Local Shuffling Research Articles

A novel hierarchical feature selection with local shuffling and models reweighting for stock price forecasting

Stock price forecasting is a challenging task due to the complexity of financial markets and the high volatility of stocks. Because of the strong nonlinear representation ability of neural network models, such as long-short memory network (LSTM) and deep learning, they are used extensively in recent years for stock price forecasting. However, due to the volatility of financial data, neural network models often suffer from overfitting or instability problems. In addition, quantitative trading with feature mining tools can generate a growing number of features for financial data. Therefore, selecting effective features for financial data is an urgent problem. To address these problems, we propose a novel hierarchical feature selection with local shuffling (HFSLS) and models reweighting (MR) based on LSTM, named HFSLSMR-LSTM, for stock price forecasting. Specifically, for each layer, local shuffling perturbs each feature to re-predict, and its predicted value is compared with the true value to calculate the feature importance, and the important features are selected and returned to the next layer. Besides, a proximity reweighting scheme is presented to adjust the weight for each layer model that learns from hierarchical features. The HFSLSMR-LSTM model is still effective for financial data with multiple features and frequent fluctuations. Experimental results on stock index dataset and Dow Jones Industrial Average dataset demonstrate that the HFSLSMR-LSTM outperforms Informer, DoubleEnsemble, LSTM, GRU, BI-GRU and BI-LSTM on the metrics MSE, RMSE, MAE, MAPE and R2.

Convergence analysis of distributed stochastic gradient descent with shuffling

When using stochastic gradient descent (SGD) to solve large-scale machine learning problems especially deep learning problems, a common practice of data processing is to shuffle the training data, partition the data across multiple threads/machines if needed, and then perform several epochs of training on the re-shuffled (either locally or globally) data. The above procedure makes the instances used to compute the gradients no longer independently sampled from the training data set, which contradicts with the basic assumptions of conventional convergence analysis of SGD. Then does the distributed SGD method have desirable convergence properties in this practical situation? In this paper, we give answers to this question. First, we give a mathematical formulation for the practical data processing procedure in distributed machine learning, which we call (data partition with) global/local shuffling. We observe that global shuffling is equivalent to without-replacement sampling if the shuffling operations are independent. Second, we prove SGD with global shuffling and local shuffling has convergence guarantee for non-convex tasks like deep learning. The convergence rate for local shuffling is slower than that for global shuffling, since it will lose some information if there’s no communication between partitioned data. We also consider the situation when the permutation after shuffling is not uniformly distributed (We call it insufficient shuffling), and discuss the condition under which this insufficiency will not influence the convergence rate. Finally, we give the convergence analysis in convex case. An interesting finding is that, the non-convex tasks like deep learning are more suitable to apply shuffling comparing to the convex tasks. Our theoretical results provide important insights to large-scale machine learning, especially in the selection of data processing methods in order to achieve faster convergence and good speedup. Our theoretical findings are verified by extensive experiments on logistic regression and deep neural networks.

Novel Cross-Slip Mechanism of Pyramidal Screw Dislocations in Magnesium.

Compared to cubic metals, whose primary slip mode includes twelve equivalent systems, the lower crystalline symmetry of hexagonal close-packed metals results in a reduced number of equivalent primary slips and anisotropy in plasticity, leading to brittleness at the ambient temperature. At higher temperatures, the ductility of hexagonal close-packed metals improves owing to the activation of secondary ⟨c+a⟩ pyramidal slip systems. Thus, understanding the fundamental properties of corresponding dislocations is essential for the improvement of ductility at the ambient temperature. Here, we present the results of large-scale abinitio calculations for ⟨c+a⟩ pyramidal screw dislocations in magnesium and show that their slip behavior is a stark counterexample to the conventional wisdom that a slip plane is determined by the stacking fault plane of dislocations. A stacking fault between dissociated partial dislocations can assume a nonplanar shape with a negligible energy cost and can migrate normal to its plane by a local shuffling of atoms. Partial dislocations dissociated on a {21[over ¯]1[over ¯]2} plane "slither" in the {011[over ¯]1} plane, dragging the stacking fault with them in response to an applied shear stress. This finding resolves the apparent discrepancy that both {21[over ¯]1[over ¯]2} and {011[over ¯]1} slip traces are observed in experiments while abinitio calculations indicate that dislocations preferably dissociate in the {21[over ¯]1[over ¯]2} planes.

Understanding Solid–Solid (fcc → ω + bcc) Transition at Atomic Scale

An atomic transition model of a face-centered cubic (fcc) crystal to a primitive hexagonal ω and body-centered cubic (bcc) structures has been crystallographically built. The fcc structure can transform into the ω structure through a local shuffling or displacement of atoms about 0.4014 Å in iron for a fcc iron = 3.59 Å. The bcc structure can form either after the ω formation or concurrently by the similar mechanism, or the ω structure can be treated as an intermediate stage during the transition of fcc → bcc. Such a transition (fcc → ω + bcc transition) can be confirmed by Widmanstätten pattern formed in an iron meteorite, pearlitic structure and martensite composed of bcc-ferrite and ultra-fine ω particles in iron–carbon steels. The present fcc–bcc orientation relationship matches with Pitsch’s one.

Highly anisotropic slip-behavior of pyramidal I 〈 c+a 〉 dislocations in hexagonal close-packed magnesium

Abstract In hexagonal-closed-pack (HCP) metals, slip of 〈 c + a 〉 dislo c ations on pyramidal planes is considered to be the most difficult slip mode that controls the overall plastic behavior. Nevertheless, pyramidal 〈 c + a 〉 slip is a requisite for accommodation of c -axis plastic deformation. In the present study, glissile pyramidal 〈 c + a 〉 dislocations with different characters gliding on type I pyramidal planes, informed by direct atomistic simulations, are reproduced and studied in HCP magnesium single crystals. The Peierls stresses for these dislocations are quantitatively evaluated via molecular dynamics simulations under pure shear loading. A high anisotropy in the Peierls stress is observed for different dislocation characters, with the near-screw having the lowest Peierls stress, and the near-edge dislocations having the highest stress. Local shuffling is also found to significantly reduce the Peierls stress of near-edge dislocations. These quantifications of pyramidal 〈 c + a 〉 slip provide better understanding of plastic deformation in HCP metals, and also provide necessary inputs for meso-scale dislocation models such as discrete dislocation dynamics simulations and crystal plasticity simulations.

Formation and slip of pyramidal dislocations in hexagonal close-packed magnesium single crystals

Slip of pyramidal 〈c+a〉 dislocations in hexagonal close-packed (hcp) crystals is a requisite for accommodation of homogeneous c-axis deformation. However, fundamental aspects of the formation and slip of pyramidal dislocations, including the formation mechanism, dissociation, core structure and slip features, are still poorly characterized. In this study, large-scale molecular dynamics simulations reveal that the formation of 〈c+a〉 dislocations in magnesium single crystals during c-axis loading occurs by sequential nucleation of leading and trailing partial dislocations on pyramidal I planes, owing to their lower lattice resistance to shear compared with pyramidal II planes. Local shuffling on pyramidal I planes was also found to be a mediating mechanism for nucleation and slip of pyramidal I 〈c+a〉 dislocations. Subsequent transition of pyramidal I slip to pyramidal II planes is achieved either by cross-slip of screw-segments or by cooperative slip of edge-segments on two equal and alternative pyramidal I planes. Consequently, at moderate strains, slip occurs predominantly on pyramidal II planes, in excellent agreement with experimental observations. Climb was also observed for both pyramidal I and pyramidal II 〈c+a〉 dislocations even at very low temperatures. This results in production of an abundance of interstitials and vacancies in the crystal. Formation of pyramidal I 〈a〉 dislocations by reaction of two pyramidal I 〈c+a〉 dislocations was also observed. These findings uncover unique features of pyramidal slip in low-symmetry hcp magnesium crystals and have important implications for understanding their distinct mechanical behavior and also for improving their performance.

Atomic Mixing in Metals Under Shear Deformation

The fundamental processes of shear-induced chemical mixing in heterogeneous Cu-based alloy systems have been studied by molecular dynamics computer simulations. These simulations reveal that two very disparate mechanisms operate depending on whether or not the two phases are coherent. For the coherent systems, mixing occurs as dislocations transfer across phase boundaries. The mixing in these systems is “superdiffusive,” and for spherical precipitates, the rate of mixing increases quadratically with precipitate radius. In systems that have incoherent phases, the mixing occurs by a local shuffling of atoms at the interface, and for them, the mixing is diffusive, with the mixing rates of spherical precipitates scaling linearly with particle radius. The morphologies of the interfaces for the two situations are also different. Coherent precipitates form rough interfaces that are relatively sharp, whereas the interfaces of incoherent precipitates are smooth but diffuse. These simulations also show that for incoherent precipitates, shear-induced mixing can be very different at different crystallographic interfacial planes as well as for different strain directions.

Extended zonal dislocations mediating twinning in titanium

Using molecular dynamics (MD) simulations, the twinning mechanism in titanium (Ti) was studied by analyzing the interfacial structure at the twin boundary (TB). The simulation results reveal interesting twin growth controlled by interfacial dislocations at the TB. The elementary twinning dislocations (bT ) nucleate and glide in pairs but separately and sequentially on two neighboring planes, significantly different from conventional zonal dislocations, which spread over two or more twinning planes with each plane comprising one Burgers vector of an elementary twinning dislocation. The twin growth can be approximately described as These two separate elementary twinning dislocations amount to a net Burgers vector 2bT ≈ 0.16 nm along the twinning vector , with the components in the in-plane direction perpendicular to η 1 canceled out. These results support the classical twinning theory in which a homogeneous shear and local shuffling have to be involved. A mechanism taking into consideration local structure of the twinning plane for such extended zonal dislocations is discussed.

Local Shuffling of Spike Trains Boosts the Accuracy of Spike Train Spectral Analysis

Spectral analysis of neuronal spike trains is an important tool in understanding the characteristics of neuronal activity by providing insights into normal and pathological periodic oscillatory phenomena. However, the refractory period creates high-frequency modulations in spike-train firing rate because any rise in the discharge rate causes a descent in subsequent time bins, leading to multifaceted modifications in the structure of the spectrum. Thus the power spectrum of the spiking activity (autospectrum) displays elevated energy in high frequencies relative to the lower frequencies. The spectral distortion is more dominant in neurons with high firing rates and long refractory periods and can lead to reduced identification of low-frequency oscillations (such as the 5- to 10-Hz burst oscillations typical of Parkinsonian basal ganglia and thalamus). We propose a compensation process that uses shuffling of interspike intervals (ISIs) for reliable identification of oscillations in the entire frequency range. This compensation is further improved by local shuffling, which preserves the slow changes in the discharge rate that may be lost in global shuffling. Cross-spectra of pairs of neurons are similarly distorted regardless of their correlation level. Consequently, identification of low-frequency synchronous oscillations, even for two neurons recorded by a single electrode, is improved by ISI shuffling. The ISI local shuffling is computed with confidence limits that are based on the first-order statistics of the spike trains, thus providing a reliable estimation of auto- and cross-spectra of spike trains and making it an optimal tool for physiological studies of oscillatory neuronal phenomena.

Dissociation of dislocations in MgAl2O4spinel deformed at low temperatures

Abstract When spinel is deformed in compression at 400°C along 〈110〉, the primary slip plane is found to be {111} with cross-slip occurring on a {001} plane. A comparison of weak-beam images of dislocations from both systems indicates that all dislocations which belong to the primary slip plane are dissociated out of the {111} plane independent of the character of the dislocation. It is proposed that deformation occurs by motion of dislocations in their dissociated state and that the partial dislocations actually glide on parallel glide planes. Movement of these dissociated dislocations is then accompanied by a concurrent migration of the stacking fault which takes place by a local shuffling of the cations. A stacking fault energy for conservative dissociation at 400°C on {001} of 530±90mJ m−2 has been determined from weak-beam images of screw dislocations.