Time evolution of the frequencies of each of the different categories of officers officers in the partially symmetrized game.

<p>The panels show the outcome of the stochastic ABS (A & B) and deterministic simulations (C & D) for <i>p</i>_<i>e</i> = <b>0</b> (A & C) and <i>p</i>_<i>e</i> = <b>0.5</b> (B & D) case. Other values of parameters are: <i>c</i> = 1, <i>v</i> = 1, <i>p</i>_<i>o</i> = 1.3, <i>p</i>_<i>c</i> = 0, <i>k</i> = 0.4, <i>b</i> = 0.4, <i>r</i> = 0, <i>t</i> = 0.1. Number of officers in ABS: <i>N</i>₀ = 100; Number of pure citizens in ABS: <i>N</i>_<i>C</i> = 100.</p

Equilibrium population for the four-strategy model as a function of bribe amount <i>b</i>, and punishment <i>p</i> with refund (A, C) and without-refund (B, D) for asymmetric liability scenario.

<p>Shades of white and black color denote the equilibrium abundance of <i>O</i>₁ and <i>O</i>₂ type of officers. Shades of white and cyan color denote the stationary frequencies of <i>C</i>₁ and <i>C</i>₂ type of citizens. The values of other parameters are: <i>c</i> = 1, <i>v</i> = 1, <i>k</i> = 0.6. The initial condition corresponds to <i>x</i>_<i>C</i>1 = 0.5, <i>x</i>_<i>C</i>2 = 0.5, <i>x</i>_<i>O</i>1 = 0.5, <i>x</i>_<i>O</i>2 = 0.5</p

Equilibrium population structure for the five-strategy model for variable punishment <i>p</i>, and prosecution rate <i>k</i> ‘with refund’ (A, D) and ‘without-refund’ (B, E) in the asymmetric liability and symmetric liability scenarios (C, F).

<p>Shades of white and black colors denote the equilibrium abundance of officers of type <i>O</i>₁ and <i>O</i>₂. Shade of green and blue and red colors denote the stationary frequencies of <i>C</i>₁, <i>C</i>₂ and <i>C</i>₃ categories of citizens. The values of other parameters are <i>c</i> = 1, <i>v</i> = 1, <i>b</i> = 0.4, <i>t</i> = 0.1. The initial condition corresponds to <i>x</i>_<i>C</i>1 = 1/3, <i>x</i>_<i>C</i>2 = 1/3, <i>x</i>_<i>C</i>3 = 1/3, <i>x</i>_<i>O</i>1 = 1/2, <i>x</i>_<i>O</i>2 = 1/2 i.e. all strategies are initially equally abundant in the population.</p

Phase diagram of the four-strategy model with asymmetric liability for variable initial conditions.

<p>Panel A-C corresponds to situations ‘with refund’, ‘without refund’ and ‘no complaining cost without refund’ respectively. Each point in this phase plot (simplex) specifies the population structure of officers and citizens. Arrows represents the direction of the change in frequency of a strategy in the phase space. Red represents fast dynamics and blue represents slow dynamics, close to fixed points. The values of the parameters are: <i>c</i> = 1, <i>v</i> = 1, <i>p</i>_<i>o</i> = 1.5, <i>k</i> = 0.4, <i>b</i> = 0.4, <i>t</i> = 0.1 for panel A and B. Parameter values are: <i>c</i> = 1, <i>v</i> = 1, <i>p</i>_<i>o</i> = 3, <i>k</i> = 0.4, <i>b</i> = 0.4, <i>t</i> = 0 for panel C.</p

Policy & practice of public human services : the journal of the American Public Human Services Association

<p>Shades of white and black color denote the equilibrium abundance of <i>O</i>₁ and <i>O</i>₂ type of officers. Shades of white and cyan color denote the stationary frequencies of <i>C</i>₁ and <i>C</i>₂ type of citizens. The values of other parameters are: <i>c</i> = 1, <i>v</i> = 1, <i>b</i> = 0.4, <i>t</i> = 0.1. The initial condition corresponds to <i>x</i>_<i>C</i>1 = 0.5, <i>x</i>_<i>C</i>2 = 0.5, <i>x</i>_<i>O</i>1 = 0.5, <i>x</i>_<i>O</i>2 = 0.5</p

Equilibrium population structure for the five-strategy model as a function of bribe amount <i>b</i>, and cost of complaining <i>t</i>, ‘with refund’ (A, D) and ‘without-refund’ (B, E) in the asymmetric liability and symmetric liability scenarios (C, F).

<p>Shades of white and black colors denote the equilibrium abundance of officers of type <i>O</i>₁ and <i>O</i>₂. Shade of green and blue and red colors denote the stationary frequencies of <i>C</i>₁, <i>C</i>₂ and <i>C</i>₃ categories of citizens. The values of other parameters are: <i>c</i> = 1, <i>v</i> = 1, <i>p</i>_<i>o</i> = 2 <i>k</i> = 0.4. The initial condition corresponds to <i>x</i>_<i>C</i>1 = 1/3, <i>x</i>_<i>C</i>2 = 1/3, <i>x</i>_<i>C</i>3 = 1/3, <i>x</i>_<i>O</i>1 = 1/2, <i>x</i>_<i>O</i>2 = 1/2.</p

Equilibrium population for the four-strategy model while varying of bribe amount <i>b</i>, and cost of complaining <i>t</i> with refund (A, C) and without-refund (B, D) for asymmetric liability scenario.

<p>Shades of white and black colors denote the equilibrium abundance of <i>O</i>₁ and <i>O</i>₂ type of officers. Shade of white and cyan colors denote the stationary frequencies of <i>C</i>₁ and <i>C</i>₂ type of citizens. The values of other parameters are: <i>c</i> = 1, <i>v</i> = 1, <i>p</i>_<i>o</i> = 2, <i>k</i> = 0.6. The initial condition corresponds to <i>x</i>_<i>C</i>1 = 0.5, <i>x</i>_<i>C</i>2 = 0.5, <i>x</i>_<i>O</i>1 = 0.5, <i>x</i>_<i>O</i>2 = 0.5</p

Time evolution of the total fraction of honest and corrupt officers in the population for stochastic ABS (A & B) and deterministic simulation (C & D) for p_<i>e</i> = 0 (A & C) and <i>p</i>_<i>e</i> = 0.5 (B & D).

<p>Other values of parameters: <i>c</i> = 1, <i>v</i> = 1, <i>p</i>_<i>o</i> = 1.3, <i>p</i>_<i>c</i> = 0, <i>k</i> = 0.4, <i>b</i> = 0.4, <i>r</i> = 0; <i>t</i> = 0.1. Number of officers in ABS: <i>N</i>₀ = 100; Number of pure citizens in ABS: <i>N</i>_<i>C</i> = 100.</p

Subtype B classification using the improved method.

<p>(a) Distribution of Z-scores for group M sequences; (b) Frequency distribution of Z-scores, when six sequences of subtype B are used in the positive training set.</p

Subtype C classification using the standard method.

<p>Distribution of Z-scores for all HIV-1, group M sequences in the database when the training set (labelled TS) is constructed using six sequences belonging to the subtype C. Tp (dashed line) denotes the minimum score of some sequences belonging to the test set and Tn (solid line) denotes the maximum score of the remaining sequences.</p