Computing Approximate Pure Nash Equilibria in Shapley Value Weighted Congestion Games

We study the computation of approximate pure Nash equilibria in Shapley value (SV) weighted congestion games, introduced in [19]. This class of games considers weighted congestion games in which Shapley values are used as an alternative (to proportional shares) for distributing the total cost of each resource among its users. We focus on the interesting subclass of such games with polynomial resource cost functions and present an algorithm that computes approximate pure Nash equilibria with a polynomial number of strategy updates. Since computing a single strategy update is hard, we apply sampling techniques which allow us to achieve polynomial running time. The algorithm builds on the algorithmic ideas of [7], however, to the best of our knowledge, this is the first algorithmic result on computation of approximate equilibria using other than proportional shares as player costs in this setting. We present a novel relation that approximates the Shapley value of a player by her proportional share and vice versa. As side results, we upper bound the approximate price of anarchy of such games and significantly improve the best known factor for computing approximate pure Nash equilibria in weighted congestion games of [7].Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-71924-5_1

Class-specific restrictions define primase interactions with DNA template and replicative helicase

Bacterial primase is stimulated by replicative helicase to produce RNA primers that are essential for DNA replication. To identify mechanisms regulating primase activity, we characterized primase initiation specificity and interactions with the replicative helicase for gram-positive Firmicutes (Staphylococcus, Bacillus and Geobacillus) and gram-negative Proteobacteria (Escherichia, Yersinia and Pseudomonas). Contributions of the primase zinc-binding domain, RNA polymerase domain and helicase-binding domain on de novo primer synthesis were determined using mutated, truncated, chimeric and wild-type primases. Key residues in the β4 strand of the primase zinc-binding domain defined class-associated trinucleotide recognition and substitution of these amino acids transferred specificity across classes. A change in template recognition provided functional evidence for interaction in trans between the zinc-binding domain and RNA polymerase domain of two separate primases. Helicase binding to the primase C-terminal helicase-binding domain modulated RNA primer length in a species-specific manner and productive interactions paralleled genetic relatedness. Results demonstrated that primase template specificity is conserved within a bacterial class, whereas the primase–helicase interaction has co-evolved within each species

Multi-unit bilateral trade

We characterise the set of dominant strategy incentive compatible (DSIC), strongly budget balanced (SBB), and ex-post individually rational (IR) mechanisms for the multi-unit bilateral trade setting. In such a setting there is a single buyer and a single seller who holds a finite number k of identical items. The mechanism has to decide how many units of the item are transferred from the seller to the buyer and how much money is transferred from the buyer to the seller. We consider two classes of valuation functions for the buyer and seller: Valuations that are increasing in the number of units in possession, and the more specific class of valuations that are increasing and submodular. Furthermore, we present some approximation results about the performance of certain such mechanisms, in terms of social welfare: For increasing submodular valuation functions, we show the existence of a deterministic 2-approximation mechanism and a randomised e/(1 − e) approximation mechanism, matching the best known bounds for the single-item setting

Multi-unit bilateral trade

We characterise the set of dominant strategy incentive compatible (DSIC), strongly budget balanced (SBB), and ex-post individually rational (IR) mechanisms for the multi-unit bilateral trade setting. In such a setting there is a single buyer and a single seller who holds a finite number k of identical items. The mechanism has to decide how many units of the item are transferred from the seller to the buyer and how much money is transferred from the buyer to the seller. We consider two classes of valuation functions for the buyer and seller: Valuations that are increasing in the number of units in possession, and the more specific class of valuations that are increasing and submodular. Furthermore, we present some approximation results about the performance of certain such mechanisms, in terms of social welfare: For increasing submodular valuation functions, we show the existence of a deterministic 2-approximation mechanism and a randomised e/(1 − e) approximation mechanism, matching the best known bounds for the single-item setting

Normalized read abundance family level

Relative read abundance (CSS normalized) at the fungal family level by sample. Data for HMSC analysis

Magneto-structural correlation in (mu-alkoxo/hydroxo)(mu-carboxylato)dicopper(II) systems: Synthesis, X-ray structure and magnetic properties of aquo(mu-hydroxo) (mu-arylcarboxylato)bis(N,N,N ',N '-tetramethylethane-1,2-diamine)dicopper(II) diperchlorate

Asymmetrically dibridged dicopper(II) complexes, [Cu-2(OH)(O2CC6H4-p-Me)(tmen)(2)(H2O)](ClO4)(2) (1) and [Cu-2(OH)(O2CC6H4-p-OMe)(tmen)(2)(H2O)](ClO4)(2) (2) (tmen = N,N,N',N'-tetramethylethane-1,2-diamine), were prepared and structurally characterized. Complex 1 crystallizes in the monoclinic space group P2(1)/a with a = 17.718(2), b = 9.869(1), c = 19.677(2) Angstrom, beta = 115.16(1)degrees, V = 3114.3(6) Angstrom(3) and Z = 4. The structure was refined to R(wR(2)) = 0.067(0.178). Complex 2 crystallizes in the monoclinic space group P2(1)/a with a = 17.695(3), b = 9.574(4), c = 20.104(2) Angstrom, beta = 114.18(1)degrees, V = 3107(1) Angstrom(3) and Z = 4. The final residuals are R(wR(2)) = 0.067(0.182). The complexes have a [Cu-2(mu-OH)(mu-OH)(mu-O2CAr)](2+) core with tmen Ligands occupying the terminal sites of the core. In addition, one copper is axially bound to a water molecule. The Cu ... Cu distances and the Cu-OH Cu angles in the core are 3.394(1) Angstrom, 124.4(2)degrees for 1 and 3.374(1) Angstrom, 123.3(3)degrees for 2. The complexes show axial X-band EPR spectral features in methanol glass at 77 K giving g(perpendicular to) = 2.02, g(parallel to) = 2.3 (A(parallel to) = 165 x 10(-4) cm(-1)) and a visible band near similar to 630 nm in methanol. The complexes are weakly antiferromagnetic. A theoretical fit of the magnetic susceptibility data in the temperature range 40-295 K gives -J = 10 cm(-1), g = 2.05 for 1 and -J = 10 cm(-1), g = 2.0 for 2. Plots of -2J versus the Cu-OH-Cu angle (phi) in this class of asymmetrically dibridged dicopper(II) complexes having d(x2-y2)-d(x2-y2) magnetic orbitals show a linear magneto-structural correlation: -2J(cm(-1)) = 11.48 phi(deg) - 1373

Fractional Flow Reserve in the Femoral Arteries Derived through Computational Fluid Dynamics: A Non-Invasive Diagnostic Tool for Stenotic Diseases [Poster]

Introduction: Fractional flow reserve (FFR) is considered to be the current “gold standard” for assessing the severity of coronary stenotic diseases [1], however it is not yet tested at assessing diseases in other arteries. FFR is the ratio between the maximum achievable blood flow in a stenotic artery and the theoretical maximum achievable blood flow in the same artery in the absence of stenosis, during maximum hyperaemia [2]. Furthermore FFR measurement is costly and is associated with certain risks: it requires drug administration, specialist equipment, an operating room and a medical team [3]. Nevertheless, FFR is a good and relatively simple index of predicting the severity of a stenosis which makes it desirable to test this principle in other vessels, such as the femoral arteries. Purpose Computational fluid dynamics (CFD) combined with high quality medical imaging data can be a viable alternative to catheter derived pressure measurements for FFR calculation. In addition CFD analysis can be useful in predicting blood flow conditions and stenosis severity in a wider range of blood vessels in which catheter measurement may not be possible. To test this, in-silico measurement of FFR in femoral arteries has been the main focus of this study. The use of primarily open-source software has also been identified as one of the goals of the study to reduce diagnostic costs. Method: The method starts with a 3D DICOM vascular dataset of the patient in which the blood vessels of interest are identified and a surface model is generated as shown in Figure 1(a) using VMTK (www.vmtk.org). A 3D computational mesh is then generated and imported into a CFD software STAR-CCM+ (Siemens PLM, 2017) or OpenFoam (https://www.openfoam.com/), where simulations are performed with varying boundary conditions. Blood is modelled as a Newtonian fluid with density of 1060 kg/m3 and dynamic viscosity of 4 mPa·s [4]. Velocity is defined at the inlet and pressure is set at the outlet. Steady state (constant velocity) and transient (pulsatile) boundary conditions were tested. Results and Discussion: Figure 1(b) shows velocity plots on a cut surface plane though the model. Velocity profiles obtained from CFD appear realistic. Inspection of the pressure field, however, shows that it is strongly dependent on the boundary conditions. For example appropriate model needs to be used to take into account the rest of the cardiovascular system which is not otherwise represented in the 3D model. Furthermore, parameters such as vessel length, number of outlets and proximity of the outlets to the inlet also showed to have an influence on the pressure field. This emphasised that in order to use CFD derived FFR as a reliable diagnostic measure, special care needs to be taken when choosing the boundary conditions. Therefore further studies will seek to establish the optimal type of boundary conditions, with special focus on patient specific values, as well as to apply the method to a wider range of vessels