Sparse Vector Autoregressive Modeling

The vector autoregressive (VAR) model has been widely used for modeling temporal dependence in a multivariate time series. For large (and even moderate) dimensions, the number of AR coefficients can be prohibitively large, resulting in noisy estimates, unstable predictions and difficult-to-interpret temporal dependence. To overcome such drawbacks, we propose a 2-stage approach for fitting sparse VAR (sVAR) models in which many of the AR coefficients are zero. The first stage selects non-zero AR coefficients based on an estimate of the partial spectral coherence (PSC) together with the use of BIC. The PSC is useful for quantifying the conditional relationship between marginal series in a multivariate process. A refinement second stage is then applied to further reduce the number of parameters. The performance of this 2-stage approach is illustrated with simulation results. The 2-stage approach is also applied to two real data examples: the first is the Google Flu Trends data and the second is a time series of concentration levels of air pollutants.Comment: 39 pages, 7 figure

Efficient Classical Shadow Tomography through Many-body Localization Dynamics

Classical shadow tomography serves as a potent tool for extracting numerous properties from quantum many-body systems with minimal measurements. Nevertheless, prevailing methods yielding optimal performance for few-body operators necessitate the application of random two-qubit gates, a task that can prove challenging on specific quantum simulators such as ultracold atomic gases. In this work, we introduce an alternative approach founded on the dynamics of many-body localization, a phenomenon extensively demonstrated in optical lattices. Through an exploration of the shadow norm -- both analytically, employing a phenomenological model, and numerically, utilizing the TEBD algorithm -- we demonstrate that our scheme achieves remarkable efficiency comparable to shallow circuits or measurement-induced criticality. This efficiency provides an exponential advantage over the Pauli measurement protocol for few-body measurements. Our findings are corroborated through direct numerical simulations encompassing the entire sampling and reconstruction processes. Consequently, our results present a compelling methodology for analyzing the output states of quantum simulators.Comment: 11 pages, 5 figures; appendix 2 page

Tunneling through an Eternal Traversable Wormhole

The Maldacena-Qi model describes two copies of the Sachdev-Ye-Kitaev model coupled with an additional coupling, and is dual to the Jackiw-Teitelboim gravity which exhibits an eternal traversable wormhole in the low-temperature limit. In this work, we study an experimental consequence of the existence of the traversable wormhole by considering the tunneling spectroscopy for the Maldacena-Qi model. Comparing to the high-temperature black hole phase where the bulk geometry is disconnected, we find that both the tunneling probability and the differential conductance in the low-temperature wormhole phase show non-trivial oscillation, which directly provides an unambiguous signature of the underlying $\operatorname{SL}(2)$ symmetry of the bulk geometry. We also perform bulk calculations in both high and low-temperature phases, which match the results from the boundary quantum theory.Comment: 10 pages, 4 figure

Tunneling through an eternal traversable wormhole

The Maldacena-Qi model describes two copies of the Sachdev-Ye-Kitaev model coupled with an additional coupling and is dual to the Jackiw-Teitelboim gravity, which exhibits an eternal traversable wormhole in the low-temperature limit. In this work, we study an experimental consequence of the existence of the traversable wormhole by considering the tunneling spectroscopy for the Maldacena-Qi model. Making comparisons to the high-temperature black-hole phase where the bulk geometry is disconnected, we find that both the tunneling probability and the differential conductance in the low-temperature wormhole phase show nontrivial oscillation, which directly provides an unambiguous signature of the underlying SL(2) symmetry of the bulk geometry. We also perform bulk calculations in both high- and low-temperature phases, which match the results from the boundary quantum theory

The causal effect of serum micronutrients on malignant kidney neoplasm in European descent

PurposeObservational studies have revealed that serum minerals and vitamins are associated with cancer. However, the causal relationships between serum minerals and vitamins and renal malignancies remain unclear.MethodsMendelian randomization (MR) was used for causal estimation. Single nucleotide polymorphisms (SNPs) for serum minerals and vitamins were obtained from published genome-wide association studies (GWAS). GWAS for malignant kidney neoplasm was obtained from the FinnGen consortium. Methods of inverse variance weighted (IVW), MR-Egger, and weighted median were carried out for causal inference. F-statistic was calculated to ensure a robust instrumental variable. Cochran’s Q statistics was applied to calculate heterogeneity. MR-Egger regression, MR-pleiotropy residual sum and outlier methods (MR-PRESSO) methods were used to perform pleiotropy analysis. Meanwhile, confounding factors were considered to determine whether causal inference would be biased.ResultsEight different micronutrients were included (zinc, iron, magnesium, calcium, copper, selenium, phosphate, and vitamin B12). After MR analysis, we found a protective effect of serum zinc against malignant kidney neoplasm (IVW: odds ratios (ORs), 0.86; 95% confidence interval (95% CI), 0.78–0.94; p, 0.0016; MR-Egger: OR, 0.80; 95% CI, 0.64–0.97; p, 0.052; weighted median: OR, 0.85; 95% CI, 0.75–0.96; p, 0.011). Causal relationships between other micronutrients and malignant kidney neoplasm were not obtained. No heterogeneity and pleiotropy were detected, while causality was not biased by confounding factors.ConclusionWe considered that serum zinc exerted a protective effect against malignant kidney neoplasm. In clinical practice, for people with high malignant kidney neoplasm risk, an oral zinc supplementation might play a role in a potential therapeutic target

Probing Entanglement Phase Transitions of Non-Hermitian Hamiltonians by Full Counting Statistics

Performing quantum measurements produces not only the expectation value of a physical observable $O$ but also the probability distribution of all possible outcomes. The full counting statistics (FCS) $Z(\phi, O)\equiv \langle e^{i\phi O}\rangle$, a Fourier transform of this distribution, contains the complete information of the measurement. In this work, we study the FCS of $Q_A$, the charge operator in subsystem $A$, for 1D systems described by non-Hermitian SYK models, which are solvable in the large-$N$ limit. In both the volume-law entangled phase for interacting systems and the critical phase for non-interacting systems, the conformal symmetry emerges, which gives $F(\phi, Q_A)\equiv \log Z(\phi, Q_A)\sim \phi^2\log |A|$. In short-range entangled phases, the FCS shows area-law behavior which can be approximated as $F(\phi, Q_A)\sim (1-\cos\phi) |\partial A|$ for $\zeta \gg J$, regardless of the presence of interactions. Our results suggest the FCS is a universal probe of entanglement phase transitions in non-Hermitian systems with conserved charges, which does not require the introduction of multiple replicas. We also discuss the consequence of discrete symmetry, long-range hopping, and generalizations to higher dimensions.Comment: 9 pages, 3 figures; appendix 10 page