Probability-Preserving Transformer for the Time-Dependent Schrödinger Equation

Solving the time-dependent Schrödinger equation (TDSE) via traditional numerical methods is computationally intensive. Transformer models offer a compelling alternative, but standard implementations rely on soft constraints that cannot rigorously guarantee probability conservation. Here, we introduce a Transformer architecture that enforces TDSE probability conservation as a hard constraint. The design intrinsically ensures unitarity across temporal evolution without requiring repeated retraining. Our empirical findings show that this hard-constraint approach is not only physically exact but also computationally superior to conventional soft-constraint methods.

Seamless Copy Move Manipulation in Digital Images

The importance and relevance of digital image forensics has attracted researchers to establish different techniques for creating as well as detecting forgeries. The core category in passive image forgery is copy-move image forgery that affects the originality of image by applying a different transformation. In this paper frequency domain image manipulation method is being presented.The method exploits the localized nature of discrete wavelet transform (DWT) to get hold of the region of the host image to be manipulated. Both the patch and host image are subjected to DWT at the same level $l$ to get $3l + 1$ sub-bands and each sub-band of the patch is pasted to the identified region in the corresponding sub-band of the host image. The resultant manipulated host sub-bands are then subjected to inverse DWT to get the final manipulated host image. The proposed method shows good resistance against detection by two frequency domain forgery detection methods from the literature. The purpose of this research work is to create the forgery and highlight the need to produce forgery detection methods that are robust against the malicious copy-move forgery.