The bounded coalescent model: conditioning a genealogy on a minimum root date

The coalescent model represents how individuals sampled from a population may have originated from a last common ancestor. The bounded coalescent model is obtained by conditioning the coalescent model such that the last common ancestor must have existed after a certain date. This conditioned model arises in a variety of applications, such as speciation, horizontal gene transfer or transmission analysis, and yet the bounded coalescent model has not been previously analysed in detail. Here we describe a new algorithm to simulate from this model directly, without resorting to rejection sampling. We show that this direct simulation algorithm is more computationally efficient than the rejection sampling approach. We also show how to calculate the probability of the last common ancestor occurring after a given date, which is required to compute the probability of realisations under the bounded coalescent model. Our results are applicable in both the isochronous (when all samples have the same date) and heterochronous (where samples can have different dates) settings. We explore the effect of setting a bound on the date of the last common ancestor, and show that it affects a number of properties of the resulting phylogenies. All our methods are implemented in a new R package called BoundedCoalescent which is freely available online.

Improved upper bounds on the stabilizer rank of magic states

In this work we improve the runtime of recent classical algorithms for strong simulation of quantum circuits composed of Clifford and T gates. The improvement is obtained by establishing a new upper bound on the stabilizer rank of m copies of the magic state |T⟩=2−1(|0⟩+eiπ/4|1⟩) in the limit of large m. In particular, we show that |T⟩⊗m can be exactly expressed as a superposition of at most O(2αm) stabilizer states, where α≤0.3963, improving on the best previously known bound α≤0.463. This furnishes, via known techniques, a classical algorithm which approximates output probabilities of an n-qubit Clifford + T circuit U with m uses of the T gate to within a given inverse polynomial relative error using a runtime poly(n,m)2αm. We also provide improved upper bounds on the stabilizer rank of symmetric product states |ψ⟩⊗m more generally; as a consequence we obtain a strong simulation algorithm for circuits consisting of Clifford gates and m instances of any (fixed) single-qubit Z-rotation gate with runtime poly(n,m)2m/2. We suggest a method to further improve the upper bounds by constructing linear codes with certain properties.

Atomic simulation algorithm

Atomic simulation algorithm

Stochastic Simulation Algorithm for effective spreading dynamics on Time-evolving Adaptive NetworX (SSATAN-X)

Modelling and simulating the dynamics of pathogen spreading has been proven crucial to inform public heath decisions, containment strategies, as well as cost-effectiveness calculations. Pathogen spreading is often modelled as a stochastic process that is driven by pathogen exposure on time-evolving contact networks. In adaptive networks, the spreading process depends not only on the dynamics of a contact network, but vice versa, infection dynamics may alter risk behaviour and thus feed back onto contact dynamics, leading to emergent complex dynamics. However, stochastic simulation of pathogen spreading processes on adaptive networks is currently computationally prohibitive. In this manuscript, we propose SSATAN-X, a new algorithm for the accurate stochastic simulation of pathogen spreading on adaptive networks. The key idea of SSATAN-X is to only capture the contact dynamics that are relevant to the spreading process. We show that SSATAN-X captures the contact dynamics and consequently the spreading dynamics accurately. The algorithm achieves a > 10 fold speed-up over the state-of-art stochastic simulation algorithm (SSA). The speed-up with SSATAN-X further increases when the contact dynamics are fast in relation to the spreading process, i.e. if contacts are short-lived and per-exposure infection risks are small, as applicable to most infectious diseases. We envision that SSATAN-X may extend the scope of analysis of pathogen spreading on adaptive networks. Moreover, it may serve to create benchmark data sets to validate novel numerical approaches for simulation, or for the data-driven analysis of the spreading dynamics on adaptive networks. A C++ implementation of the algorithm is available https://github.com/nmalysheva/SSATAN-X

Research On Roundness Error Consistency Model For Crank Journal Cylindrical grinding

Cylindrical grinding is an important way to form the external shape error of the crank journal, and the accuracy consistency directly affects the interchangeability of products. To study the accuracy consistency of crank journal，a dynamic model of the grinding wheel-crankshaft grinding system based on Timoshenko beam is established, and the grinding transition process simulation algorithm with iterative convergence of grinding force-transient grinding amount cycle adapted to the model is proposed, which realizes the simulation of the roundness of the crank journal coupled with the process parameters of the grinding system. Aiming at the grinding position of each crank journal, the grinding roundness of five crank journals is simulated respectively. On this basis, the crank journal roundness consistency prediction model is established, and the effectiveness of the prediction model is verified by field experiments. Finally, the influence of grinding parameters on the consistency of the roundness of crank journal is studied. The research conclusion can provide a reference for the grinding accuracy consistency design of this type of crank journal.

Optimization of Pipe Network Simulation Algorithm for Tree-shaped Water Injection System in Large-scale Oilfield

As intelligence technology develops, there is a higher requirement for computing speed and accuracy of water injection system simulation. In this paper, aiming at the tree-shaped water injection pipe network system of large-scale oilfields, based on the energy equation for calculating the pressure drop [Formula: see text] of pipe section, a mathematical model of the pipeline unit and the node unit is established, and finally, a mathematical model of pipe network for the entire water injection system is established; then, the improved iterative algorithm is used to solve the simulation model of water injection system. In this way, we determine the boundary calculation conditions, take the water injection station as reference node, and use the maximum pressure of water injection well as the initial value of the reference node for calculation, which reduces the number of iterations in model calculation; by comparing the simulation results of different iteration steps, 0.01 is selected as the iteration step size due to its higher calculation accuracy; and the calculation process has also been optimized. The process of solving the characteristic matrix [Formula: see text] is combined with the process of calculating the pressure drop [Formula: see text] of pipe section, and placed outside the algorithm loop, thereby shortening the calculation time of a single cycle and reducing the calculation amount of the algorithm. The application cases show that the proposed optimization algorithm for water injection system pipe network simulation can be used as an effective method to improve the solution speed and calculation accuracy of the simulation algorithm of tree-shaped water injection system in large-scale oilfields.

Signals of electromagnetic tool with toroidal coils in highly deviated wells

The research is aimed at expanding the applicability of the logging tool with toroidal coils from vertical to highly deviated wells. Its electromagnetic signals are computed with a three-dimensional finite-difference simulation algorithm on the computing resources of the Siberian Supercomputer Center of SB RAS, which is accompanied by a multi-aspect numerical analysis of the signals. We consider a wide range of geoelectric models with various resistivity contrasts: those of oil-, gas- and water-saturated reservoirs having a different number of horizontal boundaries and varying thicknesses, including the case of fine layering.

Recent progress for different inertial confinement fusion schemes: a systematical review

The pursuing of controlled fusion energy has been continuously developed for more than half a century. Inertial confinement fusion (ICF) is one of two major approaches to actualize controlled fusion. Here, we systematically reviewed several typical forms of ICF on the part of their physical principles and encountering technical barriers currently. Besides, some great simulation results of the implosion for each ICF scheme are shown, and the simulation algorithm of Vlasov-Fokker-Planck (VFP) is introduced. In addition, several instabilities in the fusion process are analyzed. These results offer a guideline for future ICF research.