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We present a two-component formulation of algebraic diagrammatic construction theory for simulating spin-orbit coupling and electron correlation in charged electronic states and photoelectron spectra. Our implementation supports Hartree-Fock and multiconfigurational reference wavefunctions, enabling efficient correlated calculations of relativistic effects using single-reference (SR-) and multireference (MR-) ADC. We combine the SR- and MR-ADC methods with three flavors of spin-orbit two-component Hamiltonians and benchmark their performance for a variety of atoms and small molecules. When multireference effects are not important, the SR-ADC approximations are competitive in accuracy to MR-ADC, often showing closer agreement with experimental results. However, for electronic states with multiconfigurational character and in non-equilibrium regions of potential energy surfaces, the MR-ADC methods are more reliable, predicting accurate excitation energies and zero-field splittings. Our results demonstrate that the two-component ADC methods are promising approaches for interpreting and predicting the results of modern spectroscopies.

This paper presents an innovative approach to Extreme Value Analysis (EVA) by introducing the Extreme Value Dynamic Benchmarking Method (EVDBM). EVDBM integrates extreme value theory to detect extreme events and is coupled with the novel Dynamic Identification of Significant Correlation (DISC)-Thresholding algorithm, which enhances the analysis of key variables under extreme conditions. By integrating return values predicted through EVA into the benchmarking scores, we are able to transform these scores to reflect anticipated conditions more accurately. This provides a more precise picture of how each case is projected to unfold under extreme conditions. As a result, the adjusted scores offer a forward-looking perspective, highlighting potential vulnerabilities and resilience factors for each case in a way that static historical data alone cannot capture. By incorporating both historical and probabilistic elements, the EVDBM algorithm provides a comprehensive benchmarking framework that is adaptable to a range of scenarios and contexts. The methodology is applied to real PV data, revealing critical low - production scenarios and significant correlations between variables, which aid in risk management, infrastructure design, and long-term planning, while also allowing for the comparison of different production plants. The flexibility of EVDBM suggests its potential for broader applications in other sectors where decision-making sensitivity is crucial, offering valuable insights to improve outcomes., Comment: 33 pages, 8 figures

Modern visual recognition models often display overconfidence due to their reliance on complex deep neural networks and one-hot target supervision, resulting in unreliable confidence scores that necessitate calibration. While current confidence calibration techniques primarily address single-label scenarios, there is a lack of focus on more practical and generalizable multi-label contexts. This paper introduces the Multi-Label Confidence Calibration (MLCC) task, aiming to provide well-calibrated confidence scores in multi-label scenarios. Unlike single-label images, multi-label images contain multiple objects, leading to semantic confusion and further unreliability in confidence scores. Existing single-label calibration methods, based on label smoothing, fail to account for category correlations, which are crucial for addressing semantic confusion, thereby yielding sub-optimal performance. To overcome these limitations, we propose the Dynamic Correlation Learning and Regularization (DCLR) algorithm, which leverages multi-grained semantic correlations to better model semantic confusion for adaptive regularization. DCLR learns dynamic instance-level and prototype-level similarities specific to each category, using these to measure semantic correlations across different categories. With this understanding, we construct adaptive label vectors that assign higher values to categories with strong correlations, thereby facilitating more effective regularization. We establish an evaluation benchmark, re-implementing several advanced confidence calibration algorithms and applying them to leading multi-label recognition (MLR) models for fair comparison. Through extensive experiments, we demonstrate the superior performance of DCLR over existing methods in providing reliable confidence scores in multi-label scenarios., Comment: submitted to TIP

We study the classic problem of correlation clustering in dynamic node streams. In this setting, nodes are either added or randomly deleted over time, and each node pair is connected by a positive or negative edge. The objective is to continuously find a partition which minimizes the sum of positive edges crossing clusters and negative edges within clusters. We present an algorithm that maintains an $O(1)$-approximation with $O$(polylog $n$) amortized update time. Prior to our work, Behnezhad, Charikar, Ma, and L. Tan achieved a $5$-approximation with $O(1)$ expected update time in edge streams which translates in node streams to an $O(D)$-update time where $D$ is the maximum possible degree. Finally we complement our theoretical analysis with experiments on real world data., Comment: ICML'24 (spotlight)

Voxel hierarchy on dynamic brain graphs is produced by k core percolation on functional dynamic amplitude correlation of resting-state fMRI. Directed graphs and their afferent/efferent capacities are produced by Markov modeling of the universal cover of undirected graphs simultaneously with the calculation of volume entropy. Positive and unsigned negative brain graphs were analyzed separately on sliding-window representation to underpin the visualization and quantitation of mental dynamic states with their transitions. Voxel hierarchy animation maps of positive graphs revealed abrupt changes in coreness k and kmaxcore, which we called mental state transitions. Afferent voxel capacities of the positive graphs also revealed transient modules composed of dominating voxels/independent components and their exchanges representing mental state transitions. Animation and quantification plots of voxel hierarchy and afferent capacity corroborated each other in underpinning mental state transitions and afferent module exchange on the positive directed functional connectivity graphs. We propose the use of spatiotemporal trajectories of voxels on positive dynamic graphs to construct hierarchical structures by k core percolation and quantified in- and out-flows of information of voxels by volume entropy/directed graphs to subserve diverse resting mental state transitions on resting-state fMRI graphs in normal human individuals.

We present a formulation and implementation of second-order quasidegenerate N-electron valence perturbation theory (QDNEVPT2) that provides a balanced and accurate description of spin-orbit coupling and dynamic correlation effects in multiconfigurational electronic states. In our approach, the energies and wavefunctions of electronic states are computed by treating electron repulsion and spin-orbit coupling operators as equal perturbations to the non-relativistic complete active-space wavefunctions and their contributions are incorporated fully up to the second order. The spin-orbit effects are described using the Breit-Pauli (BP) or exact two-component Douglas-Kroll-Hess (DKH) Hamiltonians within spin-orbit mean-field approximation. The resulting second-order methods (BP2- and DKH2-QDNEVPT2) are capable of treating spin-orbit coupling effects in nearly degenerate electronic states by diagonalizing an effective Hamiltonian expanded in a compact non-relativistic basis. For a variety of atoms and small molecules across the entire periodic table, we demonstrate that DKH2-QDNEVPT2 is competitive in accuracy with variational two-component relativistic theories. BP2-QDNEVPT2 shows high accuracy for the second- and third-period elements, but its performance deteriorates for heavier atoms and molecules. We also consider the first-order spin-orbit QDNEVPT2 approximations (BP1- and DKH1-QDNEVPT2), among which DKH1-QDNEVPT2 is reliable but less accurate than DKH2-QDNEVPT2. Both DKH1- and DKH2-QDNEVPT2 hold promise as efficient and accurate electronic structure methods for treating electron correlation and spin-orbit coupling in a variety of applications.

The connectivity of stock markets reflects the information efficiency of capital markets and contributes to interior risk contagion and spillover effects. We compare Shanghai Stock Exchange A-shares (SSE A-shares) during tranquil periods, with high leverage periods associated with the 2015 subprime mortgage crisis. We use Pearson correlations of returns, the maximum strongly connected subgraph, and $3\sigma$ principle to iteratively determine the threshold value for building a dynamic correlation network of SSE A-shares. Analyses are carried out based on the networking structure, intra-sector connectivity, and node status, identifying several contributions. First, compared with tranquil periods, the SSE A-shares network experiences a more significant small-world and connective effect during the subprime mortgage crisis and the high leverage period in 2015. Second, the finance, energy and utilities sectors have a stronger intra-industry connectivity than other sectors. Third, HUB nodes drive the growth of the SSE A-shares market during bull periods, while stocks have a think-tail degree distribution in bear periods and show distinct characteristics in terms of market value and finance. Granger linear and non-linear causality networks are also considered for the comparison purpose. Studies on the evolution of inter-cycle connectivity in the SSE A-share market may help investors improve portfolios and develop more robust risk management policies.

We study the classic correlation clustering in the dynamic setting. Given $n$ objects and a complete labeling of the object-pairs as either similar or dissimilar, the goal is to partition the objects into arbitrarily many clusters while minimizing disagreements with the labels. In the dynamic setting, an update consists of a flip of a label of an edge. In a breakthrough result, [BDHSS, FOCS'19] showed how to maintain a 3-approximation with polylogarithmic update time by providing a dynamic implementation of the Pivot algorithm of [ACN, STOC'05]. Since then, it has been a major open problem to determine whether the 3-approximation barrier can be broken in the fully dynamic setting. In this paper, we resolve this problem. Our algorithm, Modified Pivot, locally improves the output of Pivot by moving some vertices to other existing clusters or new singleton clusters. We present an analysis showing that this modification does indeed improve the approximation to below 3. We also show that its output can be maintained in polylogarithmic time per update.

The new generation of proposed light-emitting molecules for OLEDs has raised a considerable research interest due to its exceptional feature-a negative singlet-triplet (ST) gap violating the Hund's multiplicity rule in the excited S1 and T1 states. We investigate the role of spin polarization in the mechanism of ST gap inversion. Spin polarization is associated with doubly excited determinants of certain types, whose presence in the wavefunction expansion favors the energy of the singlet state more than that of the triplet. Using a perturbation theory-based model for spin polarization, we propose a simple descriptor for prescreening of candidate molecules with negative ST gaps and prove its usefulness for heptazine-type molecules. Numerical results show that the quantitative effect of spin polarization is approximately inverse-proportional to the HOMO-LUMO exchange integral. Comparison of single- and multireference coupled- cluster predictions of ST gaps shows that the former methods provide good accuracy by correctly balancing the effects of doubly excited determinants and dynamic correlation. We also show that accurate ST gaps may be obtained using a complete active space model supplemented with dynamic correlation from multireference adiabatic connection theory.

Recent studies have demonstrated the superior performance of introducing ``scan-wise" contrast labels into contrastive learning for multi-organ segmentation on multi-phase computed tomography (CT). However, such scan-wise labels are limited: (1) a coarse classification, which could not capture the fine-grained ``organ-wise" contrast variations across all organs; (2) the label (i.e., contrast phase) is typically manually provided, which is error-prone and may introduce manual biases of defining phases. In this paper, we propose a novel data-driven contrastive loss function that adapts the similar/dissimilar contrast relationship between samples in each minibatch at organ-level. Specifically, as variable levels of contrast exist between organs, we hypothesis that the contrast differences in the organ-level can bring additional context for defining representations in the latent space. An organ-wise contrast correlation matrix is computed with mean organ intensities under one-hot attention maps. The goal of adapting the organ-driven correlation matrix is to model variable levels of feature separability at different phases. We evaluate our proposed approach on multi-organ segmentation with both non-contrast CT (NCCT) datasets and the MICCAI 2015 BTCV Challenge contrast-enhance CT (CECT) datasets. Compared to the state-of-the-art approaches, our proposed contrastive loss yields a substantial and significant improvement of 1.41% (from 0.923 to 0.936, p-value$<$0.01) and 2.02% (from 0.891 to 0.910, p-value$<$0.01) on mean Dice scores across all organs with respect to NCCT and CECT cohorts. We further assess the trained model performance with the MICCAI 2021 FLARE Challenge CECT datasets and achieve a substantial improvement of mean Dice score from 0.927 to 0.934 (p-value$<$0.01). The code is available at: https://github.com/MASILab/DCC_CL, Comment: 11 pages

Recent practical approaches for the use of current generation noisy quantum devices in the simulation of quantum many-body problems have been dominated by the use of a variational quantum eigensolver (VQE). These coupled quantum-classical algorithms leverage the ability to perform many repeated measurements to avoid the currently prohibitive gate depths often required for exact quantum algorithms, with the restriction of a parameterized circuit to describe the states of interest. In this work, we show how the calculation of zero-temperature dynamic correlation functions defining the linear response characteristics of quantum systems can also be recast into a modified VQE algorithm, which can be incorporated into the current variational quantum infrastructure. This allows for these important physical expectation values describing the dynamics of the system to be directly converged on the frequency axis, and they approach exactness over all frequencies as the flexibility of the parameterization increases. The frequency resolution hence does not explicitly scale with gate depth, which is approximately twice as deep as a ground state VQE. We apply the method to compute the single-particle Green's function of ab initio dihydrogen and lithium hydride molecules, and demonstrate the use of a practical active space embedding approach to extend to larger systems. While currently limited by the fidelity of two-qubit gates, whose number is increased compared to the ground state algorithm on current devices, we believe the approach shows potential for the extraction of frequency dynamics of correlated systems on near-term quantum processors., Comment: 13 pages, 4 figures. Added new citations

Estimating dynamic correlation between a pair of time series is of importance in many applications. We present new estimators for the dynamic correlation between a pair of correlated Brownian motions and separately for dynamic correlation between a pair of correlated Geometric Brownian motions. We show that, as the sample size increases, all estimators presented in this paper converge in probability to the underlying true dynamic correlation., Comment: 26 pages. The old version had dynamic correlation estimators (and corresponding consistency results) for Brownian motion pairs. Note that in the new version we added estimators and consistency results for Geometric Brownian motion pairs

We consider the problem of computing dynamic correlation functions of quantum integrable models employing the thermodynamic form-factor approach. Specifically, we focus on correlations of local operators that conserve the number of particles and consider the 2-particle-hole contribution to their two-point functions. With the method developed being generally applicable to any finite energy and entropy state, our primary focus is on the thermal states. To exemplify this approach, we chose the Lieb-Liniger model and study the leading contribution from 2-particle-hole excitations at small momenta to the dynamic density-density correlation function. We also consider analogous contributions to two-point functions of higher local conserved densities and currents present in integrable theories., Comment: 27 pages, 1 figure, revised version

We present an ab-initio dynamical configuration interaction (DCI) study of free- and Mg-porphyrin. DCI is a recently developed active space theory based on the L\"owdin downfolding technique. In the active space, static correlation is described exactly with full configuration interaction. In the high energy, dynamically correlated subspace, we treat correlation at the quasiparticle level in the $GW$ approximation of Green's function theory. The final theory combines wave function and Green's function methods to give a balanced description of static and dynamic correlation. The theory and algorithm give a multireference treatment of ground and excited states for low computational cost. The four orbital Gouterman model of porphyrin offers an ideal active space in a large, correlated system to test the cost and accuracy of the embedding for large systems. Our parameter free, fully ab-initio DCI calculations in the minimal four-level active space agree well with both experiment and more expensive benchmark theories for the $Q_x$ and $Q_y$ transitions of free- and Mg-porphyrin. Studying the convergence of the excitation energies suggests that DCI correctly captures size extensive correlation effects, making it a promising active space theory for large, strongly-correlated systems.