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SUNY-NTG-98/15
Thouless Energy and Correlations of QCD Dirac Eigenvalues
J.C. Osborn and J.J.M. Verbaarschot
Department of Physics and Astronomy, SUNY, Stony Brook, New York 11794
Eigenvalues and eigenfunctions of the QCD Dirac operator are studied for gauge field configurations given by a liquid of instantons. We find that for energy differences δE below an energy scale Ec the eigenvalue correlations are given by Random Matrix Theories with the chiral symmetries of the QCD partition function. For eigenvalues near zero this energy scale shows a weak volume dependence that is not consistent with Ec∼1/L2 which might be expected from the pion Compton wavelength and from the behavior of the Thouless energy in mesoscopic systems. However, the numerical value of Ec for our largest volumes is in rough agreement with estimates from the pion Compton wavelength. A scaling behaviour consistent with Ec∼1/L2 is found in the bulk of the spectrum. For δE>Ec the number variance shows a linear dependence with a slope which is larger than the nonzero multifractality index of the wave functions. Finally, the average spectral density and the scalar susceptibilities are discussed in the context of quenched chiral perturbation theory. We argue that a nonzero value of the disconnected scalar susceptibility requires a linear dependence of the number variance on δE.
Random matrix theories have been applied extensively to disordered mesoscopic systems (for recent reviews we refer to [1, 2, 3] ). In particular, correlations of energy eigenvalues have been studied in great detail. One important energy scale that enters in these studies is the Thouless energy, Ec, which is essentially the inverse diffusion time of an electron through the sample [4] . If the diffusion constant is given by D and the linear dimension of the sample is equal to L the Thouless energy is given by
Ec=ℏDL2. (1)
What has been found is that eigenvalues closer than Ec are correlated according to the invariant random matrix ensembles. Because such correlations are characteristic for classically ergodic and chaotic quantum system this regime is also known as the ergodic energy domain. A second energy scale is given by ℏ/τe, where τe is the elastic collision time. The energy regime with δE>ℏ/τe is known as the ballistic regime whereas the domain Ec<δE<ℏ/τe is known under the names of diffusive regime or Altshuler-Shklovskii regime. The different energy regimes have received a great deal of attention in recent literature [5, 6, 7, 8, 9, 10, 11] (for further references we refer to [1, 2, 3] ). A semiclassical interpretation in terms of the return probability has been given in [12] .
A convenient way to measure the pair correlations of eigenvalues is by means of the number variance Σ2(n). This statistic is defined as the variance of the number of eigenvalues in an interval containing n eigenvalues on average. In the ergodic regime the number variance is given by the invariant random matrix ensembles Σ2(n)∼(2/βπ2)log(n). The behavior of the number variance in the diffusive is less well-established. One proposal is [4] that Σ2(n)∼nd/2 (where d is the number of Euclidean dimensions) if the coupling is below the critical value for a localization transition. However, for critical values of the coupling constant, for which the localization length scales with the size of the sample, a linear dependence on n is predicted, i.e., Σ2(n)∼χn. In this regime, the slope has been related to the multifractality index of the wave functions [13, 14] .
In this letter we investigate to what extent such scenarios are realized in QCD. In QCD the order parameter of the chiral phase transition is related to the spectral density, ρ(λ), of the Dirac operator by means of the Banks-Casher formula [15] , Σ=limπρ(0)/V (the space-time volume is denoted by V=L4). For broken chiral symmetry, Σ≠0, this results in eigenvalues near zero virtuality that are spaced as ∼1/V. It is therefore natural to introduce the microscopic limit V→∞ such that u=λVΣ is kept constant. The microscopic spectral density is then defined by [16] ,
ρS(u)=limV→∞1VΣ⟨ρ(uVΣ)⟩, (2)
where the spectral density is defined by
ρ(λ)=∑kδ(λ−λk), (3)
and the brackets denote ensemble averaging. There is ample evidence from lattice QCD [17, 18, 19] and instanton liquid simulations [20] that ρS(u) and other correlators on the scale of individual level spacings [21] are given by chiral Random Matrix Theory, i.e. random matrix theories with the chiral symmetries of the QCD partition function. However, at scales beyond a few eigenvalue spacings in both instanton simulations [20] and lattice QCD simulations [17, 18] the Dirac eigenvalues near zero show stronger fluctuations than those in the chiral random matrix theories. This indicates the presence of an energy scale in QCD which may be identified as the Thouless energy.
In the regime where the pion loops can be ignored the correlations of the eigenvalues near zero are given by the chiral random matrix ensembles [16, 22] . They can be mapped onto an effective partition function given by the mass term generated by the spontaneous breaking of chiral symmetry [16] . From the work of Gasser, Leutwyler and Smilga [23, 24] , we expect that the boundary of the ergodic regime is given by a mass scale mc where the Compton wavelength of the associated Goldstone boson with mass m2π=mcK (according to the PCAC relation K=Σ/F2π, where Fπ is the pion decay constant) is of the order of the linear dimension of the box. This condition can be written as [25, 26]
mc=1KL2. (4)
It is therefore tempting to interpret 1/K as the diffusion constant. Because K is large on a hadronic scale (K≈1660MeV) the diffusion constant is relatively small, and we expect a Thouless energy that is small as well. We emphasize that mc is a valence quark mass that is not present in the fermion determinant. In other words, the spectral density does not depend on mc. For example, the valence quark mass of the chiral condensate is related to the spectral density by [27]
Σ(m)=1V∫∞02mρ(λ)dλλ2+m2. (5)
Therefore, the spectral density and, similarly, higher order correlation functions, can be obtained from the valence quark mass dependence of the effective partition function. It can be obtained with the help of quenched chiral perturbation theory [28] or by means of the replica trick in which we start from nf valence flavors and take the limit nf→0 at the end of the calculation. In the thermodynamic limit, the mass scale (4) is much less than the scale of massive quarks which leads to a decoupling of the valence quark mass dependent part of the partition function. The Dirac spectrum and its correlations are thus given by the valence quark mass dependence of the effective partition function which below the scale (4) is given by chiral random matrix theory. For massless quarks the argument is simpler. Now the Compton wavelength of the physical pions is always much larger than the size of the box. The crossover point is thus given by the value of the valence quark mass where the corresponding Goldstone boson (in the sense of quenched or partially quenched chiral perturbation theory) is equal to the size of the box. In this case, however, the microscopic spectral correlations depend on the number of massless flavors. Alternatively, one can study the boundaries of the domain where the pion loops can be neglected via relations between microscopic spectral correlators and finite volume partition functions as given in [29] .
In the bulk of the spectrum, chiral symmetry is broken explicitly by the valence quark mass, and the 'Goldstone bosons' associated with the valence quark masses are no longer in the low energy spectrum of QCD. However, in this case, spontaneous symmetry breaking in the generating function for the correlation functions results in the usual nonlinear σ− model for disordered mesoscopic systems [30] . The critical energy scale is then given by the Thouless energy mc∼1/K′L2, where K′=πρ(E)/VF2π and ρ(E) is the spectral density at E. Since the group manifold is different in this case [31] the numerical constant in this relation differs by a factor of the order unity from the constant in (4).
Using that according to the Banks Casher relation [15] the eigenvalue spacing is given by Δ=π/ΣV, the condition (4) can be rewritten in dimensionless form as
gc=mcΔ=F2ππL2. (6)
Here, gc plays the role of the dimensionless conductivity. At this point we wish to mention that a relation between transport properties of mesoscopic systems and the pion decay constant was established recently in [32] . In lattice QCD for an Na4 lattice this relation reads gc=F2πa2√N/π. On a 164 lattice with a lattice spacing of 0.1 fm this results in a dimensionless Thouless energy of a couple of lattice spacings.
In order to investigate the presence of a Thouless energy in QCD we perform our calculations for gauge field configurations given by a liquid of instantons. For such configurations we study correlations of the eigenvalues of the corresponding Dirac operator. In particular, we investigate the number variance, and establish a crossover between the ergodic and the diffusive domain. The linear dependence will be compared with the multifractality index of the wave functions. We will argue that results for chiral perturbation theory apply to the diffusive regime. The above observables are studied for a variety of system sizes and as a function of the number of flavors.
2 Instanton liquid model
In this model the gauge field configurations are given by a superposition of instantons. We use the streamline Ansatz which for a dilute system reduces to the sum Ansatz defined as a simple superposition of instanton profiles Aμ=∑IAI,μ. Each instanton is described by 4Nc (the number of colors is denoted by Nc) collective coordinates. The Euclidean QCD partition function is then approximated by
Zinst=∫DΩdetNf(γ⋅D+m)e−SYM, (7)
where the integral is over the collective coordinates of the instantons and the covariant derivative is defined by Dμ=∂μ+iAμ. The Yang-Mills action of the gauge field configurations is denoted by SYM. We will only consider configurations with an equal number of instantons and anti-instantons. The fermion determinant is evaluated in the space of the fermionic zero modes of the instantons.
This partition function obeys the flavor and chiral symmetries of the QCD partition function. It reproduces results obtained in chiral perturbation theory as well as many other details of the low energy hadronic phenomenology [33, 34, 35, 36] . In our calculations we use the standard instanton liquid parameters with instanton density N/V=1 (in units of fm−1). For more details on the instanton liquid partition function we refer to a recent review by Schäfer and Shuryak [37] .
3 Random matrix model
The chiral random matrix ensembles for Nf massless quarks in the sector of topological charge ν are defined by the partition function [16, 22]
ZβNf,ν=∫DWdetNf(cc0iWiW†0)e−nβTrV(W†W), (8)
where W is a n×(n+ν) matrix. As is the case in QCD, we assume that ν does not exceed √2n. The parameter 2n is identified as the dimensionless volume of space time. It can be thought of as the total number of instantons in the partition function (7). The matrix elements of W are either real (β=1, chiral Orthogonal Ensemble (chOE)), complex (β=2, chiral Unitary Ensemble (chUE)), or quaternion real (β=4, chiral Symplectic Ensemble (chSE)). The simplest ensemble is the Gaussian case with V(x)=Σ2x (also known as the Laguerre ensemble). In that case one can easily show that the microscopic spectral density (2) is given by [22]
ρS(u)=u2(J2a(u)−Ja+1(u)Ja−1(u)). (9)
where a=Nf+|ν| (the result for a=0 was obtained in [38] ). It is also straightforward to derive the microscopic correlation functions [38, 18] . In the bulk of the spectrum, the eigenvalue correlations of the chiral ensembles are given by the invariant random matrix ensembles.
It was shown by Akemann et al. [39] that, for β=2, the microscopic spectral density and the microscopic spectral correlators do not depend on the potential V(x) and are given by the results [38] for the Laguerre ensemble. Their work greatly extends an earlier result by Brézin and Zee [40] who studied the potential V(x)=x+αx2. The microscopic spectral density is also invariant with respect to the addition of an arbitrary constant matrix to the off-diagonal blocks in the determinant [41, 42] . The application of chRMT has been put on a firm foundation by these and other universality proofs [43] . Whether or not QCD is in this universality class is a dynamical question that only can be proven by explicit numerical simulations.
4 Numerical Results
In this section we simulate the instanton liquid model introduced in section 2. We evaluate the partition function (7) by means of a Metropolis algorithm. Typically, we perform on the order of 10,000 sweeps for each set of parameters. For the equilibrated configurations the eigenvalues and eigenvectors of the Dirac operator are calculated by means of standard diagonalization procedures. Most of our calculations have been performed in the quenched approximation (Nf=0). The motivation for this choice is twofold. First, calculations at Nf≠0 require the evaluation of a determinant for each update of the integration variables which is extremely costly and restricts us to a total number of instantons not larger than 128. For Nf=0, we are able to generate ensembles up to 512 instantons which turns out to be important in the study of the thermodynamic limit. Second, our results are compared with ideas from disordered mesoscopic systems where no fermion determinant is present.
In order to separate the fluctuations of the eigenvalues from the average spectral density we unfold the spectrum, i.e. we rescale the spectrum in units of the local average level spacing. Specifically, the unfolded spectrum λunfk is obtained from the original spectrum λk according to
λunfk=∫λk0¯ρ(s)ds, (10)
where ¯ρ(s) is the smoothened average spectral density. The number variance, the nearest neighbor spacing distribution and the microscopic spectral density are all calculated from the unfolded spectrum.
In Figs. 1 and 2 we show the number variance, Σ2(n) versus n for Nf=0 and various total numbers of instantons as given in the legend of the figure. The instanton density N/V=1. The random matrix result for Σ2(n) for the chGUE [18] is depicted by the solid curve. In both figures, the right figure (with results for only two different volumes) is a blown-up version of the left figure. In Fig. 1 the number variance is calculated for the interval that contains on average the n smallest positive eigenvalues. Fig. 2 represents the number variance in the bulk of the spectrum obtained from an interval that is symmetric about the average unfolded positive eigenvalue. In both cases we observe a transition point nc below which the number variance is given by random matrix theory. In Fig. 1 the value of the crossover point, nc≈2, depends only weakly on the total number of instantons (or the volume). This is not in agreement with the theoretical expectation (6) that nc≈F2π√V/π in four dimensions. For standard instanton liquid parameters the numerical value of nc for N instantons is given by nc≈0.08√N which is on the order of the results found in Fig. 1. In the bulk of the spectrum (Fig. 2) the value of nc is consistent with a √V scaling but the numerical constant appears to be larger than the above estimate (even if we take into account that the spectral density in the bulk is considerably less than near λ=0). This result is in agreement with the finding that correlations of lattice QCD eigenvalues for 124 and 164 lattices are given by RMT up to distances of 100 and 300 level spacings, respectively [21, 44] . Notice that the condition that the pion Compton wavelength is equal to the size of the box (leading to (4)) provides us only with an order of magnitude estimate for the transition point.
Beyond the crossover point the number variance shows a linear behavior with a slope χ≈0.08 for eigenvalues near zero and χ≈0.04 in the bulk of the spectrum. The downward trend of the curves for larger values of n is a finite size effect. For example, for a finite number of uncorrelated eigenvalues Σ2(n) does not behave linearly, but rather as Σ2(n)=n−2n2/N (notice that we have only N/2 positive eigenvalues). This finite size effect prevents us from saying more about the ballistic regime, an energy scale of roughly the inverse distance between instantons.
In the ergodic regime we expect that eigenvalue correlations are given by the invariant random matrix ensembles. This is shown in Fig. 3 where we plot the nearest neighbor spacing distribution P(S) versus S (left) and the microscopic spectral density ρS(z) versus z (right) (in terms of the variable z=u/π in (2)). The full circles and the open squares represent results for 512 and 128 instantons, respectively. Results obtained for the (chiral) random matrix ensembles are depicted by the full line. Clearly, below the Thouless energy we are in close agreement with RMT. However, beyond the Thouless energy of about two level spacings the oscillatory structure in the microscopic spectral density is no longer reproduced. This implies that beyond this point the QCD Dirac eigenvalues fluctuate more than the chGUE eigenvalues which is consistent with the number variance shown in Fig. 1. A similar increase in eigenvalue fluctuations at a scale of a few eigenvalue spacings has been observed in lattice QCD spectra [17] indicating that also in that case the Thouless energy for the region around λ=0 is less than predicted by the scaling behavior of disordered mesoscopic systems.
The inverse participation ratio which is a measure for the number of significant components in the wave function is defined as
I2(λ)=⟨∑k|ψk(λ)|4⟩, (11)
The ψk(λ) are the normalized eigenfunctions of the Dirac operator in the space of fermionic zero modes corresponding to eigenvalue λ. The number of components of the wave function will be denoted by N. For the chGUE we find I2=2/(N+2) whereas for uncorrelated eigenvalues (the chiral Poisson ensemble) we find I2=1/2. Results for NI2(λ) as a function of λ are depicted in Fig. 4 (left). The general impression is that the wave-functions are extended with a participation ratio that is not too different from the random matrix result (full line). The eigenfunctions corresponding to small and large eigenvalues appear to be somewhat more localized. A more definitive result for the character of the wavefunctions follows from the scaling behavior of I2(λ) with the volume.
A double logarithmic plot of NI2(λ) versus N is shown in Fig. 4 (right). Results are given both for the energy intervals [0.1,0.2] (open circles) and [0.7,0.8] (full circles). The first region corresponds to a part of the spectrum where the number variance shows a linear behavior for the volumes shown in Fig. 1, and the second region corresponds to the bulk of the spectrum.
The multifractality index η of the wave functions is defined by [13]
I2∼Vη/d−1. (12)
According to an argument given in [13] the value of η=2χd (where χ is the slope of the linear piece in the number variance) in the critical domain. From the volume dependence of the inverse participation ratio shown in Fig. 4 (right) we find a value for η/d of about 0.02 and 0.04 for the intervals [0.1,0.2] and [0.7,0.8], respectively. These values are well below the theoretical result of 2χ. Apparently, the ensemble of instantons is not in the critical region for Nf=0. The localization properties of eigenfunctions have also been studied for the Wilson lattice QCD Dirac operator [45] . In that case it was found that the eigenstates are localized. We have no explanation for this discrepancy.
The flavor dependence of the number variance of eigenvalues near zero is shown in Fig. 5. Results are given for 128 instantons and massless flavors. Again the Thouless energy is about two level spacings (in order to avoid a cluttered figure we have not plotted the random matrix results for the number variance). We observe an enhancement of eigenvalue fluctuations for 3 flavors (chiral symmetry is already restored for Nf=4 [37] ) and conclude that the critical number of flavors is approximately equal to three. However, our volumes (of up to 128 instantons) were too small to reliably extract the multifractality index. For completeness we mention that a similar enhancement of fluctuations for Nf=3 also takes place in the bulk of the spectrum.
Fig. 5. The flavor dependence of the number variance Σ2(n) versus n calculated for an ensemble of 128 instantons.
5 Spectral density and chiral susceptibility
In this section we consider the average spectral density, the valence quark mass dependence of the chiral condensate and the connected and disconnected scalar susceptibilities. In order to compare our results with quenched chiral perturbation theory [28] we put particular emphasis on the extrapolation to the thermodynamic limit. These quantities were calculated elsewhere for smaller volumes (64 instantons) [26, 46] .
Fig. 6. The normalized spectral density ρ(λ) versus λ for Nf=0 and 128 and 512 instantons.
The spectral density of the Dirac eigenvalues for a liquid of instantons was studied before for Nf=0 with the help of mean field techniques [34, 33] . For large values of Nc the overlap matrix elements are independent resulting in a semi-circular distribution [34] . For small values of Nc the matrix elements are correlated and the natural distribution is a Gaussian [33] . On the other hand, from the asymptotic dependence of the matrix elements of the Dirac operator it was concluded that [47] the spectral density diverges as 1/√λ. Another estimate comes from quenched chiral perturbation theory [28] . For λ→0 one obtains a linear dependence [48] for Nf≠0, and a logarithmic divergence [49] for Nf=0. For Nf≠0 the slope of the Dirac spectral density for λ→0 is consistent with the analytical result [50] . Here we only consider the quenched case.
In order to study the thermodynamic limit of the spectral density we have unfolded the calculated spectrum with the known result for the microscopic spectral density. The resulting normalized average spectral density for Nf=0 is shown in Fig. 6. Inspection of the normalized eigenvalue density in an interval [0.0,0.05] shows that it grows logarithmically with N. This suggests that ρ(λ) diverges for λ→0 in the thermodynamic limit. In order to understand the nature of this divergence we have compared results obtained for the instanton liquid with the analytical results for the a chiral version of the α-ensenbles [51] (dotted curve). These are random matrix ensembles with potential V(x)=xα/2 in (8). The spectral density of the chiral α-ensembles diverges logarithmically for λ→0 at α=1. The value of ρ(0) is finite for α>1 . For N=64, 128, 256 and 512 we find α=1.217,1.132,1.073,1.039 by fitting to the energy interval [0.05,0.5], respectively. In the thermodynamic limit this extrapolates to a value of α=1.00±0.02, resulting in a logarithmic divergence of the spectral density. We also compare the average spectral density to a simple power law behavior a−bλβ. We find that the spectra are equally well fitted by such dependence (see full curve in Fig. 6). By fitting to the interval [0.05,0.5] we find β=0.28,0.25,0.13,0.09 for N=64, 128, 256, and 512, respectively. This extrapolates to a value of β=0.03±0.04 and is also consistent with a logarithmic singularity for λ→0. We conclude that our results are consistent with an average spectral density that diverges logarithmically for λ→0 in the limit V→∞. However, larger volumes need to be studied in order to arrive at definite conclusions. We wish to emphasize that our results disagree with estimates obtained by mean field methods.
Fig. 7. The valence quark mass dependence of the chiral condensate for Nf=0 and a total number of instantons as indicated in the legend of the figure.
The valence quark mass dependence of the chiral condensate defined in (5) is shown in Fig. 7. Results are given for Nf=0 and different values of the total number of instantons. The downward trend for small masses is a finite size effect that can be understood analytically in terms of the microscopic spectral density [25] . The large volume dependence of the "plateau" prevents us from comparing our results with quenched chiral perturbation theory [28] which predicts a logarithmic dependence on the valence quark mass. For the same reason, the connected scalar susceptibility, ∂mΣ(m), shows an even larger volume dependence.
Fig. 8. The disconnected chiral susceptibility for Nf=0 both for 128 and 512 instantons.
Finally, we consider the disconnected scalar susceptibility. It is related to the two-point correlation function according to the formula [52]
χd=−2V∫∞0∫∞0dλdλ′m1m2(λ2−λ′2)2Rc(λ,λ′)(λ2+m21)(λ2+m22)(λ′2+m21)(λ′2+m22) (13)
where Rc(λ,λ′) is the connected two-point correlation function,
Rc(λ,λ′)=⟨ρ(λ)ρ(λ′)⟩−⟨ρ(λ)⟩⟨ρ(λ′)⟩. (14)
In the derivation of (13) we have used that that Rc satisfies the sum-rule ∫∞0dλRc(λ,λ′)=0. In the bulk of the spectrum, a number variance given by Σ2(n)=χn is reproduced by a two-point correlation function Rc(λ,λ′)=χ(δ(λ−λ′)ρ(λ)−2ρ(λ)ρ(λ′)/N) (For an extensive discussion of the relation between a linear dependence of the number variance and the sum rule for the two-point function we refer to [53] ). This results in the disconnected susceptibility
χd=χ(Σm−∂mΣ−2Σ2). (15)
A 1/m behavior for the susceptibility was observed in unquenched lattice QCD simulations [54] . In Fig. 8 we show the disconnected scalar susceptibility mχd/Σ(m) versus m. We observe a 'plateau' that would indicate a 1/m dependence for N=128, but it disappears for larger volumes. Apparently, finite size effects prevent us from making any definite conclusions.
Let us finally make a naive estimate of the disconnected susceptibility. The two-point correlation function T2(λ,λ′), which is related to Rc(λ,λ′) by T2(λ,λ′)=δ(λ−λ′)ρ(λ)−Rc(λ,λ′), can be expressed in terms of the two-level cluster function as
T2(λ,λ′)≈ρ(λ)ρ(λ′)Y2(r), (16)
where r=∫λ′λρ(s)ds. According to [9] Y2(r) is related to the number variance as
Y2(r=n)=−12∂2nΣ2(n). (17)
This results in T2(λ,λ′)≈12∂λ∂λ′Σ2(r). Combining (16) and (17) with (13) we find that a finite value of χd, which is expected according to quenched chiral perturbation theory [49] and lattice QCD simulations [54] , requires that
limN→∞Σ2(Nx)N (18)
is finite. In other words, a nonzero disconnected chiral susceptibility requires a number variance that shows a linear behavior on macroscopic scales. In chiral random matrix theory we find that χd=0 in the thermodynamic limit. Because of the large volume dependence of the spectral density this argument could not be verified in detail. In future work, though, we hope confirm relations of this type.
We have identified an energy scale below which the eigenvalue correlations of the QCD Dirac operator are given by the chiral random matrix ensembles. In analogy with the theory of mesoscopic systems, this scale will be called the Thouless energy. For eigenvalues near zero the volume dependence of the Thouless energy is weak but its numerical value is of the same order as estimates from the pion Compton wavelength. For eigenvalues in the bulk of the spectrum the Thouless energy scales roughly with the square root of the volume which is in agreement with results from the theory of mesoscopic systems. However, we find a proportionality constant that is larger than given by our simple estimates.
For energy scales beyond the Thouless energy a linear n-dependence of the number variance is found which, according to the work by Altshuler and Shklovskii, corresponds to a critical system. We have shown that the corresponding Dirac eigenfunctions show a multifractal behavior. However, our multicritical exponents are not in agreement with relations derived for a critical system. Obviously, our ensemble of instantons is below critical. One way to increase the criticality of the system is to increase the number of flavors. However, at Nf≠0 simulations for the large volumes that are required for the extraction of the multifractality index became to costly. Alternatively, one expects that pion loops become important at energy scales beyond the Thouless energy, and that results from chiral perturbation theory apply to this region. Due to large finite size effects we were unable to make a detailed comparison. However, the spectral density near zero in the quenched approximation is consistent with a logarithmic dependence predicted by quenched chiral perturbation theory.
Acknowledgements We wish to thank A. Smilga for encouraging us to study localization properties for a liquid of instantons and Y. Fyodorov for his suggestion that the transition point in our results is related to the Thouless energy. During the completion of this work we received a preprint by R. Janik, M. Nowak, G. Papp and I. Zahed in which similar questions are discussed.
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[33] D.I. Diakonov and V.Yu. Petrov, Sov. Phys. JETP 62 (1985) 204.
[34] D.I. Diakonov and V.Yu. Petrov, Nucl. Phys. B 272 (1986) 457.
[35] D.I. Diakonov and V.Yu. Petrov, Leningrad preprint LNPI-1153 (1986).
[36] E.V. Shuryak and J.J.M. Verbaarschot, Nucl. Phys. B410 (1993) 55.
[37] T. Schäfer and E.V. Shuryak, hep-ph/9610451, Rev. Mod. Phys. (1998) (in press).
[38] J. Verbaarschot and I. Zahed, Phys. Rev. Lett. 70, 3852 (1993).
[39] G. Akemann, P. Damgaard, U. Magnea and S. Nishigaki, Nucl. Phys. B 487[FS] (1997) 721.
[40] E. Brézin, S. Hikami and A. Zee, Nucl. Phys. B464 (1996) 411.
[41] T. Guhr and T. Wettig, Nucl. Phys. B506, 589 (1997).
[42] A.D. Jackson, M.K. Sener and J.J.M. Verbaarschot, Nucl. Phys. B479, 707 (1996); Nucl. Phys. B506, 612 (1997).
[43] P.H. Damgaard, hep-th/9711047; P.H. Damgaard and S.M. Nishigaki, hep-th/9711023; S.M. Nishigaki, P.H. Damgaard and T. Wettig, hep-th/9803007; T. Wilke, T. Guhr and T. Wettig, hep-th/9711057; M.K. Sener and J.J.M. Verbaarschot, hep-th/9801042.
[44] T. Guhr, private communication.
[45] K. Jansen and C. Liu, Nucl. Phys. Proc. Suppl. 53 (1997) 974.
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[54] F. Karsch and E. Laermann, Phys. Rev. D50 (1994) 6954.


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Do three sets: Set #1: 3 reps; Set #2: 2 reps, Set #3: 1 rep.


text:
Cahokia is de locatie van een oude Indiaanse stad van de Mississippicultuur die van ongeveer 650 tot 1400 bestond. De stad lag aan de Mississippi, nabij het huidige Collinsville en was in zijn periode de grootste stad ten noorden van de Rio Grande.

Het oppervlak van Cahokia besloeg 8,9 km². Hierop waren 120 kunstmatige aarden heuvels (mounds) door 'moundbuilders' aangelegd, waarvan er nog tachtig behouden zijn. De grootste heuvel is Monks Mound, bestaande uit vier verdiepingen en groter dan de Grote Piramide van Gizeh. Monks Mound is met een oppervlakte van 5 ha en een hoogte van 30 m de grootste prehistorische aarden heuvel op het Noord-Amerikaanse continent.

Cahokia Mounds is een treffend voorbeeld van een complexe chiefdom-samenleving met veel grafheuvel-centra en tal van afgelegen gehuchten en dorpen. Op haar hoogtepunt tussen 1050 en 1150 telde deze agrarische samenleving waarschijnlijk 10.000-20.000 bewoners

Cahokia staat op de Werelderfgoedlijst en is aangemerkt als een National Historic Landmark.

Literatuur
William R. Iseminger, Cahokia Mounds. America's First City, 2010. ISBN 1596297344

Externe link
Website Cahokia Mounds

Archeologische plaats in de Verenigde Staten
Geschiedenis van Illinois
Museum in Illinois
Noord-Amerikaanse oudheid
Werelderfgoed in de Verenigde Staten
National Historic Landmark
Staatspark in de Verenigde Staten
Indianen van het Noordoosten
Postklassieke periode

redpajama_set_name: RedPajamaWikipedia


Aurelie Muller of France became the first female open water swimmer to qualify for the 2016 Olympic Games winning the 10km event at the Kazan 2015 FINA World Championships in 1:58.04.3. Muller claims the first gold medal for France in open water swimming. France had previously won three silver medals and three bronze medals in open water events including Muller's silver medal in 2011 at the Shanghai Worlds. She finished 2.4 seconds ahead of her training partner Sharon Van Rouwendaal of The Netherlands under brilliant weather conditions and a pleasant air temperature of 26 degrees at the start of the race.Muller had a run of bad luck having missed qualification for the 2012 London Olympics. The French swimmer was disqualified at the finish line from the 10km in Roberval in 2010. She recalls a poor 1500m freestyle result because her goggles filled with water, failing to qualify for the 2011 Shanghai World Championships. In the 23 degree placid water of the Kazanka River her luck changed for the better. Pacing herself with an easy 30.33.9 first lap she stayed relaxed in the pack of swimmers, passing the 2.5km mark tied for 19th position. In her second of four laps she found herself leading her 54 challengers from 34 countries.
Muller's time at the 5km was 1:00.21.3, almost two seconds ahead of Hungary's Eva Risztov. The Magyar would stay with Muller for another lap but fell off the pace to finish 32.1 seconds behind the French swimmer. The Hungarian finished in 10th place and qualified for the Olympic Games. Muller kept up her pace leading by about two seconds over Italy's Rachele Bruni at the 7.5km mark. Bruni has won three 10km races this year but she fell off the pace, finishing 4th and is still without a world championship medal. A consolation is her qualification for the Olympic Games.
Today's silver medalist Rouwendaal won gold in 10km at the 2014 European Championships and earned a bronze medal in the 800m in Shanghai in 2011. She is the second woman to win medals in swimming and open water swimming following the USA's Haley Lewis who won five swimming and one open water medals between 1991 and 2001. She can give Netherlands a third gold medal in this event at the world championships, equalling Russia and Germany on most gold. Her programme in the pool starts on Sunday with the 400m freestyle and also includes the 800m and 1500m freestyle events.
Capturing the bronze medal a distant 22.2 seconds behind the two European swimmers was Ana Marcela Cunha (BRA) in a time of 1:15.26.5. She was the silver medallist in the 2013 edition in Barcelona. Her teammate Poliana Okimoto finished in sixth place to qualify for the home Olympic Games to be held in Rio de Janeiro next year. Swimmers who finished in the top 10 places in today's race are the first qualifiers for next year's Olympic Marathon. Brazil was the only nation to qualify two athletes. As the host nation they would have been automatically eligible for one swimmer, but any nation placing two in the top 10 would qualify both athletes.
Yesterday's Allan do Carmo from Brazil also qualified for his home Olympic Games joining Cunha and Okimoto who each qualified today. Also in the men's race, two Italian swimmers (Simone Ruffini and Federico Vanelli) punched their tickets to Rio and will be joined by today's 4th place finisher Bruni. The USA's Haley Anderson finished 9th place today and will be joined by the men's 10km champion Jordan Wilimovsky and 4th place finisher Sean Ryan. Only Brazil, Italy and the USA have qualified in Kazan three swimmers for the 2016 Olympic Marathon.
Aurelie Muller (FRA, gold): "I am very happy with the gold medal and I am also happy for Sharon and Ana Marcela. It was a crazy race today. I took the lead so I would not encounter any fighting".
"This is my first world championships but it is very well organised. Sharon and I train together but I never beat her in training. Sharon also swims events in the pool but I don't, just open water races".
Sharon Van Rouwendaal (NED, silver): "I'm very happy that I qualified for the Olympic Games because it was my goal to finish in the top 10. I saw that we were just three at the end and I thought maybe I could win a medal".
"My programme in the pool begins on Sunday with the 400m freestyle. I will also swim the 800m and 1500m freestyle events".
"I swam the 5km on Saturday and had two days rest. I thought I recovered very well but my legs did not feel very fresh so maybe if I didn't swim the 5km… but we won't know that. In the 5km my strategy was to swim in the front because I didn't want to get hit. In the last 500m of the 5km I thought I would be ok to make a move to the front but my legs were not there and I arrived in 4th place. For the 10km my coach and I had a different strategy where I would save my energy for a strong finish and today's plan worked".
Ana Marcela Cunha (BRA, bronze): "I am very satisfied, not because I won a bronze medal but because I finished in the top 10 and have qualified for the Olympics. It was a crazy race, I was in 6th or 7th and I am not sure who I passed on the way to the finish. I'm pleased because I have been training for seven years for this moment. Four years ago, I finished 11th in Shanghai and I narrowly missed the qualification for the London Olympics".


text:
hong kong sar workforce encouraged to seek professional career advice to stay competitive: randstad workmonitor.
related press releases.
randstad delivers solid and competitive performance in an exceptional 2020.
randstad risesmart continues to drive expansion and growth across asia pacific, the middle east and africa with key leadership appointments.
randstad hong kong wins best recruitment agency the APAC business award 2020.
randstad hong kong wins the premium service agency award at the CTgoodjobs best HR awards 2020.
nikki gao recognised in topHR's 'top women entrepreneurs in human resource industry 2020' list.
Many employees may have planned their careers perfectly, but it is very likely that they would seek specialists' professional career advice intermittently.
According to the latest Randstad WorkMonitor, nearly half of employees around the world (46%) say that they need professional career advice from a specialist. This sentiment spiked in Singapore, Hong Kong SAR and Malaysia, as seven in 10 employees (71%) reach out to specialists for career advice. Across all three markets, employees in Hong Kong SAR are the least likely to seek professional advice but is well above global average.
Natellie Sun, Managing Director for Randstad Hong Kong SAR said, "Human resource specialists have first-hand insights such as market demands, salary benchmarks and remuneration packages. We encourage job seekers in Hong Kong SAR to reach out to specialists for industry insights and expert advice to better prepare them for their next career move or simply to find out what it would take for them to remain competitive in the workforce."
Among the three markets, Hong Kong SAR employees are the least likely to seek career advice from a specialist, with only 58% stating so. Younger employees however are more likely to seek specialist for advice to achieve their career goals.
Among the three markets, employees in Singapore are the most eager to seek career advice from a specialist, with 83% of employees doing so. This is 37% more than the global average, indicating a highly competitive workforce.
72% of employees in Malaysia stated that they needed specialist career advice. Employees held a similar demographic split with Singapore, as males and younger employees are more likely to reach out to specialists for career advice.
"I need career advice from a specialist (%)"
91% of hong kong sar employees feel obligated to upgrade skillsets to remain competitive.
employees realizing their full potential in singapore, hong kong sar and malaysia.
the Randstad Workmonitor
The Randstad Workmonitor was launched in the Netherlands in 2003 and now covers 34 markets around the world, encompassing Asia Pacific, Europe and the Americas. The Randstad Workmonitor is published four times a year, making both local and global trends in mobility regularly visible over time. The Workmonitor Mobility Index, which tracks employee confidence and captures expectations surrounding the likelihood of changing employers within a six month time frame, provides a comprehensive understanding of job market sentiments and employee trends. In addition to measuring mobility, it provides insights into employee satisfaction and personal motivation, as well as explores sentiments around key trends shaping the world of work for employees each quarter. The quantitative study is conducted via an online questionnaire among a population aged 18-65, working a minimum of 24 hours a week in a paid job (not self-employed). The minimal sample size is 400 interviews per market, using Survey Sampling International.
Randstad is a global leader in the HR services industry, with Asia-Pacific operations in Singapore, Malaysia, Hong Kong SAR, China, Australia and New Zealand. Our offices in Southeast Asia have been supporting people and organisations in realising their true potential, helping find the best permanent and contracting talent in accounting & finance, banking & financial services, construction, property & engineering, corporate & secretarial support, human resources, information technology, legal, life science, sales, marketing & communications and supply chain & procurement.
Human connection is at the heart of our business. Our personal approach, supported by state-of-the-art technology, is what sets us apart in the world of work. We express this with a new brand promise: Human Forward.
Hear what our leaders have to say about #HumanForward or head over to our new website and learn more about our Human Forward brand promise.
Rena Tan, Regional Marketing and Communications Director
E: rena.tan@randstad.com.sg | t: +65 9464 2798
Alistar Lien, Senior PR & Communications SpecialistE: alistar.lien@randstad.com | t: +65 9711 8665

redpajama_set_name: RedPajamaCommonCrawl


text:
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The SENs: Friday 22nd August 2014
We're now opening up bookings for Senscot's 10th SE Conference and Ceilidh on 13th/14th November at the Westerwood Hotel, Cumbernauld. This event has become a fixture in our SE calendar and has very much been for front-line social enterprises and SEN members. This year, we will be looking to reflect on the progress made over the last 10 years and the challenges that lie ahead. We're aiming to make it as informative and interactive as possible – giving attendees plenty opportunities to contribute and participate in discussions. The intention is to ensure that as many active SEN members as possible are able to attend. If you would like a booking form, contact ceilidh@senscot.net. This week, Scottish Govt published the list of organisations successful in securing awards from the £6m Enterprise Ready Fund. We're delighted to see so many SEN members being successful – with 51 of the 115 awardees being engaged with SENs. The Enterprise Ready Fund is helping organisations to develop, become more efficient and self-sustaining and/or diversifying into new markets. Priority was given to activities that contribute towards the Scottish Govt's Prevention and Welfare Reform agendas. The fund is being delivered by a consortium of third sector organisations led by Foundation Scotland in partnership with Community Enterprise in Scotland (CEiS), Developing Strathclyde Ltd (DSL) and Social Value Lab, more details. Glasgow SEN members, Glasgow Wood Recycling and Impact Arts have been in the news this week. Glasgow Wood Recycling has secured around £400k from the BIG Lottery Fund – to launch its "Making Wood Work" initiative – a training and employment project providing opportunities for 144 people. This is the first of its kind in Scotland. Impact Arts' Craft Café project which helps older people connect through arts and craft also featured on STVs Riverside Show. SCVO has opened a new European funded grants programme aimed at supporting growth across the third sector – with a particular focus on this active in the digital, creative and green industries. The £2 million project will enable the third sector to take on 400 interns over the next 12 months (120 in the digital field). To find out more, email interns@scvo.org.uk. Senscot and ABSEN are working in partnership to pilot a Cultural & Creative Group in Argyll & Bute. This follows on from the ABSEN Conference in March, when members expressed interest in working more closely with the thematic SENs to address specific sector needs. The development of the Argyll & Bute Cultural Assembly, Place Partnership funding from Creative Scotland and the Collaborative Communities programme through Highlands and Islands Enterprise all mean that opportunities for cultural and creative social enterprise in Argyll and Bute are opening up. A meeting is to be held in Oban on 22nd Sept. If you are interested in attending, either in person or by conference call, please contact Sarah. Just Enterprise is now accepting bookings for a range of leadership development programmes designed specifically to support individuals working in the enterprising third sector. Delivered by the Social Enterprise Academy, these leadership programmes will support people working across the sector, with opportunities for individuals at the start-up stage through to senior managers working in established third sector organisations. See more.Four new social enterprises are benefitting from Firstport's latest round of 'Build It' awards ranging from £10,000 to £25,000. More details. Notices TENDERS: King George V Skate Park – West Lothian Council, Volunteer-Led Generalist Advice Services – Stirling Council, Zero Waste Scotland Website Development Projects and Invitation to Tender for Micro Hydro Feasibility Studies in Argyll – Colintraive and Glendaruel Development Trust. Join the Ready for Business Linked-In group and follow on Twitter. EVENT: Alongside its AGM, Social Firms Scotland is hosting a free and informal networking event with drinks and nibbles courtesy of the bread maker on 17th September. HUB: Looking for a venue? Forth Sector's Enterprise and Employability hub at Duddingston Yards provides a flexible environment to deliver training and workshops, conduct seminars, conferences and meetings. DEBATE: There is a debate being held on 1st Oct, Glasgow by DTAS and The Glass-house. The "Does practice make perfect in place?" debate is free but requires registration. BIKES: The NZ Commonwealth team bikes that were donated to The Glasgow Bike Shed are now on sale on the shop floor and on EBay. AWARDS: The Social Enterprise Academy announced that Registration for the 2014/15 Social Enterprise in Education Awards is now open. FESTIVAL: Findhorn Bay Arts Festival is Scotland's newest arts festival: a spectacular celebration of arts and culture taking place at the heart of Moray between 24 and 28 September, showcasing artists of national and international renown. Dates for the Diary
Falkirk SEN, 27th AugustFife SEN AGM, 3rd SeptemberWest Lothian SEN, 7th SeptemberSocial In The Square, 12th SeptemberArgyll & Bute SEN Cultural Meeting, 22nd SeptemberFalkirk SEN, 25th SeptemberMoray SEN / Glasgow SEN, 1st OctoberSport SEN North, 3rd OctoberEast Lothian SEN, 9th OctoberSport SEN West, 22nd OctoberFalkirk SEN, 31st OctoberSocial Enterprise Conference & Ceilidh, 13th NovemberSouth Ayrshire SEN Conference, 21st November Best wishes, Kimkim@senscot.net
G2 1EG
mail@senscot.net
EH3 7HX
Happy New Year and all the best for 2020!
That's a wrap for 2019 have a fab festive period and we'll see you all in 2020! pic.twitte…
This week's bulletin out now. Headlines include: *Private schools will lose charitable status *Right to Food in…
Great opportunity https://t.co/4npqdBg5t7
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Social Entrepreneurs Network Scotland (Senscot) is registered as a Scottish charity under Scottish Charity No. SC029210 and as a limited company under Company Registration No. SC278156. It's registered office is at 21 Walker Street, Edinburgh, EH3 7HX.


Freddy joined us as a youngster and was originialy from the Shetland Isles. He was entire and very cheeky and difficult to handle. Since being gelded and handled more he is turning into a nice riding pony.
Freddy will continue to be ridden and will hopefully progress with his canter work. We hope that Freddy will learn to pull his cart, and eventually have someone in it. He will also continue with his in hand showing which he is very successful at. We also hope to be able to take him into schools with Mini and Tiffany to educate young children about ponies.


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Arthur Conan Doyle Fills Out the Questionnaire Made Famous By Marcel Proust (1899)
in Literature | March 1st, 2013 Leave a Comment
Note: click on the image for a larger version
Ah, the Proust Questionnaire: does it reveal everything about one's personality, or nothing at all? Presumably Marcel Proust, who gave the questionnaire its name by filling it out so wholeheartedly, wouldn't have cared either way. French interviewer Bernard Pivot must have seen some usefulness in it, since he applied its questions so regularly to guests on his literary television program Apostrophes that it gained the second name of "Pivot Questionnaire." Open Culture readers know James Lipton also adapted a version on Inside the Actors Studio. (See our previous post here.) And now, thanks to archivists at the University of Texas at Austin's Harry Ransom Center, we have Proust Questionnaire answers from one more luminary: Sir Arthur Conan Doyle, creator of Sherlock Holmes.
Not that Conan Doyle responds with quite so much style as does Proust. His favorite qualities in a man? Manliness. In a woman? Why, womanliness. His favorite food and drink? Anything when hungry or thirsty — nothing when not. Favorite activity? Work. This all has a certain utilitarian charm, but if you read the questionnaire itself, you also find the particular flavor of half-hidden wit that Conan Doyle's readers would expect. But we care about his responses, as we care about Proust's, because of all the other words they wrote. And lest we get caught up in questionnaires, let us not forget that Swann's Way, the first volume of Proust's In Search of Lost Time, turns one hundred this year.
via Slate
Famous Actors & Actresses Answer Revealing Questions on Inside the Actors Studio: A Compilation
Arthur Conan Doyle Discusses Sherlock Holmes and Psychics in a Rare Filmed Interview (1927)
Arthur Conan Doyle & The Cottingley Fairies: How Two Young Girls Fooled Sherlock Holmes' Creator
Colin Marshall hosts and produces Notebook on Cities and Culture and writes essays on literature, film, cities, Asia, and aesthetics. He's at work on a book about Los Angeles, A Los Angeles Primer. Follow him on Twitter at @colinmarshall.


These pads work great under heavier machines. The Typhoon Resin Floor pads are 10mm with a beveled edge to easily go over joints.
Click the button below to add the 3" Typhoon Resin Floor Pad 10mm to your wish list.


It's not by chance that Jesus utilized the intimacy of the small group setting to raise up His disciples. Most of what must be accomplished in the believers life, is best accomplished in the small group setting. In fact, it would be safe to say that unless you are connected to a small group of believers that you meet with regularly, you are probably not experiencing all that the Lord would have for you in your walk of faith as His disciple. If you would like to connect with other believers and be a part of a small group or would just like additional information about our groups, please use the "Join a Core Group" button below. We'll contact you, answer any questions that you have and connect you with a healthy small group. We look forward to hearing from you.


US Special Forces Fighting Alongside the SDF during the Raqqa offensive, Wearing YPG/YPJ Patches 4.6 out of 5 based on 5 ratings. 5 user reviews.
Recently, the Syrian Democratic Forces (SDF), supported by the US-led coalition, liberated a number of villages from ISIS in Northern Raqqa. Al-Fatsah, Bir Sadr, Bin Hammud, Abu Kabra and Matmasraja are among them.
Initially, there have been reports that some "American fighters", apparently US special operation forces, are among SDF ranks in order to coordinate the military operation.
However, the recent reports confirm that US special operation forces are participating in the clashes against the ISIS terrorist groups, de-facto, spearheading the Kurdish forces. They wear YPG/YPJ patches, in an alleged attempt to hide the fact of their presense. However, these guys hardly look as Kurds.
Is it even legal for the US to deploy special forces in that area?
The only force deployed in Syria by an official request is the Russian military grouping. Even Iranian troops operate at an "unofficial" level.
Except for Hezbollah, which Assad has said is welcome. He also gave Lebanon's and Syria's and Iraq's different Hezbollah groups permission to keep whatever they take on the battle fields of Syria. Even if it is equipment that use to belong to the Syrian army. If ISIS took it, then it is payment for liberating that equipment from ISIS.
Syria has officially allowed Iranian trainers. But as for combat roles, you are correct.
Though I suspect that Syria has been close to inviting Iran in, and Iran has been close to rushing in another 1,000 volunteers.
Look at those US troops proudly displaying the Communist-Red-Star on their shoulders.
I always knew they were a bunch of Communist-Zionist-bigots.
Russia or Iran or Syria should bomb these invading Imperial solders till they are all nullified. They are conquering planet earth, one ethnic group at a time. Like old Babylon use to do to everybody.


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ADRA's Keep Girls Safe program helps girls stay in school and out of human trafficking.
Over 200 girls, from ages 8 to 19, can now enjoy just being kids!
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Life can be difficult and dangerous for young girls living in the hills of northern Thailand. Due to the lack of awareness, language challenges, and poverty, these ethnic minorities are vulnerable to human trafficking. ADRA Thailand uses unique ways to address core issues, including the operation of a shelter for vulnerable girls called Keep Girls Safe.
The Keep Girls Safe program was established by ADRA Thailand in 2004 as a result of the human trafficking dilemma which many marginalized, ethnic minorities face. Young girls have found security and well-being through ADRA's Keep Girls Safe program. They have found an opportunity to be a kid, get an education, and when age appropriate, enter a fair work program for a brighter future.


Linus Galleries, a Los Angeles contemporary art gallery, presents The Artist Interview Series. Our Linus artists are from all over the world and come from a variety of different practices and backgrounds. Read on to gain insight into the creative process and personality of our featured artist. This week we feature Len Upin who recently exhibited two of his incredibly detailed ink drawings in our Vulnerability vs. Strength show.
I'm Len Upin and live in a suburb Northwest of Chicago, Illinois. For the past eight years I have been drawing large portraits with pen and ink.
I earned a BFA degree in Art Education from the University of Illinois and a MA degree in painting from Northern Illinois University.
I've always been interested in the human face. When I grew up there was always artwork, mainly portraits, in my parents home. My father was a very creative, self-taught person and my older brother, is a formally trained painter. Both of them choose to create portraits. There were also two walls filled with photos of generations of our family members. Portraiture was a 'no brainer' for me. It is just another extension of my make-up.
I work from photos and an opaque projector to enlarge my large images. I concentrate on the humorous and dramatic elements of the expressions. I crop the portraits showing extreme close-up views. The images cropped and oversized images is a powerful combination.
5) Do you have any secret party tricks or talents unrelated to your art making?
I am a "Big-Time" gardener along with my wife. We have six different flower areas and two vegetable gardens on all four sides around our house. It can be a full time, around-the-calendar hobby. I draw mostly in the winter and on rainy days. When I start commissioned portraits, that becomes a priority.
6) Tell us about your 'aha' moment, or any kind of artistic breakthrough or evolution you experienced?
I had a stroke in 2003. My aphasia disability forced me to take an early retirement as a teacher. For a few years I worked with a number of speech therapists to help me regain my art of language. At the same time, I enrolled in a local junior college and private art studios to keep my art skills fresh. My "Aha" moment happened when I was looking in the mirror playing around with a self-portrait. I started on a loose, continuous line contour and continued to fill in the fields of values using random scribble marks. The drawing was loose, fresh and well – therapeutic.
Over the years, I taught, mentored, coached, advised and parented more then 2500 budding artists. Most of my students just took my classes for fun, a break out of their academic schedule. However, many others were planning or realized they may be able to go beyond their young aesthetic experiences. I told them they need a solid academic training about the 'classics'. At the same time, I pushed them to create new ideas and new experiences. Variety is important, yes, but continuity of individual styles and statement are key.


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Q: How is "<" in HTML handled by browsers? In the following snippet, < gets rendered as expected in Firefox 37.0.2 and I have seen the same in many other modern browsers as well.  Is this textarea specification valid HTML5? Ideally shouldn't it be &amplt; by escaping the "<"
<html>
<textarea>
Hello World <
</textarea>
</html>

How does the HTML parsers distinguish between a Tag Open and "<"? Most browsers do a lot to handle errors automatically by guessing, is this one such case?
The reason I am interested in this is because when we use WYSIWYG editors in Web Apps - we save the HTML from the editors source mostly. When we Template it back for the frontend, this behaviour makes it is not mandatory to HTML Quote stuff from the backend. It works without HTML Quoting but it can cause undesired effects like freezing / infinite loop's atleast with the TinyMCE Editor's 3.5.8 version.

A: This is indeed just guessing. The proper way to use literal < in HTML is to use < (and > for >).
That said, textarea is a bit specific in that it can never contain any other HTML elements - so the parser can be sure you meant literal < and not a starting tag. Of course, it breaks down for </textarea> :)
From HTML 4 specification:
Section 5.3.2:

Authors wishing to put the "<" character in text should use "<" (ASCII decimal 60) to avoid possible confusion with the beginning of a tag (start tag open delimiter). Similarly, authors should use ">" (ASCII decimal 62) in text instead of ">" to avoid problems with older user agents that incorrectly perceive this as the end of a tag (tag close delimiter) when it appears in quoted attribute values.

So it's not necessary for HTML 4, but it's still good practice. And of course, XHTML and / or HTML 5 may be a bit more strict.
HTML specification is actually quite non-specific in a lot of things, which goes a long way to ensuring the browsers are incompatible with each other in (more or less) subtle ways. Your best bet is not to rely on all the things HTML allows, but only on those that are very explicit and specific. The reason is quite simple - two browsers can be 100% fully compliant with the HTML specification, and still process the same HTML in ways that make it completely useless.

A: It is hard to say without insight in the actual code, but common HTML parsers try to find the closing tag when an opening tag is encountered.
All characters that to not resemble to an element are printed as if they were escaped if you are lucky! This is certainly true for elements that only allow text, like the <textarea> in your sample.
This is not valid HTML and should be avoided obviously.

A: The Mozilla HTML parser will ignore any any 'less than' angle bracket not immediately succeeded by a valid tag type.
Any white space character (space, tab, newline etc.) renders the bracket 'not a tag'.
Also anything inside a textarea can only ever be text.

A: Whatever the validity, the HTML5 spec defines the precise parsing rules completely.
When the tree construction rules encounter a <textarea> tag, the tokeniser gets switched into the RCDATA state
In that state, if the tokeniser encounters a < character it switches to the RCDATA less-than sign state
In that state, unless the next character is a /, it treats the < simply as a < and continues. Otherwise, the tokeniser switches to the RCDATA end tag open state
And so on, with the objective of allowing the parser to detect the </textarea> tag, but passing everything else through as text.
There is no "guessing" involved, and all modern browsers, including IE since IE10 follow these rules.

redpajama_set_name: RedPajamaStackExchange


For other uses, see Order of Friendship (disambiguation).
The Order of Friendship is awarded to Russian and foreign nationals for special merit in strengthening peace, friendship, cooperation and understanding between nations, for fruitful work on the convergence and mutual enrichment of cultures of nations and peoples; for the active conservation, development and promotion of the cultural and historical heritage of Russia; for great contribution to the implementation of joint ventures with the Russian Federation, major economic projects and attracting investments into the economy of the Russian Federation; for broad charitable activities.
The badge of the Order of Friendship is made of gilded silver and enamels. It is a pentagonal star created from diverging golden rays. On the obverse at the center of the star is a terrestrial globe, with the oceans covered in blue enamel. The globe is surrounded by a green enamelled wreath of olive branches. On the reverse is the inscription "Peace and Friendship" (Russian: "Мир и дружба") and the etched serial number of the individual award. The distance between opposite tips of the star is 44 mm.
The badge of the order is connected by a ring through the suspension loop to a standard Russian pentagonal mount covered with an overlapping 24 mm wide green silk moiré ribbon with 6 mm wide light blue stripes along its edges. When worn in the presence of other Orders and medals of the Russian Federation, the Order of Friendship is located immediately after the Order of Honour.
^ a b c d "Decree of the President of the Russian Federation of 2 March 1994 No. 442" (in Russian). Commission under the President of the Russian Federation on state awards. 15 December 1999. Archived from the original on 18 February 2001. Retrieved 11 February 2012.
^ "Decree of the President of the Russian Federation of 6 January 1991 No. 19" (in Russian). Commission under the President of the Russian Federation on state awards. 15 December 1999. Archived from the original on 18 February 2001. Retrieved 11 February 2012.
^ "Decree of the President of the Russian Federation of 7 September 2010 No. 1099" (in Russian). Russian Gazette. 7 September 2010. Retrieved 7 February 2012.
^ "Decree of the President of the Russian Federation of 16 December 2011 No 1631" (in Russian). Russian Gazette. 16 December 2011. Archived from the original on 31 March 2013. Retrieved 7 February 2012.
^ a b "Decree of the President of the Russian Federation of 16 March 2012 No. 308" (in Russian). Consultants, legal library of Russia. 16 March 2012. Retrieved 11 May 2012.
^ "Decree of the President of the Russian Federation of 12 April 2012 No. 433" (in Russian). Russian Presidential Executive Office. 12 April 2012. Archived from the original on 5 August 2013. Retrieved 19 April 2012.
^ "Compiled from the site of the President of the Russian Federation" (in Russian). Kremlin News. Retrieved 7 February 2012.
^ "PM receives Russia's highest award". The Star. 6 August 2003.
^ a b "Медведева, Загитова, Большунов, Спицов удостоены Ордена Дружбы" (in Russian). sports.ru. 28 February 2018.
^ a b c d Vladislav Dunaev (19 April 2001). Консульство в Сан-Франциско чествует исследователей - Энтузиасты Русской Америки получают ордена Дружбы [Consulate in San Francisco celebrates researchers - Enthusiasts of Russian America to receive the Order of Friendship] (in Russian). Nezavisimaya Gazeta. Archived from the original on 14 January 2005. Retrieved 12 March 2010.
^ Berthiaume, Lee (5 March 2014). "From Russia with Love: Chretien gets friendship award from Moscow". o.canada.com.
^ "Meeting with Patriarch Ignatius IV of Antioch and All The East". Eng.news.kremlin.ru. 11 May 2010. Retrieved 18 January 2016.
^ Wroe, Nicholas (16 July 2010). "Victor Hochhauser: 'My great stroke of luck came when Stalin died'". Retrieved 24 March 2019 – via www.theguardian.com.
^ "Jayakanthan awarded Order of Friendship award".
^ "Jayakanthan awarded Order of Friendship".
^ Hoe, Yeen Nie (16 November 2009). "Russia, S'pore move towards closer ties with new governmental body". Channel NewsAsia. Archived from the original on 6 December 2012. Retrieved 12 March 2010.
^ "Former Vatican Ambassador to Russia is decorated with Order of Friendship". interfax-religion.com. 18 February 2010.
^ Adam Sweeting (16 March 2011). "Riccardo Muti: a profile". The Telegraph. Retrieved 23 April 2011.
^ "God Nisanov WJC Vice-President". World Jewish Congress. Archived from the original on 9 February 2015. Retrieved 9 February 2015.
^ "Russia honours BrahMos chief with 'Order of Friendship' award". Business-standard.com. Press Trust of India. 26 February 2014. Retrieved 18 January 2016.
^ "Указ Президента Российской Федерации от 29.01.2016 г. № 29" (in Russian). kremlin.ru. 29 January 2016.
^ Указ Президента Российской Федерации от 22.09.2015 г. № 469 - О награждении государственными наградами Российской Федерации иностранных граждан [Presidential Decree of 22.09.2015, the № 469 - On conferring state awards of the Russian Federation on foreign citizens] (in Russian). Kremlin.ru. 22 September 2015. Retrieved 18 January 2016.
^ "Putin awards Indian director NPP "Kudankulam" Order of Friendship". Russia Beyond The Headlines. 29 January 2016. Retrieved 29 January 2016.
^ "Dr Rowan Williams is honoured for work on Russia". BBC. 12 March 2010. Retrieved 12 March 2010.
^ "Vladimir Putin Awards Rescuers in Latok I Epic". Gripped Magazine. 2018-09-05. Retrieved 2019-01-19.
^ a b c "Vladimir Putin Awards Rescuers in Latok I Epic". Gripped Magazine. 2018-09-05. Retrieved 2019-03-07.
Wikimedia Commons has media related to Order of Friendship (Russia).


text:
Reforms please Cubans, but is it communism?
Cuba's President Raul Castro, left, and Culture Minister Abel Prieto at the 7th Congress of Cuban Artists and Writers in Havana on Tuesday.Ismael Francisco / AP
April 3, 2008, 12:25 AM UTC / Source: The Associated Press
It's not the stuff of Lenin or Marx, or even of Fidel Castro, but it's hardly free-market capitalism, either. In fact, steps to encourage a Cuban spending spree may help the communist system and its new president survive.
In rapid-fire decrees over the past week, Raul Castro's government has done away with some despised restrictions, lifting bans on electric appliances, microwaves and computers, inviting average citizens to enter long-forbidden resorts and declaring they can even legally have their own cell phones.
More could be on the way. Rumors are rampant the government could ease travel restrictions and tolerate free enterprise that would let more people start their own small businesses. And hopes that it will tweak the dual-currency system that puts foreign products out of reach for most Cubans have sparked a run on the peso.
"We're going to get out and buy more and more," said retiree Roberto Avila. "That's the future in Cuba, and it is a strong future."
Cuba is still far from a buyers' paradise. Nearly everyone holds government jobs, earning an average of $19.50 a month, though many get dollars from tourism jobs or relatives abroad. It would take the average Cuban five months to earn enough to buy a low-end DVD player that an American could buy with five hours of minimum-wage work.
By doing away with rules ordinary Cubans hate, Raul Castro may defuse clamor for deeper economic and political change in the single-party communist system.
On the other hand, the small changes could just whet Cubans' appetites for more.
"These measures to allow Cubans to buy DVDs and everything else are just to entertain the people," said Maite Moll, a 45-year-old state engineer. "It's not really important because it resolves nothing."
'People are better'
Some Cubans worry that even the small measures already taken will create class tensions and increase resentment between those earning state salaries and those with access to dollars, given the new opportunities for conspicuous consumption. Raul Castro is clearly hoping that greater buying power will distract from any friction.
Certainly, the 76-year-old president has bolstered his popularity, addressing for now the doubts that Cuba's government can survive without his charismatic brother Fidel.
"If low-income groups have access to essential goods like food, clothing and construction materials, and can sell and buy homes and use them as collateral, it doesn't matter if you have a significant income gap. People are better," said Carmelo Mesa-Lago, a Cuba economics expert at the University of Pittsburgh. "That's what happened in China and Vietnam."
The new president is said to be an admirer of free-market reforms that allowed those countries to revolutionize their economies while maintaining single-party communist political control, though top officials have said Cuba isn't about to follow a Chinese or Vietnamese path.
Loaning state land to farmers
The food part of the equation could be profoundly affected by another initiative promoted this week. The government is lending uncultivated state-controlled land to private farmers and cooperatives to plant cash crops such as coffee and tobacco, while paying producers more for basics such as milk, meat and potatoes.
Over time, this could reduce chronic food shortages and change the face of Cuban farming.
It's not new for the government to let private farmers take a crack at putting state land to good use. But this time the government is letting farmers more easily buy equipment and supplies at government stores, removing a key impediment to their success.
The changes implemented barely a month into Raul's presidency are all measures Fidel bitterly opposed for decades, publicly declaring that even the smallest initiatives to increase economic and social freedoms could create a Cuban "new rich" and destroy the island's hard-fought social and economic equality.
A disconnect
Raul has pledged to consult his brother on all major decisions, but if the elder Castro doesn't like what's going on, he has kept his views to himself. Recuperating from an undisclosed illness in a secret location, the 81-year-old Fidel has written essays every few days focusing on international issues, making no mention of daily life in Cuba.
The latest changes are a far cry from perestroika or glasnost — the political opening and economic restructuring of the Gorbachev era in the Soviet Union. But there are movements for greater freedoms among Cuban intellectuals as well.
Raul Castro presided this week over the Congress of the Union of Cuban Writers and Artists, hearing their call for more open debate about "mechanisms of control and institutional censorship."
"It seems clear that there is a disconnect between the cultural project of the revolution and the references that broad sectors of the people establish for themselves," said the group, an arm of the Communist Party which in the past has been used to enforce ideological discipline.
And that disconnect could lead to unrest if more changes don't quickly benefit the vast majority of Cubans. While people are excited to walk around stores and hotel lobbies, they will soon become frustrated that they can't afford to do more than look, said Juan Antonio Blanco, a Cuban academic based in Ontario, Canada.
"This government is totally myopic and shortsighted if it doesn't understand that it's sitting on dynamite," he said. "They have to do more than the things that will play in the international media."


text:
from django.utils.functional import SimpleLazyObject

from twitter import User

def twitter_userinfo(request):
    twitter_userinfo = getattr(request, 'twitter_userinfo', '')
    if not twitter_userinfo:
        return {}
    return {'twitter_userinfo': twitter_userinfo}

redpajama_set_name: RedPajamaGithub


text:
Category: omega
Replica vogue Omega Ref. 2383-4 30T2 and Tissot Research IDEA 2001 Astrolon
This week I'd like to bring something different for you, a wide collection of timepieces should be satisfied with various collect tastes. Firstly, there's an Omega replica equipped with 30T2 movement, along with a Zodiac powered by the venerable Valjoux 72. Slightly older than the rest are the Universal Geneve Tri-Compax and Lemania CH27 chronograph, both of which ought to give a deep impression for those who appreciate seldom-seen retailer signatures and impressive early timepieces alike. While for those who are more avant-garde, there's an innovative Tissot that paved the way for Swatch to announce more edition recently, along with a Movado which has a bracelet that still looks significantly modern. Let's go ahead with it, yeah?
Omega Ref. 2383-4 30T2
There's always something to be said for a marvelous time-only watch. Except for the packaging timepiece in its most basic form, it's a great way to evaluatea special brand's design chopsd. I might have mentioned this before, but I entirely believe that it's the truest test of a watchmaker's ability to tap into the exclusive club of icon status. There's simply less leniency for error when you distill something down basically.
Omega's history is chock full of time-only pieces, which are regarded to be some of the most significant time-only pieces in watchmaking history by any person. This can be accounted for by their extensive back catalog of aesthetically and mechanically genius calibers, the cal. 30T2 is one of them definitely. While browsing the inventory of a newly released dealer outfit, I met by chance an example of one of my favorite references which crafted the aforementioned movement, the Ref. 2383-4, along with such pretty luminous Arabic indices, pairing with syringe-style hands.
Since the condition of this model is top excellent, personally I thought it's so wonderful. Its case remains thick, all luminous applications are original, and while the dial has aged, it has achieved a pleasing warm tone, without any significant flaws. There's a line between patina and damage, and undoubtedly this dial falls into the camp of the former. If you have a pretty handle on the concept of restraint, this timepiece can be easy to become your only watch ever.
1971 Tissot Research IDEA 2001 Astron
Well, we've got rather an interesting chronograph, although it's a significant and innovative one. What you're looking at is one of the earlier mechanical replica watches to be cased in plastic, and the very first timepiece to feature a mechanical movement crafted out of plastic components. The IDEA 2001 Astron, one of the most futuristic pieces I've ever heard of, which was inspired by the Stanley Kubrick film probably and was announced just a few years ago. This example is in new-old-stock condition, which is always nice to see.
In 1971 Tissot announced this piece after quietly experimenting with new materials, and it would pave the way for Swatch's smash hit recently, the Sistem51. The Astron 2250 caliber was produced mainly out of plastic, which made it not only antimagnetic but also free from requiring lubrication. It was composed of just 52 parts, indicating that it would be the future of watchmaking at the time, considering the simpler production process.
Even if the IDEA 2001 Astrolon was not the success Tissot had hoped it would be, in my opinion, it indeed has made a huge impact on the future of watchmaking, since it broadened material horizons in an industry that remains today through its ways. It's not exactly rare to see the use of composite materials and plastics in high-end perfect fake watches at present, and probably we have no chance to see such glorious modern watchmaking without timepieces like this.
Posted in omega
Best Replica Omega Involved in the America's Cup Game with Two New Watches
Last time, we have talked about the special model replica watch of Pieria, and we all know that the replica Zenith is putting out for the 35th America's Cup in Bermuda. Now, Omega is getting into the game with two new limited edition timepieces in support of the Emirates Team New Zealand (ETNZ). This team may face the defending champions, Oracle Team USA, if ETNZ wins the qualifying rounds and then the semifinals.
To make progress, they'd have to beat Land Rover BAR (supported by Zenith) but with qualifiers barely underway, anything could break out. The field is wide open currently with other challengers still running which consist of Artemis Racing of Sweden, Groupama Team France, and SoftBank Team Japan. As ETNZ's special partner and official timekeeper, the replica Omega has created several watches for their own and is hoping to make a good showing in Bermuda.
According to the fake Omega, these timepieces were made with "the DNA of the Emirates Team New Zealand in mind." The unique edition Speedmaster innovated for the team could have been a big chance to do something really great, however, it has come out as sort of a Frankenstein.
With serious competition against Zenith and Panerai, Omega brings their own watches to the table. The Speedmaster X-33 Regatta ETNZ Limited Edition is worn by the crew while onboard. While the watch's combination of both analog and digital functions is actually practical, it seems like a disservice to the timeless layout of the Speedmaster.
The timepiece consists of the essential regatta function to keep track of the critical five-minute countdown to the start of each race. Looking underneath the watch's sail, so to say, we see the Omega Calibre 5620 quartz multifunctional chronograph movement. Be quick, as production is limited to 2,017 pieces.
When most people think the Seamaster Planet Ocean ETNZ from the fake Omega is the better looking of the two, there are other qualities apart from its design. Inspired by the New Zealand flag, its black base with red and blue detailing is no nice. It features a ceramic bezel in blue and red rubber for the first 10 minutes and starts in "LiquidMetal" for the final 5. The dot at 12 o'clock is full of Super-Luminova which emits a green glow. Its vertically-brushed ceramic dial has 18K white gold indexes and a GMT ring with a day/night display. The replica Omega's admirable Co-Axial Master Chronometer Calibre 8906 powers the timepiece. The caseback which covers the caliber has the ETNZ logo and is surrounded by the words "CHALLENGER 35TH AMERICA'S CUP", which makes it to be the winner with the biggest possibilities.
Comparing review: The Globemaster VS The Omega Deville Replica
If my decision would be based solely on the design, I would choose the De Ville Omega because I like more casual-looking timepieces. The designs of these two Omega replica watches are quite different. One is more casual but it still works with dressier outfits, while the other one is more elegant. The movements aren't that different. They are both automatic Japanese watches and keep good time. The Globemaster Co-Axial is still a good-looking watch, but I don't wear a dres' watch that often. As for their accuracy when it comes to copying the details found on the original models, they are both pretty precise and look like authentic watches.
The Omega De Ville collection of watches was launched in 1967 and it's a mix between the technical abilities Omega Replica watches are known for and a simple and contemporary design. just like the De Ville, the Globemaster Co-Axial combines superior technical aspects with a simple, dressy design. The Globemaster is a bit newer and it was launched at Baselworld, in 2015. This Omega Deville replica looks really good. I said it when I first reviewed it and I can say it again now. The old De Ville collection was revamped and it resulted in some new, amazing models. The simple, unmarked chronograph at 3 and 9 o'clock makes the dial look balanced and it also gives it a more casual look. It has a vintage-inspired design, similar to the one of the Constellation. Also, the date window located at 6 o'clock, and the De Ville markings look like the one on the original. The case and bezel are plated with rose gold and it really gives it a nice finish. It gives it a nice shine and a luxury feel. The dial is covered with a scratch-proof crystal. Overall, I am pleased with its quality. It's a nice casual watch that can be worn at dressier events and that's why I like it. It's not as thin as the Globemaster.
The back case of this De Ville is see-through and it gives the whole design a nice touch. The leather strap and the Omega engraved folding clasp look good too. Plus, the rose gold and blue combination look good on any kind of watch. This is an Omega Deville quartz replica, meaning that it's powered by automatic movements. The second's hand has a good sweeping motion, but it could be improved.
The Globemaster Co-Axial Master Chronometer's design was inspired by one of the Constellation watches, from the 1960s. The fluted bezel is also a particular feature. Besides this, the dial looks clean and symmetrical. That is why it has a vintage feel. It features a pie-pan dial which is an interesting, vintage detail. The case is mostly brushed, but it also has some polished elements. This looks pretty accurate, apart from the closing detail. The original one has a clasp. The numerals are stylized lines and you can also find a date section on the dial. This replica is a good copy and it copies all the details you can find on the authentic watch. Apart from this and the writing that comes in three fonts, there aren't other elements, so it makes it look clean and sleek.
Even if these replica Omega watches are both dres' watches, they are still quite different. Let's see which one is the best Omega replica. I have few dress watches and two of them are Omega. I prefer casual timepieces, but since I have these and many readers have asked me what to get between the Omega Deville replica and the Globemaster, here's a comparison of the two. Regarding its movements, this is an automatic Omega Japanese replica. It has good sweepings hands and there isn't a big difference between this one and the De Ville.


Hi guys. This is my first project featuring my song writing and vocals. I wanted to do something different & unique. This was a crazy learning experience for me and I'm very proud of what I created! I hope you enjoy it.
Send Moods is about love and lust and longing throughout time from the heat-of-the-moment present to mourning a future you imagined with someone, and finally, reminiscing on a past relationship.
Diggin' U is about knowing you're bad for someone but wanting them regardless of inevitable destruction.
Sippin' On Danger is about realizing that you're more in love with the idea of someone than the actual person and that what you really will miss is the fantasy of what could have been.
We Were is about reminiscing for a past love that you never really got closure for. It came from a dark place after losing someone to an overdose and realizing that they were gone forever.
Carter, you're the best !!! I love you, so much ❤ From São Paulo/Brasil, with love.
I love it A lot, you're the best.
your music is my favorite.
Wow really great! I love it!


text:
> Science & Technology
> Airbnb to lay off 25% of employees
Airbnb to lay off 25% of employees
Airbnb announces nearly 1,900 employees will be let go worldwide due to the coronavirus pandemic.
Ben Ariel
Coronavirus Airbnb
Airbnb iStock
Airbnb announced on Tuesday it would be laying off about 25% of its workforce as the coronavirus pandemic upends the travel industry and threatens the company's core business.
The short-term rental startup said nearly 1,900 employees will be let go worldwide, out of 7,500, according to CNN.
"We are collectively living through the most harrowing crisis of our lifetime, and as it began to unfold, global travel came to a standstill," Airbnb CEO and cofounder Brian Chesky said in a letter to employees.
He added that Airbnb's business has been "hit hard" and revenue this year is expected to be less than half of what the company earned in 2019.
In the US, Airbnb said it will cover 12 months of health insurance for its employees through COBRA. In all other countries, it will cover health insurance costs through the end of this year.
"I have a deep feeling of love for all of you," Chesky wrote in the letter. "I am truly sorry. Please know this is not your fault. The world will never stop seeking the qualities and talents that you brought to Airbnb."
Airbnb has also grappled with appeasing frustrated customers with refunds, and supporting its hosts, many of whom are struggling to make mortgage payments and pay bills due to coronavirus-related cancellations.
The company made headlines in Israel in 2018 when it decided to remove listings for about 200 homes in Jewish communities in Judea and Samaria.
It later announced that it will not remove listings in Israeli towns in Judea and Samaria from its website, as part of a court settlement with American Jewish plaintiffs who had sued the company.
In addition to the lawsuit by the group of Jewish Americans, several states took action against Airbnb following the move.
In Florida, Governor Ron DeSantis agreed to place Airbnb on the state's scrutinized companies list which prohibits state investment in companies that boycott Israel.
Texas similarly prohibited investment in Airbnb, placing the company on the state comptroller's "list of companies that boycott Israel pursuant to Chapter 808 of the Texas government code," which prohibits investment in companies that boycott Israel.
In addition, an independent board in Illinois voted to notify Airbnb that it is violating state laws barring the economic boycott of Israel, making Illinois the first state to take firm action against the online lodging company.
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Published in The Annals of Probability, Volume 17, Issue 3, September 1, 1989, pages 1325-1334.
Copyright © 1989 Institute of Mathematical Statistics.
NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.
The definitive version is available at https://doi.org/10.1214/aos/1176347272.
Optimal-partitioning and minimax risk inequalities are obtained for the classification and multi-hypotheses testing problems. Best possible bounds are derived for the minimax risk for location parameter families, based on the tail concentrations and Levy concentrations of the distributions. Special attention is given to continuous distributions with the maximum likelihood ratio property and to symmetric unimodal continuous distributions. Bounds for general (including discontinuous) distributions are also obtained.