text:
import Layer from '../../Layer'
import Tensor from '../../Tensor'
import { webgl2 } from '../../WebGL2'
import ops from 'ndarray-ops'
import programSource from './BatchNormalization.glsl'

/**
 * BatchNormalization layer class
 */
export default class BatchNormalization extends Layer {
  /**
   * Creates an BatchNormalization layer
   *
   * @param {Object} [attrs] - layer config attributes
   */
  constructor(attrs = {}) {
    super(attrs)
    this.layerClass = 'BatchNormalization'

    const { epsilon = 0.001, axis = -1, center = true, scale = true } = attrs

    this.epsilon = epsilon
    this.center = center
    this.scale = scale

    // no batch axis, so axis is less 1 compared to representation in keras
    // will be set in call(), as input tensor shape is needed to calculate axis
    // if axis < 0
    this.axis = axis
    this.axisNormalized = false

    // Layer weights specification
    this.params = []
    if (this.scale) {
      this.params.push('gamma')
    }
    if (this.center) {
      this.params.push('beta')
    }
    this.params = this.params.concat(['moving_mean', 'moving_variance'])

    // GPU setup
    if (this.gpu) {
      this.program = webgl2.compileProgram(programSource)
    }
  }

  /**
   * Layer computational logic
   *
   * @param {Tensor} x
   * @returns {Tensor}
   */
  call(x) {
    if (this.gpu) {
      this._callGPU(x)
    } else {
      this._callCPU(x)
    }
    return this.output
  }

  /**
   * CPU call
   *
   * @param {Tensor} x
   */
  _callCPU(x) {
    if (!this.axisNormalized) {
      this.axis = this.axis < 0 ? x.tensor.shape.length + this.axis : this.axis - 1
      this.axisNormalized = true
    }

    let broadcast = []
    for (let d = 0; d < x.tensor.shape.length; d++) {
      if (d === this.axis) broadcast.push(1)
      else broadcast.push(null)
    }

    // broadcast weights
    let _gamma = new Tensor([], x.tensor.shape)
    let _beta = new Tensor([], x.tensor.shape)
    for (let i = 0; i < x.tensor.shape[this.axis]; i++) {
      broadcast[this.axis] = i
      if (this.scale) {
        ops.assigns(_gamma.tensor.pick(...broadcast), this.weights['gamma'].tensor.get(i))
      }
      if (this.center) {
        ops.assigns(_beta.tensor.pick(...broadcast), this.weights['beta'].tensor.get(i))
      }
    }

    let _mean = new Tensor([], x.tensor.shape)
    let _std = new Tensor([], x.tensor.shape)

    // feature-wise normalization
    for (let i = 0; i < x.tensor.shape[this.axis]; i++) {
      broadcast[this.axis] = i
      ops.assigns(_mean.tensor.pick(...broadcast), this.weights['moving_mean'].tensor.get(i))
      ops.assigns(_std.tensor.pick(...broadcast), this.weights['moving_variance'].tensor.get(i) + this.epsilon)
    }
    ops.sqrteq(_std.tensor)

    this.output = new Tensor(x.tensor.data, x.tensor.shape)

    ops.subeq(this.output.tensor, _mean.tensor)
    ops.diveq(this.output.tensor, _std.tensor)
    if (this.scale) {
      ops.muleq(this.output.tensor, _gamma.tensor)
    }
    if (this.center) {
      ops.addeq(this.output.tensor, _beta.tensor)
    }
  }

  /**
   * Pre-compute index maps for GPU batchnorm function
   *
   * @param {number[]} glTextureShape
   * @param {Object} indicesForReshaped
   */
  _createIndexMap(glTextureShape, indicesForReshaped) {
    if (this.normAxisIndexMap) {
      return
    }

    const _normAxisIndexMap = new Tensor([], this.inputShape, { type: Int32Array })
    this.normAxisIndexMap = new Tensor([], glTextureShape, { type: Int32Array })

    const slice = Array(this.inputShape.length).fill(null)
    for (let i = 0; i < this.inputShape[this.axis]; i++) {
      slice[this.axis] = i
      ops.assigns(_normAxisIndexMap.tensor.pick(...slice), i)
    }

    if (indicesForReshaped) {
      for (let i = 0; i < indicesForReshaped.data.length; i++) {
        this.normAxisIndexMap.tensor.data[indicesForReshaped.data[i]] = _normAxisIndexMap.tensor.data[i]
      }
    } else {
      this.normAxisIndexMap = _normAxisIndexMap
    }

    this.normAxisIndexMap.createGLTexture({ type: '2d', format: 'int', supportsTextureFragments: true })
  }

  /**
   * GPU call
   * (will only work on the 2D-reshaped representation for post-convolutional BN)
   *
   * @param {Tensor} x
   */
  _callGPU(x) {
    if (!this.axisNormalized) {
      if (x.is2DReshaped || x.is2DSquareReshaped) {
        this.inputShape = x.originalShape
      } else {
        this.inputShape = x.tensor.shape
      }
      this.axis = this.axis < 0 ? this.inputShape.length + this.axis : this.axis - 1
      this.axisNormalized = true
    }

    if (!x.glTexture && !x.glTextureFragments) {
      if (x.tensor.shape.length <= 2) {
        x.createGLTexture({ type: '2d', format: 'float', supportsTextureFragments: true })
      } else if (x.tensor.shape.length > 2 && !x.is2DReshaped) {
        // defaults to square reshaped
        x.reshapeTo2DSquare()
        x.createGLTexture({ type: '2d', format: 'float', supportsTextureFragments: true })
      }
    }

    this._createIndexMap(x.glTextureShape, x.indicesForReshaped)

    // create output textures if doesn't already exist
    if (!this.output) {
      this.output = new Tensor([], x.glTextureShape)
      this.output.createGLTexture({ type: '2d', format: 'float', supportsTextureFragments: true })
      if (x.is1D) {
        this.output.is1D = x.is1D
      } else if (x.is2DReshaped || x.is2DSquareReshaped) {
        if (x.is2DReshaped) {
          this.output.is2DReshaped = x.is2DReshaped
        } else if (x.is2DSquareReshaped) {
          this.output.is2DSquareReshaped = x.is2DSquareReshaped
        }
        this.output.originalShape = x.originalShape
        this.output.indicesForReshaped = x.indicesForReshaped
      }
    }

    const programInputs = [{ input: x, name: 'X' }, { input: this.normAxisIndexMap, name: 'normAxisIndexMap' }]
    if (this.scale) {
      programInputs.push({ input: this.weights['gamma'], name: 'gamma' })
    }
    if (this.center) {
      programInputs.push({ input: this.weights['beta'], name: 'beta' })
    }
    programInputs.push({ input: this.weights['moving_mean'], name: 'mean' })
    programInputs.push({ input: this.weights['moving_variance'], name: 'std' })
    const programUniforms = [
      { value: this.epsilon, type: 'float', name: 'epsilon' },
      { value: +this.scale, type: 'bool', name: 'scale' },
      { value: +this.center, type: 'bool', name: 'center' }
    ]
    webgl2.runProgram({
      program: this.program,
      output: this.output,
      inputs: programInputs,
      uniforms: programUniforms,
      supportsTextureFragments: true
    })

    // GPU -> CPU data transfer
    if (this.outbound.length === 0) {
      this.output.transferFromGLTexture()
      if (this.output.is2DReshaped) {
        this.output.reshapeFrom2D()
      } else if (this.output.is2DSquareReshaped) {
        this.output.reshapeFrom2DSquare()
      }
    }
  }
}


In the last episode we looked at why you should be hedging with Gold & Silver right now.
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In the next episode I'm going to talk about the 3 asset classes you should be looking at buying now. Stay tuned for that on Monday.
Thanks i want more learning from you.


Looking to make your family history last? Whether you want to write your own Roots or Angela's Ashes or just hope to record your research in a form your relatives might actually read, here's how to plan, write and publish your own family history book.
Your book doesn't have to be a tome. The first family history I wrote, The Ebetino and Vallarelli Family History, contained only 112 pages (8½x11 format), including the index. The one I'm working on now probably won't be longer than 75 pages in a 6×9 format. It can be far better and more efficient to write a smaller family history; the project won't be nearly as overwhelming and your goal is more attainable.
Knowing that other researchers—genealogists and historians—might read and use your family history might change the way you write your family history. If you're writing solely for family members, your inclination might be to skip footnotes, endnotes or other documentation, thinking that your family won't care where you got your information. But even family members may want to pick up where you left off or take one of the branches further, which means they'd want you to include your sources.
This entry was posted in Save and Share Family History and tagged family, history, last, looking, make, plan, roots, want, whether, write. Bookmark the permalink.


text:
\section{abstract}
We derive the two-loop evolution equations for the Cabibbo-Kobayashi-Maskawa
matrix. We show that to leading order in the mass and CKM hierarchies the
scaling of the mixings $|V_{ub}|^2$, $|V_{cb}|^2$, $|V_{td}|^2$, $|V_{ts}|^2$
and of the rephase-invariant CP-violating parameter $J$ is universal to all
orders in perturbation theory. In leading order the other CKM elements do not
scale. Imposing the constraint $\lambda _b=\lambda _{\tau}$ at the GUT scale
determines the CKM scaling factor to be $\simeq 0.58$ in the MSSM.
\end{abstract}

\newpage
The weak interaction quark eigenstates and the quark mass eigenstates differ
in the Standard Model as described by the Cabibbo-Kobayashi-Maskawa (CKM)
matrix. In this paper we
show that the scaling of the CKM matrix follows a universal pattern to leading
order in the mass and CKM hierarchies; namely, the CKM mixing elements that
involve the third generation and CP violation scale together, while the other
components of the CKM matrix do not scale to leading order. This makes it
much simpler to consider the form of the quark mixings at any other scale, in
particular at the scale of a grand unified theory (GUT). The common scaling is
a model-independent feature of the evolution, but the amount of scaling can
vary between theories.

The Yukawa matrices ${\bf U}$ and ${\bf D}$ can be diagonalized by biunitary
transformations
\begin{eqnarray}
{\bf U^{diag}}&=&V_u^L{\bf U}V_u^{R\dagger} \;, \\
{\bf D^{diag}}&=&V_d^L{\bf D}V_d^{R\dagger} \;.
\end{eqnarray}
The CKM matrix is then given by
\begin{equation}
V\equiv V_u^LV_d^{L\dagger } \;.
\end{equation}
The Yukawa matrices evolve with energy scale as determined by renormalization
group equations (RGE). This in turn
determines an evolution equation for the ``running'' CKM matrix $V(\mu )$.

The renormalization group scaling to leading order in the mass and CKM
hierarchies can be represented schematically in the following way:
\begin{equation}
{\bf U^{diag}}(M_G^{}) = \left( \begin{array}{c@{\quad}c@{\quad}c}
S_u(\mu )\lambda _u(\mu ) & 0 & 0 \\ 0 &
S_u(\mu )\lambda _c(\mu ) & 0 \\
0 & 0 & S_t(\mu )\lambda _t(\mu )
\end{array} \right) \;,
\end{equation}
\begin{equation}
{\bf D^{diag}}(M_G^{}) = \left( \begin{array}{c@{\quad}c@{\quad}c}
S_d(\mu )\lambda _d(\mu ) & 0 & 0 \\ 0 &
S_d(\mu )\lambda _s(\mu ) & 0 \\
0 & 0 & S_b(\mu )\lambda _b(\mu )
\end{array} \right) \;,
\end{equation}
\begin{equation}
{\bf E^{diag}}(M_G^{}) = \left( \begin{array}{c@{\quad}c@{\quad}c}
S_e(\mu )\lambda _e(\mu ) & 0 & 0 \\ 0 &
S_e(\mu )\lambda _{\mu}(\mu ) & 0 \\
0 & 0 & S_{\tau}(\mu )\lambda _{\tau}(\mu )
\end{array} \right) \;,
\end{equation}
\begin{equation}
{\bf |V|}^2(M_G^{}) = \left( \begin{array}{c@{\quad}c@{\quad}c}
|V_{ud}|^2(\mu )& |V_{us}|^2(\mu ) & S(\mu )|V_{ub}|^2(\mu ) \\
|V_{cd}|^2(\mu ) & |V_{cs}|^2(\mu ) & S(\mu )|V_{cb}|^2(\mu ) \\
S(\mu )|V_{td}|^2(\mu ) & S(\mu )|V_{ts}|^2(\mu ) & |V_{tb}|^2(\mu )
\end{array} \right) \;,
\label{schematic}
\end{equation}
where the scale $\mu $ is the range $m_t\leq \mu \leq M_G^{}$ with $M_G^{}$
the GUT scale. The CP-violating rephase invariant parameter $J$\cite{Jarlskog}
also scales as $J(M_G^{})=S(\mu )J(\mu )$ to leading order.
We have defined
our scaling factors to be unity at the GUT scale, but one could equally well
choose any convenient scale.

The two light generation quark and lepton Yukawa couplings evolve in a common
manner determined by the gauge couplings and traces of the Yukawa matrices,
while the third generation Yukawa couplings receive additional
Yukawa contributions.
This implies that the ratios $\lambda _u/\lambda _c$, $\lambda _d/\lambda _s$,
$\lambda _e/\lambda _{\mu}$ do not evolve.
The scaling pattern in Eq.~(\ref{schematic}) violates unitarity of $V$, but
only at subleading order. For example the relation
$|V_{ud}|^2+|V_{us}|^2+|V_{ub}|^2=1$ is violated by terms that are neglected
to leading order in the evolution of $|V_{ud}|^2$ and $|V_{us}|^2$.
The elements $|V_{ud}|^2$ and $|V_{us}|^2$ must evolve to subleading order to
preserve unitarity. A practical
strategy is to evolve the small mixings $X=|V_{ub}|^2$, $Y=|V_{us}|^2$,
$Z=|V_{cb}|^2$, and $J$ which completely determine the other entries in
the CKM matrix.

In terms of $t=\ln (\mu /M_G^{})$ the two-loop RGEs can be written as
\begin{eqnarray}
{{d{\bf U}}\over {dt}}={1\over {16\pi ^2}}
\Bigg[&\Big (&x_1{\bf I}+x_2{\bf UU^{\dagger }}+a_u{\bf DD^{\dagger }}
\Big )
+{1\over {16\pi ^2}}\Bigg (x_3{\bf I}
+x_4{\bf UU^{\dagger }} \nonumber \\
&+&x_5({\bf UU^{\dagger }})^2+b_u{\bf DD^{\dagger }}+c_u({\bf DD^{\dagger }})^2
+d_u{\bf UU^{\dagger }}{\bf DD^{\dagger }}
+e_u{\bf DD^{\dagger }}{\bf UU^{\dagger }}
\Bigg )\Bigg ]{\bf U} \nonumber \;, \\
\label{dUdt}
\end{eqnarray}
\begin{eqnarray}
{{d{\bf D}}\over {dt}}={1\over {16\pi ^2}}
\Bigg[&\Big (&x_6{\bf I}+x_7{\bf DD^{\dagger }}+a_d{\bf UU^{\dagger }}
\Big )
+{1\over {16\pi ^2}}\Bigg (x_8{\bf I}
+x_9{\bf DD^{\dagger }} \nonumber \\
&+&x_{10}({\bf DD^{\dagger }})^2+b_d{\bf UU^{\dagger }}
+c_d({\bf UU^{\dagger }})^2
+d_d{\bf DD^{\dagger }}{\bf UU^{\dagger }}
+e_d{\bf UU^{\dagger }}{\bf DD^{\dagger }}
\Bigg )\Bigg ]{\bf D} \nonumber \;, \\
\label{dDdt}
\end{eqnarray}
\begin{eqnarray}
{{d{\bf E}}\over {dt}}={1\over {16\pi ^2}}
\Bigg[x_{11}{\bf I}+x_{12}{\bf EE^{\dagger }}
+{1\over {16\pi ^2}}\Bigg (x_{13}{\bf I}
+x_{14}{\bf EE^{\dagger }}+x_{15}({\bf EE^{\dagger }})^2
\Bigg )\Bigg ]{\bf E} \;,
\label{dEdt}
\end{eqnarray}
where the coefficients $x_i$, $a_i$, etc. depend upon the particle content of
the theory and are functions of the gauge and Yukawa couplings, i.e.
$a_i=a_i(g_1^2,g_2^2,g_3^2,
{\bf Tr}[{\bf UU^{\dagger }}],{\bf Tr}[{\bf DD^{\dagger }}],
{\bf Tr}[{\bf EE^{\dagger }}])$ and Higgs quartic couplings.
The coefficients $x_i$ do not enter into the running of the CKM
matrix but do influence the diagonal quark Yukawa evolution; only terms
involving a factor of ${\bf DD^{\dagger}}$ can rotate the ${\bf U}$ matrix,
and only terms with a factor of ${\bf UU^{\dagger}}$ can rotate the ${\bf D}$
matrix.
In the minimal supersymmetric standard model (MSSM) the other
coefficients are
\begin{eqnarray}
a_u&=&a_d=1\;, \\
b_u&=&{2\over 5}g_1^2-{\bf Tr}[3{\bf DD^{\dagger }}
+{\bf EE^{\dagger }}]\;, \\
b_d&=&{4\over 5}g_1^2-{\bf Tr}[3{\bf UU^{\dagger }}]\;, \\
c_u&=&c_d=-2\;, \\
d_u&=&d_d=-2\;, \\
e_u&=&e_d=0\;.
\end{eqnarray}
In the Standard Model they are given by
\begin{eqnarray}
a_u&=&a_d=-{3\over 2}\;, \\
b_u&=&=-{43\over 80}g_1^2+{9\over 16}g_2^2-16g_3^2-2\lambda
+{5\over 4}Y_2(S)\;, \\
b_d&=&=-{79\over 80}g_1^2+{9\over 16}g_2^2-16g_3^2-2\lambda
+{5\over 4}Y_2(S)\;, \\
c_u&=&c_d={11\over 4}\;, \\
d_u&=&d_d=-{1\over 4}\;, \\
e_u&=&e_d=-1\;,
\end{eqnarray}
where
\begin{equation}
Y_2(S)={\bf Tr}[3{\bf UU^{\dagger}}+3{\bf DD^{\dagger}}+{\bf EE^{\dagger}}]\;.
\end{equation}
The coefficients $x_i$ can be found in Refs.~\cite{MV,BBO}.

Following Ma, Pakvasa, Sasaki and Babu\cite{MPS,Babu} we find
the CKM evolution equation
\begin{eqnarray}
{{dV_{i\alpha }}\over {dt}}&=&{1 \over {16\pi ^2}}\left [
a_u\sum _{\beta,j\ne i}
{{\lambda _i^2+\lambda _j^2}\over {\lambda _i^2-\lambda _j^2}}
\hat{\lambda} _{\beta}^2
V_{i\beta }V_{j\beta }^*V_{j\alpha }+a_d\sum _{j,\beta \ne \alpha}
{{\lambda _{\alpha }^2+\lambda _{\beta }^2}\over {\lambda _{\alpha }^2
-\lambda _{\beta }^2}}\hat{\lambda} _j^2
V_{j\beta }^*V_{j\alpha }V_{i\beta }\right ] \nonumber \\
&&\qquad \qquad +{1 \over {(16\pi ^2)^2}}\left [\sum _{\beta,j\ne i}
{{2d_u\lambda _i^2\lambda _j^2+e_u(\lambda_i^4+\lambda _j^4)}
\over {\lambda _i^2-\lambda _j^2}}
\lambda _{\beta}^2
V_{i\beta }V_{j\beta }^*V_{j\alpha }\right .\nonumber \\
&&\qquad \qquad \qquad \qquad \left . +\sum _{j,\beta \ne \alpha}
{{2d_d\lambda _{\alpha }^2\lambda _{\beta }^2+e_d(\lambda _{\alpha }^4
+\lambda _{\beta }^4)}
\over {\lambda _{\alpha }^2
-\lambda _{\beta }^2}}\lambda _j^2
V_{j\beta }^*V_{j\alpha }V_{i\beta }\right ]\;, \label{dVckmdt}
\end{eqnarray}
where
\begin{eqnarray}
\hat{\lambda} _{\beta}^2&=&\lambda _{\beta}^2\left (
1+{{b_u+c_u\lambda _{\beta}^2}
\over {16\pi ^2a_u}}\right )\;, \\
\hat{\lambda} _j^2&=&\lambda _j^2\left (
1+{{b_d+c_d\lambda _j^2}
\over {16\pi ^2a_d}}\right )\;.
\end{eqnarray}
Here $i,j,k=u,c,t,\dots;\;
\alpha,\beta,\gamma =d,s,b,\dots$
We henceforth restrict our considerations to the three-generation case.
Defining the four independent quantities
$X=|V_{ub}|^2$, $Y=|V_{us}|^2$, $Z=|V_{cb}|^2$, and the
parameter $J={\rm Im}V_{ud}^{}V_{cs}^{}V_{us}^*V_{cd}^*$
which can completely specify a unitary CKM matrix, the other elements are
given by\cite{Babu}
\begin{eqnarray}
|V_{ud}|^2&=&1-X-Y\;, \label{Vud} \\
|V_{cs}|^2&=&{{[XYZ+(1-X-Y)(1-X-Z)-2K]}\over {(1-X)^2}}\;,\\
|V_{cd}|^2&=&{{[XZ(1-X-Y)+Y(1-X-Z)+2K]}\over {(1-X)^2}}\;,\\
|V_{tb}|^2&=&1-X-Z\;,\\
|V_{ts}|^2&=&{{[XY(1-X-Z)+(1-X-Y)Z+2K]}\over {(1-X)^2}}\;,\\
|V_{td}|^2&=&{{[X(1-X-Y)(1-X-Z)+YZ-2K]}\over {(1-X)^2}}\;, \label{Vtd}
\end{eqnarray}
where
\begin{equation}
K=[XYZ(1-X-Y)(1-X-Z)-J^2(1-X)^2]^{1/2}\;.
\end{equation}
The full evolution equations for $X$, $Y$, $Z$ and $J$ are given in the
appendix.
Keeping only the leading terms in the mass ($\lambda _c/\lambda _t,
\lambda _u/\lambda _c,
\lambda _s/\lambda _b, \lambda _d/\lambda _s  << 1$)
and CKM ($X, Z, J << 1$) hierarchies, these equations
simplify considerably\cite{BBO} and a universal scaling is found
\begin{equation}
{{dW_1}\over {dt}}=-{{W_1}\over {8\pi ^2}}
\Bigg [\left (a_d\hat{\lambda} _t^2
+a_u\hat{\lambda} _b^2\right )+{{1}\over {(16\pi ^2)}}(e_d+e_u)
\lambda _t^2\lambda _b^2\Bigg ] \;, \label{dW1dt}
\end{equation}
where $W_1=|V_{cb}|^2, |V_{ub}|^2, |V_{ts}|^2, |V_{td}|^2, J$ and
\begin{equation}
{{dW_2}\over {dt}}=0\;, \label{dW2dt}
\end{equation}
where $W_2=|V_{us}|^2, |V_{cd}|^2, |V_{tb}|^2, |V_{cs}|^2, |V_{ud}|^2$.
One does not need the mixing between the first two generations to be small
($Y<<1$) which makes the universality an especially good approximation. To
leading order it is only necessary to include the third generation Yukawa
couplings in $\hat{\lambda }_t^2$ and $\hat{\lambda }_b^2$.
Notice that Eqs.~(\ref{dW1dt})-(\ref{dW2dt})
violate unitarity of $V$, but only at subleading order.
The solution of Eq.~(\ref{dW1dt}) is
\begin{equation}
W_1(M_G^{})=W_1(\mu )S(\mu )\;,
\end{equation}
where $S$ is a scaling factor defined by
\begin{equation}
S(\mu ) = \exp \left \{ -{1\over {8\pi ^2}}\int\limits_{\mu}^{M_G}
\Bigg [\left (a_d\hat{\lambda} _t^2
+a_u\hat{\lambda} _b^2\right )+{{1}\over {(16\pi ^2)}}(e_d+e_u)\lambda _t^2
\lambda _b^2\Bigg ]
d\ln\mu' \right \}
\label{defS} \;.
\end{equation}
This reduces\cite{BBO,DHR} to the scaling factor $y^2(\mu )$ in the one-loop
semianalytic treatment (neglecting $\lambda _b$ and $\lambda _{\tau}$), with
\begin{equation}
y(\mu ) = \exp \left \{ -{1\over {16\pi ^2}}\int\limits_{\mu}^{M_G}
a_d\lambda _t^2(\mu')d\ln\mu' \right \} \label{defy} \;.
\end{equation}
The general behavior of $S(\mu )$
is determined by the sign of $a_d$ (and perhaps also
$a_u$ in models where $\tan \beta$ is large).
In the Standard Model the scaling
factors are greater than one since the one-loop coefficients $a_u$ and $a_d$
are negative.

One might naively have expected there to be contributions to the scaling of
the $W_1$ that are not proportional to $W_1$; for example a contribution to
the running of $|V_{ub}|^2$ of
the form $\lambda _c^2|V_{cb}|^2$ on the right hand side of Eq.~(\ref{dW1dt})
can be of the same order as the contribution $\lambda _t^2|V_{ub}|^2$. We
conclude that no such terms arise.

We find the following RGEs for the Yukawa couplings
\begin{eqnarray}
{{d\lambda _i}\over {dt}}&=&{{\lambda _i}\over {16\pi ^2}}
\Bigg [x_1+x_2\lambda _i^2+
a_u\sum_ {\alpha}\lambda _{\alpha}^2|V_{i\alpha }|^2\nonumber \\
&&+{1\over {16\pi ^2}}\Bigg (x_3+x_4\lambda _i^2+x_5\lambda _i^4
+\sum _{\alpha}\Big (b_u\lambda _{\alpha}^2+c_u\lambda _{\alpha}^4
+(d_u+e_u)\lambda _i^2\lambda _{\alpha}^2\Big )
|V_{i\alpha }|^2\Bigg )\Bigg ]\;, \\
{{d\lambda _{\alpha}}\over {dt}}&=&{{\lambda _{\alpha}}\over {16\pi ^2}}
\Bigg [x_6
+x_7\lambda _{\alpha }^2+
a_d\sum_ i\lambda _i^2|V_{i\alpha }|^2\nonumber \\
&&+{1\over {16\pi ^2}}\Bigg (x_8+x_9\lambda _{\alpha }^2+x_{10}
\lambda _{\alpha }^4
+\sum _i\Big (b_d\lambda _i^2+c_d\lambda _i^4
+(d_d+e_d)\lambda _{\alpha }^2\lambda _i^2\Big )
|V_{i\alpha }|^2\Bigg )\Bigg ]\;, \\
{{d\lambda _a}\over {dt}}&=&{{\lambda _a}\over {16\pi ^2}}
\Bigg [x_{11}+x_{12}\lambda _a^2
+{1\over {16\pi ^2}}\Bigg (x_{13}+x_{14}\lambda _a^2+x_{15}\lambda _a^4
\Bigg )\Bigg ]
\;,
\end{eqnarray}
where $a=e, \mu ,\tau $.
Including only the third generation in the sums, these equations
reduce to the leading order
expressions for $\lambda _t$, $\lambda _b$, $\lambda _{\tau}$ yielding
\begin{eqnarray}
S_t(\mu ) &=& \exp \Bigg \{ {1\over {16\pi ^2}}\int\limits_{\mu}^{M_G}
\Bigg [x_1+x_2\lambda _t^2+
a_u\lambda _b^2\nonumber \\
&&+{1\over {16\pi ^2}}\Bigg (x_3+x_4\lambda _t^2+x_5\lambda _t^4
+\Big (b_u\lambda _b^2+c_u\lambda _b^4
+(d_u+e_u)\lambda _t^2\lambda _b^2\Big )
\Bigg )\Bigg ]d\ln\mu' \Bigg \} \;, \\
S_b(\mu ) &=& \exp \Bigg \{ {1\over {16\pi ^2}}\int\limits_{\mu}^{M_G}
\Bigg [x_6+x_7\lambda _b^2+
a_d\lambda _t^2\nonumber \\
&&+{1\over {16\pi ^2}}\Bigg (x_8+x_9\lambda _b^2+x_{10}\lambda _b^4
+\Big (b_d\lambda _t^2+c_d\lambda _t^4
+(d_d+e_d)\lambda _b^2\lambda _t^2\Big )
\Bigg )\Bigg ]d\ln\mu' \Bigg \} \;, \\
S_{\tau }(\mu ) &=& \exp \Bigg \{ {1\over {16\pi ^2}}\int\limits_{\mu}^{M_G}
\Bigg [x_{11}+x_{12}\lambda _{\tau }^2
+{1\over {16\pi ^2}}\Bigg (x_{13}+x_{14}\lambda _{\tau }^2
+x_{15}\lambda _{\tau }^4\Bigg )\Bigg ]d\ln\mu' \Bigg \} \;,
\end{eqnarray}
respectively. For the first and second generations the corresponding
expressions are
\begin{eqnarray}
S_u(\mu ) &=& \exp \left \{ {1\over {16\pi ^2}}\int\limits_{\mu}^{M_G}
\Bigg [x_1+{1\over {16\pi ^2}}x_3\Bigg ]d\ln\mu' \right \} \;, \\
S_d(\mu ) &=& \exp \left \{ {1\over {16\pi ^2}}\int\limits_{\mu}^{M_G}
\Bigg [x_6+{1\over {16\pi ^2}}x_8\Bigg ]d\ln\mu' \right \} \;, \\
S_e(\mu ) &=& \exp \left \{ {1\over {16\pi ^2}}\int\limits_{\mu}^{M_G}
\Bigg [x_{11}+{1\over {16\pi ^2}}x_{13}\Bigg ]d\ln\mu' \right \} \;.
\end{eqnarray}

In Figure 1 we show contours of constant $S(m_t)$
in the MSSM versus the values
of the Yukawa couplings $\lambda _t$ and $\lambda _b$ at scale $m_t$ and also
at the GUT
scale. The contribution to the scaling from $\lambda _t$ can traded off
against the contribution for $\lambda _b$ as indicated by Eq.~(\ref{defS}).
These contours are shown
versus $m_t$ and $\tan \beta$ in Figure 2. The $m_b(m_b)=4.4$ GeV contour,
which requires $\lambda _b(M_G^{})=\lambda _{\tau}(M_G^{})$,
is plotted as well. The evolution equation for
$R_{b/{\tau}}\equiv \lambda _b/\lambda _{\tau}$ at one-loop
in the MSSM is given by
\begin{equation}
{{dR_{b/\tau}}\over {dt}}={{R_{b/\tau}}\over {16\pi ^2}}
\left (-\sum d_ig_i^2+\lambda _t^2
+3\lambda _b^2-3\lambda _{\tau}^2\right )\;.
\label{dRdt}
\end{equation}
where $d_i=(-4/3,0,16/3)$. For small $\tan \beta $ the bottom and tau Yukawa
couplings can be neglected, and the scaling of $R_{b/\tau }$ factorizes into
scaling due to the gauge couplings and the scaling factor $S$ due to the top
Yukawa. Given a fixed gauge sector scaling, the $m_b$ contours and the
contours of constant $S$ coincide for small $\tan \beta $.
Note that $m_b\simeq 4.4$ GeV implies $S(m_t)\simeq 0.58$.

The numerical calculations performed here are similar to those described in
Ref.~\cite{BBO}. The input values are $\alpha _1(M_Z)^{-1}=58.89$,
$\alpha _2(M_Z)^{-1}=29.75$, and $\alpha _3(M_Z)=0.116$
for the gauge couplings and
$m_b(m_b)=4.4$ GeV, $m_c(m_c)=1.2$ GeV, $m_s(1 {\rm GeV})=0.15$ GeV,
$m_d({\rm 1 GeV})=0.008$ GeV, $m_u(1 {\rm GeV})=0.005$ GeV for the running
fermion masses. We take the lepton masses to be $m_{\tau }=1.7841$ GeV,
$m_{\mu }=0.10566$ GeV and $m_e=5.1100\times 10^{-4}$ GeV.
The GUT scale $M_G^{}$ is determined as the scale at which
unification of $\alpha _1$ and $\alpha _2$ is achieved.
Given an input value for $\tan \beta$ the input masses and the gauge couplings
determine the Yukawa
couplings at the scale $m_t$. We integrate the two-loop RGEs for the gauge
and Yukawa couplings as well as the evolution equations for $X$, $Y$, $Z$, and
$J$ given in the appendix. Our results are
not sensitive to the values of the first and second generation fermion
masses or to the input CKM magnitudes $|V_{cb}(m_t)|=0.043$,
$|V_{ub}(m_t)|=0.0045$, $|V_{us}(m_t)|=0.221$,  $J(m_t)=1.95\times 10^{-5}$.
For experimentally acceptable
values of the quark masses and CKM matrix elements, the exact scaling as
given by the equations in the appendix differ from the universal behavior
described by Eq.~(\ref{dW1dt}) by \raisebox{-.4ex}{\rlap{$\sim$}} \raisebox{.4ex}{$<$} 0.1\%.

A good approximation
for evolving the CKM matrix is to use Eq.~(\ref{dW1dt}) to evolve $|V_{ub}|^2$,
$|V_{cb}|^2$ and $J$ and leave $|V_{us}|^2$ constant as in Eq.~(\ref{dW2dt}).
Then calculate the remaining magnitudes $|V_{i\alpha }|$ using
Eqs.~(\ref{Vud})-(\ref{Vtd}).

One can show that the universal scaling behavior described by
Eqs.~(\ref{dW1dt})-(\ref{dW2dt}) is maintained
to all orders in perturbation theory.
However the quantitative effects of the
three-loop contribution are generally smaller
than the sub-leading contributions in the mass and CKM hierarchies.

We now give a sketch of a proof of
the universal behavior at an arbitrary order in
perturbation theory. A higher order contribution will be of the general form
\begin{eqnarray}
{{d{\bf U}}\over {dt}}= {1\over {(16\pi ^2)^q}}
&\Bigg [&f_u^{mn\dots op}({\bf DD^{\dagger }})^m({\bf UU^{\dagger }})^n\dots
({\bf UU^{\dagger }})^o({\bf DD^{\dagger }})^p\Bigg ]{\bf U}+\dots \;,
\label{qloop}
\end{eqnarray}
where $q\geq m+n+\dots +o+p$ represents the loop order. There is an analogous
contribution to $d{\bf D}/dt$.
The exponents $m$ and $p$ could be zero. The coefficient $f_u^{mn\dots op}$ is
calculable in perturbation theory but can be obtained only with tedious
effort; it is a function of the gauge couplings $g_i$ and the sum of the
eigenvalues of the Yukawa couplings matrices, ${\bf Tr}[{\bf UU^{\dagger}}]$,
${\bf Tr}[{\bf DD^{\dagger}}]$, ${\bf Tr}[{\bf EE^{\dagger}}]$, and possibly
other couplings like the quartic Higgs coupling in the standard model.
The term in Eq.~(\ref{qloop}) generates a new contribution
to Eq.~(\ref{dVckmdt}),
\begin{eqnarray}
{{dV_{i\alpha }}\over {dt}}= {1 \over {(16\pi ^2)^q}}&\Bigg [&
f_u^{mn\dots op}\sum _{j\ne i}\Bigg \{
{{1}\over {\lambda _i^2-\lambda _j^2}}\nonumber \\
&&\;\;\;
\sum _{\beta ,k,\gamma,\dots l,\delta }
\Big (\lambda _{\beta}^{2m}\lambda _k^{2n}\dots \lambda _l^{2o}
\lambda _{\delta }^{2p}\lambda _j^2
+\lambda _i^2\lambda _{\beta}^{2p}\lambda _k^{2o}\dots
\lambda _l^{2n}\lambda _{\delta }^{2m}\Big )
V_{i\beta }V_{k\beta }^*V_{k\gamma }V_{l\gamma}^*\dots V_{j\delta}^*
V_{j\alpha }\Bigg \}\Bigg ]+\dots \nonumber \;. \\
\end{eqnarray}
The only terms that contribute to leading order in $dX/dt$, $dY/dt$, $dZ/dt$,
$dJ/dt$ are those in which the indices in the second sum above involve the
third generation
\begin{eqnarray}
{{dV_{i\alpha }}\over {dt}}= {1 \over {(16\pi ^2)^q}}&\Bigg [&
f_u^{mn\dots op}\sum _{j\ne i}\Bigg \{
{{\lambda _i^2+\lambda _j^2}\over {\lambda _i^2-\lambda _j^2}}
\Big (\lambda _b^{2m}\lambda _t^{2n}\dots \lambda _t^{2o}
\lambda _b^{2p}\Big )
V_{ib}V_{tb}^*V_{tb}V_{tb}^*\dots V_{jb}^*
V_{j\alpha }\Bigg \}\Bigg ]+\dots \nonumber \;. \\
\end{eqnarray}
Then to leading order, $|V_{tb}|^2\simeq 1$, and one has
\begin{eqnarray}
{{dV_{i\alpha }}\over {dt}}= {1 \over {(16\pi ^2)^q}}&\Bigg [&
f_u^{mn\dots op}\sum _{j\ne i}\Bigg \{
{{\lambda _i^2+\lambda _j^2}\over {\lambda _i^2-\lambda _j^2}}
\Big (\lambda _t^{2(n+\dots +o)}
\lambda _b^{2(m+\dots +p)}\Big )
V_{ib}V_{jb}^*V_{j\alpha }\Bigg \}\Bigg ]+\dots\nonumber \;,
\end{eqnarray}
which has the same form as Eq.~(\ref{dVckmdt}). Consequently
\begin{equation}
{{dW_1}\over {dt}}= -{{2W_1}\over {(16\pi ^2)^q}}
\Bigg [f_u^{mn\dots op}\left (\lambda _t^{2(n+\dots +o)}
\lambda _b^{2(m+\dots +p)}\right )\Bigg ]+\dots \;. \label{dW1dtf}
\end{equation}
A similar argument applies to the cases $m=0$ and/or $p=0$.

In summary
we have shown that there is a universal scaling pattern in the evolution of the
CKM matrix when only the leading order terms in the mass and CKM hierarchies
are kept. This is a very good approximation given the observed hierarchy
of the quark masses and CKM matrix elements. This scaling
behavior persists to all orders in perturbation theory. Imposing a GUT scale
constraint $\lambda _b(M_G^{})=\lambda _{\tau}(M_G^{})$ constrains the
amount of scaling. For $m_b(m_b)=4.4$ GeV the scaling factor of the CKM matrix
is $S\simeq 0.58$.

After this work was completed we learned that similar conclusions about
the scaling
of the CKM elements have been obtained at the one-loop level
by Babu and Shafi\cite{BS}.

\acknowledgements
This research was supported
in part by the University of Wisconsin Research Committee with funds granted by
the Wisconsin Alumni Research Foundation, in part by the U.S.~Department of
Energy under contract no.~DE-AC02-76ER00881, and in part by the Texas National
Laboratory Research Commission under grant no.~RGFY9273.  Further support was
also provided by U.S. Department of Education under Award No. P200A80214.
PO was supported in part by an NSF Graduate Fellowship.

\nonum\section{appendix}
The evolution equations for $|V_{i\alpha }|^2$ can be derived from
Eq.~(\ref{dVckmdt}) using the substitutions in Eqs.~(\ref{Vud})-(\ref{Vtd}),
as performed by Babu\cite{Babu} at the one-loop level. At the two-loop level
one obtains
\begin{eqnarray}
{{dX}\over {dt}}&=&{2\over {16\pi ^2}}\Bigg [a_u{{\lambda _u^2+\lambda _c^2}
\over {\lambda _u^2-\lambda _c^2}}
\Bigg \{(\hat{\lambda} _b^2-\hat{\lambda} _d^2)XZ
\nonumber \\
&&+{{(\hat{\lambda} _d^2-\hat{\lambda} _s^2)}\over {1-X}}(XYZ-K)\Bigg \}
\nonumber \\
&&+a_u{{\lambda _u^2+\lambda _t^2}
\over {\lambda _u^2-\lambda _t^2}}
\Bigg \{(\hat{\lambda} _b^2-\hat{\lambda} _d^2)X(1-X-Z)
\nonumber \\
&&+{{(\hat{\lambda} _d^2-\hat{\lambda} _s^2)}\over {1-X}}(XY(1-X-Z)+K)\Bigg \}
\nonumber \\
&&+a_d{{\lambda _b^2+\lambda _s^2}
\over {\lambda _b^2-\lambda _s^2}}
\Bigg \{(\hat{\lambda} _u^2-\hat{\lambda} _t^2)XY
\nonumber \\
&&+{{(\hat{\lambda} _t^2-\hat{\lambda} _c^2)}\over {1-X}}(XYZ-K)\Bigg \}
\nonumber \\
&&+a_d{{\lambda _b^2+\lambda _d^2}
\over {\lambda _b^2-\lambda _d^2}}
\Bigg \{(\hat{\lambda} _u^2-\hat{\lambda} _t^2)X(1-X-Y)
\nonumber \\
&&+{{(\hat{\lambda} _t^2-\hat{\lambda} _c^2)}
\over {1-X}}(XZ(1-X-Y)+K)\Bigg \}\Bigg ]
\nonumber \\
&+&{2\over {(16\pi ^2)^2}}\Bigg [{{2d_u\lambda _u^2\lambda _c^2+e_u
(\lambda _u^4+\lambda _c^4)}
\over {\lambda _u^2-\lambda _c^2}}
\Bigg \{(\lambda _b^2-\lambda _d^2)XZ
\nonumber \\
&&+{{(\lambda _d^2-\lambda _s^2)}\over {1-X}}(XYZ-K)\Bigg \}
\nonumber \\
&&+{{2d_u\lambda _u^2\lambda _t^2+e_u(\lambda _u^4+\lambda _t^4)}
\over {\lambda _u^2-\lambda _t^2}}
\Bigg \{(\lambda _b^2-\lambda _d^2)X(1-X-Z)
\nonumber \\
&&+{{(\lambda _d^2-\lambda _s^2)}\over {1-X}}(XY(1-X-Z)+K)\Bigg \}
\nonumber \\
&&+{{2d_d\lambda _b^2\lambda _s^2+e_d(\lambda _b^4+\lambda _s^4)}
\over {\lambda _b^2-\lambda _s^2}}
\Bigg \{(\lambda _u^2-\lambda _t^2)XY
\nonumber \\
&&+{{(\lambda _t^2-\lambda _c^2)}\over {1-X}}(XYZ-K)\Bigg \}
\nonumber \\
&&+{{2d_d\lambda _b^2\lambda _d^2+e_d(\lambda _b^4+\lambda _d^4)}
\over {\lambda _b^2-\lambda _d^2}}
\Bigg \{(\lambda _u^2-\lambda _t^2)X(1-X-Y)
\nonumber \\
&&+{{(\lambda _t^2-\lambda _c^2)}\over {1-X}}(XZ(1-X-Y)+K)\Bigg \}\Bigg ]
\nonumber \;, \\ \label{dXdt}
\\
\nonumber \\
{{dY}\over {dt}}&=&{2\over {16\pi ^2}}\Bigg [a_u{{\lambda _u^2+\lambda _c^2}
\over {\lambda _u^2-\lambda _c^2}}
\Bigg \{{{(\hat{\lambda} _d^2-\hat{\lambda} _b^2)}\over {1-X}}(XYZ-K)
\nonumber \\
&&+{{(\hat{\lambda} _s^2-\hat{\lambda} _d^2)}\over {(1-X)^2}}
Y(XYZ+(1-X-Y)(1-X-Z)-2K)\Bigg \}
\nonumber \\
&&+a_u{{\lambda _u^2+\lambda _t^2}
\over {\lambda _u^2-\lambda _t^2}}
\Bigg \{{{(\hat{\lambda} _b^2-\hat{\lambda} _d^2)}\over {1-X}}(XY(1-X-Z)+K)
\nonumber \\
&&+{{(\hat{\lambda} _s^2-\hat{\lambda} _d^2)}\over {(1-X)^2}}
Y(XY(1-X-Z)+Z(1-X-Y)+2K)\Bigg \}
\nonumber \\
&&+a_d{{\lambda _s^2+\lambda _b^2}
\over {\lambda _s^2-\lambda _b^2}}
\Bigg \{(\hat{\lambda} _u^2-\hat{\lambda} _t^2)XY
\nonumber \\
&&+{{(\hat{\lambda} _t^2-\hat{\lambda} _c^2)}\over {1-X}}(XYZ-K)\Bigg \}
\nonumber \\
&&+a_d{{\lambda _s^2+\lambda _d^2}
\over {\lambda _s^2-\lambda _d^2}}
\Bigg \{(\hat{\lambda} _u^2-\hat{\lambda} _t^2)Y(1-X-Y)
\nonumber \\
&&+{{(\hat{\lambda} _c^2-\hat{\lambda} _t^2)}\over {(1-X)^2}}
(XYZ(1-X-Y)-Y(1-X-Y)(1-X-Z)-K(1-X-2Y))\Bigg \}\Bigg ] \nonumber \\
&+&{2\over {(16\pi ^2)^2}}\Bigg [{{2d_u\lambda _u^2\lambda _c^2
+e_u(\lambda _u^4+\lambda _c^4)}
\over {\lambda _u^2-\lambda _c^2}}
\Bigg \{{{(\lambda _d^2-\lambda _b^2)}\over {1-X}}(XYZ-K)
\nonumber \\
&&+{{(\lambda _s^2-\lambda _d^2)}\over {(1-X)^2}}
Y(XYZ+(1-X-Y)(1-X-Z)-2K)\Bigg \}
\nonumber \\
&&+{{2d_u\lambda _u^2\lambda _t^2+e_u(\lambda _u^4+\lambda _t^4)}
\over {\lambda _u^2-\lambda _t^2}}
\Bigg \{{{(\lambda _b^2-\lambda _d^2)}\over {1-X}}(XY(1-X-Z)+K)
\nonumber \\
&&+{{(\lambda _s^2-\lambda _d^2)}\over {(1-X)^2}}
Y(XY(1-X-Z)+Z(1-X-Y)+2K)\Bigg \}
\nonumber \\
&&+{{2d_d\lambda _s^2\lambda _b^2+e_d(\lambda _s^4+\lambda _b^4)}
\over {\lambda _s^2-\lambda _b^2}}
\Bigg \{(\lambda _u^2-\lambda _t^2)XY
\nonumber \\
&&+{{(\lambda _t^2-\lambda _c^2)}\over {1-X}}(XYZ-K)\Bigg \}
\nonumber \\
&&+{{2d_d\lambda _s^2\lambda _d^2+e_d(\lambda _s^4+\lambda _d^4)}
\over {\lambda _s^2-\lambda _d^2}}
\Bigg \{(\lambda _u^2-\lambda _t^2)Y(1-X-Y)
\nonumber \\
&&+{{(\lambda _c^2-\lambda _t^2)}\over {(1-X)^2}}
(XYZ(1-X-Y)-Y(1-X-Y)(1-X-Z)-K(1-X-2Y))\Bigg \}\Bigg ]
\nonumber \;, \\
\\
\nonumber \\
{{dZ}\over {dt}}&=&{2\over {16\pi ^2}}\Bigg [a_u{{\lambda _c^2+\lambda _u^2}
\over {\lambda _c^2-\lambda _u^2}}
\Bigg \{(\hat{\lambda} _b^2-\hat{\lambda} _d^2)XZ
\nonumber \\
&&+{{(\hat{\lambda} _d^2-\hat{\lambda} _s^2)}\over {1-X}}(XYZ-K)\Bigg \}
\nonumber \\
&&+a_u{{\lambda _c^2+\lambda _t^2}
\over {\lambda _c^2-\lambda _t^2}}
\Bigg \{(\hat{\lambda} _b^2-\hat{\lambda} _d^2)Z(1-X-Z)
\nonumber \\
&&+{{(\hat{\lambda} _s^2-\hat{\lambda} _d^2)}\over {(1-X)^2}}
(XYZ(1-X-Z)-Z(1-X-Y)(1-X-Z)-K(1-X-2Z))\Bigg \}
\nonumber \\
&&+a_d{{\lambda _b^2+\lambda _s^2}
\over {\lambda _b^2-\lambda _s^2}}
\Bigg \{{{(\hat{\lambda} _u^2-\hat{\lambda} _t^2)}\over {1-X}}(K-XYZ)
\nonumber \\
&&+{{(\hat{\lambda} _c^2-\hat{\lambda} _t^2)}\over {(1-X)^2}}
Z(XYZ+(1-X-Y)(1-X-Z)-2K)\Bigg \}
\nonumber \\
&&+a_d{{\lambda _b^2+\lambda _d^2}
\over {\lambda _b^2-\lambda _d^2}}
\Bigg \{{{(\hat{\lambda} _t^2-\hat{\lambda} _u^2)}\over {1-X}}(XZ(1-X-Y)+K)
\nonumber \\
&&+{{(\hat{\lambda} _c^2-\hat{\lambda} _t^2)}\over {(1-X)^2}}
Z(XZ(1-X-Y)+Y(1-X-Z)+2K)\Bigg \}\Bigg ] \nonumber \\
&+&{2\over {(16\pi ^2)^2}}\Bigg [{{2d_u\lambda _c^2\lambda _u^2
+e_u(\lambda _c^4+\lambda _u^4)}
\over {\lambda _c^2-\lambda _u^2}}
\Bigg \{(\lambda _b^2-\lambda _d^2)XZ
\nonumber \\
&&+{{(\lambda _d^2-\lambda _s^2)}\over {1-X}}(XYZ-K)\Bigg \}
\nonumber \\
&&+{{2d_u\lambda _c^2\lambda _t^2+e_u(\lambda _c^4+\lambda _t^4)}
\over {\lambda _c^2-\lambda _t^2}}
\Bigg \{(\lambda _b^2-\lambda _d^2)Z(1-X-Z)
\nonumber \\
&&+{{(\lambda _s^2-\lambda _d^2)}\over {(1-X)^2}}
(XYZ(1-X-Z)-Z(1-X-Y)(1-X-Z)-K(1-X-2Z))\Bigg \}
\nonumber \\
&&+{{2d_d\lambda _b^2\lambda _s^2+e_d(\lambda _b^4+\lambda _s^4)}
\over {\lambda _b^2-\lambda _s^2}}
\Bigg \{{{(\lambda _u^2-\lambda _t^2)}\over {1-X}}(K-XYZ)
\nonumber \\
&&+{{(\lambda _c^2-\lambda _t^2)}\over {(1-X)^2}}
Z(XYZ+(1-X-Y)(1-X-Z)-2K)\Bigg \}
\nonumber \\
&&+{{2d_d\lambda _b^2\lambda _d^2+e_d(\lambda _b^4+\lambda _d^4)}
\over {\lambda _b^2-\lambda _d^2}}
\Bigg \{{{(\lambda _t^2-\lambda _u^2)}\over {1-X}}(XZ(1-X-Y)+K)
\nonumber \\
&&+{{(\lambda _c^2-\lambda _t^2)}\over {(1-X)^2}}
Z(XZ(1-X-Y)+Y(1-X-Z)+2K)\Bigg \}\Bigg ]
\nonumber \;, \\
\\
\nonumber \\
{{dJ}\over {dt}}&=&{-(J/2) \over {16\pi ^2}}\left [a_u\sum _{\beta,j\ne i}
{{\lambda _i^2+\lambda _j^2}\over {\lambda _i^2-\lambda _j^2}}
\hat{\lambda} _{\beta}^2
(|V_{i\beta }|^2-|V_{j\beta }|^2)+a_d\sum _{j,\beta \ne \alpha}
{{\lambda _{\alpha }^2+\lambda _{\beta }^2}\over {\lambda _{\alpha }^2
-\lambda _{\beta }^2}}\hat{\lambda} _j^2
(|V_{j\alpha }|^2-|V_{j\beta }|^2)
\right ] \nonumber \\
&&+{-(J/2) \over {(16\pi ^2)^2}}\left [\sum _{\beta,j\ne i}
{{2d_u\lambda _i^2\lambda _j^2+e_u(\lambda _i^4+\lambda _j^4)}
\over {\lambda _i^2-\lambda _j^2}}
\lambda _{\beta}^2
(|V_{i\beta }|^2-|V_{j\beta }|^2)\right . \nonumber \\
&&\vspace*{1in}\left . +\sum _{j,\beta \ne \alpha}
{{2d_d\lambda _{\alpha }^2\lambda _{\beta }^2+e_d
(\lambda _{\alpha}^4+\lambda _{\beta}^4)}\over {\lambda _{\alpha }^2
-\lambda _{\beta }^2}}\lambda _j^2
(|V_{j\alpha }|^2-|V_{j\beta }|^2)
\right ] \;. \label{dJdt}
\nonumber \\
\end{eqnarray}
Replacing $\hat{\lambda }_i\rightarrow \lambda _i$,
$\hat{\lambda }_{\alpha }\rightarrow \lambda _{\alpha }$ and omitting the
second contributions proportional to $(16\pi ^2)^{-2}$, one recovers the
one-loop results of Babu\cite{Babu} (our definitions of $X$ and $Z$
differ from Ref.~\cite{Babu}). The
two-loop equations have the same overall structure as the one-loop
equations because both contain the same factor
$V_{i\beta }V_{j\beta }^*V_{j\alpha }$ in Eq.~(\ref{dW1dt}).
Eqs.~(\ref{dXdt})-(\ref{dJdt}),
together with the evolution equations for the gauge couplings $g_i$
and the Yukawa couplings $\lambda _i$, form a coupled set of differential
equations that can be solved numerically. In their full form these equations
together with Eqs.~(\ref{Vud})-(\ref{Vtd})
preserve the unitarity of the CKM matrix to all orders in the hierarchy.

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Q: changing the size of textarea using setsize In actionScript,am trying to change the text area using setSize()here is the code..please help me
var prbDesc_txt:TextArea = new TextArea();
prbDesc_txt.text = "Hello world!";
reportAProblemPopUp.addChild(prbDesc_txt);
reportAProblemPopUp.prbDesc_txt.setSize(100,100);

Here am trying to add the textarea to reportAProblemPopUpmc.

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reportAProblemPopUp.prbDesc_txt.setSize(100,100);

remove the reportAProblemPopUp and just reference it directly:
prbDesc_txt.setSize(100,100);

Otherwise you need to use getChildByName() on your reportAProblemPopUp if you want to reference it the way you were thinking of.

redpajama_set_name: RedPajamaStackExchange


With the busy life of most people today, there is need to exercise and keep fit if you want to avoid certain types of diseases. The good news is that you can purchase this piece of equipment and have it in your home whenever you want to use. However, with the increasing number of vendors around, you might easily be swayed into purchasing the wrong equipment if you lack the knowledge on how to go about this. The following for tips should be your ultimate buying guide whenever you want to buy your WBVM.
When choosing which type of dkn xg10 pro machine to purchase, it is important that you do some research in the market or better yet ask the right questions. Unlike in the old days when you'd just walk into a local store and purchase a WBVM basing your reasons on the sales agent recommendations, currently consumers are looking into more. A WBVM is a complex piece of equipment which may be of importance to your physical and psychological wellbeing if bought right. Begin your research by looking for up information concerning the machine online.
Go further and sample some of the opinions and views of previews users of the equipment. Look out for online review sources that are accredited by trustworthy institutions if you are to benefit from your sources. Know more about vibrate at https://en.wikipedia.org/wiki/Vibrate.
WBVM is an equipment that helps you keep fit by sending vibrations throughout your body. While this is the underlying working principle behind WBVM, there is more to it than what meets the eye. Make sure you know what you are buying first before you make the payments as this will help you make the most use of the equipment without compromising on its condition.
When it comes to WBVM Don't Just make blind purchases because Incorrect purchases won't just cost you your money but also your health. Not all WBVM manufacturers can guarantee you on the quality and wellness of your equipment. If you want nothing short of quality then you also need yourself to it. Additionally he should have insurance and also be in a capacity to provide you with warranty for his or her equipment.
Just like with any vibration plate equipment It's Important to test drive Your WBVM before you purchase it. Regardless of how well conditioned an equipment may look in picture, the actual reality of the matter may be different from what is on the ground. You can either pass by your fitness center or shop on stores with WBVM units on displays.


Awesome center console rentals near Kornati, Šibensko-kninska županija.
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Rent or charter a center console to head out for an entire day of fishing and fun during your next vacation in Kornati, Šibensko-kninska županija. Center console boat rentals are great if you're planning an all-day fishing trip during your next family vacation or on a day trip with friends. Book a center console boat for a memorable experience in Kornati, Šibensko-kninska županija.


text:
<?php

namespace o;

class Validator {

    private $parser;

    private $functionScopes = [];
    private $scopes = [];
    private $scopeDepth = -1;

    private $seenVars = [];
    private $userFunctions = [];

    function __construct ($parser) {

        $this->userFunctions = [
            'defined' => [],
            'called'  => [],
        ];

        $this->seenVars = [];

        $this->parser = $parser;
    }

    function error($msg, $token) {

        ErrorHandler::addSubOrigin('validator');
        $this->parser->error($msg, $token);
    }

    function postParseValidation() {

        $this->validateFunctionCalls();
    }

    function newFunctionScope() {

        $this->functionScopes []= $this->scopes;
        $this->scopes = [];
        $this->scopeDepth = -1;
    }

    function popFunctionScope() {

        $this->scopes = array_pop($this->functionScopes);
        $this->scopeDepth = count($this->scopes) - 1;
    }

    function newScope () {

        $this->scopeDepth += 1;

        $this->scopes []= [
            'exact'   => [],
            'fuzzy'   => [],
            'pending' => [],
        ];
    }

    function popScope () {

        $pending = $this->scopes[$this->scopeDepth]['pending'];
        if (count($pending)) {

            // Variable that was not initialized immediately after it appeared in the code
            $undefVarName = array_keys($pending)[0];
            $undefVar = $pending[$undefVarName];

            if ($this->skipLambdaVar($undefVarName)) { return; }

            if ($this->seenVars[$undefVarName]) {
                ErrorHandler::setHelpLink('/language-tour/functions#scope', 'Variable Scope');
            }

            $this->error("Unknown variable: `". $undefVarName . "`", $undefVar->token);
        }

        $this->scopeDepth -= 1;
        array_pop($this->scopes);
    }

    // Check if already defined.  Otherwise wait to see if it is defined.
    function registerVar($symbol) {

        $token = $symbol->token;
        $name = '$' . $symbol->getValue();

        $this->seenVars[$name] = true;

        // implicit vars
        // if ($name == '$this' || $name == '$' || $name == '$$') {
        //     return;
        // }
        if ($this->skipLambdaVar($name)) { return; }

        $this->validateVarFormat($name, $symbol->token);

        $exactName = $this->isDefined($name, 'fuzzy');
        if ($exactName) {
            if ($exactName !== $name) {
                $this->error("Typo in variable name: `$name` Try: `" . $exactName . "` (exact case)", $token);
            }
        }
        else if (isset($this->scopes[$this->scopeDepth]['pending'][$name])) {
            // e.g. $a = $a + 1
            $this->error("Unknown variable: `$name`", $token);
        } else {
            $this->scopes[$this->scopeDepth]['pending'][$name] = $symbol;
        }
    }

    function skipLambdaVar($name) {
        if ($this->parser->lambdaDepth > 0) {
            if ($name == '$a' || $name == '$b' || $name == '$c') {
                return true;
            }
        }
        return false;
    }

    function defineVar($symbol, $isStrict = false) {

        $name = '$' . $symbol->getValue();
        $lowerName = strtolower($name);

        // TODO: fix this workaround -- should not be getting registered
        if ($name == '$[' || $name == '$.') { return; }

        if ($isStrict && $this->isDefined($name, 'fuzzy')) {
            $this->error("Variable already defined in this scope: `$name`", $symbol->token);
        }

        $this->scopes[$this->scopeDepth]['fuzzy'][$lowerName] = $name;
        $this->scopes[$this->scopeDepth]['exact'][$name] = $name;

        unset($this->scopes[$this->scopeDepth]['pending'][$name]);
    }

    // is defined in scope
    function isDefined ($name, $match) {

        if ($name == CompilerConstants::$ANON) {  return false;  }

        if ($match == 'fuzzy') {
            $name = strtolower($name);
        }

        foreach ($this->scopes as $s) {
            if (isset($s[$match][$name])) {
                return $s[$match][$name];
            }
        }

        return false;
    }

    function getAllInScope() {

        $vars = [];

        foreach ($this->scopes as $s) {
            foreach ($s['exact'] as $var) {
                $vars []= $var;
            }
        }

        return $vars;
    }

    function validateFunctionCalls() {
        // Make sure called user functions have been defined (exact match)
        $defined = $this->userFunctions['defined'];
        foreach ($this->userFunctions['called'] as $calledToken) {
            $calledName = $calledToken[TOKEN_VALUE];
            $calledNameFuzzy = strtolower($calledName);

            if (isset($defined[$calledNameFuzzy])) {
                $exactName = $defined[$calledNameFuzzy];
                if ($calledName !== $exactName) {
                    $this->error("Typo in function name: `$calledName` Try: `$exactName` (exact case)", $calledToken);
                }
            }
            else {
                $l = $calledName[0];
                if (!preg_match('/^[A-Z]/', $l)) {
                    $this->error("Unknown function: `$calledName`", $calledToken);
                }
            }
        }
    }

    // mark a function as 'defined' or 'called'
    function registerUserFunction($context, $token) {

        if ($token[TOKEN_VALUE] == CompilerConstants::$ANON) {
            return;
        }

        if ($context === 'defined') {
            $exact = $token[TOKEN_VALUE];
            $lowerName = strtolower($exact);

            if (isset($this->userFunctions['defined'][$lowerName])) {
                $correct = $this->userFunctions['defined'][$lowerName];
                $as = '';
                if ($exact !== $correct) {
                    $as = " as `$correct`";
                }
                $this->error("Function `" . $exact . "` already defined$as.", $token);
            }

            $this->userFunctions['defined'][$lowerName] = $exact;

            if (u_Bare::isa($lowerName)) {
                $this->error("Name `" . $lowerName . "` is already the name of a core function.", $token);
            }
            else if (in_array($lowerName, CompilerConstants::$KEYWORDS)) {
                $this->error("Name `" . $lowerName . "` is a reserved word.", $token);
            }
            else if (preg_match('/^[A-Z]/', $exact)) {
                $this->error("Name `" . $exact . "` must be pure lowerCamelCase.", $token);
            }

        } else {
            $this->userFunctions['called'] []= $token;
        }
    }

    function validateVarFormat($name, $token) {

        if ($name == '$') {
            $this->error("Variable is missing a name.", $token);
        }
        else if (preg_match('/[A-Z]/', $name[1])) {
            $this->error("Variable name `$name` should be lower camelCase.", $token);
        }
        else if (preg_match('/[0-9]/', $name[1])) {
            $this->error("Variable name `$name` must start with a letter.", $token);
        }
        else if (preg_match("/[A-Z][A-Z]/", $name)) {
            $this->error("Variable name `$name` should be pure camelCase.", $token);
        }
        else if (strrpos($name, '_') > -1) {
            $this->error("Variable name `$name` should be camelCase. No underscores.", $token);
        }
        else if (strrpos($name, '$') > 0) {
            $this->error("Variable name `$name` should have only one `$` prefix.", $token);
        }
        else if (strlen($name) > CompilerConstants::$MAX_WORD_LENGTH) {
            $this->error("Variable names must be " . CompilerConstants::$MAX_WORD_LENGTH . " characters or less.", $token);
        }
    }

    function validateWordFormat($name, $token, $type) {

        if (strrpos($name, '_') > -1) {
            $this->error("Word `$name` should be camelCase. No underscores.", $token);
        }
        else if (preg_match("/[A-Z][A-Z]/", $name)) {
            if (preg_match("/^[a-z]/", $name)) {
                $this->error("Word `$name` should be pure lowerCamelCase.", $token);
            }
            else {
                $this->error("Word `$name` should be camelCase or UpperCamelCase.", $token);
            }
        }
        else if (strlen($name) === 1 && $name >= 'A' && $name <= 'Z') {
            $this->error("Word with only 1 character must be lower-case.", $token);
        }
        else if (strrpos($name, '$') > -1) {
            $this->error("Non-variable word can not contain a `$`.", $token);
        }
        else if (strlen($name) > CompilerConstants::$MAX_WORD_LENGTH) {
            $this->error("Words must be " . CompilerConstants::$MAX_WORD_LENGTH . " characters or less.", $token);
        }
    }

    function validateFlagFormat($name, $token) {

        if (preg_match("/[A-Z][A-Z]/", $name) || preg_match("/^-[A-Z]/", $name)) {
            $this->error("Flag `$name` should be lowerCamelCase.", $token);
        }
    }
}

redpajama_set_name: RedPajamaGithub


Those of you that know me or have been reading this blog for a long time will know that I am a huge fan of James Joyce, in particular his book Ulysses. I think this book will teach you more about NLP and the use of language than most NLP books written (read my post on it here)!
Today is "Bloomsday", the day in which Ulysses is set and the day Joyce fans celebrate his work.
BBC Radio 4 are celebrating Bloomsday by broadcasting a brand new recording of Ulysses. Joyce came from the bardic traditional and I am sure he wrote Ulysses to be read out loud and to be heard. You can listen to it and download the podcasts here (I think it is UK only I am afraid).


If the Admirals come out of every 3-in-3 set this year with four points, that'll bode well for the team.
Both the Admirals and San Antonio Rampage were playing their third game in three days Sunday evening, but a pair of first period Admiral goals created a hill that was too steep for the Rampage to climb, as the Admirals were victorious 3-1.
Coach Muller says the last two games have been some of the most complete hockey the team has played this year.
Why has the team been good so far closing out the three-in-three sets?
At 10:04 of the first period, Kyle Wilson gathered the puck along the near side boards and sent a pass to Juuso " I'd like to buy a U" Puustinen. Juuso fired a slapper that beat Brian Foster top left to give the Ads the early lead. Puusitinen did a great job of getting into the open area, but full credit goes to Wilson who got the pass right on the tape while fighting for the puck along the boards.
Just over 5 minutes later Chris Mueller got a great feed from Taylor Beck to give the Ads the 2-0 lead. With Beck behind the net he fought off a defender and sent a nifty "no look" pass to the slot where a crashing Mueller got his stick on it and put it towards Foster. It looked like Foster had it covered up, but either through a helping attempt by his own D-man or just sheer determination the puck squeezed though Foster's 5 hole and trickled across the line for the goal.
The Rampage struck back at 14:30 of the second period with Bracken Kearns getting the tally. Kearns was skating in and attempted a shot on net when Victor Bartley went to the ice and deflected the shot. The puck bounced off of Bartley and was re-aquired by Kearns who fluttered a shot that beat Smith. It was a great second effort by Kearns to finish the play.
The Admirals went back on the attack right away. This time it was Ryan Ellis who found himself on the GOOD side of a scoring play giving the Ads the 3-1 lead. Just as Nolan Yonkman's two minute sentence ended at the Penalty Box Penitentiary, Gabriel Bourque dished a pass from behind the net into the slot where it found Ellis' stick. Ellis wasted no time in sending the puck towards the net, beating Foster, who looked like he was over-committed on Bourque.
And that would be all of the scoring for this game as the Admirals cruised to the 3-1 victory.
– As aforementioned, it was very nice to see Ellis find a way to help his team offensively especially since he has been the center of many discussions around our water cooler on his recent string of bad turnovers and their direct correlation to goals against. An improved game from him tonight, so Ryan Ellis — EYE Salute You.
– The Admirals again held their opponent to a low number of shots….it was 15 shots on goal tonight. We asked Coach what he credits for that.
– Joel Champagne returned to the lineup as Ben Ryan sat out. And this was the second straight game that Coach Muller went with Taylor Aronson instead of Scott Valentine on the D. Here are Coach's thoughts on the lineup changes.
– Good cheese race tonight.
– So the week ahead. They'll probably do what the rest of the hockey world will be doing….watch the griping reality television that will be Sidney Crosby's return to action. It'll be a TV event not unlike the first time they put a man on the moon. Everyone will remember where they were the night that Cindy Criesby was cleared to play an NHL game. Of course they saved it for November sweeps!!!
So that'll happen. And then they'll prepare for a pair of weekend games against the Charlotte Checkers after Thanksgiving.
Glad to see them win, but there is no physical presence at all besides two big hits.
The team played well in all three periods. I loved the Victor Bartley hit on Kearns. The BC may have to fix the boards at that spot!
Raul/Taylor — are you only in it for the fights? That seems to always be your #1 gripe.
Next time, I'll sucker punch my girlfriend, should satisfy any fight needs.
My main gripe is the stinky kid who sits in front of us. I can't carry in a soda from Panera, but they can't mandate a shower?
Anywho, good game, was very surprised at how much more energy they had in this game than San Antonio and based on Lata's intermission interview, you knew damn well these guys were gassed.
That is one of my favorite parts of the game. I said I was glad they won, sorry for stating my thoughts.
And in a game played so well by the team yesterday, I think that is the only "gripe" to have.


This is a placeholder page for June Menard, which means this person is not currently on this site. We do suggest using the tools below to find June Menard.
You are visiting the placeholder page for June Menard. This page is here because someone used our placeholder utility to look for June Menard. We created this page automatically in hopes June Menard would find it. If you are not June Menard, but are an alumni of Montpelier High School Montpelier, VT, register on this site for free now.


text:
Crewsaver unveils new safety lines at METSTRADE
The Crewline Pro range Photo: Crewsaver
Crewsaver Ltd
Crewsaver has launched a range of new safety lines.
The Crewline Pro safety line range is designed for those who have a need to tether to a yacht in unstable conditions, where there may be risk of falling overboard.
"Our goal is to introduce a brand-new safety line range, for those in high performance racing environments, where nothing but the best technology will do," explained Crewsaver's commercial director, Matt Bridge.
The full range
Self-locking safety hooks with a wide opening allow the user to easily attach the Crewline Pro to the lifejackets or safety harness attachment point and a suitable anchor point on the yacht as required.
The hydrophobic webbing helps to keep the safety line as light as possible, even in the harshest environments, as it reduces the amount of water absorbed compared with more conventional safety lines. The range is available in four models including elastic and non-elastic with a choice of a single, double or triple hook set up.
Crewline Pro is ISO 12401 approved and includes an overload indicator which is activated once placed under an excessive load of 400kg. The range will be available from March 2020.
Start-up Crewbands, is ready to launch its person-over-board (POB) system....
Crewbands POB ready to launch 15/01/20
Spinlock has developed a top-of-the-range automatic inflating lifejacket harness - the Deckvest 6D....
Spinlock continues development... 15/01/20
Plastimo plays an import role in the design and manufacture of safety products and has more than 50 years' experience perfecting this, explains Richard Pardoe of UK distributor Aquafax....
Plastimo - supporting marine s... 14/01/20

redpajama_set_name: RedPajamaCommonCrawl


The organization is primarily for French speaking expatriates, but other nationalities living in Delhi/NCR are welcome. Currently, they have over 240 members and it is run by expatriate housewives. Once a week they have a coffee morning and organise other regular activites.
Salaam Baalak Trust is an Indian non-profit and non-governmental organization that provides a sensitive and caring environment to street and working children in Delhi. They help nurture their dreams and make them realize that their fate can be crafted by their own heart, their own hands and a firm resolve.


text:
Q: File upload progress Custom page RestAPI SPO The code below is working fine to upload files to SPO through RestAPI. No feedback is received on file upload progress. An alert is thrown once the upload is complete.
I would like to have a progress bar to display the upload percentage and reload this upload page while clicking OK to the successful alert message.
Kindly assist.

<link rel="stylesheet" href="https://code.jquery.com/ui/1.12.1/themes/base/jquery-ui.css">

Select File:<input type="File" id="inputTypeFiles" />

Departname: <input id="departname" type="textbox"/>

Date: <input type="text" id="datepicker" autocomplete="off" name="hidden">

Filename: <input id="filename" type="textbox"/>

ACFTREG: <select id="ACFTREG" class="select">
<option selected="selected">Select</option>

<input type="button" id="btnUploadFiles" value="Upload"/>

A: Inside the $.ajax({}) function, you can add the xhr setting inside the ajax.
$.ajax({
xhr: function() {
    var xhr = new window.XMLHttpRequest();
    xhr.upload.addEventListener("progress", function(evt) {
        if (evt.lengthComputable) {
            var percentComplete = (evt.loaded / evt.total) * 100;
            // Place upload progress bar visibility code here
        }
    }, false);
    return xhr;
},
type: 'POST',
//add the rest of ajax settings

check this link for ajax documentation
jQuery/ajax
check this link for example on upload progress
jQuery-upload-progress/example


text:
Blind Skier Races Up to 70 MPH
Danelle Umstead uses Bluetooth to negotiate the mountains.
Hurtling through the dark, Danelle Umstead can't see anything as she skis down the slopes.
Instead, the blind alpine ski racer relies on communication with her husband and guide, via Bluetooth technology, to get her down safely, CNN reports.
Umstead was diagnosed with retinitis pigmentosa at 13 and her vision steadily deteriorated after that.
"It seemed like my life was just crumbling day by day," she told CNN. "I spent a long time feeling like there was not an easy way out or a way out at all."
But then her dad called her up and invited her to go skiing. "He said, 'We're gonna go skiing. ... I'm gonna be your eyes, and you and I are gonna go skiing.' We went down the mountain, and my life changed from that moment forward."
Umstead competes on the US Paralympic Team and won two bronze medals in 2010. The she was diagnosed with multiple sclerosis, and had to learn how to walk again. But her determination got her back on skis to compete again at the Paralympic Games in Sochi, Russia, where she brought home another bronze. Now she's aiming for the 2018 games in South Korea.


River Peak Dental is proud to provide modern dentistry services here in the beautiful rural town of Ridgway, Colorado. Cosmetic dentistry is used to help patients who wish to improve the appearance of their smiles. Our entire dental staff believes that everyone deserves to have a beautiful smile that they feel confident showing off. Dr. Chris Poe, DDS, leads River Peak Dental with excellence and specific training in cosmetic dentistry to help you achieve the smile that you have always wanted.
Dr. Chris Poe, DDS, believes that everyone deserves a beautiful smile, and he is committed to helping patients not only achieve optimal oral health, but also a smile that is attractive in its appearance. Our dental practice utilizes the latest in technology in order to help patients achieve the smile that they have dreamed about for years. Your smile is one of the most recognized features on your face, and people gather a great deal about who you are by how easily you share your smile with others. If you are feeling self-conscious about the appearance of your smile it will keep you from sharing it – causing people to think of you as unfriendly or unapproachable.
At River Peak Dental, we are committed to helping you achieve the smile that you have always wanted. Our modern dental practice is led by our trusted dentist, Dr. Poe, and we are here to help you reveal a beautiful and confident smile. Contact us today to schedule a consultation regarding any of our cosmetic dentistry treatments.


The "Manage My Relay" platform has been temporarily decommissioned.
As part of the Relay For Life brand update, the Cancer Council team is currently working on updating all of the resources and collaterals necessary to support your preparations and fundraising.
In the meantime, please feel free to access our Useful Downloads section.


For some, the crisis in Venezuela is all about the endemic corruption of Nicolás Maduro, continuing the broken legacy of Chavez's ideological experiment in socialism under the mounting insidious influence of Putin. For others, it's all about the ongoing counter-democratic meddling of the United States, which has for years wanted to bring Venezuela — with its huge oil reserves — back into the orbit of American power, and is now interfering again to undermine a democratically elected leader in Latin America.
Neither side truly understands the real driving force behind the collapse of Venezuela: we have moved into the twilight of the Age of Oil.
So how does a country like Venezuela with the largest reserves of crude oil in the world end up incapable of developing them? While various elements of socialism, corruption and neoliberal capitalism are all implicated in various ways, what no one's talking about — especially the global oil industry — is that over the last decade, we've shifted into a new era. The world has moved from largely extracting cheap, easy crude, to becoming increasingly dependent on unconventional forms of oil and gas that are much more difficult and expensive to produce.
Oil isn't running out, in fact, it's everywhere — we've more than enough to fry the planet. But as the easy, cheap stuff has plateaued, production costs have soared. And as a consequence the most expensive oil to produce has become increasingly unprofitable.
In a country like Venezuela, emerging from a history of US interference, plagued by internal economic mismanagement, combined with external intensifying pressure from US sanctions, this decline in profitability became fatal.
This entry was posted in Energy, Foreign Policy, Geopolitics, Governments, History and tagged Oil, Venezuela. Bookmark the permalink.


text:
BRAINTREE – On Jan. 21, MacDonald and a busload of 54 local women will head to the nation's capital for the Women's March on Washington, an anti-Trump demonstration to take place after the Presidential Inauguration. The march has garnered national attention and earned the blessing of Bernice King, the Rev. Dr. Martin Luther King Jr's youngest daughter.
Soon after the election, MacDonald began organizing a bus to bring participants to the march in D.C, and it reached capacity within six weeks.
"I just felt like I needed to do something. I was grief stricken and overwhelmed (when Trump was elected)," she said. "Doing nothing and staying silent is affirming his message and saying that our rights don't matter."
People like MacDonald, 55, have popped up all over the East Coast to help women get to the march, which could draw more than 100,000 attendees. Buses are also leaving from Boston, Cambridge and Providence, among others.
"We are sending a message to the president elect and to all our elected officials that this is not what we expect from the president," MacDonald said.
Florence Rawls, of Dorchester, plans to be on the bus, which leaves from the Braintree MBTA station at 12:30 a.m. on Saturday, Jan. 21.
"The decision was made before I thought about it," Rawls said. "I'm 71, and I come from a background in the '60s of participatory action. You have to show up."
Rawls cited women's health issues, threats to services like Planned Parenthood and a plethora of legislative issues as concerns going into the Trump administration.
"You keep supporting people who have agendas you believe in, but the sense now is all the progress is going to be ripped out from under us," she said.
MacDonald said the response to her organizing has been mixed. When she posted about the trip on a community page online, she said there were plenty of comments from those criticizing her for not supporting the next president, but also a number of positive responses from women.
"For me, it's very personal," MacDonald said. "I feel like I'm in the twilight zone. We have to become vigilant and we cant act like this is normal."
Mary Whitfill may be reached at mwhitfill@ledger.com.


Alan arrived at Latymer Upper School on a scholarship in 1956. It was in the School's Main Hall that the young Alan first trod the boards, treating his audience to lively performances in many a school play. These shows sparked a love of drama that would shape his life to come.
« Alan's performances reached across the generations. Many of our alumni remember him from his theatre performances as a member of the RSC, including his Tony nominated role as Vicomte de Valmont in the play Les Liaisons Dangereuses, or from his parts in the films Truly, Madly, Deeply, Robin Hood: Prince of Thieves and Die Hard, to mention but a few. But it is his role as Severus Snape in the Harry Potter film series that resonates so strongly with our current pupils.
Alan was hugely supportive of his old school. He was due to speak at a Latymer event in aid of the School's Bursaries Appeal only this month – a cause very dear to his heart having attended Latymer Upper, as he did, on a free place. Alan's speech at one of the School's Prize Giving evenings was captivating – and reflective of his views. In it he tasked Latymerians to decide "what sort of person" they are and to make a difference to the world. Today's children were the "hopes and voices" of so many people – in a few years they could be in seats of power and he called for them to show imagination and to be "brave and socially and globally responsible".
Hello, you would know when is Alan's funeral and where?


OSTI.GOV Conference: The Development of the Heliostat Focusing and Canting Enhancement Technique.
Title: The Development of the Heliostat Focusing and Canting Enhancement Technique.
Conference: Proposed for presentation at the ASME 2011 Energy Sustainability Conference held August 7-10, 2011 in Washington DC.
Chavez, Kyle Feliciano, Yellowhair, Julius, and Sproul, Evan. The Development of the Heliostat Focusing and Canting Enhancement Technique.. United States: N. p., 2011. Web.
Chavez, Kyle Feliciano, Yellowhair, Julius, & Sproul, Evan. The Development of the Heliostat Focusing and Canting Enhancement Technique.. United States.
Chavez, Kyle Feliciano, Yellowhair, Julius, and Sproul, Evan. Mon . "The Development of the Heliostat Focusing and Canting Enhancement Technique.". United States. https://www.osti.gov/servlets/purl/1106091.
Development and Analysis of the Heliostat Focusing and Canting Enhancement Technique for Full Heliostat Alignments.
The Development of the Heliostat Focusing and Canting Enhancement Technique: An Optical Heliostat Alignment Tool for the National Solar Thermal Test Facility.
Heliostat canting and focusing methods : an overview and comparison.
Canting of heliostat facets using a target in reflection.


text:
Q: Android - Firestore toObject() cannot deserialize an object with a nested Array of Strings This is my Class data model in Firestore:

Here is the Class in my Kotlin model.
data class Class(
    var teacher: String = "",

    val capacity: Int = 0,

    val location: String = "",

    var roster: List<String> = ArrayList() // this doesn't work and neither does String or HashMap<String, String>
)

I attempt to grab the data for the class as such using Coroutines:
val snapshot = database.collection("class").get().await()
val class = snapshot.toObject(Class::class.java)

However, it fails to map the roster to an ArrayList and gives me the following stacktrace:

E/FirebaseServiceImpl: getClass: FAILURE java.lang.RuntimeException: Could not deserialize object. Expected a List, but got a class java.lang.String (found in field 'roster')
--------- beginning of crash
E/AndroidRuntime: FATAL EXCEPTION: main
Process: com.packagename.myapp, PID: 8809
java.lang.RuntimeException: Could not deserialize object. Expected a List, but got a class java.lang.String (found in field 'roster')

I've also tried making roster a String and a HashMap but when I do it says it detects an ArrayList.
How can I grab an array of strings nested within an object if I'm using toObject()?

A: OK, so there was absolutely nothing wrong with the code, it seems. When I deleted the collection and re-uploaded my collection's seed data to Firebase it resolved my issues, and I changed nothing in the code. Unfortunately I can't say what caused it but if you're having a similar issue maybe re-importing your data will help as well?


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A seven-year-old boy from Hyderabad became one of the youngest people to scale Mount Kilimanjaro.
Posted byVikram Roy Mehta March 17, 2021 March 17, 2021 Posted inIndia, News, TrendingTags:Bharat Thammineni, Cricket, highest mountain in Africa, Horombo hut, Mount Kilimanjaro, Skating, Uhuru peak, Virat Chandra Telukunta, Yoga
Mount Kilimanjaro soars almost 5,895 metres above sea level and is the highest mountain in Africa as well as the highest single free-standing mountain in the world. Embarking on an expedition to Mount Kilimanjaro is never easy feet to achieve, it can be the pinnacle of a climbing career and a seven-year-old boy from Hyderabad became one of the youngest people to scale the highest single free-standing mountain in the world. Every year thousands of men and women alike set their goals to make it to the highest point.
Yes, you read it right, Virat Chandra Telukunta etched his names in history books by becoming one of the youngest people to scale Mount Kilimanjaro. In doing so, the youngster has made the whole country proud as he climbed the highest mountain in Africa. He achieved this foot on 6th March along with his coach Bharat Thammineni post doing one-month of rigorous training.
Virat has the passion to climb ever hence he heard inspirational stories of the experiences of his cousins. The youngster got very motivated when saw his cousins at Rudugaira Mountains in Uttarakhand where they had gone for a trekking trip. He shared his dream with his parents and which led to his parents contacting now coach Bharath to train him. The seven-year-old and his life trainer followed all the protocol during the journey.
Telangana: A seven-year-old boy, Virat Chandra, from Hyderabad has scaled Mount Kilimanjaro, the highest mountain in Africa
"We took all precautions & had decided that we'd return if he'd feel uneasy but he made us proud," said Bharat, who led Virat's expedition (15.03) pic.twitter.com/Z04qwwQvn6
His coach Bharat Thammineni was quoted saying, his pupil was very thrilled to train, was astonished to with his determination to finish training and did not quit midway through the training sessions. Virat too preparation very seriously and finished all the tasks such as running and mock climbing with dedication. While Interacting with ANI, Bharat Thammineni was quoted saying, "we had started the journey on March 5 and in between we took rest. As Virat is still a child so all us took all the precautions so that he does not feel uneasy. We started the climb on March 5 and reached the Uhuru peak of Kilimanjaro on March 6."
Talking about his experience of climbing the highest single free-standing mountain in the world was quoted saying, "My parents accompanied me until Horombo hut. From there, I continued the journey with my guides. It took almost five hours to reach Kibo hut, which is at an elevation of 4,720 metres, also had to deal with heavy snow and windy conditions at that place. I was frightened because it was still dark. I could hear the wind whistling and there was a heavy downpour of snow. It took almost eight hours to reach the summit. I am happy to accomplish the mission."
Watch | 7-year-old Virat Chandra Telukunta from Hyderabad scales Mount Kilimanjaro
(Video: ANI) pic.twitter.com/z50NswGXsL
— NDTV (@ndtv) March 16, 2021
Besides Climbing, The Class 2 student also enjoys Skating, playing Cricket, running 6 km every day and doing yoga. "I even took part in a 5K run to prove my mettle. "My guides said Mt Kilimanjaro would be ideal to travel and climb."
Inspirational Story: CA Bhavani Devi became the first-ever Indian fencer to qualify for the Tokyo Olympics!
The sensational duo of Saurabh Chaudhary and Manu Bhaker Create another record at ISSF World Cup in Delhi


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States General of the Netherlands
Legislature of the Netherlands
States General
Staten-Generaal
Jan Anthonie Bruijn, VVD
since 2 July 2019
Khadija Arib, PvdA
since 13 January 2016
150 Representatives
Senate political groups
VVD (12)
CDA (9)
Opposition (43)
PvdA (6)
PVV (5)
PvdD (3)
FvD (2)
SGP (2)
OSF (1)
Ind. groups (10) [a]
Van Pareren (7)
Otten (3)
House of Representatives political groups
Government (75) [1]
D66 (19)
PVV (20)
DENK (3)
Member Krol ( 1)
Member Van Kooten (1)
Vacant (1)
Senate voting system
Indirect election
House of Representatives voting system
Party-list proportional representation
Senate last election
House of Representatives last election
The Hague, Netherlands
staten-generaal.nl
The States General of the Netherlands ( Dutch: Staten-Generaal [ˌstaː.tə(n).ɣeː.nəˈraːl] ( listen)) is the bicameral legislature of the Netherlands consisting of the Senate (Eerste Kamer) and the House of Representatives (Tweede Kamer). Both chambers meet at the Binnenhof in The Hague.
The States General originated in the 15th century as an assembly of all the provincial states of the Burgundian Netherlands. In 1579, during the Dutch Revolt, the States General split as the northern provinces openly rebelled against Philip II, and the northern States General replaced Philip II as the supreme authority of the Dutch Republic in 1581. The States General were replaced by the National Assembly after the Batavian Revolution of 1795, only to be restored in 1814, when the country had regained its sovereignty. The States General was divided into a Senate and a House of Representatives in 1815, with the establishment of the United Kingdom of the Netherlands. After the constitutional amendment of 1848, members of the House of Representatives were directly elected, and the rights of the States General were vastly extended, practically establishing parliamentary democracy in the Netherlands.
Since 1918, the members of the House of Representatives are elected for four years using party-list proportional representation, while the 75 members of the Senate are elected by the States-Provincial every four years. On exceptional occasions, the two houses form a joint session known as the United Assembly. The President of the Senate serves as President of the States General during a United Assembly. Jan Anthonie Bruijn ( VVD) has been President of the Senate since 2019.
2.1 Burgundian and Habsburg rule
2.2 Dutch Republic
2.3 Kingdom of the Netherlands
4 Oldest living members of the States General
5 Notes and references
The archaic Dutch word staten originally related to the feudal classes (" estates", or standen in Dutch) in which medieval European societies were stratified; the clergy, the nobility and the commons. The word eventually came to mean the political body in which the respective estates were represented. Each province in the Habsburg Netherlands had its own staten. These representative bodies (and not their constituent estates) [2] in turn were represented in the assembly that came to be known as Staten-Generaal (a plurale tantum), or Algemene Staten (General States). [3]:5–15 The English word "states" may have a similar meaning as the Dutch word staten, as in e.g. States of Jersey. The English phrases "States General" is probably a literal translation of the Dutch word. [4] Historically, the same term was used for the name of other national legislatures as, for example, the Catalan and Valencian Generalitat and the Estates General of France during the Ancien Régime.
Several geographic place names are derived from the States General. In 1609, Henry Hudson established Dutch trade in Staten Island, New York City and named the island Staaten Eylandt after the States General. Isla de los Estados, now an Argentine island, was also named after this institution, the Spanish name being a translation of the Dutch name. Abel Tasman originally gave the name Staten Landt to what would become New Zealand. Staaten River is a river in the Cape York Peninsula, Australia.
Burgundian and Habsburg rule
Historically, the convocation of the States General consisted of delegates from the States of the several provinces, like the States of Brabant, and dated from about the middle of the 15th century, under the rule of the Dukes of Burgundy. The first important session was the Estates General of 1464 that met on 9 January 1464 in Bruges, Flanders, on the initiative of the States of Holland, the States of Flanders, and the States of Brabant, with the initially reluctant agreement of Philip the Good. [3]:31 Later, regular sessions were held at Coudenberg in Brussels, Brabant. The next important event was the convocation of the States General by the ducal Council for 3 February 1477 after the death of Charles the Bold. In this session the States General forced the grant of the Great Privilege by Mary of Burgundy in which the right of the States General to convene on their own initiative was recognised. [3]:42ff. The main function of the States General in these early years was to form a platform for the central government to discuss matters of general importance with the States of the provinces, especially the special subsidies known as beden or aides. Legislative and executive functions were still reserved for the Sovereign in these years [3]:29,35–36, 97
The Great Assembly of the States General in 1651.
At the start of the Dutch Revolt the States General (who were then not continually in session) remained loyal to the overlord of the Habsburg Netherlands, Philip II of Spain (who did not have the title of King in the Netherlands, but held the title of duke and count in the several provinces). In 1576 the States General as a whole, however, openly rebelled against the Spanish crown. In 1579 the States General split as a number of southern provinces, united in the Union of Arras returned to obedience, while other provinces, united in the Union of Utrecht continued the rebellion. [3]:260–268,288–296 After the Act of Abjuration in 1581 the northern States General replaced Philip II as the supreme authority of the northern Netherlands, which then became known as the United Provinces.
This was a confederation in which most government functions remained with the provincial States (and local authorities, like the Vroedschappen). These delegated representatives to the States General as a kind of ambassadors acting with a mandate limited by instruction and obligatory consultation (last en ruggespraak). The States General, in which the voting was by province, each of the seven provinces having one vote, [5] took on many executive functions after the Council of State of the Netherlands had temporarily come under English influence, due to the Treaty of Nonsuch. [3]:305–315 [6]:293–294 The States General for this reason since 1593 remained continually in session until their dissolution in 1795. The presidency rotated weekly among the senior representatives of the provinces. Under the Union of Utrecht treaty the States General formally was the sovereign power, representing the Republic in foreign affairs and making treaties with foreign monarchs. [6]:292–293 As such the honorific title of the States General collectively was Hoogmogende Heren (mightiest, or very mighty, lords). [7]
The Binnenhof, seat of the Staten-Generaal
Due to the vagaries of the Eighty Years' War in which territories were lost and (partially) reconquered, not all territories that had originally signed up for the Union of Utrecht remained represented in the States General. The States of Brabant and of Flanders lost their representation after 1587 as most of their territory had been conquered by the Army of Flanders, and it was not restored after part of that territory (together with parts of the Duchy of Limburg) was reconquered by the Dutch Republic. The Drenthe territory was never directly represented in the States General. Twenty per cent of the new Republic's territory, known as the Generality Lands, was so under the direct rule of the Generality (generaliteit). [6]:297–300 The Dutch East India Company and the Dutch West India Company were also under its general supervision; for this reason Staten Island in New York City (originally New Amsterdam) and Staten Island, Argentina (Discovered by Dutchman Jacob le Maire), are among places named after the Staten-Generaal.
The "southern" States General after 1579 were a continuation of the States General as they had been under the Habsburg Netherlands. After the (re)conquest of most of the territory of the States of Brabant and of Flanders these States again sent representatives to these States General for the Southern Netherlands, together with the "obedient" provinces of the Union of Arras. The southern States General only occasionally came in session, however. The last regular session was in 1634, when Philip IV of Spain dissolved them. [3]:315–321
The States General in both The Hague and Brussels came to an end after 1795; the South was annexed by France, and the North saw the proclamation of the Batavian Republic and the subsequent convocation of the National Assembly (1 March 1796).
The Trêveszaal, where the Council of the Ministers takes place every week and foreign delegations are received
The name Staten-Generaal was resurrected in the title of subsequent Dutch parliaments in and after 1814, after the end of the annexation to the First French Empire by Napoleon I of France in 1813. These had, however, little resemblance to the States General under the Republic. Beginning with the Sovereign Principality of the United Netherlands the States General was a unicameral legislature, without executive functions, in which the 55 representatives no longer represented the States-Provincial (though those newly constituted entities elected them, now acting as electoral colleges), but the entire people of the Netherlands and without last en ruggespraak (the Netherlands had become a unitary state under the Batavian Republic and the federal structure of the Dutch Republic was not restored). [8]:136 The States General became a bicameral legislature under the United Kingdom of the Netherlands in 1815, in which the 50 members of the Senate were appointed for life by the new King from the resurrected ridderschappen, representative bodies of the aristocracy, and the 110 members of the House of Representatives (55 for the North and 55 for the South) were elected by the States-Provincial (in their new form). [8]:138
After the Belgian Revolution of 1830 under the Kingdom of the Netherlands the States General remained bicameral, but after the revision of the Constitution of the Netherlands in 1848, the (now 39) members of the Senate were elected by the States-Provincial, and the members of the House of Representatives were directly elected in electoral districts (one for every 45,000 electors, so the number of members of that House became variable for a while). The House of Representatives became more powerful at the same time, as it received the important rights of inquiry and amendment, while its budgetary rights were strengthened. Formally, the position of the States General was strengthened, because henceforth the ministers of the Crown became politically accountable to them, making the role of the King largely ceremonial. [8]:142–145
With the constitutional revision of 1888 the number of members of the House of Representatives was fixed at 100, while the Senate was enlarged to 50 members. The suffrage was enlarged at the same time, but still limited to male citizens possessing a certain wealth. Universal male suffrage would be granted in 1917 and women would receive suffrage in 1919. At this occasion, the electoral system was changed to proportional representation. The States General were suspended from 1940 to 1945, during the German occupation. In 1956 the number of members of the Senate was enlarged to 75, and that of the House of Representatives to 150. [8]:151,153–155, 329
The Dutch Senate (Eerste Kamer)
The Dutch House of Representatives (Tweede Kamer)
King Willem-Alexander giving the annual speech from the throne in the Ridderzaal, 2015
This article is part of a series on the
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Speaker: Khadija Arib
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The States General meets in joint session at least once a year, at the opening of the parliamentary year, when the king gives his Speech from the Throne on Prince's Day. On special occasions, such as when a States Generate vote on a marriage of a member of the royal house, an inauguration of the monarch, or the death of a member of the royal house, both houses also meet in a joint session (Verenigde Vergadering), with the President of the Senate presiding. They take place in the Ridderzaal (Hall of Knights) in the Binnenhof, except for the inauguration of the monarch, which occurs in the Nieuwe Kerk in Amsterdam. The rest of the time, the two chambers sit separately.
Constitutionally, all functions of the parliament are given to both houses, except for the rights of initiative and amendment, which only the Tweede Kamer has. The Joint Session also appoints the monarch if there is no heir to the throne and the regent is unable to exercise his or her powers. [9]
An important question is whether the relationship between cabinet and parliament should be dualistic or monistic. That is, whether ministers and leaders of governing parliamentary parties should prepare important political decisions. According to the dualistic position, members of parliament of governing parties should remain independent of the cabinet. The term 'monism' is used to refer to a stance that important decisions should be prepared by the people of the governing coalition in order to promote political stability.
Oldest living members of the States General
Cabinet position
1 Ton van Baars (1922-03-06) 6 March 1922 (age 98) Catholic People's Party 15 April 1980 – 10 June 1981
(1 year, 56 days)
19 January 1982 – 3 June 1986
(4 years, 135 days) 5 years, 191 days [10]
2 Jan Reehorst (1923-03-21) 21 March 1923 (age 97) Labour Party 23 October 1956 – 21 February 1967
(10 years, 121 days) [11]
3 André Mensert Spaanderman (1924-10-10) 10 October 1924 (age 96) Democratic Socialists '70 11 May 1971 – 7 July 1971
(57 days) [12]
4 Johan Visser (1925-10-28) 28 October 1925 (age 95) Labour Party 5 March 1968 – 10 May 1971
(3 years, 66 days) [13]
Edmundson, George (1911). "Netherlands" . In Chisholm, Hugh (ed.). Encyclopædia Britannica. 19 (11th ed.). Cambridge University Press. pp. 413–421.
^ Schaart, Eline (2019-10-07). "Dutch coalition loses majority in parliament". Politico Europe. Retrieved 2019-10-07. The Dutch coalition government on Monday lost its majority in parliament when an MP who had been expelled from Prime Minister Mark Rutte's party said he would sit as an independent.
^ Unlike the Estates General of France, which were organised by estate.
^ a b c d e f g Koenigsberger, H.G. (2001). Monarchies, States Generals and Parliaments: The Netherlands in the Fifteenth and Sixteenth Centuries. Cambridge U.P.
^ In treaties, such as the Treaty of Westminster (1654), the States General were called:"Celsos Potentesque Dominos Ordines Generales Foederatarum Belgii Provinciarum", or "High and Mighty Lords States General of the united Netherlands' Provinces", where ordines corresponds with "states."
^ Martin, Kimberly. "The Political Institutions of the Dutch Republic, 1572–1672" (PDF). umassd.edu. University of Massachusetts Dartmouth. Retrieved 4 June 2014.
^ a b c Israel, Jonathan I. (1998). The Dutch Republic: Its Rise, Greatness and Fall, 1477–1806. Clarendon Press.
^ Hoogmogende ( superlative of the adjective mogend(e)) Heren was translated into Latin in international treaties not as potentissimos (superlative of potens) Dominos, as it should have been, but as Celsos Potentesque Dominos, and the latter wording was rendered in English as "high and mighty lords", which is still the standard translation.
^ a b c d Pot, C.W. van der; et al. (2006). Van der Pot, Handboek van het Nederlandse staatsrecht, 15th edition. Kluwer.
^ "Democracy in the Netherlands". www.houseofrepresentatives.nl. April 12, 2011.
^ (in Dutch) Drs. A.W.B. (Ton) van Baars Parlement & Politiek
^ (in Dutch) J. (Jan) Reehorst Parlement & Politiek
^ (in Dutch) Mr. A.P. (André) Mensert Spaanderman Parlement & Politiek
^ (in Dutch) Ir. J. (Johan) Visser Parlement & Politiek
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States ➭ General ➭ Of ➭ The ➭ Netherlands ➭