{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "1eb0b409", "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "from warnings import filterwarnings\n", "filterwarnings('ignore')\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from ML_in_AERSP.MiA_utils.ds_utils import pltEnergy, pltNumRange, pltInitGain, pltGainSweep, pltSVDsweep, \\\n", " makeSys2D, frMIMO, pltGainResp, pltPseudoSpec\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "id": "422d8c84", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## AERSP 597 - Machine Learning in Aerosapce Engineering\n", "## Lecture 22, Dynamical System: Nonnormality\n", "### Instructor: Daning Huang" ] }, { "cell_type": "markdown", "id": "0068a128", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "$$\n", "\\newcommand\\norm[1]{{\\left\\lVert #1 \\right\\rVert}}\n", "\\newcommand{\\bR}{\\mathbb{R}}\n", "\\newcommand{\\vf}{\\mathbf{f}}\n", "\\newcommand{\\vg}{\\mathbf{g}}\n", "\\newcommand{\\vv}{\\mathbf{v}}\n", "\\newcommand{\\vw}{\\mathbf{w}}\n", "\\newcommand{\\vx}{\\mathbf{x}}\n", "\\newcommand{\\vy}{\\mathbf{y}}\n", "\\newcommand{\\vA}{\\mathbf{A}}\n", "\\newcommand{\\vB}{\\mathbf{B}}\n", "\\newcommand{\\vU}{\\mathbf{U}}\n", "\\newcommand{\\vV}{\\mathbf{V}}\n", "\\newcommand{\\vW}{\\mathbf{W}}\n", "\\newcommand{\\vX}{\\mathbf{X}}\n", "\\newcommand{\\vtf}{\\boldsymbol{\\phi}}\n", "\\newcommand{\\vty}{\\boldsymbol{\\psi}}\n", "\\newcommand{\\vtF}{\\boldsymbol{\\Phi}}\n", "\\newcommand{\\vtS}{\\boldsymbol{\\Sigma}}\n", "\\newcommand{\\vtL}{\\boldsymbol{\\Lambda}}\n", "\\newcommand{\\cF}{\\mathcal{F}}\n", "\\newcommand{\\cK}{\\mathcal{K}}\n", "$$" ] }, { "cell_type": "markdown", "id": "b2f8d40f", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## TODAY: Dynamical System - II\n", "\n", "* Finite-time stability analysis\n", " - Transient growth\n", " - Maximum gain\n", " - Resolvent analysis\n", " \n", "### Example problem and code:\n", "+ Available [here](https://github.com/smanist/MiA_utils/blob/master/ds_utils.py).\n", "\n", "### References:\n", "\n", "+ [Schmid2009](https://fluids.ac.uk/files/resources/1_Schmid.pdf) P. Schmid, Nonmodal stability analysis, 2009; or a more formal paper version [Schmid2014](https://asmedigitalcollection.asme.org/appliedmechanicsreviews/article/66/2/024803/395151/Analysis-of-Fluid-Systems-Stability-Receptivity)\n", "+ [AIAAJ2017](https://arc.aiaa.org/doi/pdf/10.2514/1.J056060) Modal Analysis of Fluid Flows: An Overview, 2017\n", "+ [AIAAJ2020](https://arc.aiaa.org/doi/pdfplus/10.2514/1.J058462) Modal Analysis of Fluid Flows: Applications and Outlook, 2020" ] }, { "cell_type": "markdown", "id": "9fb5f1df", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Stability analysis (Nonnormal)" ] }, { "cell_type": "markdown", "id": "162dfb7e", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "The example from previous lecture suggests that we need to differentiate **two types of stability**:\n", "+ Linear stability: we are interested in the **minimum** critical parameter above which a specific initial condition of **infinitesimal** amplitude grows exponentially\n", "+ Energy stability: we are interested in the **maximum** critical parameter below which a general initial condition of **finite** amplitude decays monotonically" ] }, { "cell_type": "markdown", "id": "6c3201e8", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Strategies for transient behaviors\n", "\n", "Take a closer look at the response in terms of \"energy\"\n", "$$\n", "E(t)=\\norm{x(t)}^2\n", "$$" ] }, { "cell_type": "markdown", "id": "9b28d0d7", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Continuing to use the previous example 2D linear system\n", "The eigenvectors and eigenvalues of $A$ are\n", "$$\n", "V=\\begin{bmatrix}\n", "\\cos(\\pi/4-\\delta) & \\cos(\\pi/4+\\delta) \\\\\n", "\\sin(\\pi/4-\\delta) & \\sin(\\pi/4+\\delta)\n", "\\end{bmatrix},\\quad\n", "\\Lambda=\\begin{bmatrix} -0.1 & 0 \\\\ 0 & -0.2 \\end{bmatrix}\n", "$$\n", "> So the linear system should be stable, at least when $t\\rightarrow \\infty$\n", "\n", "But when $\\delta\\rightarrow 0$, $V$ becomes ill-conditioned." ] }, { "cell_type": "code", "execution_count": 2, "id": "a108d6da", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X0 = [1, 0.1]\n", "ds = [np.pi/4, 0.1, 0.05, 0.02]\n", "pltEnergy(X0, ds)" ] }, { "cell_type": "markdown", "id": "a7c06e33", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "+ The energy certainly decay to zero over long time, since the system is linearly stable\n", "+ Black arrows: The initial growth rate of energy gives a good estimate how high the energy may go\n", " - This leads to the **Transient growth analysis**\n", "+ Red bars: The maximum growth in energy gives a more direct characterization for stability\n", " - This leads to the **Maximum gain analysis**\n", " - w.r.t. either initial conditions or inputs" ] }, { "cell_type": "markdown", "id": "90f85081", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Some preparations" ] }, { "cell_type": "markdown", "id": "f1458587", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Consider a linear system,\n", "$$\n", "\\dot{x} = Ax + f,\\quad x(0)=x_0\n", "$$\n", "When $f=0$, the solution is (by matrix exponential)\n", "$$\n", "x(t) = \\exp(At)x_0\n", "$$\n", "When $x_0=0$, the solution is (by convolution)\n", "$$\n", "x(t) = \\int_0^t \\exp((\\tau-t)A)f(\\tau)d\\tau\n", "$$\n", "\n", "> We will first focus on the zero-input case" ] }, { "cell_type": "markdown", "id": "d40f5f4c", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Using the concept of energy, define the stability in the sense of *the growth of perturbation energy over time*, based on the matrix exponential.\n", "$$\n", "G(t) = \\max_{x_0}\\frac{\\norm{x(t)}^2}{\\norm{x_0}^2} = \\max_{x_0}\\frac{\\norm{\\exp(At)x_0}^2}{\\norm{x_0}^2} = \\norm{\\exp(At)}^2\n", "$$\n", "which represents the **maximum possible** amplification of perturbation energy over all initial conditions.\n", "> Recall that a matrix norm $\\norm{A}$ can be \"induced\" by a vector norm (typically L2), $\\norm{A}=\\max_x \\frac{\\norm{Ax}}{\\norm{x}}$" ] }, { "cell_type": "markdown", "id": "0112b5a4", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "If we diagonalize $A=V\\Lambda V^{-1}$, then\n", "$$\n", "G(t) = \\norm{\\exp(At)}^2 = \\norm{V\\exp(\\Lambda t)V^{-1}}^2\n", "$$\n", "\n", "> Again, if we follow linear stability analysis, then we would deduce the behavior of $G(t)$ from $\\exp(\\Lambda t)$, or simply $\\Lambda$, **only**. But this is insufficient to characterize $G(t)$ as shown in the previous example." ] }, { "cell_type": "markdown", "id": "0f96f0a2", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Let's think in terms of the following bounds of $G(t)$,\n", "$$\n", "\\exp(2\\lambda_\\max t) \\leq G(t) \\leq \\norm{V}^2\\norm{V^{-1}}^2\\exp(2\\lambda_\\max t)\n", "$$\n", "\n", "> The second inequality is a property of matrix norm $\\norm{ABC}\\leq\\norm{A}\\norm{B}\\norm{C}$\n", "\n", "If the system is linearly stable, i.e., $Re(\\lambda)<0$\n", "+ When $t\\rightarrow\\infty$, both sides decay to zero, so $G(t)$ is certainly zero.\n", "+ But before that, would $G(t)$ do something else?\n", " - Or, would $G(t)$ go to (close-to-)infinity in **finite time**?" ] }, { "cell_type": "markdown", "id": "613c8387", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "+ Note that term $\\norm{V}\\norm{V^{-1}}$ - looking familiar? It is the condition number of $V$, $\\kappa(V)$.\n", " - Recall we have argued before that when $\\kappa(A)$ is large, it would be difficult to numerically solve linear system of equations $Ax=b$.\n", "\n", "+ Now, if $V$ is \"well-behaved\", so that $\\kappa(V)\\approx 1$, then\n", "$$\n", "G(t) \\approx \\exp(2\\lambda_\\max t)\n", "$$\n", "i.e. the energy amplification is governed by the least stable eigenvalue, $\\lambda_\\max$.\n", "\n", "+ But if $V$ is \"badly-behaved\", so that $\\kappa(V)\\gg 1$, then\n", "$$\n", "\\exp(2\\lambda_\\max t) \\leq G(t) \\leq \\kappa(V)^2\\exp(2\\lambda_\\max t)\n", "$$\n", "i.e. the energy amplification is governed by $\\lambda_\\max$ **only for large times**." ] }, { "cell_type": "markdown", "id": "5dc4dbf4", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Now we introduce the concept of **normality** of a matrix $A$.\n", "+ $A$ is normal iff it is diagonalizable and its different eigenspaces are orthogonal to each other\n", " - In other words, $A=V\\Lambda V^H$, i.e. $V$ is unitary, $V^{-1}=V^H$\n", " - Then $\\kappa(V)=1$\n", " - Eigenvalue analysis captures the **entire** dynamics\n", "+ Otherwise $A$ is non-normal\n", " - Characterized by non-orthogonal eigenvectors\n", " - $\\kappa(V)$ can be large\n", " - Eigenvalue analysis captures the **asymptotic** dynamics, but not the short-time behavior" ] }, { "cell_type": "markdown", "id": "e61b4a30", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Transient short-term analysis" ] }, { "cell_type": "markdown", "id": "23b8b809", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Consider the rate of change for $E(t)$, considering that $\\dot x=Ax$\n", "$$\n", "\\frac{dE(t)}{dt} = (\\dot x^H) x + x^H (\\dot x) = (x^HA^H)x + x^HAx = 2Re((Ax)^H x)\n", "$$\n", "> The last step is because $(x^HA^H)x$ and $x^HAx$ are scalars and complex conjugates of each other - so only the real part remains" ] }, { "cell_type": "markdown", "id": "fc1b4fe2", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "With the form of $dE(t)/dt$, some people found it compelling to define the **numerical range**\n", "$$\n", "F(A) = \\left\\{ z\\ |\\ z=\\frac{(Ax)^H x}{x^Hx} \\right\\}\n", "$$\n", "i.e. the (scaled) relative growth rate of energy, normalized by the initial energy\n", "\n", "> If you have heard of Rayleigh's quotient, then $F(A)$ is essentially all possible values of the quotient." ] }, { "cell_type": "markdown", "id": "11067e66", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Things we need to know about numerical range:\n", "+ It is convex;\n", "+ It contains the spectrum of $A$, i.e. all of its eigenvalues;\n", "+ It is the convex hull of the spectrum, if $A$ is normal.\n", "\n", "Also, we define the maximum real number in the numerical range as the **numerical abscissa**, $\\alpha(A)$\n", "\n", "+ Alternatively\n", "$$\\alpha(A)=Re[\\lambda_\\max(A+A^H)/2]$$\n", "Think about why." ] }, { "cell_type": "code", "execution_count": 3, "id": "3c2730e9", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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n4ffcjV+nTmZHE7VAWhKEEHWan5+fFAgmsvj6Enr99STN/I3IRx6hZNMm9lx9DXtvu43idevMjifqKSkShBBu8f777/P++++bHaPBs/j6EnbTjSTNmknEgw9QsmYtu68cwb67xlC6bZvZ8UQ9I6cbhBBuIR0X6yZnQQHZX3xB5ief4ioqInjYP4i45x7s0dFmRxNuJKcbhBBCVJs1IIDwO++k+czfCB01irwpP7Nj0GAyXn8dZ26u2fFEHSdFghBCNAC2kBCiHn+MZtOnEzR4EJmffGoM9/zJp7hkmmpxElIkCCFEA+IVF0vMq6/S9MdJ+HboQMZrr7Fz6CXkz5qFJ55+FmdHigQhhGiAfFq1IuHjj4j/+GOUl53Uu+9h7403UbJli9nRRB0iHReFEKKB0w4H2RMmcvidd3Dm59PoyiuJuO9ebKGhZkcTVSQdF4UQQtQIZbMRet21NP91BiHXXEPO99+zY9Bgsr7+Gu10mh1PmEiKBCGEW7z++uu8/vrrZscQZ8HaqBHRTz1Js8k/4dO2LQf//Ty7R4yUwZgaMCkShBBuMXXqVKZOnWp2DOEG3klJJHz2KTGvv055xkF2jxjJgeeek0smGyApEoQQQhxHKUXw0Itp/ssvhIy6jpyJ37LjoiHkTp4sV0E0IFIkCCGEOClrYCDRTzxB0x++xys+nv2PPsa+W2+jPC3N7GiiFkiRIIQQ4rR8WremyTdfE/XUUxT9+Sc7LrmUrC++RLtcZkcTNUiKBCGEW/j6+uLr62t2DFGDlMViXAXx8xT8unTh4Isvsufa6yjdscPsaKKGyDgJQgghqk1rTd6UKRx86WVcRUWE33sPYTfdhLJazY7WIMk4CUIIIeoMpRTBl11Gs1+mEdC/P4fe+D/2XDeKsr17zY4m3EiKBCGEWzz//PM8//zzZscQtcwWFkbsm/8l5rXXKN2xg53/GEb2hAlyBYSHkCJBCOEWs2fPZvbs2WbHECZQShF8yVCaTZmMX0oK6c8+x77bbqf84EGzo4mzJEWCEEIIt7BHRxP/yVii/vU0RcuXs+vSy8ifM8fsWOIsSJEghBDCbZRShF5zDU1/nIQtNobUu8aQ/sKLuEpLzY4mzoAUCUIIIdzOu2lTEidMIPT60WR/+SW7R15F6c6dZscS1SRFghDCLcLCwggLCzM7hqhDLF5eRD3+OHEf/A/HwYPsumI4OT9MMjuWqAYZJ0EIIUSNKz+Ywf5HHqFo6VKCr7ic6KefxuLjY3YsjyHjJAghhKi37FGRJHz6CWF33kHuD5PYfc01lKWmnna73Nxchg0bRpcuXWjfvj1jx46t0vvNmDGD5ORkkpKSeOWVV6q9XmJiIu3btyclJYWuXd3+2Vtv2MwOIITwDI8//jgAL7/8sslJRF2lrFYi77sP344d2f/Io+y6Yjix/3mVgPPPP+k2P/zwA4GBgaxcuRKA4uLi076P0+lkzJgxzJw5k7i4OLp168all15KmzZtqrXe3LlzCQ8PP4sjrv+kJUEI4RZLlixhyZIlZscQ9UBg3740/eF77DEx7Lv9Dg69/c5JJ4rq3Lkz8+fPp2vXrjzzzDN4e3ufdv/Lli0jKSmJZs2a4eXlxVVXXcXkyZPPeL2GTFoShBBC1Dqv+HgSv/ma9H8/z+H336dk6xZiX30Vi79/5Tq5ubk88sgjrF27Fn9/f/r3709KSgrDhg2jd+/e5OfnH7ff119/nZycHOLj4yufi4uLY+nSpcetm5aWdtL1lFJceOGFKKW4/fbbue2229x5+PWGFAlCCCFMYfHxofGLL+DTqhUHX3mF3ddcS/z772GPjQXgww8/ZNCgQQQHBwPQo0cP0tPTAVi4cOFJ9/vdd98d95xS6rjnTtRx/8h6v//+OzExMWRkZDBw4EBatWpFnz59qn+Q9ZycbhBCCGEapRSho0cR/9FHlO/fz64rR1BU0f9g1apVtG3btnLdVatW0b59ewB69+5NSkrKccusWbOIi4tj3759ldulpqYSExNz3Hufar0jt5GRkQwbNoxly5a5/+DrAWlJEEK4RVxcnNkRRD0WcF4vEidOJPWuu9hzw400fvZZQkJCWLVqFYMHD2batGnk5eXRs2dP4NQtCQ6Hg23btrFr1y5iY2OZMGECX3/99XHrdevW7YTrFRYW4nK5CAwMpLCwkN9++41//etfNXbsdZkUCUIIt/jyyy/NjiDqOe9mTUmcOIG0fz7AgSef5KaRI7nrxx+ZMGECTZs2ZdKkSVgsp28At9lsvPvuuwwaNAin08lNN91U2SIxZMgQxo4dS0xMzEnX27lzJ8OGDQOMguOaa65h8ODBNXrsdZUMpiSEEKJO0eXlHHjmWXInTSL48stp/NyzKLvd7Fh1Wk0NpiQtCUIIt7j//vsBePPNN03NIeo/ZbfT+MUXsMfEcPjdd3FkZBD75ptYA/xPv7FwK+m4KIRwi9WrV7N69WqzYwgPoZQi4u4xNH7xBQqXLGHP6FGUZ2SYHavBkSJBCCFEndXoiiuI/+B/lO3ew57rRlGWmmZ2pAZFigQhhBB1WkDv3jT57FOcubnsue46mXK6FkmRIIQQos7z7diRJp+PRzsc7LluFCUbN5odqUGQIkEI4RYtW7akZcuWZscQHswnOZkmX3yO8vZmz/U3UPTnKrMjeTy5BFIIIUS9Ur5/P3tvvInyQ4dI+Pgj/Lp0MTuS6WrqEkhpSRBCCFGv2GNiSPjic+yRkey79TZpUahBMk6CqPdKnaXkleZRUF5AiaOEEmcJxY5iSh2llDhLKHGUUOosxamdaK1xaZexYNxqrbFarNiUDbvVjs1iw27569bX5oufzQ9/uz/+dn/87H742fzwtfmecNKYhurILHkfffSRyUlEQ2CPjCRh/Hj2jh7NvltvJX7sx/h16mR2LI8jRYKoc0qdpRwuPsyhokNkFmdyqPgQh4oPcbj4MFnFWeSV5RlLaR65ZbmUOktNyWlRFgK9AgnxDiHEJ4RG3o0I9QmlkXcjQnxCCPMNI9ovmij/KKL8ovCyepmSs7Zs3brV7AiigbFHRZLw+Xj2jB7NvltuJeGTsfimpJgdy6NIkSBqXbmznNSCVPYX7CetIK1yOfI4qyTruG0sykKoTyhhPmEEeQeRGJRIkHcQQV5/LYFegfjYfIzFeuytl9ULm7KhlMKiLMcsCoXD5cChHZQ7y4+5X+4qp8RRQqGjkMLyQorKi4xbh3GbW5pLTmkO2SXZpBaksu7wOnJKcnBox3HHEOoTSpRfFFH+UcT4x5AQlEB8YDwJgQnEBsRit8qws0JUlz0qiibjx7Nn9PXsveVWmnzxOT6tW5sdy2NIkSBqTH5ZPjtzd7Ird1fl7a7cXaTmp+LUzsr1bBYbMf4xxAbE0i++H439GxPpF0mYbxgRvhFE+EUQ4h2C1WKtsazu/JavtSa/PJ/DxYdJL0znYOFBDhZVLIUHSStIY3n6cgrLCyu3sSgLjf0bEx8YT9PgpiQ1SqJFSAuaN2pOkFeQ27IJ4Yns0dE0GT+O3ddcy95bbiXxqy/xSkw0O5ZHkCJBnDWtNemF6WzK2sTmrM1sytrElqwtHCg8ULmOzWKjSWATWoa05MImF5IYnEhsQCyxAbFE+kViUZ7Th1YpVdm60Sy42QnX0VqTVZLFvvx97Mvfx978vezNM5YpO6YcU0BE+UWRFJJEi0YtSA5Npm1YW5oENfGofzMhzpa9cWMSPhnLnmuvY+9NN9Pkm6+xR0WZHavekyJBVFt2STZrD61lzaE1rD28ls1Zm8ktzQVAoUgMTiQlIoURySNoHtycpsFNiQuMw2aRH7cjlFKE+YYR5htGSmTKMa8dKbq25Wxje852tmdvZ3vOdr4+8DVlrjIAAuwBtAlrQ9uwtrQJN27jAuJM7UiZIueChcm8mzUj/qOP2Hv99ey75RaafPEF1kaNzI5Vr8k4CeKUXNrF9pztrM5YzZpDa1hzaA178vYAYFM2WoS0oE1YG1qHtiY5NJmWIS3xs/uZnNozOVwOdubuZMPhDWzI3MCGwxvYkr2Fclc5ABG+EXSK7ETnqM50iepCi0YtavQUjRB1VeEfS9l36634tGlDwrjPsPj6mh2pxtXUOAlSJIhjaK3Zk7eHZenLWHpgKSsOrqjsSBjqE0rHiI6VS9vwtvjaPP+Xry4rd5azLWcb6w6t48+MP/kz40/SC9MBo7WhY2RHukZ1pUdMD1qHtpZTFKLByPvtN9Luu5/AgQOJffO/KItn/+xLkVANUiRUT05JDov2L2Jx2mKWpi8lo8iYjjXKL4pzG5/LOdHn0Dmqs+nN2aJqDhQcYGXGSlYdXMWfGX+yPWc7ACHeIXRv3J0eMT3oEdODaP9ot77vddddB8CXX37p1v0KcaYyx40j45VXCbvlZiIfesjsODWqpooEOUncAGmt2ZK9hYWpC1mQuoC1h9fi0i5CvEOMoqDxOZwTfQ4JgQlSFNRDjQMaMzRgKEObDQXgcPFh/jjwB0v2L2Hx/sVM3z0dgGbBzTg/7nz6JfSjQ3iHsz41kZqaetbZhXCn0Ouvp2zPHjLHfoI9IYGQESPMjlTvSEtCA+FwOVh5cCUz98xk7r65la0FbcLa0CeuD31i+9A2vK00R3s4rTXbcraxZP8SFqUtYkX6ChzaQahPqFEwxPejR0wPfGw+1d533759AZg3b557QwtxFrTDwb4776Jw8WLiP/qQgF69zI5UI+R0QzVIkWBwuBwsT1/Ob3t+Y87eOWSVZOFr86VXTC/6xPXhvNjziPCLMDumMFF+WT6L0hYxd+9cFqYtpKC8AB+rD73jejOk6RB6x/XG2+pdpX1JkSDqKmdBAXuuuZby9HSafv8dXgkJZkdyOykSqqEhFwlaa1YfWs2UHVOYtWcWOaU5+Np86RvXl4GJAzkv9jzpbChOqNxZzvKDy5mzdw4z98wkqySLAHsA/RP6M6TpEM5tfO4pL2OVIkHUZWWpqey+Yji2qCgSJ3yDxc+zrsLyyCJBKTUYeAuwAmO11q/87fVrgUcrHhYAd2qt15xuvw2xSEgrSGPKjin8vONn9uXvw9fmS7/4flyYeCG9YnqdUfOxaLgcLgfL0pcxfdd0Zu+ZTX55PiHeIVzU9CIub3E5yaHJx23z+OOPA/Dyyy/XdlwhqqRg0e/su+02ggYPIuaNNzyqz5XHFQlKKSuwFRgIpALLgau11huPWqcnsElrna2Uugh4Vmt97un23VCKhBJHCb/u/pWftv/EioMrUCjOiT6HS5pfwsAmA2W8AuEWZc4yFqUt4pddvzBn7xzKXeW0DWvL5S0u56KmFxHoFWh2RCGq7PBHH3Po//6PyEceIeymG82O4zaeWCT0wPjQH1Tx+HEArfUJv4YopUKA9Vrr2NPt29OLhL15e/l2y7f8uP1H8sryaBLUhEubX8olzS6hcUBjs+MJD5ZTksO0XdP4YdsPbMveho/VhwsTL2RE8gg6RnQ0O54Qp6W1Ju3+f5I/cyZNxo/Dr1s3syO5hScWCcOBwVrrWyoejwLO1VrffZL1HwJaHVn/BK/fBtwGkJCQ0GXPnj01E9wkDpeD+anz+XbLtyzevxibsjGgyQBGJo+ka1RXj2o2E3Wf1poNmRuYtG0Sv+z6hcLyQnI+yiE+MJ750+bLjJaiTnMWFLL7iitwlZTQ9KcfsYWEmB3prHlikXAlMOhvRcI5Wut7TrBuP+B94Dytdebp9u1JLQlF5UX8uP1Hvtj4BWkFaUT5RTG85XCuaHGFXJkg6oTC8kKm7JjC3cPvpsRRwjn/PocRySO4suWVhPuGmx1PiBMq3rCBPVddjf955xH3/nv1/ouWJw6mlArEH/U4Dtj/95WUUh2AscBFVSkQPEVmcSZfb/6aiVsmkluaS0pECg91fYi+8X1loiRRp/jb/bm61dV8GP4huaW5tAptxfur3+fjtR8zLGkYN7a7kbjAOLNjCnEM37ZtiXz4YQ6+9BLZX3xJ6OhRZkeqk8z8tFkOtFBKNQXSgKuAa45eQSmVAEwCRmmtt9Z+xNq3v2A/Y9eNZfL2yZS7yukX348b29143EyBQtRFwd7B/O+C/7Erdxefb/ycH7f/yA/bfmBI0yHc3P5mmjdqbnZEISqFjLqOwiVLyHjtNXy7dMa3bVuzI9U5Zl8COQR4E+MSyE+11i8qpe4A0Fp/oJQaC1wBHOlg4KhKc0p9PN2QXpjOx2s/ZtL2SSgUlza/lOvbXk/T4KZmRxOiSk40TsLBwoOM3zie77d+T4mjhAEJA7ij4x0nvIRSCDM4srPZddk/sAYHkfjDD1i8vMyOdEY8rk9CTapPRUJGUQZj143l+63fo9FcnnQ5t3a41e2T7whR055//nkAnn766eNeyy7J5qtNX/H1pq/JL8/noqYXcXfK3SQEed7Id6L+KViwgH233U7YrbcS+eADZsc5I1IkVEN9KBLyy/IZu24sX236CqfLyWVJl3Fbh9uICYgxO5oQNSa3NJdxG8bx1aavKHeWM6zFMO7oeAeRfpFmRxMN3P6nniJ30o8kfvM1vh3r3+W8UiRUQ10uEhwuBz9s/YH317xPVkkWQ5sN5a6Uu4gPjD/9xkJ4iMPFh/lwzYd8v/V7bBYbo9qM4pb2t8gAYMI0zvx8dl56GRZfX5pO+gGLT/0apVaKhGqoi0WC1pqFaQt5Y8Ub7MzdSdeorjzU7SHahklHGeEZLrroIgCmT59e5W325e/j3VXv8suuX4j0jeSBrg8wpOmQen85mqifCn7/nX0330LYLTcT+dBDZseplpoqEmRe4FqQVpDGPXPuYczsMTi1kzf7vcmngz6VAkF4lOLiYoqLi6u1TXxgPK/2eZUvLvqCcL9wHlv4GNfPuJ5NmZtqKKUQJxfQqxfBV1xO5rjxlGxtEBfUnZYUCTWo3FXOp+s/ZdjkYSxLX8aDXR7kx0t/ZEDCAPmmJMRRUiJT+Obib3iu53PsydvDyKkjefGPFyksLzQ7mmhgIh96CKu/P+nP/Rvtcpkdx3RSJNSQ1RmrGTl1JP9d+V+6N+7O5Msmc0O7G2S4WiFOwqIsXN7icn4e9jNXt7qaiVsm8o/J/2BB6gKzo4kGxBYSQuQjD1O8ciW5P/5kdhzTSZHgZqXOUl5b/hqjp48mvyyft/q9xdv935aJl4SooiCvIB4/93E+v+hz/G3+jJk9hscWPkZ2SbbZ0UQDETxsGL6dO5Px2ms4shv2z50UCW604fAGRvw8gs83fs6I5BFMvmwy/RP6mx1LiFoxdOhQhg4d6rb9pUSm8O0l33Jnxzv5dfevXPbTZczZO6fK2+fm5jJs2DC6dOlC+/btGTt2bJW2mzFjBsnJySQlJfHKK6+cdL2bbrqJyMhI2rVrd0bbi7pLWSxEP/sMzvx8Dr/zrtlxzKW19rilS5cuujaVOcv0e6ve0x3Hd9T9v+2vf0/9vVbfXwhPtzVrq75yypW63bh2+t+L/62LyotOu80nn3yiR40aVfm4qOj02zgcDt2sWTO9Y8cOXVpaqjt06KA3bNhwwnXnz5+vV65cqdu2bXtG24u6b/+zz+qNbdrqkh07zI5yWsAKXQOfp9KScJYOFBzghhk38L81/+Oiphcx6dJJ9IztaXYsITxKi5AWfDXkK25seyPfbv2Wq6ZexZasLafcpnPnzsyfP5+uXbvyzDPP4O3tfdr3WbZsGUlJSTRr1gwvLy+uuuoqJk+efMJ1+/TpQ2ho6BlvL+q+iLvvxuLjQ8brb5gdxTRSJJyFBakLuHLqlezI2cFr57/Gy71fJtg72OxYQpiib9++lfM31AS71c4DXR/go4EfkV+Wz9XTrubrTV+jTzDWS25uLo888ghr167ljz/+YO7cuZUf1r179yYlJeW4ZdasWaSlpREf/9fAZnFxcaSlpVU549luL+oWW1gYYbfdRsGcORQuXWZ2HFPInMNnwOFy8N7q9xi7bizJIcm80fcNmgQ1MTuWEA1Cj5ge/HDpDzz9+9O8vOxl1h9ez9M9nsbX5lu5zocffsigQYMIDjaK9h49epCeng7AwoULT7rv77777rjnqnO58okKFrncuX4LvX402RMnkPHqqyT+8H2D+/+UloRqyi3N5faZtzN23ViuaHEFXw75UgoEIWpZiE8Ib/d/mzEpY5i6cyqjp48mreCvb+yrVq2i7VHT/q5atYr27dsDp25JiIuLY9++fZXbpaamEhNT9flUznZ7UfdYfHyIuOdeSjZupGD2bLPj1DppSaiG3bm7uXvO3ewv2M8LvV7gsqTLzI4kRINlURbu6HgHbcLa8NiCxxg5dSSvn/863Rt3JyQkhFWrVjF48GCmTZtGXl4ePXsafYVO1ZLgcDjYtm0bu3btIjY2lgkTJvD1119XOVO3bt3OantRNwVfMpTDH/yPQ++9T8CAhjUYnhQJVfTHgT94YN4D2C12Phn0CZ0iO5kdSRyhNZTkQn46FB027pfkQkneX/fLC8HpAFc5OMvBWQYuh7Gt1W4sFjtYvcBqA5sv+ASDT1DFbcXiGwqBjcEvFBrQH4q6rE9cH74Z+g33z72fO2feyXO9nuPhhx9m5MiRTJgwgaZNmzJp0iQsltM3nNpsNt59910GDRqE0+nkpptuqmyRGDJkCGPHjq1sGbj66quZN28ehw8fJi4ujueee46bb775pNuL+kvZbITfeScHHnucgtmzCbzgArMj1RqZ4KkKftz2I/9e8m8SgxN5d8C7xAbEum3fogq0hsJDkLkDsnYYtzl7jKIg/4BxW1508u29AsDuV1EI2CqKAi/jvlJG8eAsO6qAKIfyYijLP/k+rV4QGG0UDIGNITgOwppDaHMISzKeq8KHkid5//33AbjrrrtMef/8snz+OfefLE1fyj2d7uHW9rc2qG98omZph4MdF1+Mxc+fppN+qHM/WzILZDW4s0gYt34cb6x8g14xvXj9/NcJ8Apwy37FSZTkwcH1cGAtpK+FgxsgayeU5v21jsUGwfEQFHPUB3XFrX84+DT665u/d5DRMnAmXE7jfY9ukSg6DPkHIX+/UZzkVdzm7gNHyV/b2v0gtBlEtILo9tC4A0R3BP+ws/rnEadW7izn6cVPM23nNIa3HM6T5z6JzSINpsI9cn76iQOPPU7c++8T2L+f2XGOIUVCNbijSNBa886qd/h43ccMThzMS+e9JPMuuJvTYRQEe5fA3j/gwBrI3vXX6/4RENXO+GYelmR8Uw9rDsEJZ/7BX1NcLqNwyNxutHRk7jDuZ2w0CogjgmKhcUeI6wYJPSC2M9hOf/1+fVBUZLTm+Pn5mZpDa83bq95m7LqxXJBwAf/p8x/53RVuocvL2X7hILzi42ny+Xiz4xxDioRqONsiwaVdvLLsFb7Z/A1XtLiCp7s/jdVidWPCBsrpgLQVsGsB7FkMqcuhrMB4LTgBYjtBdAdjadwBAqI847x/UZbRKpK+zmghObAaDldMQ2v1htgukNAdEs+DJr3A7mNq3DN1ZIyEefPmmZrjiC83fsmry1+lb1xf3uj7Bl5WL7MjCQ+Q+cmnZLz2Gok/fI9vHepvIkVCNZxNkaC15oU/XuDbrd9yQ9sbeKDLA3Xu3FO9UpAB22fBtpmwYw6U5AAKotoaH4wJPYwluIH18yjMrGhBqVj2rwbtNE5TNO0DSRdAi4EQkmh20iqra0UCwMTNE3lh6Qv0iunFm/3exMdWPwswUXc48/PZfn5fAgYMIPa1/5gdp1JNFQl1rM3WXFpr/rP8P3y79VtuancT93e+XwqEM5GzDzb+BBt+hLSVxnMBUdDqYuPDr1lf4+qAhsw/DFoPNRaAskLY/Tts+w22z4StM4znI1pBm8ug7TCIbG1e3npqZKuR2K12nl38LA/Nf4j/9vsvdoucehBnzhoYSKMrh5P11ddEPvgA9uhosyPVKCkSjvLOqnf4ctOXXNv6WikQqivvgFEUbPgRUiuGL22cAv2fNr4RR7VvcL39q8XLH1peaCxaG/0Zts2ELb/Agtdg/qsQnmwUCx1HGp0iRZVc3uJyypxlvLj0RZ5a9BQv934Zi5KfRXHmQkaNIuvzL8j59jsi7r3H7Dg1SoqECt9s/oaP133MFS2u4NFuj0qBUBVOh3EqYeU42PYraJdRDAz4l/FhJh9kZ0YpCG9hLD3uMq6m2DQFNvxkFAvzX4Em50Gn66DNpUaBIU7pqlZXkV+Wz9ur3ibIK4gnzn1CfsfFGfOKi8O/Vy9yJk0ifMxdKKvn9lmTIgGYu3curyx7hb5xfXm6+9Pyx+N0ctOMwmDVl0aPfv9I6HkvpFwLES3NTud5AqPgnFuNJTcN1nxj/Nv/dAf88jCkXA3n3mFc+WGiG264wdT3P51b2t9Cbmku4zeOJz4wntFtR5sdSdRjjYYPJ+3++yn8/XcC+vQxO06NafAdFzcc3sANM26geaPmfDroU/zs5l6+VacdWAtL3oX1PxhjCCQNgM7XQ/JFxgBFovZobVwh8ud4WD/JGD2yxYXQ/U6jz4cUuifk0i4enPcgs/fO5u3+b9M3vq/ZkUQ9pcvK2Na3H35duhD3zttmx5GrG6qjqkVCZnEmI6eOxKqsfHXxV4T7htdCunpo9++w4D+wcx7Y/aHzaOh+R73qee/R8g/Cik9g+SfGYE8xneD8R6Hl4FotFg4fPgxAeHjd/j0qdhRz44wb2Zm7ky+HfEnLEGn9Emfm4H9eI+vzz2kxby42k3/ua6pIaLC9dxwuB48seISc0hz+2++/UiCcyL7l8PllMG4IZGyCC56FBzbARa9IgVCXBEZBvyfgnxvgkreNcRm+uQo+7AObpxmtDrVg+PDhDB8+vFbe62z42nx5p/87BNgDeGDeAxQcGatDiGpqNOwf4HCQ9+uvZkepMQ22SHh71dssS1/G092fpk1YG7Pj1C2Ht8HXI+GTCyB9PVz4Ity3Bs77J/iGmJ1OnIzdB7pcD/eshMveNwaqmnANfHYRpK40O12dEuEXwWvnv0Zqfir/WvwvPLFFVdQ87xYt8G6RRN706WZHqTENskhYvH8xn63/jBEtR8h0z0crzoEZT8D73Y3z3QP+ZRQHPe8Gu6/Z6URVWe3Q6VoYsxyGvmkMET22P3x/E+SmVnk3ubm5DBs2jC5dutC+fXvGjh1bpe1mzJhBcnIySUlJvPLKKydd76abbiIyMpJ27dpVPrdlyxZSUlIql6CgIN58880qZ66OLlFduK/zfczcM5OvN8t0zuLMBA4eTPHKPyk/eNDsKDWiwfVJyCnJ4YopVxDgFcCEoRPwtcmHH1rDuu9gxuNQlGn0Oej/NAREmJ1MuENpPvz+Nix+B5QF+j8F594Opxlq/NNPP2XevHl8/vnnABQXF+Pre/Lfl759+6K1JjU1lZkzZxIXF0e3bt345ptvaNPm+Na6BQsWEBAQwOjRo1m/fv1xrzudTmJjY1m6dClNmjSp5kFXjdaaMbPHsCx9Gd9e8i3NguWyXVE9pTt3snPIxUQ98Tiho827Ykb6JLjJv//4N1mlWbzS+xUpEMD4Zvn1SJh0K4Q2hdvnw6VvS4HgSbwDof+TMGYpNOkJvz4OH/c3rlY5hc6dOzN//ny6du3KM888g7f36SeiysvLIykpiWbNmuHl5cVVV13F5MmTT7hunz59CA09+cibs2fPpnnz5jVWIAAopXiu53P42Hx4atFTOFyOGnsv4Zm8mzXDOzmZvBme2S+hQRUJc/bOYeaemdzV8S5ah8kQt6z+Bt7rDrsXwuBX4KZfjRkKhWcKaQLXfgfDPzOmuP64P/z+ljGD5d/k5ubyyCOPsHbtWv744w/mzp1b+WHfu3fvY04JHFnOO+88+vbtS3x8fOV+4uLiSEtLO6O4EyZM4Oqrrz6zY62GCL8Injr3KdYdXse4DeNq/P2E5wkcMIDi1atx5uSYHcXtGsxgSoXlhby09CVahLTghnY3mB3HXKX5MO0hWDvBmHXwsveMVgTh+ZSCdpcbYyn8fC/M/Jcx/POwD4+ZZOvDDz9k0KBBBAcHA9CjRw/S09MBWLhw4Ul3/9133/Hr33p6n8ngZGVlZUyZMoWXX3652tueicFNB/Pr7l/5cM2HXNT0ImIDGtiEY+KsBPTpzeH336fg998Jvvhis+O4VYNpSXhv9XtkFGXwTI9nGvYELwc3wofnw7pvoe/jcP3PUiA0RH6hMOILuPRdSPsTPjrf6KxaYdWqVbQ9ahrcVatW0b59e+DkLQlff/01drudffv2VW6XmppKTExMteNNnz6dzp07ExUVdRYHWT2PnmMMx/7qsldr7T2FZ/Bp3x5ro0YULjh5AV1fNYiWhN25u/lm0zdc3uJyOkY04Ob0rb8aPdy9/I3iIPE8sxMJMykFnUdB/DnGpZLjLzFOO3W7hZCQEFatWsXgwYOZNm0aeXl59OzZEzh5S8KRjov79u1j165dxMbGMmHCBL7+uvpXDnzzzTe1cqrhaNH+0dzR8Q7+u/K/LExdSO+43rX6/qL+UlYr/r16UbBoEdrlQnnQZHaecySn8Nafb2G32rm7091mRzHPkveMDoqhzeDWuVIgiL9EJMOtc6D5APjlIfj1CR5+8EF+/PFHOnbsyMcff8ykSZOwVOEPn1KKd999l0GDBtG6dWtGjBhR2SIxZMgQ9u/fX7nu1VdfTY8ePdiyZQtxcXF88sknABQVFTFz5kwuv/zymjneUxjVehQJgQm8+eebuPTxfTWEOJmAPr1xZmZSumWL2VHcyuNbElZnrGbW3lmMSRnTMEdV1BrmvAALX4fWlxjnnmXWQPF3PsFw9QT49Qn4432aFh5m2eJFYPOq9q6GDBnCkCFDjnv+l19+OebxN998c8Lt/fz8yMzMrPb7uoPdamdMyhgeXfgo03dN5+JmnnV+WdQcv27dACha+Sc+rT2nY7zHtyR8sPYDQn1CGd2mAc74prUx9sHC142xD64cLwWCODmLBQa/bAyite5b+HYUOMrMTlXrBjcdTHJIMu+uelcuiRRVZo+JwRYdTfGfnjW6qUcXCRszN/J72u+MajOq4c3uqDX89hQs/R90v8sY0/80g+cIgVLQ+0G4+P9g6wyYdAs4G9YHpUVZuDPlTlILUpm1Z5bZcUQ94te5M0Ur//SoYb49ukgYu24sAfYARiaPNDtK7fv9LWNa53Nug0EvydTBonq63Wz83GycDFPuqdIkUQ8++CAPPvhgLYSref3i+5EYlMhnGz7zqD/4omb5du6M4+BBHEf1vanvPLZISC9MZ/be2VyZfCWBXoFmx6lda7+DWc9Auytg8KtSIIgz02OMcZnsmq9h4RunXf2SSy7hkksuqYVgNc+iLIxuO5qNmRtZcfD0084LAeDbKQWA4rWnHs20PvHYIuHHbT/i0i6ubHml2VFqV/o645tfk17wjw+M88xCnKnzH4X2V8Kc52HTz6dcdcuWLWzxoJ7dlzS7hECvQL7f+r3ZUUQ94d2iBVitlHjQ74HHfoL8sO0Hesb0JD4w/vQre4riHJh4Hfg2givHnVHPdCGOoRRc+g7EdIYf74TsPSdd9fbbb+f222+vxXA1y8fmw8VNL2bWnlnkluaaHUfUAxYvL7ybNaV0sxQJdVpheSEHiw5yeYvav87aVDMeh5x9MOJzCIg0O43wFHZfo+gE+PF2cDlNjVObhrUYRpmrjOm7ppsdRdQT3i2TKdkqRUKdlleWh6/Nlz5xfcyOUnu2/mqcO+79gDGCnhDuFNIELn4d9i4xBuZqIFqHtqZ5cHN+2/Ob2VFEPeHdKhnH/gM48/LMjuIWHlsk9Inr03Cmgi4vhqn/hMg20Odhs9MIT9VhJLS8COa/CnkHzE5TK5RS9E/oz58H/ySnJMfsOKIe8E5KAqBs506Tk7iHRxYJDpeDAQkDzI5Re/54H/LSYMjrYPM2O43wVErB4JfAWWZcPdNA9E/oj1M7WZC2wOwooh7wiosDoCz1zKZIr2s8skgA6N64u9kRakdhJiz8LyQPgcReZqcRni60mTE419qJkLH5mJeeeuopnnrqKZOC1Zw2YW0I8wljyf4lZkcR9YA91phmvDw11eQk7uGRRYKvzZcQnxCzY9SOFZ9CWT70f9rsJKKh6Hkv2P3g9zePefqCCy7gggsuMCdTDbIoC12iurDyoGcNtytqhsXPD2toKOVp0pJQZ/nZGsgQzI5SWP6xMXtfVBuz04iGwj8MutwAa7+FvL9Gllu9ejWrV682LVZN6hLVhQOFB9hf4Dkj6YmaY4+LozytAbUkKKVCT7DYazrcmWowHRa3TIeCg0bzrxC1qdstoJ2w7rvKp+6//37uv/9+8zLVoE6RnQBYe8hzRtITNcceFUV5RobZMdyiqi0JfwKHgK3Ator7u5RSfyqlutRUuDPlY/MxO0Lt2PAj+EdA835mJxENTVhziOsGayaYnaRWNGvUDKuysj1nu9lRRD1gDQnBmeMZA3BVtUiYAQzRWodrrcOAi4BvgbuA92sq3JnytjaAHv7lxbDtN2h9iczuWA/l5uYybNgwunTpQvv27Rk7dmyVtpsxYwbJyckkJSXxyiuvHPf6li1bSElJqVyCgoJ48803AXjrrbdo164dbdu2rXzurLQbDhkbIWvX2e+rjvO2epMQlCBFgqgSa0gIzuxsj5gczFbF9bpqre848kBr/ZtS6iWt9QNKqQbwiVwHpa2E8iJoMcjsJOIM/PDDDwQGBrJypdEZrri4+LTbOJ1OxowZw8yZM4mLi6Nbt25ceumltGnzV3+U5OTkyn4BTqeT2NhYhg0bxvr16/n4449ZtmwZXl5eDB48mIsvvpgWLVqc+UE062vc7l4IoU3PfD/1RLPgZuzK9fyCSJw9a0gjcDpx5edjDQoyO85ZqWpLQpZS6lGlVJOK5REgWyllBVw1mE+czL6lxq2Mrlgvde7cmfnz59O1a1eeeeYZvL1PX2svW7aMpKQkmjVrhpeXF1dddRWTJ08+6fqzZ8+mefPmNGnShE2bNtG9e3f8/Pyw2Wycf/75/Pjjj2d3EBHJEBAFuxed3X7qiWj/aDKKPOM8s6hZ1kaNAHBmZ5sbxA2q2pJwDfAM8BOggEUVz1mBETWSTJza/lUQ2hz8Qs1OIqopNzeXRx55hLVr1+Lv70///v1JSUlh2LBh9O7dm/z8/OO2ef3118nJySE+/q8Jy+Li4li6dOlJ32fChAlcffXVALRr144nn3ySzMxMfH19+eWXX+jatevZHYhSEN0eMjYB8NJLL53d/uq4CN8ICsoLKCovws/eQK6gEmfE4mf8fLhKSkxOcvaqVCRorQ8D95zk5TM+SaeUGgy8hVFsjNVav/K311XF60OAIuAGrfWfZ/p+HiV7j9F5TNQ7H374IYMGDSI4OBiAHj16kJ6eDsDChQtPut1333133HPGr8jxysrKmDJlCi+//DIArVu35tFHH2XgwIEEBATQsWNHbLaqfkc4hbAWsGcxuFz07Nnz7PdXh0X4RQBwuPgwCfYEk9OIukx5GTPw6rIyk5OcvSr9lVBKRQCPAG2ByksHtNb9z/SNK05VvAcMBFKB5UqpKVrrjUetdhHQomI5F/hfxa3I2etZpxratoWNR/3Xt2kDGzaYl8eNoqOjGX/wIBdWPF4FtAOiX3uN9PR0Vq1axSWXXAJwypaEuLg49u3bV/lcamoqMTExJ3zP6dOn07lzZ6Kioiqfu/nmm7n55psBeOKJJ4irGD72TI/p4MGDfz3xlNF5NiQkhKysrDPeb1119PE2uaFJ5fNRUVGVBZ4Q8LffjQ4dKp+vrz8rVf0q8RUwERgK3AFcj3EZ5Nk4B9iutd4JoJSaAFwGHF0kXAZ8ro0uon8opRoppRprrRvG7DKnUpILvh4yquTfCwQwHrdt6xGFwpEC4ch3/pCK++MPHmTatGnk5eVVfgs/VUuCw+Fg27Zt7Nq1i9jYWCZMmMDXX399wnW/+eabylMNR2RkZBAZGcnevXuZNGkSS5ac+TDDxxQIR8n2gHOwJ3Ky4z3Z86Lh8rSflaoWCWFa60+UUvdprecD85VS88/yvWOBfUc9TuX4VoITrRMLNOwiweUENFjq7HhW1fP3AqGC3riRpo9Nq+Uw7reLvwoEgIeBkRhVd9OPP2bSpElYLKfvQ2yz2Xj33XcZNGgQTqeTm266ibZt2wIwZMgQxo4dS0xMDEVFRcycOZMPP/zwmO2vuOIKMjMzsdvtvPfee4SEeEiRKYSoMVUtEsorbg8opS4G9gNn3lZpONHJ1L9fVFqVdYwVlboNuA0gIcHDzxfqigtKTnI+WtRtTYFlGD/I6qefqrXtkCFDGDJkyHHP//LLL5X3/fz8yMzMPG6dU7VSCCHEiVS1SHhBKRUMPAi8AwQB/zzL904F4o96HIdRfFR3HQC01h8BHwF07dq1/o9gcSpWO3gFQLFnNu0eoYDdr1xsdoyzpl81O4EQQpyZKo2ToLWeqrXO1Vqv11r301p30VpPOcv3Xg60UEo1VUp5AVcBf9/nFGC0MnQHcqU/QgW/MCg8224hdUSbk0xOdbLn65nfOL75S1c8L4QQdVlVJ3hqqpT6P6XUJKXUlCPL2byx1toB3A38CmwCvtVab1BK3aGUOjK64y/ATozLLD/GGAZaADRKgKydZqdwjw0bji8IPOjqhuujoioLhSPLbxXP11dRJ8keGuqZ43ac7HhP9rxouDztZ0VVZWxppdQa4BNgHUeNsFjRibHO6dq1q16xYoXZMWrWjMdhxWfwRJrM3SDM834PCI6Ha781O0mNe3fVu3y09iNWjVqFVX7nxCnkTp7M/kcfo/lvv+JVS33klFIrtdZnOULa8araJ6FEa/22u99cnIXoDuAoNka7i25ndhrREJUWwKEt0MroNzJr1iwALrjgAjNT1Zi0gjSi/KOkQBCn5SwsBP4aebE+q2qR8JZS6hmMVtLSI0/K6Icmana+cbt9phQJwhw754J2QlPjZ/GFF14APLdI2Ju3lyaBTU6/omjwXA2wSGgPjAL689fpBl3xuM5xaqfZEWpeUIwxbv7W3+C8s73QRIgzsGUGeAdDQnezk9Q4rTV78vcwsMlAs6OIesCZmYXy9UX5+pod5axVtUgYBjTTWteLgahLHPV/Uo0qaX0pzH0RsndDSKLZaURDUlYEm36GloOMS3I9XHphOrmlubQMaWl2FFEPODIysEVGnHRulfqkqlNFrwEa1WAOtyp2FJsdoXakXAvKAivHm51EVIPVaiUlJYV27dpxySWXkJOT49b9l5aWMnLkSJKSkjj33HPZvXv3Cdd78skniY+PJyAgoPrbb5gEpbnQ5YbKY1qxYgXLly839ZhWrlxJ+/btSUpK4t577+VIx+yqbn8y6w6vA6B9eHugZv4Px48fT4sWLWjRogXjx5/4d3rBggV07twZm83G999/X+3tRe1wZGRgizAmBDPrZ6XiSsF1SqnVSqlFSqk2R73mrHh+9WmvVNRan3YB5gFZGJcrTjmyVGVbM5aIlhG6wfhqpNavNtW6tMDsJKKK/P39K++PHj1av/DCC27d/3vvvadvv/12rbXW33zzjR4xYsQJ11uyZInev3//MXmqtL3LpfX/ztP6nW7GfW0c0/nnn6/PP/98U4+pW7duevHixdrlcunBgwfrX375pVrbn8zry1/XnT7vpMscZVpr9/8fZmZm6qZNm+rMzEydlZWlmzZtqrOyso5bb9euXXrNmjV61KhR+rvvvqv29qJ2bL9wkE795z+11rX3swKs0Md+bgcddf9SYMZRjwt0FT9Pq9qS8AzGKYeXgDeOWuqkovIinK4G0C8BjP4IRZmw7GOzk4gz0KNHD9LS0gDYsWMHgwcPpkuXLvTu3ZvNmzef0T4nT57M9ddfD8Dw4cOZPXt25Tfqo3Xv3p3GjRtXf/vNUyF9LfS675ihwT/88EM+/PBD047pwIED5OXl0aNHD5RSjB49mp8qhr2u6r/JySw9sJT24e2xn+DUijuO99dff2XgwIGEhoYSEhLCwIEDmTFjxnHrJSYm0qFDh+Pm+qjq9qLmaa0pz8jAFhF53Gu1+bOitc476qE/J5nS4HSq1CdB19HxEE7GqZ2sO7yOlMgUs6PUvIRzIekC+P0to+nXt5HZiUQVOZ1OZs+eXTl982233cYHH3xAixYtWLp0KXfddRdz5szhq6++4rXXXjtu+6SkpOOanAHS0tKIjzdGM7fZbAQHB5OZmUl4eHiVcp1ye5cT5r4EYS2gw8hjtktOTsbpdPLUU0+ZckxpaWnHTH8dFxdX+Qf5bP5NDhcfZlPWJu7tdO9xr7nr//DofH/PXhVnu71wH8fBg+jiYuxNjh0fwYyfFaXUGOABwItjLzTwUUqtABzAK1rrn052PKcsEpRS+Zy4+lCA1loHnWp7sygUC1IXNIwiAaD/0/BxP5jzPFxcZxt4RIXi4mJSUlLYvXs3Xbp0YeDAgRQUFLB48WKuvPLKyvVKS42rja+99lquvfbaKu//RN+Qq9OB6pTbL/sIMjbClePB+tefj+LiYpo1a0ZGRgbnnnuuKcd0qnXO5t9kyX5jSu1esb0qn3P3/2GN/p+JWlVW0d/Fu2lTwNyfFa31e8B7SqlrgKeA6yteStBa71dKNQPmKKXWaa13nGgfpzzdoLUO1FoHnWAJrKsFAoCf3Y85e+dUqzmxXotJgXNug+WfwL7lZqcRp+Hr68vq1avZs2cPZWVlvPfee7hcLho1asTq1asrl02bNgHw1VdfkZKSctwyfPhwwOiAeOQ5ML5Z7NtnzLDucDjIzc2t1nDJJ90+Zx/Mfh6SBkKby447poSEBFJSUkw7pri4OFJTUysfp6amEhMTc9b/Jr/t+Y1I30hahbY65njd+X94dL6/Z6+Ks91euE/Zrl0AeFUUCXXkZ2UC8I8jD7TW+ytud2L0Oex00i2r2nmhPi3N2jbT7ca10xsPbzxV/w/PUpyr9RuttX67s9Yl+WanEadwdEemP//8U8fHx+uysjLdo0cP/e2332qttXa5XHr16tVntP933333mE56V155ZZXznHR7p0Pr8Zdq/UK01lm7T7iPIx0XzTymrl276iVLllR2XJw2bVq1tv+7nJIcnfJ5in5t2WvHHe8R7jjezMxMnZiYqLOysnRWVpZOTEzUmZmZJ13/+uuvP67jYnW2FzXnwIsv6k0pnbTL6dRa197PCsd3XGxx1P1LjrwOhADeFffDgW1AG32Sz1PTP9BrYknpnKJTPk/R/1n2nyr9o3uMXQu1fraR1j/cWtnrXNQ9f/9QHjp0qP7888/1zp079aBBg3SHDh1069at9XPPPXdG+y8uLtbDhw/XzZs31926ddM7duyofK1jx46V9x9++GEdGxurlVI6NjZWP/PMMyfffu4rWj8TpPXKz096TEeKBDOPafny5bpt27a6WbNmesyYMdpV8Xtwqu1P5bst3+l249rpDYc3HHe8R3PH8X7yySe6efPmunnz5vrTTz+tfP7pp5/WkydP1lprvWzZMh0bG6v9/Px0aGiobtOmzWm3F7Vrz4036R3DhlU+rq2fFWAF8G/gUuMhbwEbgNXAXKBtxfM9MeZhWlNxe7M+xedplSZ4qm+6du2qe/2nF6sPrWbm8Jl4Wb3MjlR75r0K814y+iZ0u8XsNMITbJ8NX15hdFQc9sExVzQcrW/fvgDMmzev9rLVsKunXk2Ro4ifLvtJzvGL09Jas7V7D4IuHEjj55+v1feuqQmeqnoJZL0zInkEWSVZ/Lr7V7Oj1K4+D0HLwfDLw8aQzUKcjfR18O31ENXWKDwb0Afl2kNrWZ+5nqtaXSUFgqiS8rQ0XLm5+LT1nPl0PLZI6BnTk6bBTfly05d4YmvJSVmscMUnENUOvrsB0mQOLnGGcvbBVyPAJwiu/Q68A065+hdffMEXX3xRS+Fq3tebv8bf7s+lzS81O4qoJ0rWrwfAp50UCXWeUoprW13LxsyNrDi4wuw4tcs7AK75FvzD4It/wP5VZicS9U3OPhg/FMoKjJ+loNP3lI+Pjz/m+u36LDU/lV93/cqwpGH42/3NjiPqiZL161F2Oz4tW5gdxW08tkgAuCzpMsJ9w/nfmv+ZHaX2BTWG66eCTzB8fpm0KIiqy94D44ZAUTaM+qnKU5FPnDiRiRMn1my2WjJ23ViUUtzQ9gazo4h6pGjVarzbtEZ5eU4/OI8uEnxsPtzS/haWpy9n2YFlZsepfSFN/ioUxl8C22aanUjUdQfWwqeDoCQXRv8EcV2qvOn//vc//ve/+l+QpxWkMXn7ZK5ocQVR/lFmxxH1hKuoiOK1a/E/5xyzo7iVRxcJAMNbDifSN5K3Vr3VsPomHBHSBG76DUKbwtcjYeU4sxOJumrbTPjsImNm0RunQ2xnsxOZ4p1V72BRFm5uf7PZUUQ9UvTnKigvx+/c7mZHcSuPLxK8rd7c3elu1h5ay9SdU82OY46gxsYf/eb94Of7YNpD4Cg1O5WoK7SGRW8aRWRoM7hltnE1QwO05tAapu2cxvVtryfaP9rsOKIeKVr6B9jt+HU++eCF9ZHHFwlg9E1oF9aON1e+SVF5kdlxzOEdCFdPgB53w/KP4bMhkJt6+u2EZyvOhgnXwKxnoNXFRjEZdPzMkA2BS7v4z7L/EO4bzi3tZYwRUT2FfyzFt317LH5+ZkdxqwZRJFiUhcfOfYyM4oyG2YnxCKsdBr0IIz6HQ1vgg/Ng/Q9mpxJm2f07fNgHtv0Gg181fi5Oc5mjJ/t+6/esPbyW+zvfj5/ds/7Qi5rlOHyYkvXr8e/V0+wobtcgigSAjhEduaLFFXy+8XPWHlprdhxztbkMbptnNC1/fxN8dyMUZZmdStSWsiKY8TiMuxiUFW6cAd3vOOuBkr7//vsTTvNcH6QXpvN/K/+Pc6PPlXERRLXlz50LWhM4YIDZUdyuwRQJAA92fZAI3wie/v1pSp0N/Jx8eJLRobH/07DpZ3jvXFgz0Tg/LTzXjrlGC9If7xvDdt/5O8R3c8uuw8PDCQ8Pd8u+apPWmuf/eB6XdvFMz2dkdEVRbQVz5mKPicE7OdnsKG7XoIqEQK9Anu35LDtzd/LOn++YHcd8VpsxjPNtc6FRPPx4G4wbChmbzE4m3C031Rhe+Yt/gHbB6Mlw8evg5b6BgsaNG8e4cePctr/a8t3W71iQuoB7Ot1DfKBnDAYlao+rqIjCxYsJ6N/fIwvMBlUkAJwXex4jk0cyfuN4FqQuMDtO3RDdHm6eBZe8BRkbjG+aUx+A/INmJxNnqyQP5r4M73aDrb9Cv6fgrj+gWV+3v1V9LBK2ZW/jP8v/Q6+YXlzb+lqz44h6qOD339GlpQQO6G92lBrR4IoEgIe7PUzLkJY8uehJDhbKByEAFgt0uQHuXgldboQ/x8PbKTD7eWNgHVG/lJfAkvfgrY4w/xVocSGMWQrnPwx2H7PT1QnFjmIenv8wAfYAXjjvBSyqQf45FGcp7+epWEND8evq9gkY64QG+VvhbfXm9fNfp9RZykPzH6LMWWZ2pLrDP8xohh6zDJIvgoWvw3/bG8VC4WGz04nTKS0wioO3O8GvT0DjjnDrXBgx3hhYSwBGP4R//f4vdubu5KXeLxHuW//6UgjzOfPyKJg7l6CLL0bZ7WbHqRENskgAaBrclBd6vcDqQ6t5/o/nG+ZojKcS1hyGfwq3L4Bm58PCN+C/7WD6o8bY/qJuKTxsnFZ4s51RHIQ1h9FTjKGVG+jIiafyyfpPmLF7Bvd1vo+eMZ532ZqoHXkzZqDLywm+1HOviLGZHcBMFyZeyB05d/DBmg9o0agFo9uONjtS3dO4I4z8whhXYdGbsHwsLP0QWg6Gc26FZv2MUxWi9mkN+5YZ/ycbfwJnGSRfDOf9021XLHii+fvm8/afb3NR4kXc1O4ms+OIeixvys94NW2KTzvPHaFUeeI36K5du+oVK6o2PbRLu3hg3gPM2TuHN/q+wcAmA2s4XT2XmworPjP6LBQegtDm0HkUtB8BwbFmp2sYinOMQbBWfAoH14NXIHS8yrikMbKVabGKiozRTP3q8Ihzaw+t5ZbfbqFpcFPGDR6Hr83X7Eiinirbu5cdFw4i4v77CL/jDrPjoJRaqbV2e8eIBl8kABSVF3HrzFvZlLmJDwd+SLdo+RZ2Wo5S2DgFVnwCe5cAyugx3/FqY3jfBjxyX40oLzauTlj3nTFCorPMuCql683Q/kr5966C3bm7GTV9FAH2AL4Y8oX0QxBn5eB/XiNr/HiS5szBHhVpdhwpEqqjukUCQE5JDtfPuJ6Mogw+HfQprcNa11A6D5S5A9ZOhDXfQM5esHpD0gBofSkkDwbfELMT1k+lBbBzHmyeZgx4VZYPAVHQ7gpoPxxiOp/1KInu9P777wNw1113mZzkeOmF6dww4waKHcV8cdEXJAQlmB1J1GOukhK2n98Xv+7diXvrTbPjAFIkVMuZFAlg/CEZNX0UJY4Sxl44luRQzxs9q0a5XLDvD6OFYdPPkJcKFhs06WUUDc37Q1S7OvXBVufk7DVaDLZMh90LjRYD72Boc4nRYpDYGyxWs1OeUN++fQGYN2+eqTn+7mDhQW789UayS7IZe+FY2oZ77vljUTtyJv3IgSeeIGH8ePzPPcfsOIAUCdVypkUCwL68fdz4642UOkulUDgbWsP+P42CYdtvkLHReN4/0piyulk/aNIDGjVp2EVDbhrs+d0oCHb/Dlk7jOfDkozOoS0HQ0J3Y3KuOq4uFgkZRRnc9OtNHC4+zIcDP6RjREezIwkPsOvKEbiKimg29ec6M8piTRUJDfrqhhOJD4rns0GfceOvN3LLb7fw4cAPaRPWxuxY9Y9SENvFWAY+B3kHYOdc2DEHts82Tk+AUTTEn2MscedATArYPbQzWXkxpK+H/auMZe8SyN5lvOYTbLS4dLsZWgwy5tYQZyWtII3bZ97OoaJDUiAItylauZKSdeuIevqpOlMg1CRpSTiJfXn7uPm3m8ktzeWt/m/RvXF3N6UTuFxGy8K+pcYlfKnLIGun8ZqyGFdMRLU1Tk1EtYWoNhCcUH8utXQ5IXcfHN4Gh7fCwY1wYLUxJ4Z2Guv4R0BcN0g8z1ii2tXZ0whVVZdaErZlb+P2mbdT4izh/QHvkxKZYnYk4SH23n47JWvXkTRnNhbfuvOFRloSall8UDxfXPQFd8y6gztn3cnLvV9mcOJgs2N5BosFotsZS7ebjecKDhnFwoE1cHCDcbvxp7+2sXoZpyZCm0JIIoRU3AZGG535/CPA5lU7+bU2Bi/KSzVOF+SmGvdz9kHmdmNxlPy1vl8YNE4xTh3EdDJaS4JiG/Zplhq0KmMVY2aPwdfqy/jB42kR0sLsSMJDlGzZQuH8BUTcd2+dKhBqkrQknEZuaS73zrmXVRmrePScR2USmNpUmg8Zm41Jp7J2QtYuo3k+a7fR0//vfEP+Khi8g8A70Lg00Cvgr1uLzWitsFiNW2U1PqydZeAoMz7cHaUVtyVQkgNF2VB8ZMmCoixwlR/73lZvY5yIsCQIb3ns4h9WG/9aApi7dy6PLHiEKP8oPhz4IbEBMnaHcJ+0Bx+iYO5ckubOwRocbHacY0hLgkmCvYP5cOCHPLLgEV5Z9gq7c3fzyDmPYLfU/Y5k9Z53oDFy4N9HD9Ta+KDO3g0FByuWDCjMqLh/yHitLN+4jLCswCgCqkNZwOZr9BXwCzUKkPAk8K24HxRjtAYEx0JQHPiHS8uAibTWfLL+E97+823ahLXhvQHvEeYrxZlwn7K9e8mbPp3QG26ocwVCTZIioQp8bD78t+9/eevPt/hsw2dsz9nOG33fINQn1OxoDZNSxrfz6nxDd5RCWaHRX0A7Qbsq7ruMxeoFNh+weRu3VvnVqK7XX38dgIceeqhW37fYUcwzvz/D9N3TuajpRfy757/xsclMl8K9Dr37LsrLi9Drrzc7Sq2Sv4RVZLVYeaDrA7QMbcmzi5/l6qlX81b/t2gVat4wuKIabN7GImrM1KlTgdotEtIL07lv7n1sytzEfZ3v4+Z2NzeIHueidpVs2Urez1MJu/mmOjG6Ym2qJ93F646hzYYyfvB4nNrJqF9G8cPWH2QGSSFMMH/ffIb/PJzdubt5u//b3NL+FikQRI049PbbWPz9CbvlFrOj1DopEs5A2/C2TBg6gY6RHXl2ybM8suAR8k/UkU4I4XblznJeW/4ad8+5m8b+jZk4dCJ94/uaHUt4qOLVqymYPZuwm2/C2qiR2XFqnRQJZyjcN5yPBn7EfZ3vY+aemVz585WsO7TO7FhCeLR9+fsYPX00n2/8nKuSr+LLIV+SGJxodizhobTWHHz9dayhoYSOHm12HFNIkXAWLMrCLe1vYdzgcWitGT19NB+s+YDyv18eJ0QD4Ovri28NXTuutebbLd8yfMpw9uTt4b99/8uT3Z/E2yr9TETNyZ8+neIVK4m47z4s/v5mxzGFjJPgJrmluby49EWm75pOq9BWPN/reenUKIQb7C/YzzOLn+GPA3/QvXF3nuv5HDEBMWbHEh7OVVzMjiEXYw1pRNPvvkNZ6/aIqDU1ToK0JLhJsHcw/+nzH97s9yaHig5x9dSreW/1e5Q7pVVBiDOhteb7rd9z+ZTLWXtoLU93f5qPBn4kBYKoFZkfj8Vx4ADRTz5Z5wuEmiRFgpsNSBjA5H9MZnDTwXyw5gNGTB3BivTabdUQwgzPP/88zz//vFv2tTV7KzfMuIHnljxHu7B2TLpsEiOSR8jVC6JWlKWmkfnJJwRdfDF+XbqYHcdUcrqhBs3fN58Xl77IgcIDXNzsYh7s8iARfhFmxxKiRrhjgqfC8kLeX/0+X236ikCvQO7vfD/DWgzDouT7jKgdWmv23X47RStW0vyXadijo82OVCUyLHM9dH78+ZzT+BzGrhvLZ+s/Y96+edzV8S6ubn21DOssxFG01vy6+1deW/4ah4oPcUXLK7iv03008mlkdjTRwORNnUbhgoVEPflkvSkQapKU5zXM1+bLPZ3u4cfLfqRTZCdeW/Eaw6cMZ+7euTIIkxAYszaOmj6Khxc8TLhfOF8N+YpnejwjBYKodY7sbA6+9BI+HTsQcs3VZsepE6QloZY0CWrC+wPeZ+6+ufx35X+5d+69dI7szD+7/FPmuhcN0q7cXbz151vM3jubSN9Inuv5HJc1vwyrpeF2EhPmynjlFZz5+SQ8/3yD7qx4NCkSapFSiv4J/ekd15sft/3I/9b8j1HTRzEgYQD3dr6XZsHNzI4oxBkLC6vahFsHCw/y8bqP+X7r9/jYfLin0z1c1/o6/Ox+NZxQiJMrmD+f3MlTCL/rTnxatjQ7Tp0hHRdNVFRexBcbv+CzDZ9R7ChmUOIgbu9wO80bNTc7mhBul16Yzth1Y5m0bRJaa4a3HM4dHe+QKZ2F6RxZWey89DJsoaEkfv8dFi8vsyNVW011XJQioQ7IKsli3IZxTNg8gRJHCQObDOS2DreRHJpsdjQhztr+gv18su4TJm2fBMA/kv7Bze1uJi4wzuRkQhidZlPvuYfC+QtI/P57fJLrZyuCXN3gwUJ9QnmgywPc2PZGvtj4Bd9s/obf9vxGv/h+3NTuJjpGdJTrw0Wd9/jjjwPw8ssvA8ZYB19s/IKpO40ppC9Pupyb298sgyGJOiX3hx8omDWbyEceqbcFQk0ypSVBKRUKTAQSgd3ACK119t/WiQc+B6IBF/CR1vqtquy/vrUk/F1uaS5fb/qaLzd9SV5ZHu3D2zOqzSguaHKBXDop6qwj4yS8+NWLjN8wniUHluBr8+UfSf/gpnY3Ee0vl5OJuqVs7152/mMYvu3bk/DZpyhL/b3gz6NONyil/gNkaa1fUUo9BoRorR/92zqNgcZa6z+VUoHASuAfWuuNp9t/fS8SjigqL2LKjil8uelL9uTtIcovimtaX8MVLa4g2DvY7HhCVCp2FNOtVzfSC9Np/HBjInwjuKb1NVzZ8kr5WRV1kqu0lD1XX0NZairNJv+EvXFjsyOdFU8rErYAfbXWByqKgXla61OegFdKTQbe1VrPPN3+PaVIOMKlXSxMXcgXG79gafpSfKw+XJh4IVe2vFJORQhTbcvexndbv2Pqjqms+fca/Ox+fPLTJ1yUeBF2q7R6ibrrwLPPkjNhInHvv0dg//5mxzlrntYnIUprfQCgolCIPNXKSqlEoBOw9BTr3AbcBpCQkOC+pHWARVk4P/58zo8/ny1ZW/h2y7dM2zWNKTumkNQoiStaXMElzS+Rb2yiVpQ4Svh19698v/V7Vh9ajd1iZ2CTgZSGlhLoFcilzS81O6IQp5T781RyJkwk9OabPKJAqEk11pKglJqF0Z/g754ExmutGx21brbWOuQk+wkA5gMvaq0nVeW9Pa0l4USKyouYsXsG32/9nnWH1+Fl8WJAwgAubnYxPWN7St8F4VYu7WLlwZVM3TmVmbtnkl+eT2JQIsNbDufS5pcS4hPCddddB8CXX35pclohTq50xw52XTkCn9ataTLuM5TdM/5WNsjTDUopOzAV+FVr/X9V3X9DKBKOtiVrC99v/Z7pu6eTW5pLI+9GDEocxNBmQ+V0hDgr27O3M3XnVKbtmkZ6YTp+Nj8uaHIB/0j6B12jusrPlqhXnAUF7B55Fc7sbJr+OAl7VJTZkdzG04qE14DMozouhmqtH/nbOgoYj9HB8f7q7L+hFQlHlDvL+X3/70zbOY25++ZS6iwlNiCWwYmDGZAwgHbh7eSPujglrTU7cnYwa+8sZu2ZxZbsLViVlZ4xPRnabCh94/vKyIiiXtJOJ6l3jaFg0SISPvkE/+7nmh3JrTytSAgDvgUSgL3AlVrrLKVUDDBWaz1EKXUesBBYh3EJJMATWutfTrf/hlokHK2wvJDZe2czbec0lh5YilM7ifSLZEDCAAYkDKBLVBdsFhkmQxiFwcbMjZWFwe683QCkRKQwKHEQg5sOJtw3/LT7uf/++wF48803ay6sEGco4403yPx4LFH/eprQa64xO47beVSRUNOkSDhWbmku81PnM3vPbBbvX0yJs4Rg72D6xPbhvNjz6BHTgxCfE3YJER6qsLyQPw78waK0RSxKW0R6YTpWZaVbdDcuSLiA/gn9ifCLqNY+j4yTMG/ePPcHFuIs5E6Zwv5HHqXRVSNp/OyzZsepEZ52dYOoRcHewVza/FIubX4pReVFLNm/hFl7Z7EwbSE/7/wZhaJdeDt6xfaiV0wv2oW3k1YGD6O1ZlvONn5P+51FaYv4M+NPHC4HfjY/ujfuzpiUMfSN6yvTMwuPU7x6NQeeehq/bt2IfvJJs+PUO9KS0IA5XU42Zm5k0f5F/J72O+sOr8OlXQR6BdIlqgtdo7rSNaoryaHJUjTUM1prdubuZHn6clYcXMHy9OVklWQB0CKkBefFnkfv2N6kRKS4bTwDaUkQdU3Z7t3svvoaLAEBJH47EVuI57aYSkuCcDurxUr7iPa0j2jPnR3vJLc0lyUHlrA4bTErDq5g3r55APjb/ekU2YmuUV3pEtWFVqGt8LH5mJpdHKvcWc6W7C2sObSGlQdXsvLgysqiIMovip4xPekW3Y2eMT1leGTRIDgOH2bvrbcBkPDxRx5dINQkKRJEpWDvYAYnDmZw4mAADhYeZOXBlaw4uIKVB1fyZtqbANiUjRYhLWgf3p524e1oH96epsFNsVqsJqZvOLTWpBaksu7QOtYdXsfaw2vZnLmZMlcZANH+0fSK6UW36G50je5KXEBcrVzV0rKlTI4j6gZXYSH77rgTx6FDNBk/Dq/ERLMj1VtyukFUWWZxJmsPrWXdYePDacPhDeSX5wPgZ/MjOTSZliEtK5ekRkkEeAWYnLp+K3GUsCN3B1uztrIlewtbsrawNXsreWV5APhYfWgT1ob24UaLUIfwDkT7R8ulrqLB0g4H+8aMoXDhIuLee5fAfv3MjlQr5OqGapAioXa4tIs9eXuMouHQOrZmb2Vr9lYKygsq14kNiKVFSAuaBjelSWATmgQ1ITE4kTCfMPkgO0puaS6783azO3c3u/N2sydvDztydrA7bzcubVwB7GvzpUWjFrQMbUnr0Na0D29PUkiSjK4pRAXtdLL/0cfImzqV6GefJeSqkWZHqjVSJFSDFAnm0VqTXpheWTBszd7Ktuxt7M3fS7mrvHI9f7s/TYKa0CSwCY0DGtPY31ii/aNpHNCYQHugRxURxY5iDhQcYH/hfg4UHqi8n5afxp68PWSX/jVTuk3ZiAuMIzE4kZYhLUkOSSY5NJn4wHgsqu5OZXvbbcb5348++sjkJKIh0lqT/q9nyPnuOyIeeIDw2241O1Ktko6Lol5QShkf+gGNOT/+/MrnnS4nBwoPsCdvD7vzdrM3b29lK8TMvTNxuBzH7Mff7k+0XzThvuGE+oQS6htKqE8oYT5hlY8DvQIJsAcQYA/A1+Zba0WF1ppSZyn5Zfnkl+dTUFZAbmkumSWZZBZnHn9bnHlMEQBgVVai/KKICYihf0J/EoMSSQxOJDEokdjA2HrZOrB161azI4gGSmtNxiuvkPPdd4TdcXuDKxBqkhQJolZYLVbiAuOIC4yjV2yvY15zaReZxZnGN+zCA6QXplfeZpVksSFzA1klWcecxjhu/8qKv93fKBq8AvC2euNl9cLL4mXcWr2wW+x4Wb2wKqODpcZoRTu6Nc2pnZQ6Syl1llLmLKu8LXOWUeworiwM/l7UHM3X5kuYTxhhvmEkBCbQObLzMa0lMQExRPhGSEdPIdzk8DvvkDX+c0JGjyLivvvMjuNRpEgQprMoCxF+EUT4RdAhosNJ1yt1lpJdkl35Lb2grICC8oql7NjbIx/uhY5CckpzjA96l/Fhf8wpNnXkxrhjVVa8bd5GkVFRYAR5BeFl9cLH6mO0XngFEOgVSKA9sPJxkFdQZWEgcxsIUXsOvf8+h9//H8HDryDq8cc96jRlXSBFgqg3vK3eRPtHy3X+Qgi01hx6+20y//cBwZddRuPnnpMCoQZIkSCEcIuUlBSzI4gGQmvNof/7PzI/HkujK4cT/dxzKEvd7dRbn0mRIIRwC5n9UdQGo5Piq2SNH0+jq68i+umnpUCoQVIkCCGEqBe000n6Cy+Q880EQkaNIuoJ6YNQ06RIEEK4xXXXXQfAl19+aXIS4YlcZWXsf/RR8qfPIOyWm4l48EEpEGqBFAlCCLdITU01O4LwUM6CQtLuvYfCxUuIfPhhwm6+yexIDYYUCUIIIeosR1YW+26/g5KNG2n80ks0unyY2ZEaFCkShBBC1Ell+/ax79bbKD9wgLh33iGwf8OYrKkukSJBCCFEnVP05ypSx4xBu1wkfDIWv65un5ZAVIEUCUIIt+jRo4fZEYSHyPvlF/Y/9ji2xtHEf/AB3k2bmh2pwZIiQQjhFi+//LLZEUQ9p7Um86OPOfTf/+LbpQtx776DLSTE7FgNmhQJQgghTOcqLSX9uX+TO2kSQUOH0vilF7F4eZkdq8GTIkEI4RZXXHEFAD/88IPJSUR9U37wIKn33kvJmrWEjxlD+N1jZAyEOkKKBCGEW2RmZpodQdRDRX/+Sep996ELi4h9522CBg40O5I4igx4LYQQwhTZE79lz/U3YPHzI3HiBCkQ6iBpSRBCCFGrXCUlHHzxJXK++w7/3r2Jff01rMHBZscSJyBFghBCiFpTtns3qff/k9LNmwm77TYi7rsXZbWaHUuchBQJQgi3GDBggNkRRB2XN2MGB558CmWzEf/hBwScf77ZkcRpSJEghHCLp59+2uwIoo5ylZWR8ep/yP7qK3xTUoj9vzewx8SYHUtUgRQJQgghakzpzl3sf+ghSjZuJPTGG4l84J8ou93sWKKKpEgQQrjFRRddBMD06dNNTiLqAq01ORO/5eArr2Dx8SHuvXcJlFNS9Y4UCUIItyguLjY7gqgjHFlZHHjqaQrmzMG/Z08av/wy9qhIs2OJMyBFghBCCLcpWLiI/U88jisnl8jHHiV09GiURYbkqa+kSBBCCHHWnAWFZLz2GjkTJ+KV1JyEjz/Gp1Urs2OJsyRFghBCiLNSuGQJB558ivIDBwi98UYi7rsXi4+P2bGEG0iRIIRwi6FDh5odQdQyV2EhGW+8QfbX3+DVpAlNvvoSv86dzY4l3EiKBCGEWzz00ENmRxC1qPCPPzjw1NOUp6URev31RNx/HxZfX7NjCTeTIkEIIUSVObKzyXjlVXInT8beJIEmX36BX5cuZscSNUSKBCGEW/Tt2xeAefPmmZpD1AytNbmTJ5Pxyqs4CwoIu/12wu+8Q/oeeDgpEoQQQpxS2e7dHHjuOYqW/IFvSgrR/34On5YtzY4laoEUCUIIIU7IVVJC5sdjyfz4Y5SXF9HPPkOjESNk3IMGRIoEIYQQx9Bakz9rFhmvvEp5WhpBQ4YQ+eijMmpiAyRFghBCiEqlO3dx8MUXKfz9d7xbtCBh/Hj8zz3H7FjCJFIkCCHcYsSIEWZHEGfBmZ/P4Q8+IOvzL7B4exP1xBOEXHM1yiYfEw2Z/O8LIdzirrvuMjuCOAPa4SD72285/O57OLOyCB42jMgHH8AWHm52NFEHSJEghHCLoqIiAPz8/ExOIqpCa03BvHlkvPY6ZTt34te1K5Effohv+3ZmRxN1iBQJQgi3GDJkCCDjJNQHJZs2cfDV/1D0xx94JSYS9967BPTvj1LK7GiijpEiQQghGoiyvXs59PY75E2bhjU4mKgnnyTkqpEou93saKKOkiJBCCE8XPnBgxx+/3/k/PADymYj7JabCbv1VqxBQWZHE3WcFAlCCOGhHNnZZH48luyvvkK7XISMGEHYHbdjj5TxDkTVSJEghBAexpmTQ9bnX5D1+ee4CgsJvvQSwu++G6/4eLOjiXpGigQhhFvccMMNZkdo8BzZ2WSNH0/2F1/iKiwkcOBAwu+5W+ZZEGdMigQhhFtIkWAeR3Y2WZ9+RvZXX+EqKiJw0CDC77oTn+Rks6OJek6KBCGEWxw+fBiAcBmEp9aUH8wg6/PxZH8zAV1cTNBFgwm74w5pORBuI0WCEMIthg8fDsg4CbWhdOcuMj/9hLzJU9BOJ0EXXUT4nXfgnZRkdjThYaRIEEKIeqJ4zRoyx44lf9ZslJcXwcOvIOzGG/FKSDA7mvBQphQJSqlQYCKQCOwGRmits0+yrhVYAaRprYfWVkYhhKgLtMtFwfz5ZH02jqJly7AEBRF2+22EjhqFLSzM7HjCw5nVkvAYMFtr/YpS6rGKx4+eZN37gE2AjPohhGgwXIWF5Pz4E1lffE75nr3YoqOJfPRRGl15JdYAf7PjiQbCrCLhMqBvxf3xwDxOUCQopeKAi4EXgQdqKZsQQpimLDWN7K++Iuf773Hl5+PbsSOR991H4MCBMnyyqHVmFQlRWusDAFrrA0qpkw3/9SbwCBB4uh0qpW4DbgNIkPNzQtS6O++80+wI9ZZ2uShaupTsr78hf/ZsUIqgQRcSOno0vikpZscTDViNFQlKqVlA9AleerKK2w8FMrTWK5VSfU+3vtb6I+AjgK5du+qqJxVCuMPIkSPNjlDvOLKzyf3xJ3ImTqRszx6swcGE3XQjIddei71xY7PjCVFzRYLW+oKTvaaUOqiUalzRitAYyDjBar2AS5VSQwAfIEgp9aXW+roaiiyEOAv79u0DIF6G/j0lrTXFq1aRPWEC+TN+RZeV4du5MzFj7iJw0CAs3t5mRxSiklmnG6YA1wOvVNxO/vsKWuvHgccBKloSHpICQYi6a9SoUYCMk3Ayzvx8cqdMIWfCREq3bcPi70+j4cNpNHIkPsky+JGom8wqEl4BvlVK3QzsBa4EUErFAGO11kNMyiWEEG6jXS6Kli0j98efyPvtN3RxMT5t2hD9/L8JHjIEi79cpSDqNlOKBK11JjDgBM/vB44rELTW8zCugBBCiDqvbM8ecn76idzJk3HsP4AlIIDgoUNpNGIEvu3bmR1PiCqTEReFEMINnPn55E2fTu5Pkyn+80+wWPDv2ZPIBx8kcMAALD4+ZkcUotqkSBBCiDOky8ooXLKE3Ck/kz9rFrq0FK/mzYl48AGCL70Ue1SU2RGFOCtSJAgh3OLBBx80O0Kt0A4HRcuWkTd9Onm/zcSVm4slOJhGV1xO8LBh+LRrh1LK7JhCuIVnFglahkkQorZdcsklZkeoMdrppGjlSvKmTyf/199wZmVh8fMjYMAAgi66CP/zemHx8jI7phBu55FFQsnmzex/9DECBw3Cv1dPue5YiFqwZcsWAJKTk01O4h7a5aJ49RqjMJgxA8ehQygfHwL69SXooosI6NNH+hkIj6e0B37r7ti4sf42PgFXXh4Wf38C+vUjcNCFBPTuLb/UQtSQvn37AvV7nARXWRlFf/xB/uw5FMyZYxQGXl749+lN8JAhBPTti8XPz+yYQhxHKbVSa93V3fv1yJYEe2wsLRctpHDpMvJ+nUHBzFnkTZ2K8vXFv1dPAvv2JeD887FFRJgdVQhhMmduLgULFpA/ew6FCxbgKirC4ueHf+/eBA7oT0D//lgDAsyOKYQpPLJIAFBeXgT0Po+A3uehn3mGouXLyZs5k4J58ymYNRsAn/btCejXl8C+ffFu3Vo6GwnRQJTv30/+nLnkz55F0fIV4HBgjQgnaOhQAgf0x697dzlNKQQeerqha9euesWKFSd8TWtN6ZYtFMybR/7cuZSsXQdaY4uKIqBvXwL6no9/jx5yWkKIaqrLpxtcZWUUr1hBwcJFFC5aSOm27QB4NWtG4IABBA7oj0+HDiiLxeSkQpwZOd3gJkopfFq1wqdVK8LvuAPH4cMUzF9Awbx55P38MzkTJ6K8vfHr0gX/Xr3w79UT75Yt5Y+HEPVM2Z49RlGwcCGFy5ahi4tRdjt+3boS/I9hBPTrh3ezpmbHFKJOa3AtCafiKiujaNlyCubPp3DxYsp27ADAGhaGf48e+PfsiX+vnjJAihAnMGvWLAAuuOCkE8DWKGd+PkXLV1C4aCEFCxdRXjErpb1JAgHn9ca/93n4n3OOdDwUHqmmWhKkSDiF8vR0ChcvoXDxYgqXLMGZmQmAV/PmRsHQswd+XbtiDQw86/cSQlSPs6CQ4j9XUrh0KUXLllOyYQO4XCg/P/zPPRf/3ucRcN55eCUkmB1ViBonRUI1uKtIOJp2uSjdupXC3xdTuHgxRStWoEtLwWLBu1Uyfl27Vi620FC3vrcQ9cHq1asBSElJqZH9uwoLKfpzFUXLllK4bBkl6zeA0wl2O74dO+B/zjn4nXMuvp07ycBGosGRIqEaaqJI+DtXaSnFq1ZRtHwFRStWULx6tVE0YLQ0VBYN3bpij46u0SxC1AXu7rjoyMykePVq4/dsxUqK168HhwNsNnzbt8fv3HPwP/dcfFNSsPj6uuU9haivpONiHWPx9sa/e3f8u3cHjIleitdvoGjFCopWLCdv2jRyJk4EwB4Xh2/nTvh26Ihvxw74JCej5JuOEJW000nptm1/FQWrVlO+d6/xot2Ob5s2hN14I37nnotf507Sr0CIWiJFgpsoLy/8OnfCr3MnuO1W44/eli1G0bB8BUVL/iBvys+V6/q0bo1Pxw6VhYM9Lk7GaRANhiMzk5INGyhevZqiVasoWbMWV1ERANbwcHxTOhIycgS+nTrh06aNXJIshEmkSKghymrFp00bfNq0IXT0aLTWONLTKV6zluK1ayles4acb78j+/MvALCGhuLbvj0+HTsY27VujS0yUgoHUe85Dh2ieMMGSjZupGTDRko2bMCRnm68aLHgnZxM8D8uw7dTJ3xTUqRgFqIOkSKhliilsDdujL1xY4IGDwJAl5cbTaxr11K8dh3Fa9dQsGBB5SyW1tBQfFq1wrt1K3xatcanTWu8EhNRVquZhyLESemyMmOQsopioGTDBhwZGcaLSuGVmIhfly74tG2LT9u2+LZri8Xf39zQQoiTko6LdYyzoJDSrVso2biJks2bKN20mdKtW9Hl5QAoHx+8W7bEp3VrvJNb4t08Ce+k5lhDQ+Xbl6g1zpwcSrZupXTbNmPZuo0lq/5EFxXRydfPKAiaNq0oBtrg27Yt3q1byxwIQtQQubqhGupzkXAiuryc0p27KNm0kdJNmynZvJmSTZtw5eVVrmNt1AivpOZG0dC8GV7Nm+OdlCSnLMRZcWRnU7Z7N2U7d1UUA0Zh4Dh0qHIdS1AQ3i1a4N0iyShgW7bEu1VrrAHSQiBEbZGrGxowZbfjk9wSn+SW8A/juSN9HEp37KRs5w5Kt++gdMcO8mbMwJWbW7mtJSAA7+bN8UpMxN4kAa/4BLyaJGCPj8faqJEUEAJXYSFle/caxUDFUrp7N2W79xzzs6S8vfFOSsK/Vy+jKGjZAu+WLSsL0cWLFwPQs6vb/04JIUwiLQkeRmuNMzPTKBp27qBs+w5Kt2+nbM8eHAcPHrOuJTAQr4QE7AnxeCU0wSshHnt8PF6xscYffrvdpKMQ7qTLyyk/eJDytP2Up6VRvn+/saSmUrZ79199BirYGjfGK7EJXk2a4JWYiFdiIt6Jidjj40/ZH6YuT/AkhKeTlgRRJUopbOHh2MLD8e9+7jGvuUpKKN+3j7J9+yjbu5fyvXsp27uPkg0byf9tpjF63REWC7aICOzR0dgaN8YeHY29ccX9isfWsDCZ+Mpk2uXCmZWFIyMDx6FDlGdkGAXAkWIgbb9RHLpcf22kFLbISOwxMfj36mUUAk2a4NU0Ea+EBBmYSAhRSYqEBsTi41Nx7rjFca9ph4PyAwco27OX8v1pONLTKT+QTnn6AUo3b6Zg7tzKESWPUHY71ohwbGHh2MLCsIaHVd63hYdhDa24DQuTUxvVoF0uXHl5OHNycObk4MjKxnHokLFUFAOV9zMzjy3uwCjwoqPwionF/5xu2GNjscfEGLexsdiio2XYYiFElUiRIABQNhte8fF4xcef8HWttfGBdeAA5enplB84gCM9HUfGIRyZmZQfPGhc7paVdfyHFoDNhrVRI6xBQViDgrAEB2ENCjYeBwdhCap4HFzxemAgFl9flK8vFj8/4349ufRTu1y4iopxFRb+bSmovO/ML6gsApzZ2X/dz8nBmZt77Df/o1hDQ7FFRGCLiDD6A1Tct0Uat/bISDlVJIRwGykSRJUopbCFhGALCcGnTZuTrqddLpy5uTgPH8aRmYnjcCbOzMPGbU4Ozrw8nHm5OA8dpmzHTpx5ebjy8yvHhjhlBrsdVVEwHFmUry8WHx+UzQZ2G8pmR9lsxmK3gdX613MVj42gGO+ptfFAa7TWfz3vcgEaXe5Al5ehy8pwlZWhy8rRpaXosrK/lvKK14pLjCKgqKhqx+PtjTUkxCieGjXCOzkZa6NgrI0aYTvqeWtIiFEIhIXJcN5CiFolRYJwK2WxVBYTJzqtcSLa5cKVn19RQOQZTe35+ejiYlzFxca38uIidElJxf2KxxX3nfn54HCgj1nKweE85jnKy9FHWjmUqlzU3x5jsVQ+p2w2lJfXX4u3d8V9OxY/X1SjRn+95uON1T8Ai7//iZcAf6yV9wM87tz/m2++aXYEIYSbeeTVDUqpfGCL2TlqSDhw2OwQNUiOr36T46u/PPnYwPOPL1lrHejunXpqS8KWmrgUpC5QSq3w1GMDOb76To6v/vLkY4OGcXw1sV+5fk0IIYQQJyRFghBCCCFOyFOLhI/MDlCDPPnYQI6vvpPjq788+dhAju+MeGTHRSGEEEKcPU9tSRBCCCHEWar3RYJSKlQpNVMpta3iNuQU61qVUquUUlNrM+PZqMrxKaV8lFLLlFJrlFIblFLPmZH1TFTx+OKVUnOVUpsqju8+M7Keiar+fCqlPlVKZSil1td2xupSSg1WSm1RSm1XSj12gteVUurtitfXKqU6m5HzTFXh+FoppZYopUqVUg+ZkfFsVOH4rq34f1urlFqslOpoRs4zVYXju6zi2FYrpVYopc4zI+eZOt3xHbVeN6WUUyk1/KzeUFeMNFdfF+A/wGMV9x8DXj3Fug8AXwNTzc7tzuMDFBBQcd8OLAW6m53djcfXGOhccT8Q2Aq0MTu7u46v4rU+QGdgvdmZT3M8VmAH0AzwAtb8/f8CGAJMr/i57A4sNTu3m48vEugGvAg8ZHbmGji+nkBIxf2LPPD/L4C/TrV3ADabndudx3fUenOAX4DhZ/Oe9b4lAbgMGF9xfzzwjxOtpJSKAy4GxtZOLLc57fFpQ0HFQ3vFUl86m1Tl+A5orf+suJ8PbAJiayvgWarSz6fWegGQVUuZzsY5wHat9U6tdRkwAeMYj3YZ8HnFz+UfQCOlVOPaDnqGTnt8WusMrfVyoNyMgGepKse3WGudXfHwDyCuljOejaocX4Gu+CQF/Kk/fyuhar9/APcAPwAZJ3itWjyhSIjSWh8A48MEo8o/kTeBR4ATz5xTd1Xp+CpOpazG+KGYqbVeWnsRz0pV//8AUEolAp0wWkvqg2odXz0QC+w76nEqxxdsVVmnrqrP2auiusd3M0arUH1RpeNTSg1TSm0GpgE31VI2dzjt8SmlYoFhwAfueMN6MeKiUmoWEH2Cl56s4vZDgQyt9UqlVF83RnOLsz0+AK21E0hRSjUCflRKtdNa14nz2+44vor9BGBUx/drrfPckc0d3HV89cSJ5vv++zexqqxTV9Xn7FVR5eNTSvXDKBLq0zn7Kh2f1vpHjL+TfYDngQtqOpibVOX43gQe1Vo7lTrR6tVTL4oErfVJ/wOVUgeVUo211gcqmjRP1LzSC7hUKTUE8AGClFJfaq2vq6HI1eKG4zt6XzlKqXnAYKBOFAnuOD6llB2jQPhKaz2phqKeEXf+/9UDqcDR84nHAfvPYJ26qj5nr4oqHZ9SqgPGqdmLtNaZtZTNHar1/6e1XqCUaq6UCtda14d5HapyfF2BCRUFQjgwRCnl0Fr/dCZv6AmnG6YA11fcvx6Y/PcVtNaPa63jtNaJwFXAnLpSIFTBaY9PKRVR0YKAUsoXoyreXFsBz1JVjk8BnwCbtNb/V4vZ3OG0x1fPLAdaKKWaKqW8MH6fpvxtnSnA6IqrHLoDuUdOudQDVTm++uy0x6eUSgAmAaO01ltNyHg2qnJ8SRV/U6i48sYLqC+F0GmPT2vdVGudWPF59z1w15kWCEd2WK8XIAyYDWyruA2teD4G+OUE6/elfl3dcNrjw+ihuwpYi9F68C+zc7v5+M7DaFJbC6yuWIaYnd1dx1fx+BvgAEZnuFTgZrOzn+KYhmBcYbIDeLLiuTuAOyruK+C9itfXAV3Nzuzm44uu+D/KA3Iq7geZnduNxzcWyD7qd22F2ZndfHyPAhsqjm0JcJ7Zmd15fH9bdxxneXWDjLgohBBCiBPyhNMNQgghhKgBUiQIIYQQ4oSkSBBCCCHECUmRIIQQQogTkiJBCCGEECckRYIQ4rQqZpNbrZRar5T6+ci4HGewnxuUUu+6OZ4QooZIkSCEqIpirXWK1rodxkRUY8wOJISoeVIkCCGqawkVk8pUDGk7Qym1Uim1UCnVquL5S5RSS5VSq5RSs5RSUaYmFkKcESkShBBVppSyAgP4ayjYj4B7tNZdgIeA9yueXwR011p3wpjO9pHaziqEOHv1YoInIYTpfCumIk8EVgIzK2bl7Al8d9Rsc94Vt3HAxIpJrbyAXbWaVgjhFtKSIISoimKtdQrQBONDfwzG34+cir4KR5bWFeu/A7yrtW4P3I4x+6oQop6RIkEIUWVa61zgXoxTC8XALqXUlWDM1qmU6lixajCQVnH/+uN2JISoF6RIEEJUi9Z6FbAGY5raa4GblVJrMGbWu6xitWcxTkMsBA6bkVMIcfZkFkghhBBCnJC0JAghhBDihKRIEEIIIcQJSZEghBBCiBOSIkEIIYQQJyRFghBCCCFOSIoEIYQQQpyQFAlCCCGEOCEpEoQQQghxQv8PUHlc45o9rMwAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ds = [np.pi/4, 0.175, 0.1, 0.05] # Note at \\delta=0.175, \\alpha(A)~=0\n", "pltNumRange(ds)" ] }, { "cell_type": "code", "execution_count": 4, "id": "090ec933", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X0 = [1, 0.1]\n", "ds = [np.pi/4, 0.175, 0.1, 0.05] # As expected at \\delta=0.175, energy growth~=0\n", "pltEnergy(X0, ds, awid=0.1)" ] }, { "cell_type": "markdown", "id": "823957ff", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Let's think about the meaning of $\\alpha(A)$ and the initial condition $x_0^*$ that generates $\\alpha(A)$\n", "+ If $\\alpha(A)>0$, then if the system starts from $x_0^*$, the system energy will **grow**\n", "+ In short time the growth can be high and the system may show some **instability**\n", "+ This is true even when all the eigenvalues are on the left half plane (i.e. stable when $t\\rightarrow\\infty$)\n", "\n", "Think again the matrix normality\n", "+ If $A$ is normal, $\\alpha(A)=Re(\\lambda_\\max(A))$, then long-term stability **equals to** short-term stability\n", "+ If $A$ is non-normal, it is possible that $\\alpha(A) \\gg Re(\\lambda_\\max(A))$, then long/short-term analysis **differ**" ] }, { "cell_type": "markdown", "id": "195a7e4e", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Maximum-gain analysis: Initial conditions\n", "\n", "Consider a non-normal system that initially undergoes fast growth and eventually decay to zero. It is of interest to estimate the maximum amplitude of the growth, or the **maximum gain** of the system\n", "$$\n", "G_\\max = \\max_{t\\geq 0}\\norm{\\exp(tA)}\n", "$$\n", "+ If the amplitude is low, we are probably still in a linearizable region and the system is still stable over all\n", "+ If the amplitude is high, then the linearization itself might break - i.e. the long-term behavior becomes meaningless" ] }, { "cell_type": "markdown", "id": "790d72da", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### For a given time\n", "+ Starting from zero-input solution\n", "$$\n", "x(t) = \\exp(At)x_0\n", "$$\n", "+ What is the $x_0$ that maximizes the energy amplification at a given time $t^*$?" ] }, { "cell_type": "markdown", "id": "58daa28a", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We essentially want\n", "$$\n", "\\tilde{G}_\\max(t^*) = \\max_{x_0} \\frac{\\norm{\\exp(t^*A)x_0}}{\\norm{x_0}} = \\norm{\\exp(t^*A)}\n", "$$\n", "Then the SVD of $\\exp(t^*A)=U\\Sigma V^H$ solves the problem\n", "+ The first right singular vector $v_1$ defines the (unit) $x_0$\n", "+ The first left singular vector $u_1$ defines the maximum state $x$ at $t=t^*$\n", "+ The first singular value $\\sigma_1$ is the maximum gain\n", "\n", "> Also, the minimum $\\sigma$ corresponds to the minimum gain of the system, i.e. we cannot get lower than that!" ] }, { "cell_type": "code", "execution_count": 5, "id": "31aa7c4b", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "delta = 0.05 # This is a highly non-normal case, and we get a pretty large gain (and disparity in gains)\n", "ti = 14\n", "pltInitGain(delta, ti)" ] }, { "cell_type": "markdown", "id": "6b7d8e85", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### For any time\n", "\n", "We would like **maximum gain** of the system\n", "$$\n", "G_\\max = \\max_{t\\geq 0}\\norm{\\exp(tA)} = \\max_{t\\geq 0}\\tilde{G}_\\max(t)\n", "$$\n", "Consider the Laplace Transform of the solution\n", "$$\n", "\\tilde{x}(s) = \\int_0^\\infty \\exp(-st)\\exp(tA)x_0 dt = (sI-A)^{-1}x_0\n", "$$\n", "Here we can define the **resolvent operator**\n", "$$\n", "H(s) = (sI-A)^{-1} \\equiv \\int_0^\\infty \\exp(-st)\\exp(tA) dt\n", "$$" ] }, { "cell_type": "markdown", "id": "3338ad26", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Using inequalities for integrals, we can find the lower bound of $G_\\max$\n", "$$\n", "\\norm{H(s)} \\leq \\int_0^\\infty \\norm{\\exp(-st)} \\norm{\\exp(tA)} dt \\leq \\frac{1}{Re(s)} \\max_{t\\geq 0}\\norm{\\exp(tA)}\n", "$$\n", "or\n", "$$\n", "\\max_{Re(s)} Re(s)\\norm{H(s)} \\leq G_\\max\n", "$$\n", "The lower bound is also called the **Kreiss constant**, $K(A)$.\n", "> $K(A)\\geq 1$; and $K(A)=1$ if $A$ is normal - think about why?" ] }, { "cell_type": "markdown", "id": "bc4732bb", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "It turns out one can also find an upper bound using $K(A)$, so that\n", "$$\n", "K(A)\\leq G_\\max \\leq e n K(A)\n", "$$\n", "where $e=\\exp(1)$ and $n$ is dimension of $A$.\n", "> So Kreiss constant is very useful for characterizing the max gain." ] }, { "cell_type": "markdown", "id": "f359316b", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Side note\n", "One may also find another upper bound for $G_\\max$ from complex analysis\n", "$$\n", "\\exp(tA) = \\frac{1}{2\\pi i} \\oint_\\Lambda \\exp(zt) (zI-A)^{-1} dz \\leq \\frac{1}{2\\pi} \\oint_\\Lambda \\norm{(zI-A)^{-1}} |dz|\n", "$$\n", "Then\n", "$$\n", "G_\\max \\leq \\frac{1}{2\\pi} \\oint_\\Lambda \\norm{H(s)} |ds|\n", "$$" ] }, { "cell_type": "code", "execution_count": 6, "id": "9b5d8b05", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "delta = 0.05\n", "ts = range(1,80)\n", "pltGainSweep(delta, ts) # So Kreiss constant does provide an estimate of the lower bound of gains" ] }, { "cell_type": "markdown", "id": "674bfaf9", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Maximum-gain analysis: Forced response\n", "\n", "Similarly, we can think about the zero-initial-condition solution\n", "$$\n", "x(t) = \\int_0^t \\exp((\\tau-t)A)f(\\tau)d\\tau\n", "$$\n", "+ What is the (harmonic) input $f$ that maximizes the energy amplification over time?" ] }, { "cell_type": "markdown", "id": "6604ec0c", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Assume $f(t)=\\hat{f}\\exp(i\\omega t)$ and do Fourier Transform\n", "$$\n", "\\hat{x} = (i\\omega I-A)^{-1} \\hat{f}\n", "$$\n", "Then we essentially want\n", "$$\n", "G_\\max = \\max_{\\hat{f}} \\frac{\\norm{(i\\omega I-A)^{-1} \\hat{f}}}{\\norm{\\hat{f}}}\n", "$$\n", "Again the SVD gives the solution. Let $(i\\omega I-A)^{-1}=U(\\omega)\\Sigma(\\omega) V(\\omega)^H$, then\n", "+ $V(\\omega)$ gives the forcing and $U(\\omega)$ gives the output\n", "+ $\\Sigma(\\omega)$ gives the gain\n", "\n", "> The range of $\\sigma(\\omega)$'s give the range of possible gains at the given frequency $\\omega$" ] }, { "cell_type": "code", "execution_count": 7, "id": "cb38d7a2", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "W = np.linspace(0.01, 0.75, 51)\n", "ds = [np.pi/4, 0.05]\n", "pltSVDsweep(W, ds)" ] }, { "cell_type": "code", "execution_count": 8, "id": "af014e7b", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "S = makeSys2D(0.785) # The normal system behaves \"normally\", no extremely large gains\n", "ugv = frMIMO(S, [0.3], ifFull=True)\n", "pltGainResp(S, 0.3, ugv, 0)\n", "pltGainResp(S, 0.3, ugv, 1)" ] }, { "cell_type": "code", "execution_count": 9, "id": "39621681", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "S = makeSys2D(0.05) # But things get crazy in non-normal systems\n", "ugv = frMIMO(S, [0.3], ifFull=True)\n", "pltGainResp(S, 0.3, ugv, 0)\n", "pltGainResp(S, 0.3, ugv, 1)" ] }, { "cell_type": "markdown", "id": "73276b75", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Think about the example more,\n", "$$\n", "\\norm{(i\\omega I-A)^{-1}} = \\norm{V(i\\omega I-\\Lambda)^{-1}V^{-1}} \\leq \\frac{\\kappa(V)}{\\norm{i\\omega I-\\Lambda}}\n", "$$\n", "+ For a normal system, $\\kappa(V)=1$, and the norm becomes infinite (if no damping) if the forcing frequency coincides with the spectrum - then we have resonance, *as expected*.\n", "+ For non-normal system, it is possible to have **pseudo-resonance**, i.e. large response to external forcing, even though the forcing frequency is far from the actual spectrum." ] }, { "cell_type": "markdown", "id": "cc28d9d5", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Alternative view of $\\norm{H(s)}$\n", "\n", "Consider the eigenvalue problem of $A$, perturbed by another matrix $E$, $\\norm{E}=\\epsilon$ is small\n", "$$\n", "(A+E)u=\\lambda u,\\quad \\mbox{or}\\quad (A-\\lambda I)u = -Eu\n", "$$\n", "Using the matrix norm inequality\n", "$$\n", "\\begin{align}\n", "\\norm{(A-\\lambda I)u} &= \\norm{-Eu} \\leq \\norm{E}\\norm{u} = \\epsilon\\norm{u} \\\\\n", "\\epsilon^{-1} &\\leq \\norm{u}/\\norm{(A-\\lambda I)u} = \\norm{(A-\\lambda I)^{-1}}\n", "\\end{align}\n", "$$\n", "Or\n", "$$\n", "\\norm{H(s)} \\geq \\epsilon^{-1}\n", "$$\n", "In other words,\n", "+ The resolvent contours represent the eigenvalue distribution of all possible perturbed $A$'s\n", " - Therefore the contours are also called **pseudospectrum**\n", "+ If the eigenvalues change a lot with a small $\\epsilon$, i.e. are sensitive to perturbations, then the system is likely to be non-normal" ] }, { "cell_type": "code", "execution_count": 10, "id": "2a7aa04e", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# note how as non-normality increases, the pseudospectrum extrudes into positive side,\n", "# which indicates the potential (easier) destabilization of the system.\n", "pltPseudoSpec([np.pi/4, 0.175, 0.1, 0.05], range(-5, 0))" ] }, { "cell_type": "markdown", "id": "e3043db5", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Spectrum and Pseudospectrum\n", "\n", "One can define the **spectrum** of $A$, which is equivalent to eigenvalues\n", "$$\n", "\\sigma(A) = \\left\\{ z\\in\\mathbb{C}\\ |\\ (zI-A)^{-1} \\mbox{ does not exist} \\right\\}\n", "$$\n", "\n", "> Here we are following the common notation in literature, but be careful to differentiate from singular values of $A$.\n", "\n", "Then pseudospectrum can be thought of the generalization of eigenvalues\n", "$$\n", "\\sigma_\\epsilon(A) = \\left\\{ z\\in\\mathbb{C}\\ |\\ \\norm{(zI-A)^{-1}} > \\epsilon^{-1} \\right\\}\n", "$$\n", "\n", "So that we formally have\n", "$$\n", "\\lim_{\\epsilon\\rightarrow 0}\\sigma_\\epsilon(A)=\\sigma(A)\n", "$$\n", "since as $\\epsilon\\rightarrow 0$, $\\norm{(zI-A)^{-1}} > \\infty$, meaning $(zI-A)^{-1}$ does not exist.\n", "\n", "In fact, there is a theorem, stating that the intersection of $\\sigma_\\epsilon(A)$ of all $\\epsilon$ gives $\\sigma(A)$\n", "$$\n", "\\cap_{\\epsilon>0}\\sigma_\\epsilon(A)=\\sigma(A)\n", "$$" ] }, { "cell_type": "markdown", "id": "e6a062e2", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "With the above connection, one can also have the following equivalent definitions\n", "$$\n", "\\sigma_\\epsilon(A) = \\left\\{ z\\in\\mathbb{C}\\ |\\ \\exists \\norm{E}<\\epsilon,\\ z\\in\\sigma(A+E) \\right\\}\n", "$$\n", "$$\n", "\\sigma_\\epsilon(A) = \\left\\{ z\\in\\mathbb{C}\\ |\\ \\exists v,\\ \\norm{(zI-A)v}=\\epsilon \\norm{v} \\right\\}\n", "$$\n", "\n", "And one can also define the abscissa of the pseudospectrum, similar to numerical abscissa, as\n", "$$\n", "\\alpha_\\epsilon(A) = \\max Re(\\sigma_\\epsilon(A))\n", "$$\n", "Then this connects to the Kreiss constant again\n", "$$\n", "K(A) = \\max_{\\epsilon>0} \\frac{\\alpha_\\epsilon(A)}{\\epsilon}\n", "$$" ] }, { "cell_type": "markdown", "id": "094852ef", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Summary\n", "\n", "To characterize a linear system, esp. in terms of stability, now we know\n", "- Linear stability analysis: Real parts of eigenvalues\n", "- Transient growth analysis: Numerical range and abscissa\n", "- Maximum gain analysis: Resolvent operator and its SVD; Pseudospectrum and the Kreiss constant\n", "\n", "> In the next lecture let's revisit Dynamic Mode Decomposition in terms of resolvent analysis" ] }, { "cell_type": "markdown", "id": "25239660", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Side note\n", "Finally, the analysis using resolvent operator can extend to more complex dynamical systems, such as\n", "+ stochastic forcing\n", "+ parameter and mean-flow uncertainty\n", "+ time-periodic and generally time-dependent flow\n", "+ nonlinear perturbation dynamics\n", "+ multiple inhomogeneous directions/complex geometry \n", "using Lyapunov analysis, Floquet theory, adjoint analysis, and so on.\n", "\n", "See [Schmid2009] for more details." ] }, { "cell_type": "markdown", "id": "4cdd1df4", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Properties of Nonnormal matrices (Optional)\n", "\n", "Summary based on [this post](https://nhigham.com/2020/11/24/what-is-a-nonnormal-matrix/) by Nick Higham.\n", "\n", "This discussion is from a pure linear algebra perspective, different from the previous discussion based on linear systems." ] }, { "cell_type": "markdown", "id": "d2c45a14", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Definitions\n", "\n", "$A$ is **normal** if it is **unitarily diagonalizable**: $A = QDQ^H$\n", "- $D$ diagonal, having the eigenvalues\n", "- $Q$ unitary, representing a complete set of orthonormal eigenvectors\n", "- The condition number $\\kappa(Q)=\\norm{Q} \\norm{Q^{-1}}=\\norm{Q} \\norm{Q^H}=1$\n", "\n", "> $A$ is normal iff it is diagonalizable and its different eigenspaces are orthogonal to each other\n", "\n", "For a general diagonalizable matrix, $A = XDX^{-1}$, the condition number $\\kappa(X)$ can be arbitrarily large, which may pose an issue in numerical computation.\n", "\n", "> Yet, one should also keep the non-diagonlizable matrices in mind" ] }, { "cell_type": "markdown", "id": "9a84865d", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "For example, in 2D, normal matrices can only be of the following two forms,\n", "$$\n", "\\begin{bmatrix} a & b \\\\ b & c \\end{bmatrix}, \\begin{bmatrix} a & b \\\\ -b & a \\end{bmatrix}\n", "$$\n", "\n", "And one example type of non-normal matrix is\n", "$$\n", "\\begin{bmatrix} a & b \\\\ 0 & a \\end{bmatrix}\n", "$$" ] }, { "cell_type": "markdown", "id": "af8191e2", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Alternatively, we can define a **commutator**, which is always Hermitian,\n", "$$\n", "C = AA^H- A^HA\n", "$$\n", "and apparently when $A$ is normal $C=0$.\n", "\n", "When $A$ is non-normal - general properties of $C$\n", "- $C$ has zero trace, because the diagonal cancels out; then the eigenvalues sum to zero\n", "- But if $C$ is nonzero, there should be at least two different nonzero eigenvalues (so they cancel out and make trace zero)\n", "- And the rank of $C$ is at least 2." ] }, { "cell_type": "markdown", "id": "056af42d", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Measurement of non-normality\n", "\n", "There are many ways to do so. In the previous sections, we have seen numerical range/abscissa." ] }, { "cell_type": "markdown", "id": "f9bbd882", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Using Triangularization\n", "While $A$ is not necessarily unitarily diagonalizable, it always has a **Schur decomposition**,\n", "$$\n", "A = QTQ^H\n", "$$\n", "where $Q$ is unitary and $T=D+M$ is upper triangular. $D$ is still the eigenvalue matrix, and $M$ is a strict upper triangular matrix.\n", "\n", "When $A$ is normal, certainly $M=0$ and Schur decomposition reduces to eigendecomposition.\n", "- Then $\\norm{M}_F$ is a natural measure of how far $A$ is from being normal\n", "- Formally, one can use the following equivalent form, given by Henrici in 1960s\n", "$$\n", "\\nu(A) = \\norm{M}_F \\equiv \\biggl( \\norm{A}_F^2 - \\sum_{j=1}^n |\\lambda_j|^2 \\biggr)^{1/2}. \n", "$$\n", "\n", "It is bounded as\n", "$$\n", "\\frac{\\norm{C}_F}{4\\norm{A}_2} \\le \\nu(A) \\le \\Bigl( \\frac{n^3-n}{12} \\Bigr)^{1/4} \\norm{C}_F^{1/2}. \n", "$$" ] }, { "cell_type": "markdown", "id": "4e8070f1", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Using Frobenius norm\n", "Alternatively, one can define the distance to normality by \"brutal force\" as the minimum \"effort\" $E$ required to make $A$ normal,\n", "$$\n", "d(A) = \\min \\left\\{ \\norm{E}_F: A+E \\in \\mathbb{C}^{n\\times n} \\mbox{ is normal} \\right\\}\n", "$$\n", "See [Higham1988](https://www.maths.manchester.ac.uk/~higham/narep/narep161.pdf) for algorithms for $d(A)$.\n", "\n", "It is bounded as\n", "$$\n", "\\frac{\\nu(A)}{n^{1/2}} \\le d(A) \\le \\nu(A)\n", "$$" ] }, { "cell_type": "markdown", "id": "d6924e6f", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Using condition number\n", "\n", "Considering only the diagonalizable matrices, $A=X\\Lambda X^{-1}$, one may simply use the condition number of $X$ to quantify the non-normality. Specifically, we consider the L2-norm condition number\n", "$$\n", "\\kappa_2(X) = \\norm{X}\\norm{X^{-1}}\n", "$$\n", "\n", "But since in the diagonalization process, $X$ is not unique, we pick the one with the smallest $\\kappa_2$, i.e.,\n", "$$\n", "\\kappa_2(X) = \\min\\left\\{ \\kappa_2(Y): A = YDY^{-1}, D \\mbox{ diagonal} \\right\\}. \n", "$$" ] }, { "cell_type": "markdown", "id": "f3c09013", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Next we show a series of bounds relevant to $\\kappa_2(X)$ and observe that when $\\kappa_2(X)=1$, i.e. when $A$ is normal, all the bounds **simplify to equalities**. This makes $\\kappa_2(X)$ a good indicator of non-normality.\n", "\n", "Notations\n", "+ Order the eigenvalues of $A$ as $|\\lambda_1| \\ge |\\lambda_2| \\ge \\cdots \\ge |\\lambda_n|$\n", "+ $\\rho(A)$ denotes the spectral radius of $A$, the largest absolute value of any eigenvalue of $A$, so $\\rho(A)=|\\lambda_1|$.\n", "+ Assume $A$ has singular values $\\sigma_1 \\ge \\sigma_2 \\ge \\cdots \\ge \\sigma_n$" ] }, { "cell_type": "markdown", "id": "32d0362f", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "+ Utilizing the norm inequality on $A=X\\Lambda X^{-1}$\n", "$$\n", "\\frac{\\|A\\|_2}{\\kappa_2(X)} \\le \\rho(A) \\le \\|A\\|_2. \n", "$$\n", "\n", "+ Relating singular values and eigenvalues\n", "$$\n", "\\frac{\\sigma_i(A)}{\\kappa_2(X)} \\le |\\lambda_i(A)| \\le \\kappa_2(X) \\sigma_i(A) \n", "$$\n", "\n", "+ For any real $p > 0$,\n", "$$\n", "\\frac{\\rho(A)^p}{\\kappa_2(X)} \\le \\norm{A^p}_2 \\le \\kappa_2(X) \\rho(A)^p.\n", "$$\n", "\n", "+ For any function $f$ defined on the spectrum of $A$,\n", "$$\n", "\\frac{\\max_i|f(\\lambda_i)|}{\\kappa_2(X)} \\le \\norm{f(A)}_2 \\le \\max_i|f(\\lambda_i)|. \n", "$$" ] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.6" } }, "nbformat": 4, "nbformat_minor": 5 }