SearcharxivSearch

arXiv subjects

Arijit Chakraborty

Publications and source records attributed to Arijit Chakraborty.

4 recordsLinked to original sources

A power-saving error term in counting $C_2 \wr H$ extensions of an arbitrary base field parametrized by discriminants

We study Malle's conjecture for the group $C_2 \wr H$ where $H$ is a permutation group. Malle's conjecture for this case was proved by Jürgen Klüners in \cite{arXiv:1108.5597} under mild conditions for $H$. In this article, we provide an alternative method to obtain the explicit main term and a power-saving error term for $C_2 \wr H$ extensions of an arbitrary number field. Furthermore, our method allows us to relax the assumptions for $H.$

math.NT

Quo Vadis ChatGPT? From Large Language Models to Large Knowledge Models

The startling success of ChatGPT and other large language models (LLMs) using transformer-based generative neural network architecture in applications such as natural language processing and image synthesis has many researchers excited about potential opportunities in process systems engineering (PSE). The almost human-like performance of LLMs in these areas is indeed very impressive, surprising, and a major breakthrough. Their capabilities are very useful in certain tasks, such as writing first drafts of documents, code writing assistance, text summarization, etc. However, their success is limited in highly scientific domains as they cannot yet reason, plan, or explain due to their lack of in-depth domain knowledge. This is a problem in domains such as chemical engineering as they are governed by fundamental laws of physics and chemistry (and biology), constitutive relations, and highly technical knowledge about materials, processes, and systems. Although purely data-driven machine learning has its immediate uses, the long-term success of AI in scientific and engineering domains would depend on developing hybrid AI systems that use first principles and technical knowledge effectively. We call these hybrid AI systems Large Knowledge Models (LKMs), as they will not be limited to only NLP-based techniques or NLP-like applications. In this paper, we discuss the challenges and opportunities in developing such systems in chemical engineering.

cs.AI

Anisotropic two-dimensional RF-dressed potentials for ultracold atoms

In this work, the RF-dressed potentials generated using a static magnetic field of a quadrupole trap and various radio frequency (RF) fields, have been theoretically investigated for trapping and manipulations of cold atoms in a two-dimensional (2D) geometry. It is shown that, in this scheme, the RF fields of some particular polarizations and phases can give rise to some novel static and time-dependent anisotropic two-dimensional potentials which are useful to trap and manipulate the cold atoms in the 2D geometry. The generated time-dependent 2D potentials, rotating on the circular ring, can be used for the controlled rotation and oscillation of the cold atom cloud on the circular ring path. The ultracold atoms trapped in these potentials may be used to investigate the interesting physics phenomena such as tunnelling and super-fluidity.

quant-ph

Speed Optimization In Unplanned Traffic Using Bio-Inspired Computing And Population Knowledge Base

Bio-Inspired Algorithms on Road Traffic Congestion and safety is a very promising research problem. Searching for an efficient optimization method to increase the degree of speed optimization and thereby increasing the traffic Flow in an unplanned zone is a widely concerning issue. However, there has been a limited research effort on the optimization of the lane usage with speed optimization. The main objective of this article is to find avenues or techniques in a novel way to solve the problem optimally using the knowledge from analysis of speeds of vehicles, which, in turn will act as a guide for design of lanes optimally to provide better optimized traffic. The accident factors adjust the base model estimates for individual geometric design element dimensions and for traffic control features. The application of these algorithms in partially modified form in accordance of this novel Speed Optimization Technique in an Unplanned Traffic analysis technique is applied to the proposed design and speed optimization plan. The experimental results based on real life data are quite encouraging.

cs.CY