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ME Vol.9 No.3 , March 2018
Could Noise Spectra of Strange Attractors Better Explain Wealth and Income Inequalities? Evidence from the S&P-500 Index
C-René Dominique
Department of Economics, Laval University, Quebec City, Canada.
Abstract: Inequity in wealth and income distributions is ubiquitous and persistent in markets economies. Economists have long suspected that this might be due to the workings of a power law. But studies in financial economics have focused mainly on tail exponent while attempting to recover the Pareto and Zipf's laws. The estimation of tail exponents from log-log plots, as in stock market returns, produces biased estimators and has little impact on policy. This paper argues that economic time series are output signals of a multifractal process driven by strange attractors. Consequently, estimating noise spectra thrown-up by strange attractors stands to produce a much richer set of information, including the lower and upper bounds of unequal income distribution.
Keywords: Income Inequality, Multifractals, Strange Attractors, Singularity Spectrum, Correlation Dimension
The World Inequality Report 2018 [1] is out. It shows that during 2015-16 the top 10% of individuals captured some 37% of total wealth in the European Union that has the best score among other huge economies such as China (41%), Russia (46%), Brazil (55%), the USA (47%), India (55%), etc. In terms of income inequality, the report also shows that from 1980 to 2018, the world's richest 1% captured about 27% of new income, while the poorest 50% of the world population received only 13%. Thus, compared to the years preceding globalization, income inequality has increased almost everywhere, that is, in developing or developed countries, including those that enjoy the highest level of development. At first sight, one would tend to suspect similar policy structure as the culprit. However, observing that the top 10% had captured some 61% of total wealth in Sub-Sahara Africa, wealth and income inequality then appears to be a ubiquitous phenomenon. It is then reasonable to suspect that indeed some homogeneous power law lurks behind the distribution of wealth and income in market economies.
A homogeneous power law can be represented as: F ( x ) = K x α , where F ( ⋅ ) is a variable; K is a constant; x is the other variable of interest; and α is the scale exponent. Financial economists have attempted to study the impact of power law identified in stock market activities, such as firms' size distributions, returns on investments, traded volume, etc. [2] [3] , among others. But, their studies attempt to reproduce Zipf's hyperbolic law, which relates word rank and word frequency in natural languages, or they are simply influenced by the so-called Pareto Law, expressed as: ( p ( x ) > x ) = K / f α . Moreover, estimates are obtained from log-log plots [4] . Experimental data of quantities that follow a power law are usually very noisy and therefore obtaining reliable estimates for the exponent a is difficult. In fact, estimates obtained from graphical methods based on linear least squares fit of some empirical data points, such as a time series, produce biased estimators. If precision is a requirement, then it is advised to use maximum likelihood methods as an alternative, e.g. the so-called Hill's estimator that gives the inverse of the exponent of the Pareto distribution. In practice, however, one never knows for certain whether an observed quantity is drawn from a power law distribution. At any rate, the information obtained either from graphical methods or others is of little use in policy formulation. For example, an α = 2, say, means that if F ( ⋅ ) is doubled, then x will go up by 22. Even if a power law is really present, the researcher will not know how it manifests itself. More importantly, if the output signal is from a multifractal, endowed with many scale exponents and driven by a strange attractor, what scale is being estimated? Clearly, graphical methods are of little use in such situations.
Yet, power laws with fractional exponents showing scale invariance are perhaps the only way to study many critical phenomena in the real-world settings. The values of exponents reflect a large number of regularities found in physics, biology, psychology, etc., and in many human constructs such as music, economics, etc. Whether the exponent is an integer or a non-integer, relations between variables are characterized by the notion of self-similarity. And we contend that by knowing why self-similarity or dissimilarity exists is to know much more about the phenomenon that we wish to study in this paper.
For tractability, however, let us first recall that self-similarity is more than a welcomed attribute, because it is fundamental to our nature whether we are aware of it or not, and also because it is the concept that underlies fractals, complexity, and many laws of nature. In this paper we intend to look at income distribution through the lens of fractals, and there, self-similarity plays a huge role, as evidenced by the difficulty of distinguishing between minute-by-minute or second-by-second stock averages [5] [6] [7] [8] . Indeed, power laws are found in many scientific and human constructs. Proper analyses in these areas require some generalization of the fractal concept either with many exponents (where they are called multifractals), or fractal 'tout court' with one scaling exponent; at any rate, self-similarity may appear on many scales. Hence, it would really be surprising if some power law did not underlie stocks and commodity exchanges.
Power laws also govern the noise spectra of various processes. But, interpreting noise spectra has its own pitfalls, because non-stationarity in the data can produce fake scaling behavior, or as evidenced by the excessive association of the Zipf's law with pink noise or 1/f noise. The latter is a signal that gives a power spectral density (power per frequency interval) that is inversely proportional to the frequency of the signal. Maybe, the attachment of economists to 1/f noise ((where β (=1) is the squared modulus of the Fourier transform) is from the fact that 1/f noise is connected to systems that are near their equilibrium. Whereas β > 1 is associated with non-equilibrium driven systems. Thus, values of α = 1 or 3 found in the studies mentioned above probably will not occur in spectral analyses, because economic systems are most often far from their equilibrium, and economic data are very noisy. Spectral analysis provides representations of outputs of systems that are as much as possible noise-free, from which on can derive precious quantitative and qualitative information concerning the system's behavior.
The stochastic behavior of a deterministic dynamic system could show a Power Spectrum Density (PSD) that is qualitatively similar to that of a truly random time series, as in a broad-band power spectrum. On the other hand, a purely stochastic system may also contain a flicker noise, because low frequency components dominate high frequency ones; this is known as the intermittency problem. That is why we believe that it is safer to start by first characterizing the attractor in view of ascertaining whether or not the system under study is stochastic or one that has structure.
Power laws abound in the human experience. Its operation can easily be inferred from a few casual observations such as: Distributively, the frequency of "smalls" exceeds that of "bigs"; the fact that there are more small stars than big ones; the fact that the frequency of unstable configurations in the universe is higher than that of stable configurations; or why the frequency of small words exceeds that of long words, etc. It then follows that it might be natural that the frequency of smaller income earners would exceed the frequency of big earners, if market economies are driven by power laws. However, one must be careful in dealing with spectral power that is continuous and diverges to low frequencies. There exist a plethora of methods, such as the multitaper method, to handle these situations. Here however, we are less interested in precise measurements than in determining the upper and lower bounds of power spectra of multifractals whose fractal attractors are characterized by fractional exponents.
If the S&P-500 Index is the output signal of a multifractal, it is then worth investigating whether income distributions (which is of interest here) are better studied by noise spectra (their power spectrum) than by reconstructed distributions from tails exponents. To do so, however, it is necessary to first express the power law in frequency domain, i.e., P ( f ) = K / f β , where k is a constant; b is the power spectrum; and f ( t ) is the power function that measures the power of the signal per unit of time. We next characterize the attractor of the index to determine its fractal dimension. We will attempt that in the next two sections. The second will be devoted to the data, to preliminaries to the computation of the singularity spectrum (to demonstrate both its multi-fractality and its non-randomness), and to the noise spectra of the S&P-500. Our findings will be summarized in the Third Section.
2. Data and Preliminaries
We used the Grand Microsoft Excel series of closing prices of the S&P-500 from January 3rd 1961 to February 28th 2011, sampled at daily intervals, and expressed as a Mixed Fractional Brownian Motion ((MfBm), see Appendix A), assuming its non-randomness. The series was next truncated into 7 segments (the b's in Appendix A) that were previously determined in [9] , and each segment was de-trended using 3 logarithmic differences and filtered for white noise. Segment length varies from 29 to 211.
The analysis will be done in two stages. In the first, we will use the wavelet multi-resolution software of Trusoft International, the Benoit version, to determine the boundaries of the observational range of the Hurst exponents (H), the power spectrum, as well as the Hausdorff dimensions ((D0), see Appendices B and D). In the second stage, D0 being the first scale exponent will be used as the starting point in the determination of the generalized fractal dimensions or the singularity spectra of the segments.
As shown in Appendix B, the Hausdorff dimension (D0) is a more efficient measure than either the topological or the box-counting dimension, and also a more natural measure within the multifractal formalism. For, if a closed bounded set E ∈ ℝ n (where ℝ is the real line) is a manifold, then the value of its dimension must accordingly be either i) an integer or a non-integer; and ii) points and countable unions of points of zero volume must have zero dimension. It can then be seen that the topological dimension fails on these conditions since it is always an integer, giving zero for the Cantor set for example, which is obviously not true. By a similar argument, the box-counting measure also fail on ii), whereas D0 satisfies both i) and ii), and D 0 ( E ) ≤ d i m b o x ( E ) .
Recalling, at the same time, that if V ⊆ X and G is a collection of subsets of X whose union contains V, then G is a cover of V. If further X is a topological space, then G is an open cover if each of its subsets is an open set. Therefore, the term 'fractal dimension', more generally referred to as the capacity dimension of fractal sets, is also the exponent D0 in the expression η ( e ) = e 0 − D , where η ( e ) is the minimum number of open sets of diameter (e) needed to cover the set [10] . The D0 given by the software will be the starting point in the computation of the singularity spectrum, including the correlation dimension.
2.1. The Singularity Spectrum
The method of multifractal cascades is now known as the multifractal formalism introduced by [11] [12] in response to systematic experimental deviations observed in the Kolmogorov theory of homogeneous and isotropic turbulence. It has since undergone considerable theoretical development and practical applications in many disciplines as it seems well adapted to reveal the hierarchy governing special distributions of singularities of multifractal measures.
In this paper it is referred to as the Mandelbrot Method [13] which is a simple iterative construction that asymptotically models strange attractors. It consists of an "initiator" (the unit interval) on which a unit mass is uniformly distributed, and a "generalized generator" (ρ) with two intervals (ei), i ∈ ( 1 , 2 ) . The initiator is first divided into two bins with equal probability (pi). Next, the exponent q is assigned to the probabilities, while the exponent t is assigned to the support intervals. The exponent τ(q) is the Renyi's scaling exponent, and q is a real parameter that can take positive as well as negative values. In the case of mono-fractal (or self-affine), τ(q) depends linearly on q; otherwise the process is a multifractal.
Quadratic maps have the same structure, but different intervals. Experimentally, Schroeder [14] has found that an interval size e1 = 0.400 to be a good approximation of ei for the logistic map. By using Equation (3) below, our e1 = 0.408903, which is equivalent to a generalized generator of ρ = 2.445564 instead of the approximated value of 2.5, chosen initially by Schroeder. The difference is due to the fact that the logistic map is not exactly self-similar. Since the approximate map of a given process might not be known in advance, one should appeal to Equation (1) below to yield the size of the generator and intervals from the Hausdorff dimension obtained from the wavelet. Once e1 is known, then all the Renyi's generalized fractal dimensions, except D1 (the information dimension), can be computed. But beforehand, the Legendre Transform posits: α ( q ) = − d t ( q ) / d q ; d f ( a ) / d a = q , and f ( a ) = q d t / d q − t ( q ) . While the Holder analysis decomposes a measure into a sum of measures, where each is characterized by a value of the Holder exponent a; the latter measures the strength of the local singularity or roughness. Everything is then on hand to construct the multifractal spectrum; thus, the generality of D0 in this approach cannot be over-emphasized. To wit:
From the partition function:
∑ i ( p i q e i τ ) = 1 , positing e 1 = ( ρ − 1 ) , e 2 = ( ρ − 1 ) 2 and τ ( q ) = ( 1 − q ) D q (1)
We can derive two equations in quadratic form:
e 1 2 D 0 + e 1 D 0 − 1 = 0 e 1 2 τ + e 1 τ − 1 = 0 (2)
Equation (2) is derived from positing q = 0, Dq = D0, and p 1 = p 2 = 1 / 2 . Then, e 1 D 0 = [ ( 5 ) 1 / 2 − 1 ] / 2 = G , where G is the Golden Mean; hence,
D 0 = log G / log e 1 (3)
From (3), we have:
e 1 τ = { [ 1 + 4 ( 2 ) q ] 1 / 2 − 1 } / 2 , (4)
τ = log { [ ( 1 + 4 ( 2 ) q ) 1 / 2 − 1 ] / 2 } / log e 1 (5)
As the exponent τ(q) describes the same aspect of the multifractal spectrum, denoted f(a), we have;
τ / ( 1 − q ) = D q = lim e 1 → 0 log { [ 1 + 4 ( 2 ) q ] 1 / 2 − 1 } / 2 / ( 1 − q ) log e 1 , for q ≠ 1 (6)
Equation (6) is Renyi's [15] , [16] generalized dimensions of order q, which handles every portion of the support of the attractor in a uniform manner and describes the nature of singularities at the same time. It works for all q's, except of course q = 1.
For D1, we have:
D 1 = 2 log 2 / ∑ 1 2 log ( 1 / e i ) ; (7)
but, for D∞ and D−∞, it is easier to expand the numerator of (6). That is,
D q = − 2 [ log 2 ( 1 + q ) ] / ( 1 − q ) log e 1 ; (8)
using log2 and letting q ® ¥ or (-¥), we have:
D ∞ = lim q → ∞ e 1 → 0 ( − 1 / log 2 e i ) ; D − ∞ = lim q → − ∞ e 2 → 0 [ − 1 / log 2 ( e 1 ) 2 ]
What is needed here is the correlation dimension that can be computed for q = 2; that is:
D 2 = lim e 1 → 0 log ∑ i = 1 n ( p i 2 ) / log e 1 (9)
The importance of D2 lies in its relation with the concept of correlation. It can be shown that as e ® 0, the sum in (9) equals the total counts, defined as C(r) and used in the method proposed by Grassberger and Procaccia [17] . One of the many roles played by the correlation dimension lies in its ability to distinguish between chaos and random determinism. In the Grassberger and Procaccia method, one builds a d-dimensional data vector from d measurements spaced equidistantly in time, and determines D2 of the d-dimensional point set. If the data were random, then as d increases, D2 would increase continuously with d. However, if the system is deterministic, D2 will not increase any more once the embedding dimension exceed D2. For more on this, the reader is referred to Appendix C.
2.2. The Power Spectrum
The wavelet multi-resolution software computes the Hurst exponent (H) for each segment of the S&P-500 Index, and the segments are used to calculate the power spectrum as shown in Appendix D. It should stress at this juncture that self-similarity is at play, indicating that there exist relations between variables, and D0 is at hand. The power spectrum can then be computed for each segment of the Index. The Hurst exponent, defined as: H = log ( R / S ) / log ( Δ t ) , is also a measure of persistence (H > 0.5) and anti-persistence (H < 0.5) in statistical time series. Persistence is related to long memory in time series, meaning that an increase in values is most likely be followed by another increase; while anti-persistence (H < 1/2) relates to short-term memory or return to the mean, meaning that an increase will most likely be followed by a decrease, and vice versa. An H = 0.5 is taken to mean randomness as in Brown noise spectrum.
Interestingly, the rescaled range and segment sizes follow a power law, and H is its exponent. The intensity of fluctuations in anti-persistence mode increases as H moves closer to zero; hence, its connection to frequency.
The results are summarized in Table 1, while Table 2 provides some additional information that might not be apparent in Table 1. As it can be seen, the power spectrum β, that describes how much different frequencies contribute to the average power of the signal, fluctuates from segment to segment. Values between 1 and 2 reflect anti-persistence in the index, and values between 2 and 3 reflect long-term memory or persistence. Readers interested in knowing the wave length of the memory are referred to the excellent paper by Peters [18] . Thus, over the whole period, 4 segments reflect anti-persistence and three reflect persistence.
Table 1. The power spectrum and the correlation dimension of the S&P Index: 1961-2011.
Table 2. More information about persistence and anti-persistence modes.
The symbols  and ¯ indicate improvement or deterioration in ordinal space or increase and decrease in real space. D2 indicates the frequency of orbit's visits to different subspaces in the attractor.
The interesting observation for the present purpose is that the power spectrum lying between 1 and 2 reflects dark-pink noise spectra; and that implies thereby a deterioration in income distribution. While values lying between 2 and 3 reflect dark-brown spectra coinciding to improvement. Interestingly, over the whole range of the data considered, no brown noise was detected; and we note in passing that this should be significant for studies based on Brownian motion.
For an additional verification, we consider some values obtained from another measure, called the Gini Index. The latter has a few interpretative limitations. For example, it measures relative income; thus two countries could have the same Gini value and yet are very different in terms of economic status. Or the Gini index may exceed a value of 1.0 when some individuals make a negative contribution to the total income, etc. However, these limitations do not apply in the present case. In essence, a value of zero in the Gini Index reflects perfect equality, while a value of 1 reflects perfect inequality.
Now consider how the Gini Indices of the US economy vary over time. Over the period 1961-72, the S&P-500 Index was in persistence mode with a value of β = 2.044; the Gini index went down from 0.52 in 1961 to 0.42 in 1972. In contrast, from 1972 to 1983, when the S&P-500 was in anti-persistence mode, the power spectrum was 1.4, probably due to changes in the status of the US dollar, war, and the oil shock.
We would then expect a deterioration in the Gini index over that period. That is what happens; the Gini coefficient went from 0.42 to 0.46. During the whole period 2003-2011, the system was again in anti-persistence mode, the Gini coefficient again went from 0.51 to 0.53. During the brief period 1998-2002, when the S&P-500 index was in persistence mode, the Gini coefficient remained at 0.50; that is the only glitch observed. But from 2003 to 2008, it increased from 0.49 to 0.50. From 2007 to 2008, the Gini index increased from 0.50 to 0.52. Thus, during the economic meltdown from 2007 to 2011, the index was in anti-persistence mode and the Gini coefficient increased from 0.50 to 0.53. If we were to examine the Gini indices for other countries, we would most likely observe a similar situation, except where it is mitigated by equality-like policies.
In summary therefore, dark-pink noise (1 < β < 2) implies deterioration in income distribution, while dark-brown noise (2 < β < 3) reflects improvement in income distribution.
Turning now to the correlation dimension D2 in 2-D, it remained between 2 and 3 over the whole period under study, implying that the S&P-500 was never a random process. The other interesting result is that the correlation dimension (which detects probabilistic structure among variables)of each segment is a non-integer, implying that its dynamics should show a countable set of periodic orbits of arbitrary long periods, and an uncountable set of non-periodic orbits. Such a situation might appear random to the naked eyes, but in fact the process is deterministic. Furthermore, when the system was in anti-persistence mode, D2 increased, and it decreased in persistence mode, as can be seen in the last column of Table 1. This means that there is a sort of phase shift that occurred at the fold at H = 1/2. This is explained by an enlargement or a shrinking of the singular spectrum at the values of the b's in Appendix A. For example, during the period 1961-72, the process was in persistence mode, while during the period 1972-83, it was in anti-persistence mode. Consequently, the information dimension D1 went from 2.4192 to 2.7083; D0 went from 2.4780 to 2.7791, and so on. That is, the size of the attractor increases in anti-persistence mode and decreases in persistence mode, as we would expect.
Further verifications come from similar studies as in [19] . He found that for 3-D fractal attractors of continuous-time dissipative systems, the non-integer fractal dimension is between 2 < D2 < 3, as found in the last column of Table 1. To take yet another example, consider the findings of Edgar Peters who used the Grassberger/Procaccia procedure to compute D2 of the S&P-500 Index, sampled at monthly intervals from January 1980 to July 1989. He found that the embedding dimension was 2.33. Even though we do not have the same series' length nor the same sampling interval, nevertheless this study arrives a value of 2.3345 for the period 1983-87. This might be due the fact that D2 remained constant over the time interval, or due to the fact that segment as well as all the others were filtered for white noise prior to the analysis since both methods are sensitive to noise, or due to a combination of both; at any rate, this kind of concordance in that statistic is rather rare in economics.
Our initial contention was that wealth and income inequalities in market economies are too ubiquitous and systematic not to be driven by some power law. To verify that assertion, the S&P-500 Index, sampled daily over a span of 50 years, was examined. It was found that the index varies from anti-persistence to persistence modes during the period studied. Consequently, its noise spectrum varies from dark-pink, when the power spectrum was between 1 and 2, to dark-brown, when the power spectrum lied between 2 and 3. On the assumption that the Index is the output of a multifractal, its singularity spectrum, including the correlation dimension of each segment, was also computed using the method proposed by Mandelbrot. The value computed for the correlation dimension is compared to that obtained from another procedure advocated by Grassberger and Procaccia. Values from the two methods were found to be in perfect agreement.
It was further found that both noise spectra and correlation dimensions vary with persistence modes. When the index was in anti-persistence mode (the power spectrum lies between 1 and 2), the correlation dimension was over 2.5; but in persistence mode (the power spectrum was between 2 and 3) the correlation dimension was below 2.5. More interestingly, in anti-persistence mode, income distribution became more unequal than when it was in persistence mode. This finding confirms the original suspicion that power spectra faithfully reflect the state of the economy and drive income distribution. Moreover, the fact that the correlation dimension is not an integer also shows that the whole process is deterministic and driven by a strange attractor with a fractional exponent.
If this is true that income and wealth distributions are driven by a power law, then perfect equality in this area is unattainable, even with strong equitable policies, since one would be fighting not only the rich but also the power law along the way. Incidentally, power laws should be operational in many other areas of economics. For example, if economists could muster the courage to drop the unobservable appendage called utility function, they would see that what they term law of demand is none other than a power law whose exponent a is 1; for more on this, the reader is referred to [20] .
Before closing, let us say that we believe that an equitable policy is desirable, but policy makers must bear in mind that producing "effective policies" is also a fight against the power law. As policy approaches equity, the power law constraint becomes more and more unsurmountable. Nonetheless, what is obvious is what Table 2 reveals. That is, all would-be effective policies should focus on the stabilization of fluctuations.
Appendix A. The Mixed Fractional Brownian Motion
The Mixed Fractional Brownian Motion is given by:
Z t = ∑ i n ( b i X H i ) , where b ∈ ℜ , i ∈ n . and H i ∈ ( 0 , 1 ) , ∀ i ∈ n . (A2.1)
Zt is an observed combination of Gaussian processes ( X H i ), each with its own H index. X H i are the unobserved Mandelbrot-van Ness [21] nputs into Zt. The latter not only captures the properties of the dynamic input/output construct describing the financial market, but its structure allows the analysis of the data segment by segment, depending on their scaling limit of self-similarity. That setting allows the judicious use of both the wavelet multi-resolution analysis and the Mandelbrot Method of multifractal analysis. For, if outputs are only approximately self-similar, they must be decomposed into subsets supporting a Borel probability measure having some sort of symmetry, which can reproduce copies of the sets on arbitrarily small scales up to a given precision (For more on this, see [22] [23] .
If now we consider price index as the observable output or an observable signal, Zt, we have:
(The Process): Z t = ∑ i n ( b i X t H i ) , where b ∈ ℜ , i ∈ n , is a combination of
observed Gaussian processes, each with its own H index, while X t H are unobservable inputs into Zt, arriving as "cars" or as "trains" in the sense of Sottinen [24] . Further:
E ( Z t ) = 0 (A2.2)
E ( Z t 2 ) = ∑ r = 1 n b r 2 ( X t H ) 2 = ∑ r = 1 n ( b r ) 2 | t | 2 H r . (A.2.3)
Then Zt is completely characterized by its covariance function R ( t , s ) :
R ( t , s ) = 2 − 1 ∑ r = 1 n ( b r ) 2 [ t 2 H r + s 2 H r − | t − s | 2 H r ] , ∀ t , s ∈ ℜ + , r ∈ n . (A2.4)
Zt has the following essential properties:
Property 1. (Scale invariance). X t H r , t ≥ 0 and m H r [ X t H r , t ≥ 0 ] ( m ∈ ℜ + , r ∈ n ) have the same probability distribution. This property is a consequence of the covariance function, R(t, s), which is homogeneous of order 2H.
Property 2. (Stationary Increments). Over the interval (t, s), X t H r has a normal distribution with zero mean and variance given by E [ ( X t H r , X H r ) ] = | t − s | 2 H r .
Property 3. (Dependence). Defining S 1 = { H r ∈ ℜ + | 0 < H r < 1 / 2 } ; S 2 = { H r ∈ ℜ + | H r = 1 / 2 } , and S 3 = { H r ∈ ℜ + | 1 / 2 < H r < 1 } . If H r ∈ S 1 , Zt is anti-persistent and STD exists; if, on the other hand, H r ∈ S 3 , Zt is persistent and LTD exists.
In the literature, Zt is termed: Mixed Fractional Brownian Motion (MfBm) (see, [25] [26] [27] ). While X t H i is the Mandelbrot-van Ness process (fBm).
Appendix B. The Hausdorff Dimension
According to Warwick.ac.uk"s [28] lectures on Fractals and Dimension Theory, the Hausdorff dimension is a description of the geometry of a fractal set. If E is a fractal set whose dimension is sought, then let C ( e , C ) = [ c 1 , c 2 , ⋯ , c u ] be a finite covering of E into sets whose diameters are less than e. Then E Ì Uici and the dimension of its set satisfy some dI = d(ci). If the function:
f ( E , D , e ) = inf c ( B , e ) ∑ i δ i D , (B2.1)
where the infimum (over all coverings satisfying dI < e) defines a measure for the set E. Then f ( E , D , e ) decreases monotonically with D. Therefore, there is a unique transition point H that satisfies the Hausdorff dimension. That is:
f ( E , D , e ) = lim sup e → 0 f ( E , D , e ) = ∞ for D < D H and 0 for D > D H (B2.2)
so that D 0 = inf [ D : f ( E , D , e ) ] = 0 , (DH is henceforth denoted, D0).
For a greater ease of exposition, one might wish to define a probability u on E and consider upper and lower dimensions of u as measurable functions du(sup) and du(inf)−, where
du ( b ) = lim sup e → 0 log [ ball ( b , e ) ] / log e ≥ d , ∀ b ∈ E , then dim H ( u ) ≥ d ; and du − ( b ) = lim inf e → 0 log u [ ball ( b , e ) ] / log e ≤ d , ∀ b ∈ E , then dim H ( u ) ≤ d (B2.3)
where ball(b, e) is a ball of radius e > 0 about b.
Moreover, if a closed bounded set E ∈ ℜ n is a manifold, the value of its dimension must satisfy the Warwick criteria. That is, its dimension must be:
1) either an integer or a non-integer; and
2) points and countable unions of points of zero volume must have zero dimension.
It can then be seen that the topological dimension (dimT), for example, fails on both criteria since it is always an integer, giving 0 for the Cantor set, which is not true. By a similar argument, the Box-counting measure fails on ii), whereas dimH(E) satisfies both i) and ii), and dimH(E) £ dimBox(E).
Both the so-called capacity and the Hausdorff dimensions are closely related in the sense that both are fractal and geometric measures, but in general the Hausdorff dim is the lower limit of capacity dim. Both are geometric, not probability measures, indicating how orbits fill the phase space under the flow of a dynamic system.
Appendix C. The Correlation Dimension
This presentation is provided by Medio. For n discrete points and an arbitrary fixed time interval, the correlation function is:
C ( r ) = lim n → ∞ ( 1 / N 2 ) ∑ i , j = 1 N θ ( r − | x i − x j | ) , (C2.1)
where θ(s) is the Heavyside function, i.e., θ(s) = 1 if (s) ³ 0 and 0 if (s) < 0.
For small r, C(r) behaves as a power of r. Then:
C ( r ) ≅ r 2 D , (C2.2)
where D2 is the correlation dimension. In reality, one proceeds by counting how many points have a smaller Euclidean distance than some given distance r. As r varies, so does C(r), defined here as the total count, divided by the squared number of points. The quantity C(r) is also called the correlation sum. As r ® 0, the sum ∑ p i 2 = C ( r ) , which yields the correlation dimension. The latter is another fractal dimension and a probability measure describing the frequency with which orbits visit different parts of the attractor of a dynamic system.
Appendix D. The Hurst Exponent
The Hurst exponent [29] is used to measure the long-term memory of time series. It involves the correlations of the series with the rate at which these decrease as the lag between pairs of values increase. The Hurst exponent (H) is then defined as the asymptotic behavior of the rescaled range as a function of the time span of a time series as follows:
E [the range of the first n values/the standard deviation of the first n values] = C n H as n ® ¥, where E stands for expected value, C is a constant, and n is the number of data points in the time series.
The Hurst exponent H is also related to both the Hausdorff dimension and the power spectrum as follows:
( 2 − D 0 ) = H = ( β − 1 ) / 2 . (D2.1)
This relation is valid for a given range, i.e., 0 ≤ H ≤ 1.
Cite this paper: Dominique, C. (2018) Could Noise Spectra of Strange Attractors Better Explain Wealth and Income Inequalities? Evidence from the S&P-500 Index. Modern Economy, 9, 449-462. doi: 10.4236/me.2018.93030.
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[2] Gabais, X. (1999) Zipf's Law for Cities: An Explanation. Quarterly Journal of Economics, 114, 739-767.
https://doi.org/10.1162/003355399556133
[3] Gabais, X., Gopikrishnan, P., et al. (2003) A Theory of Power Law Distributions in Financial Market Fluctuations. Nature, 423, 267-330.
https://doi.org/10.1038/nature01624
[4] Gopikrisnan, P., Plerou, U., et al. (2000) Statistical Properties of Share Volume Traded in Financial Markets. Physical Review E, 62, R4403-r4496.
[5] Mandelbrot, B. (1982) The Fractal Geometry of Nature. W. H. Freeman, New York.
[6] Priya, R.A. (2010) Fractals: A More Dynamic and Multidimensional Approach to Business Analytics. Journal of Emerging Knowledge on Emerging Markets, 2, Article 6.
[7] Koulakis, B., Ruseckas, J., et al. (2006) Non-Linear Stochastic Models of 1/f Noise and Power Law Distribution. Physica A, 365-397.
[8] West, B.J. and Shlesinger, M.F. (1990) The Noise in Natural Phenomena. American Scientist, 78, 40-45.
[9] Rasban, S.N. (1990) "Fractal Dimensions" in Chaotic Dynamics of Non-linear Systems. John Wiley, New York, 71-83.
[10] Dominique, C.-R. and Rivera, S.L. (2012) Short-Term Dependence in Time Series as an Index of Complexity: Example from the S&P-500 Index. International Business Research, 5, 38-47.
https://doi.org/10.5539/ibr.v5n9p38
[11] Mandelbrot, B. (1974) Intermittent Turbulence in Self-Similar Cascades: Divergence of High Moments and Dimension of the Carrier. Journal of Fluid Mechanics, 62, 331-358.
[12] Frish, U. (1995) Turbulence. Cambridge University Press, Cambridge.
[13] Mandelbrot, B. (2003) Multifractal Power Law Distributions: Negative and Critical Dimensions and Other Anomalies, Explained by s Simple Example. Journal of Statistical Physics, 110, 739-774.
[14] Schroeder, M. (2009) Fractals, Chaos, Power Laws. Dover Pub., Inc., New York.
[15] Renyi, A. (1995) On a New Axiomatic Theory of Probability. Acta Mathematica, 6, 285-335.
[16] Renyi, A. (1970) Probability Theory. North-Holland, Amsterdam.
[17] Grassberger, P. and Procaccia, I. (1983) Characterization of Strange Attractors. Physical Review Letters, 50, 346-349.
https://doi.org/10.1103/PhysRevLett.50.346
[18] Peters, E. (1991) A Chaotic Attractor for the S&P-500. Financial Analyst Journal, 47, 55-62.
https://doi.org/10.2469/faj.v47.n2.55
[19] Medio, A. (1992) Chaotic Dynamics: Theory and Applications to Economics. Cambridge University Press, Cambridge.
[20] Dominique, C.-R. (2017) On the Scientificity of Microeconomics: Individual Demand and Value Determination. Theoretical and Practical Research in Economic Field, 8, 106-110.
[21] Mandelbrot, B. and van Ness, J.W. (1968) Fractional Brownian Motions, Fractional Noises and Applications. SIAM Review, 10, 422-437.
[22] Armeodo, A., et al. (1995) The Thermodynamics of Fractals Revisited with Wavelets. Physica A, 213, 232-275.
https://doi.org/10.1016/0378-4371(94)00163-N
[23] Ameodo, A., De Coster, N. and Roux, S.G. (2000) A Wavelet-Based Method for Multifractal Image Analysis. European Physical Journal B, 15, 567-600.
[24] Sottinen, T. (2003) Fractional Brownian Motion in Finance and Queuing. Doctoral Dissertation, University of Helsinki, Helsinki.
[25] Zili, M. (2006) On the Mixed Fractional Brownian Motion. Journal of Applied Mathematics and Stochastic Analyses, 2006, Article ID: 32435.
https://doi.org/10.1155/JAMSA/2006/32435
[26] Maio, Y., Ren, W. and Ren, Z. (2006) On the Fractional Mixed Brownian Motion. Applied Mathematical Science, 35, 1759-1738.
[27] Thale, C. (2009) Further Remarks on Mixed Fractional Brownian Motion. Applied Mathematical Sciences, 3, 1-17.
[28] Warwick.Ac.uk (2012) Lectures on Fractals and Dimension Theory.
http://warwick.ac.uk/mas dbl/dimension-total.pdf
[29] Hurst, E., et al. (1951) Long-Term Storage: An Engineering Study. Transactions of the American Society of Civil Engineers, 116, 770-790


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Q: How to style a part of place holder text with a class? I've found this article Change an HTML5 input's placeholder color with CSS which is extremely relevant and hence quoting it here.
Now, I unlike most the given articles I now know how to style the text inside but I dont know how to make it completely customizable. For instance, I would like to high a particular part of my placeholder to be of blue and the rest to be red. Here is an example that I try to illustrate my point.
Had it been a normal text I can just add some classes as per my choice. But in this case, what is the workaround for it?
http://jsfiddle.net/johnjacob/018fabmu/

redpajama_set_name: RedPajamaStackExchange


Watch for Harper Loveseat By Wayfair Custom Upholstery?
Watch out for sales when buying Camryn Fine Furniture Convertible Sofa By Winston Porter. More often than not furniture is put on selling. If you need a a number of part, it will save you a lot of money by with patience waiting for the retail price to be reduced. You could even ask your preferred Camryn Fine Furniture Convertible Sofa By Winston Porter shop when the item will probably be labeled for less money. Should you need a new sofa, consider discovering a single with a few totally taken care of pillows. These pillows last longer and will be switched on a regular basis. Essentially, you should obtain a furniture with easily removed covers so you can quickly rinse them. Detachable addresses can also be substituted quickly in case you are unable to clear a mark Buy Camryn Fine Furniture Convertible Sofa By Winston Porter later during. At the conclusion of this season, it really is popular for merchants to acquire these items off of their display room surface. This can lead to some great product sales and discounts.
In this fast changing world of competitors and advancement, it has been a undeniable fact that people hardly get enough time to spend in their homes, looking after themselves. It's obligatory for us that we invest at least half from the days amount of time in office, performing our job. When the workplace does not have in proper equipments and amenities for the employees, the workers start getting serious health issues. Likewise, the decorum and also the equipments from the offices are provided immense importance. These days, the majority of the equipments are chosen in a cautious method so as to ensure the employees comfort and ease. One such essential item in the office is the ergonomic desk office chairs. As most of the offices have turned out to be wise, which means they rely more on machine than manual labor, ergonomic workplace seats are especially created for such workplaces. They are the chairs used for the use of the workplaces getting pc workstations. These are specially designed seats that help in the reduction of demands around the a number of anxiety from the spine wires, thereby restricting the risk of muscular and nerve diseases. Also they assist to maintain the correct physique position. It lines up the over arms, arms, lower back, neck and also the head in the correct jobs, thereby decreasing lower back pain, function related bone and joint disorders and other this kind of illnesses. And if you simply searching for a seat to relax, then think about one of the reclining chair from our checklist. In the following paragraphs we will talk about the top fifteen greatest ergonomic seats to be able to provide the visitors using the correct knowledge so that once they purchase such seats, it might be easy for them to choose the correct one.
Just like its namesake, the camelback couch includes a difficulty or possibly two that highlights the main silhouette of this couch design. This can be a conventional design which was made popular within the 18th century by Chippendale and households who desired aristocratic, formal furniture often chosen this design. These days, this couch design lends a far more official air to the space, particularly when padded in a formal fabric. A far more casual textile choice would make it suitable for a family space that doesnt need a great deal of formality. Either way, the camelback sofa has some factors that define the design and style. The thighs are usually exposed, the sofa doesn't have back again soft cushions and it normally has sq . or rolled arms.
The word this is actually the comfort and ease and complicated look. This set includes a tufted backrest and toe nail head highlight that provides the subtle look. Its grey color adds to its impressive look. It may fit up to 8 in . bed mattress. That alone lets you know how comfortable the established could be. Notably, it doesn't incorporate a mattress. So you may need to buy one. The trundle includes a castor to enable quick access. You may also pull the trundle for people to sit on. Simply to point out, it should take assembling, however its very easy to assemble.
When the Chesterfield may be the elegant man amongst sofas, the Cabriole is the grande dame. Noted for its uncovered wooden and elegant thighs, similar to the Louis XV period, the cabriole also offers a distinctive outline. It was also a well-liked shape in the work of furniture producer Jones Chippendale. Typically, the rear is one continuous piece without soft cushions and has an elegant curving collection. This particular cabriole edition includes jewels in the tufts for added glamour. It's a couch style that can be as simple or luxurious as you wish. Upholstered having a luxurious materials like velvet produces a much various style sensation than whether it had been padded in a more muted, textural neutral. The primary aura of elegance stems from its general shape and lithe legs which means it will always lend a processed atmosphere to some room.
Much like its namesake, the camelback sofa has a hump or possibly two that accents the primary silhouette of this sofa style. This is a traditional style that was made popular in the 18th century by Chippendale and households who wanted aristocratic, official furniture often opted for this design. Today, this sofa style lends a more formal atmosphere to the room, particularly when upholstered in a formal fabric. A more informal textile option would make it suitable for a family room that does not need a great deal of custom. In either case, the camelback couch has some factors that characterize the design and style. The legs are usually exposed, the sofa doesn't have back again cushions and it usually has square or rolled hands.
Using the current boost in interest in the Mid-Hundred years Modern style style, this sofa style is a hot product. Whether true classic pieces, reproductions or new styles that incorporate Mid-Hundred years Modern components, they are really versatile sofas. Usually utilized in a minimal or mid-century style scheme, they are fantastic for including a retro really feel to a space. The differentiating elements include the uncovered legs and linear structure. Most middle-hundred years sofas but not every one of them may have some tufting on the back.
This reclining loveseat requires the second place because its an excellent inexpensive, super comfortable choice that can participate in most home decorations styles. Its solid wood frame is cushioned with coils (for some spring) and high-density froth (for some soft), and padded with dark brown faux leather which makes it an extremely-versatile piece of furniture. Combine it with the person cavern for any cozy spot to watch the game (and do not worry about any spillsits vinyl fabric upholstery tends to make clean-up simple) or perhaps your living room with a couple of decorative throw cushions for that perfect spot to cozy up following a long day. Actual-existence clients adore this lying loveseat because its comfortable, long lasting, simple to assemble 1 reviewer even noted that they was able to assemble two units within forty-five minutes! and shipping in the vendor is a breeze.
This set of RTA sofas comes in various upholstery textures. A number of them include bonded leather, linen, corduroy, bed linen consistency, rayon. You just need to choose the right tapestry in importance for your well balanced requirements. Accessible materials provide an simple-to-thoroughly clean component. A characteristic that suggests its adaptability to resist drinks and food. The luxurious seat and back again soft cushions vote in favor of a reducing-edge look. The square shaped arm that starts just over them enhances the elegance. You will find the comforts and gentle designs that strike your entrance.
The Bridgewater is a sofa style that is mainly informal and definitely comfortable. This style may be the beloved of numerous a designer because it can be used to create a informal, friendly room. Bridgewater couches are flexible, with respect to the upholstery you choose. Completed in a neutral material, this style of sofa does not compete with additional factors within the room which may be much more dramatic, such as artwork or any other large functions. More formal fabric will produce a more stately type of couch. A number of qualities distinguish Bridgewater couches: Typically they have low arms along with a higher back, which contributes to the sporadic appear. Most also have a tailored skirt that conceals the legs and free soft cushions for that seat and back again. This particular style was designed to accommodate slipcovers, which also lend a casual atmosphere to the couch.
This reclining loveseat requires the 2nd place because its an excellent affordable, extremely comfy option that can participate in most home dcor designs. Its wood body is cushioned with coils (for many spring) and high-density foam (for many soft), and padded with brownish fake leather which makes it an extremely-versatile piece of furniture. Add it to the person cavern for any cozy destination to view the game (and do not worry about any spillsits vinyl fabric upholstery tends to make clean-up easy) or perhaps your living room with a few decorative throw pillows for the perfect place to comfortable up following a long day. Real-existence clients adore this lying loveseat simply because its comfy, durable, easy to put together one rater even mentioned that she could assemble two models within 45 minutes! and shipping in the merchant is a breeze.
With regards to buying living room furniture, leather-based is always a good option. It doesn't only look good with most designs, but its very long lasting (it is the perfect material for a home with children or pets) and its ultra-simple to thoroughly clean, as well. The down-side of leather furniture? It may have a higher cost than material, micro-fiber or faux leather furniture. This reclining loveseat stays a financial budget-friendly choice because of 1 genius trick: its sitting area is padded with leather, while the attributes are padded with increased affordable fake leather-based. Which means you receive the appear and feel of a full leather-based loveseat without the significant cost. Make use of the lever on the loveseats equip to kick back and relax on its higher-density froth filling up, and think about all the money held on. This particular loveseat comes with an added reward: professional assembly will come in many locations of the country for an additional fee.
Copyright © Camryn Fine Furniture Convertible Sofa By Winston Porter in Loveseats All right reserved.


The AcroMaster Pro is the logical evolution of the very popular Acromaster first introduced in 2006. It has been important for multiplex during the development to improve the model but not fundamentally change it. So the appearance of the AcroMaster PRO is familiar at first glance, but still completely new and fresh.
With all these changes, the AcroMaster PRO is doing better than ever before - and due to its good-natured flight characteristics and its versatility in aerobatics the ideal basis for relaxed flying and training aerobatics. Like its predecessor, the AcroMaster PRO is designed as an all-rounder. This means that you can fly both precise and classic aerobatics, as well as 3D.


Argentines need to decide whether to pursue justice or surrender to terrorists.
Mrs. Kirchner initially called his death a suicide – even though his fingerprints were not found on the Bersa pistol left close to his body, and there was no gunpowder residue on his hands.
Nevertheless, Mr. Taiano is continuing to investigate, focusing most immediately on the calls made over more than 150 phone lines – many of them reportedly assigned to intelligence agents – on the day Mr. Nisman's body was found.
Mr. Nisman had found solid evidence that officials of the Islamic Republic of Iran planned and financed the AMIA bombing, and that Hezbollah, its terrorist proxy, carried it out.


text:
Archive Archive
The Benefits of Networking Offline in an Online World
By Brian Anthony Hernandez, BusinessNewsDaily Staff Writer November 6, 2010 05:20 am EST
Despite the explosive growth of networking on social media websites – LinkedIn, for example, has grown from 60 million users to 80 million since January – some budding and seasoned entrepreneurs alike are finding success interacting the way people have done for centuries: in person.
Within the past few years, entrepreneurs have gradually begun relying heavily on social media to meet new people. Relationships flourish and evolve through e-mail, social media and mobile applications to stay connected.
But Aditi Gautam, founder of NY Smart Business Networking Group on Meetup.com, said online networking can only do so much. Face-to-face interaction, she added, can offer an additional boost for any business professional.
"Social media might be able to introduce you to certain number of people, but I believe that if you want to build long-lasting alliances and grow your referral network, you need to know and believe in the other person's work," by meeting in person, Gautam told BusinessNewsDaily.
Trust, she said, is built during one-on-one sessions, whether they are at conferences and trade shows, during lunch or after work over drinks.
A crop of young entrepreneurs, who throughout their college tenures used the popular social media platforms, may understand more than any generation the importance of offline networking while still maintaining a digital presence.
"During online interactions, a potential consumer gets to know a company or entity through the content they produce, not the character or mission of those in charge of operations," said Benjamin Roberts, who graduated from Cornell University in May and plans to launch Terran Exchange, a business-to-business marketplace for commercial software, in December.
"You are far more likely to win over a customer with a firm handshake, confident smile and well-rehearsed pitch than page upon page of industry data supporting your product."
Roberts recently attended technology conference Interop where he put his philosophy to the test. There, he mingled and soon met someone who wanted to display a patent on Roberts' forthcoming business website.
"I believe there is no better way to explain your company's vision, message or purpose better than a face-to-face conversation," Roberts said.
Gautam and Roberts shared a few Dos and Don'ts to help you network at events:
Do understand the other person's needs
Don't just exchange business cards
Do set as many one-on-one meetings as you can during or after an event.
Do ask yourself, "What is the greatest need within my business right now?" Then, determine who you would like to meet to fill those needs and prepare a pitch that would appeal to that select audience.
"In-person networking is instant gratification," Roberts said. "If people understand your business, idea, product and understand your value, great."
And it's a sensible measurement of your networking tactics on and off the Internet.
"If they can't understand you or you can't distill your message into a couple of sentences (in person), how can you build trust on the Web?"
Military Outranks Disney, Microsoft as Happy Place to Work
Reach BusinessNewsDaily staff writer Brian Anthony Hernandez at Bhernandez@techmedianetwork.com. Follow him on Twitter (@BAHjournalist) and become his friend on Facebook (BAH Journalist) to interact or stay updated on news about small businesses.
Business News Daily Editor
Business News Daily was founded in 2010 as a resource for small business owners at all stages of their entrepreneurial journey. Our site is focused exclusively on giving small business advice, tutorials and insider insights. Business News Daily is owned by Business.com.
Starting a Business After College? Advice for Entrepreneurial Grads
WebiMax Review:Best Reputation Management Service for Businesses
How to Open a Retail Store

redpajama_set_name: RedPajamaCommonCrawl


Is any one still playing this - or the new contents? (well newish) Stasis Interrupted!
"You gotta run stuff by me before you go talking in crazy"
13th Regiment, 1st battalion the Freebooters.
Last edited by pelikan on Tue Oct 22, 2013 3:49 am, edited 1 time in total.
Hudson974 is mine, so feel free to add/accept if you want!
Ive been playing a lot of CM lately, no matter what anyone says i still enjoy it.
I have Halo, Halo 3, Halo 4 and Reach.
ALIENS:Colonial Marines....... play this all the time.
"Nuke the site from orbit, only way to be sure"
Thats was an intense game session, nrrve wracking as hell.
I'm not MedwayPVB on 360 any more.


Beards: they came, they saw, they stayed! Less than a decade ago, beards started sprouting up everywhere. They were on the faces of celebrities, key figures in the creative and tech industries and the work-at-home dad down the street. For guys who have no problems growing beards, joining the movement isn't a question of how, but when. For guys who have difficulty growing a healthy-looking beard, the search is on for the best beard growth products. If you're one of these guys, we want to help. There are some great companies out there whose missions are to develop beard growth products that allow everyone to join in on the facial hair movement. We've compiled a list of the best beard growth products currently on the market.
1. What are beard growth products?
Beard growth products are products that make it easy to grow even the hardest-to-sprout beards. These products range from beard oils infused with herbs and essential oils known to encourage growth to combs and brush kits that gently tame and smooth the hair, eliminating tangles and adding shine.
Beard growth products work in different ways. Topical solutions work by softening and conditioning the existing beard hair, preventing breakage and encouraging length retention. Others work by penetrating the skin and providing nutrients to the follicles beneath the hair shaft. You'll choose the products that work for your particular beard growth issues.
3. Where can you buy beard growth products?
You can buy them directly from the brands' sites or on shopping sites like Amazon.com.
The price range for these products vary. Expect to pay between $1 and $50 for the items we've reviewed.
We know that beard hair growth is a serious issue for many men, so we made sure that we thoroughly researched and covered the pros and cons of each product.
The price range for the best beard growth products ranged from $1 to $50. The amount you pay will vary based on the exact product you're getting and the amount of product you receive. You can also expect price differences based on the types of ingredients used. For instance, beard oils made with organic ingredients will generally cost more than those produced with non-organic or generic materials.
Grow Your Beard Fast, Full, and Thick!
Beard Farmer Growther Beard Oil for is considered one of the best beard growth products on the market. The company has put an extensive amount of time and research into the development and creation of its oil. Its created a proprietary formula that's comprised of a blend of key oils, including lavender oil and castor oil for growth, ylang-ylang oil and sage oil for conditioning and olive oil and avocado oil as carrier oils.
The seller offers a money back guarantee.
Overall, men really love Beard Farmer Growther beard oil. One of the best things about the oil is the scent. It has a light, heady scent that men like so much that many choose not to use any other scent. With continued use, men noticed that their beard hair grew in more evenly and became softer and more supple.
Some men felt that the scent was actually too strong, making it clear that it all boils down to personal preference. Some people were able to ignore the scent since the oil worked so well for them, while others had to stop using it altogether. This oil would not be a good choice for people who are allergic to any of the many oils found in the mix.
The Best Selling Sandalwood Beard Oil for Dry Skin is made from a combo of nine oils that work together to soften beard hair while preventing dryness and itchiness. The idea behind this oil is that a smooth, conditioned beard will grow in full, healthy and shiny. It contains oils like sweet almond oil, argan oil, avocado oil and hempseed oil.
The company orders a 100% satisfaction guarantee.
Many men consider this one of the best beard growth products around simply because of its pleasant, masculine sandalwood scent. The avocado oil in the formula contains antioxidants that help clear out clogged pores, encouraging growth.
Some men (and their significant others) felt that the oil's scent made it difficult to wear, either because it clashed with their colognes or because they preferred unscented oils.
Beard Flux XL Caffeine Beard Growth Stimulation Oil for Facial Hair Growth has a large, enthusiastic online following, making it one of the best beard growth products on the market. In addition to stimulating beard growth, it also helps with itchy skin and beard roughness.
Beard Flux XL Caffeine Beard Growth Stimulation Oil is 100% organic, using only the purest of ingredients. It's infused with caffeine which acts as a stimulating agent, allowing users to see results quickly. The fact that the oil was made without GMOs, fillers, and fragrances makes it perfect for people looking for completely pure and holistic growth aids. People who are sensitive to scents will love the fact that Beard Flux XL oil is completely fragrance-free.
Some people did detect a slight scent which bothered them initially, but they also noted that it was a very natural scent which faded quickly.
The Beard & Mustache Brush and Comb Kit - Boar Bristle Beard Brush and Wooden Grooming Comb are not usually what someone thinks of when searching for the best beard growth products around. The brush is made with wild boar bristles which are noted for their ability to smooth and detangle hair, distributing natural oils which then aid in beard hair growth and overall beard health.
The company offers a 100% Satisfaction Guarantee on its products.
The comb is made out of strong, durable pearwood and is compact enough to fit into your pocket, making it easy to do quick touchups on the go. The comb and brush work brilliantly when paired with beard oil and/or beard balm.
Some people, especially those with coarse or very full beards, felt that the brush and comb were not sturdy enough. They felt they needed something stronger to slide through their beard hair.
Exteren Hair Growth Essence is a hair growth oil that is used for beard hair growth as well as for hair growth on the head. You use it by adding a few drops to your favorite shampoo. It works by penetrating the roots of the hair shaft. It's infused with growth-promoting ingredients like ginseng, grapeseed oil, ginger, loca festival oil and fleece-flower root.
There is no information about a product guarantee.
It adds a healthy sheen to the hair without allowing it to become too greasy. It penetrates the hair shaft, making it thicker and more elastic. It could be a great choice for people with thinning hair.
People who are allergic to grapeseed oil will not be able to use this product.
The Inglorious Fuzz Beard Oil by Inglorious Fuzz is hugely popular and makes many people's best beard growth product lists. The company created the oil with input from barbers, ensuring they had expert input on what was needed to make the perfect oil.
The company offers a 100% satisfaction guarantee.
The product is light and easy to use. You simply have to rub it in between your hands and spread it onto your beard. It works great on all skin types, including sensitive skin, and it's particularly helpful at eliminating ingrown beard hair.
Several people mentioned that the oil seemed to have no effect on beard growth, especially as it pertained to patchy, hairless areas on their faces.
SEARCH IS OVER! You've found the finest beard oil for men dedicated to a finest beard.
NATURALLY MAGNIFICENT. Infused with Olive, Jojoba, Avocado & Argan oils for naturally magnificent beard volume.
SMELL TREMENDOUS. Create sensory delight with rosemary & cedarwood oil extract.
Made in America, Organic Beard Oil Growth uses eucalyptus globulus, Simmondsia Chinensis (jojoba), melaleuca alternifolia (tea tree oil) and Cedrus Atlantica (Atlas cedar). These ingredients work together to moisturize, soften and strengthen the hair, encouraging hair growth.
Organic Beard Oil Growth uses all organic ingredients, making it perfect for people who wish to only use pure ingredients on their skin and hair.
With no expiration date, it's hard to know if the oil is still fresh.
Men's Beard Oil - Mustache & Beard Growth Oil is ranked high on the list of the best beard growth products. This unscented, fully natural and organic beard oil contains no artificial colors or ingredients. Loaded with growth-inducing, softening ingredients like aloe vera, jojoba, and vitamin E oil, it helps make beards supple and soft while filling in patchy areas.
Men's Beard Oil is extremely light, making it easy to apply it to the beard and facial skin.
It only takes three drops of oil to condition a beard, and It successfully works on all skin types and ethnicities.
The fact that it's unscented appealed to many people, but some found the fact that it didn't have a scent a downside.
The Beard Grooming Kit contains beard balm, beard oil, beard wash and a beard comb, everything needed to nurture a beard and enhance its growth.
The entire kit is compact enough to be taken anywhere, and it contains everything you need to keep your beard clean, shiny and groomed.
The balm is made from ingredients like grapeseed oil and jojoba for moisturization and conditioning, while the oil is lightweight enough to be used anywhere as needed.
Some users found the oil and balm a bit too greasy.
When it comes to the best beard growth products around, the Bossman Beard Kit is one of those at the top of the list. It contains an intense conditioning cream, jelly beard oil, and a relaxing beard balm. Each item offers a relaxing scent, thanks to ingredients like patchouli, frankincense, and bergamot.
When it comes to the best beard growth products around, the Bossman Beard Kit is one of those at the top of the list.
It contains an intense conditioning cream, jelly beard oil, and a relaxing beard balm. Each item offers a relaxing scent, thanks to ingredients like patchouli, frankincense, and bergamot.
Some people find the scent too cloying and sweet.
When it comes down to choosing the best beard growth products, price and efficacy were key. If you're looking for the least expensive yet effective product, you can't beat the price of the $1 Exteren Hair Growth Essence. If you're looking for quick results and you're willing to pay a bit more, you can't beat the caffein-powered Beard Flux XL. At $50, it's a relatively small price to pay for big results.


The first destination in our itinerary for 2019 will be Los Angeles, California for the Upper Deck 2019 Certified Diamond Dealer Conference at the Westin Bonaventure Hotel. If you own a hobby shop and are an Upper Deck Certified Diamond Dealer then be sure to join us January 8th-10th for what is sure to be another great Conference hosted by Upper Deck!
COMC will be in attendance with our own booth set up for the duration of the conference. We will be available to meet with hobby shop owners to discuss how COMC can help their shops become more successful. We'll also be available to help shop owners set up and manage their accounts, offer demonstrations of our service, and answer any and all questions they may have about our service.
If you will be in attendance at the event and would like to drop off consignment submissions, we will be accepting submissions at our booth throughout the conference. We look forward to seeing you there!
We hope that you had a fantastic Holiday Bonus Sale! Now that 2019 is here we want to tell you about some changes that have gone into effect today on COMC. Some of these changes were already covered in our previous announcement regarding changes coming in 2019.
Our 20% Cash-Out Fee has been replaced with a 10% Cash-Out Fee and a 5% Transaction Fee. The specific details of this change can be found in-depth in our earlier blog post.
To qualify for cash outs under our new commission structure, COMC credit must either be earned after January 1st, 2019. Store credit earned prior to this date is considered Legacy COMC Credit. While this credit will spend the exact same as new COMC credit earned in 2019 and beyond, the key difference between Legacy COMC Credit and new COMC Credit earned after January 1st is that it Legacy COMC Credit cannot be cashed out until it has been converted to new COMC Credit via the Request Refund page.
When Legacy COMC Credit is converted to New COMC Credit, a 5% conversion fee is assessed, and the credit is now eligible to be cashed out under the new commission structure. Alternatively, if you have Legacy COMC Credit in your account, you can simply choose to wait until January 1st, 2020 when the concept of Legacy COMC Credit is retired, and any existing Legacy COMC Credit still in your account will be automatically converted to new credit without the 5% conversion fee.
Legacy COMC Credit only needs to be converted to New COMC Credit if you wish to cash out. Otherwise, it spends exactly the same as credit earned after January 1st on COMC. When you use COMC Credit to consign items, make offers, buy items, request a shipment, or pay for any other COMC services, we will use up your Legacy COMC Credit first. When you Cash-Out COMC Credit, we will use the new COMC Credit first. We will always use the credit that is most advantageous for you.
Regardless of how you use your Legacy Store Credit, you will ultimately be better off than before with our previous 20% cash-out fee. If you wish to maximize your cash out earnings, the best option would be to wait until January 1st, 2020, when all COMC credit, regardless of when it was earned, is eligible for the new commission structure. Waiting until this date to cash out Legacy COMC Credit will allow you to circumvent the 5% conversion fee, putting that savings directly into your pocket.
If you still have questions, our Customer Service Team is here to help! Simply send an email to staff@comc.com and our team will get back with you shortly. Happy New Year and here's looking forward to a great year of collecting!
You will need Microsoft Access 2010 or later to run it. If you don't have Microsoft Access, you can get the free Microsoft Office 365 Access Runtime. You must use the 32-bit version.
You will see a message like this the first time you open the Bulk Price Editor.
Click open on this prompt.
After opening it, there will be a new shortcut on your desktop.
For a full walk through tutorial on how to use the COMC Bulk Price Editor, please click here.
'Yule' love this! The COMC Holiday Bonus Sale is coming! We know that the Holiday season is the busiest time of the year, but we want you to join us from December 25th through 31st as we end 2018 in spectacular style! Millions of items from all of your favorite teams, players and sets will be marked down throughout our week-long sale. Now is the perfect time to treat yourself to the cards that you've wanted all year long!
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COMC Members who make qualifying Store Credit purchases at any point throughout the sale will receive this bonus. Credit purchased must be spent on COMC.com. Bonus credit will be removed from accounts if you request a refund on any Store Credit purchased during the promotion.
With the giving spirit still in mind, we're giving our sellers the opportunity to run a Sales Promotion throughout the Holiday Bonus Sale by waiving our usual $3/day promotion set-up fee. To get started, simply head on over to the Promotions Page and set up your Sales Promotion now! We want you to end 2018 with a bang, so be sure to offer buyers the best prices they've seen all year, so that they can enter 2019 with new additions to their collection!
One of the biggest advantages of shopping with COMC Credit using your COMC account is that you can INSTANTLY purchase items when you find them and ship everything all together at any time in the future! When you buy items with COMC Credit using your COMC account, they stay safe and secure in our warehouses until you're ready to request shipment of them. You can buy items throughout the Holiday Bonus Sale and request a shipment for your items next week, next year (so, next week…), or even in 2020 and beyond! You pay shipping just once, regardless of how many items you buy.
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It is important to vacuum upholstery regularly to remove the surface dust that builds up and slowly contributes to a graying effect that diminishes the clarity of the original color.
Please note that vacuuming should be done with the proper attachments to avoid breaking down the fibers and contributing to "pilling." In addition to regular vacuuming, a professional dry cleaner should come in at least once or twice a year to thoroughly clean the fabrics and remove the soiling that a normal vacuum cleaner cannot reach. The expense of this service is small compared to the reward of seating that looks good as new after a lot of use.
W – Water-based cleaning agents or foam may be used for cleaning this fabric.
S – Only mild, pure water-free dry cleaning solvents may be used for cleaning this fabric.
X – Fabric should be vacuumed or brushed lightly to remove soil. WARNING: Do not use water-based foam or liquid cleaning agents of any type on this fabric.
There are two types of stains: water-based and oil-based. The key to removing either type is prompt action. The longer a stain is allowed to remain on a fabric, the more difficult it will be to remove.
For water-based stains, a solution of warm soapy water (not overly soapy) used in the following manner should remove them. In removing oil-based stains, the same procedure can be followed, but instead of warm water, a spray dry cleaning solution should be used. Either treatment should be tried in an inconspicuous part of the fabric first, to make sure there will be no adverse reaction between the dye stuffs and the cleaning solution.
Soak up excess staining material immediately with a soft absorbent material. Do not dry the stain completely or it may set.
Either by using the warm soapy water or a dry cleaning solution and a clean sponge begin working the stain with light, quick strokes. Start at the outside of the stain and work toward the center. Be careful not to overly saturate the stain with cleaning solution or you may get a ring. Do not rub too vigorously or you may damage the nap of the fabric or break fibers.
Once the stain is removed, soak up all remaining cleaning solution and then use another clean cloth or sponge dipped in cool water to remove any residue that will attract further soiling.
Allow fabric to dry thoroughly and then vacuum well with an upholstery attachment before using.
It has been proven that several light applications are less harmful to fabrics than one concentrated one. If you go through the above steps and there is still a stain, repeat the entire procedure.
Remember, never use anything hot to clean fabric, as heat will set stains. Also, avoid a scrubbing motion.
If the stain is stubborn, call a professional cleaner and ask their advice.
As soon as possible, blot liquid spills with tissue paper to wash or a clean colorfast cloth. Scrape and vacuum away dry solid material. Avoid working soilant deeper into the fabric.
Apply household or commercial upholstery cleaner sparingly to the soiled area, as over wetting may spread the stain and damage cushion material under the fabric. Rub gently with a clean, white cloth Turn the damp cloth frequently to a clean surface to avoid re-depositing the soilant.
Work from the outer edge toward the center of the spot to reduce ringing. Cleaning the entire fabric panel, or at least a large area around the spot, further reduces the likelihood of ringing.
Some stains (i.e. perspiration/body oils) respond well to dry cleaning such as "Host" (Racine Industries), "Capture" (Milliken), "Bonafides" (Drummond American), "Keft" (Texize) and "Carbons". Carefully follow the directions on the label.
Crypton is an engineered fabric. With its patented process, Crypton is the only textile that is stain, water, and bacteria resistant. The key to this fabric is its weaving process coupled with its proven barrier; nothing gets through Crypton to the cushion.
Made by DuPont, this fabric protector is a powerful stain fighting system. If provides an invisible molecular barrier around the individual fibers of the fabrics. Liquid spills bead up and roll off and ground-in stains are released during cleaning.
Nano-Tex fabric protection is a chemical enhancement, attached at the molecular level, to fundamentally transform the fibers. Tiny "whiskers" aligned by proprietary "spines," are designed to repel liquids and are attached to the fibers utilizing molecular "hooks". These "whiskers" and "hooks" are very, very small… in fact they are no more than 1/1000th the size of a cotton fiber. Because the chemistry is created on a "nano-scale" the performance is durable and the hand and breathability are not altered. Nano-Tex fabrics are NOT considered waterproof nor are they considered a barrier product. Nano-Tex fabrics incorporate a superior repellant technology.
wallpapers you and your décor will probably be rejuvenated.
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text:
Writing a referral letter for a student
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The thesis statement usually appears in the introductory paragraph
The question of henry james a collection of critical essays
Colorado U; Calgary, Alberta: But Daisy, on this occasion, continued to present herself as an inscrutable combination of audacity and innocence.
Are we to deprive ourselves of the help and guidance of that vast body of knowledge which is daily growing upon the world, because neither we nor any other one person can possibly test a hundredth part of it by immediate experiment or observation, and because it would not be completely proved if we did?
However many nations and generations of men are brought into the witness-box they cannot testify to anything which they do not know. However plain and obvious these reasons may be, so that no man of ordinary intelligence, reflecting upon the matter, could fail to arrive at them, it is nevertheless true that a great many persons do habitually disregard them in weighing testimony.
When the labours and questionings of honest and brave men shall have built up the fabric of known truth to a glory which we in this generation can neither hope for nor imagine, in that pure and holy temple he shall have no part nor lot, but his name and his works shall be cast out into the darkness of oblivion for ever.
A belief was not a mental entity which somehow mysteriously corresponded to an external reality if the belief were true. James had grown up in a well-to-do family, and he was able to fraternize with the upper-class, gaining from them many of the impressions he would eventually include in his fiction, just as Honore de Balzac had once done in Parisian salons.
Small physical changes occur in the The question of henry james a collection of critical essays which eventually form complex ideas or associations. Roderick Hudson is a bildungsroman that traces the development of the title character, an extremely talented sculptor. His pragmatic theory of truth was a synthesis of correspondence theory of truth and coherence theory of truthwith an added dimension.
Fame can be fleeting, and what you think you should be known for may not be what lasts consider Arthur Conan Doyle, who never seemed to understand the appeal of Holmes!
He was encouraged to do this by reading Charles Renouvierwhose work convinced James to convert from monism to pluralism. This Library of America volume and its companion are a fitting testimony to his unprecedented achievement. The pure ego was not a substance and therefore could not be examined by science.
The many titles by San Francisco native Jack London. I did a new version for Firsts: The Turn of the Screw: For people who know the streets, these Continental Op tales are a vein of ultra-tough solid gold — among the best hard-boiled fiction of all time, set on pavement you can walk any time you feel like it.
For an example let us go to the telegraph, where theory and practice, grown each to years of discretion, are marvellously wedded for the fruitful service of men. If we are to trust the accounts of his early followers, he believed himself to have come upon earth with a divine and cosmic mission to set rolling the wheel of the law.
Medwin," for instance—are briefer and more straightforward in style than some tales of his earlier years. James suffered a stroke in London on December 2,and died three months later.
Let us first take care to distinguish a kind of tradition which especially requires to be examined and called in question, because it especially shrinks from inquiry.
Spade had no original. They ranged from such problems as the land settlement of the Punjabor the introduction of civil marriage to provide for the needs of unorthodox Hindusto the question of how far the study of Persian should be required or encouraged among European civil servants.
This impressive achievement is the story of a spirited young American woman, Isabel Archer, who "affronts her destiny" and finds it overwhelming. How long books hovering in the hypermodern price range will hold their value is hard to say.
It is most probable that he himself never doubted of the matter, or thought of asking the question; but we are in the position of those to whom the question has been asked, and who are bound to answer it.
They also were called true for human reasons. You are not currently authenticated. The story line concerns the contest between Ransom and Olive for Verena's allegiance and affection, though the novel also includes a wide panorama of political activists, newspaper people, and quirky eccentrics.
View freely available titles: Since he believed that good writing should resemble the conversation of an intelligent man, the process of dictating his works may perhaps account for a shift in style from direct to conversational sentences.
The Critical Heritage London: A major goal of emotion research is still to elucidate this stimulus-to-feeling sequence—to figure out what processes come between the stimulus and the feeling.
James's description of the mind-world connection, which he described in terms of a " stream of consciousness ", had a direct and significant impact on avant-garde and modernist literature and art, notably in the case of James Joyce. James continued the more involved, psychological approach to his fiction with What Maisie Knewthe story of the sensitive daughter of divorced and irresponsible parents.
This first volume focuses especially on his responses to American and English writers; the second volume contains his essays on European literature and the Prefaces to the New York Edition of his fiction.
In I began doing the Dashiell Hammett Tour through the streets of the city, a tribute to the greatest private eye writer ever to live in San Francisco.+ free ebooks online. Did you know that you can help us produce ebooks by proof-reading just one page a day?
Go to: Distributed Proofreaders. These essays are not intended to replace library research.
They are here to show you what others think about a given subject, and to perhaps spark an interest or an idea in you. To take one of these essays, copy it, and to pass Chaucer's Adherence to the "Three Estates" in the General Prologue.
Henry James. The Turn of the Screw: Authoritative Text, Contexts, Criticism. Yet their very appearance begs the question of their provenance--whence and why?--even as it forecloses on that very question.
(especially a second one) of any work has the air of a tautological self-justification. And a collection of New Critical Essays. Middle English Literature: Essays and Articles.
Extensive resource of textual criticism, scholarly and student essays, and articles on Medieval texts. In Don Herron began leading The Dashiell Hammett Tour, now the longest-running literary tour in the nation.
On this site you'll find information on current walks — dates, where to meet, arranging tours by appointment — plus a hard-boiled blog with news, reviews of books and film, and a dash of noir.
Dupee, F. W.The question of Henry James: a collection of critical essays / edited by F. W. Dupee H. Holt and Company New York Wikipedia Citation Please see Wikipedia's template documentation for further citation fields that may be required.
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Perhaps the statistics are still just statistics for you. In this podcast we want to put faces to the numbers because it's important that we realize this fight impacts all of us. Let's rise up together for the next generation!
God gave us a burden for what is happening in the next generation of the Church. Do you share it with us? Perhaps the statistics are still just statistics for you. But what if they were kids you know - kids in your own church, kids in your own family? In this podcast we want to put faces to the numbers because it's important that we realize this fight impacts all of us. Let's rise up together for the next generation!


text:
The Office: 10 Things We Learned From The Full Cut Of Threat Level Midnight
By Kelly West
It seems The Office has deemed us all admirable this holiday season, as the beloved NBC series has bestowed upon us the great lost film of Michael Scott, Threat Level Midnight. The full version of this gem of a home movie arrived this month, and in addition to offering us nearly 25 minutes of suspense and action-packed glory, the full version of Michael Scott's movie offers a few reveals and new tidbits to appreciate.
As The Office fans likely recall, Threat Level Midnight screened during an episode of Season 7. After three years of writing, one year of shooting, four years of re-shooting and two years of editing, Michael Scott's movie was finally ready for its audience. However, since the film was screened during an episode, there were snippets of the movie that were unseen by us, as the camera occasionally cut away for reactions from the Dunder Mifflin employees watching the movie in the conference room or reacting with their own behind-the-scenes facts. Now that we've finally seen the full version of Threat Level Midnight, a few missing pieces of the epic story have come to light. Here are some of the best reveals and additions...
How Michael Scarn's Wife Died
One of the earlier extended scenes we're treated to in Threat Level Midnight has Michael talking to the President about the villainous Goldenface's attempted assaults on all-star sporting events. The day Michael Scarn decided to take some personal time also happened to be the day of the WNBA All-Star game. And Scarn's wife just so happened to be playing in that game. If Michael Scarn hadn't been out running a 20k with his friend Robin Williams, he might've been there to stop Goldenface's attack.
The First Time Toby Patted Pam's Leg
Remember the awkwardness that ensued in Season 4's "Night Out," when Toby made a joke, Pam laughed and he responded by patting her knee, which created a moment of weird silence, which was broken by Toby's announcement that he was moving to Costa Rica, after which he bolted from the building, hopped the fence and ran home? As it turns out, that wasn't the first time Toby patted Pam's leg. During one of the hostage scenes in Threat Level Midnight, Toby casually and effortlessly removes one of his hands from his gold bindings and pats Pam's leg. She doesn't have any visible reaction to the gesture this time, even with Roy sitting right next to her.
It's probably safe to assume that the basement hostage scene of Threat Level Midnight was filmed before Season 4's "Night Out." After all, Roy is one of the hostages, and it's unlikely he would've been participating in Michael's movie after he and Pam split up. Plus, Pam's hair is tied back, which was pretty much her signature hairstyle before she and Jim got together. If that's correct, then this would've been the first time Toby's hand made contact with Pam's leg.
The Strangulation Scene Is Excruciatingly Long
This one is less of a reveal and more of an observation. In the "Threat Level Midnight" episode of The Office, the cameraman shows us mercy by cutting from the scene in which Michael Scarn strangles the medal-winning speed skater, played by Oscar, to the uncomfortable reactions of the staff watching the violent moment play out on the conference room TV. The uncut version isn't so generous, which leaves us to experience our own uncomfortable reactions as Scarn slowly strangles Speed Skater with the flag. It takes a while, with lots of kicking, grabbing and gasping on Oscar's part.
Tony Gardner is the Piano Player at the Funky Cat
In the "Threat Level Midnight" episode cut of the film, if you look closely enough at the man seated at the piano when Michael enters the Funky Cat (the hippest jazz club in town), you might be able to recognize the man playing piano before Michael Scott sits at the bench. The uncut version of the film reveals the identity of the piano player beyond a shadow of a doubt. Remember Tony Gardner? He worked at Dunder Mifflin Stamford, and then at Dunder Mifflin Scranton after the merge for about a day, before trying to quit due to his incompatibility with Michael's management style. Michael subsequently fired him for attempting to quit. Well, apparently, despite knowing him for only a day, Tony still managed to make a cameo in Michael's film.
Exactly when did Tony have time to appear in Michael's movie? Who knows. It wouldn't be entirely out of character for Michael to cast Tony after he left Dunder Mifflin for good. Especially considering the only exchange Michael Scarn has with Tony in the Funky Cat scene is to tell him to "Beat it, turd." To which Tony responds by thanking him and promptly exiting. Just as Michael isn't above having the last word twice, Tony might've actually been polite enough to accept the opportunity to be featured in the movie.
Meredith Plays a Man
Meredith somehow manages to get two parts in Threat Level Midnight. The first is a random appearance as a mustached man at the Funky Cat. Michael initially mistakes mustached Meredith for Jasmine Windsong before spotting Jan's character lounging on top of the piano.
Meredith's acting abilities are clearly so good that Michael had to cast her in a second role. She joins Phyllis, Angela and Karen as the bachelorettes at the bar.
The Bachelorettes Had More Lines
In "Threat Level Midnight," Karen's ridiculous bachelorette line is an opportunity for the camera crew to check in on Jim's old flame, who seems baffled that they would even care about her line in the movie, like a million years later. Little did we know that Phyllis, Meredith and Angela -- who all play bachelorettes as well -- had their own ridiculous lines to add to the scene.
The winning line of the three previously unaired responses has to go to Angela, who looks physically uncomfortable at having to utter the words, "Come and ride the choo-choo... the sex choo-choo."
Goldenface's Origin Story Is Explained
This whole time, we had no idea why Goldenface's face was gold... until now. As Jim Halpert's character explains to Pam's Sandra, he worked at a gold factory and they didn't get a lunch break, so he had to eat the gold. One day, he looked in the mirror and it turns out, you are what you eat. This bit of background information leads to the reveal that Goldenface is trying to blow up trophies so everyone would be gold like him.
"Judge Attapow" To Make A Movie About Michael Scarn
Near the end of the movie, while cooking breakfast and basking in the glow of his All-Stars trophy, Michael Scarn suggests to Samuel that someone should make a movie out of his adventure. Dwight's character is holding up a newspaper with the headline "Scarn Saves Day," under which is subtitled "Judge Attapow To Make Movie About Him." It's probably safe to assume that "Judge Attapow" is Michael Scott's misspelled attempt at a nod to Judd Apatow, the director and co-writer to The 40-Year-Old Virgin (which starred Steve Carell). It's a great little easter egg that didn't make it into the episode, but will live on in the uncut version of Threat Level Midnight... along with Michael's self-bleeped Lethal Weapon reference ("I'm getting too old for this BLEEP.")
The Threat Level Midnight Song Is Sung By Andy Bernard
Sharp-eared Office fans may have already guessed this one, but it's not officially credited in the "Threat Level Midnight" episode. That's because the closing credits don't actually appear over the song in the episode version of the film. This newly released cut does include credits, and apparently, in addition to playing Billy the Bartender, Ed Helms' Andy Bernard is also the voice we hear singing the "Threat Level Midnight" song at the end of the film. And if the style of music sounds familiar, the credits also include "Inspired by the music of Will Smith."
There's A Post Credits Scene
After the credits role, we're treated to a post-credits scene that'll seem very familiar to anyone who's seen Ferris Bueller's Day Off. Just as Ferris shows up at the end of his movie to ask viewers why they're still watching and tell them the movie's over and to go home, Michael Scarn appears after the credits of Threat Level Midnight to do the same. He's even wearing his own striped bathrobe. The awkwardness of the bit is doubled as Dwight's Samuel joins in on the gag, which goes on a few beats too long.
Apart from its nod to a beloved '80s movie, the post-credits scene does reveal is the the level setting for when things are ok. Threat Level Noon, obviously.
Bonus Item: A Change To The Intro And Michael Scarn's Wife
One thing that appears to be missing from the full Threat Level Midnight cut is Stanley's voiceover at the beginning of the movie, which features a series of newspaper and magazine clippings recapping the loss of Michael Scarn's wife, Catherine Zeta Jones. The actress, who only appears via the clippings in the original "Threat Level Midnight" episode, seems to have been omitted from this version of the movie. When Dwight's Samuel wakes Scarn up and tells Michael "It's Goldenface," he follows with "The man who killed..." And Michael quickly responds, "Don't say her name," presumably because he's too grief-stricken to hear it. But it's a slight adjustment from the scene from the episode, in which Dwight only says "It's Goldenface." and Michael responds, "Goldenface. This makes it personal."
Those are just some of the tidbits we spotted in Threat Level Midnight, but there are more great little moments and unseen or extended bits worth checking out.
Kelly West
Kelly joined CinemaBlend as a freelance TV news writer in 2006 and went on to serve as the site's TV Editor before moving over to other roles on the site. At present, she's an Assistant Managing Editor who spends much of her time brainstorming and editing feature content on the site.
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