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It is shown that the least order dynamic output feedback which stabilizes a given linear time invariant plant can be found via a semi-definite program.
Abstract In this article, we introduce a methodology for improving the accuracy and efficiency of reduced order models (ROMs) constructed using the least‐squares Petrov–Galerkin (LSPG) projection method through the introduction of preconditioning. Unlike prior related work, which focuses on preconditioning the linear systems arising within the ROM numerical solution procedure to improve linear solver performance, our approach leverages a preconditioning matrix directly within the minimization problem underlying the LSPG formulation. Applying preconditioning in this way has the potential to improve ROM accuracy for several reasons. First, preconditioning the LSPG formulation changes the norm defining the residual minimization, which can improve the residual‐based stability constant bounding the ROM solution's error. The incorporation of a preconditioner into the LSPG formulation can have the additional effect of scaling the components of the residual being minimized to make them roughly of the same magnitude, which can be beneficial when applying the LSPG method to problems with disparate scales (e.g., dimensional equations, multi‐physics problems). Importantly, we demonstrate that an “ideal preconditioned” LSPG ROM (a ROM in which the preconditioner is the inverse of the Jacobian of its corresponding full order model) emulates projection of the full order model solution increment onto the reduced basis. This quantity defines a lower bound on the error of a ROM solution for a given reduced basis. By designing preconditioners that approximate the Jacobian inverse—as is common in designing preconditioners for solving linear systems—it is possible to obtain a ROM whose error approaches this lower bound. The proposed approach is evaluated on several mechanical and thermo‐mechanical problems implemented within the Albany HPC code and run in the predictive regime, with prediction across material parameter space. We demonstrate numerically that the introduction of simple Jacobi, Gauss‐Seidel, and ILU preconditioners into the proper orthogonal decomposition/LSPG formulation reduces significantly the ROM solution error, the reduced Jacobian condition number, the number of nonlinear iterations required to reach convergence, and the wall time (thereby improving efficiency). Moreover, our numerical results reveal that the introduction of preconditioning can deliver a robust and accurate solution for test cases in which the unpreconditioned LSPG method fails to converge.
A measurement of the top quark pair ($ \textrm{t}\overline{\textrm{t}} $) production cross section in proton-proton collisions at a centre-of-mass energy of 5.02 TeV is presented. The data were collected at the LHC in autumn 2017, in dedicated runs with low-energy and low-intensity conditions with respect to the default configuration, and correspond to an integrated luminosity of 302 pb$^{−1}$. The measurement is performed using events with one electron or muon, and multiple jets, at least one of them being identified as originating from a b quark (b tagged). Events are classified based on the number of all reconstructed jets and of b-tagged jets. Multivariate analysis techniques are used to enhance the separation between the signal and backgrounds. The measured cross section is $ 62.5\pm 1.6{\left(\textrm{stat}\right)}_{-2.5}^{+2.6}\left(\textrm{syst}\right)\pm 1.2\left(\textrm{lumi}\right) $ pb. A combination with the result in the dilepton channel based on the same data set yields a value of 62.3 ± 1.5 (stat) ± 2.4 (syst) ± 1.2 (lumi) pb, to be compared with the standard model prediction of $ {69.5}_{-3.7}^{+3.5} $ pb at next-to-next-to-leading order in perturbative quantum chromodynamics.
A search for pair production of the supersymmetric partner of the top quark, the top squark, in proton-proton collisions at $ \sqrt{s} $ = 13 TeV is presented in final states containing at least one hadronically decaying tau lepton and large missing transverse momentum. This final state is highly sensitive to scenarios of supersymmetry in which the decay of the top squark to tau leptons is enhanced. The search uses a data sample corresponding to an integrated luminosity of 138 fb$^{−1}$, which was recorded with the CMS detector during 2016–2018. No significant excess is observed with respect to the standard model predictions. Exclusion limits at 95% confidence level on the masses of the top squark and the lightest neutralino are presented under the assumptions of simplified models. The results probe top squark masses up to 1150 GeV for a nearly massless neutralino. This search covers a relatively less explored parameter space in the context of supersymmetry, and the exclusion limit is the most stringent to date for the model considered here.[graphic not available: see fulltext]
A search for resonances in events with at least one isolated lepton (e or μ ) and two jets is performed using 139 fb -1 of $\sqrt{s}$ = 13 TeV proton–proton collision data recorded by the ATLAS detector at the LHC. Deviations from a smoothly falling background hypothesis are tested in three- and four-body invariant mass distributions constructed from leptons and jets, including jets identified as originating from bottom quarks. Model-independent limits on generic resonances characterised by cascade decays of particles leading to multiple jets and leptons in the final state are presented. The limits are calculated using Gaussian shapes with different widths for the invariant masses. The multi-body invariant masses are also used to set 95% confidence level upper limits on the cross-section times branching ratios for the production and subsequent decay of resonances predicted by several new physics scenarios.
A search for new physics in final states consisting of at least one photon, multiple jets, and large missing transverse momentum is presented, using proton-proton collision events at a center-of-mass energy of 13 TeV. The data correspond to an integrated luminosity of 137 fb$^{−1}$, recorded by the CMS experiment at the CERN LHC from 2016 to 2018. The events are divided into mutually exclusive bins characterized by the missing transverse momentum, the number of jets, the number of b-tagged jets, and jets consistent with the presence of hadronically decaying W, Z, or Higgs bosons. The observed data are found to be consistent with the prediction from standard model processes. The results are interpreted in the context of simplified models of pair production of supersymmetric particles via strong and electroweak interactions. Depending on the details of the signal models, gluinos and squarks of masses up to 2.35 and 1.43 TeV, respectively, and electroweakinos of masses up to 1.23 TeV are excluded at 95% confidence level.[graphic not available: see fulltext]
This paper presents the first search for a cH signal sensitive to the coupling of the charm quark (c) to the Higgs boson (H) in the associated production of at least one charm quark with a Higgs boson decaying to two photons. The results are based on a data set of proton-proton collisions at a center-of-mass energy of 13 TeV collected with the CMS experiment at the LHC, corresponding to an integrated luminosity of 138 fb −1 . Assuming the standard model (SM) rates for all other Higgs boson production processes, the observed (expected) upper limit at 95% confidence level on the cH signal strength is 243 (355) times the SM prediction. Under the same assumption, the observed (expected) allowed interval on the Higgs boson to charm quark coupling modifier, κ c , is |κ c | < 38.1 (|κ c | < 72.5) at 95% confidence level.
We propose an improved density integration methodology for Background-Oriented Schlieren (BOS) measurements that overcomes the noise sensitivity of the commonly used Poisson solver. Here, the method employs a weighted least-squares (WLS) optimization of the 2D integration of the density gradient field by solving an over-determined system of equations. Weights are assigned to the grid points based on density gradient uncertainties to ensure that a less reliable measurement point has less effect on the integration procedure. Synthetic image analysis with a Gaussian density field shows that WLS constrains the propagation of random error and reduces it by 80% in comparison to Poisson for the highest noise level. Using WLS with experimental BOS measurements of flow induced by a spark plasma discharge shows a 30% reduction in density uncertainty in comparison to Poisson, thereby increasing the overall precision of the BOS density measurements.
Approximating differential operators defined on two-dimensional surfaces is an important problem that arises in many areas of science and engineering. Over the past ten years, localized meshfree methods based on generalized moving least squares (GMLS) and radial basis function finite differences (RBF-FD) have been shown to be effective for this task as they can give high orders of accuracy at low computational cost, and they can be applied to surfaces defined only by point clouds. However, there have yet to be any studies that perform a direct comparison of these methods for approximating surface differential operators (SDOs). The first purpose of this work is to fill that gap. For this comparison, we focus on an RBF-FD method based on polyharmonic spline kernels and polynomials (PHS+Poly) since they are most closely related to the GMLS method. Additionally, we use a relatively new technique for approximating SDOs with RBF-FD called the tangent plane method since it is simpler than previous techniques and natural to use with PHS+Poly RBF-FD. Further, the second purpose of this work is to relate the tangent plane formulation of SDOs to the local coordinate formulation used in GMLS and to show that they are equivalent when the tangent space to the surface is known exactly. The final purpose is to use ideas from the GMLS SDO formulation to derive a new RBF-FD method for approximating the tangent space for a point cloud surface when it is unknown. For the numerical comparisons of the methods, we examine their convergence rates for approximating the surface gradient, divergence, and Laplacian as the point clouds are refined for various parameter choices. We also compare their efficiency in terms of accuracy per computational cost, both when including and excluding setup costs.
Non-targeted analysis of complex chemical mixtures can be difficult considering the convoluted nature of the matrix and the potential unknown chemical differences between samples or classes of samples. Ultrahigh pressure liquid chromatography coupled to quadrupole time-of-flight mass spectrometry (UHPLC-QTOF) is an ideal technique to probe chemical differences for a wide variety of samples. While UHPLC-QTOF can discover minute chemical differences down to low part per billion (ppb) concentrations with a high degree of confidence, the application of high-resolution mass spectrometry can yield massive amounts of information (∼ 10 gb per sample) that cannot be analyzed manually. Therefore, the application of chemometric techniques is mandatory for the interrogation of complex samples. Fisher's ratio (FR) assisted multivariate curve resolution-alternating least squares (MCR-ALS) was used to the discover and identify the chemical differences between two classes of materials: 1) a pond water matrix and 2) the matrix spiked with a pharmaceutical standard mix containing 17 compounds. Thirteen of the seventeen spiked compounds were discovered using FR analysis, and then five were successfully deconvoluted using MCR-ALS wherein the number of curves chosen were automatically determined using singular value decomposition (SVD). In conclusion, the use of an automated FR assisted MCR-ALS will aid in discovering trace levels of chemical components without the need for the researcher to provide potentially biased input which will aid in non-targeted workflow.
Herein a search for the pair-production of vector-like quarks optimized for decays into a Z boson and a third-generation Standard Model quark is presented, using the full Run 2 dataset corresponding to 139fb –1 of pp collisions at $\sqrt{s}$ = 13TeV, collected in 2015–2018 with the ATLAS detector at the Large Hadron Collider. The targeted final state is characterized by the presence of a Z boson with high transverse momentum, reconstructed from a pair of same-flavour leptons with opposite-sign charges, as well as by the presence of b-tagged jets and high-transverse-momentum large-radius jets reconstructed from calibrated smaller-radius jets. Events with exactly two or at least three leptons are used, which are further categorized by the presence of boosted W, Z, and Higgs bosons and top quarks. The categorization is performed using a neural-network-based boosted object tagger to enhance the sensitivity to signal relative to the background. No significant excess above the background expectation is observed and exclusion limits at 95% confidence level are set on the masses of the vector-like partners T and B of the top and bottom quarks, respectively. The limits depend on the branching ratio configurations and, in the case of 100% branching ratio for T→Zt and 100% branching ratio for B→Zb, this search sets the most stringent limits to date, allowing m T >1.60TeV and m B >1.42TeV, respectively.
A search is presented for the pair-production of heavy vector-like quarks in the lepton+jets final state using 140 fb -1 of proton–proton collisions at $\sqrt{s}$ = 13 TeV collected with the ATLAS detector. The search is optimised for vector-like top-quarks (T) that decay into a W boson and a b-quark, with one W boson decaying leptonically and the other hadronically. Other vector-like quark flavours and decay modes are also considered. Events are selected with one high transverse-momentum electron or muon, large missing transverse momentum, a large-radius jet identified as a W boson, and multiple small-radius jets, at least one of which is b-tagged. Vector-like T-quarks with 100% branching ratio to Wb are excluded at 95% CL for masses below 1700 GeV. These limits are also applied to vector-like Y-quarks, which decay exclusively into a W boson and a b-quark. Isospin singlets with B(T→Wb:Ht:Zt)=1/2:1/4:1/4 are excluded for masses below 1360 GeV.
Here, this study presents a novel analytical approach for quantifying Pu(IV) in glove box environments using fiber-optic-based visible–near-infrared absorption spectroscopy in combination with partial least squares regression (PLSR) and design of experiments. The method addresses significant challenges posed by overlapping spectral features arising from Nd(III), which is a common fission product impurity, and the speciation variability of Pu(IV) nitrato complexes in HNO 3 concentrations ranging from 2.5 to 11 M. A curated training set consisting of data from 20 samples was developed via D-optimal design to enable robust PLSR model calibration for Pu(IV) using the near-infrared band near 1050 nm. The training set was acquired from samples in cuvettes with a 1-cm path length and was used to build the PLSR model. The robustness of the model was validated with data collected using a dip probe with a 1-cm path length and varying Pu(IV) concentrations. The strong performance of the model indicates good model transfer from cuvette to dip probe and highlights the potential for in situ measurements and online monitoring of reactions in a crystallization reactor vessel. The results demonstrate that this combined spectroscopic and chemometric approach can accurately and simultaneously quantify Pu(IV) and HNO 3 , thereby offering a promising tool for real-time monitoring in process environments.
The principle of least action is the cornerstone of classical mechanics, theory of relativity, quantum mechanics, and thermodynamics. Here, we describe how a neural network (NN) learns to find the trajectory for a Lennard-Jones (LJ) system that maintains balance in minimizing the Onsager–Machlup (OM) action and maintaining the energy conservation. The phase-space trajectory thus calculated is in excellent agreement with the corresponding results from the “ground-truth” molecular dynamics (MD) simulation. Furthermore, we show that the NN can easily find structural transformation pathways for LJ clusters, for example, the basin-hopping transformation of an LJ 38 from an incomplete Mackay icosahedron to a truncated face-centered cubic octahedron. Unlike MD, the NN computes atomic trajectories over the entire temporal domain in one fell swoop, and the NN time step is a factor of 20 larger than the MD time step. The NN approach to OM action is quite general and can be adapted to model morphometrics in a variety of applications.
Least Squares Tensor Hypercontraction (LS-THC) has received some attention in recent years as an approach to reduce the significant computational costs of wavefunc- tion based methods in quantum chemistry. However, previous work has demonstrated that the LS-THC factorization performs disproportionately worse in the description of wavefunction components (e.g. cluster amplitudes T 2 ) than Hamiltonian compo- nents (e.g. electron repulsion integrals (pq|rs)). This work develops novel theoretical methods to study the source of these errors in the context of the real-space T 2 kernel, and reports, for the first time, the existence of a “correlation feature” in the errors of the LS-THC representation of the “exchange-like” correlation energy EX and T 2 that is remarkably consistent across ten molecular species, three correlated wavefunctions, and four basis sets. This correlation feature portends the existence of a “pair-point kernel” missing in the usual LS-THC representation of the wavefunction, which critically depends upon pairs of grid points situated close to atoms and with inter-pair distances between one and two Bohr radii. These findings point the way for future LS-THC developments to address these shortcomings.
Certain correlation structures in the data covariance matrix (DCM) used for generalized least squares (GLS) regression can result in biased estimates, commonly known in the field of nuclear data evaluation as Peele’s Pertinent Puzzle (PPP). This article introduces a generative, forward modeling framework within which the PPP bias is characterized through an eigenspectrum analysis of the DCM. This analysis highlights the root cause of the bias, generalizes the problem beyond the nuclear data field, and provides insight to the problem regimes where it can occur. What follows is an understanding that the bias can show up for any experimental neutron time-of-flight data for which systematic uncertainties have been quantified. Lastly, a discussion of the adaptation of cross validation approaches that require pre-whitening to incorporate the known ‘fix’ to the PPP bias in the GLS estimator.
Inductively coupled plasma-optical emission spectra were modeled with partial least squares regression models to quantify trace elements in uranium (20–5000 μg per g U) without chemical separations or matrix matched calibration standards.
Context. Giant radio galaxies (GRGs, or colloquially ‘giants’) are the Universe’s largest structures generated by individual galaxies. They comprise synchrotron-radiating active galactic nucleus ejecta and attain cosmological (megaparsec-scale) lengths. However, the main mechanisms that drive their exceptional growth remain poorly understood. Aims. To deduce the main mechanisms that drive a phenomenon, it is usually instructive to study extreme examples. If there exist host galaxy characteristics that are an important cause for GRG growth, then the hosts of the largest GRGs are likely to possess them. Similarly, if there exist particular large-scale environments that are highly conducive to GRG growth, then the largest GRGs are likely to reside in them. For these reasons, we aim to perform a case study of the largest GRG available. Methods. We reprocessed the LOFAR Two-Metre Sky Survey DR2 by subtracting compact sources and performing multi-scale CLEAN de-convolutions at 60" and 90" resolution. The resulting images constitute the most sensitive survey yet for radio galaxy lobes, whose diffuse nature and steep synchrotron spectra have allowed them to evade previous detection attempts at higher resolution and shorter wavelengths. We visually searched these images for GRGs. Results. We have discovered Alcyoneus, a low-excitation radio galaxy with a projected proper length l p = 4.99 ± 0.04 Mpc. Both its jets and lobes are detected at very high significance, and the SDSS-based identification of the host, at spectroscopic redshift z spec = 0.24674 ± 6 × 10 -5 , is unambiguous. The total luminosity density at ν = 144 MHz is L ν = 8 ± 1 × 10 25 W Hz -1 , which is below average, though near median (percentile 45 ± 3%) for GRGs. The host is an elliptical galaxy with a stellar mass M* = 2.4 ± 0.4 × 10 11 M ⊙ and a super-massive black hole mass M• = 4 ± 2 × 10 8 M ⊙ , both of which tend towards the lower end of their respective GRG distributions (percentiles 25 ± 9% and 23 ± 11%). The host resides in a filament of the Cosmic Web. Through a new Bayesian model for radio galaxy lobes in three dimensions, we estimate the pressures in the megaparsec-cubed-scale northern and southern lobes to be P min,1 = 4.8 ± 0.3 × 10 -16 Pa and P min,2 = 4.9 ± 0.6 × 10 -16 Pa, respectively. The corresponding magnetic field strengths are B min,1 = 46 ± 1 pT and B min,2 = 46 ± 3 pT. Conclusions. We have discovered what is in projection the largest known structure made by a single galaxy – a GRG with a projected proper length l p = 4.99 ± 0.04 Mpc. The true proper length is at least l min = 5.04 ± 0.05 Mpc. Beyond geometry, Alcyoneus and its host are suspiciously ordinary: the total low-frequency luminosity density, stellar mass, and super-massive black hole mass are all lower than, though similar to, those of the medial GRG. Thus, very massive galaxies or central black holes are not necessary to grow large giants, and, if the observed state is representative of the source over its lifetime, neither is high radio power. A low-density environment remains a possible explanation. The source resides in a filament of the Cosmic Web, with which it might have significant thermodynamic interaction. The pressures in the lobes are the lowest hitherto found, and Alcyoneus therefore represents the most promising radio galaxy yet to probe the warm–hot inter-galactic medium.