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We provide a complete elaboration of the L2-Hilbert space hypocoercivity theorem for the degenerate Langevin dynamics with multiplicative noise, studying the longtime behavior of the strongly continuous contraction semigroup solving the abstract Cauchy problem for the associated backward Kolmogorov operator. Hypocoercivity for the Langevin dynamics with constant diffusion matrix was proven previously by Dolbeault, Mouhot and Schmeiser in the corresponding Fokker–Planck framework and made rigorous in the Kolmogorov backwards setting by Grothaus and Stilgenbauer. We extend these results to weakly differentiable diffusion coefficient matrices, introducing multiplicative noise for the corresponding stochastic differential equation. The rate of convergence is explicitly computed depending on the choice of these coefficients and the potential giving the outer force. In order to obtain a solution to the abstract Cauchy problem, we first prove essential self-adjointness of non-degenerate elliptic Dirichlet operators on Hilbert spaces, using prior elliptic regularity results and techniques from Bogachev, Krylov and Röckner. We apply operator perturbation theory to obtain essential m-dissipativity of the Kolmogorov operator, extending the m-dissipativity results from Conrad and Grothaus. We emphasize that the chosen Kolmogorov approach is natural, as the theory of generalized Dirichlet forms implies a stochastic representation of the Langevin semigroup as the transition kernel of a diffusion process which provides a martingale solution to the Langevin equation with multiplicative noise. Moreover, we show that even a weak solution is obtained this way.
We examine the predictability of 299 capital market anomalies enhanced by 30 machine learning approaches and over 250 models in a dataset with more than 500 million firm-month anomaly observations. We find significant monthly (out-of-sample) returns of around 1.8–2.0%, and over 80% of the models yield returns equal to or larger than our linearly constructed baseline factor. For the best performing models, the risk-adjusted returns are significant across alternative asset pricing models, considering transaction costs with round-trip costs of up to 2% and including only anomalies after publication. Our results indicate that non-linear models can reveal market inefficiencies (mispricing) that are hard to conciliate with risk-based explanations.
The simulation of Dynamic Random Access Memories (DRAMs) on system level requires highly accurate models due to their complex timing and power behavior. However, conventional cycle-accurate DRAM subsystem models often become a bottleneck for the overall simulation speed. A promising alternative are simulators based on Transaction Level Modeling, which can be fast and accurate at the same time. In this paper we present DRAMSys4.0, which is, to the best of our knowledge, the fastest and most extensive open-source cycle-accurate DRAM simulation framework. DRAMSys4.0 includes a novel software architecture that enables a fast adaption to different hardware controller implementations and new JEDEC standards. In addition, it already supports the latest standards DDR5 and LPDDR5. We explain how to apply optimization techniques for an increased simulation speed while maintaining full temporal accuracy. Furthermore, we demonstrate the simulator’s accuracy and analysis tools with two application examples. Finally, we provide a detailed investigation and comparison of the most prominent cycle-accurate open-source DRAM simulators with regard to their supported features, analysis capabilities and simulation speed.
This article presents a methodology whereby adjoint solutions for partitioned multiphysics problems can be computed efficiently, in a way that is completely independent of the underlying physical sub-problems, the associated numerical solution methods, and the number and type of couplings between them. By applying the reverse mode of algorithmic differentiation to each discipline, and by using a specialized recording strategy, diagonal and cross terms can be evaluated individually, thereby allowing different solution methods for the generic coupled problem (for example block-Jacobi or block-Gauss-Seidel). Based on an implementation in the open-source multiphysics simulation and design software SU2, we demonstrate how the same algorithm can be applied for shape sensitivity analysis on a heat exchanger (conjugate heat transfer), a deforming wing (fluid–structure interaction), and a cooled turbine blade where both effects are simultaneously taken into account.
Comparative public policy is a blooming research area. It also suffers from some curious blind spots. In this paper we discuss four of these: (1) the obsession with covariance, which means that important phenomena are ignored; (2) the lack of agency, which leads to underwhelming explanatory models; (3) the unclear universe of cases, which means the inferential value of theories and the empirical results are unclear; and (4) the focus on outputs, even though most theories contain strong assumptions about the political process leading to certain outputs. Following this discussion, we then outline how a closer integration of policy process theories may be fruitful for future research.
Algorithmic systems that provide services to people by supporting or replacing human decision-making promise greater convenience in various areas. The opacity of these applications, however, means that it is not clear how much they truly serve their users. A promising way to address the issue of possible undesired biases consists in giving users control by letting them configure a system and aligning its performance with users’ own preferences. However, as the present paper argues, this form of control over an algorithmic system demands an algorithmic literacy that also entails a certain way of making oneself knowable: users must interrogate their own dispositions and see how these can be formalized such that they can be translated into the algorithmic system. This may, however, extend already existing practices through which people are monitored and probed and means that exerting such control requires users to direct a computational mode of thinking at themselves.
In this note, we define one more way of quantization of classical systems. The quantization we consider is an analogue of classical Jordan–Schwinger map which has been known and used for a long time by physicists. The difference, compared to Jordan–Schwinger map, is that we use generators of Cuntz algebra O∞ (i.e. countable family of mutually orthogonal partial isometries of separable Hilbert space) as a “building blocks” instead of creation–annihilation operators. The resulting scheme satisfies properties similar to Van Hove prequantization, i.e. exact conservation of Lie brackets and linearity.
Recently, phase field modeling of fatigue fracture has gained a lot of attention from many researches and studies, since the fatigue damage of structures is a crucial issue in mechanical design. Differing from traditional phase field fracture models, our approach considers not only the elastic strain energy and crack surface energy, additionally, we introduce a fatigue energy contribution into the regularized energy density function caused by cyclic load. Comparing to other type of fracture phenomenon, fatigue damage occurs only after a large number of load cycles. It requires a large computing effort in a computer simulation. Furthermore, the choice of the cycle number increment is usually determined by a compromise between simulation time and accuracy. In this work, we propose an efficient phase field method for cyclic fatigue propagation that only requires moderate computational cost without sacrificing accuracy. We divide the entire fatigue fracture simulation into three stages and apply different cycle number increments in each damage stage. The basic concept of the algorithm is to associate the cycle number increment with the damage increment of each simulation iteration. Numerical examples show that our method can effectively predict the phenomenon of fatigue crack growth and reproduce fracture patterns.
In a widely-studied class of multi-parametric optimization problems, the objective value of each solution is an affine function of real-valued parameters. Then, the goal is to provide an optimal solution set, i.e., a set containing an optimal solution for each non-parametric problem obtained by fixing a parameter vector. For many multi-parametric optimization problems, however, an optimal solution set of minimum cardinality can contain super-polynomially many solutions. Consequently, no polynomial-time exact algorithms can exist for these problems even if P=NP. We propose an approximation method that is applicable to a general class of multi-parametric optimization problems and outputs a set of solutions with cardinality polynomial in the instance size and the inverse of the approximation guarantee. This method lifts approximation algorithms for non-parametric optimization problems to their parametric version and provides an approximation guarantee that is arbitrarily close to the approximation guarantee of the approximation algorithm for the non-parametric problem. If the non-parametric problem can be solved exactly in polynomial time or if an FPTAS is available, our algorithm is an FPTAS. Further, we show that, for any given approximation guarantee, the minimum cardinality of an approximation set is, in general, not ℓ-approximable for any natural number ℓ less or equal to the number of parameters, and we discuss applications of our results to classical multi-parametric combinatorial optimizations problems. In particular, we obtain an FPTAS for the multi-parametric minimum s-t-cut problem, an FPTAS for the multi-parametric knapsack problem, as well as an approximation algorithm for the multi-parametric maximization of independence systems problem.
Wear phenomena in worm gears are dependent on the size of the gears. Whereas larger gears are mainly affected by fatigue wear, abrasive wear is predominant in smaller gears. In this context a simulation model for abrasive wear of worm gears was developed, which is based on an energetic wear equation. This approach associates wear with solid friction energy occurring in the tooth contact. The physically-based wear simulation model includes a tooth contact analysis and tribological calculation to determine the local solid tooth friction and wear. The calculation is iterated with the modified tooth flank geometry of the worn worm wheel, in order to consider the influence of wear on the tooth contact. Experimental results on worm gears are used to determine the wear model parameter and to validate the model. A simulative study for a wide range of worm gear geometries was conducted to investigate the influence of geometry and operating conditions on abrasive wear.