Explicit Algorithm Research Articles

Portfolio risk allocation through Shapley value

We argue that using the Shapley value of cooperative game theory as the scheme for risk allocation among non-orthogonal risk factors is a natural way of interpreting the contribution made by each of such factors to overall portfolio risk. We discuss a Shapley value scheme for allocating risk to non-orthogonal greeks in a portfolio of derivatives. Such a situation arises, for example, when using a stochastic volatility model to capture option volatility smile. We also show that Shapley value allows for a natural method of interpreting components of enterprise risk measures such as VaR and ES. For all applications discussed, we derive explicit formulas and/or numerical algorithms to calculate the allocations.

Improved Explicit Integration Algorithms with Controllable Numerical Damping for Real-Time Hybrid Simulation

The paper proposes an improved single-step method of explicit displacement and velocity (SSMEDV) with controllable numerical damping based on the discrete control theory, which can be applied to real-time hybrid simulation (RTHS). The stability, overshoot, and numerical damping characteristics of the proposed algorithms are studied. It is shown that certain algorithms have unconditional stability for linear and softening nonlinear structures. The overshoot phenomenon is small, where the displacement is one power of the time step due to the initial velocity, whereas the velocity does not. The amount of numerical damping is adjusted by a single parameter to control the divergence of false higher-order modes. The analysis of RTHS was performed on a multiple degrees-of-freedom (MDOF) structure and complex building–damper structure to verify the theoretical analysis. The comparison with two typical algorithms of the explicit Newmark and Gui-λ demonstrates the effectiveness of the proposed algorithms in improving stability, accuracy, and computational efficiency, which can be applied to complex RTHS.

Discussion of “New Family of Explicit Structure-Dependent Integration Algorithms with Controllable Numerical Dispersion”

Discussion of “New Family of Explicit Structure-Dependent Integration Algorithms with Controllable Numerical Dispersion”

An explicit total Lagrangian Fragile Points Method for finite deformation of hyperelastic materials

This research explored a novel explicit total Lagrangian Fragile Points Method (FPM) for finite deformation of hyperelastic materials. In contrast to mesh-based methods, where mesh distortion may pose numerical challenges, meshless methods are more suitable for large deformation modelling since they use enriched shape functions for the approximation of displacements. However, this comes at the expense of extra computational overhead and higher-order quadrature is required to obtain accurate results. In this work, the novel meshless method FPM was used to derive an explicit total Lagrangian algorithm for finite deformation. FPM uses simple one-point integration for exact integration of the Galerkin weak form since it employs simple discontinuous polynomials as trial and test functions, leading to accurate results even with single-point quadrature. The proposed method was evaluated by comparing it with FEM in several case studies considering both the extension and compression of a hyperelastic material. It was demonstrated that FPM maintained good accuracy even for large deformations where FEM failed to converge.

Complex Envelope Weaker HIE With Higher Order PML Algorithm for FDTD Simulation

Weaker hybrid implicit–explicit (WHIE) algorithm with complex envelope (CE) method is proposed for structures with fine details along a single direction in bandpass problems. Higher order perfectly matched layer (PML) formulation is proposed for absorption improvement in open regions. By introducing alternating-direction implicit (ADI) discretized form and adding proper disturbance terms, it can obtain relaxed stability condition under the same Courant–Friedrichs–Levy (CFL) numbers (CFLNs) compared with the other implicit algorithms resulting in the improvement of efficiency. Furthermore, time step can also be enlarged according to the bandpass lowpass-sampling theorem which improves the efficiency in bandpass circumstances.

Implicit Algorithm of the SBSP-R Model for Predicting the Non-Unique Critical State of Soils

The non-unique critical state represents the distance between the critical state line (CSL) and the isotropic consolidation line (ICL) that significantly varies with stress paths and particle size distribution of soils. A structural bounding surface plasticity model with spacing ratio r (SBSP-R model) was implemented using an explicit algorithm. However, the explicit algorithm did not well capture the non-unique critical state of soils with a large spacing ratio r, which prevented the soil mechanics research on non-unique critical state via finite element analysis. To overcome the limitation, the implicit algorithm of the SBSP-R model is formulated, and it mainly includes elastic prediction and plastic correction. The plastic correction is realized using the Newton–Simpson scheme with a controlling equation set related to consistency condition, plastic flow, hardening parameter, structural bounding surface, plastic modulus, and mapping rule. Case studies indicate that the implicit algorithm of the SBSP-R model is right and stable in predicting non-unique critical states. Comparisons between predicted and tested results indicate that the implicit algorithm of the SBSP-R model not only captures the critical state, stress-strain, and stress paths of various soils but also shows higher computational accuracy and efficiency compared with the previous explicit algorithm. These results indicate that the formulated implicit algorithm of the SBSP-R model is an alternative approach to the previous explicit algorithm.

The analysis of frictional rolling contact behavior and key affecting factors on uneven wear in a switch panel

To analyze the wheel-rail frictional rolling contact solutions and uneven wear in a switch panel, the wheel-rail frictional rolling contact model based on explicit integral algorithm considering coupling effect of structural vibration and contact mechanics, arbitrary contact geometry and nonlinear material is established. Then the wheel-rail explicit dynamics theory, unrepeatable saturated design, wear prediction method and data statistical processing methods are integrated as a method to figure out the key affecting factors, recognizing the influence of key factors on wheel-rail contact behavior and uneven wear in switch panel, including the contact force, the instantaneous and drastic changes of size, stress and microslip in contact patch and the distribution and magnitude of wear. The results of numerical simulations can provide guidance for investigation of contact mechanism and understanding of rail maintenance in switch panel.

Simplifying indefinite fibrations on 4-manifolds

The main goal of this article is to connect some recent perspectives in the study of 4 4 -manifolds from the vantage point of singularity theory. We present explicit algorithms for simplifying the topology of various maps on 4 4 -manifolds, which include broken Lefschetz fibrations and indefinite Morse 2 2 -functions. The algorithms consist of sequences of moves, which modify indefinite fibrations in smooth 1 1 -parameter families. These algorithms allow us to give purely topological and constructive proofs of the existence of simplified broken Lefschetz fibrations and Morse 2 2 -functions on general 4 4 -manifolds, and a theorem of Auroux–Donaldson–Katzarkov on the existence of certain broken Lefschetz pencils on near-symplectic 4 4 -manifolds. We moreover establish a correspondence between broken Lefschetz fibrations and Gay–Kirby trisections of 4 4 -manifolds, and show the existence and stable uniqueness of simplified trisections on all 4 4 -manifolds. Building on this correspondence, we also provide several new constructions of trisections, including infinite families of genus- 3 3 trisections with homotopy inequivalent total spaces, and exotic same genera trisections of 4 4 -manifolds in the homeomorphism classes of complex rational surfaces.

The explicit Zelevinsky–Aubert duality

In this paper, we give an explicit computable algorithm for the Zelevinsky–Aubert duals of irreducible representations of $p$-adic symplectic and odd special orthogonal groups. To do this, we establish explicit formulas for certain derivatives and socles. We also give a combinatorial criterion for the irreducibility of certain parabolically induced representations.

Motion control framework for unmanned wheel-legged hybrid vehicle considering uncertain disturbances based robust model predictive control

The paper proposes a motion control framework for the unmanned wheel-legged hybrid vehicle to track the motion trajectory considering uncertain disturbances. The whole-body dynamic model is built with the contact force of each rolling wheel, which serves as the foundation to obtain trajectory tracking. The angular momentum and linear momentum are optimized by the robust model predictive control algorithm considering the soft constraint of the relaxation variable. The contact force between wheel and ground is solved by the quadratic programming algorithm to efficiently obtain the flexion/extension joint and wheel motion planning. Then, the explicit algorithm to calculate the torque commands of the flexion/extension joint considering the feed-forward torque and feedback torque to improve the control accuracy. Simulation results validate that the control framework based on the robust model predictive control algorithm can solve the uncertain disturbances in process of the vehicle running on the rough road.

Explicit distributed model predictive control design for chemical processes under constraints and uncertainty

AbstractIn multivariable industrial processes, the common distributed model predictive control strategy is usually unable to deal with complex large‐scale systems efficiently, especially under system constraints and high control performance requirements. Based on this situation, we use the distributed idea to divide the large‐scale system into multiple subsystems and transform them into the state space form. Combined with the output tracking error term, we build an extended non‐minimal state space model that includes output error and measured output and input. When dealing with system constraints, the new constraint matrix is divided into range and kernel space by using the explicit model predictive control algorithm, which reduces the difficulty of solving constraints in the extended system and further improves the overall control performance of the system. Finally, taking the coke furnace pressure control system as an example, the proposed algorithm is compared with the conventional distributed model predictive control algorithm using non‐minimal state space, and the simulation results show the feasibility and superiority of this method.

A novel class of forward-backward explicit iterative algorithms using inertial techniques to solve variational inequality problems with quasi-monotone operators

<abstract><p>The theory of variational inequalities is an important tool in physics, engineering, finance, and optimization theory. The projection algorithm and its variants are useful tools for determining the approximate solution to the variational inequality problem. This paper introduces three distinct extragradient algorithms for dealing with variational inequality problems involving quasi-monotone and semistrictly quasi-monotone operators in infinite-dimensional real Hilbert spaces. This problem is a general mathematical model that incorporates a set of applied mathematical models as an example, such as equilibrium models, optimization problems, fixed point problems, saddle point problems, and Nash equilibrium point problems. The proposed algorithms employ both fixed and variable stepsize rules that are iteratively transformed based on previous iterations. These algorithms are based on the fact that no prior knowledge of the Lipschitz constant or any line-search framework is required. To demonstrate the convergence of the proposed algorithms, some simple conditions are used. Numerous experiments have been conducted to highlight the numerical capabilities of algorithms.</p></abstract>

Time-adaptive Lagrangian variational integrators for accelerated optimization

<abstract><p>A variational framework for accelerated optimization was recently introduced on normed vector spaces and Riemannian manifolds in <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup> and <sup>[<xref ref-type="bibr" rid="b2">2</xref>]</sup>. It was observed that a careful combination of time-adaptivity and symplecticity in the numerical integration can result in a significant gain in computational efficiency. It is however well known that symplectic integrators lose their near-energy preservation properties when variable time-steps are used. The most common approach to circumvent this problem involves the Poincaré transformation on the Hamiltonian side, and was used in <sup>[<xref ref-type="bibr" rid="b3">3</xref>]</sup> to construct efficient explicit algorithms for symplectic accelerated optimization. However, the current formulations of Hamiltonian variational integrators do not make intrinsic sense on more general spaces such as Riemannian manifolds and Lie groups. In contrast, Lagrangian variational integrators are well-defined on manifolds, so we develop here a framework for time-adaptivity in Lagrangian variational integrators and use the resulting geometric integrators to solve optimization problems on vector spaces and Lie groups.</p></abstract>

Deep learning - cancer genetics and application of deep learning to cancer oncology

Arguably the human body has been one of the most sophisticated systems we encounter but until now we are still far from understanding its complexity. We have been trying to replicate human intelligence by way of artificial intelligence but with limited success. We have discovered the molecular structure in terms of genetics, performed gene editing to change an organism’s DNA and much more, but their translatability into the field of oncology has remained limited. Conventional machine learning methods achieved some degree of success in solving problems that we do not have an explicit algorithm. However, they are basically shallow learning methods, not rich enough to discover and extract intricate features that represent patterns in the real environment. Deep learning has exceeded human performance in pattern recognition as well as strategic games and are powerful for dealing with many complex problems. High-throughput sequencing and microarray techniques have generated vast amounts of data and allowed the comprehensive study of gene expression in tumor cells. The application of deep learning with molecular data enables applications in oncology with information not available from clinical diagnosis. This paper provides fundamental concepts of deep learning, an essential knowledge of cancer genetics, and a review of applications of deep learning to cancer oncology. Importantly, it provides an insightful knowledge of deep learning and an extensive discussion on its challenges. The ultimate purpose is to germinate ideas and facilitate collaborations between cancer biologists and deep learning researchers to address challenging oncological problems using advanced deep learning technologies.

Numerical Simulation of Bunker Buster Slab under Projectile Impact

In the present investigation, 3-D finite element modelling is carried out to predict the penetration depth and residual velocity of a projectile impacting a target. For the purpose of numerical simulation, target is a concrete slab of planar dimension 5 m × 4 m with an unconfined compressive strength of 50 MPa. This target is considered to be part of protective structure like bunker buster slab. The explicit algorithm of ABAQUS/Explicit® is employed in the simulation of projectile impact. The projectile is modelled as a rigid body and the concrete slab as a deformable body using Lagrangian formulation. The energy dissipation, penetration depth and residual velocities of the projectile impacting at different velocities are compared with the empirical equation as available by simulating a real impact scenario numerically. Investigation is carried out over a wide range of impacting velocities under sub-hydrodynamic range.

A viscoelastic–viscoplastic constitutive model for polymer bonded explosives under low impact loading

Viscoplastic work is very important to explosive ignition under impact loading. At present, a large number of constitutive models only consider the viscoelastic and damage behavior of explosives, ignoring the plastic effect under low impact loading. A new viscoelastic–viscoplastic (VE–VP) model was developed and studied to describe the dynamic mechanical behaviors of polymer-bonded explosives (PBXs). The total strain was assumed to be the sum of the viscoelastic (VE) and viscoplastic (VP) components. A generalized Maxwell model was used to determine the VE responses. A VP model was developed by using the classical J2 rate-dependent model with isotropic hardening. Viscoplastic flow was considered in hyperbolic sinusoidal form. The explicit algorithms of VE model were proposed and assessed by using two different integration methods. The accuracy and efficiency of these two methods are similar at high strain rates. The coupled algorithms of VE–VP model were developed by referring to the classical elasto-viscoplasticity (EVP) provided and using the expression of incremental relaxation modulus. The proposed model was implemented in the ABAQUS using a user-subroutine (VUMAT) to predict the response behaviors of PBX 9501 under low impact loading. Several numerical simulations illustrated the computational efficiency and the accuracy of the proposed methods. The model predictions were compared with experimental data, and reasonable agreement was obtained.

Competitive Equilibrium Always Exists for Combinatorial Auctions with Graphical Pricing Schemes

We show that a competitive equilibrium always exists in combinatorial auctions with anonymous graphical valuations and pricing, using discrete geometry. This is an intuitive and easy-to-construct class of valuations that can model both complementarity and substitutes, and to our knowledge, it is the first class besides gross substitutes that have guaranteed competitive equilibrium. We prove through counter-examples that our result is tight, and we give explicit algorithms for constructing competitive pricing vectors. We also give extensions to multi-unit combinatorial auctions (also known as product-mix auctions). Combined with theorems on graphical valuations and pricing equilibrium of Candogan, Ozdagar and Parrilo, our results indicate that quadratic pricing is a highly practical method to run combinatorial auctions.

Wave propagation in thermo-poroelasticity: A finite-element approach

We have developed continuous and discrete-time finite-element (FE) methods to solve an initial boundary-value problem for the thermo-poroelasticity wave equation based on the combined Biot/Lord-Shulman (LS) theories to describe the porous and thermal effects, respectively. In particular, the LS model, which includes a Maxwell-Vernotte-Cattaneo relaxation term, leads to a hyperbolic heat equation, thus avoiding infinite signal velocities. The FE methods are formulated on a bounded domain with absorbing boundary conditions at the artificial boundaries. The dynamical equations predict four propagation modes, a fast P (P1) wave, a Biot slow (P2) wave, a thermal (T) wave, and a shear (S) wave. The spatial discretization uses globally continuous bilinear polynomials to represent solid displacements and temperature, whereas the vector part of the Raviart-Thomas-Nedelec of zero order is used to represent fluid displacements. First, a priori optimal error estimates are derived for the continuous-time FE method, and then an explicit conditionally stable discrete-time FE method is defined and analyzed. The explicit FE algorithm is implemented in one dimension to analyze the behavior of the P1, P2, and T waves. The algorithms can be useful for a better understanding of seismic waves in hydrocarbon reservoirs and crustal rocks, whose description is mainly based on the assumption of isothermal wave propagation.

An explicit cavitation multigrid algorithm for accelerating simulation of surface-textured bearings

The cavitation has a potential effect on the performance of surface-textured bearings. The traditional mass-conserving cavitation algorithms based on the Gauss-Seidel iteration method become slow as the grid increases. The computation time is unacceptable once the grid consists of a large array of textures. This study developed an explicit cavitation multigrid algorithm to accelerate the simulation of surface-textured bearings. The algorithm was based on the Ausas cavitation algorithm with the advantage of a matrix-free implementation. Novel numerical technologies were developed to overcome the difficulty of the floating free boundaries caused by the cavitation characteristics. An example of surface-dimpled thrust bearings was studied to analyze the algorithm efficiency. The algorithm is shown to be approximate optimal under reasonable solution parameters. It is an alternative to other cavitation algorithms.

Simulation analysis of rolling bearings based on explicit dynamics

Based on LS-PrePost software, the three-dimensional display of healthy cylindrical roller bearings was established finite element model for dynamic simulation. Based on the explicit algorithm, the model analyzes the law of bearing stress level with radial outward load under the conditions of friction contact, speed and load, and based on the healthy roller bearing model, simulates the local spalling fault of the outer raceway by setting the unit defect, and analyzes the equivalent force change process when the roller through the fault area. The simulation results are compared with the theoretical calculation results to verify the correctness of the finite element model of the faulty bearings, and provide a certain reference for the fault diagnosis of rolling bearings.