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Message passing on hypergraphs has been a standard framework for learning higher-order correlations between hypernodes. Recently-proposed hypergraph neural networks (HGNNs) can be categorized into spatial and spectral methods based on their design choices. In this work, we analyze the impact of change in hypergraph topology on the suboptimal performance of HGNNs and propose DPHGNN, a novel dual-perspective HGNN that introduces equivariant operator learning to capture lower-order semantics by inducing topology-aware spatial and spectral inductive biases. DPHGNN employs a unified framework to dynamically fuse lower-order explicit feature representations from the underlying graph into the super-imposed hypergraph structure. We benchmark DPHGNN over eight benchmark hypergraph datasets for the semi-supervised hypernode classification task and obtain superior performance compared to seven state-of-the-art baselines. We also provide a theoretical framework and a synthetic hypergraph isomorphism test to express the power of spatial HGNNs and quantify the expressivity of DPHGNN beyond the Generalized Weisfeiler Leman (1-GWL) test. Finally, DPHGNN was deployed by our partner e-commerce company for the Return-to-Origin (RTO) prediction task, which shows ~7% higher macro F1-Score than the best baseline., Comment: Accepted in SIGKDD'24 -- Research Track

An incremental approach for computation of convex hull for data points in two-dimensions is presented. The algorithm is not output-sensitive and costs a time that is linear in the size of data points at input. Graham's scan is applied only on a subset of the data points, represented at the extremal of the dataset. Points are classified for extremal, in proportion with the modular distance, about an imaginary point interior to the region bounded by convex hull of the dataset assumed for origin or center in polar coordinate. A subset of the data is arrived by terminating at until an event of no change in maximal points is observed per bin, for iteratively and exponentially decreasing intervals., Comment: 12 pages, 6 figures

The Unitary Group Adapted State-Specific Multi-Reference Perturbation Theory (UGA-SSMRPT2) developed by Mukherjee et al [J. Comput. Chem. 2015, 36, 670] has successfully realized the goal of studying bond dissociation in a numerically stable, spin-preserving and size-consistent manner. In this paper, we explore and analyse the UGA-SSMRPT2 theory in the description of avoided crossings and interlacing between a manifold of states belonging to the same space-spin symmetry. In a state-specific formalism, since each state is an eigenstate of its own effective operator, to include the information of the other states requires the theory to be sufficiently accurate. Three different aspects of UGA-SSMRPT2 have been studied: (a) We introduce and develop the most rigorous version of UGA-SSMRPT2 which emerges from the rigorous version of UGA-SSMRCC utilizing a linearly independent virtual manifold; we call this the 'projection' version of UGA-SSMRPT2 denoted as UGA-SSMRPT2 Scheme P. We compare and contrast this approach with our earlier formulation that used extra sufficiency conditions via amplitude equations, which we will denote as UGA-SSMRPT2 Scheme A. (b) We present the results for a variety of electronic states of a set of molecules which display the striking accuracy of both the two versions of UGA-SSMRPT2; with respect to three different situations involving weakly avoided crossings, moderate/strongly avoided crossings and interlacing in a manifold of PECs of same symmetry. Accuracy of our results has been benchmarked against IC-MRCISD+Q. (c) For weakly avoided crossing between states displaying differently charged sectors in the asymptotes, the insufficient inclusion of state-specific orbital relaxation in a second order perturbative theory might lead to an artefact of double crossing between the pair of PECs.

Approximating data points in three or higher dimension space based on cubic B-spline curve is presented. Representations for planar curves, are merged and extended to the higher dimension. The curve is fitted to the order of data points, or uniform parameter values are assumed for the points. Tangents are assumed at the data points, corresponding to the property used in cardinal splines, for shape preserving and visually pleasing fit. Control points of piecewise continuous cubic bezier curves, meeting the boundary conditions of cardinal spline segments, are used for b-spline curve in corresponding coordinate planes. Approximation using error computed in the least square sense, based on a fraction of data points, is also presented., Comment: 14 pages, 6 figures

The relativistic theory for the electric dipole moment (EDM) of paramagnetic atoms arising from the electric dipole moment of the electron is presented. A novel approach using the relativistic coupled-cluster method that incorporates the residual Coulomb interaction to all orders and a weak parity and time-reversal violating interaction to one order has been employed in Fr to obtain the enhancement of the EDM of that atom compared to the EDM of the electron. Trends of the different correlation effects and leading contributions from different physical states are discussed. Our result in combination with that of the Fr EDM that is currently in progress, has the potential to probe the validity of the Standard Model (SM) of elementary particle physics.

The effects of parity and time reversal violating potential, in particular the tensor-pseudotensor electron nucleus interaction are studied. We establish that selected terms representing the interplay of these effects and the residual Coulomb interaction in the coupled-cluster method are equivalent to the coupled perturbed Hartree-Fock. We have shown that the {\em normal} CPHF diagrams have a one-one correspondance in the coupled-cluster theory, but the CPHF pseudo diagrams are present in a subtle way. We have studied the {\em pseudo} diagrams in great detail and have shown explicitly their origin in coupled-cluster theory. This is demonstrated by considering the case of the permanent electric dipole moment of atomic Hg and our results are compared with the results of an earlier calculation., Comment: Accepted in J.Phys. B

The electric dipole moments of closed-shell atoms are sensitive to the parity and time-reversal violating phenomena in the nucleus. The nuclear Schiff moment is one such property, it arises from the parity and time reversal violating quark-quark interactions and the quark-chromo electric dipole moments. We calculate the electric dipole moment of atomic $^{199}{\rm Hg}$ arising from the nuclear Schiff moment using the relativistic coupled-cluster theory. This is the most accurate calculation of the quantity to date. Our calculations in combination with the experiment data provide important insights to the P and T violating coupling constants at the elementary particle level. In addition, a new limit on the tensor-pseudo tensor induced atomic EDM, calculated using the relativistic coupled-cluster theory is also presented., Comment: Published in J.Phys. B Conference Proceedings

We report the result of our {\it ab initio} calculation of the $6s ^2S_{1/2} \to 5d ^2D_{3/2}$ parity nonconserving electric dipole transition amplitude in $^{137}\text{Ba}^+$ based on relativistic coupled-cluster theory. Considering single, double and partial triple excitations, we have achieved an accuracy of less than one percent. If the accuracy of our calculation can be matched by the proposed parity nonconservation experiment in Ba$^+$ for the above transition,then the combination of the two results would provide an independent non accelerator test of the Standard Model of particle physics., Comment: 4 pages, 1 figure, Submitted to PRL

We report the results of our calculations of the atomic electric dipole moments of cesium and thallium arising from the electron-nucleus scalar-pseudoscalar interaction. The calculations are based on the all order relativistic coupled-cluster theory. Electron correlation effects, particularly in the case of thallium are of crucial importance. We obtain a new limit for the scalar-pseudoscalar interaction by combining the result of our thallium calculation and the measured value of the electric dipole moment of that atom., Comment: 5 pages, 1 figure

The relativistic coupled-cluster theory has been employed to calculate the magnetic dipole and electric quadrupole hyperfine structure constants for the stable isotopes $^{45}$Sc and $^{89}$Y. The role of electron correlation is found to be very important. The trend exhibited by these effects is rather different from previously studied single valence atomic systems., Comment: 5 pages, 1 figure, 3 tables

This work presents a first time accurate calculation of the magnetic dipole hyperfine structure constants for the ground state and some low-lying excited states of Pb$^+$. By comparing different levels of approximation with experimental results, we demonstrate the importance of correlation effects which reach beyond lower order relativistic many body perturbation theory. Employing relativistic coupled-cluster theory we obtain a quantitative understanding of the core-polarization and correlation effects inherent in this system and observe completely different trends compared to $Ba^+$., Comment: 4 pages, 2 figures research article

Relativistic coupled-cluster(RCC) theory has been employed to calculate the life time of the $6 ^2P_{3/2}$ state of single ionized lead($^{207}Pb$) to an accurac y of 3% and compared with the corresponding value obtained using second order r elativistic many-body perturbation theory(RMBPT). This is one of the very few ap plications of this theory to excited state properties of heavy atomic systems. C ontributions from the different electron correlation effects are given explicitl y.

The existence of a finite electric dipole moment (EDM) d_a of the closed-shell atom Yb implies parity and time reversal violations involving the nuclear sector. An important effect which can contribute to the Yb EDM is the tensor-pseudotensor electron-nucleus interaction characterized by the coupling constant C_T. Within the Standard Model (SM) of particle physics C_T=0, as this form of interaction is not allowed. If a finite d_a of Yb is observed in experiments, then an estimate of C_T can be obtained by combining with the theoretical calculations. A non-zero C_T implies physics beyond the standard model. In this paper we present the result of our ab initio calculation of the EDM Yb using different many-body methods., Comment: 19 pages, 13 figures