Sixth-order schemes for laser-matter interaction in the Schrödinger equation

Control of quantum systems via lasers has numerous applications that require fast and accurate numerical solution of the Schr\"odinger equation. In this paper we present three strategies for extending any sixth-order scheme for Schr\"odinger equation with time-independent potential to a sixth-order method for Schr\"odinger equation with laser potential. As demonstrated via numerical examples, these schemes prove effective in the atomic regime as well as the semiclassical regime, and are a particularly appealing alternative to time-ordered exponential splittings when the laser potential is highly oscillatory or known only at specific points in time (on an equispaced grid, for instance). These schemes are derived by exploiting the linear in space form of the time dependent potential under the dipole approximation (whereby commutators in the Magnus expansion reduce to a simpler form), separating the time step of numerical propagation from the issue of adequate time-resolution of the laser field by keeping integrals intact in the Magnus expansion, and eliminating terms with unfavourable structure via carefully designed splittings.Comment: 33 pages, 7 figure

LG-Traj: LLM Guided Pedestrian Trajectory Prediction

Accurate pedestrian trajectory prediction is crucial for various applications, and it requires a deep understanding of pedestrian motion patterns in dynamic environments. However, existing pedestrian trajectory prediction methods still need more exploration to fully leverage these motion patterns. This paper investigates the possibilities of using Large Language Models (LLMs) to improve pedestrian trajectory prediction tasks by inducing motion cues. We introduce LG-Traj, a novel approach incorporating LLMs to generate motion cues present in pedestrian past/observed trajectories. Our approach also incorporates motion cues present in pedestrian future trajectories by clustering future trajectories of training data using a mixture of Gaussians. These motion cues, along with pedestrian coordinates, facilitate a better understanding of the underlying representation. Furthermore, we utilize singular value decomposition to augment the observed trajectories, incorporating them into the model learning process to further enhance representation learning. Our method employs a transformer-based architecture comprising a motion encoder to model motion patterns and a social decoder to capture social interactions among pedestrians. We demonstrate the effectiveness of our approach on popular pedestrian trajectory prediction benchmarks, namely ETH-UCY and SDD, and present various ablation experiments to validate our approach.Comment: Under Revie

Enhancing Trajectory Prediction through Self-Supervised Waypoint Noise Prediction

Trajectory prediction is an important task that involves modeling the indeterminate nature of traffic actors to forecast future trajectories given the observed trajectory sequences. However, current methods confine themselves to presumed data manifolds, assuming that trajectories strictly adhere to these manifolds, resulting in overly simplified predictions. To this end, we propose a novel approach called SSWNP (Self-Supervised Waypoint Noise Prediction). In our approach, we first create clean and noise-augmented views of past observed trajectories across the spatial domain of waypoints. We then compel the trajectory prediction model to maintain spatial consistency between predictions from these two views, in addition to the trajectory prediction task. Introducing the noise-augmented view mitigates the model's reliance on a narrow interpretation of the data manifold, enabling it to learn more plausible and diverse representations. We also predict the noise present in the two views of past observed trajectories as an auxiliary self-supervised task, enhancing the model's understanding of the underlying representation and future predictions. Empirical evidence demonstrates that the incorporation of SSWNP into the model learning process significantly improves performance, even in noisy environments, when compared to baseline methods. Our approach can complement existing trajectory prediction methods. To showcase the effectiveness of our approach, we conducted extensive experiments on three datasets: NBA Sports VU, ETH-UCY, and TrajNet++, with experimental results highlighting the substantial improvement achieved in trajectory prediction tasks.Comment: Under revie

Improving Trajectory Prediction in Dynamic Multi-Agent Environment by Dropping Waypoints

The inherently diverse and uncertain nature of trajectories presents a formidable challenge in accurately modeling them. Motion prediction systems must effectively learn spatial and temporal information from the past to forecast the future trajectories of the agent. Many existing methods learn temporal motion via separate components within stacked models to capture temporal features. Furthermore, prediction methods often operate under the assumption that observed trajectory waypoint sequences are complete, disregarding scenarios where missing values may occur, which can influence their performance. Moreover, these models may be biased toward particular waypoint sequences when making predictions. We propose a novel approach called Temporal Waypoint Dropping (TWD) that explicitly incorporates temporal dependencies during the training of a trajectory prediction model. By stochastically dropping waypoints from past observed trajectories, the model is forced to learn the underlying temporal representation from the remaining waypoints, resulting in an improved model. Incorporating stochastic temporal waypoint dropping into the model learning process significantly enhances its performance in scenarios with missing values. Experimental results demonstrate our approach's substantial improvement in trajectory prediction capabilities. Our approach can complement existing trajectory prediction methods to improve their prediction accuracy. We evaluate our proposed approach on three datasets: NBA Sports VU, ETH-UCY, and TrajNet++.Comment: Under Revie

Efficient Representation Learning for Healthcare with Cross-Architectural Self-Supervision

In healthcare and biomedical applications, extreme computational requirements pose a significant barrier to adopting representation learning. Representation learning can enhance the performance of deep learning architectures by learning useful priors from limited medical data. However, state-of-the-art self-supervised techniques suffer from reduced performance when using smaller batch sizes or shorter pretraining epochs, which are more practical in clinical settings. We present Cross Architectural - Self Supervision (CASS) in response to this challenge. This novel siamese self-supervised learning approach synergistically leverages Transformer and Convolutional Neural Networks (CNN) for efficient learning. Our empirical evaluation demonstrates that CASS-trained CNNs and Transformers outperform existing self-supervised learning methods across four diverse healthcare datasets. With only 1% labeled data for finetuning, CASS achieves a 3.8% average improvement; with 10% labeled data, it gains 5.9%; and with 100% labeled data, it reaches a remarkable 10.13% enhancement. Notably, CASS reduces pretraining time by 69% compared to state-of-the-art methods, making it more amenable to clinical implementation. We also demonstrate that CASS is considerably more robust to variations in batch size and pretraining epochs, making it a suitable candidate for machine learning in healthcare applications.Comment: Accepted at MLHC 2023. Extended conference version of arXiv:2206.0417

Performance Evaluation of Some Index Funds-Indian Perspective

The popularity of the index funds as an investment option has increased manifolds ever since they were introduced. This is primarily because of the merits that the investor enjoys through passive style of funds management. This includes the low cost involved in managing such funds and the significant tax savings. However the index funds of US and for that reason other parts of the world are different from that of India. Unlike other countries in India the benchmark indices comprise of very less number of securities and thus are unable to represent the entire economy. So in Indian context comparison of performance of actively managed funds with index funds is not logical. Therefore this paper attempts to make an intra-class performance evaluation of some Indian index funds based on some statistics

Related Rhythms: Recommendation System To Discover Music You May Like

Machine Learning models are being utilized extensively to drive recommender systems, which is a widely explored topic today. This is especially true of the music industry, where we are witnessing a surge in growth. Besides a large chunk of active users, these systems are fueled by massive amounts of data. These large-scale systems yield applications that aim to provide a better user experience and to keep customers actively engaged. In this paper, a distributed Machine Learning (ML) pipeline is delineated, which is capable of taking a subset of songs as input and producing a new subset of songs identified as being similar to the inputted subset. The publicly accessible Million Songs Dataset (MSD) enables researchers to develop and explore reasonably efficient systems for audio track analysis and recommendations, without having to access a commercialized music platform. The objective of the proposed application is to leverage an ML system trained to optimally recommend songs that a user might like

Optimal Control of Spins by Analytical Lie Algebraic Derivatives

Computation of derivatives (gradient and Hessian) of a fidelity function is one of the most crucial steps in many optimization algorithms. Having access to accurate methods to calculate these derivatives is even more desired where the optimization process requires propagation of these calculations over many steps, which is in particular important in optimal control of spin systems. Here we propose a novel numerical approach, ESCALADE (Efficient Spin Control using Analytical Lie Algebraic Derivatives) that offers the exact first and second derivatives of the fidelity function by taking advantage of the properties of the Lie group of $2\times 2$ Hermitian matrices, $\mathrm{SU}(2)$, and its Lie algebra, the Lie algebra of skew-Hermitian matrices, $\mathfrak{su}(2)$. A full mathematical treatment of the proposed method along with some numerical examples are presented