A tutorial on reproducing a predefined autocovariance function through AR models: application to stationary homogeneous isotropic turbulence

Sequential methods for synthetic realisation of random processes have a number of advantages compared with spectral methods. In this article, the determination of optimal autoregressive (AR) models for reproducing a predefined target autocovariance function of a random process is addressed. To this end, a novel formulation of the problem is developed. This formulation is linear and generalises the well-known Yule-Walker (Y-W) equations and a recent approach based on restricted AR models (Krenk-Møller approach, K-M). Two main features characterise the introduced formulation: (i) flexibility in the choice for the autocovariance equations employed in the model determination, and (ii) flexibility in the definition of the AR model scheme. Both features were exploited by a genetic algorithm to obtain optimal AR models for the particular case of synthetic generation of homogeneous stationary isotropic turbulence time series. The obtained models improved those obtained with the Y-W and K-M approaches for the same model parsimony in terms of the global fitting of the target autocovariance function. Implications for the reproduced spectra are also discussed. The formulation for the multivariate case is also presented, highlighting the causes behind some computational bottlenecks.

The GAMBIT Universal Model Machine: from Lagrangians to likelihoods

We introduce the Universal Model Machine (), a tool for automatically generating code for the global fitting software framework , based on Lagrangian-level inputs. accepts models written symbolically in and formats, and can use either tool along with and to generate model, collider, dark matter, decay and spectrum code, as well as interfaces to corresponding versions of , , and (C "Image missing"). In this paper we describe the features, methods, usage, pathways, assumptions and current limitations of . We also give a fully worked example, consisting of the addition of a Majorana fermion simplified dark matter model with a scalar mediator to via , and carry out a corresponding fit.

Ratiometric 4Pi single molecule localization with optimal resolution and color assignment

4Pi single molecule localization microscopy (4Pi-SMLM) with two opposing objectives achieves sub-10 nm isotropic 3D resolution with as few as 250 photons collected by each objective. Here, we developed a new ratiometric multi-color imaging strategy for 4Pi-SMLM which employed the intrinsic multi-phase interference intensity without increasing the complexity of the system and achieved both optimal 3D resolution and color separation. By partially linking the photon parameters between channels with interference difference of π during global fitting of the multi-channel 4Pi single molecule data, we showed on simulated data that the loss of the localization precision is minimal compared with the theoretical minimum uncertainty, the Cramer-Rao lower bound (CRLB).

Thermal WIMPs and the scale of new physics: global fits of Dirac dark matter effective field theories

We assess the status of a wide class of WIMP dark matter (DM) models in light of the latest experimental results using the global fitting framework . We perform a global analysis of effective field theory (EFT) operators describing the interactions between a gauge-singlet Dirac fermion and the Standard Model quarks, the gluons and the photon. In this bottom-up approach, we simultaneously vary the coefficients of 14 such operators up to dimension 7, along with the DM mass, the scale of new physics and several nuisance parameters. Our likelihood functions include the latest data from Planck, direct and indirect detection experiments, and the LHC. For DM masses below 100 GeV, we find that it is impossible to satisfy all constraints simultaneously while maintaining EFT validity at LHC energies. For new physics scales around 1 TeV, our results are influenced by several small excesses in the LHC data and depend on the prescription that we adopt to ensure EFT validity. Furthermore, we find large regions of viable parameter space where the EFT is valid and the relic density can be reproduced, implying that WIMPs can still account for the DM of the universe while being consistent with the latest data.

Global fitting for high-accuracy multi-channel single-molecule localization

Multi-channel detection in single-molecule localization microscopy (SMLM) greatly increases information content for various biological applications. Here, we present globLoc, a graphics processing unit (GPU) based global fitting algorithm with flexible PSF modeling and parameter sharing, to extract maximum information from multi-channel single molecule data. We show, both in simulations and experiments, that global fitting can substantially improve the 3D localization precision for biplane and 4Pi SMLM and color assignment for ratiometric multicolor imaging.

On the Measurement of Particle Contact Curvature and Young’s Modulus Using X-ray μCT

Contact curvature plays a pivotal role in the Young’s modulus determination and mechanical response of a particle. This paper presents the sensitivity analysis of a particle morphology to contact curvature and its influence on the Young’s modulus determination during the elastic deformation of a particle. X-ray computed micro-tomography (μCT) was conducted to obtain the prototype of a single particle. The digital information of the scanned particle, including 2D slices and 3D rendering was processed and the variation of contact curvature of the particle was examined using the circular (spherical at 3D) and polynomial fitting methods. The fitting sections of the particle are taken into account. The effect of contact curvature on Young’s modulus determination was investigated and it was found that Young’s modulus changed substantially from global fitting to local fitting. Young’s modulus is highly related to the surface roundness, which exerts a significant influence on the determination of Young’s modulus.

The solution structures of higher-order human telomere G-quadruplex multimers

Human telomeres contain the repeat DNA sequence 5′-d(TTAGGG), with duplex regions that are several kilobases long terminating in a 3′ single-stranded overhang. The structure of the single-stranded overhang is not known with certainty, with disparate models proposed in the literature. We report here the results of an integrated structural biology approach that combines small-angle X-ray scattering, circular dichroism (CD), analytical ultracentrifugation, size-exclusion column chromatography and molecular dynamics simulations that provide the most detailed characterization to date of the structure of the telomeric overhang. We find that the single-stranded sequences 5′-d(TTAGGG)n, with n = 8, 12 and 16, fold into multimeric structures containing the maximal number (2, 3 and 4, respectively) of contiguous G4 units with no long gaps between units. The G4 units are a mixture of hybrid-1 and hybrid-2 conformers. In the multimeric structures, G4 units interact, at least transiently, at the interfaces between units to produce distinctive CD signatures. Global fitting of our hydrodynamic and scattering data to a worm-like chain (WLC) model indicates that these multimeric G4 structures are semi-flexible, with a persistence length of ∼34 Å. Investigations of its flexibility using MD simulations reveal stacking, unstacking, and coiling movements, which yield unique sites for drug targeting.

The solution structures of higher-order human telomere G-quadruplex multimers

ABSTRACTHuman telomeres contain the repeat DNA sequence 5’(TTAGGG), with duplex regions that are several kilobases long terminating in a 3’ single-stranded overhang. The structure of the single-stranded overhang is not known with certainty, with disparate modes proposed in the literature. We report here the results of an integrated structural biology approach that combines small-angle X-ray scattering, circular dichroism (CD), analytical ultracentrifugation, size-exclusion column chromatography and molecular dynamics simulations that provide the most detailed characterization to date of the structure of the telomeric overhang. We find that the single-stranded sequences 5’(TTAGGG)n, with n=8, 12, and 16, fold into multimeric structures containing the maximal number (2, 3, and 4, respectively) of contiguous G4 units with no long gaps between units. The G4 units are a mixture of hybrid-1 and hybrid-2 conformers. In the multimeric structures, G4 units interact, at least transiently, at the interfaces between units to produce distinctive CD signatures. Global fitting of our hydrodynamic and scattering data to a worm-like chain (WLC) model indicates that these multimeric G4 structures are semi-flexible, with a persistence length of about 34 Å. Investigations of its flexibility using MD simulations reveal stacking, unstacking, and coiling movements, which yield unique sites for drug targeting.