nr. 477 - 2011 - Institut for Natur, Systemer og Modeller (NSM)

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Index W s of NODf1-USB, 79 dimension of, 80 W u , 79 of NODf1-USB, 79 dimension of, 80 β-Cell, 1, 7 apoptosis, 7 apoptotic, 25 necrosis, 7 necrotic, 25 neogenesis, 15 proliferation during inflammation, 36 replication, 14 matlab, 42, 73, 76, 77 matlab, 34, 73, 88, 108 Activated Macrophages, 82 Activation due to necrotic cells, 36 Activation Step, 38 Active Macrophages behavior of concentration and heteroclinic orbits, 83 Akaike Information Criterion, 38 Akaike information criterion, 38 Alloxan, 15 Andrew C. Ivy, 2, 8 Animal Model, 7 Sprague Dawley rat, 120 Antigen Presenting Cell (APC), 9 Antigen Therapy, 16 Apoptosis, 7 in healthy individuals, 33 maximal cytokine induced rate of, 25 natural Model A, 107 Model B, 110 Model C, 114 Apoptotic Wave, 19, 19, 25, 26, 73 and β-cell population, 107 and bifurcation analysis, 89 depence on time, 131 Arrow fully drawn, 23 stippled, 23 Autoantibodies, 8 Autoantibody, 7 and risk of developing T1D, 8 Autoantigen, 8, 15 Autoimmune Response, 7 Autoimmunity, 15 autoimmune response, 14 B Cell, 9, 18 Bacteria, 133 Balb/c Mouse, 18 Bifurcation, 65 codimension of, 66 codimension one, 65 diagram, 73 Hopf, 77 local, 66 parameter, 66 pitchfork, 66 point, 66 saddle-node, 66, 95 transcritical, 66 codimension one, 73 codimension two, 101 global, 71, 83 pitchfork, 86 point, 77 saddle-node, 81 173
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- I, OM OG MED MATEMATIK OG FYSIK E
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Exploring Treatment Strategies for
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Preface iii questions that were out
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vi Contents Significance of the Apo
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List of Tables 5.1 summarizes the m
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x List of Figures 8.3 Phase space p
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xii
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2 Introduction In the following dec
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4 Introduction There are several sc
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6 Introduction because I had to mak
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8 Type 1 Diabetes and Its Etiology
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10 Type 1 Diabetes and Its Etiology
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3 Prospects for Therapy - A Mini Re
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3.3 Gastrin 15 eration in situ Urus
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4 Mathematical Modelling The langua
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5 The DuCa Model In the following w
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5.3 The DuCa Model - An Appetiser 2
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5.4 The DuCa Model - Compartment Mo
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5.6 Our Compartment Model 29 migrat
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5.6 Our Compartment Model 31 a ✓
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5.7 Discussion of Marée et al. (20
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5.7 Discussion of Marée et al. (20
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5.8 Discussion of Parameters 37 Fig
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5.8 Discussion of Parameters 39 Par
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5.8 Discussion of Parameters 41 tha
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5.8 Discussion of Parameters 43 Fig
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46 The Intermediated Model The diff
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48 The Intermediated Model expected
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50 The Intermediated Model Stabilit
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52 The Intermediated Model restrict
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54 The Intermediated Model We see t
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56 The Intermediated Model paramete
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58 The Intermediated Model ✻ Ma(t
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60 The Intermediated Model 6.2 The
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62 The Intermediated Model ✻ Ma(t
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7 A Brief Introduction to Bifurcati
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7.2 The Hopf bifurcation 67 the gen
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7.3 Biological Relevance of Bifurca
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7.5 Locating the Fixed Points 71 Ev
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74 Bifurcation Diagrams and Analysi
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98 Discussion of the Bifurcation An
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100 Discussion of the Bifurcation A
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106 Expanding and Modifying the DuC
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118 Discussion of the Expanded Mode
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120 Discussion of the Expanded Mode
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Page 140 and 141: 126 Bibliography Christen, U. and M
Page 142 and 143: 128 Bibliography Notkins, A. L. and
Page 144 and 145: 130 Bibliography Yu, J. and G. S. E
Page 146 and 147: 132 Mathematical Appendices the com
Page 148 and 149: 134 Mathematical Appendices in that
Page 150 and 151: 136 Mathematical Appendices A.6 Dim
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Page 154 and 155: 140 Additional Figures Figure B.2 P
Page 156 and 157: 142 Additional Figures B.2 Eigenval
Page 158 and 159: 144 Additional Figures Figure B.8 P
Page 162 and 163: 148 Additional Figures Figure B.14
Page 172 and 173: 158 matlab Code w(r+1)=w(r)+dw; g=w
Page 174 and 175: 160 matlab Code end V_11(r)=E(1); V
Page 176 and 177: 162 matlab Code n=675; w_5=0; dw_5=
Page 178 and 179: 164 matlab Code M=M’; % end s_7(r
Page 180 and 181: 166 matlab Code w_7,V_34,’.b’,w
Page 182 and 183: 168 matlab Code M=M’; % M must be
Page 184 and 185: 170 matlab Code %options = odeset(
Page 188 and 189: 174 Index value, 73 Bifurcation Ana
Page 190 and 191: 176 Index of diabetes, 2 Michaelis
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nr. 477 - 2011 - Institut for Natur, Systemer og Modeller (NSM)

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