspace{0.17em}}\text{\hspace{0.17em}}\frac{\left(b-\Delta \right)n+2}{a+b}+i$in Theorem 3 is best in some sense.

## 4 Conclusion

The graph model is the most commonly used framework in computer networks. By representing the network

as a graph, the corresponding network problem can be transformed into a graph problem, and the knowledge of graph theory can be used to analyze and solve the corresponding graph problems. This note focuses on the data transmission problem in the network, and uses the fractional factor theory to analyze the feasibility of data transmission in the network under certain conditions. The independent set neighborhood union condition reflects the basic organizational structure of the network and is an important parameter for network designing. We present an independent set neighborhood union condition for a graph admits including a fractional (g, f )-factor containing given edge e and excluding a m-matching. This result indicates that under the condition where m station doesn’t intersect channels blocking or damaging, a certain range of data can still be transmitted between stations, and the route can pass through a specified channel. Furthermore, the presented conclusion has important guiding significance for the scientists in the network designing stage of data transmission networks. From a theoretical point of view, the independent set neighborhood union bound obtained in this note is tight.

## Acknowledgement

We thank the reviewers for their insightful comments in the improvement of the paper. The work has been partially supported by a postdoctoral research grant in Jiangsu province (1701128B) and a Postdoctoral Research Grant of China (2017M621690).

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Accepted: 2018-11-23

Published Online: 2018-12-31

Conflict of InterestConflict of Interests The authors hereby declare that there is no conflict of interests regarding the publication of this paper.

Citation Information: Open Physics, Volume 16, Issue 1, Pages 889–895, ISSN (Online) 2391-5471,

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A tool for performing quantum many-body simulations based on dynamical mean-field theory. In addition to predefined models, one can construct and solve an ab-initio tight-binding model by using wannier 90 or RESPACK. We provide a post-processing tool for computing physical quantities such as the density of state and the momentum resolved spectral function. DCore depends on external libraries such as TRIQS and ALPSCore.

## Homepage

MateriApps: https://ma.issp.u-tokyo.ac.jp/en/app/1004

3.3.1 (2022/2/1)

## How to use DCore on the ISSP supercomputer

• The directory where DCore is installed.

/home/issp/materiapps/dcore/

• The directory where the execution file of DCore is installed.

/home/issp/materiapps/dcore-3.3.1-1/bin/

In this folder, dcore, dcore_check, dcore_post, dcore_pre are located.

(*) This binary was built using MPT. If you are using intelMPI instead of the default (MPT) setting, you need to switch to MPT with the module command. For more information on build options, please refer to

$less /home/issp/materiapps/dcore/dcore-2.0.2-1.log . • The directory where sample scripts and input files are stored. Sample scripts： /home/issp/materiapps/triqs/sample_jobscript/dcore.sh Input files：/home/issp/materiapps/dcore/dcore-2.0.2-1/examples • How to run DCore (ex. Calculation of self-energy for single-band 2D Hubbard model) 1. Preparing the computing environments $ source /home/issp/materiapps/dcore/dcorevars.sh

This will pass the PATH to the binary files of the latest version of Core. It also stores the path to the DCore installation directory in the environment variable DCORE_ROOT.

2. Preparing  input files
$cp -rf /home/issp/materiapps/dcore/dcore-2.0.2-1/examples/square . 3. Submitting job A sample script is available in /home/issp/materiapps/triqs/sample_jobscript/. Copy the script to the current folder and submit the job. $ cd square && cp /home/issp/materiapps/triqs/sample_jobscript/dcore.sh .
\$ qsub dcore.sh
4.  Check the results

The result is output in square.out.h5. The calculation results can be checked with dcore_check and dcore_pre.


text:
# ComboStrap Metadata - Page Name

The page name is a short text composed of a couple of words (one or two) that describes a page.

This name will show up:

## How to set a name

By default, the value of the name is the last part of the path but you can overwrite it by setting a name property in the metadata manager

## Template

You can use the $name variable in a template. Example: • The template <template> The name of this page is: ''$name''
</template>

• The result:


text:
Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.

QUESTION

# What is the Gaussian function?

The basic Gaussian function is simply:

y=e^(-x^2)

where the normal distribution is a specific parameterization:

f(x | mu, sigma^2) = 1/sqrt(2 pi sigma^2) e^(-(x-mu)^2 /(2 sigma^2))

The basic Gaussian function is simply:

y=e^(-x^2)

We can parameterize is with some additional constants:

y = A e^(-b(x-c)^2)

If we want to use it for statistical purposes, we would want to make it into where:

c becomes the mean i.e. c implies bar x b becomes the reciprocal of half of the variance, i.e. b implies 1/(2sigma^2) and we choose A such that the integral of the function over all x is 1, i.e. A implies 1/sqrt(2 pi sigma^2)

The normal distribution function is then given by

f(x | mu, sigma^2) = 1/sqrt(2 pi sigma^2) e^(-(x-mu)^2 /(2 sigma^2))


text:
# QB/AstroGalileanMoons

< QB

• Quizbank now resides on MyOpenMath at https://www.myopenmath.com (although I hope Wikiversity can play an important role in helping students and teachers use these questions!)
• At the moment, most of the physics questions have already been transferred. To see them, join myopenmath.com as a student, and "enroll" in one or both of the following courses:
• Quizbank physics 1 (id 60675)
• Quizbank physics 2 (id 61712)
• Quizbank astronomy (id 63705)

The enrollment key for each course is 123. They are all is set to practice mode, giving students unlimited attempts at each question. Instructors can also print out copies of the quiz for classroom use. If you have any problems leave a message at user talk:Guy vandegrift.

See special:permalink/1863352 for a wikitext version of this quiz.

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\title{AstroGalileanMoons}
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Attribution for each question is documented in the Appendix}
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\question How does the density of a Galilean moon depend on its distance from Jupiter?  \ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863352}}}\fi
\begin{choices}
\choice all the moons have nearly the same density
\CorrectChoice the more dense moon is closer to Jupiter (always)
\choice the density of the moons is unknown
\choice the less dense moon is closer to Jupiter (always)
\choice the most dense moon is neither the closest nor the most distant
\end{choices}

\question How does the mass of a Galilean moon depend on its distance from the central body?  \ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863352}}}\fi
\begin{choices}
\choice the less massive moon is closer to Jupiter (always)
\choice the mass of the moons is unknown
\CorrectChoice the most massive moon is neither the closest nor the most distant
\choice the more massive moon is closer to Jupiter (always)
\choice all the moons have nearly the same mass
\end{choices}

\question Does Jupiter's moon Io have craters?   \ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863352}}}\fi
\begin{choices}
\choice no, the surface is too new
\choice yes, from impacts
\CorrectChoice yes, from volcanoes
\choice no, the surface is too old
\choice yes, about half from impacts and the others from volcanoes
\end{choices}

\question The mechanism that heats the cores of the Galilean moons is   \ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863352}}}\fi
\begin{choices}
\choice radiation from the Sun and from Jupiter
\choice tides from Jupiter
\choice radioactive decay of heavy elements
\CorrectChoice tides from the other moons and Jupiter
\end{choices}

\question Immediately after publication of Newton's laws of physics (Principia), it was possible to "calculate" the mass of Jupiter.  What important caveat applied to this calculation?   \ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863352}}}\fi
\begin{choices}
\choice The different moons yielded slightly different values for the mass of Jupiter.
\choice The different moons yielded vastly different values for the mass of Jupiter.
\CorrectChoice Only the mass of Jupiter relative to that of the Sun could be determined.
\choice tides from the other moons and Jupiter.
\choice They needed to wait over a decade for Jupiter to make approximately one revolution around the Sun.
\end{choices}

\question Ganymede, Europa, and Io have ratios in \_\_\_\_\_\_\_\_\_\_ that are 1:2:4. \ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863352}}}\fi
\begin{choices}
\choice orbital period
\choice Argon isotope abundance
\CorrectChoice Two other answers are correct (making this the only true answer).
\choice density
\choice rotational period
\end{choices}

\question Which of Jupiter's moons has an anhydrous core? \ifkey\endnote{ placed in Public Domain by Guy Vandegrift: {\url{https://en.wikiversity.org/wiki/special:permalink/1863352}}}\fi
\begin{choices}
\choice Europa
\choice Ganymede
\choice Two other answers are correct (making this the only true answer).
\CorrectChoice Io
\choice Ganymede
\end{choices}

\end{questions}
\newpage


text:
# Binary cellular automata and computable functions

1) Let's consider a set of all binary cellular automata on a finite (and finite dimensional) rectangular* grid.

• The state of a cell in the next generation is determined by the state of the cell itself and/or a finite number of other (specified) cells during a finite number of previous steps by a finite logical expression (i.e., informally, there is a 'finite' deterministic rule).
• The appropriate boundary conditions are introduced, or more generally, the rules for each cell can only reference the existing cells.
• The rules for every cell stay the same for each generation (so the CA is deterministic, otherwise we would have to introduce an additional rule for the changing of rules).

We consider the binary values (states) of all the cells and an integer number $N$ of generations as input (a finte string of integers).

We consider the sum of values of the cells in the generation $N$ as the output.

Would this set of cellular automata be equivalent to the set of all computable functions $f(X)$?

Here $X$ is the input string of integers.

Can we narrow the definition above and still obtain the set of all computable functions? How?

Now for the more complicated case of cellular automata on an infinite grid (beloved by Stephen Wolfram).

• There is an infinite (rectangular, finite dimensional) grid with almost all the cells initially in the $0$ state.
• The input is given by the binary values of a finite number of cells in a finite region of the grid and the number of the generation $N$. The output is the sum of values of all cells in the infinite grid in the generation $N$.
• The state of a cell in the next generation is determined by the state of the cell itself and/or a finite number of other cells in a finite neighborhood (meaning they are separated by a finite taxicab distance) during a finite number of previous steps.
• If all the 'reference cells' of a given cell have the state $0$ in all the 'reference generations', then the cell's state is unchanged. (In this way we deal with the infinite size of the grid, so we really only have to 'track' a finite number of cells in any generation with finite $N$).

Would this set of cellular automata be equivalent to all computable functions?

* it could also be another regular grid, like hexagonal on the plane but let's take rectangular, since it generalizes for any dimension in Euclidean space, and the choice of grid doesn't affect the argument here anyway.

• In the finite-grid case, why aren't the CAs just plain deterministic finite-state automata? (If I read correctly, each cell has one bit of state.) Dec 17, 2016 at 20:53

In the finite case: no, it's definitely not equivalent to all computable functions. There's only finitely many possible cells, so only finitely many possible outputs; let $K$ be the largest possible output. The constant function $f(x) = K + 1$ is clearly computable, but can't even be expressed under these constraints.
In the general case: also no. Construct a function $f$ as follows: enumerate all possible cellular automaton rule sets $C_0, C_1, C_2, \ldots$. Given input $x$ in the format specified above (binary values in a finite region of the grid, together with $N$), run the $x$th cellular automaton ($C_x$) for $N$ stages, and let $M$ be the resulting output. Let $f(x) = 0$ if $M \neq 0$, and $f(x) = 1$ if $M = 0$. This is a computable function, because we can run the automaton computably; but it can't be computed by a cellular automaton, because if it were computed by $C_i$ for some $i$, then $f(i)$ would be the output of $C_i$, but we've constructed $f$ so that this is not the case.
• @YuriyS Oh, I assumed you meant a fixed finite board. It's still too limited - if each function is limited to a single board size, then even $f(x) = x$ can't be expressed. If a function is allowed to change board size depending on input, then you're effectively in the infinite-board case. Dec 17, 2016 at 21:18


text:
# Seminar at SMU Delhi

March 11, 2014 (Tuesday) , 3:30 PM at Webinar
Speaker: Anirban Bose, Indian Statistical Institute, Delhi
Title: Some conjugacy problems in algebraic groups
Abstract of Talk
In this talk we discuss two problems related to the study of algebraic groups and Lie groups. \vspace*{2mm} \noindent Problem 1: Let $G$ be a group. Consider the action of $G$ on itself by conjugation. For $g\in G$, let $\mathcal{O}_g$ denote the orbit of $g$ under this action. Two elements $x,y\in G$ are said to have the same orbit type if $\mathcal{O}_x$ and $\mathcal{O}_y$ are isomorphic as $G$-sets. We describe a method of computing the number of orbit types of simply connected algebraic groups over an algebraically closed field and that of compact simply connected Lie groups. \vspace{2mm} \noindent Problem 2: Let $G$ be a group (resp. an algebraic group defined over a field $k$). For the latter case, let $G(k)$ denote the group $k$-rational points of $G$. An element $g \in G$ (resp. $G(k)$) is called real (resp. $k$-real) if there exists $h\in G$ (resp. $G(k)$) such that $hgh^{-1}=g^{-1}$. An element $g\in G$ (resp. $G(k)$) is said to be strongly real (resp. strongly $k$-real) if there exists $h\in G$ (resp. $G(k)$) such that $hgh^{-1}=g^{-1}$ and $h^2=1$. We prove that in a compact connected Lie group of type $F_4$, every element is strongly real. We also describe the structure of $k$-real elements in algebraic groups of type $F_4$ defined over a field $k$.


text:
Acta Chimica Sinica ›› 2000, Vol. 58 ›› Issue (12): 1499-1503.

Original Articles

### 改进的相对论量子化学计算ZORA方法

1. 北京大学化学与分子工程学院;北京大学稀土材料化学及应用国家重点实验室. 北京
• 发布日期:2000-12-15

### An improved ZORA method for relativistic quantum chemical calculations

Wang Fan;Li Lemin

1. .
• Published:2000-12-15

An improved ZORA 9Zeroth-Order Regular Approximation to the Dirac Equation) method is presented. The related eigen equation reads [σ· p(c^2/2c^2-V~0)σ·p+V(r)]ψ=εψ. Where V~0 is a proper space-limited potential function; V~0(r=~A∑V~0^A(r~A)， r~A=|r-R~A|, V~0^A(r~A) =V^A(r~A){1+exp[α(r~A-r~0^A]}^-^1. Where A denotes any one of the constitutional atoms of a molecule, V^A(r~A) is the potential of atom A in its free state. r~A=|r-R~A|, R~A is the position vector of atom A. α and r~0^A are parameters to be fixed. the improved ZORA method possesses all the advantages of the ZORA method, while the error due to gauge dependence is reduced considerably. The calculations by use of the improved ZORA method on several molecules containing heavy elements show that with suitably selected parameters α and r~0^A the gauge dependence errors in the calculation of bond lengths and bonding energies are reduced to be comparable with those of the ESA or Scaled method presented by Lenthe et al. whereas the related computation is simpler.

CLC Number:


text:
# Derivation of Backward Kolmogorov Equation

I'm following Kallianpur-Gopinath's textbook "Stochastic analysis and diffusion processes" to study Kolmogorov equations and I got stuck in a step of the derivation of the backward equation.

In particular the authors (guess it's a pretty standard construction actually) start from the solution of a d-dimensional SDE

$$dX_t = b(t,X_t)dt + \sigma(t,X_t)dB_t$$

and, after computing the Taylor expansion of the probability transition function, arrive to write something like

$$-\big(p(s,x;t,y) -p(s-h,x;t,y)\big) = \sum_{i=1}^d \frac{\partial}{\partial x_i}p(s,x;t,y) \int_{\mathbb{R}^d}(z_i-x_i)p(s-h,x;s,z)dz + \\ \frac{1}{2} \sum_{i=1}^d\sum_{j=1}^d \frac{\partial^2}{\partial x_i \partial x_j}p(s,x;t,y) \int_{\mathbb{R}^d}(z_i-x_i)(z_j-x_j)p(s-h,x;s,z)dz +\\ \int_{\mathbb{R}^d} o\big(|z-x|^3\big) p(s-h,x;s,z)dz\\$$

By dividing by $h$ and letting $h \to 0$ we should get the backward equation

$$-\frac{ \partial p(s,x;t,y) }{ \partial s } = b(s,x) \cdot \nabla p(s,x;t,y) + \frac{1}{2} (\sigma(s,x), \nabla^2 p(s,x;t,y) \sigma(s,x) )$$

what I don't understand is the step

$$\lim_{h\to 0} \frac{1}{h} \int_{\mathbb{R}^d} (z_i-x_i) p(s-h,x;s,z)dz \stackrel{?}{=} b_i(s,x)$$

I understand this should be related with the fact that the solutions of SDE are diffusion processes, but the definition of diffusion process requires

$$\lim_{h\to 0} \frac{1}{h} \int_{U_x} (z_i-x_i) p(s-h,x;s,z)dz = b_i(s,x)$$

for any bounded neighborhood $U_x$ of $x$, but instead we are considering an integral over $\mathbb{R}^d$. Even if I split the integral in two, one over a bounded set and one over its complement I don't see how to prove that the second goes to $0$. Any help is appreciated.

EDIT:

Quoting from the same book:

A Markov process $X_t$ with transition function $p(s,x;t,A)$ is called a diffusion process if it has continuous paths and if there exists an $\mathbb{R}^d$-valued function $b(s,x)$ and a $d \times d$-matrix-valued function $a(t,x)$ s.t. for every bounded open neighborhood $U_x$ of $x$

• $\lim_{h \downarrow 0} \frac{1}{h} \int_{U_x^c} p(t,x;t+h,dy) = 0$

• $\lim_{h \downarrow 0} \frac{1}{h} \int_{U_x} (y_i - x_i) p(t,x;t+h,dy) = b_i(t,x) \ \ \ \ i \in \{1...d\}$

• $\lim_{h \downarrow 0} \frac{1}{h} \int_{U_x} (y_i - x_i)(y_j - x_j) p(t,x;t+h,dy) = a_{i,j}(t,x) \ \ \ \ i,j \in \{1...d\}$

and immediately after there is a theorem that states that the solution of the SDE written at the top of this post, under the usual hypotheses of Lipschitzianity of $b$ and $\sigma$, is a diffusion process with drift $b$ and diffusion coefficient $\sigma \sigma^*$.

• Could you please add the definition of a diffusion process to your question? There are several ones and it is hard to answer your question without knowing the "proper" definition.
– saz
Jun 15, 2015 at 15:56
• @saz Sorry, didn't know there are different definitions for diffusions. I edited the post with the definition written on the book, thanks! Jun 15, 2015 at 20:13
• Because of the first condition $\lim_{h \downarrow 0} \frac{1}{h} \int_{U_x^c} p(t,x;t+h,dy) = 0$, the integration outside $U_x$ is 0. Jan 4 at 22:30


text:
# Reinforcement learning

Reinforcement learning

## What is Reinforcement Learning

"Reinforcement learning (RL) is learning from interaction with an environment, from the consequences of action, rather than from explicit teaching." -- Rich Sutton

## Evaluative Feedback (Chapter 2)

### Softmax Action Selection

Softmax action selection is the way to maintain exploration and exploitation balance. The softmax policy will choose action a on period t with probability: ${\displaystyle {\frac {\exp({\frac {Q_{t}(a)}{\tau }})}{\sum _{b=1}^{n}\exp({\frac {Q_{t}(b)}{\tau }})}}}$

## Related Terms

• Machine Learning