vi CONTENT S
Chapter 6 . Polynomia l System s i n Economic s 7 1
6.1. Three-Perso n Game s wit h Tw o Pur e Strategie s 7 1
6.2. Tw o Numerica l Example s Involvin g Squar e Root s 7 3
6.3. Equation s Definin g Nas h Equilibri a 7 7
6.4. Th e Mixe d Volum e o f a Produc t o f Simplice s 7 9
6.5. Computin g Nas h Equilibri a wit h PHCpac k 8 2
6.6. Exercise s 8 5
Chapter 7 . Sum s o f Square s 8 7
7.1. Positiv e Semidefinit e Matrice s 8 7
7.2. Zero-dimensiona l Ideal s an d SOStool s 8 9
7.3. Globa l Optimizatio n 9 2
7.4. Th e Rea l Nullstellensat z 9 4
7.5. Symmetri c Matrice s wit h Doubl e Eigenvalue s 9 6
7.6. Exercise s 9 9
Chapter 8 . Polynomia l System s i n Statistic s 101
8.1. Conditiona l Independenc e 101
8.2. Graphica l Model s 104
8.3. Rando m Walk s o n th e Intege r Lattic e 109
8.4. Maximu m Likelihoo d Equation s 114
8.5. Exercise s 17
Chapter 9 . Tropica l Algebrai c Geometr y 119
9.1. Tropica l Geometr y i n the Plan e 119
9.2. Amoeba s an d thei r Tentacle s 123
9.3. Th e Bergma n Comple x o f a Linea r Spac e 127
9.4. Th e Tropica l Variet y o f an Idea l 129
9.5. Exercise s 13
Chapter 10. Linea r Partia l Differentia l Equation s
with Constan t Coefficient s 133
10.1. Wh y Differentia l Equations ? 133
10.2. Zero-dimensiona l Ideal s 135
10.3. Computin g Polynomia l Solution s 137
10.4. Ho w to Solv e Monomia l Equation s 140
10.5. Th e Ehrenpreis-Palamodo v Theore m 141
10.6. Noetheria n Operator s 142
10.7. Exercise s 144
Bibliography 147
Index 151
Previous Page Next Page