745 research outputs found
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. 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
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 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
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 but also the probability distribution of all possible
outcomes. The full counting statistics (FCS) , a Fourier transform of this distribution, contains the complete
information of the measurement. In this work, we study the FCS of , the
charge operator in subsystem , for 1D systems described by non-Hermitian SYK
models, which are solvable in the large- 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 . In short-range entangled
phases, the FCS shows area-law behavior which can be approximated as for , 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
- …