A Matrix Organization Functional authority Project authority President President Farm FarmMachinery Machinery Division Division Production Production department department Legal Legal department department Engineering Engineering department department Accounting Accounting department department Project Project Alpha Alpha manager manager Production Production support support group group Legal Legal support support group group Engineering Engineering support support group group Accounting Accounting support support group group Project Project Beta Beta manager manager Production Production support support group group Legal Legal support support group group Engineering Engineering support support group group Accounting Accounting support support group group Project Project Gamma Gamma manager manager Production Production support support group group Legal Legal support support group group Engineering Engineering support support group group Accounting Accounting support support group group

Alpha-beta algorithm initiation : • Two functions recursively call each other : : function MAX-value (n, alpha, beta) if n is a leaf node then return f(n); for each child n’ of n do alpha :=max{alpha, MIN-value(n’, alpha, beta)}; if alpha >= beta then return beta /* pruning */ end{do} return alpha function MIN-value (n, alpha, beta) if n is a leaf node then return f(n); for each child n’ of n do beta :=min{beta, MAX-value(n’, alpha, beta)}; if beta <= alpha then return alpha /* pruning */ end{do} return beta

The Alpha and the Beta for Performance Evaluation(1/2) • The regression model for calculating the beta is useful as it also provides a means of performance evaluation. If we regress (R-Rf) on (Rm-Rf), then the intercept of the regression, or the “alpha”, provides an estimate of the amount by which the stock or a portfolio has beaten the market after adjusting for the beta risk. • In other words: R-Rf = alpha + beta (Rm-Rf). • A positive alpha means that the portfolio has outperformed the market. A negative alpha means that it has lagged behind the market. • If we regress R on Rm, then the intercept will not directly estimate the alpha. However, we can easily calculate it by noting that: R = alpha + Rf - beta Rf + beta Rm so that the intercept of the regression will be equal to [alpha + Rf(1 - beta)]. So alpha = intercept - Rf(1-beta).

FSMA-Summary of Key Requirements Farm Definition Secondary Activities Farm: This is an operation not located on the Primary Production Farm that is devoted to harvesting, packing and/or holding raw agricultural commodities. It must be majority owned by the Primary Production Farm that supplies the majority of the raw agricultural commodities harvested, packed, or held by the Secondary Activities Farm. This definition for a Secondary Activities Farm was provided, in part, so that farmers involved in certain formerly off-farm packing now fit under the definition of “farm,” as the packing is still part of the farming operation. In addition to off-farm produce packing operations, another example of a Secondary Activities Farm could be an operation in which nuts are hulled and dehydrated by an operation not located at the orchard before going to a processing plant. If the farmer that owns the orchards and supplies the majority of the nuts is a majority owner of the hulling/dehydrating facility, that operation is a Secondary Activities Farm.

int NegaScout ( position p; int alpha, beta ) { /* compute minimax value of position p */ int a, b, t, i; if ( d == maxdepth ) return Evaluate(p); /* leaf node */ determine successors p_1,...,p_w of p; a = alpha; b = beta; for ( i = 1; i <= w; i++ ) { t = -NegaScout ( p_i, -b, -a ); if ( (t > a) && (t < beta) && (i > 1) && (d < maxdepth-1) ) a = -NegaScout ( p_i, -beta, -t ); /* re-search */ a = max( a, t ); if ( a >= beta ) return a; /* cut-off */ b = a + 1; /* set new null window */ } return a; } int NegaScout ( position p; int alpha, beta ) { /* compute minimax value of position p */ int a, b, t, i; if ( d == maxdepth ) return Evaluate(p); /* leaf node */ determine successors p_1,...,p_w of p; a = alpha; b = beta; for ( i = 1; i <= w; i++ ) { t = -NegaScout ( p_i, -b, -a ); if ( (t > a) && (t < beta) && (i > 1) && (d < maxdepth-1) ) a = -NegaScout ( p_i, -beta, -t ); /* re-search */ a = max( a, t ); if ( a >= beta ) return a; /* cut-off */ b = a + 1; /* set new null window */ } return a; }

Get Involved! Student Organizations • • • • • • • • • • • • Association for Computing Machinery President: Quintin Donnelly | Email Quintin: [email protected] American Medical Student Association President: Brooks Becton | Email Brooks: [email protected] Forensic Science Society President: Ashley Aucoin | Email Ashley: [email protected] Institute of Electrical and Electronic Engineers President: Keith Conley | Email Keith: [email protected] Instructional Technology Student Association President: Robin Jackson | Email Robin: [email protected] Polymer Science Association President: Kristin Van de Voorde | Email Kristen: [email protected] Society for Industrial and Applied Mathematics (SIAM) President: Haley Dozier| Email Haley: [email protected] Society of Physics Students President: Andrew Giovengo | Email Andrew: [email protected] Southern Geological Society President: Daniel Winkler |Email Daniel: [email protected] Student Constructors President: Caleb Kergosien| Email Caleb: [email protected] The American Chemical Society - Student Affiliates Chapter USM President: David Sliman | Email David: [email protected] Women in Science and Engineering (WiSE) President: Cassandra Reese | Email Cassandra: [email protected]

Alpha-beta pruning • Traverse the search tree in depth-first order • At each MAX node n, alpha(n) = maximum value found so far • At each MIN node n, beta(n) = minimum value found so far – The alpha values start at -∞ and only increase, while beta values start at +∞ and only decrease • Beta cutoff: Given MAX node n, cut off search below n (i.e., don’t generate/examine any more of n’s children) if alpha(n) >= beta(i) for some MIN node ancestor i of n. • Alpha cutoff: stop searching below MIN node n if beta(n) <= alpha(i) for some MAX node ancestor i of n.

References • • • • • • • • • [1] Gamma Knife Overview. (2015, November 16). [2] Gamma Knife Sugery: Pros and Cons. (2015, November 16). [3] Caruso, JP, Moosa, S, Fezeu, F, Ramesh, A, Sheehan, JP. (2015, November 16). A cost comparative study of Gamma Knife radiosurgery versus open surgery for intracranial pathology. [4]Taban, A. (2015, November 14). A gamma knifre case study: Acoustic Neuroma. [5] Gamma Knifre Radiosurgery. (2015, November 14). [6]Niranjan, A. (2015, November 14). Gamma Knife Radiosurgery: Current Technique. [7] The Gamma Knifre: A Technical Overview. (2015, November 14). [8] MayoClinic: Brain Stereotactic radiosurgery. (2015, November 14). [9] RWJ University Hospital. (2015, November 16). Gamma Knife.

Beta-Amyloid Plaque Formation Key enzymes: •Alpha-secretase •Beta-secretase •Gamma-secretase Protein fragments: p3 alpha and gamma harmless 40 amino acid string beta and gamma harmless 42 amino acid string beta and gamma TOXIC Beta-Amyloid Precursor Protein (APP) is cut or cleaved by these enzymes three different protein fragments form

//////////////////////////////////////////// // Class implementation file: Matrix.cpp // // The implementation of the copy and // // initializing constructors, the setEle- // // ment, determinant, and minor member // // functions, and the output operator. // //////////////////////////////////////////// #include #include #include #include #include #include "Matrix.h" using namespace std; // Copy constructor: Copies existing mat.// matrix::matrix(const matrix &m) { size = m.size; for (int row = 0; row < m.size; row++) for (int col = 0; col < m.size; col++) table[row][col] = m.table[row][col]; } // Initializing constructor: Sets *this // // up as a sz x sz matrix of zeros. // matrix::matrix(int sz) { size = sz; for (int row = 0; row < sz; row++) for (int col = 0; col < sz; col++) table[row][col] = 0; } CS 240 // SetElement Member Function: Sets the // // (i,j) element of the matrix to item. // void matrix::setElement(int i, int j, elementType e) { assert ((0<=i) && (i