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Engineering » Control Engineering » "Quality Control and Assurance - An Ancient Greek Term Re-Mastered", book edited by Leo D. Kounis, ISBN 978-953-51-2922-6, Print ISBN 978-953-51-2921-9, Published: February 22, 2017 under CC BY 3.0 license. © The Author(s).

The Use of Control Charts in the Study of Bitcoin’s Price Variability

By Beata Szetela
DOI: 10.5772/66360

Article top

Overview

Figure 1. Control chart scheme.

Figure 2. xbar-s chart BTC/USD 2010-2016.

Figure 3. xbar-s chart BTC/USD 2010-2012.

Figure 4. MR chart BTC/USD 2010-2012.

Figure 5. CUSUM BTC/USD 2010-2012.

Figure 6. xbar-s chart BTC/USD 2013.

Figure 7. MR chart BTC/USD 2013.

Figure 8. xbar-s chart BTC/USD 2014-2016.

Figure 9. CUSUM chart BTC/USD 2014-2016.

Figure 10. xbar-s chart EUR/USD 2010-2016.

Figure 11. CUSUM chart EUR/USD 2010-2016.

The Use of Control Charts in the Study of Bitcoin’s Price Variability

Beata Szetela
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Abstract

The focus of this research is bitcoin’s variability and its comparison with the variability of the EURO/USD exchange rate. Virtual currencies have been evolving in a dynamic way in the last few years. Under 600 different virtual currencies, the most successful was bitcoin. Its adherents saw in it an alternative to the traditional means of payments allowing the performance of real-time transactions at low costs. The accessibility, where no financial infrastructure is ensured or where either limited or no international agreements exist between financial and banking institutions was also an advantage. The opponents perceived this as a temporary curiosity with no future. Time confirmed that bitcoin has gained on popularity and the exchange rate to the main currencies rose in a dynamic way. The analysts, however, underline that the bitcoin is too volatile and unpredictable, so it cannot compete against the main currencies. The aim of this research is to compare the bitcoin (BTC) to US Dollar (USD) exchange rate and Euro to USD exchange rate volatility using control charts. The results have shown that BTC/USD exchange rate volatility is strongly affected by unexpected price jumps during the period (2010–2016), an act that significantly distinguishes it from more stable and predictable EUR/USD exchange rate variability.

Keywords: bitcoin, virtual currency, control chart, volatility, exchange rate, BTC/USD, EUR/USD

1. Introduction

Bitcoin is a virtual currency and a quite new phenomenon. It was created in 2008 by Satoshi Nakamoto, who published an article "Bitcoin: A Peer-to-Peer Electronic Cash System” in 2008, in which he described a concept of virtual, decentralized and independent means of payment, which is based on a cryptographic blockchain protocol [1]. His main idea was to build a currency based not on trust but on an algorithm, which cannot be influenced or manipulated. It was thought to be independent of any legal or governmental body. After the first release of bitcoin, by generating the ‘block genesis’ in 2009, this currency was gaining rapidly in popularity.

As in September 2015 ca. 667 crypto currencies were established.1 Among them, bitcoin is considered to be the most popular and the most widely used. According to data published on bitinfocharts.com, bitcoin has the highest market capitalization of more than $7 billion, representing 89% of the total capitalization of all cryptocurrency. Further down are the Ethereum$574 million (7.1%), litecoin $179 million (2.2%) and Dash$39 million (0.5%). Data published by blockchain.info at the beginning of 2012 indicated that bitcoin had ca. 400 users. This number increased by ca. 970 k at the beginning of 2014 and reached ca. 8.5 m in September 2016 [2].

Within 4 years since its creation, the European Central Bank (ECB) and other financial institutions still have not come to a final conclusion, as to the classification of bitcoin and other cryptocurrencies. They have not recognized virtual currency as money or as a commodity. As such, the current legislation does not regulate events resulting thereof. The official definition of a ‘virtual currency’ was set up by a European Central Bank in 2012 for the first time, according to which ‘a virtual currency is a type of unregulated, digital money, which is issued and usually controlled by its developers and used and accepted among the members of a specific virtual community’ [3]. This definition associated virtual currency with a virtual world in a strict sense and the connection to the real economy was nearly neglected. Nowadays, bitcoin is similar to other virtual currencies that can be traded or exchanged for real money and goods and is accepted by many merchants all over the world. That is why in 2016, the International Monetary Fund (IMF) has extended the definition specifying, that ‘virtual currencies can be obtained, stored, accessed and transacted electronically and can be used for a variety of purposes, as long as the transacting parties agree to use them’ [4].

According to the IMF, the impact of virtual currencies on the real economy and the financial system is limited. It is, however, possible that with the increase of trading volume and acceptability, virtual currencies can become a serious threat to the financial and banking sector. One of the obstacles to the development of bitcoin named by IMF is its unstable variability.

The purpose of this study is to assess the validity of whether the dollar (USD) is more stable than the bitcoin (BTC) using xbar-s and CUSUM control charts. Depending on the outcome thereof, it will evaluate the concerns of sceptics pertaining to bitcoin and its further development and acceptance in the long term. If it turns out that the volatility of bitcoin does not deviate significantly from the volatility of dollar, then the fears of some financial institutions might appear to be valid.

2. Literature review

Bitcoin is gaining much more popularity not only among financiers but also among scientists. However, a limited number of scientific papers pertaining to cryptocurrency have been published. Given the above, the proposed content will be an important contribution to studies of both control cards and bitcoin. Current scientific achievements can be divided into four main fields of interest.

• A general and theoretical background concerning the origin, formation and characteristics of bitcoin, e.g. [59].

• A number of reports focusing mainly on issues relating to acquisition (mining), trade and broadly understood security, e.g. [1015].

• The third large group of articles concerns the regulatory environment, including tax-specific policies and possible solutions that regulate the functioning of cryptocurrency in the financial area, e.g. [1618]. This group also includes various types of reports, publications or banks, financial institutions and government statements on bitcoin, i.e. European Central Bank [1921] Congressional Research Service acting on the needs of the US Congress [22, 23], Canadian Central Bank [2426].

• The last group of papers focuses on the application of quantitative methods in the study of Bitcoin.

Generalized autoregressive conditional heteroscedasticity models (GARCHs) were applied to investigate similarities between bitcoin and both US dollar and gold [27, 28]. It was found that bitcoin-like other cryptocurrency tend to generate bubbles and that they do not have fundamental value [29]. Moreover, bitcoin fluctuations are characterized by sudden jumps and extreme pricing, which is characteristic for immature markets [30]. Autoregressive moving average and log-periodic power law models were applied to show that the price of bitcoin depends on the Chicago Board Options Exchange Index Volatility Index, which is indicative of speculation potential [31]. Other scientists argue that fluctuations in the price of Bitcoin are positively correlated with the amount of BTC users and are determined by the shocks of unknown sources of origin. The latter have an endogenous character and are not generated by the impact of specific variables, such as indexes S&P 500, gold rate against the US dollar or (XAU) and the Shanghai stock exchange index (SSE) [32]. According to Bouoiyour et al. [33], bitcoin’s price fluctuations are best characterized by a generalized hyperbolic distribution.

The variability of bitcoin against the dollar in 2015 significantly decreased compared with the preceding period. The authors also claimed that bitcoin can be characterized by excessive asymmetry and the price is prone to the negative shocks negative than positive once.

3. Methodology

Statistical process control (SPC) has found its application in many scientific areas. One of the tools, which are used by the SPC, is control charts (see Figure 1 ). A control chart (CC) is a graphical representation of a process. It presents an average value of the quality characteristics reflected on the chart by a central line (CL). Auxiliary lines, called upper control limit (UCL) and lower control limit (LCL), are used for the presentation of deviations from the mean of the process. Control limits are usually set as three times the standard deviation (3-sigma (σ) limits). The main idea behind control charts is to monitor an underlying process. If the observations fluctuate in a natural way within set advance control limits and if they do not reveal any specific patterns, then it is said that the process is under control. If, however, the monitored process breaks the established control limits, then it is understood that the process is out of control and specific actions should be launched to return the process under control. For further details considering control charts, please refer to Ref. [34].

Figure 1.

Control chart scheme.

SPC uses different types of charts, depending on the type of data used. For the continuous data, the following charts dedicated to variables are used:

• xbar-s charts (controlling the mean and standard deviation of a process),

• xbar-r chart (calculating the mean and the range of a process),

• charts for moving ranges, etc.

For data based on countcharts for attributes are applied, e.g. np chart, p chart, c chart, u chart, etc.

For the purpose of this research, the following control charts will be applied, namely an xbar-s chart and a CUSUM with the moving range chart.

3.1. Xbar-s chart

Xbar-s charts are used to monitor the variation and mean of the process. If the sample size (n) is not constant and is relatively large (n > 10), in such a case xbar-s charts are preferable against xbar-R chart.

For the unknown parameters of the s-bar chart and the variable sample size, the central line is defined as an average standard deviation for all samples (Eq. (1))

 s¯=∑i=1m(ni−1)si2∑i=1mni−m (1)

where m is the number of samples, n i is the individual sample size and s i is an individual value of standard deviation for each sample defined as s=i=1n(xix¯)2n1 .

The upper (Eq. (2)) and lower control limit (Eq. (3)), which define the boundaries for the (3σ)-three-sigma control limits are calculated based on the following formulae:

 UCL=(1+3c41−c42)s¯ (2)
 LCL=(1−3c41−c42)s¯ (3)

where c 4 is a constant.

Similarly, the control limits are determined for the xbar chart, which accompanies the s-chart. The central line is calculated as an average value of the individual averages (Eq. (4))

 CL=x¯¯=∑i=1mnix¯i∑i=1mni (4)

The three-sigma control limit is determined by the upper control limit (Eq. (5)) and the lower control limit (Eq. (6)) in the form:

 UCL=x¯¯+3s¯c4n (5)
 UCL=x¯¯−3s¯c4n (6)

It is assumed that the underlying process is under control if it varies between defined control limits. The breach of any of the control limits points at the process being out of control.

3.2. CUSUM and MR chart

Moving range chart enables to plot the sum of ranges of the adjacent pairs of observation within the investigated period. The central line (see Eq. (7)) is calculated as an average range of k-samples and the control limits (see Eqs. (8) and (9)) are set as m-times deviation from the average process range.

 R¯=∑i=1kRik (7)
 LCL=R¯−md3σ^ (8)
 LCL=R¯+md3σ^ (9)

where R i is a range in sample i, k is the number of samples, m is a multiplier chosen to establish control limits, usually set to 3 and d 3 is a constant and σ^ is an estimated variance of a process.

CUSUM control charts plot the cumulative sum of deviation from the assumed target value (see Eq. (10)).

 Ci=∑j=1i(x¯j−μ0) (10)

where C i is a cumulative sum, x¯j is mean of a process in sample j, average and μ 0 is target value.

If the process is under control, then a cumulative sum (C i ) follows a random walk process with mean equals 0 [35]. It is assumed that the process is out of control, if the average values drift from the target value. If the values move in the positive direction, then the upper cumulative sum is written as in Eq. (11).

If, however, they move into the negative values, then the lower cumulative sum is defined as in Eq. (12). Finally, if the process exceeds the decision interval, which is contained between the positive and negative sum, then it is assumed, that the process is out of control:

 CI+=max(0,X¯i−(μ0+K)+Ci−1+) (11)
 CI−=max(0,(μ0+K)−X¯i+Ci−1−) (12)

where k is a target value, C0+=C0=0 , C i is cumulative sum for sample i.

4. Results

4.1. BTC/USD

The main goal of this research was to compare the variability of two exchange rates: bitcoin to US Dollar (BTC/USD) and Euro to US Dollar (EUR/USD). The average exchange rates for the quarterly data between 2010 and 2016 will be taken into consideration. The final result of the appliance of the xbar-s chart for BTC/USD is presented in Figure 2 .

Figure 2.

xbar-s chart BTC/USD 2010-2016.

It is visible that the process is out of control and the layout of the chart is strongly affected by the significant volatility exchange rate increase in 2013. In the period before, it was a long run of very low prices. After the peak in 2013, the level of the exchange rate has never reached a comparable value. Taking the above into consideration, the whole investigated period should be divided into consistent and disjoint periods, i.e. the covering time before the positive price shock, namely the year 2013 and the period after 2013. An attempt to analyse the whole period can be misleading due to the faultily estimated control lines understood as a process average and standard deviation.

The first studied period was the initial phase of the development of bitcoin. Within that time, the exchange rate has changed significantly, starting from 0.08 USD for 1 BTC, reaching 13.51 USD for 1 BTC at the end of 2012. The xbar-s chart ( Figure 3 ) has generated the CL at the level of 0.62. The layout of the chart suggests that the process being out of control in the period reaching April 2011, when the average volatility was significantly under the LCL equalling to 0.31.

Figure 3.

xbar-s chart BTC/USD 2010-2012.

This is justified, as within that time, the price was significantly lower than in other periods. Small changes in prices had almost no effect on volatility. The numbers for May and June have breached the UCL, which equals to 0.93. This peak was connected with strong price jumps, up to 18.50 USD for BTC. The other periods were relatively stable.

A permanent breach of control limits on both sides of CL may be observed, but the deviations are not essential. It is worth to mention that between the years 2010–2012, the graph may imply a pattern. The observed standard deviations tend to move in the same direction almost every 4 months. The extension to the bitcoin volatility analysis gives the MR chart ( Figure 4 ) and CUSUM chart for the standard deviation ( Figure 5 ). At the beginning of the investigated process, the exchange rate volatility was dropping constantly. Commencing in April 2011 it is starting to grow, in par with the price increase. After a strong peak in price, which has also a solid and positive effect on price volatility, the bitcoin faced a volatility decrease at the end of 2011, after which the process started to normalize. This phase lasted until the next shock at the end of 2012, where the volatility has started to grow again.

Figure 4.

MR chart BTC/USD 2010-2012.

Figure 5.

CUSUM BTC/USD 2010-2012.

In 2013, the BTC/USD sudden price jump was observed, which has affected the average price volatility strongly. Throughout the year 2013, the exchange rate was developing steadily (see Figure 6 ). The jump took place between October and November. In this period, exchange rate has risen from 155 to 870. The average price volatility for the year 2013 equals to 51.87. If only the first 10 months of the year were considered, then the CL would be at the level of 12.65.

Figure 6.

xbar-s chart BTC/USD 2013.

Moreover, the MR chart ( Figure 7 ) shows that within the period between January and October 2013 ranges have fluctuated at the zero line until the exchange rate jumps, which caused an increase of almost 150, thereby, the whole process is said to be significantly out of balance.

Figure 7.

MR chart BTC/USD 2013.

Bitcoin development during the period (2014–2016) was more stable compared to the previous years. The value for the central line in s-chart ( Figure 8 ) has declined to 28.4 compared with the year 2013. At the beginning and at the end of the investigated period the price fluctuations were observed. In January 2014, the exchange rate has reached the level of 649, which was the continuation of the price increase from the year 2013 and in 2016, when the price reached again the limit of 687 US Dollars for a Bitcoin.

Figure 8.

xbar-s chart BTC/USD 2014-2016.

The s-chart has produced warning signals concerning a high volatility between February and May 2014 and for June 2016 by breaching the UCL (45.25), as well as signals for low volatility between March and September 2015 by breaching the LCL (11.53). This downturn shift in price was also reflected by the CUSUM chart ( Figure 9 ).

Figure 9.

CUSUM chart BTC/USD 2014-2016.

These have caused a shift in a process, which was followed by the constant movement with the decreasing tendency of deviations from the process mean until the end of the considered period.

4.2. EUR/USD

The USD/EUR exchange rate volatility seems to be more stable within whole investigated period (see Figure 10 ) compared to the results for BTC/USD ( Figure 2 ). The CL generated by the s-chart was at the level of 0.012. The volatility during the years 2010 and 2011 passes the UCL. Global financial crisis has impacted EUR/USD exchange rates strongly. After the crisis hit Greece in 2009 it has moved on and inadvertently affected other European countries, e.g. Spain and Italy. This was the most significant and long-lasting process disruption signalled by the control chart. The other breaches, which appeared in 2014 and at the beginning of 2015, are very close to the LCL (= 0.0052) and UCL (= 0.02). The deviation from CL seems to be not substantial, especially considering the process standard deviation at the level of 0.002.

Figure 10.

xbar-s chart EUR/USD 2010-2016.

This development was also reflected by the CUSUM chart ( Figure 11 ), where mainly the above average values for the standard deviation were signalled in the year 2010 and the beginning of the year 2011. The rest of the process despite the visible downturn trend remained between the UCL (0.029) and LCL (−0.029).

Figure 11.

CUSUM chart EUR/USD 2010-2016.

The central line, which reflects the average standard deviation for the entire process equals 0.1272. If the time after 2013 was considered, then the average standard deviation would be equal to 0.1040, hence both results were at a comparable level.

The EUR/USD exchange rate volatility starting from June 2010 was in the downward trend, which ended in December 2014. The s-chart has produced warning signals for points beyond the control limits, which were set at a level of 0.02027 for the UCL and 0.00516 for the LCL, respectively. The first signals were produced for the period between August 2010 and October 2011. Strong fluctuations in this time were caused by weak economic data mainly from the United States. It is worth to mention that this was the period short after the economic crisis, when most of the world economies were unstable.

5. Conclusion and further work

Bitcoin, a virtual currency, seems to be a promising alternative to a traditional means of payment. According to a survey published by the IMF, bitcoin has many advantages like low transition costs. It offers the possibility to make transactions with countries with weak financial infrastructure and might contribute to transferring developed technologies and solutions to undeveloped countries. At this point, it is worth mentioning that the idea on which the bitcoin is based has a huge potential in many areas, such as banking, accounting, data gathering and transfer, etc. At the same time, it is not without flaws. Reports and surveys concerning bitcoin mention money laundering issues, low recognisability and lack of stability.

In this chapter, an attempt was made to compare the exchange rate volatility between EUR/USD and BTC/USD. The analysis has shown that the EUR/USD exchange rate volatility is much more stable compared to the BTC/USD exchange rate. In the entire investigated period, the average exchange rate volatility was at the level of 0.013. The first period after the world crisis, when the international economy was unstable and USA has published economic reports below market expectations, the exchange rate volatility has recorded an increase and charts have produced warning signals for the process being out-of-control. In the remaining period, the exchange rate volatility development did not behave in an unpredictable pattern. The downward trend is visible, but no significant shocks were observed. The lack of sudden fluctuations characterises mature economies.

BTC/USD exchange rate volatility is developing in a completely different way. Figure 2 shows three establishing phases of this virtual currency; the first one before 2013, when the price level and the overall recognition were nearly zero. The average volatility was equal to 0.6. This value was affected by the price increase from June 2011. In the year 2013, another strong price jump was visible, when the exchange rate has risen from 155 to 870. The third period under consideration was also susceptible to price shocks, namely at the beginning of 2014 and in June of 2016. This unexpected price increase has strongly affected the average exchange rate volatility of BTC/USD. What is positive, the declining tendency in volatility can observe.

In 2013, the average process volatility including outliers caused by price jumps was equal to 51.8, between 2014 and 2016 it has decreased to 28.4. The xbar-s chart and MR-chart for BTC/USD have showed that except for the above-mentioned price fluctuations the process was most of the time under control. It is worth noting at this point that the range between the upper and lower control limits for the bitcoin is broad, which was caused by the extreme price movements. Because of this lack of stability, it is difficult to model bitcoin behaviour. As such, an attempt to forecast its future behaviour based on its past values would be impossible.

The lack of BTC/USD exchange rate predictability and its excessive volatility causes that at least at this stage of development bitcoin cannot threaten the traditional and regarded as stable, currencies such as USD or EUR. It is also associated with a small recognisability and is still limited to a number of places where it can be exchanged or traded. The bitcoin’s founder Satoshi Nakamoto said that he is not sure if the bitcoin in this form will survive, but he is convinced that virtual currencies will exist in the future, in this form or in a different one, due to the increasing loss of confidence and trust among the business partners [36].

References

1 - Blockchain Waller Users. Available from: https://blockchain.info/charts/my-wallet-n-users?timespan=all# [Accessed: 2016.09.05]
2 - Nakamoto, S. http://nakamotoinstitute.org [Internet].2008. Available from: http://nakamotoinstitute.org/bitcoin.pdf [Accessed: 2016.08.09]
3 - European Central Bank. https://www.ecb.europa.eu [Internet]. October 2012. Available from: https://www.ecb.europa.eu/pub/pdf/other/virtualcurrencyschemes201210en.pdf [Accessed: 2016.08.09]
4 - Dong, He, Habermeier, K. F., Leckow,R. B., Haksar, V., Almeida,Y., Kashima, M., Kyriakos-Saad, N., Oura, H., Sedik, T. S., Stetsenko, N., Verdugo-Yepes,C. Virtual Currencies and Beyond: Initial Considerations . IMF Staff Discussion Note. 2016; 3.
5 - Dwyer, G., The economics of bitcoin and similar private digital currencies. Journal of Financial Stability, 2015, 17, pp. 81–91.
6 - Dopierała, Ł., Borodo, A. Meaning of the Bitcoin cryptographic currency as a medium of exchange. Contemporary Economy Electronic Scientific Journal, 2014, 5(2), pp. 1–12.
7 - Liu, J., Kauffman, R., Ma, D. Competition, cooperation and regulation: Understanding the evolution of the mobile payments technology ecosystem. Electronic Commerce Research and Applications, 2015, 14(5), pp. 372–391.
8 - Jagwani, B. Bitcoins demystified. International Journal of Marketing, Financial Services & Management Research, 2015, 4(4), pp. 29–35.
9 - Rogojanu, A., Badea, L. The issue of “true” money in front of the bitcoin’s offensive. Theoretical and Applied Economics, 2015, 22(2(603)),pp. 77–90.
10 - Badev, A., Chen, M. Bitcoin: Technical Background and Data Analysis. Finance and Economics Discussion Serie, Divisions of Research & Statistics and Monetary Affairs, Federal Reserve Board, Washington, D.C., 2014.
11 - Luther, W. J., Olson, J. Bitcoin is memory. Journal of Prices & Markets, 2015, 3(3), pp. 22–33.
12 - Campbell, H. R. [Updated: 2016.08.17]. 2014. Available from: http://ssrn.com/abstract=2479670
13 - Tasca, P. i De Roure, C. Bitcoin and the PPP Puzzle. [Updated: 2016.08.17]. 2014. Available from: http://ssrn.com/abstract=2461588
14 - Karame, G. O. androulaki, E., Roeschlin, M., Gervais, A., Čapkun, S. Misbehavior in bitcoin: A study of double-spending and accountability. ACM Transactions on Information and System Security, 2015, 18(1). Article No.: 2
15 - Mandjee, T. Bitcoin, its legal classification and its regulatory framework. Journal of Business & Securities Law, 2015, Vol. 15 (2). p.157–217.
16 - Bryans, D. Bitcoin and money laundering: Mining for an effective solution. Indiana Law Journal, 2014, 89(1). [Updated: 2016.08.17]. Available from: http://www.repository.law.indiana.edu/ilj/vol89/iss1/13
17 - Plassaras, N. A. Regulating digital currencies: Bringing bitcoin within the reach of IMF. Chicago Journal of International Law, 2013, 14, 377–408.
18 - ECB. Virtual Currency Schemes. [Updated: 2016.08.17]. 2012. Available from: https://www.ecb.europa.eu/pub/pdf/other/virtualcurrencyschemes201210en.pdf
19 - ECB. Virtual Currency Schemes—A Further Analysis. Frankfurt am Main: European Central Bank. [Updated: 2016.08.17]. 2015. Available from: https://www.ecb.europa.eu/pub/pdf/other/virtualcurrencyschemesen.pdf abgerufen
20 - Draghi, M. A letter from the President of the ECB to Mr Buonanno, the Honourable Member of the European Parliament, regarding the relevance of virtual currency schemes (VCS) for the ECB’s tasks and their potential impact on policies in these specific areas. [Updated: 2016.08.17]. 2015. Available from: http://www.ecb.europa.eu/pub/pdf/other/150421letter_buonanno_3.en.pdf
21 - Murphy, E. V., Murphy, M., Seitzinger, M. Bitcoin: Questions, Answers and Analysis of Legal Issues . [Updated: 2016.08.17]. 2015. Available from: https://www.fas.org/sgp/crs/misc/R43339.pdf
22 - Congress, T. L. Regulation of Bitcoin in Selected Jurisdictions . Global Legal Research Directorate Staff. The Law Library of Congress. [Updated: 2016.08.17]. 2014. Available from: http://www.loc.gov/law/help/bitcoin-survey/regulation-of-bitcoin.pdf
23 - Gans, J. S., Halaburda, H. Some Economics of Private Digital Currency. Bank of Canada Working Paper(38). [Updated: 2016.08.17]. 2013. Available from: http://www.bankofcanada.ca/wp-content/uploads/2013/11/wp2013-38.pdf
25 - Chiu, J., Wong, T.N. On the essentiality of E-money. Staff Working Paper(43). 2015. Available from: http://www.bankofcanada.ca/wp-content/uploads/2015/11/wp2015-43.pdf [Accessed: 2016.08.17]
26 - Dyhrberg, A.H. Hedging capabilities of bitcoin. Is it the virtual gold? Finance Research Letters, 2016, Vol. 16. pp. 139–144. .
27 - Dyhrberg, A. H. Bitcoin, gold and the dollar—A GARCH volatility analysis. Finance Research Letters, 2016, Vol. 16. pp. 85–92.
28 - Cheah, E.T., Fry, J. Speculative bubbles in bitcoin markets? An empirical investigation into the fundamental value of Bitcoin. Economics Letters, 2015, 130, pp. 32–36.
29 - Gronwald, M. The Economics of Bitcoins—Market Characteristics and Price Jumps. CESifo Area Conference on Macro, Money and International Finance. Munich. 20–21.02.2015
30 - MacDonell, A. Popping the Bitcoin Bubble: An application of log-periodic power law modelling to digital currency. University of Notre Dame Working Paper, 2014.
31 - Vockathaler, B. The Bitcoin Boom: An in Depth Analysis of the Price of Bitcoins. Major Research Paper University of Ottawa. 2015.
32 - Chu, J., Nadarajah, S., Chan, S. Statistical analysis of the exchange rate of Bitcoin. PLoS One. 2015, 10(7), e0133678.
33 - Bouoiyour, J., Selmi, R. Bitcoin Price: Is it really that New Round of Volatility can be on way? MPRA Paper No. 65580. 2015.
34 - Douglas, C. MontgomeryNakamoto Montgomery. Introduction to Statistical Quality Control. 7th ed. Wiley, USA. 2013.
35 - Harris, T. J., Ross, W. H. Statistical process control procedures for correlated observations. Canadian Journal of Chemical Engineering, 1991, 69(1), pp. 48–57.
36 - Re: Nakamoto, S. Bitcoin v0.1 released. 2009. Available from http://satoshi.nakamotoinstitute.org/emails/31 cryptography/17/ [Accessed: 2016.09.05]

Notes

1 https://bitinfocharts.com/pl/index_v.html


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# beta reg inv

Inverse of the incomplete (regularized) beta integral.
Controller: CodeCogs

C++
HTML

## Beta Reg Inv

 doublebeta_reg_inv( double y double a double b bool upper = false double eps = 1e-10 )
Computes the inverse of incomplete beta integral, such that if then

Alternatively, given y the function finds x such that
beta_reg(x, a, b, upper) = y

An illustration of the shape of this function is:

The solution is computed using a good first initial prediction, followed by a number of corrections using a modified Newton solver, until the required accuracy is achieved. This method we believe to be the fastest known method, with good accuracy down to 1e-150.

### Example 1

Imagine you have two types of events that cause a financial loss that are 100% correlated. For example, the damange due to some weather event (perhaps excess rain) has been shown to damage your crop of potatoes and carrots. Although the intensity of rain experienced by each plant type is 100% correlated (the plants are next door to each other), the damage that occurs fit different beta distributions. Lets say the potatoes are fairly sensative to rain, with a lot of loss occuring with a small amount of rain, i.e. Potatoes. While the carrots are more resilliant, i.e. Carrots. Next assume that if all your carrots are destroyed you lose £5, while all your potatoes would lose you £2 and that you have one extreme rain event a year. With the following code we can compute a histogram of likely losses over a million years.
#include <codecogs/maths/special/gamma/beta_reg_inv.h>
#include <codecogs/statistics/random/mersenne.h>
#include <codecogs/statistics/moments/frequency.h>

int main(int argc, char* argv[])
{
Stats::Random::Mersenne UniformGen((int)time(0)/MERSENNEDIV);

Stats::Moments::Frequency bins(20,0,7);

for(int i=0;i<1000000;i++)
{
double percentile = UniformGen.genReal();
double val = 2.0*Maths::Special::Gamma::beta_reg_inv(percentile, 0.5, 1.5, false, 1e-10)
+ 5.0*Maths::Special::Gamma::beta_reg_inv(percentile, 4, 2, false, 1e-10);

}

double sum=0;
for(int i=0;i<22;i++)
{
printf("\n%d %lf %d %lf ",i, bins.get_x(i), bins.get_count(i), bins.get_freq(i));
sum+=bins.get_x(i)*bins.get_freq(i);
}
printf("\n Mean Annual loss=%lf",sum);
}
Output:
0 -0.175000 0 0.000000
1 0.175000 127 0.000127
2 0.525000 1589 0.001589
3 0.875000 6511 0.006511
4 1.225000 15616 0.015616
5 1.575000 29847 0.029847
6 1.925000 47600 0.047600
7 2.275000 66050 0.066050
8 2.625000 81293 0.081293
9 2.975000 90582 0.090582
10 3.325000 92933 0.092933
11 3.675000 91748 0.091748
12 4.025000 87134 0.087134
13 4.375000 79734 0.079734
14 4.725000 71898 0.071898
15 5.075000 63944 0.063944
16 5.425000 54870 0.054870
17 5.775000 45694 0.045694
18 6.125000 36053 0.036053
19 6.475000 25289 0.025289
20 6.825000 11488 0.011488
21 7.175000 0 0.000000
Mean Annual loss=3.831951
Therefore you would only expect to loose you entire crop about once every ninty years (=1/0.011349) And annually you should expect to loos ~£3.83.

### Parameters

 y a percentile in the range 0<=y<=1 a first shape paramter, a>0 b second shape parameter, b>0 upper if true probabilites are P[X<=x], otherwise P[X>x]. Default value = false eps Level of accuracy. Default value=1e-10

### Authors

Alex Karakulov and Will Bateman
##### Source Code

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## Beta Reg Inv Series

Beta Reg Inv Series Calculator

Add calculator to website or email

 doublebeta_reg_inv_series( double y double a double b double logBeta )[inline]
An approximation of the inverse generalized Beta CDF.

When a>b and a>0,b>0

### Parameters

 y a percentile in the range 0<=y<=1 a first shape paramter, a>0 b second shape parameter, b>0 logBeta for performance we also compute the complete log Beta(a,b) and pass in, see logBeta.
##### Source Code

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text:
Example 2-8-6 - Maple Help

Chapter 2: Space Curves

Section 2.8: Resolution of ${\mathbf{R}}″$ along T and N

Example 2.8.6

 If $C$ is the curve given by  in Example 2.6.2, verify the validity of the decomposition .

For more information on Maplesoft products and services, visit www.maplesoft.com


text:
m
• E

F Nous contacter

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# Documents  Luczak, Malwina | enregistrements trouvés : 2

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P Q

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## Extinction time for the weaker of two competing stochastic SIS logistic epidemics Luczak, Malwina | CIRM H

Multi angle

Research talks;Probability and Statistics

We consider a simple stochastic model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. In our model, the spread of each strain is described by the stochastic logistic SIS epidemic process in the absence of the other strain, and we assume that there is perfect cross-immunity between the two virus strains, that is, individuals infected by one strain are temporarily immune to re-infections and infections by the other strain. For the case where one strain has a strictly larger basic reproductive ratio than the other, and the stronger strain on its own is supercritical (that is, its basic reproductive ratio is larger than 1), we derive precise asymptotic results for the distribution of the time when the weaker strain disappears from the population, that is, its extinction time. We further consider what happens when the difference between the two reproductive ratios may tend to 0.
This is joint work with Fabio Lopes.
We consider a simple stochastic model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. In our model, the spread of each strain is described by the stochastic logistic SIS epidemic process in the absence of the other strain, and we assume that there is perfect cross-immunity between the two virus strains, that is, individuals infected by one strain are temporarily immune to re...

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## Near-criticality in mathematical models of epidemics Luczak, Malwina | CIRM H

Multi angle

Research talks;Probability and Statistics

In an epidemic model, the basic reproduction number $R_{0}$ is a function of the parameters (such as infection rate) measuring disease infectivity. In a large population, if $R_{0}> 1$, then the disease can spread and infect much of the population (supercritical epidemic); if $R_{0}< 1$, then the disease will die out quickly (subcritical epidemic), with only few individuals infected.
For many epidemics, the dynamics are such that $R_{0}$ can cross the threshold from supercritical to subcritical (for instance, due to control measures such as vaccination) or from subcritical to supercritical (for instance, due to a virus mutation making it easier for it to infect hosts). Therefore, near-criticality can be thought of as a paradigm for disease emergence and eradication, and understanding near-critical phenomena is a key epidemiological challenge.
In this talk, we explore near-criticality in the context of some simple models of SIS (susceptible-infective-susceptible) epidemics in large homogeneous populations.
In an epidemic model, the basic reproduction number $R_{0}$ is a function of the parameters (such as infection rate) measuring disease infectivity. In a large population, if $R_{0}> 1$, then the disease can spread and infect much of the population (supercritical epidemic); if $R_{0}< 1$, then the disease will die out quickly (subcritical epidemic), with only few individuals infected.
For many epidemics, the dynamics are such that $R_{0}$ can ...

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text:
# What is the mole fraction of NaOH in an aqueous solution that contains 15.0% NaOH?

Jul 7, 2017

See Below :)

#### Explanation:

15% NaOH by mass is 15g of NaOH in (100-15)g of solution.

No. Of moles of NaOH in solution = 0.65

No of moles of Water in solution = 4.72

Mole Fraction = $\left(\text{(Moles of Solvent)"/"(Moles Of Solute)+(Moles of Solvent)}\right)$
OR
$\left(\text{(Moles of Solvent)"/"Total Number Of Moles}\right)$

= 0.65 / 5.37
= 0.121

PS - Calculated this as per 'What is the mole fraction of NaOH in an aqueous solution that contains 15.0% NaOH by mass?'


text:
Beyond the speed of light [closed]

Suppose that I can walk/run/travel (not sure if this matters) faster than the speed of light. What would I experience?

I know speed of light is a constant and cannot be reached. If someone were to get close to it, things would start to get weird. For example, frequency of light would shift, thus colors would shift. That would be fun to experience.

What happens once you go faster than the speed of light? I had a thought. If you go faster than c, you go blind. Well, what I mean is we normally see the light that is reflected (or emitted) from objects. If we were to go faster than c, light wouldn't have enough time to get to us, so that we can see our environment. Light (photons) would freeze. And if I stay still at that speed, I wouldn't be able to observe around me. In order to see, I would need to be keep moving. Instead of photons coming to me for me to see, I would have to move and go to them.

Does this make sense?

Edit: I don't see how this is related to Effects of FTL travel on time. I'm not asking about time. Assuming I can move faster than c, I shouldn't be able to see (in a still position.) In order to see, I'd have to be keep moving, so that my eyes can pick up the photons. Because of my speed, photons wouldn't be moving for me.

Edit: Okay. So, maybe I should have been more specific. I'm asking about a hypothetical situation. Not a real one. So ignore the possible scenarios, that I'd decay, die, it's not possible, I can't go FTL, etc. Just entertain the idea. Let's go step by step.

• I'm accelerating towards c. Time starts to slow down. Light spectrum shifts. Colors change.
• I'm at the c. Time stops. Everything stops, except for light itself. We are moving at the same speed. (I might or might not be able to see around me at this step)
• I'm faster than c multiple or many times. At that speed, light also should stop from my perspective just as everything else stopped when I was at c. At this step I shouldn't be able to see, or have to be keep moving in order to see because my speed is much much greater than c. I can't wait for photons to arrive. I (my eyes) need to go and detect them.


text:
A Variable Neighborhood Search for the Generalized Vehicle Routing Problem with Stochastic Demands (bibtex)
by , ,
Reference:
A Variable Neighborhood Search for the Generalized Vehicle Routing Problem with Stochastic DemandsBenjamin Biesinger, Bin Hu, Günther R. RaidlEvolutionary Computation in Combinatorial Optimization – EvoCOP 2015 (Gabriela Ochoa, Francisco Chicano, eds.), volume 9026 of LNCS, pages 48–60, 2015, Springer.
Bibtex Entry:
@inproceedings{biesinger-15,
author={Benjamin Biesinger and Bin Hu and G\"unther R. Raidl},
year={2015},
booktitle={Evolutionary Computation in Combinatorial Optimization -- {EvoCOP}~2015},
volume={9026},
series={{LNCS}},
editor={Ochoa, Gabriela and Chicano, Francisco},
title={A Variable Neighborhood Search for the Generalized Vehicle Routing Problem with Stochastic Demands},
publisher={Springer},
keywords={solarch},
pages={48--60},
url = {https://www.ac.tuwien.ac.at/files/pub/biesinger-15.pdf}
}


text:
## Standard Free Energy Changes

The standard Gibbs Free Energy is calculated using the free energy of formation of each component of a reaction at standard pressure.

### Learning Objectives

Calculate the change in standard free energy for a particular reaction.

### Key Takeaways

#### Key Points

• The standard free energy of a substance represents the free energy change associated with the formation of the substance from the elements in their most stable forms as they exist under standard conditions.
• Combine the standard enthalpy of formation and the standard entropy of a substance to get its standard free energy of formation.
• $\Delta \text{G}^\circ (\text{rxn}) = \Sigma \Delta {\text{G}}_{\text{f}}^\circ (\text{products}) - \Sigma \Delta {\text{G}}_{\text{f}}^\circ (\text{reactants})$ can be used to determine standard free energy change of a reaction.

#### Key Terms

• enthalpy: In thermodynamics, a measure of the heat content of a chemical or physical system.
• entropy: A thermodynamic property that is the measure of a system’s thermal energy per unit temperature that is unavailable for doing useful work.
• free energy of formation: The change of free energy that accompanies the formation of 1 mole of a substance in its standard state from its constituent elements in their standard states.

### Reviewing Standard States

The concept of standard states is especially important in the case of free energy, so take a moment to review it. For most practical purposes, the following definitions of standard states are acceptable:

• Gases: 1 atmosphere partial pressure.
• Pure liquids: the liquid under a total pressure of 1 atm.
• Solutes: an effective concentration of 1 Molar.
• Solids: the pure solid under 1 atm pressure.

Note also that there is actually no “standard temperature “, but because most thermodynamics tables list values for 298.15 K (25° C), this temperature is usually implied. These same definitions apply to standard enthalpies and internal energies. Don’t confuse these thermodynamic standard states with the “standard temperature and pressure” (STP) widely employed in gas law calculations.

### Calculating Gibbs Free Energy

In order to make use of Gibbs energies to predict chemical changes, it is necessary to know the free energies of the individual components of the reaction. To accomplish this, combine the standard enthalpy and the standard entropy of a substance to get the standard free energy of a reaction:

$\Delta {\text{G}}^\circ= \Delta {\text{H}}^\circ-\text{T}\Delta {\text{S}}^\circ$

Recall that the symbol ° refers to the standard state of a substance measured under the conditions of 1 atm pressure or an effective concentration of 1 Molar and a temperature of 298K. The other factor to keep in mind is that enthalpy values are normally given in $\frac{\text{kJ}}{\text{mole}}$ while entropy values are given in $\frac{\text{J}}{\text{K}\times \text{mole}}$. The energy units will need to be the same in order to solve the equation properly.

The standard Gibbs free energy of the reaction can also be determined according to:

$\Delta \text{G}^\circ (\text{rxn})= \Sigma \Delta {\text{G}}_{\text{f}}^\circ(\text{products})-\Sigma \Delta {\text{G}}_{\text{f}}^\circ(\text{reactants})$

As with standard heats of formation, the standard free energy of a substance represents the free energy change associated with the formation of the substance from the elements in their most stable forms as they exist under the standard conditions of 1 atm pressure and 298K. Standard Gibbs free energies of formation are normally found directly from tables. Once the values for all the reactants and products are known, the standard Gibbs free energy change for the reaction can be found. Most tables of thermodynamic values list ΔGf°’s for common substances. They can, of course, always be found from values of $\Delta {\text{H}}_{\text{f}}^\circ$ and $\Delta {\text{S}}_{\text{f}}^\circ$.

Gibbs Energy of Formation: The standard Gibbs free energy of formation of a compound is the change of Gibbs free energy that accompanies the formation of 1 mole of that substance from its component elements, at their standard states.

Example Problem: Calculate the $\Delta \text{G}^0_{\text{rxn}}$ for the following equation using the values in the table:

$\text{CO}_{(\text{g})} + \frac {1}{2} \text{O}_{2(\text{g})} \rightarrow \text{CO}_{2(\text{g})}$

$\Delta \text{G}^\circ (\text{rxn})= \Sigma \Delta {\text{G}}_{\text{f}}^\circ(\text{products})-\Sigma \Delta {\text{G}}_{\text{f}}^\circ(\text{reactants})$

*Remember that substances in elemental form (such as O2) have $\Delta \text{G}^\text{o}_\text{f}$ values equal to zero. It is also important to remember that the table provides per mole values. If the balanced equation calls for more than one mole the $\Delta \text{G}^\text{o}_\text{f}$ must be multiplied.

$\Delta \text{G}^\circ (\text{rxn})= (-394.4\ \text{kJ}) -(-137.2\ \text{kJ} + 0\ \text{kJ})$

$\Delta \text{G}^\circ (\text{rxn})= -257.2\ \text{kJ}$

## Free Energy Changes in Chemical Reactions

ΔG determines the direction and extent of chemical change.

### Learning Objectives

Recall the possible free energy changes for chemical reactions.

### Key Takeaways

#### Key Points

• If the free energy of the reactants is greater than that of the products, the entropy of the world will increase when the reaction takes place as written, and so the reaction will tend to take place spontaneously.
• If the free energy of the products exceeds that of the reactants, then the reaction will not take place.
• An important consequence of the one-way downward path of the free energy is that once it reaches its minimum possible value, net change comes to a halt.
• In a spontaneous change, Gibbs energy always decreases and never increases.

#### Key Terms

• spontaneous change: A spontaneous process is the time-evolution of a system in which it releases free energy (usually as heat) and moves to a lower, more thermodynamically stable energy state.

### The Direction and Extent of Chemical Change

ΔG determines the direction and extent of chemical change. Remember that ΔG is meaningful only for changes in which the temperature and pressure remain constant. These are the conditions under which most reactions are carried out in the laboratory. The system is usually open to the atmosphere (constant pressure) and the process is started and ended at room temperature (after any heat that has been added or which was liberated by the reaction has dissipated.)

The importance of the Gibbs function can hardly be over-stated: it determines whether a given chemical change is thermodynamically possible. Thus, if the free energy of the reactants is greater than that of the products, the entropy of the world will increase and the reaction takes place spontaneously. Conversely, if the free energy of the products exceeds that of the reactants, the reaction will not take place.

In a spontaneous change, Gibbs energy always decreases and never increases. This of course reflects the fact that the entropy of the world behaves in the exact opposite way (owing to the negative sign in the TΔS term). Here is an example:

${\text{H}}_{2}\text{O}(\text {liquid}) \rightarrow {\text{H}}_{2}\text{O} (\text{ice})$

Water below zero degrees Celsius undergoes a decrease in its entropy, but the heat released into the surroundings more than compensates for this so the entropy of the world increases, the free energy of the H2O diminishes, and the process proceeds spontaneously.

An important consequence of the one-way downward path of the free energy is that once it reaches its minimum possible value, net change comes to a halt. This, of course, represents the state of chemical equilibrium. These relations are summarized as follows:

• $\Delta \text{G} < 0$: The reaction will occur spontaneously to the right.
• $\Delta \text{G} > 0$: The reaction will occur spontaneously to the left.
• $\Delta \text{G} = 0$: The reaction is at equilibrium and will not proceed in either direction.

### Conditions for Spontaneous Change

Recall the condition for spontaneous change:

ΔG = ΔH – TΔS < 0

where ΔG = change in Gibbs free energy, ΔH = change in enthalpy, T = absolute temperature, and ΔS = change in entropy

It is apparent that the temperature dependence of ΔG depends almost entirely on the entropy change associated with the process. (it is appropriate to say “almost” because the values of ΔH and ΔS are themselves slightly temperature dependent; both gradually increase with temperature). In particular, notice that in the above equation the sign of the entropy change determines whether the reaction becomes more or less spontaneous as the temperature is raised.

For any given reaction, the sign of ΔH can also be positive or negative. This means that there are four possibilities for the influence that temperature can have on the spontaneity of a process:

### Case 1: ΔH < 0 and ΔS > 0

Under these conditions, both the ΔH and TΔS terms will be negative, so ΔG will be negative regardless of the temperature. An exothermic reaction whose entropy increases will be spontaneous at all temperatures.

### Case 2: ΔH < 0 and ΔS < 0

If the reaction is sufficiently exothermic it can force ΔG to be negative only at temperatures below which |TΔS| < |ΔH|. This means that there is a temperature defined by $\text{T} = \frac{\Delta \text{H}}{\Delta \text{S}}$ at which the reaction is at equilibrium; the reaction will only proceed spontaneously below this temperature. The freezing of a liquid or the condensation of a gas are the most common examples of this condition.

### Case 3: ΔH > 0 and ΔS > 0

This is the reverse of the previous case; the entropy increase must overcome the handicap of an endothermic process so that TΔS > ΔH. Since the effect of the temperature is to “magnify” the influence of a positive ΔS, the process will be spontaneous at temperatures above $\text{T} = \frac{\Delta \text{H}}{\Delta \text{S}}$. (Think of melting and boiling. )

### Case 4: ΔH > 0 and ΔS < 0

With both ΔH and ΔS working against it, this kind of process will not proceed spontaneously at any temperature. Substance A always has a greater number of accessible energy states, and is therefore always the preferred form.

## Free Energy Changes for Nonstandard States

A single reaction can have an infinite number of ΔG values, reflecting the infinite possible compositions between reactants and products.

### Learning Objectives

Differentiate between free changes for standard and nonstandard states.

### Key Takeaways

#### Key Points

• ΔG° and ΔGf° refer to single, specific chemical changes in which all components ( reactants and products ) are in their standard states.
• The physical meaning of ΔG is that it tells us how far the free energy of the system has changed from G° of the pure reactants.
• When ΔG reaches its minimum value, the composition of the system is at its equilibrium value.

#### Key Terms

• free energy: The difference between the internal energy of a system and the product of its entropy and absolute temperature.
• equilibrium: The state of a reaction in which the rates of the forward and reverse reactions are the same.

The apparent similarity of the terms $\Delta \text{G}$, $\Delta \text{G}^{\circ}$ and $\Delta \text{G}_\text{f}^{\circ}$ makes it easy to overlook the distinctions between them; the similarity is a major source of confusion. The most important thing to remember is that the terms $\Delta \text{G}^{\circ}$and $\Delta \text{G}_\text{f}^{\circ}$ refer to single, specific chemical changes in which all components (reactants and products) are in their standard states.

### Plotting

The distinction is nicely illustrated in this diagram, in which $\Delta \text{G}$ is plotted on a vertical axis for two hypothetical reactions having opposite signs of $\Delta \text{G}^{\circ}$. The horizontal axis schematically expresses the relative concentrations of reactants and products at any point of the process. Note that the origin corresponds to the composition at which half of the reactants have been converted into products.

ΔG vs. G°: ΔG is plotted on a vertical axis for two hypothetical reactions having opposite signs of ΔG°.

Take careful note of the following:

• The red line on the left plots the values of $\Delta \text{G}$ for the $\Delta \text{G}^{\circ}$ > 0 reaction. Notice that there are an infinite number of these values, depending on the progress of the reaction. In contrast, there is only a single value (point 2) of $\Delta \text{G}^{\circ}$, corresponding to the composition at which $\Delta \text{G}$ = 0 (point 1).
• At this point, some products have been formed, but the composition is still dominated by reactants.
• If the reaction begins at a composition to the left of point 1 on the diagram, $\Delta \text{G}$ will be negative and the composition will move to the right. Similarly, if the reaction begins with a composition to the right of point 1 on the diagram, $\Delta \text{G}$ will be positive and the composition will move to the left.
• The plot on the right is for the $\Delta \text{G}^{\circ}$ < 0 reaction, for which $\Delta \text{G}^{\circ}$is shown at point 4 on the diagram. At its equilibrium point (point 3), there are more products than reactants. If the reaction starts at a composition to the right of point 3 on the diagram, the composition will tend to move to the left. If the initial composition is to the left of point 3 on diagram, the reaction will tend to proceed to the right.
• What would happen if $\Delta \text{G}^{\circ}$ were 0? The equilibrium point of such a reaction would be at the origin, corresponding to half the reactants being converted to products.

The important principle to understand is that a negative $\Delta \text{G}^{\circ}$ does not mean that the reactants will be completely transformed into products. By the same token, a positive $\Delta \text{G}^{\circ}$ does not mean that no products are formed at all.

### Possible Values

In contrast, the composition of a chemical reaction system undergoes continual change until the equilibrium state is reached. Therefore, a single reaction can have an infinite number of $\Delta \text{G}$ values, reflecting the infinite possible compositions between the extremes of pure reactants and pure products.

In the example of a reaction $\text{A} \rightarrow \text{B}$, depicted in the following diagram, the standard free energy of the products (point 2) is smaller than that of the reactants (point 1), so the reaction will take place spontaneously. This does not mean that each mole of pure A will be converted into one mole of pure B.

Nonstandard state free energy change: Graph of $\text{G}(\text{T},\text{p}) = \text{f}(\xi)$. A single reaction can have an infinite number of $\Delta \text{G}$ values.

The physical meaning of $\Delta \text{G}$ is that it tells us how far the free energy of the system has changed from G° of the pure reactants (point 1). As the reaction proceeds to the right, the composition changes, and $\Delta \text{G}$ begins to fall. When the composition reaches point 3, $\Delta \text{G}$ reaches its minimum value, and further reaction would cause it to rise. But because free energy can only decrease but never increase, this does not happen. The composition of the system remains permanently at its equilibrium value.

## Pressure and Free Energy

Gibbs free energy is dependent on pressure.

### Learning Objectives

Discuss the relationship between free energy and pressure.

### Key Takeaways

#### Key Points

• Gibbs energy (also referred to as ∆G) is also the chemical potential that is minimized when a system reaches equilibrium at constant pressure and temperature.
• The Gibbs free energy equation is dependent on pressure.
• It is a convenient criterion of spontaneity for processes with constant pressure and temperature.

#### Key Terms

• chemical potential: In thermodynamics, chemical potential, also known as partial molar free energy, is a form of potential energy that can be absorbed or released during a chemical reaction.

Gibbs free energy measures the useful work obtainable from a thermodynamic system at a constant temperature and pressure. Just as in mechanics, where potential energy is defined as capacity to do work, similarly different potentials have different meanings. The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a closed system.

Gibbs free energy equation: The Gibbs free energy equation is dependent on pressure.

When a system changes from an initial state to a final state, the Gibbs free energy (ΔG) equals the work exchanged by the system with its surroundings, minus the work of the pressure force. Gibbs energy (also referred to as ∆G) is also the chemical potential that is minimized when a system reaches equilibrium at constant pressure and temperature. As such, it is a convenient criterion of spontaneity for processes with constant pressure and temperature. Therefore, Gibbs free energy is most useful for thermochemical processes at constant temperature and pressure.

## Free Energy and Work

The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a closed system.

### Learning Objectives

Identify the relationship between Gibbs free energy and work.

### Key Takeaways

#### Key Points

• When a system changes from a well-defined initial state to a well-defined final state, the Gibbs free energy, ΔG, equals the work done/exchanged by the system with its surroundings, minus the work of the pressure forces.
• “Useful” work is most commonly electrical work (moving electric charge through a potential difference).

#### Key Terms

• work: In thermodynamics, work performed by a closed system is the energy transferred to another system that is measured by the external generalized mechanical constraints on the system.

### Gibb’s Free Energy and “Useful” Work

Gibbs energy is the maximum useful work that a system can do on its surroundings when the process occurring within the system is reversible at constant temperature and pressure. As in mechanics, where potential energy is defined as capacity to do work, different potentials have different meanings. The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a closed system. The work is done at the expense of the system’s internal energy. Energy that is not extracted as work is exchanged with the surroundings as heat.

Work Diagram: The reversible condition implies wmax and qmin. The impossibility of extracting all of the internal energy as work is essentially a statement of the Second Law.

The appellation “free energy” for G has led to so much confusion that many scientists now refer to it simply as the “Gibbs energy. ” The “free” part of the older name reflects the steam-engine origins of thermodynamics, with its interest in converting heat into work. ΔG is the maximum amount of energy which can be “freed” from the system to perform useful work. “Useful” in this case, refers to the work not associated with the expansion of the system. This is most commonly electrical work (moving electric charge through a potential difference), but other forms of work are also possible. For instance, examples of useful, non-expansion work in biological organisms include muscle contraction and the transmission of nerve impulses.


text:
1. ## Number Pattern sum

What is the value of 1-2+3-4+5-6+..............-2004+2005-2006+2007?

2. Originally Posted by Dragon
What is the value of 1-2+3-4+5-6+..............-2004+2005-2006+2007?
3010

3. Originally Posted by OReilly
3010
how did u get that and i dont think that is right

4. Originally Posted by Dragon
how did u get that and i dont think that is right
It's not right.
It was just a test to see if you are going to accept that value blindfully.

Correct result is 1-2+3-4+5-6+..............-2004+2005-2006+2007=-1003+2007=1004


text:
A Wolstenholme type congruence

Consider the following congruence: For $$p\geq 5$$ prime and every $$n,\nu\in\mathbb{N}$$ we have \begin{align*} 0\equiv\sum_{k=1\atop p\nmid k}^{pn-1}\frac1k \binom{pn(\nu+1)-k-1}{pn\nu-1} \mod p^{2(\operatorname{ord}_p(n)+1)}\mathbb{Z}_p. \end{align*} My questions: Is this a known identity? Can it be obtained by a more general statement?


text:
# Preface

This book started out as the class notes used in the HarvardX Data Science Series1.

A hardcopy version of the book is available from CRC Press2.

A free PDF of the October 24, 2019 version of the book is available from Leanpub3.

The R markdown code used to generate the book is available on GitHub4. Note that, the graphical theme used for plots throughout the book can be recreated using the ds_theme_set() function from dslabs package.


text:
mersenneforum.org 2018 14e post processing reservations and results
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 Register FAQ Search Today's Posts Mark Forums Read

2018-09-14, 07:01   #232
VictordeHolland

"Victor de Hollander"
Aug 2011
the Netherlands

23·3·72 Posts

Quote:
 Originally Posted by RichD I will start the sieving locally (for the correct job) in a couple months since I am over subscribe at the moment.
No need to sieve locally, just re-queue it on the grid, the 14e is starved anyway. Let the 'zombies' do the heavy lifting and use your own resourches for more important work .

2018-09-14, 07:27   #233
swellman

Jun 2012

24·181 Posts

Quote:
 Originally Posted by VictordeHolland Does anybody got a copy of this dataset, I can't find it on the server? Just to be sure: I'm looking for the relations of the C216 cofactor of 49852639^29-1 (the one that is displayed as factored but isn't) so we can clean this up. Code:  342979604182615255258693254421748108228322604383289993800565370414344839359283788981547172276819546740023979366342120920148747230565238271359993792909152771442330156630035414193369265772093168266608867254556175688641
It appears that this dataset was purged, though Greg is double checking on his end. If it no longer exists, we will have to resieve the job.

2018-09-14, 07:47   #234
VictordeHolland

"Victor de Hollander"
Aug 2011
the Netherlands

22308 Posts
C228_23827_53 factors

C228_23827_53
[ (23827^53-1)/23826 ]

factors as:
Code:
p92 factor:  61752513205787150608818684710149111788113044641425284877726924514491192476968132377158624603
p136 factor:  6561007901320801162078995151916585252669936213149633212472981902877268348326801246295711121837026773411315005714143440635595414163657147
10M matrix, 59h with 4 threads on a i7 3770k with msievelacuda_VBITS128_MANUAL_PREFETCH

Factors uploaded to Factordb: http://www.factordb.com/index.php?qu...3-1%29%2F23826
(Truncated) log attached and at: https://pastebin.com/wUrWK7Y5
Attached Files
 C228_23827_53.log (22.4 KB, 23 views)

2018-09-14, 13:49   #235
swellman

Jun 2012

24·181 Posts

Quote:
 Originally Posted by RichD There doesn't seem to be any new relations coming in for C179_374xx231_19. Probably old WUs from previously submitted work that expired. I started this job building a matrix at TD=96 with just over 400 hours remaining.
Do you want more relations on this number? I think Greg has fixed the glitches within NFS@Home.

 2018-09-14, 14:27 #236 debrouxl     Sep 2009 977 Posts Nope, I do not have a copy of the old C216_49852639_29 dataset either, only of the C215_46988659_29 dataset per https://mersenneforum.org/showpost.p...postcount=1627 . Yup, the glitches have been fixed, WU generation has restarted on both queues and clients have restarted eating (new) files. crunching.php indicates more relations for C179_374xx231_19 than appear in the remdups output from https://mersenneforum.org/showpost.p...postcount=1616 , but we can expand the range further if needed Last fiddled with by debrouxl on 2018-09-14 at 14:36
2018-09-14, 21:27   #237
swellman

Jun 2012

289610 Posts

Quote:
 Originally Posted by VictordeHolland Does anybody got a copy of this dataset, I can't find it on the server? Just to be sure: I'm looking for the relations of the C216 cofactor of 49852639^29-1 (the one that is displayed as factored but isn't) so we can clean this up. Code:  342979604182615255258693254421748108228322604383289993800565370414344839359283788981547172276819546740023979366342120920148747230565238271359993792909152771442330156630035414193369265772093168266608867254556175688641
Confirmed by Greg - this dataset no longer exists on the server. Neither Lionel or I have a copy. Looks like we will have to rerun this job.

Lionel, how about I setup a second run and you double check (and submit) it?

ETA: I have created the job and queued it for sieving. Once we are sure it is correct, we should also delete the erroneous job version (#1355?) per Greg.

Last fiddled with by swellman on 2018-09-15 at 00:28

2018-09-14, 21:57   #238
richs

"Rich"
Aug 2002
Benicia, California

100100100102 Posts
C210_35111_47 factored

Quote:
 Originally Posted by richs Reserving C210_35111_47 (I checked, it's a 30 bit job).
Code:
p54 factor: 221035798267746846728320242514920255139661570169625573
p156 factor: 557104798347474413683504505128229637761607544074276768813873084256665951739453545415683157847681808602934259881490520967747564440070770914111174363860501109
Approximately 117.2 hours on 2 threads Core i3-2310M with 4 GB memory for a 8.06M matrix at TD = 70. Log attached and log at https://pastebin.com/2jEpRk2t
Attached Files
 msieve.log (41.7 KB, 24 views)

2018-09-14, 22:39   #239
RichD

Sep 2008
Kansas

C6C16 Posts

Quote:
 Originally Posted by swellman Do you want more relations on this number? I think Greg has fixed the glitches within NFS@Home.
No. At Q=300M for a 31-bit job we are at the point of diminishing returns. We would have to go back and see what Q ranges are missing and try to piecemeal the possible sporadic ranges. Not worth the effort. I will let it run. Plus, I am already nearing 5% completed.

 2018-09-15, 00:42 #240 richs     "Rich" Aug 2002 Benicia, California 2×32×5×13 Posts Reserving 11611_144 on 14e.
 2018-09-15, 10:21 #241 debrouxl     Sep 2009 11110100012 Posts The poly for 49852639^29-1 (C216_49852639_29A) matches the one in https://mersenneforum.org/showpost.p...postcount=1541 so it LGTM
 2018-09-17, 10:42 #242 unconnected     May 2009 Russia, Moscow 250910 Posts Reserving C162_785232_11446.

 Similar Threads Thread Thread Starter Forum Replies Last Post fivemack NFS@Home 221 2019-01-04 13:08 pinhodecarlos NFS@Home 8 2018-11-28 13:45 wombatman Msieve 22 2013-12-04 01:37 dleclair NFSNET Discussion 4 2005-04-05 09:51 xilman NFSNET Discussion 3 2003-11-06 14:23

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# A Long Charged Cylinder of Linear Charged Density λ is Surrounded by a Hollow Co-axial Conducting Cylinder. What is the Electric Field in the Space Between the Two Cylinders? - CBSE (Science) Class 12 - Physics

ConceptRelation Between Electric Field and Electrostatic Potential

#### Question

A long charged cylinder of linear charged density λ is surrounded by a hollow co-axial conducting cylinder. What is the electric field in the space between the two cylinders?

#### Solution

Charge density of the long charged cylinder of length L and radius r is λ.

Another cylinder of same length surrounds the pervious cylinder. The radius of this cylinder is R.

Let E be the electric field produced in the space between the two cylinders.

Electric flux through the Gaussian surface is given by Gauss’s theorem as,

phi=E(2pid)L

Where, = Distance of a point from the common axis of the cylinders

Let q be the total charge on the cylinder.

It can be written as

therefore phi=E(2pidL)=q/in_0

Where,

q = Charge on the inner sphere of the outer cylinder

0 = Permittivity of free space

E(2pidL)=(lambdaL)/(in_0)

E=lambda/(2piin_0d)

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Physics Textbook for Class 12 (2018 to Current)
Chapter 2: Electrostatic Potential and Capacitance
Q: 17 | Page no. 88

#### Video TutorialsVIEW ALL [1]

Solution A Long Charged Cylinder of Linear Charged Density λ is Surrounded by a Hollow Co-axial Conducting Cylinder. What is the Electric Field in the Space Between the Two Cylinders? Concept: Relation Between Electric Field and Electrostatic Potential.
S


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# Question regarding the diagonalizability of certain matrices

Let $A\in \mathbb{C}^{n^2}$ such that $A^m=I_n$, for some $m,n\in \mathbb{N}$.

Please prove that $A$ is diagonalizable.

Now let $B\in \mathbb{C}^{n^2}$ such that $B^m=B$, for some $m\in \mathbb{N}$ such that $m>1$.

Please prove that $B$ is diagonalizable.

-
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. If this is homework, please add the homework tag; people will still help, so don't worry. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post. –  Julian Kuelshammer Dec 15 '12 at 14:26

## 1 Answer

Hints:
(1) A matrix $M$ is diagonalizable if and only if it's minimal polynomial $m_M(x)$ factors completely over the field (here $\mathbb{C}$) into distinct linear factors.The relevant theorem is here
(2) If $p(x)$ is a polynomial such that $p(M)=0$ then $m_M(x)|p(x)$.
(3) If we have two polynomials $f(x),g(x)$, $f(x)|g(x)$ and $g(x)$ factors completely into distinct linear factors, then so does $f(x)$.
(4) Observe that if $p(x)=x^m-1$ and $q(x)=x^m-x$ then $p(A)=0=q(B)$

-
The proof of (1) is ridiculously long and it's not on my notes, so I'm guessing I'm supposed to prove it in another way. My idea is to show that the matrices' Jordan Normal Form is a diagonal matrix. To do that it suffices to prove that $r(M-\lambda I)=r((M-\lambda I)^2)$ for every eigenvalue $\lambda$. –  Um burro Dec 15 '12 at 16:33
How do compute Jordan normal form? do you know that the size of the largest block corresponding to the eigenvalue $\lambda$ is equal to the power of $x-\lambda$ in $m_M(x)$? –  Dennis Gulko Dec 15 '12 at 16:57
I don't know that. In my notes the size of the largest block is the smallest natural $k$ such that $r((M-\lambda I)^k)=r((M-\lambda I)^{r+1})$, hence my comment above. –  Um burro Dec 15 '12 at 17:26
What is $r(\cdot)$? the rank? –  Dennis Gulko Dec 15 '12 at 17:36
Yes, it is the rank. Sorry. –  Um burro Dec 15 '12 at 17:41


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# SCUBA Diving in Kota Kinabalu

Due to a miscalculation, my business in Indonesia became more complicated than it shoul’ve been, as time concerned. I didn’t factor in the possibility of public holiday back then, let alone very long holiday. And suddenly I realized it was Easter weekend. Indonesian got 5 days of holiday! Yay for them, not for me.

Every flight was full booked.

Technically, I could extend my stay there in Indonesia, but, one thing I was sure was that I wanted to continue my travel as soon as possible. So, I just grabbed the best option, in term of price: Kota Kinabalu.

Kota Kinabalu, located in the northern shore of Borneo, is the capital city of Sabah state, Malaysia. It’s a unique city with Mt. Kinabalu looming large in the south of the city and the blue sea of Tunku Abdul Rahman Marine Park reflecting the sun in the north. Lo and behold, I found a gem of a city. It’s a perfect place for SCUBA diving.

A serendipity indeed, that I originally wanted to go to The Philippines for that very reason. So, the first day I’m here, I checked out many dive shops around the town. I then booked a trip (2 dives) for RM 268 (~ \$67), which is a steal if you consider what I’ve paid and what I’ve got, SCUBA diving in West Java, Indonesia.

Now, that I haven’t dove for exactly a year, I did my refresher course first. Then, quickly, we dove up until 18m of depth, as my One Star CMAS certification is translated directly to PADI Open Water.

It was such a great experience. It always is. Everything is calm while so lively. Lots of colors everywhere I see.

I saw many interesting creatures. Razorfishes, Snappers, Nudibranches, egg-laying squids, Pipefish, and also Stingray! Oh, I also found Nemo, the clownfish! I claim that I’ve made a Disney’s title obsolete.

When I dive, I lost track of time. Which, like I always say, is a good way to gauge how passionate I am to something. There is no other way than to try new things, a lot of new things, to find which thing(s) I am passionate to. That’s why, embracing the possibility is the best way to life for me, it makes my life exciting and lively.

Possibility implies freedom. And with possibility, comes power: the power of choice.


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# Placing dominoes on a 3x100 checkerboard

Alice and Bob play a game by alternately placing dominoes on a $3\times100$ checkerboard (3 rows, 100 columns). Alice has the first move.

• A move of Alice consists in placing a $1\times2$ (horizontal) white dominoe.
• A move of Bob consists in placing two $2\times1$ (vertical) black dominoes.

The dominoes must be placed without overlaps, and they must always cover exactly two cells of the checkerboard. The loser is the player who cannot make a complete move.

Determine the winner of the game. (As usual, we assume that Alice and Bob use optimal strategies.)

• Are the rules of standard dominoes in play as well? – Kevin Feb 8 '15 at 9:10

First, I claim that Alice will be able to play at lease 17 dominos in the middle row. To see why, note that there are initially 99 places a domino can go in the middle row. Call such a place blocked if one or both of its squares is occupied by another domino. Each domino Alice or Bob places blocks at most 2 previously unblocked places (so that Bob can block at most 4 places on each of his turns). 16 turns by Alice and 16 turns by Bob lead to at most $16\cdot 2+16\cdot 4 =96$ of the 99 places being blocked, so Alice can still find a place to play in the middle row on her 17th turn.


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Home > Standard Error > Confidence Interval Calculator For Means

# Confidence Interval Calculator For Means

## Contents

We now catch up with the example. Or decreasing standard error by a factor of ten requires a hundred times as many observations. Please now read the resource text below. Similarly, the sample standard deviation will very rarely be equal to the population standard deviation.

v t e Statistics Outline Index Descriptive statistics Continuous data Center Mean arithmetic geometric harmonic Median Mode Dispersion Variance Standard deviation Coefficient of variation Percentile Range Interquartile range Shape Moments If you had wanted to compute the 99% confidence interval, you would have set the shaded area to 0.99 and the result would have been 2.58. However, the mean and standard deviation are descriptive statistics, whereas the standard error of the mean describes bounds on a random sampling process. Because the age of the runners have a larger standard deviation (9.27 years) than does the age at first marriage (4.72 years), the standard error of the mean is larger for

## Confidence Interval Calculator For Means

If σ is known, the standard error is calculated using the formula σ x ¯   = σ n {\displaystyle \sigma _{\bar {x}}\ ={\frac {\sigma }{\sqrt {n}}}} where σ is the The standard deviation is 3.6. Since each tail is to contain 0.025 of the scores, you find the value of z for which 1-0.025 = 0.975 of the scores are below.

The ages in that sample were 23, 27, 28, 29, 31, 31, 32, 33, 34, 38, 40, 40, 48, 53, 54, and 55. If we take the mean plus or minus three times its standard error, the interval would be 86.41 to 89.59. How many standard deviations does this represent? Standard Error Of The Mean This problem is solvable, because we know that the mean of a sample is the best possible estimation of the population mean.

Since 95% of the distribution is within 23.52 of 90, the probability that the mean from any given sample will be within 23.52 of 90 is 0.95. 95 Confidence Interval Formula Excel Moreover this formula works for positive and negative ρ alike.[10] See also unbiased estimation of standard deviation for more discussion. With n = 2 the underestimate is about 25%, but for n = 6 the underestimate is only 5%. The standard error of the mean of one sample is an estimate of the standard deviation that would be obtained from the means of a large number of samples drawn from

The standard error of a proportion and the standard error of the mean describe the possible variability of the estimated value based on the sample around the true proportion or true 95% Confidence Interval The 95% confidence interval for the average effect of the drug is that it lowers cholesterol by 18 to 22 units. It is useful to compare the standard error of the mean for the age of the runners versus the age at first marriage, as in the graph. It is useful to compare the standard error of the mean for the age of the runners versus the age at first marriage, as in the graph.

## 95 Confidence Interval Formula Excel

Question 5.1 Why is the distribution of sample means around the population mean narrower and higher than that of the scores around the mean of a sample? Repeating the sampling procedure as for the Cherry Blossom runners, take 20,000 samples of size n=16 from the age at first marriage population. Confidence Interval Calculator For Means The standard deviation of the age for the 16 runners is 10.23, which is somewhat greater than the true population standard deviation σ = 9.27 years. Standard Error Formula It is rare that the true population standard deviation is known.

The sample proportion of 52% is an estimate of the true proportion who will vote for candidate A in the actual election. The correct response is to say "red" and ignore the fact that the word is "blue." In a second condition, subjects named the ink color of colored rectangles. Using the t distribution, if you have a sample size of only 5, 95% of the area is within 2.78 standard deviations of the mean. Dividing the difference by the standard deviation gives 2.62/0.87 = 3.01. Standard Error Vs Standard Deviation

To compute the 95% confidence interval, start by computing the mean and standard error: M = (2 + 3 + 5 + 6 + 9)/5 = 5. σM = = 1.118. When the true underlying distribution is known to be Gaussian, although with unknown σ, then the resulting estimated distribution follows the Student t-distribution. For this purpose, she has obtained a random sample of 72 printers and 48 farm workers and calculated the mean and standard deviations, as shown in table 1. A consequence of this is that if two or more samples are drawn from a population, then the larger they are, the more likely they are to resemble each other -

If σ is not known, the standard error is estimated using the formula s x ¯   = s n {\displaystyle {\text{s}}_{\bar {x}}\ ={\frac {s}{\sqrt {n}}}} where s is the sample Standard Error Confidence Interval Calculator The term may also be used to refer to an estimate of that standard deviation, derived from a particular sample used to compute the estimate. The concept of a sampling distribution is key to understanding the standard error.

## Between -3 and +3 standard deviations you include 99% of the cases (sample means).

However, without any additional information we cannot say which ones! Because the 5,534 women are the entire population, 23.44 years is the population mean, μ {\displaystyle \mu } , and 3.56 years is the population standard deviation, σ {\displaystyle \sigma } This number is greater than 2.576 but less than 3.291 in , so the probability of finding a deviation as large or more extreme than this lies between 0.01 and 0.001, 95 Confidence Interval Z Score The standard deviation of all possible sample means is the standard error, and is represented by the symbol σ x ¯ {\displaystyle \sigma _{\bar {x}}} .

It is important to realise that we do not have to take repeated samples in order to estimate the standard error; there is sufficient information within a single sample. The graph shows the ages for the 16 runners in the sample, plotted on the distribution of ages for all 9,732 runners. These assumptions may be approximately met when the population from which samples are taken is normally distributed, or when the sample size is sufficiently large to rely on the Central Limit Table 2: Probabilities of multiples of standard deviation for a normal distribution Number of standard deviations (z) Probability of getting an observation at least as far from the mean (two sided

Figure 1. Two data sets will be helpful to illustrate the concept of a sampling distribution and its use to calculate the standard error. A medical research team tests a new drug to lower cholesterol. One of the printers had a diastolic blood pressure of 100 mmHg.

The standard deviation of all possible sample means is the standard error, and is represented by the symbol σ x ¯ {\displaystyle \sigma _{\bar {x}}} . We do not know the population mean. However, without any additional information we cannot say which ones. The mean time difference for all 47 subjects is 16.362 seconds and the standard deviation is 7.470 seconds.

Of course, T / n {\displaystyle T/n} is the sample mean x ¯ {\displaystyle {\bar {x}}} . As will be shown, the mean of all possible sample means is equal to the population mean. The sampling distribution of the mean for N=9. National Center for Health Statistics typically does not report an estimated mean if its relative standard error exceeds 30%. (NCHS also typically requires at least 30 observations – if not more


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How to interpret regression diagnostic plots for multiple linear regression analysis (with specific example)

I recently using the day.csv file which is downloaded from http://archive.ics.uci.edu/ml/machine-learning-databases/00275/ to build a regression model for the last column “cnt” in R. This is the number of bikes rented a day. I first drop the variable "dteday" since it is not useful in building the model, and fit the model predicting cnt with the other 14 variables. Seeing that from the summary of fit1, we notice that there are only 4 significant variables with very small p-value < 0.05, which are season, atemp, casual, and registered.

    #model1
fit1=lm(cnt~instant+season+yr+mnth+holiday+weekday+workingday+weathersit+temp+atemp+hum+windspeed+casual+registered)
summary(fit1)
Call:
lm(formula = cnt ~ instant + season + yr + mnth + holiday + weekday +
workingday + weathersit + temp + atemp + hum + windspeed +
casual + registered)

Residuals:
Min         1Q     Median         3Q        Max
-2.541e-11 -2.540e-13 -3.000e-15  2.151e-13  2.653e-11

Coefficients:
Estimate Std. Error    t value Pr(>|t|)
(Intercept) -6.216e-13  4.601e-13 -1.351e+00  0.17710
instant      1.442e-15  6.651e-15  2.170e-01  0.82848
season      -9.284e-13  1.060e-13 -8.761e+00  < 2e-16 ***
yr          -6.468e-13  2.455e-12 -2.630e-01  0.79229
mnth         2.040e-13  2.051e-13  9.940e-01  0.32043
holiday     -1.644e-13  3.642e-13 -4.510e-01  0.65190
weekday      3.328e-14  2.971e-14  1.120e+00  0.26307
workingday  -3.965e-13  2.203e-13 -1.799e+00  0.07238 .
weathersit   5.849e-14  1.482e-13  3.950e-01  0.69324
temp        -2.146e-12  2.535e-12 -8.460e-01  0.39766
atemp        8.693e-12  2.873e-12  3.026e+00  0.00256 **
hum          7.270e-13  5.709e-13  1.273e+00  0.20333
windspeed    7.140e-13  8.390e-13  8.510e-01  0.39505
casual       1.000e+00  1.590e-16  6.288e+15  < 2e-16 ***
registered   1.000e+00  9.141e-17  1.094e+16  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.569e-12 on 716 degrees of freedom
Multiple R-squared:      1, Adjusted R-squared:      1
F-statistic: 7.944e+31 on 14 and 716 DF,  p-value: < 2.2e-16

Warning message:
In summary.lm(fit1) : essentially perfect fit: summary may be unreliable

Then I fit my second model with:

    fit2=lm(cnt~season+atemp+casual+registered)
summary(fit2)
par(mfrow=c(2,2))
plot(fit2)
Call:
lm(formula = cnt ~ season + atemp + casual + registered)

Residuals:
Min         1Q     Median         3Q        Max
-2.923e-12 -2.195e-13 -8.280e-14  5.450e-14  2.630e-11

Coefficients:
Estimate Std. Error    t value Pr(>|t|)
(Intercept)  4.593e-12  1.732e-13  2.652e+01  < 2e-16 ***
season       3.785e-13  5.035e-14  7.518e+00 1.65e-13 ***
atemp       -5.717e-12  4.115e-13 -1.389e+01  < 2e-16 ***
casual       1.000e+00  8.827e-17  1.133e+16  < 2e-16 ***
registered   1.000e+00  4.052e-17  2.468e+16  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.36e-12 on 726 degrees of freedom
Multiple R-squared:      1, Adjusted R-squared:      1
F-statistic: 3.701e+32 on 4 and 726 DF,  p-value: < 2.2e-16

Warning message:
In summary.lm(fit2) : essentially perfect fit: summary may be unreliable

Right now I am little confused on my regression diagnostic plots, the QQ plot seems not normal but I do not know how to interpret it. Do I need a log transformation in order to fix the plot? Also, I noticed that both my models have a very small residual standard error, and both R^2 and Adjusted R^2 are 1. Does it mean that my models are overfitted? How can I possibly fix it in this case?

Thank you so much for your help!

• R has given you a warning that you essentially have a perfect fit and that the summary is unreliable. Try examining the three points which stand out in your plots. – mdewey May 29 '16 at 11:47

No, transformations, log or any other, will not help here. R is warning you that you have an essentially perfect fit. Look at the residual standard error, about $10^{-12}$, that is, essentially zero. The few points standing out in the plots are irrelevant here, it might be just numerics. This residuals (unstandardized!) are also essentially zero, just a bit larger than the others. The number of residual degrees of freedom is large, so it is not clear why you have a perfect fit. You should investigate that.


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Home > Burst Error > Burst Error Correcting Codes

# Burst Error Correcting Codes

## Contents

Although the dimensions of the block interleaver can be arbitrary, it is useful to pick to be the length of the codeword, as it facilitates the writing phase, since we can Since is irreducible, then is either or . Therefore, the Binary RS code will have [ 2040 , 1784 , 33 ] 2 {\displaystyle [2040,1784,33]_{2}} as its parameters. Thus, the number of subsets would be at least q 2 ℓ {\displaystyle q^{2\ell }} . his comment is here

## Burst Error Correction Using Hamming Code

For example, the previously considered error vector E = ( 010000110 ) {\displaystyle E=(010000110)} , is a cyclic burst of length ℓ = 5 {\displaystyle \ell =5} , since we consider For binary linear codes, they belong to the same coset. Your cache administrator is webmaster.

This code was employed by NASA in their Cassini-Huygens spacecraft.[6] It is capable of correcting ⌊ 33 / 2 ⌋ = 16 {\displaystyle \lfloor 33/2\rfloor =16} symbol errors. This code was employed by NASA in their Cassini-Huygens spacecraft.[6] It is capable of correcting ⌊ 33 / 2 ⌋ = 16 {\displaystyle \lfloor 33/2\rfloor =16} symbol errors. Coding Theory: A First Course. Burst And Random Error Correcting Codes This is single dimension interleaving.

Further bounds on burst error correction There is more than one upper bound on the achievable code rate of linear block codes for multiple phased-burst correction (MPBC). Burst Error Correction Example If l e n g t h ( P 1 ) + l e n g t h ( P 2 ) ⩽ n + 1 , {\displaystyle \mathrm γ 3 Cambridge, UK: Cambridge UP, 2004. Print ^ http://webcache.googleusercontent.com/search?q=cache:http://quest.arc.nasa.gov/saturn/qa/cassini/Error_correction.txt ^ a b c Algebraic Error Control Codes (Autumn 2012) – Handouts from Stanford University ^ McEliece, Robert J.

Hamming Bound for Burst Error Correction [3] Theorem: If , a binary -burst error correcting code code has at most codewords Proof: Since , we know that there are bursts of Signal Error Correction Finally, it also divides: x k − p − 1 = ( x − 1 ) ( 1 + x + … + x p − k − 1 ) {\displaystyle The error can then be corrected through its syndrome. By the above observation, we know that for two different codewords c i {\displaystyle \mathbf − 3 _ − 2} and c j , B ( c i ) {\displaystyle \mathbf

## Burst Error Correction Example

Theorem (Burst error detection ability). http://www.sciencedirect.com/science/article/pii/S001999586180048X We define a a burst description to be a tuple where is the pattern of the error (that is the string of symbols beginning with the first nonzero entry in the Burst Error Correction Using Hamming Code Definitions A burst : Consider a binary representation of length l such that l > 1. Burst Error Correcting Codes Ppt Thus, we can formulate γ {\displaystyle \gamma } as γ = M t + 1 M N ≈ t N . {\displaystyle \gamma ={\frac {Mt+1}{MN}}\approx {\frac {t}{N}}.} Drawbacks of block interleaver:

It is capable of correcting any single burst of length l = 121 {\displaystyle l=121} . http://fakeroot.net/burst-error/burst-error-correcting-cyclic-codes.php Conversely, if h > λ ℓ , {\displaystyle h>\lambda \ell ,} then at least one row will contain more than h λ {\displaystyle {\tfrac {h}{\lambda }}} consecutive errors, and the ( Suppose that we have two code words c 1 {\displaystyle \mathbf − 3 _ − 2} and c 2 {\displaystyle \mathbf − 9 _ − 8} that differ by a burst Upon receiving c 1 {\displaystyle \mathbf − 3 _ − 2} , we can not tell whether the transmitted word is indeed c 1 {\displaystyle \mathbf γ 9 _ γ 8} Burst Error Correcting Convolutional Codes

Then, it follows that p ( x ) {\displaystyle p(x)} divides ( 1 + x + ⋯ + x p − k − 1 ) {\displaystyle (1+x+\cdots +x^{p-k-1})} . We can further revise our division of j − i {\displaystyle j-i} by g ( 2 ℓ − 1 ) {\displaystyle g(2\ell -1)} to reflect b = 0 , {\displaystyle b=0,} When we take difference between the errors e1 and e2, we get c (c = e1 - e2) such that c is a code-word. http://fakeroot.net/burst-error/burst-error-correcting-codes-ppt.php Since just half message is now required to read first row, the latency is also reduced by half which is good improvement over the block interleaver.

A frame can be represented by L 1 R 1 L 2 R 2 … L 6 R 6 {\displaystyle L_{1}R_{1}L_{2}R_{2}\ldots L_{6}R_{6}} where L i {\displaystyle L_{i}} and R i {\displaystyle Burst Error Correction Pdf Now, suppose that every two codewords differ by more than a burst of length ℓ . {\displaystyle \ell .} Even if the transmitted codeword c 1 {\displaystyle \mathbf γ 9 _ Cambridge, UK: Cambridge UP, 2004.

## For example, E = ( 0 1000011 0 ) {\displaystyle E=(0{\textbf γ 5}0)} is a burst of length ℓ = 7. {\displaystyle \ell =7.} Although this definition is sufficient to describe

We consider those bounds in this section. Thus, our assumption of v ( x ) {\displaystyle v(x)} being a codeword is incorrect, and therefore x i a ( x ) {\displaystyle x^{i}a(x)} and x j b ( x We confirm that 2 ℓ − 1 = 9 {\displaystyle 2\ell -1=9} is not divisible by 31 {\displaystyle 31} . Burst Error Detection And Correction Since the separation between consecutive symbols is n d , {\displaystyle nd,} the number of errors that the deinterleaved output may contain is ℓ n d + 1 . {\displaystyle {\tfrac

Let n {\displaystyle n} be the number of delay lines and d {\displaystyle d} be the number of symbols introduced by each delay line. By using this site, you agree to the Terms of Use and Privacy Policy. Interleaver Efficiency [4] A particularly useful definition for an interleaver is its efficiency. http://fakeroot.net/burst-error/burst-error-correcting-fire-codes.php Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply.

The interleaver will just reorganize the input symbols at the output. By the induction hypothesis, p | k − p {\displaystyle p|k-p} , then p | k {\displaystyle p|k} . Thus, there are a total of 2 ℓ − 1 {\displaystyle 2^{\ell -1}} possible such patterns, and a total of n 2 ℓ − 1 {\displaystyle n2^{\ell -1}} bursts of length Inst.

McEliece ^ a b c Ling, San, and Chaoping Xing.


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2020-12-01 12:47

# Layer normalization

It would be nice to support some form of layer normalization in LSTM and GRU layer (example https://github.com/pytorch/pytorch/blob/master/benchmarks/fastrnns/custom_lstms.py#L171)

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#### 5条回答

• weixin_39761655 4月前

Here's what the haste.LayerNormLSTM implementation looks like:

$\begin{pmatrix}&space;\mathbf{f}_t&space;\&space;\mathbf{i}_t&space;\&space;\mathbf{o}_t&space;\&space;\mathbf{g}_t&space;\end{pmatrix}&space;=&space;LN(\mathbf{W}_h&space;\mathbf{h}_{t-1};&space;\boldsymbol{\gamma}_1,&space;\boldsymbol{0})&space;+&space;LN(\mathbf{W}_x&space;\mathbf{x}_{t};&space;\boldsymbol{\gamma}_2,&space;\boldsymbol{0})&space;+&space;b$ $\mathbf{c}_t&space;=&space;\sigma(\mathbf{f}_t)&space;\odot&space;\mathbf{c}_{t-1}&space;+&space;\sigma(\mathbf{i}_t)&space;\odot&space;tanh(\mathbf{g}_t)$ $\mathbf{h}_t&space;=&space;\sigma(\mathbf{o}_t)&space;\odot&space;tanh(LN(\mathbf{c}_t;&space;\boldsymbol{\gamma}_3,&space;\boldsymbol{\beta}_3))$

This implementation is nearly identical to eqs. 20–22 of the layer norm paper. The differences are: 1. we don't apply a bias term to layer norms on the input or recurrent connection; these parameters are unnecessary since there's already a bias term (... + b) applied by the LSTM 1. we use $\gamma$ instead of $\alpha$ to denote the gain parameter (notation change) 1. we initialize $\gamma$ to 1 and $\beta$ to 0 instead of the other way around (seems like a typo in the paper)

I haven't gotten around to updating the docs yet but haste.LSTM can just be replaced with haste.LayerNormLSTM. Zoneout, DropConnect, etc. are all supported in LayerNormLSTM as well.

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• weixin_39738115 4月前

Nice! Having GRU would be also great, but we can probably manage with LSTMs :)

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• weixin_39761655 4月前

Our LSTM implementation is much further ahead than the GRU one so we started with LSTMs first. When we do the GRU updates, we'll keep LayerNorm in mind. Thanks for the feature request!

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• weixin_39761655 4月前

Hmm that's an interesting implementation. They're applying layer norm to $c_t$ in addition to $h_t$. The supplementary material in Ba et al. (pp. 13–14) only applies layer norm to $h_t$ in both of their LSTM variants.

Do you know if there's any follow-up literature that explains the PyTorch variant?

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• weixin_39738115 4月前

I do not about any. I personally think that any variant of GRU/LSTM with LayerNorm would be great addition.

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text:
1084 articles – 5309 references  [version française]
 HAL: in2p3-00712952, version 1
 Future prospects for the determination of the Wilson coefficient $C_(7\gamma)^\prime$Tayduganov A.Dans Nuclear Physics B - Proceedings Supplements - 16th International Conference in Quantum ChromoDynamics (QCD12), Montpellier : France (2012) - http://hal.in2p3.fr/in2p3-00712952
 Physics/High Energy Physics - Phenomenology Physics/High Energy Physics - Experiment
Future prospects for the determination of the Wilson coefficient $C_{7\gamma}^\prime$
A. Tayduganov ()1
 1: LAL - Laboratoire de l'Accélérateur Linéaire http://www.lal.in2p3.fr/ CNRS : UMR8607 – IN2P3 – Université Paris XI - Paris Sud Centre Scientifique d'Orsay B.P. 34 91898 ORSAY Cedex France
Groupe Théorie
We discuss the possibilities of assessing a non-zero View the MathML source from the direct and the indirect measurements of the photon polarization in the exclusive b→sγ(⁎) decays. We focus on three methods and explore the following three decay modes: B→K⁎(→KSπ0)γ, B→K1(→Kππ)γ, and B→K⁎(→Kπ)ℓ+ℓ−. By studying different New Physics scenarios we show that the future measurement of conveniently defined observables in these decays could provide us with the full determination of C7γ and View the MathML source.

Conference proceedings
2013
2012-07-03
Nuclear Physics B - Proceedings Supplements
international
234
S. Narison
173-176
Elsevier

16th International Conference in Quantum ChromoDynamics (QCD12)
Montpellier
France
2012-07-02
2012-07-06
A. Tayduganov

LAL 12-237
 in2p3-00712952, version 1 http://hal.in2p3.fr/in2p3-00712952 oai:hal.in2p3.fr:in2p3-00712952 From: Françoise Marechal <> Submitted on: Thursday, 28 June 2012 15:51:17 Updated on: Thursday, 4 April 2013 11:52:10