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2022 ◽  
Vol 40 (4) ◽  
pp. 1-45
Author(s):  
Weiren Yu ◽  
Julie McCann ◽  
Chengyuan Zhang ◽  
Hakan Ferhatosmanoglu

SimRank is an attractive link-based similarity measure used in fertile fields of Web search and sociometry. However, the existing deterministic method by Kusumoto et al. [ 24 ] for retrieving SimRank does not always produce high-quality similarity results, as it fails to accurately obtain diagonal correction matrix  D . Moreover, SimRank has a “connectivity trait” problem: increasing the number of paths between a pair of nodes would decrease its similarity score. The best-known remedy, SimRank++ [ 1 ], cannot completely fix this problem, since its score would still be zero if there are no common in-neighbors between two nodes. In this article, we study fast high-quality link-based similarity search on billion-scale graphs. (1) We first devise a “varied- D ” method to accurately compute SimRank in linear memory. We also aggregate duplicate computations, which reduces the time of [ 24 ] from quadratic to linear in the number of iterations. (2) We propose a novel “cosine-based” SimRank model to circumvent the “connectivity trait” problem. (3) To substantially speed up the partial-pairs “cosine-based” SimRank search on large graphs, we devise an efficient dimensionality reduction algorithm, PSR # , with guaranteed accuracy. (4) We give mathematical insights to the semantic difference between SimRank and its variant, and correct an argument in [ 24 ] that “if D is replaced by a scaled identity matrix (1-Ɣ)I, their top-K rankings will not be affected much”. (5) We propose a novel method that can accurately convert from Li et al.  SimRank ~{S} to Jeh and Widom’s SimRank S . (6) We propose GSR # , a generalisation of our “cosine-based” SimRank model, to quantify pairwise similarities across two distinct graphs, unlike SimRank that would assess nodes across two graphs as completely dissimilar. Extensive experiments on various datasets demonstrate the superiority of our proposed approaches in terms of high search quality, computational efficiency, accuracy, and scalability on billion-edge graphs.


2021 ◽  
Author(s):  
Shota Ono ◽  
Daigo Kobayashi

Abstract Although many binary compounds have the B2 (CsCl-type) structure in the thermodynamic phase diagram, an origin of the structural stability is not understood well. Here, we focus on 416 compounds in the B2 structure extracted from the Materials Project, and study the dynamical stability of those compounds from first principles. We demonstrate that the B2 phase stability lies in whether the lowest frequency phonon at the M point in the Brillouin zone is endowed with a positive frequency. We show that the interatomic interactions up to the fourth nearest neighbor atoms are necessary for stabilizing such phonon modes, which should determine the minimum cutoff radius for constructing the interatomic potentials of binary compounds with guaranteed accuracy.


Author(s):  
Gennadiy Sandrakov ◽  
Andrii Hulianytskyi ◽  
Vladimir Semenov

Modeling of dynamic processes of diffusion and filtration of liquids in porous media are discussed. The media are formed by a large number of blocks with low permeability, and separated by a connected system of faults with high permeability. The modeling is based on solving initial boundary value problems for parabolic equations of diffusion and filtration in porous media. The structure of the media leads to the dependence of the equations on a small parameter. Assertions on the solvability and regularity of such problems and the corresponding homogenized convolution problems are considered. The statements are actual for the numerical solution of this problem with guaranteed accuracy that is necessary to model the considered processes.


2021 ◽  
Vol 18 (3) ◽  
pp. 415-421
Author(s):  
A. A. Kasyanov

In a number of complex refractive cases, the achievement of an accurate refractive result cannot be guaranteed. Simultaneous implantation of a toric or multifocal IOL for the correction of complex ametropias may be accompanied by a significant deviation from the target refraction. The tactics of two-stage implantation with the usage of an additional Sulcoflex IOL for the final correction of astigmatism and possible residual spherical ametropia allows achieving emmetropia. In our study, this method was used in 15 patients with difficult refractive cases. Toric, multifocal, and multifocal toric Sulcoflex IOL were used. Implantation of all Sulcoflex modifications was performed through a 2.4 mm temporal incision using wound assisted technology. In cases of high degree hypermetropia, preventive iridectomy was performed using a 23G vitrectome. The target refraction was achieved in the entire observation group. In the postoperative period, no significant level of ophthalmic hypertension was registered. No cases of introlens opacification, iridocyclitis, or rotational instability were registered either.The method of two-stage IOL implantation allows achieving the target refraction in difficult refractive situations with almost guaranteed accuracy. The calculation method provides good predictability of the refractive result. This technology significantly expands the indications for intraocular correction using toric and multifocal IOL, as well as the limits of correction of high degree astigmatism. Our Sulcoflex IOL implantation experience has shown their high efficiency and safety.


2021 ◽  
Vol 11 (11) ◽  
pp. 4988
Author(s):  
Jincheng Xia ◽  
Wenjia Fu ◽  
Ming Liu ◽  
Mingjiang Wang

Floating-point division is indispensable and becoming increasingly important in many modern applications. To improve speed performance of floating-point division in actual microprocessors, this paper proposes a low-latency architecture with a multi-precision architecture for floating-point division which will meet the IEEE-754 standard. There are three parts in the floating-point division design: pre-configuration, mantissa division, and quotient normalization. In the part of mantissa division, based on the fast division algorithm, a Predict–Correct algorithm is employed which brings about more partial quotient bits per cycle without consuming too much circuit area. Detailed analysis is presented to support the guaranteed accuracy per cycle with no restriction to specific parameters. In the synthesis using TSMC, 90 nm standard cell library, the results show that the proposed architecture has ≈63.6% latency, ≈30.23% total time (latency × period), ≈31.8% total energy (power × latency × period), and ≈44.6% efficient average energy (power × latency × period/efficient length) overhead over the latest floating-point division structure. In terms of latency, the proposed division architecture is much faster than several classic processors.


2021 ◽  
Vol 14 (6) ◽  
pp. 235
Author(s):  
Paolo Falbo ◽  
Juri Hinz ◽  
Piyachat Leelasilapasart ◽  
Cristian Pelizzari

Due to recent technical progress, battery energy storages are becoming a viable option in the power sector. Their optimal operational management focuses on load shift and shaving of price spikes. However, this requires optimally responding to electricity demand, intermittent generation, and volatile electricity prices. More importantly, such optimization must take into account the so-called deep discharge costs, which have a significant impact on battery lifespan. We present a solution to a class of stochastic optimal control problems associated with these applications. Our numerical techniques are based on efficient algorithms which deliver a guaranteed accuracy.


Author(s):  
О.В. Збруцький ◽  
А.С. Довгополий ◽  
О.Е. Кописов ◽  
O.O. Білобородов

Unmanned aerial vehicle must be controllable and fend off disturbing influences. The quality and effectiveness of fulfilling these tasksare completely determined by the instrumentation system and the software of the control system, which ensures the safety and reliability of the unmanned aerial vehicle. The synthesis of adaptive control algorithms in the presence of disturbances in most cases suggests the use of a certain disturbance model and is associated with the use of integral regulators, which increases the order of the system, and sometimes they are substantially non-linear. Adaptive algorithms use both predictive methods for assessing the dynamics of an object. For the synthesis of the control system, was considered the dynamic model of an unmanned aerial vehicle as a solid. Then the linearized equations of transverse motion can be represented by a system of differential equations. The study performed the synthesis of control system regulators by integrating the equations of the dynamic model of the object for a given control program, made a forecast of the movement of an unmanned aerial vehicle for a certain final period of time. By optimization of program control, was taking into account the restrictions imposed on the control and adjustable variables, the adjustable variables of the forecasting model approach the corresponding control signals on the forecast horizon. At the calculation step, which is a fixed small part of the forecast horizon, the optimal control found was realized and the actual state of the unmanned aerial vehicle was measured at the end of the step. The forecast horizon moves forward one step, and this procedure is repeated. The efficiency of the model predictive control as synthesis method for unmanned aerial vehicle’s control system is analyzed. A new synthesis method of adaptive control system with guaranteed accuracy under an arbitrary external disturbance is shown. The method is based on evaluating the effect of disturbances, predicting the behavior of the system and compensating the impact on the control object by the formation of a law for changing the parameters of the additional controller, which does not directly affect the quality of the control system.The results of control system’s mathematical modeling for aircraft and multicopter types of unmanned aerial vehicles are presented.


2020 ◽  
Vol 8 (2) ◽  
pp. 027-033
Author(s):  
A. V. Evseev ◽  
◽  
V. V. Preys ◽  
V. A. Lapina ◽  
G. V. Kasatkin ◽  
...  

В работе рассмотрены две математические методики изучения качества смесей гетерогенных (трубчатых) компонентов (длинномеров) на основе анализа синтеза смеси в автоматическом конвейерном нонмиксере с использованием двух и более барабанных дозаторов. Актуальность и новизна разработки показаны на примерах получения общей партии смесевого трубчатого продукта из малых подобных партий, при детерминированном формировании его однородности, с заданными качественными и количественными характеристиками из гетерогенных трубчатых компонентов. Также предложены критерии, позволяющие определить искомую гарантированную точность содержания компонентов в получаемых на установке смесях.


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