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Bayesian analysis of financial volatilities addressing long-memory, conditional heteroscedasticity and skewed error distribution

Rosy Oha, Dong Wan Shina, and Man-Suk Oh1,a

aDepartment of Statistics, Ewha Womans University, Korea
Correspondence to: 1Corresponding author: Department of Statistics, Ewha Womans University, 52 Ewhayeodae-gil, Seodaemun-gu, Seoul 03760, Korea. E-mail: msoh@ewha.ac.kr
Received July 6, 2017; Revised August 16, 2017; Accepted August 17, 2017.
Abstract

Volatility plays a crucial role in theory and applications of asset pricing, optimal portfolio allocation, and risk management. This paper proposes a combined model of autoregressive moving average (ARFIMA), generalized autoregressive conditional heteroscedasticity (GRACH), and skewed-t error distribution to accommodate important features of volatility data; long memory, heteroscedasticity, and asymmetric error distribution. A fully Bayesian approach is proposed to estimate the parameters of the model simultaneously, which yields parameter estimates satisfying necessary constraints in the model. The approach can be easily implemented using a free and user-friendly software JAGS to generate Markov chain Monte Carlo samples from the joint posterior distribution of the parameters. The method is illustrated by using a daily volatility index from Chicago Board Options Exchange (CBOE). JAGS codes for model specification is provided in the Appendix.

Keywords : ARFIMA, GARCH, skewed-t, JAGS, Bayesian, Markov chain Monte Carlo
1. Introduction

Volatility plays a crucial role in the theory and application of asset pricing, optimal portfolio allocation, and risk management. It is therefore important to introduce a model addressing the key features of volatility data sets and develop a valid estimation method. The most dominant features of the usual volatilities, the historic volatilities, the implied volatilities, and the realized volatilities are long memories, conditional heteroscedasticity and skewed error distribution.

The fractionally integrated autoregressive moving average (ARFIMA) model (Granger and Joyeux, 1980; Hosking, 1981) and the generalized autoregressive conditional heteroscedasticity (GARCH) model (Bollerslev, 1986) have been widely used to explain the long memory and the time-varying conditional variance features of volatilities, respectively. Park (2016) used a skewed student t distribution to incorporate asymmetry as well as fat tails of error distribution (Corsi et al., 2008; Grassi and Magistris, 2015; Graves et al., 2015; Maasoumi and McAleer, 2008; Wang et al., 2013).

However, none of the currently available methods propose a model incorporating all the above three features simultaneously. For example, Baillie et al. (1996) proposed the ARFIMA + GARCH model but did not incorporate the asymmetry of the error distribution. Park (2016) proposed a heterogeneous autoregressive (HAR) model to incorporate the long memory and then employed a GARCH + skewed-t distribution model to the estimated residuals obtained from fitting the HAR model to volatility data sets. Consequently, they incorporated the three features of volatilities in a stepwise fashion rather than simultaneously.

In this paper, we propose a model which combines ARFIMA, GARCH, and skewed-t distribution, namely ARFIMA + GARCH + skewed-t model, to simultaneously account for the long memory, time-varying variance, and asymmetric error distribution features of volatilities.

A Bayesian approach is used to estimate the parameters of the model. We employ Just Another Gibbs Sampler (JAGS, http://mcmc-jags.sourceforge.net/) to generate Markov chain Monte Carlo (MCMC) samples from the joint posterior distributions of the parameters. A key advantage of JAGS is that the software runs MCMC automatically once a user specifies a model (the distribution of data and the prior distributions of parameters); therefore, practitioners who are not experts in MCMC may also easily implement Bayesian inference using JAGS.

Given the posterior samples, several features of interest, such as the estimated marginal posterior densities, posterior moments, quantiles, scatter plots exhibiting interesting relations between parameters, may be derived in a straightforward manner. In addition, any restrictions on parameters, such as inequality restrictions on coefficients in the GARCH model to ensure stationarity, can be implemented in a straightforward way. Finally, useful prior information, which may be available from the data context or previous data analysis, can be used in Bayesian approaches (Czado and Min, 2011).

This paper is organized as follows. Section 2 presents the ARFIMA + GARCH + skewed-t model and the Bayesian estimation method. Section 3 presents analysis of a real data set. The final section draws conclusions.

2. Method

In this section, we describe the proposed model, the priors for the parameters, and a Markov chain Monte Carlo method for Bayesian inference.

2.1. Model

We consider a model that captures the features of conditional heteroscedasticity, long-memory, asymmetry, and fat tails via a combination of ARFIMA, GARCH, and skewed-t distribution. Long memories of volatility process yt is modeled by the ARFIMA(p, d, q) process

$Φ(B)(1-B)dyt=θ0+Θ(B)et,$

where et is a zero mean uncorrelated error sequence, d ∈ (−0.5, 1) is the fractional integration parameter, B is the backward-shift operator, and Φ(B) = 1−φ1B−· · ·−φpBp and Θ(B) = 1−θ1B−· · ·−θqBq are assumed to have roots outside the unit circle and have no common roots. The fractional differencing operator, (1−B)d, is defined as $(1-B)d=∑k=0∞πkBk$, where π0 = 1, and πk = πk−1(k − 1 − d)/k for k > 0. If d ∈ (−0.5, 0.5), yt is stationary; if d ∈ [0.5, 1), yt is nonstationary. For nonstationary series, Bayesian analysis can be made on the differenced series wt = (1− B)yt, which is always stationary for d ∈ (−0.5, 1]. The difference series wt is an ARFIMA(p, δ, q) given by Φ(B)(1− B)δ(wtμ) = Θ(B)et, where δ = d − 1 and μ = E(wt).

From Bollerslev et al., (1992), in general a GARCH(1, 1) model is sufficient to capture volatility clustering in the data. Therefore, in order to address the time-varying variance of yt, the error et in (2.1) can be assumed to follow a GARCH(1, 1) model given by

$et=σtɛt, σt2=α0+α1et-12+β1σt-12,$

where ɛt is a sequence of i.i.d. errors having zero mean and unit variance. Positivity of $σt2$ and stationarity of et are ensured via the standard restrictions: α0 > 0, α1 ≥ 0, β1 ≥ 0, and α1 + β1 < 1.

Asymmetry and fat tails are featured for the zero-mean-unit-variance error ɛt to have a standardized skewed-t distribution with skewness parameter θ and degrees of freedom ν (Lambert and Laurent, 2001). It has a probability density function (pdf)

$f(ɛt∣θ,ν)={2sθ+θ-1tν(θ(sɛt+m)),if ɛt<-ms,2sθ+θ-1tν(sɛt+mθ),if ɛt≥-ms,$

where m and s2 are the mean and the variance of the nonstandardized skewed-t distribution; in addition, tν(·) denotes the standard Student t density with ν degrees of freedom. The expected value and the variance of ɛt are given as E(ɛt) = 0, V(ɛt) = 1. The parameter θ indicates the direction and the degree of skewness. If θ = 1, the skewed-t distribution reduces to the Student t distribution.

Now we consider a model consisting of ARFIMA(1, d, 0), GARCH(1, 1), and skewed-t distribution, for which we have

$(1-φB)(1-B)δ(wt-μ)=et,et=σtɛt,σt2=α0+α1et-12+β1σt-12,ɛt∼iidStd.skt(θ,ν),$

with constraints α0 > 0, α1 ≥ 0, β1 ≥ 0, α1 + β1 < 1. We will refer this model as ARFIMA(1, d, 0) + GARCH(1, 1) + skewed-t model. The combined model takes into account all the previously mentioned important features of volatility data sets.

2.2. Priors

We assume prior independence among μ, φ, δ, (α0, α1, β1), θ, ν. All parameters except for μ should satisfy some constraints. We incorporate these constraints in prior distributions of the parameters so that posterior samples generated from MCMC as well as estimates of the parameters automatically satisfy the constraints.

A diffuse normal prior is used for μ, i.e., $μ~N(μμ,σμ2)$, with σμ large. We assume $φ~N(μφ,σφ2)I(-1,1)$ and $δ~N(μδ,σδ2)I(-1,0)$. For the prior of (α0, α1, β1), we assume π(α0, α1, β1) = π(α0, α1)π(β1)I(α0 > 0, α1 ≥ 0, β1 ≥ 0, α1 + β1 < 1), where I(·) is the indicator function. We choose π(β1) as $N(μβ1,σβ12)$. For π(α0, α1), we choose a hierarchical prior suggested by Ardia and Hoogerheide (2009):

$(α0,α1)~N((00),(σ02ρσ0σ1ρσ0σ1σ12)),$

$ρ~N(μρ,σρ2)I(-1<ρ<1)$, μρ ~ Unif(−1, 1), $σρ2~Gamma(1.5,10-4)$. Finally, we assume $θ~N(μθ,σθ2)I(θ>0)$, and $ν~N(μν,σν2)I(ν≥2)$.

2.3. Estimation

Clearly, the posterior distribution of the parameters Θ = (μ, δ, φ, α0, α1, β1, θ, ν) in the model (2.3) is not analytically tractable. Simple MCMC methods such as standard Gibbs sampling methods are not applicable to this model; therefore, Metropolis-Hastings (MH) algorithm is required to generate posterior samples of the parameters.

Implementation of the MH algorithm is often complicated for practitioners who are not experts in MCMC and/or coding. We get around this difficulty by generating MCMC samples by using user-friendly JAGS software. Given the model specification, it employs either Gibbs sampler when available or MH algorithm to generate posterior samples.

To use JAGS, the distribution of data needs to be specified as one of the distributions built in JAGS. However, the distributions in the ARFIMA(1, d, 0) + GARCH(1, 1) + skewed-t model are not commonly used distributions and are not provided by JAGS. Instead of specifying the data distribution, we can specify the likelihood function since JAGS derives the likelihood from the distribution of data and uses them for the Gibbs sampler or MH algorithm.

For the likelihood of Θ, we first derive the joint pdf of e = (e1, e2, …, eT ) from the GARCH(1, 1) and the skewed-t models, which is given as

$f(e1,e2,…,eT∣Θ)=f(e1∣Θ)f(e2∣e1,Θ)⋯f(eT∣e1,e2,…,eT-1,Θ)=fɛ(e1σ1)1σ1fɛ(e2σ2)1σ2⋯fɛ(eTσT)1σT,$

where fɛ(·) is the density function of standardized skewed-t distribution given in (2.2). Now we plug in the residuals in the ARFIMA model into (2.4). If wt is invertible, the residual et in the ARFIMA model can be represented as an infinite autoregressive (AR) process as;

$et=∑k=0∞πk((wt-k-μ)-φ(wt-k-1-μ))=∑k=0∞ψk(wt-k-μ),$

where ψk = πkπk−1φ, ψ0 = 1, πk = πk−1(k − 1 − d)/k and π0 = 1. The equation (2.5) is an infinite AR representation of ARFIMA(1, d − 1, 0). However, when T is sufficiently large and the first difference wt is stationary, we may replace (2.5) by a finite AR representation

$et=∑k=0t-1ψk(wt-k-μ).$

In usual financial volatility analysis, since data sets are recorded daily or more frequently and the series length is large, this approximation would be good. Now the likelihood function of Θ in the ARFIMA(1, d, 0) + GARCH(1, 1) + skewed-t model is given by (2.4) with et, t = 1, …, T, given in (2.6).

The likelihood function (2.4) can be specified in the model specification of JAGS, using the method suggested by Ntzoufras (2011) and Kruschke (2014). The Appendix contains the model specification used in JAGS.

3. Analysis of the volatility index data

3.1. Exploratory study

We consider a daily closing price for the volatility index (VIX), which is a measure of market expectations on volatility over the next 30 days conveyed by S&P 500 stock index option prices. The data set can be obtained from the Chicago Board Options Exchange (CBOE) web site, http://www.cboe.com/micro/vix/historical.aspx. We use data from January 3, 2006 to November 30, 2016, which contains 2,748 observations.

Time series plot of the VIX is presented in Figure 1. From the figure, we can see apparent conditional heteroscedastic feature of the VIX data; that high peaks from August 2007 to March 2009 due to the financial crisis of 2007–2008 cause large volatilities and that the relatively lower index values between 2013 and 2015 have smaller volatilities.

Table 1 shows basic summary statistics of the VIX. Figure 2 displays the histogram (with a normal approximation) and the autocorrelation function (ACF) plot of the VIX. The values of skewness, median, and mean (Table 1) and the histogram (Figure 2) show that the VIX is skewed to the right and has highly fat tails. The ACF plot of the VIX shows the feature of long memory which can be seen that the VIX is skewed to the right and has highly fat tails. The ACF plot of the VIX shows the feature of long memory which can be also supported by the GPH (Geweke and Porter-Hudak, 1983) test statistics of 8.663.

Table 2 presents the p-values of augmented Dicky-Fuller (ADF) test and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test on the VIX (Dickey and Fuller, 1979; Kwiatkowski et al., 1992). Null hypotheses of both the ADF and the KPSS tests are rejected at 5% level. Recall that the ADF and the KPSS tests have reversed the null hypothesis of unit root stationarity, respectively. It presumably indicates that there exists significant evidence that the process is a neither nonstationary nor stationary process but near nonstationary. To meet stationarity property of the series, we use the first differences of the VIX for analysis. Note that the differenced series is always stationary for d ∈ (−0.5, 1].

3.2. Analysis

We applied the proposed Bayesian method to the first differences of the VIX data and generated posterior samples of parameters using JAGS. The first 3,000 iterations are discarded as burn-in and we obtained 15,000 samples after the burn-in from 3 different chains. Convergence of MCMC is diagnosed by Gelman-Rubin shrink factors and trace plots of the MCMC samples.

Table 3 displays the estimated posterior mean, standard error, and an approximate 95% credible interval of each parameter. All parameters are significant in that their 95% credible intervals do not contain zero. The estimated posterior mean −0.332 of the fractional integration parameter δ indicates that process of the VIX has a nonstationary memory of fractional integration order of 0.668. The sum α̂1 + β̂1 = 0.991 indicates strong conditional heteroscedasticity. We also see significant asymmetry of the error distribution from the highly significant estimates σ̂ = 1.376 of the skewness parameter.

The estimates satisfy the stationary condition α̂1 + β̂1 < 1. Figure 3 displays the scatter plot of the samples of (α1, β1) when the constraints are ignored, in which the dark points represent the sample points satisfying the condition and white points, 69.54% of samples, represent those not satisfying the condition. The plot indicates that enforcing the constraints in the priors plays an important role to obtain the estimates within the stationarity region.

Figure 4 shows the estimated marginal posterior distributions of the parameters (solid line) with normal approximations (dashed line). The figure shows that marginally the posterior distributions of the parameters seem to be well approximated by normal distributions, except for α0 and ν whose distributions show slight deviations from the normal approximations. Note the marginal posterior distributions are close to normal; however, the joint posterior distributions may be significantly different from multivariate normal (Figure 3).

For comparison, we applied a model ARFIMA + GARCH + skewed-t, which fits ARFIMA model to the data and then fit GARCH + skewed-t model to the estimated residuals from the ARFIMA model. The results are presented in

The most notable differences are the estimates of the parameters of the ARFIMA model. In the ARFIMA + GARCH + skewed-t model, δ is much smaller and φ is much larger than those in the stepwise ARFIMA + GARCH + skewed-t model. This reveals that the heteroscedasticity and/or skewed error has affected the parameters of the ARFIMA model and hence the importance of simultaneous consideration of the three important features of volatilities.

We also applied ARFIMA + GARCH + t and ARFIMA + GARCH + normal models to the data, assuming t and normal error distributions, respectively, instead of skewed-t. Table 5 provides the Deviance Information Criteria (DIC) (Spiegelhalter et al., 2002) for ARFIMA + GARCH + skewed-t, ARFIMA + GARCH + t, and ARFIMA + GARCH + normal models. Among the three models, ARFIMA + GARCH + skewed-t model is the best, having the smallest DIC, which reveals the asymmetry and heavy-tails of the error distribution. Table 4 provides estimation results from ARFIMA + GARCH + t and ARFIMA + GARCH + normal models. Compared with a skewed-t distribution for the error, assuming a t distribution yields a larger δ and a smaller degrees of freedom, and a normal distribution yields a much smaller φ and larger δ, α0 and α1.

4. Conclusion

In this paper, we have proposed a fully Bayesian implementation of the ARFIMA + GARCH + skewed-t model which simultaneously takes into account the features of long memory, conditional heteroscedasticity, asymmetry and fat tails of volatility data sets. JAGS are used to generate MCMC samples of the parameters from their joint posterior distributions since it can be run automatically given model specification without expert knowledge on MCMC and coding.

Bayesian method naturally produce estimates that satisfy the stationary constraints in GARCH (1, 1), by incorporating constraints in the prior. The scatter plot of the samples of (α1, β1) show that restricting the parameter space is necessary to obtain parameter estimates that satisfy the constraints.

In this Bayesian implementation, since the likelihood function of the parameters of the ARFIMA + GARCH + skewed-t model is specified, modifying the model specification and choosing flat priors yield approximate conditional sum of squares (CSS) estimates within the stationary region based on MCMC samples. One may also apply an optimization method directly to the given likelihood function to obtain CSS estimates, instead of using MCMC samples. However, it is often relatively difficult to incorporate parameter constraints in optimization than in MCMC.

Acknowledgements

This research was supported by the Basic Science Research Program of the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2016R1A2 B4008914) (Rosy Oh and Man-Suk Oh) and (2016R1A2B4008780) (Dong Wan Shin).

Figures
Fig. 1. Time series plots of the volatility index.
Fig. 2. Histogram with normal density curve and ACF of the VIX. ACF = autocorrelation function; VIX = volatility index.
Fig. 3. Scatter plot for α1 and β1.
Fig. 4. Estimated posterior distribution (solid line) and normal distribution (dashed line).
TABLES

Table 1

Summary statistics of the volatility index data

MinMedianMeanMaxSDSkewnessKurtosis
9.89017.23020.06080.8609.5742.3927.546

Table 2

Test for unit root

p-value0.0422< 0.01

ADF = augmented Dicky-Fuller; KPSS = Kwiatkowski-Phillips-Schmidt-Shin.

Table 3

Estimation results for the first difference of volatility index from ARFIMA + GARCH + skewed-t model

Estimated posterior meanStandard error95 % credible interval

LowerUpper
μ−0.0080.002−0.013−0.004
φ0.1860.0360.1180.256
δ−0.3320.029−0.387−0.276
α00.0680.0140.0460.099
α10.2130.0230.1700.260
β10.7780.0220.7320.818
θ1.3760.0371.3041.450
ν4.4190.3173.8715.113

ARFIMA = autoregressive moving average; GARCH = generalized autoregressive conditional heteroscedasticity.

Table 4

Estimation results for the first difference of volatility index from various models

95 % credible interval

ARFIMA + GARCH + skewed-tARFIMA + GARCH + tARFIMA + GARCH + normal

Est.SELowerUpperEst.SELowerUpperEst.SELowerUpper
μ0.0010.010−0.0180.020−0.0210.004−0.029−0.015−0.0130.004−0.021−0.006
φ0.0280.030−0.0310.0880.1890.0440.1050.2780.1550.0460.0700.253
δ−0.1810.024−0.227−0.133−0.3050.037−0.379−0.236−0.2630.038−0.343−0.192
σ23.5040.0963.3203.697--------
α00.0950.0170.0650.1320.0970.0190.0620.1360.1430.0180.1100.180
α10.2670.0250.2230.3190.2490.0260.1930.2970.2530.0240.2080.304
β10.7270.0240.6750.7690.7430.0260.6960.7980.7180.0220.6750.760
θ1.2870.0301.2301.346--------
ν4.4710.3153.9155.1563.9210.2383.5054.435----

ARFIMA = autoregressive moving average; GARCH = generalized autoregressive conditional heteroscedasticity; Est. = Estimated posterior mean; SE = standard error.

Table 5

Deviance information criterion

skew-ttNormal
8886.2609033.8389508.023

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# Thread: Exponential Differentiation Help!

1. ## Exponential Differentiation Help!

Hello,

I'm currently doing an bridging course and the people who I usually ask for help have time off for Christmas. As such I am hoping to get some assistance here.

I am having trouble working out the second derivative of the following function: y=Ate^(-bt) with t being a variable, and A and B being unknown constants. The question I am solving is, "Verify the point of inflection occurs at t=2/b."

I have already found the first derivative to be A*(e^(-bt))-(bte^(-bt)), and assuming that is correct, I have worked out the following so far for the second derivative:

=A*(d/dt(e^(-bt)))-(b*(d/dt(t)*e^(-bt)))
=A*(e^(-bt)*(d/dt(-bt)))-(b*(d/dt(t)*e^(-bt))+(t*(d/dt(e^(-bt))))
=A*(-be^(-bt))-be^(-bt)+(t*e^(-bt)*(d/dt(-bt)))

After this point I am getting myself confused. I have been using http://www.derivative-calculator.net...=2&showsteps=1 as a guide, but am having trouble figuring out why the (d/dt(t)) becomes a +1, instead of just being a multiplier in the third to last line.

Once I get this derivative worked out, I then need to solve to 0 to find the PoI.

Any help will be appreciated.

Thanks.

2. Originally Posted by Whitey
Hello,

I'm currently doing an bridging course and the people who I usually ask for help have time off for Christmas. As such I am hoping to get some assistance here.

I am having trouble working out the second derivative of the following function: y=Ate^(-bt) with t being a variable, and A and B being unknown constants. The question I am solving is, "Verify the point of inflection occurs at t=2/b."

I have already found the first derivative to be A*(e^(-bt))-(bte^(-bt)), and assuming that is correct, I have worked out the following so far for the second derivative:

=A*(d/dt(e^(-bt)))-(b*(d/dt(t)*e^(-bt)))
=A*(e^(-bt)*(d/dt(-bt)))-(b*(d/dt(t)*e^(-bt))+(t*(d/dt(e^(-bt))))
=A*(-be^(-bt))-be^(-bt)+(t*e^(-bt)*(d/dt(-bt)))

After this point I am getting myself confused. I have been using http://www.derivative-calculator.net...=2&showsteps=1 as a guide, but am having trouble figuring out why the (d/dt(t)) becomes a +1, instead of just being a multiplier in the third to last line.

Once I get this derivative worked out, I then need to solve to 0 to find the PoI.

Any help will be appreciated.

Thanks.
That is incorrect.

d/dt[A*t*e(-bt)] = A * d/dt[t * e(-bt)] = A * [t * (-b) * e(-bt) + e(-bt)] = A * e(-bt) * [1 - bt]

d2/dt2[A*t*e(-bt)] = d/dt {A * [1 - bt]* e(-bt)} = A * d/dt {[1 - bt]* e(-bt)} = A * {[1-bt]*(-b) * e(-bt) + (-b) * e(-bt)} = A * (-b) * e(-bt) * {2-bt}

d2/dt2[A*t*e^(-bt)] = -Ab(2-bt)e(-bt)

3. Originally Posted by Subhotosh Khan
Thatis incorrect.

d/dt[A*t*e^(-bt)] = A * d/dt[t * e^(-bt)] = A * [t * (-b) * e^(-bt) + e(-bt)] = A * e^(-bt) * [1 - bt]
Thanks for your reply. Sorry if this comes across as unappreciative or rude, but shouldn't that be "e^(-bt)", making my original answer correct?

4. Originally Posted by Whitey
Thanks for your reply. Sorry if this comes across as unappreciative or rude, but shouldn't that be "e^(-bt)", making my original answer correct?
In your answer, A is multiplied with only the first term - that is incorrect.

By the way, if you notice the next line of my response you would see that I had corrected that typo.

5. Originally Posted by Subhotosh Khan
In your answer, A is multiplied with only the first term - that is incorrect.

By the way, if you notice the next line of my response you would see that I had corrected that typo.
That was my mistake. I was meant to write A*((e^(-bt))-(bte^(-bt))), but missed a set of parentheses. Downside to writing functions late at night I guess.

I was more so wondering how you got the (1 - bt) in your first derivative, as this is the only difference to my answer, and I can't quite put it together in my head.

6. Originally Posted by Whitey
That was my mistake. I was meant to write A*((e^(-bt))-(bte^(-bt))), but missed a set of parentheses. Downside to writing functions late at night I guess.

I was more so wondering how you got the (1 - bt) in your first derivative, as this is the only difference to my answer, and I can't quite put it together in my head.
Maybe easier to see without all the paren: let u = e^(-bt), then
A*((e^(-bt))-(bte^(-bt))) = A ( u - b t u) = A u (1 - b t) = A e-bt (1 - b t)
as Subhotosh Khan has.

7. Originally Posted by Ishuda
Maybe easier to see without all the paren: let u = e^(-bt), then
A*((e^(-bt))-(bte^(-bt))) = A ( u - b t u) = A u (1 - b t) = A e-bt (1 - b t)
as Subhotosh Khan has.
So if I am reading this right, (-bte^(-bt)) can be simplified to (1 - bt)? I wasn't aware that this was possible, though the booklet I have been given for this course is quite brief on explanations. Is this done by taking the derivative of (-bte^(-bt))? Or is e able to equal 1 without adding Ln to both sides?

8. Originally Posted by Whitey
So if I am reading this right, (-bte^(-bt)) can be simplified to (1 - bt)? I wasn't aware that this was possible, though the booklet I have been given for this course is quite brief on explanations. Is this done by taking the derivative of (-bte^(-bt))? Or is e able to equal 1 without adding Ln to both sides?
You are not reading it right.

9. Let's simplify the problem:
Originally Posted by Whitey
y=Ate^(-bt)
find t when y'' = 0
We can also drop the A since that is going to come out in the wash so we now have
y = te-bt
by chain rule: (y = f(x)g(x) -> y' = f'(x)g(x) + f(x)g'(x)
y' = e-bt - bt*e-bt
y'' = -b*e-bt - b[e-bt - bt*e-bt]
collect some terms:
y'' = b2t * e-bt - 2b*e-bt
y'' = (b2t -2b)*e-bt
Now solve:
b2t = 2b (since ex != 0 for any x)
t = 2/b

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text:
The steady-state response of the classic mass-spring-dashpot model when the spring stiffness decays exponentially with time (an aging spring) and the system is excited by a forcing function whose frequency is equal to the natural frequency of the system with the constant initial stiffness is investigated. The steady-state response is obtained in terms of the dumping and decay constants of the system and exhibits an oscillation about a nonzero value.

1.
Chen
,
H.
, and
Wu
,
T. T.
,
1970
, “
An Aging Spring
,”
Stud. Appl. Math.
,
XLIX
, No.
2
, pp.
183
185
.
2.
Wan, F. Y. M., 1976, “Education Notes, Applications of Differential Equations,” Applied Mathematics Note, Vol. 2, Canadian Applied Math Soc., pp. 27–31.
3.
Chopra, A. K., 2001, Dynamics of Structures, 2nd Ed., Prentice-Hall, Englewood Cliffs, NJ, Section 3.2.2.
4.
Hildebrand, F. B., 1976, Advanced Calculus for Applications, 2nd Ed., Prentice-Hall, Englewood Cliffs, NJ.


text:
# tetration

Tetration is the next iteration of arithmetic operations after addition, multiplication, and exponentiation. To tetrate a number $$a$$ to the order $$n$$ is to exponentiate $$a$$ with itself $$n$$ times:

$\mbox{ }^n\! a=\underbrace{ {{{a^{a\vphantom{h}}}^{\!\unicode{x22F0}\vphantom{h}}}^{\mbox{}\vphantom{h}} }^{\!a\vphantom{h}} }_{\text{n times}}$

Note that the base itself is counted as one of the exponents for purposes of tetration.

Just as multiplication is repeated addition and exponentiation is repeated multiplication, so tetration is repeated exponentiation. (The word was formed by use of the Greek prefix tetr, meaning “fourth,” since it is the fourth operation in the sequence beginning with addition.) This operation was popularized by Rudy Rucker in his book Infinity and the Mind, and there remain interesting open questions about it. For instance, it is not known if $$\mbox{ }^n\! q$$ is rational for any integer $$n$$ and non-integer rational number $$q$$.


text:
Seminar Calendar
for Graph Theory and Combinatorics events the next 12 months of Sunday, January 1, 2017.

.
events for the
events containing

More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
    December 2016           January 2017          February 2017
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2  3    1  2  3  4  5  6  7             1  2  3  4
4  5  6  7  8  9 10    8  9 10 11 12 13 14    5  6  7  8  9 10 11
11 12 13 14 15 16 17   15 16 17 18 19 20 21   12 13 14 15 16 17 18
18 19 20 21 22 23 24   22 23 24 25 26 27 28   19 20 21 22 23 24 25
25 26 27 28 29 30 31   29 30 31               26 27 28

Tuesday, January 24, 2017

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, January 24, 2017
 Del Edit Copy
Submitted by molla.
 Many $T$ copies in $H$-free subgraphs of random graphsAbstract: For two fixed graphs $T$ and $H$ let $ex(G(n,p),T,H)$ be the random variable counting the maximum number of copies of $T$ in an $H$-free subgraph of the random graph $G(n,p)$. We show that for the case $T=K_m$ and $\chi(H)>m$ the behavior of $ex(G(n,p),K_m,H)$ depends strongly on the relation between $p$ and $m_2(H)=\max_{H'\subset H, |V(H')|\geq 3}\left\{ \frac{e(H')-1}{v(H')-2} \right\}$. When $m_2(H)>m_2(K_m)$ we prove that with high probability, depending on the value of $p$, either one can keep almost all copies of $K_m$ in an $H$-free subgraph of $G(n,p)$, or it is asymptotically best to take a $\chi(H)-1$ partite subgraph of $G(n,p)$. The transition between these two behaviors occurs at $p=n^{-1/m_2(H)}$. When $m_2(H)< m_2(K_m)$, the above cases still exist, however for $\delta>0$ small at $p=n^{-1/m_2(H)+\delta}$ one can typically still keep most of the copies of $K_m$. The reason for this is that although $K_m$ has the minimum average degree among the $m$-color-critical graphs, it does not have the smallest $m_2(G)$ among such graphs. This is joint work with N. Alon and C. Shikhelman.

Tuesday, January 31, 2017

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, January 31, 2017
 Del Edit Copy
Submitted by molla.
 Anton Bernshteyn (Illinois Math)DP-colorings of graphs with high chromatic numberAbstract: Let $G$ be an $n$-vertex graph with chromatic number $\chi(G)$. Ohba's conjecture (now a celebrated theorem due to Noel, Reed, and Wu) claims that whenever $\chi(G) \geq (n-1)/2$, the list chromatic number of $G$ equals $\chi(G)$. DP-coloring is a generalization of list coloring introduced recently by Dvořák and Postle. We establish an analog of Ohba's conjecture for the DP-chromatic number; namely we show that the DP-chromatic number of $G$ also equals $\chi(G)$ as long as $\chi(G)$ is sufficiently large''. In contrast to the list coloring case, large'' here means $\chi(G)\geq n-O(\sqrt{n})$, and we also show that this lower bound is best possible (up to the constant factor in front of $\sqrt{n}$). This is joint work with Alexandr Kostochka and Xuding Zhu.

Tuesday, February 7, 2017

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, February 7, 2017
 Del Edit Copy
Submitted by molla.
 Ruth Luo (Illinois Math)The maximum number of cliques in graphs without long cyclesAbstract: The Erdős-Gallai Theorem states that for $k\geq 3$ every graph on $n$ vertices with more than $\frac{1}{2}(k-1)(n-1)$ edges contains a cycle of length at least $k$. Kopylov proved a strengthening of this result for 2-connected graphs with extremal examples $H_{n,k,t}$ and $H_{n,k,2}$. In this talk, we generalize the result of Kopylov to bound the number of $s$-cliques in a graph with circumference less than $k$. Furthermore, we show that the same extremal examples that maximize the number of edges also maximize the number of cliques of any fixed size. Finally, we obtain the extremal number of $s$-cliques in a graph with no path on $k$-vertices.

Tuesday, February 14, 2017

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, February 14, 2017
 Del Edit Copy
Submitted by molla.
 Sarka Petrickova (Illinois Math)Families in posets minimizing the number of comparable pairsAbstract: Given a poset $P$, we say a family $\mathcal{F} \subseteq P$ is centered if it is obtained by `taking sets as close to the middle layer as possible'. A poset $P$ is said to have the centeredness property if for any $M$, amongst all families of size $M$ in $P$, centered families contain the minimum number of comparable pairs. Kleitman showed that the Boolean lattice $\{0,1\}^n$ has the centeredness property. It was conjectured by Noel, Scott, and Sudakov, and by Balogh and Wagner, that the poset $\{0,1,\ldots,k\}^n$ (where $(A_1,\dots,A_n)\le (B_1,\dots,B_n)$ if $A_i\le B_i$ for each $i\in [n]$) also has the centeredness property, provided $n$ is sufficiently large compared to $k$. We show that this conjecture is false for all $k\geq 2$ and investigate the range of $M$ for which it holds. Further, we improve a result of Noel, Scott, and Sudakov by showing that the poset of subspaces of $\mathbf{F}_q^n$ has the centeredness property. This is joint work with Jozsef Balogh and Adam Zsolt Wagner.

Tuesday, February 21, 2017

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, February 21, 2017
 Del Edit Copy
Submitted by molla.
 Douglas B. West (Illinois Math and Zhejiang Normal University)Reconstruction from the deck of $k$-vertex induced subgraphsAbstract: The $k$-deck of a graph is its multiset of subgraphs induced by $k$ vertices; we ask whether the $k$-deck determines the graph. We show that a complete $r$-partite graph is determined by its $(r+1)$-deck. Letting $n=|V(G)|$, we generalize a result of Bollobás by showing that for $l=(1-o(1))n/2$, almost every graph $G$ is determined by various sets of ${l+2\choose 2}$ subgraphs with $n-l$ vertices. However, when $l=n/2$, the entire $(n-l)$-deck does not always determine whether $G$ is connected (it fails for $n$-vertex paths). We strengthen a result of Manvel by proving for each $l$ that when $n$ is sufficiently large (at least $l^{l^2}$), the $(n-l)$-deck determines whether $G$ is connected ($n\ge25$ suffices when $l=3$, and $n\le 2l$ cannot suffice). Finally, for every graph $G$ with maximum degree $2$, we determine the least $k$ such that $G$ is reconstructible from its $k$-deck, which involves extending a result of Stanley. This is joint work with Hannah Spinoza.

Tuesday, February 28, 2017

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, February 28, 2017
 Del Edit Copy
Submitted by molla.
 Misha Lavrov (Carnegie Mellon University)Distance-uniform graphs with large diameterAbstract: We say that a graph is epsilon-distance-uniform if there is a value d (called the critical distance) such that, for every vertex v, all but an epsilon fraction of the other vertices are at distance exactly d from v. Random graphs are distance-uniform with logarithmic critical distance, and it was conjectured by Alon, Demaine, Hajiaghayi, and Leighton that the critical distance (equivalently, the diameter) of a distance-uniform graph must always be logarithmic. In this talk, we use a generalization of the Towers of Hanoi puzzle to construct distance-uniform graphs with a much larger diameter: for constant epsilon, as large as n^O(1/log log n). We show that this construction is more or less worst possible for sufficiently small epsilon, leaving open the possibility that for large epsilon, much worse cases exist. This is joint work with Po-Shen Loh.

Tuesday, March 7, 2017

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, March 7, 2017
 Del Edit Copy
Submitted by molla.
 Gexin Yu (College of William & Mary)The strong chromatic index of graphs with maximum degree four is at most 21Abstract: A strong edge-coloring of a graph $G$ is a coloring of the edges such that every color class induces a matching in $G$. The strong chromatic index of a graph is the minimum number of colors needed in a strong edge-coloring of the graph. In 1985, Erdős and Nešetřil conjectured that every graph with maximum degree $\Delta$ has a strong edge-coloring using at most $\frac{5}{4}\Delta^2$ colors if $\Delta$ is even, and at most $\frac{5}{4}\Delta^2 - \frac{1}{2}\Delta + \frac{1}{4}$ if $\Delta$ is odd. This conjecture is widely unresolved with the only verified case being for $\Delta = 3$, due independently to Andersen as well as Horák, Qing, and Trotter. In this paper, we show that the strong chromatic index of graphs (where we allow for multiple edges) with maximum degree at most four is always at most 21. This improves a previous bound due to Cranston and moves closer to the conjectured upper bound of 20. This is joint work with Mingfang Huang and Michael Santana.

Tuesday, March 14, 2017

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, March 14, 2017
 Del Edit Copy
Submitted by molla.
 Katherine Anders (The University of Texas at Tyler)Rooted forests that avoid sets of permutationsAbstract: An unordered rooted labeled forest avoids the pattern $\pi\in\mathcal{S}_n$ if the sequence obtained from the labels along the path from the root to any vertex does not contain a subsequence that is in the same relative order as $\pi$. We enumerate several classes of forests that avoid certain sets of permutations, including the set of unimodal forests, via bijections with set partitions with certain properties. This is joint work with Kassie Archer.

Tuesday, March 28, 2017

Graph Theory and Combinatorics Semianr
3:00 pm   in 241 Altgeld Hall,  Tuesday, March 28, 2017
 Del Edit Copy
Submitted by molla.
 Zoltán Furëdi (Illinois Math and Renyi Institute of Mathematics)Combinatorial geometry problems and Turán hypergraphsAbstract: We overlook a few applications of using extremal hypergraphs in combinatorial geometry questions. A sample result: Let $h(n)$ be the maximum number of triangles among $n$ points on the plane which are almost regular (all three angles are between 59 to 61 degrees). Conway, Croft, Erdős and Guy (1979) proved an upper bound for $h(n)$ and conjectured that $h(n)=(1+o(1)) n^3/ 24$. We prove this (and other) conjectures. Among our main tools we use Razborov's flag algebra method to determine the Turán numbers of certain 3-uniform hypergraphs. This is a joint work with Imre Bárány (with some computer help from Manfred Scheucher).

Tuesday, April 4, 2017

Graph Theory and Combinatorics Semianr
3:00 pm   in 241 Altgeld Hall,  Tuesday, April 4, 2017
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Submitted by molla.
 Mariusz Meszka (AGH University of Science and Technology, Kraków, Poland)Orthogonal one-factorizations\\ of complete multipartite graphsAbstract: A one-factor of a graph $G$ is a regular spanning subgraph of degree one. A one-factorization of $G$ is a set ${\cal F}=\{F_1,\,F_2,\ldots ,F_r\}$ of edge-disjoint one-factors such that $E(G)=\bigcup_{i=1}^r E(F_i)$. Two one-factorizations ${\cal F}=\{F_1,\,F_2,\ldots ,F_r\}$ and ${\cal F'}=\{F'_1,\,F'_2,\ldots ,F'_r\}$ are orthogonal if $|F_i\cap F'_j|\leq 1$ for all $1\leq i < j \leq r$. A set of $k$ one-factorizations $\{{\cal F}^1,{\cal F}^2,\ldots ,{\cal F}^k\}$ of $G$ is mutually orthogonal if, for every $1\leq i < j\leq k$, ${\cal F}^i$ and ${\cal F}^j$ are orthogonal. A pair of orthogonal one-factorizations of an $s$-regular graph $G$ on $2n$ vertices corresponds to the existence of a Howell design of type $(s,2n)$, for which a graph $G$ is called an underlying graph. Let $S$ be a set of $2n$ symbols. A Howell design $H(s,2n)$ on the symbol set $S$ is an $s\times s$ array that satisfies the following conditions: (1) every cell is either empty or contains an unordered pair of symbols from $S$, (2) every symbol of $S$ occurs exactly once in each row and exactly once in each column of $H$, (3) every unordered pair of symbols occurs in at most one cell of $H$. Necessary condition for the existence of Howell designs $H(s,2n)$ is $n\leq s\leq 2n-1$. A pair of orthogonal one-factorizations of a complete bipartite graph $K_{n,n}$ corresponds to a Howell design $H_k(n,2n)$, and moreover they are equivalent to a pair of mutually orthogonal latin squares of side $n$. In the other extreme case, an $H(2n-1,2n)$ is a Room square of side $2n-1$, which corresponds to two orthogonal one-factorizations of a complete graph $K_n$. An important question related to Howell designs concerns properties of graphs which are underlying graphs of Howell designs. While for $s=2n-1$ and $s=2n-2$ these graphs are unique (the complete graph $K_{2n}$ and the cocktail party graph $K_{2n}\setminus F$, respectively, where $F$ is a one-factor), determining these graphs in general seems to be hopeless. The goal of this talk is to show that balanced complete multipartite graphs are underlying graphs of Howell designs. The main result provides almost complete solution to the existence problem of two orthogonal one-factorizations of a complete balanced multipartite graph $K_{p\times q}$. Some infinite families of $k$ mutually orthogonal one-factorizations of $K_{p\times q}$ for $k\geq 3$ will be also presented.

Tuesday, April 11, 2017

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, April 11, 2017
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Submitted by molla.
 Jaehoon Kim (University of Birmingham)On the number of Hamiltonian subsetsAbstract: In 1981, Komlós conjectured that among all graphs with minimum degree at least $d$, the complete graph $K_{d+1}$ minimises the number of Hamiltonian subsets, where a subset of vertices is Hamiltonian if it contains a spanning cycle. We prove this conjecture when $d$ is sufficiently large. In fact we prove a stronger result: for large $d$, any graph $G$ with average degree at least $d$ contains almost twice as many Hamiltonian subsets as $K_{d+1}$, unless $G$ is isomorphic to $K_{d+1}$ or a certain other graph which we specify. This is joint work with Hong Liu, Maryam Sharifzadeh and Katherine Staden.

Tuesday, April 18, 2017

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, April 18, 2017
 Del Edit Copy
Submitted by molla.
 Kevin Ford (Illinois Math)Permutations fixing k-sets and applications to group theoryAbstract: A $k$-set of a permutation $\pi\in S_n$ is a subset $I\in [n]$ of size $k$ which is itself permuted by $\pi$. Equivalently, $I$ is a product of a subset of the cycles of $\pi$. In this talk, we discuss two problems: (1) If one chooses $r>1$ permutations at random, what is the likelihood that for some large $k$ each contains a $k$-set? This has application to the problem of invariable generation of $S_n$, and is connected with a famous old problem of Erdős: to show that almost all integers have two divisors in some dyadic interval $(y,2y]$. (2) Given $k_1, k_2, \ldots, k_m$ what is the likelihood that a random $\pi$ has a $k_1$-set, $k_2$-set, ..., $k_m$-set (all disjoint)? Such bounds are applied to the problem of estimating how many permutations $\pi \in S_n$ lie in transitive subgroups of $S_n$ other than $S_n$ or $A_n$. This is joint work with Sean Eberhard, Ben Green and Dimitrios Koukoulopoulos.

Tuesday, April 25, 2017

Graph Theory and Combinatorics Seminar
3:00 pm   in Altgeld Hall,  Tuesday, April 25, 2017
 Del Edit Copy
Submitted by molla.
 Chao Xu (Illinois Computer Science)Small $k$-certificate in hypergraphs and representing all min-cutsAbstract: For a hypergraph $H=(V,E)$, a hypergraph $H'=(V,E')$ is called a $k$-certificate of $H$ if it preserves all the cut values up to $k$. That is, $|\delta_{H'}(S)| \geq \min(|\delta_H(S)|,k)$ for all $S\subset V$. Nagamochi and Ibaraki showed there exists a $k$-certificate with $O(kn)$ edges for graphs, where $n$ is the number of vertices. A similar argument shows this extends to hypergraphs. We show a stronger result of hypergraphs: there is a $k$-certificate with size (sum of degrees) $O(kn)$, and it can be obtained by removing vertices from edges in $H$. We also devise an algorithm that finds a representation of all min-cuts in a hypergraph in the same running time as finding a single min-cut. The algorithm uses Cunningham's decomposition framework, and different generalizations of maximum adjacency ordering. This is joint work with Chandra Chekuri.

Tuesday, May 2, 2017

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, May 2, 2017
 Del Edit Copy
Submitted by molla.
 Louis DeBiasio (Miami University)Infinite graph-Ramsey theoryAbstract: Ramsey's theorem guarantees a monochromatic copy of any countably infinite graph $G$ in any $r$-coloring of the edges of the complete graph $K_\mathbb{N}$. It is natural to wonder how "large" of a monochromatic copy of $G$ we can find with respect to some measure -- for instance, the (upper) density of the vertex set of $G$ in $\mathbb{N}$. Unlike finite graph-Ramsey theory, where this question has been studied extensively, the infinite version has been mostly overlooked. Erdős and Galvin proved that in every 2-coloring of $K_\mathbb{N}$, there exists a monochromatic path whose vertex set has upper density at least $2/3$, but it is not possible to do better than $8/9$. They also showed that there exists a monochromatic path $P$ such that for infinitely many $n$, the set $\{1,2,...,n\}$ contains the first $\frac{n}{3+\sqrt{3}}$ vertices of $P$, but it is not possible to do better than $2n/3$. We improve both results, in the former case achieving an upper density at least $3/4$ and in the latter case obtaining a tight bound of $2/3$. Inspired by this, we consider infinite analogs of well-known finite results on directed paths, trees (connected subgraphs), and graphs of bounded maximum degree/chromatic number. Joint work with Paul McKenney


text:
# Indefinite Integral

1. Sep 5, 2013

### tylersmith7690

1. The problem statement, all variables and given/known data
Sorry for the poor use of Latex, I have tried to get it to work but it seems to never come out as I would like.

Using a trigonometric or hyperbolic substitution, evaluate the following indfe nite integral,

∫$\frac{1}{\sqrt{(x^2-1)^5}}$ dx

2. Relevant equations

I have got down to a point where I am stuck and was wondering which path to go down next.

3. The attempt at a solution

let x=cosh$\phi$
dx/d$\phi$=sinh$\phi$
dx=sinh$\phi$ d$\phi$

Then (x2-1) = cosh2$\phi$-1
= sinh2$\phi$

(x2-1)1/2= sinh$\phi$
(x2-1)5/2= sinh5$\phi$

therefore ∫sinh$\phi$/sinh5$\phi$
=∫1/sinh4$\phi$
=∫cosec2$\phi$

Is this right so far, Do i then split the (cosec$\phi$)^4 into two and do the integral then.?

2. Sep 5, 2013

### Curious3141

The last integral should be $\int (\mathrm{csch} \phi)^4 d\phi$, shouldn't it?

There might well be an easier way to go about this with hyperbolic trig identities, but I would do it with a mainly algebraic integral.

First convert to the exponential form. I'm going to be using y instead of $\phi$ for ease of Latex:

You have to evaluate $\int \frac{16}{(e^y - e^{-y})^4}dy$.

Sub $u = e^y$. Simplify. You'll end up with a $u^3$ in the numerator, and a $(u^2 - 1)^4$ in the denominator. There's a clever way to split this up so you can integrate by parts. And this can be repeated one more time.

3. Sep 5, 2013

### vanhees71

So far it looks good (in the last line it must be $\text{cosech}^4 x$ of course.

My next guess is that it might help to use
$$\cosh^2 x-\sinh^2 x=1$$
in the numerator of the integrand ;-).


text:
One face of the cube is $ABCD$ having side of length 'l'
At the center of the cube a charge $+q =+l \mu c$ is placed, then according to guass's theorem , electric fluic through the six faces (all faces) of the cube will be $\large\frac{q}{6 \in_0}$$Nm^2c^{-1}$


text:
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Comment

Well, Anon 10:57, at least Mike Buck with his "abominable" comment had the insouciance to disclose his name (I'm assuming it is his name) whereas you, with your totally orthodox piece of "middle-class morality", prefer to remain incognito. Why is that? - since you said nothing in the slightest degree risqué.


text:
# statsmodels.multivariate.cancorr.CanCorr¶

class statsmodels.multivariate.cancorr.CanCorr(endog, exog, tolerance=1e-08, missing='none', hasconst=None, **kwargs)[source]

Canonical correlation analysis using singluar value decomposition

For matrices exog=x and endog=y, find projections x_cancoef and y_cancoef such that:

x1 = x * x_cancoef, x1’ * x1 is identity matrix y1 = y * y_cancoef, y1’ * y1 is identity matrix

and the correlation between x1 and y1 is maximized.

endog

array – See Parameters.

exog

array – See Parameters.

cancorr

array – The canonical correlation values

y_cancoeff

array – The canonical coeefficients for endog

x_cancoeff

array – The canonical coefficients for exog

References

Methods

 corr_test() Approximate F test Perform multivariate statistical tests of the hypothesis that there is no canonical correlation between endog and exog. fit() Fit a model to data. from_formula(formula, data[, subset, drop_cols]) Create a Model from a formula and dataframe. predict(params[, exog]) After a model has been fit predict returns the fitted values.

Attributes

 endog_names Names of endogenous variables exog_names Names of exogenous variables


text:
## How to determine the base weapon damage for weapons that exceed the size table?

So I am playing a barbarian wielding a Butchering Axe. Last night it happened that by some glory magic my human (medium sized) barbarian was being enlarged letting his terrifying weapon become even more devastating.

So we checked the rulebook for what its new base damage would be. But unfortunately, the table ends at medium sized 2d6 becoming 3d6.

But since the Butchering Axe at medium size has already a weapon damage of 3d6, we tried to make out the pattern of the table which at that point was ambiguous (for us at least) we thought it either might be 4d6 following the increase from 2d6 to 3d6, or it might be 3d10 due to the steps at lower base damage weapons.

So the question is:

What is the weapons damage to be rolled here and by which pattern would this be identified for weapons exceeding the books printed table?

## Is there a recommended party size for Waterdeep: Dragon Heist?

I’m planning on starting a campaign of Waterdeep: Dragon Heist tomorrow, but it’s looking like we may only have two players (plus me as DM) for it. The other published adventures I’ve used (Lost Mine of Phandelver and Storm King’s Thunder) each say a recommended party size for them, which we haven’t always had but helped me figure out how much I needed to adjust the included encounters when we had fewer players. But I can’t find within Dragon Heist the party size that it’s designed for. Due to it being more of an intrigue-based campaign than a hack-and-slash style, does it work just as well if you have two PCs or six?

## Obscurement encounter advice with size differences

I would like to run a 5e encounter in a grassy plains, with tall grass about 3–4ft high. Based on the RAW in the PHB, I am taken to thinking that small creatures (goblins) are effectively under heavy obscurement. That is, creatures trying to see the goblins are looking through thick grass. Normal medium sized creatures, however, are standing about waist high, and would be lucky to be lightly obscured.

Concealment is explained in the RAW on page 183:

“A given area might be lightly or heavily obscured. In a lightly obscured area, such as dim light, patchy fog, or moderate foliage, creatures have disadvantage on Wisdom (Perception) checks that rely on sight. A heavily obscured area-such as darkness, opaque fog, or dense foliage-blocks vision entirely. A creature in a heavily obscured area effectively suffers from the blinded condition (see appendix A).”

My problem is that the RAW designate an area as under concealment. In a case such as this, where there is a clear line between obscurement (grass) and no obscurement (no grass), there should be some deliberation here. It seems the lines of sight should differ for different size groups as a result of treating those groups as obscured or not. For example, these size groups in 3–4ft grass. (Read ‘→’ as “looking at”.)

• Small → Small (Small creatures would be heavily obscured. Is the grass interfering with the perception roll of the perceiver?)

• Small → Medium (Medium creatures, it would seem, should not be considered under the effects of obscurement, but would the small creatures still have trouble seeing over the grass? i.e. Are they under the effects of heavy obscurement by nature of being in the grass?)

• Medium → Small (Small creatures would be heavily obscured, so a medium creature should have trouble spotting them, but the perceiver itself isn’t in heavy obscurement.)

• Medium → Medium (Neither creature should gain any obscurement, but maybe this case could be interesting if there were stealth checks involved or prone creatures.)

My actual question is if we can treat obscurement conditionally, with different sized creatures being a factor, instead of “always on” or “always off” in a given area. It would seem errata v1.0 says:

A heavily obscured area doesn’t blind you, but you are effectively blinded when you try to see something obscured by it

Which is decidedly different, turning the condition to the area doing the obscuring to your target, rather than creatures being in a state of obscurement.

I am aware of a lengthy discussion about cloud of fog and how attacks work, so I’m pretty clear on that aspect, but I’m mostly asking about what the state of vision is like here.

How does concealment work?

Additionally, the only possible thing that was left unanswered in that discussion is about positions and whether sight is required to know a target’s position, considering creatures making noise from attacks and movement. Of note, in RAW it says heavily obscured areas block vision but not any other senses. It would be interesting if someone had input here, but in this particular case, since they’re goblins, they will be using bonus actions to hide.

## What size category is a reduced Tarrasque?

The rule for a creature’s size is as follows on Monster Manual page 6:

$$\begin{array}{lll} \textbf{Size} & \textbf{Space} & \textbf{Examples} \ \hline \text{Tiny} & \text{2½ by 2½ ft.} & \text{Imp, sprite} \ \text{Small} & \text{5 by 5 ft.} & \text{Giant rat, goblin} \ \text{Medium} & \text{5 by 5 ft.} & \text{Orc, werewolf} \ \text{Large} & \text{10 by 10 ft.} & \text{Hippogriff, ogre} \ \text{Huge} & \text{15 by 15 ft.} & \text{Fire giant, treant} \ \text{Gargantuan} & \text{20 by 20 ft. or larger} & \text{Kraken, purple worm} \ \end{array}$$

The Monster Manual page 268 states:

A scaly biped, the tarrasque is fifty feet tall and seventy feet long, weighing hundreds of tons.

And the Reduce use of the Enlarge/Reduce spell states:

The target’s size is halved in all dimensions, and its weight is reduced to one-eighth of normal. This reduction decreases its size by one category – from Medium to Small, for example.

Emphasis mine.

In the case of our Tarrasque, these statements in Reduce are contradictory. Its new size is now 25′×35′, which means it’s still classified as Gargantuan.

Which rule takes priority?

We can break the rules even more here. If we assume the Tarrasque is now huge rather than gargantuan, PHB 192 states:

Squeezing into a Smaller Space: A creature can squeeze through a space that is large enough for a creature one size smaller than it. Thus, a Large creature can squeeze through a passage that’s only 5 feet wide. While squeezing through a space, a creature must spend 1 extra foot for every foot it moves there, and it has disadvantage on attack rolls and Dexterity saving throws. Attack rolls against the creature have advantage while it’s in the smaller space.

This means our 25′×35′ beastie can now get through a 10 foot door.

## Trying to install dual boot leads to glitched screen: “Couldn’t get size”

I recently bought a Lenovo Legion Y740 laptop. It came with Windows 10 and I want to install Ubuntu as a dual boot.

I am trying to boot from a USB where I have a 18.04.3-desktop-amd64.iso image. Whenever I boot it, I get the black screen with a list of options and chose to “Install Ubuntu”. Right after, my screen goes black and get a “Couldn’t get size: 0x000000000000000a” message. Then the rest of the screen begins to get ‘glitchy’ prints. However, I still hear the Ubuntu startup sound from the speakers.

I have done this once before on another laptop and had no problems. I have no idea what it could be. I’ve heard Nvidia and Ubuntu don’t do great together and the installer says AMD. Could it be this? My other laptop where it worked had no GPU, however this one has a RTX 2070 MaxQ.

Any help would be appreciated.

Nil

## How to increase the Linux disk size in dual boot Windows 10 system

I would like to increase the my Linux disk from 40 GB ( around 3 GB is free) to 60 GB. My Dual boot system (Windows 10 and Ubuntu 18.04) does NOT have Linux swap partition.So, i can not follow the other answers in this forum. My disk DParted image

## libpng warning: Application jmp_buf size changed Segmentation fault when try to run xampp installation file

I trying to install XAMPP on my ubuntu 18.04 but I got this warning from libpng by running this command:

sudo ./xampp-linux-x64-7.3.9-0-installer.run

The thing need to be considered is that I got this warning on all versions of XAMPP. Someone already asks the same question there libpng warning : Application jmp_buf size changed – while installing XAMPP but the answer is useless. Its a humble request please help.

## ubuntu 18 screen size is too big and draggable?

Screen size of my laptop is almost 4 times and i need to drag the screen right\left or top/bottom to use it. How this can be solved?

## Maximum size for sensitive information

everyone.

I’m developing an app that allows users to manage their financial products. This app shows information about accounts and cards.

My question is: There is a maximum font size to give, for example the balance information. Considering that the person next to you can see at your screen?

## Algorithm to count the number of subsets of size k with sum of all its elements minimum possible

An array is given eg:-1 2 2 2 and we need to count the number of subsets for it of size k which has the sum of elements minimum possible

here the subsets of size k=3 are:- 122 122 122 222

we see that there are 3 subsets having the minimum sum

I did this in bruteforce approach..first I stored the subsets of size k in a vector and then found the sum for each of the subsets and stored them in another vector and then counted the frequency of the minimum element

how to optimize it?


text:
## Archive for the ‘Bible’ Category

### New MorphGNT Releases and Accentuation Analysis

Thursday, February 16th, 2017

From the post:

Back in 2015, I talked about Annotating the Normalization Column in MorphGNT. This post could almost be considered Part 2.

I recently went back to that work and made a fresh start on a new repo gnt-accentuation intended to explain the accentuation of each word in the GNT (and eventually other Greek texts). There’s two parts to that: explaining why the normalized form is accented the way it but then explaining why the word-in-context might be accented differently (clitics, etc). The repo is eventually going to do both but I started with the latter.

My goal with that repo is to be part of the larger vision of an “executable grammar” I’ve talked about for years where rules about, say, enclitics, are formally written up in a way that can be tested against the data. This means:

• students reading a rule can immediately jump to real examples (or exceptions)
• students confused by something in a text can immediately jump to rules explaining it
• the correctness of the rules can be tested
• errors in the text can be found

It is the fourth point that meant that my recent work uncovered some accentuation issues in the SBLGNT, normalization and lemmatization. Some of that has been corrected in a series of new releases of the MorphGNT: 6.08, 6.09, and 6.10. See https://github.com/morphgnt/sblgnt/releases for details of specifics. The reason for so many releases was I wanted to get corrections out as soon as I made them but then I found more issues!

There are some issues in the text itself which need to be resolved. See the Github issue https://github.com/morphgnt/sblgnt/issues/52 for details. I’d very much appreciate people’s input.

In the meantime, stay tuned for more progress on gnt-accentuation.

Was it random chance that I saw this announcement from James and Getting your hands dirty with the Digital Manuscripts Toolkit on the same day?

😉

I should mention that Codex Sinaiticus (second oldest witness to the Greek New Testament) and numerous other Greek NT manuscripts have been digitized by the British Library.

Paring these resources together offers a great opportunity to discover the Greek NT text as choices made by others. (Same holds true for the Hebrew Bible as well.)

### S20-211a Hebrew Bible Technology Buffet – November 20, 2016 (save that date!)

Tuesday, October 18th, 2016

S20-211a Hebrew Bible Technology Buffet

From the webpage:

On Sunday, November 20th 2016, from 1:00 PM to 3:30 PM, GERT will host a session with the theme “Hebrew Bible Technology Buffet” at the SBL Annual Meeting in room 305 of the Convention Center. Barry Bandstra of Hope College will preside.

The session has four presentations:

Presentations will be followed by a discussion session.

You will need to register for the Annual Meeting to attend the session.

Assuming they are checking “badges” to make sure attendees have registered. Registration is very important to those who “foster” biblical scholarship by comping travel and rooms for their close friends.

PS: The website reports non-member registration is \$490.00. I would like to think that is a mis-print but I suspect its not.

That’s one way to isolate yourself from an interested public. By way of contrast, snail-mail Biblical Greek courses in the 1890’s had tens of thousands of subscribers. When academics complain of being marginalized, use this as an example of self-marginalization.

### Modelling Stems and Principal Part Lists (Attic Greek)

Friday, June 17th, 2016

From the post:

This is part 0 of a series of blog posts about modelling stems and principal part lists, particularly for Attic Greek but hopefully more generally applicable. This is largely writing up work already done but I’m doing cleanup as I go along as well.

A core part of the handling of verbs in the Morphological Lexicon is the set of terminations and sandhi rules that can generate paradigms attested in grammars like Louise Pratt’s The Essentials of Greek Grammar. Another core part is the stem information for a broader range of verbs usually conveyed in works like Pratt’s in the form of lists of principal parts.

A rough outline of future posts is:

• the sources of principal part lists for this work
• lemmas in the Pratt principal parts
• lemma differences across lists
• what information is captured in each of the lists individually
• how to model a merge of the lists
• inferring stems from principal parts
• stems, terminations and sandhi
• relationships between stems
• ???

I’ll update this outline with links as posts are published.

(emphasis in original)

A welcome reminder of projects that transcend the ephemera that is social media.

Or should I say “modern” social media?

The texts we parse so carefully were originally spoken, recorded and copied, repeatedly, without the benefit of modern reference grammars and/or dictionaries.

Enjoy!

### Bible vs. Quran – Who’s More Violent?

Friday, January 22nd, 2016

Bible vs. Quran – Text analysis answers: Is the Quran really more violent than the Bible? by Tom H. C. Anderson.

Tom’s series appears in three parts, but sharing the common title:

Part I: The Project

From part 1:

With the proliferation of terrorism connected to Islamic fundamentalism in the late-20th and early 21st centuries, the question of whether or not there is something inherently violent about Islam has become the subject of intense and widespread debate.

Even before 9/11—notably with the publication of Samuel P Huntington’s “Clash of Civilizations” in 1996—pundits have argued that Islam incites followers to violence on a level that sets it apart from the world’s other major religions.

The November 2015 Paris attacks and the politicking of a U.S. presidential election year—particularly candidate Donald Trump’s call for a ban on Muslim’s entering the country and President Obama’s response in the State of the Union address last week—have reanimated the dispute in the mainstream media, and proponents and detractors, alike, have marshalled “experts” to validate their positions.

To understand a religion, it’s only logical to begin by examining its literature. And indeed, extensive studies in a variety of academic disciplines are routinely conducted to scrutinize and compare the texts of the world’s great religions.

We thought it would be interesting to bring to bear the sophisticated data mining technology available today through natural language processing and unstructured text analytics to objectively assess the content of these books at the surface level.

So, we’ve conducted a shallow but wide comparative analysis using OdinText to determine with as little bias as possible whether the Quran is really more violent than its Judeo-Christian counterparts.

Part II: Emotional Analysis Reveals Bible is “Angriest”

From part 2:

In my previous post, I discussed our potentially hazardous plan to perform a comparative analysis using an advanced data mining platform—OdinText—across three of the most important texts in human history: The Old Testament, The New Testament and the Quran.

Author’s note: For more details about the data sources and methodology, please see Part I of this series.

The project was inspired by the ongoing public debate around whether or not terrorism connected with Islamic fundamentalism reflects something inherently and distinctly violent about Islam compared to other major religions.

Before sharing the first set of results with you here today, due to the sensitive nature of this topic, I feel obliged to reiterate that this analysis represents only a cursory, superficial view of just the texts, themselves. It is in no way intended to advance any agenda or to conclusively prove anyone’s point.

Part III – Violence, Mercy and Non-Believers – to appear soon.

A comparison that may be an inducement for some to learn text/sentiment analysis but I would view its results with a great deal of caution.

Two of the comments to the first post read:

(comment) If you’re not completing the analysis in the native language, you’re just analyzing the translators’ understanding and interpretation of the texts; this is very different than the actual texts.

(to which a computational linguist replies) Technically, that is certainly true. However, if you are looking at broad categories of sentiment or topic, as this analysis does, there should be little variation in the results between translations, or by using the original. As well, it could be argued that what is most of interest is the viewpoint of the interpreters of the text, hence the translations may be *more* of interest, to some extent. But I would not expect that this analysis would be very sensitive at all to variations in translation or even language.

I find the position taken by the computational linguist almost incomprehensible.

Not only do we lack anything approaching a full social context for any of the texts in their original languages, moreover, terms that occur once (hapaxes) number approximately 1,300 in the Hebrew Bible and over 3,500 in the New Testament. For a discussion of the Qur’ān, see: Hapaxes in the Qur’ān: identifying and cataloguing lone words (and loadwords) by Shawkat M. Toorawa. Toorawa includes a list of hapaxes for the Qur’ān, a discussion of why they are important and a comparison to other texts.

Here is a quick example of where social context can change how you read a text:

23 The priest is to write these curses on a scroll and then wash them off into the bitter water. 24 He shall have the woman drink the bitter water that brings a curse, and this water will enter her and cause bitter suffering. 25 The priest is to take from her hands the grain offering for jealousy, wave it before the LORD and bring it to the altar. 26 The priest is then to take a handful of the grain offering as a memorial offering and burn it on the altar; after that, he is to have the woman drink the water. 27 If she has defiled herself and been unfaithful to her husband, then when she is made to drink the water that brings a curse, it will go into her and cause bitter suffering; her abdomen will swell and her thigh waste away, and she will become accursed among her people. (Numbers 5:23-27)

Does that sound sexist to you?

Interesting because a Hebrew Bible professor of my argued that it is one of the earliest pro-women passages in the text.

Think about the social context. There are no police, no domestic courts, short of retribution from the wife’s family members, there are no constraints on what a husband can do to his wife. Even killing her wasn’t beyond the pale.

Given that context, setting up a test that no one can fail, in the presence of a priest, which also deters resorting to a violent remedy, sounds like it gets the wife out of a dangerous situation where the priest can say: “See, you were jealous for no reason, etc.”

There’s no guarantee that is the correct interpretation either but it does accord with present understandings of law and custom at the time. The preservation of order in the community, no mean thing in the absence of an organized police force, was an important thing.

The English words used in translations also have their own context, which may be resolved differently from those in the original languages.

As I said, interesting but consider with a great deal of caution.

### Querying Biblical Texts: Part 1 [Humanists Take Note!]

Saturday, November 14th, 2015

From the post:

This is the first in a series on querying Greek texts with XQuery. We will also look at the differences among various representations of the same text, starting with the base text, morphology, and three different treebank formats. As we will see, the representation of a text indicates what the producer of the text was most interested in, and it determines the structure and power of queries done on that particular representation. The principles discussed here also apply to other languages.

This is written as a tutorial, and it can be read in two ways. The first time through, you may want to simply read the text. If you want to really learn how to do this yourself, you should download an XQuery processor and some data (in your favorite biblical language) and try these queries and variations on them.

Humanists need to follow this series and pass it along to others.

Texts of interest to you will vary but the steps Jonathan covers are applicable to all texts (well, depending upon your encoding).

In exchange for learning a little XQuery, you can gain a good degree of mastery over XML encoded texts.

Enjoy!

### Praise For Conservative Bible Translations

Wednesday, September 9th, 2015

I don’t often read praise for conservative Bible translations but conservative Bible translations can have unexpected uses:

Anders Søgaard and his colleagues from the project LOWLANDS: Parsing Low-Resource Languages and Domains are utilising the texts which were annotated for big languages to develop language technology for smaller languages, the key to which is to find translated texts so that the researchers can transfer knowledge of one language’s grammar onto another language:

“The Bible has been translated into more than 1,500 languages, even the smallest and most ‘exotic’ ones, and the translations are extremely conservative; the verses have a completely uniform structure across the many different languages which means that we can make suitable computer models of even very small languages where we only have a couple of hundred pages of biblical text,” Anders Søgaard says and elaborates:

“We teach the machines to register what is translated with what in the different translations of biblical texts, which makes it possible to find so many similarities between the annotated and unannotated texts that we can produce exact computer models of 100 different languages — languages such as Swahili, Wolof and Xhosa that are spoken in Nigeria. And we have made these models available for other developers and researchers. This means that we will be able to develop language technology resources for these languages similar to those which speakers of languages such as English and French have.”

Anders Søgaard and his colleagues have recently presented their results in the article ‘”If you all you have is a bit of the Bible” at the conference Annual Meeting of the Association of Computational Linguistics.

The abstract for the paper: If all you have is a bit of the Bible: Learning POS taggers for truly low-resource languages reads:

We present a simple method for learning part-of-speech taggers for languages like Akawaio, Aukan, or Cakchiquel – languages for which nothing but a translation of parts of the Bible exists. By aggregating over the tags from a few annotated languages and spreading them via word-alignment on the verses, we learn POS taggers for 100 languages, using the languages to bootstrap each other. We evaluate our cross-lingual models on the 25 languages where test sets exist, as well as on another 10 for which we have tag dictionaries. Our approach performs much better (20-30%) than state-of-the-art unsupervised POS taggers induced from Bible translations, and is often competitive with weakly supervised approaches that assume high-quality parallel corpora, representative monolingual corpora with perfect tokenization, and/or tag dictionaries. We make models for all 100 languages available.

All of the resources used in this project, along with their models, can be found at: https://bitbucket.org/lowlands/

Don’t forget conservative Bible translations if you are doing linguistic models.

### New Testament Virtual Manuscript Room

Tuesday, June 2nd, 2015

New Testament Virtual Manuscript Room

From the webpage:

This site is devoted to the study of Greek New Testament manuscripts. The New Testament Virtual Manuscript Room is a place where scholars can come to find the most exhaustive list of New Testament manuscript resources, can contribute to marking attributes about these manuscripts, and can find state of the art tools for researching this rich dataset.

While our tools are reasonably functional for anonymous users, they provide additional features and save options once a user has created an account and is logged in on the site. For example, registered users can save transcribed pages to their personal account and create personalized annotations to images.

A close friend has been working on this project for several years. Quite remarkable although I would prefer it to feature Hebrew (and older) texts. 😉

### New Testament Transcription

Thursday, July 24th, 2014

There is an excellent example of a transcription interface at: http://ancientlives.org/tutorial/transcribe. A screen shot won’t display well but I can sketch the general form of the interface:

A user selects a character in the papyrus by “clicking” on its center point. That point can be moved if need be. The character will be highlighted and you then select the matching character on the keyboard.

There are examples of the instructions that can be played if you are uncertain at any point.

I can’t imagine a more intuitive transcription interface.

I have suggested crowd sourcing transcription of the New Testament (and Old Testament/Hebrew Bible as well) before to groups concerned with those texts. The response has always been that there are cases that require expertise to transcribe. Fair enough, that’s very true.

But, with crowd transcription, we would be able to use the results of hundreds if not thousands of transcribers to identify the characters or symbols that have no consistent transcription. Those particular cases could be “kicked up stairs” to the experts.

The end result, assuming access to all the extant manuscripts, would be a traceable transcription of all the sources for the New Testament back to particular manuscripts or papyri. With all the witnesses to a particular character or word being at the reader’s fingertips. (Ditto for the Old Testament/Hebrew Bible.)

We have the technology to bring the witnesses to the biblical text to everyone who is interested. The only remaining question is whether funders can overcome the reluctance of the usual suspects to granting everyone that level of access.

Personally I have no fear of free and open access to the witnesses to the biblical text. As a text the Bible has resisted efforts to pervert it meaning for more than two (2) thousand years. It can take care of itself.

### Thirty-three Greek Biblical manuscripts added to Digitised Manuscripts

Saturday, July 12th, 2014

Thirty-three Greek Biblical manuscripts added to Digitised Manuscripts by Cillian O’Hogan.

From the post:

The third phase of the British Library's Greek Manuscripts Digitisation Project is now well underway. So far, the following items, all Greek biblical items, have been added to Digitised Manuscripts. We will continue to update the blog with new additions over the course of the year, and will also look at some individual manuscripts in more detail in later posts. We are extremely grateful to the foundations and individuals who have funded this project, especially the Stavros Niarchos Foundation, the A. G. Leventis Foundation, Sam Fogg, the Sylvia Ioannou Foundation and the Thriplow Charitable Trust.

Add MS 24112, Four Gospels in Greek (Gregory-Aland 694; Scrivener evan. 598; von Soden ε 502), written throughout with space for a Latin translation, which has been added for a small number of verses. 15th century, possibly Italy.

Add MS 24373, Four Gospels (Gregory-Aland 695; Scrivener evan. 599; von Soden ε 327), with illuminated Evangelist portraits. 13th century. Also online is an old 19th-century binding for this manuscript.

Add MS 24374, Fragments from a Gospel Lectionary with ekphonetic notation (Gregory-Aland l 325; Scrivener evst. 273). 13th century.

Add MS 24376, Four Gospels (Gregory-Aland 696; Scrivener evan. 600; von Soden ε 328), with illuminated Evangelist portraits (St Mark illustrated above). 14th century (illuminations added in the 16th century), Constantinople.

Add MS 24377, Gospel Lectionary (Gregory-Aland l 326; Scrivener evst. 274), with ekphonetic notation, imperfect. 2nd half of the 12th century, possibly from the Monastery of Patir in southern Italy.

Add MS 24378, Menaion for September, October, November, December, January and February (Gregory-Aland l 927; Scrivener evst. 275). 13th/14th century.

Add MS 24379, Gospel Lectionary (Gregory-Aland l 327; Scrivener evst. 276), imperfect. 14th century.

Add MS 24380, Gospel Lectionary (Gregory-Aland l 328; Scrivener evst. 277), with ekphonetic notation, imperfect. 14th century.

Add MS 27860, Gospel Lectionary (Gregory-Aland l 329; Scrivener evst. 278), imperfect at the beginning, with marginal decorations thruoghout. Late 10th/early 11th century, Southern Italy (possibly Capua). Also online is an old 17th-century binding for this manuscript.

Add MS 27861, Gospels (Gregory-Aland e 698; Scrivener evan 602; von Soden ε 436), imperfect (lacking Matthew). 14th century.

Add MS 28815, New Testament, imperfect (Gregory-Aland 699; Scrivener evst. 603; von Soden δ 104), with Evangelist portraits and a silver-gilt plated cover. Mid-10th century, Constantinople. The subject of a recent blog post along with Egerton 3145.

Add MS 28816, New Testament, from Acts onwards (Gregory-Aland 203; Scrivener act. 232; von Soden α 203), with Euthalian apparatus, and other works. Written between 1108 and 1111 by the monk Andreas in March 1111, in the cell of the monk Meletius in the monastery of the Saviour.

Add MS 28818, Gospel Lectionary (Gregory-Aland l 331; Scrivener evst. 280). 1272, written by the monk Metaxares.

Add MS 29713, Gospel Lectionary (Gregory-Aland l 332; Scrivener evst. 62), imperfect at the beginning. 14th century.

Add MS 31208, Gospel Lectionary with ekphonetic notation (Gregory-Aland l 333; Scrivener evst *281), imperfect. 13th century, possibly Constantinople.

Add MS 31920, Gospel Lectionary (Gregory-Aland l 335; Scrivener evst 283), imperfect and mutilated. 12th century, South Italy (possibly Reggio).

Add MS 32051, Lectionary of the Acts and Epistles, imperfect, with ekphonetic notation (Gregory-Aland l 169; Scrivener apost. 52). 13th century.

Add MS 32341, Four Gospels (Gregory-Aland 494; Scrivener evan. 325; von Soden ε 437), imperfect. 14th century.

Add MS 33214, New Testament: Acts and Epistles (Gregory-Aland 1765; von Soden α 486). 14th century.

Add MS 33277, Four Gospels (Gregory-Aland 892; von Soden ε 1016; Scrivener evan. 892). 9th century, with replacement leaves added in the 13th and 16th centuries.

Add MS 34108, Four Gospels (Gregory-Aland 1280; Scrivener evan. 322; von Soden ε 1319). 12th century, with some replacement leaves added in the 15th century.

Add MS 34602, Fragments from two Psalters (Rahlfs-Fraenkel 2017, 1217) (illustrated above). 7th century and 10th century, Egypt.

Add MS 36751, Gospel Lectionary with ekphonetic neumes, called ἐκλογάδι(ον) (Gregory-Aland l 1491). Completed in 1008 at the Holy Monastery of Iviron, Mount Athos, by the scribe Theophanes.

Add MS 36752, Four Gospels (Gregory-Aland 2280). 12th century.

Add MS 37005, Gospel Lectionary (Gregory-Aland l 1493). 11th century.

Add MS 37006, Gospel Lectionary with ekphonetic neumes (Gregory-Aland l 1494 [=l 460]). 12th century, with late 13th-century replacements, including a full-page miniature of Christ and a figure identified as Andronicus II Palaeologus (Byzantine emperor 1282-1328) (illustrated above).

Add MS 38538, New Testament, Acts and Epistles (Gregory-Aland 2484), with Euthalian apparatus. Written by the scribe John in 1312

Add MS 39589, Psalter (Rahlfs 1092) with introduction and commentary based on that of Euthymius Zigabenus (PG 128), attributed in the manuscript to Nicephorus Blemmydes, imperfect, with ornamental headpieces and the remains of a miniature of the Psalmist. 2nd half of the 12th century.

Add MS 39590, New Testament, without the book of Revelation (Gregory-Aland 547; Scrivener evan. 534; von Soden δ 157). 11th century.

Add MS 39593, Four Gospels (Gregory-Aland 550; Scrivener evan. 537; von Soden ε 250), with prefaces taken from the commentary of Theophylact, and synaxaria. 12th century.

Add MS 39612, Revelation (Gregory-Aland 2041; Scrivener apoc. 96; von Soden α1475). The quire-numbers on ff 1v and 10v show the manuscript formed part of a larger volume, possibly Athos, Karakallou 121 (268) (Gregory-Aland 1040). 14th century, possibly Mount Athos.

Add MS 39623, Fragments from a Gospel Lectionary (Gregory-Aland l 1742). Late 14th century, possibly Mount Athos.

Egerton MS 3145, Epistles and Revelation (Gregory-Aland 699; Scrivener paul. 266; von Soden δ 104), concluding portion of the manuscript of the entire New Testament of which Add. MS 28815 is the earlier portion. Mid-10th century, Constantinople. Also online is an old (18th century?) binding for this manuscript.

I know a number of scholars who will be happy to learn of this latest batch of NT manuscripts. (I am awaiting similar projects with 3-D imaging of cuneiform.)

Cillian O’Hogan is fortunate to work at an institution that fosters scholarship, biblical and otherwise.

### Codex Sinaiticus Added to Digitised Manuscripts

Tuesday, March 25th, 2014

Codex Sinaiticus Added to Digitised Manuscripts by Julian Harrison.

From the post (I have omitted the images, see the original post for those):

Codex Sinaiticus is one of the great treasures of the British Library. Written in the mid-4th century in the Eastern Mediterranean (possibly at Caesarea), it is one of the two oldest surviving copies of the Greek Bible, along with Codex Vaticanus, in Rome. Written in four narrow columns to the page (aside from in the Poetic books, in two columns), its visual appearance is particularly striking.

The significance of Codex Sinaiticus for the text of the New Testament is incalculable, not least because of the many thousands of corrections made to the manuscript between the 4th and 12th centuries.

The manuscript itself is now distributed between four institutions: the British Library, the Universitäts-Bibliothek at Leipzig, the National Library of Russia in St Petersburg, and the Monastery of St Catherine at Mt Sinai. Several years ago, these four institutions came together to collaborate on the Codex Sinaiticus Project, which resulted in full digital coverage and transcription of all extant parts of the manuscript. The fruits of these labours, along with many additional essays and scholarly resources, can be found on the Codex Sinaiticus website.

The British Library owns the vast majority of Codex Sinaiticus and only the British Library portion is being released as part of the Digitised Manuscripts project.

The world in which biblical scholarship is done has changed radically over the last 20 years.

This effort by the British Library should be applauded and supported.

### Dead Sea Scrolls Updated!

Wednesday, February 5th, 2014

Well, actually not! 😉 but the Leon Levy Dead Sea Scrolls Digital Library has been upgraded!

From their Facebook page:

A second, upgraded version of the Leon Levy Dead Sea Scrolls Digital Library was launched today. Visitors to the new website (www.deadseascrolls.org.il) will be able to view and explore 10,000 newly uploaded images of unprecedented quality. The website also offers accompanying explanations pertaining to a variety of manuscripts, such as the book of Exodus written in paleo-Hebrew script, the books of Samuel, the Temple Scroll, Songs of Shabbat Sacrifice, and New Jerusalem.

The upgraded website comprises many improvements: 10,000 new multispectral images, improved metadata, additional manuscript descriptions, content pages translated into Russian and German in addition to the current languages, a faster search engine, easy access from the site to the facebook page and to twitter and more.

Imagine that! 10,000 new images.

Pass this on to academic publishers worried about control over works they can’t give away.

The ranks of the “frightened by public access” to non-commercial content are growing thinner.

### Ancient texts published online…

Friday, December 13th, 2013

Ancient texts published online by the Bodleian and the Vatican Libraries

From the post:

The Bodleian Libraries of the University of Oxford and the Biblioteca Apostolica Vaticana (BAV) have digitized and made available online some of the world’s most unique and important Bibles and biblical texts from their collections, as the start of a major digitization initiative undertaken by the two institutions.

The digitized texts can be accessed on a dedicated website which has been launched today (http://bav.bodleian.ox.ac.uk). This is the first launch of digitized content in a major four-year collaborative project.
Portions of the Bodleian and Vatican Libraries’ collections of Hebrew manuscripts, Greek manuscripts, and early printed books have been selected for digitization by a team of scholars and curators from around the world. The selection process has been informed by a balance of scholarly and practical concerns; conservation staff at the Bodleian and Vatican Libraries have worked with curators to assess not only the significance of the content, but the physical condition of the items. While the Vatican and the Bodleian have each been creating digital images from their collections for a number of years, this project has provided an opportunity for both libraries to increase the scale and pace with which they can digitize their most significant collections, whilst taking great care not to expose books to any damage, as they are often fragile due to their age and condition.

The newly-launched website features zoomable images which enable detailed scholarly analysis and study. The website also includes essays and a number of video presentations made by scholars and supporters of the digitization project including the Archbishop of Canterbury and Archbishop Jean-Louis Bruguès, o.p. The website blog will also feature articles on the conservation and digitized techniques and methods used during the project. The website is available both in English and Italian.

Originally announced in April 2012, the four-year collaboration aims to open up the two libraries’ collections of ancient texts and to make a selection of remarkable treasures freely available online to researchers and the general public worldwide. Through the generous support of the Polonsky Foundation, this project will make 1.5 million digitized pages freely available over the next three years.

Only twenty-one (21) works up now but 1.5 million pages by the end of the project. This is going to be a treasure trove without end!

Associating these items with their cultural contexts of production, influence on other works, textual history, comments by subsequent works, across multiple languages, is a perfect fit for topic maps.

Kudos to both the Bodleian and the Vatican Libraries!

### Greek New Testament (with syntax trees)

Monday, August 12th, 2013

Greek New Testament (with syntax trees)

If you are tired of the same old practice data sets, I may have a treat for you!

The Asia Bible Society has produced syntax tress for the New Testament, using the SBL Greek New Testament text.

To give you an idea of the granularity of the data, the first sentence in Matthew is spread over forty-nine (49) lines of markup.

Not big data in the usual sense but important data.

### bibleQuran: Comparing the Word Frequency between Bible and Quran

Friday, November 4th, 2011

bibleQuran: Comparing the Word Frequency between Bible and Quran

From the post:

bibleQuran [pitchinteractive.com] by datavis design firm Pitch Interactive reveals the frequency of word usage between two of the most important holy books: the Bible and the Quran.

The densely populated interactive visualization allows people to search for any word (and similar variations of that word) to explore its frequency in both texts. As each verse is always visible, one is able to compare the relative density of ideas and topics between both passages. For instance, one could select verbs that represent acts of ‘terror’ or ‘love’, and investigate which book discusses the topics more. The appropriate little rectangles, each representing an according verse, which include such this chosen word, are then highlighted, and can be read in detail by hovering the mouse over them.

In addition to being a great graphic presentation of information, with my background and appreciation for both texts, you know why I had to include this post.

I like the synonym feature, although I reserve judgment on what is considered a synonym. 😉 I would have to read the original. Translations of both texts are, well, translations. Not really the same text in a very real sense of the word.

Just as a suggestion, I would do the word count statistics separately for the Old/New Testament.

Word of warning: Loads great with Firefox (7.1) on Windows XP, doesn’t load with IE 8 on Windows XP, doesn’t load with Firefox (3.6) on Ubuntu 10.04. So, your experience may vary.

Comments from users with other browser/OS combinations?