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Representing spectral densities, real-frequency, and real-time Green’s functions of continuous systems by a small discrete set of complex poles is a ubiquitous problem in condensed matter physics, with applications ranging from quantum transport simulations to the simulation of strongly correlated electron systems. This paper introduces a method for obtaining a compact, approximate representation of these functions, based on their parameterization on the real axis and a given approximate precision. We show applications to typical spectral functions and results for structured and unstructured correlation functions of model systems. 

Representing real-time data as a sum of complex exponentials provides a compact form that enables both denoising and extrapolation. As a fully data-driven method, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm is agnostic to the underlying physical equations, making it broadly applicable to various observables and experimental or numerical setups. In this work, we consider applications of the ESPRIT algorithm primarily to extend real-time dynamical data from simulations of quantum systems. We evaluate ESPRIT's performance in the presence of noise and compare it to other extrapolation methods. We demonstrate its ability to extract information from short-time dynamics to reliably predict long-time behavior and determine the minimum time interval required for accurate results. We discuss how this insight can be leveraged in numerical methods that propagate quantum systems in time, and show how ESPRIT can predict infinite-time values of dynamical observables, offering a purely data-driven approach to characterizing quantum phases. 

We present a minimal pole method for analytically continuing matrix-valued imaginary frequency correlation functions to the real axis, enabling precise access to off-diagonal elements and thus improving the interpretation of self-energies and susceptibilities in quantum simulations. Traditional methods for matrix-valued analytic continuation tend to be either noise sensitive or make ad hoc positivity assumptions. Our approach avoids these issues via the construction of a compact pole representation with shared poles through exponential fits, expanding upon prior work focused on scalar functions. We test our method across various scenarios, including fermionic and bosonic response functions, with and without noise, and for both continuous and discrete spectra of real materials and model systems. Our findings demonstrate that this technique addresses the shortcomings of existing methodologies, such as artificial broadening and positivity violations. The paper is supplemented with a sample implementation in PYTHON. 

Abstract Although an established model organism, Tetrahymena thermophila remains comparatively inaccessible to high throughput screens, and alternative bioinformatic approaches still rely on unconnected datasets and outdated algorithms. Here, we report a new approach to consolidating RNA-seq and microarray data based on a systematic exploration of parameters and computational controls, enabling us to infer functional gene associations from their co-expression patterns. To illustrate the power of this approach, we took advantage of new data regarding a previously studied pathway, the biogenesis of a secretory organelle called the mucocyst. Our untargeted clustering approach recovered over 80% of the genes that were previously verified to play a role in mucocyst biogenesis. Furthermore, we tested four new genes that we predicted to be mucocyst-associated based on their co-expression and found that knocking out each of them results in mucocyst secretion defects. We also found that our approach succeeds in clustering genes associated with several other cellular pathways that we evaluated based on prior literature. We present the Tetrahymena Gene Network Explorer (TGNE) as an interactive tool for genetic hypothesis generation and functional annotation in this organism and as a framework for building similar tools for other systems. 

Abstract In our previous study, we identified a shift in the synchrotron peak frequency of the blazar B2 1308+326 from 10^12.9to 10^14.8Hz during a flare, suggesting it could be a changing-look blazar (CLB). In this work, we investigate the changing-look behaviour of B2 1308+326 by analysing a newly acquired optical spectrum and comparing it with an archival spectrum. We find that between the two epochs, the continuum flux increased by a factor of ~4.4, while the Mgiiemission line flux decreased by a factor of 1.4 ± 0.2. Additionally, the equivalent width of the Mgiiline reduced from ~20 to ~3 Å, indicating an apparent shift from a flat-spectrum radio quasar (FSRQ) class to a BL Lacertae (BL Lac) class. Despite this apparent change, the ratio of accretion disk luminosity to Eddington luminosity remains >10⁻²during both epochs, indicating efficient accretion persists in B2 1308+326. The measured black hole mass remains consistent with an average $\log M_{\mathrm{BH}}=8.44$M_⊙. Our findings suggest that B2 1308+326 is not a genuine CLB but rather an intrinsic FSRQ that emerges as a BL Lac during high-flux states due to enhanced nonthermal emission. 

The accurate ab-initio simulation of molecules and periodic solids with diagrammatic perturbation theory is an important task in quantum chemistry, condensed matter physics, and materials science. In this article, we present the WeakCoupling module of the open-source software package Green, which implements fully self-consistent diagrammatic weak coupling simulations, capable of dealing with real materials in the finite-temperature formalism. The code is licensed under the permissive MIT license. We provide self-consistent GW (scGW) and self-consistent second-order Green's function perturbation theory (GF2) solvers, analysis tools, and post-processing methods. This paper summarizes the theoretical methods implemented and provides background, tutorials and practical instructions for running simulations. 

Imaginary-time response functions of finite-temperature quantum systems are often obtained with methods that exhibit stochastic or systematic errors. Reducing these errors comes at a large computational cost—in quantum Monte Carlo simulations, the reduction of noise by a factor of two incurs a simulation cost of a factor of four. In this paper, we relate certain imaginary-time response functions to an inner product on the space of linear operators on Fock space. We then show that data with noise typically does not respect the positive definiteness of its associated Gramian. The Gramian has the structure of a Hankel matrix. As a method for denoising noisy data, we introduce an alternating projection algorithm that finds the closest positive definite Hankel matrix consistent with noisy data. We test our methodology at the example of fermion Green's functions for continuous-time quantum Monte Carlo data and show remarkable improvements of the error, reducing noise by a factor of up to 20 in practical examples. We argue that Hankel projections should be used whenever finite-temperature imaginary-time data of response functions with errors is analyzed, be it in the context of quantum Monte Carlo, quantum computing, or in approximate semianalytic methodologies. Published by the American Physical Society2024 

Abstract Vasoactive-intestinal peptide (Vip) is a pleiotropic peptide with a wide range of distribution and functions. Zebrafish possess 2 isoforms of Vip (a and b), in which Vipa is most homologous to the mammalian form. In female zebrafish, Vipa can stimulate LH secretion from the pituitary but is not essential for female reproduction, as vipa−/− females display normal reproduction. In contrast, we have found that vipa−/− males are severely subfertile and sex ratio of offspring is female-biased. By analyzing all aspects of male reproduction with wild-type (WT) males, we show that the testes of vipa−/− are underdeveloped and contain ∼70% less spermatids compared to WT counterparts. The sperm of vipa−/− males displayed reduced potency in terms of fertilization (by ∼80%) and motility span and duration (by ∼50%). In addition, vipa−/− male attraction to WT females was largely nonexistent, indicating decreased sexual motivation. We show that vipa mRNA and protein is present in Leydig cells and in developing germ cells in the testis of WT, raising the possibility that endogenous Vipa contributes to testicular function. Absence of Vipa in vipa−/− males resulted in downregulation of 3 key genes in the androgen synthesis chain in the testis, 3β-hsd, 17β-hsd1, and cyp11c1 (11β-hydrogenase), associated with a pronounced decrease in 11-ketotestosterone production and, in turn, compromised reproductive fitness. Altogether, this study establishes a crucial role for Vipa in the regulation of male reproduction in zebrafish, like in mammals, with the exception that Vipa is also expressed in zebrafish testis.