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Cancer involves abnormal cell growth, with types like intestinal and oesophageal cancer often diagnosed in advanced stages, making them hard to cure. Symptoms are like burning sensations in the stomach and swallowing difficulties are specified as colorectal cancer. Deep learning significantly impacts the medical image processing and diagnosis, offering potential improvements in accuracy and efficiency. The Kruskal Szekeres Generative Adversarial Network Augmented Deep Autoencoder (KSGANA-DA) is introduced for early colorectal cancer detection and it comprises two stages; Initial stage, data augmentation uses Affine Transform via Random Horizontal Rotation and Geometric Transform via Kruskal–Szekeres that coordinates to improve the training dataset diversity, boosting detection performance. The second stage, a Deep Autoencoder Anatomical Landmark-based Image Segmentation preserves edge pixel spatial locations, improving precision and recall for early boundary detection. Experiments validate KSGANA-DA performance and different existing methods are implemented into Python. The results of KSGANA-DA are to provide higher precision by 41%, recall by 7%, and lesser training time by 46% than compared to conventional methods. [ABSTRACT FROM AUTHOR]

A systematic procedure is proposed for better understanding the evolution laws of black holes in terms of pure quantum states. We start with the two opposed regions I and I I in the Penrose diagram, and study the evolution of matter in these regions, using the algebra derived earlier from the Shapiro effect in quantum particles. Since this spacetime has two distinct asymptotic regions, one must assume that there is a mechanism that reduces the number of states. In earlier work we proposed that region I I describes the angular antipodes of region I, the 'antipodal identification', but this eventually leads to contradictions. Our much simpler proposal is now that all states defined in region I I are exact quantum clones of those in region I. This indicates more precisely how to restore unitarity by making all quantum states observable, and in addition suggests that generalisations towards other black hole structures will be possible. An apparent complication is that the wave function must evolve with a purely antisymmetric, imaginary-valued Hamiltonian, but this complication can be well-understood in a realistic interpretation of quantum mechanics. [ABSTRACT FROM AUTHOR]

The relative flow of the Schwarzschild vs. the proper time during the classical evolution of a collapsing shell in the Schwarzschild coordinates practically forces us to interpret black hole formation as a highly non-local quantum process in which a shell/anti-shell pair is created within the incipient horizon, thus canceling out the original collapsing shell exactly at the horizon. By studying quantum fields in the black hole background, we reveal similar non-local effects. Among other things, the outgoing member of the Hawking pair very quickly becomes entangled with the black hole geometry (and not its partner), which is in contrast with the usual assumption that the Hawking pair is maximally entangled according to the local geometry near the horizon. Also, an infalling wave affects the black hole geometry even before it crosses the horizon. Finally, we find that a particle takes a finite amount of time to tunnel in and out of the black hole horizon, and thus avoids infinite blue and redshift in processes happening exactly at the horizon. These findings strongly support the picture of a black hole as a macroscopic quantum object.

A global vector field on a 'spacetime' differentiable manifold , of dimension , defines a congruence of world lines: the maximal integral curves of , or orbits. The associated global space is the set of these orbits. A '-adapted' chart on is one for which the vector of the 'spatial' coordinates remains constant on any orbit . We consider non-vanishing vector fields that have non-periodic orbits, each of which is a closed set. We prove transversality theorems relevant to such vector fields. Due to these results, it can be considered plausible that, for such a vector field, there exists in the neighborhood of any point a chart that is -adapted and 'nice', i.e. such that the mapping is injective - unless has some 'pathological' character. This leads us to define a notion of 'normal' vector field. For any such vector field, the mappings build an atlas of charts, thus providing with a canonical structure of differentiable manifold (when the topology defined on is Hausdorff, for which we give a sufficient condition met in important physical situations). Previously, a local space manifold had been associated with any 'reference frame' , defined as an equivalence class of charts. We show that, if is made of nice -adapted charts, is naturally identified with an open subset of the global space manifold . [ABSTRACT FROM AUTHOR]