arXiv subjects

Vishal

Publications and source records attributed to Vishal.

4 recordsLinked to original sources

arXiv2026

Singularity Resolution in Quantum Cosmology via Page-Wootters Formalism

We investigate the problem of classical big bang singularity in a plane-symmetric Bianchi type-I universe within the Wheeler-DeWitt (WDW) framework of quantum gravity. To address the problem of time, we employ the Page-Wootters formalism, which provides a relational notion of dynamics by conditioning the global state on a clock subsystem. Using Misner variables, the WDW equation assumes a Klein-Gordon (KG) type form. Its general solution is constructed as a Gaussian superposition of momentum eigenstates, resulting in an entangled global state between the clock and the remaining subsystem. Within this relational framework, we construct conditional states and obtain the corresponding probability density consistent with the KG-type inner product. The resulting conditional probability density vanishes in the limit of zero volume for all clock values, indicating quantum resolution of the classical singularity. We further show that positivity of the probability density imposes constraints on the admissible clock values, which depend on the parameters of the Gaussian wavepacket. These results highlight the essential role of quantum correlations in the emergence of relational dynamics, and demonstrate that the Page-Wootters formalism provides a consistent and nonsingular probabilistic description of quantum cosmology.

gr-qc↗

arXiv2026

DMDSC: A Dynamic-Margin Deep Simplex Classifier for Open-Set Recognition on Medical Image Datasets

Medical imaging datasets are often characterized by extreme class imbalances, where rare pathologies are significantly underrepresented compared to common conditions. This imbalance poses a dual challenge for Open-Set Recognition (OSR): models must maintain high classification accuracy on known classes while reliably rejecting unknown samples unseen during training in the clinical settings. While recently proposed Deep Simplex Classifier (DSC)~\cite{cevikalp2024reaching} and UnCertainty-aware Deep Simplex Classifier (UCDSC)~\cite{Aditya_2026_WACV} successfully leverage Neural Collapse to ensure maximal inter-class separation, they rely on a uniform margin that does not account for the varying densities of medical classes. In this paper, we propose DMDSC an enhanced framework featuring a dynamic margin approach. Our approach automatically adapts class-specific margins based on label frequency, enforcing a higher penalty and tighter feature clustering for rare pathologies to counteract the effects of data imbalance. Extensive experiments conducted on diverse medical benchmarks on BloodMNIST\cite{medmnistv2}, OCTMNIST\cite{medmnistv2}, DermaMNIST\cite{medmnistv2}, and BreaKHis~\cite{spanhol2015dataset} datasets, demonstrate that our framework outperforms state-of-the-art methods.

cs.CV↗

arXiv2026

Bohmian singularity resolution and quantum relaxation in Bianchi type-I quantum cosmology

We investigate cosmological singularity resolution and relaxation dynamics within the Bohmian mechanics via the plane-symmetric Bianchi type-I minisuperspace model in the Wheeler-DeWitt framework of quantum cosmology by constructing wave functions as Gaussian and Lorentzian wavepackets. Our analyses of the corresponding Bohmian trajectories reveal that Gaussian superposition predominantly yields classical singular solutions, with only a low fraction of small-amplitude cyclic trajectories. On the other hand, the Lorentzian wavepacket, characterized by the power-law momentum tail, generates stronger quantum potential barrier and a substantially rich velocity field, producing a significant fraction of non-singular bounce trajectories over extended volume ranges. We further examine quantum relaxation by evolving non-equilibrium distributions under the corresponding guidance dynamics. The Gaussian superposition exhibits laminar flow leading to boundary accumulation and incomplete relaxation, with non-monotonic decay of the $H$-function followed by saturation. In contrast, the Lorentzian wavepacket induces more complex trajectories, yielding monotonic decay of the $H$-function and better, though still incomplete, approach to Born-rule equilibrium. These results demonstrate that the inherent structure of the wave packet governs both singularity resolution and quantum relaxation through the nature of the Bohmian velocity field.

gr-qc↗

arXiv2024

Emergent spin and clock variable in Bianchi type-I quantum cosmology

We consider the Bianchi type-I model of the universe in the Wheeler-DeWitt quantization scheme with the matter degree of freedom represented by a scalar field. As a consequence, the quantum mechanical equation of the universe is obtained in the minisuperspace consisting of the Misner variables and the scalar field. Employing Dirac factorization, we find that the volume parameter makes a suitable choice for the clock variable whereas the matter clock leads to various inconsistencies. We further find that the minisuperspace orbital angular momentum operator does not commute with the Hamiltonian in the Dirac-type equation. We therefore find the missing part of the angular momentum whereby the total angular momentum commutes with the Hamiltonian. We interpret this missing part as the spin of the quantum universe during its early stage of evolution. The emergence of the three-component spin vector is owing to the presence of anisotropy in the Bianchi type-I model of the universe which is absent in the quantization of isotropic models.

gr-qc↗