Additional file 1: Figure S5. of Modified posteromedial approach for treatment of posterior pilon variant fracture

Calcaneal Traction after initial evaluation. (TIF 4243 kb

Additional file 2: Figure S6. of Modified posteromedial approach for treatment of posterior pilon variant fracture

Cast stabilization after initial reduction. (TIF 5880 kb

The scheme illustrates the calculating process of the initial load on a node in our new method.

<p>Compared with <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0139941#pone.0139941.g001" target="_blank">Fig 1</a>, we here calculate the initial load on node 3. When <i>α</i> = 1, We can get that the loads generated by nodes 0, 1, 2, 3, 4, 5, 6, and 7 are <i>F</i>₀ = 1, <i>F</i>₁ = 1, <i>F</i>₂ = 4, <i>F</i>₃ = 2, <i>F</i>₄ = 2, <i>F</i>₅ = 4, <i>F</i>₆ = 1, and <i>F</i>₇ = 1, respectively. According to the preferential principle of the destination selection of the load transported, we can calculate the load exchanged between any two nodes. We can further get the loads passing through node 3 in the loads generated by every node are <i>B</i>_{3,0 →} = 3/15, <i>B</i>_{3,1 →} = 3/15, <i>B</i>_{3,2 →} = 1, <i>B</i>_{3,3 →} = 0, <i>B</i>_{3,4 →} = 0, <i>B</i>_{3,5 →} = 1, <i>B</i>_{3,6 →} = 3/15, and <i>B</i>_{3,7 →} = 3/15, respectively. Therefore, we can obtain that the total load <i>B</i>₃ transported by node 3 is 2.8, i.e., the initial load <i>L</i>₃ on node 3 is 2.8.</p

The calculation of the load transported by a node in previous work.

<p>In the betweenness method, assume that the load was transmitted along the shortest path between every pair of nodes. If calculating the initial load on a node, we need to count the effect of the load transmitted between all pairs of nodes on this node. For example, we calculate the load on node 3. We use <i>F</i>_{<i>i</i> → <i>j</i>} and <i>B</i>_{<i>m</i>, <i>i</i> →} to denote the load transported from node <i>i</i> to <i>j</i> and the load passing through node <i>m</i> in all load generated by node <i>i</i>, respectively. By calculating the load passing through node 3 and generated by every node, we get <i>B</i>_{3,0 →} = 1.5, <i>B</i>_{3,1 →} = 1.5, <i>B</i>_{3,2 →} = 1.5, <i>B</i>_{3,3 →} = 0, <i>B</i>_{3,4 →} = 1.5, <i>B</i>_{3,5 →} = 1.5, <i>B</i>_{3,6 →} = 1.5, and <i>B</i>_{3,7 →} = 1.5. Therefore, we can obtain <i>B</i>₃ = 9, which represents the total load transported by node 3.</p

Simulations_Data_arxiv_1611.03511

<div><div>## Supplementary raw data to</div><div>## https://arxiv.org/abs/1611.03511 </div><div>## and following versions of the preprint</div></div><div>## further details&explanations in the main text</div><div><br></div><div>The Folder tree structure is the following (in {} brackets variable syntax, in [] options):</div><div><br></div><div>- "{Number of qubits for the simulation}qbit" (if ambiguous, followed by "_Hstructureanalysed")</div><div><br></div><div>-- "{Typeof}States[_{number of operators in the truncated ansatz}] "</div><div>OR </div><div>-- "{Typeof}States[ _FS]" for runs adopting the FoldedSpectrum method</div><div><br></div><div>---"NMeas {number of simulated photon counts for each algorithm step, adopted to investigate the role of Poissonian noise}"</div><div><br></div><div>---- "FullData_NMeas{Poissonian counts}_Excite#_{identifier fo the excited state}_NParticles#{number of parricles used}"</div><div>## main file where for each step of each iteration of the WAVES algorithm we record:</div><div>[iteration step, final best guess for the eigenstate, fidelity of the best guess with the whole spectrum of eigenstates of the Hamiltonian analysed, fidelity with the targeted eigenstate, average energy for the particle swarm, average purity for the particle swarm, [set of particles used for the iteration, objective function for each of the particles, fidelity of each particle with the whole spectrum of eigenstates of the Hamiltonian analysed] ]</div><div><br></div><div>---- "STREAM_NMeas{Poissonian counts}_Excite#_{identifier fo the excited state}_NParticles#{number of parricles used}"</div><div>## txt summary of main performances per each attempted iteration of the WAVES algorithm</div

Experimental_Data_arxiv_1611.03511

<div><div>## Supplementary raw data to</div><div>## https://arxiv.org/abs/1611.03511</div><div>## and following versions of the preprint</div></div><div>## further details&explanations in the main text</div><div><br></div><div>"Characterisation"</div><div>contains data related to preliminary characterisation of the photonic chip</div><div><br></div><div>"GroundSearch"</div><div>contains all raw data related to the ground state search for the 1qubit Hamiltonian as in Fig, 3 of the main paper</div><div><br></div><div>"ExcitedSearch"</div><div>contains all raw data related to the excited state search for the 1qubit Hamiltonian as in Fig, 3 of the main paper</div><div><br></div><div>"ExcitedSearch"</div><div>contains all raw data related to the IPEA algorithm performed for both the ground and excited eigenstate found, as in Fig, 3 of the main paper</div

Node degree influences the number of the load generated by this node.

<p>In the Internet, traffic networks, and the power grid, in general, the bigger the degree of a node, the higher the load generated by it. We define <i>F</i>_{<i>i</i> →} to represent the total load generated by node <i>i</i>, which is transported to other nodes in a network. Owing to the effect of the node degree, <i>F</i>_{0 →} should be not equal to <i>F</i>_{5 →}.</p

The scheme illustrates the reasonable explanation of the ability paradox in the cascading propagation by a simple illustration.

<p>The scheme illustrates the reasonable explanation of the ability paradox in the cascading propagation by a simple illustration.</p

A simple illustration of the influence of on the evolution of cooperation in PDG.

<p>Here, pink nodes denote cooperators and blue nodes denote defectors. All the two top nodes’ friends overlap, therefore the tie strength between them equals one. All other relations have a tie strength equals . We set the two mutual best friends as cooperators initially. (a) When , the game is a classical PDG. The two cooperators get a payoff of and all the defectors get . Therefore, cooperators will imitate the strategy of defectors and defection becomes prevalent; (b) When , the two cooperators will invest all their investments to each other. Both cooperators get and all defectors get 0. Therefore, in the next round, all defectors will adopt C and cooperation becomes prevalent.</p

Dynamics of cascading failures in five synthetic networks, <i>N</i> = 1000, ⟨<i>k</i>⟩ = 4.

<p>(a) The scale-free networks were constructed by BA model [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0139941#pone.0139941.ref044" target="_blank">44</a>] and data is averaged over 20 independent runs of node removal. (b) Ring-coupled network. (c) The WS small world network [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0139941#pone.0139941.ref045" target="_blank">45</a>] created by a ring-coupled network with the rewiring <i>p</i> = 0.01. (d) Synthetic network constructed by a ring-coupled network with the rewiring <i>p</i> = 0.1. (e) Random network created by a ring-coupled network with the rewiring <i>p</i> = 1. (b-e) Data is from a single run. (a-e) We plot <i>G</i> and <i>S</i> as functions of the parameter <i>β</i> for five cases of <i>α</i> = 0, <i>α</i> = 0.5, <i>α</i> = 1, <i>α</i> = 1.5, and <i>α</i> = 2.</p