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Large systems are often coarse-grained in order to study their low-dimensional macroscopic dynamics, yet microscopic complexity can in principle disrupt these predictions in many ways. We first consider one form of fine-grained complexity, heterogeneity in the time scales of microscopic dynamics, and show by an algebraic approach that it can stabilize macroscopic degrees of freedom. We then show that this time scale heterogeneity can arise from other forms of complexity, in particular disordered interactions between microscopic variables, and that it can drive the system's coarse-grained dynamics to transition from nonequilibrium attractors to fixed points. These mechanisms are demonstrated in a model of many-species ecosystems, where we find a quasi-decoupling between the low- and high-dimensional facets of the dynamics, interacting only through a key feature of ecological models, the fact that species' dynamical time scales are controlled by their abundances. We conclude that fine-grained disorder may enable a macroscopic equilibrium description of many-species ecosystems., Comment: 8 pages, 4 figures, 5 supplementary figures

We discuss how the two existing approximate N$^3$LO (aN$^3$LO) sets of parton distributions (PDFs) from the MSHT20 and NNPDF4.0 series can be combined for LHC phenomenology, both in the pure QCD case and for the QCD$\otimes$QED sets that include the photon PDF. Using the resulting combinations, we present predictions for the total inclusive cross-section for Higgs production in gluon fusion, vector boson fusion, and associated production at the LHC Run-3. For the gluon fusion and vector boson fusion channels, the corrections that arise when using correctly matched aN$^3$LO PDFs with N$^3$LO cross section calculations, compared to using NNLO PDFs, are significant, in many cases larger than the PDF uncertainty, and generally larger than the differences between the two aN$^3$LO PDF sets entering the combination. The combined aN$^3$LO PDF sets, MSHT20xNNPDF40_an3lo and MSHT20xNNPDF40_an3lo_qed, are made publicly available in the LHAPDF format and can be readily used for LHC phenomenology., Comment: 22 pages, 11 figures, LHAPDF grids available from https://zenodo.org/records/13843626

Deep learning models are defined in terms of a large number of hyperparameters, such as network architectures and optimiser settings. These hyperparameters must be determined separately from the model parameters such as network weights, and are often fixed by ad-hoc methods or by manual inspection of the results. An algorithmic, objective determination of hyperparameters demands the introduction of dedicated target metrics, different from those adopted for the model training. Here we present a new approach to the automated determination of hyperparameters in deep learning models based on statistical estimators constructed from an ensemble of models sampling the underlying probability distribution in model space. This strategy requires the simultaneous parallel training of up to several hundreds of models and can be effectively implemented by deploying hardware accelerators such as GPUs. As a proof-of-concept, we apply this method to the determination of the partonic substructure of the proton within the NNPDF framework and demonstrate the robustness of the resultant model uncertainty estimates. The new GPU-optimised NNPDF code results in a speed-up of up to two orders of magnitude, a stabilisation of the memory requirements, and a reduction in energy consumption of up to 90% as compared to sequential CPU-based model training. While focusing on proton structure, our method is fully general and is applicable to any deep learning problem relying on hyperparameter optimisation for an ensemble of models., Comment: 27 pages, 7 figures

Disordered systems theory provides powerful tools to analyze the generic behaviors of highdimensional systems, such as species-rich ecological communities or neural networks. By assuming randomness in their interactions, universality ensures that many microscopic details are irrelevant to system-wide dynamics; but the choice of a random ensemble still limits the generality of results. We show here, in the context of ecological dynamics, that these analytical tools do not require a specific choice of ensemble, and that solutions can be found based only on a fundamental rotational symmetry in the interactions, encoding the idea that traits can be recombined into new species without altering global features. Dynamical outcomes then depend on the spectrum of the interaction matrix as a free parameter, allowing us to bridge between results found in different models of interactions, and extend beyond them to previously unidentified behaviors. The distinctive feature of ecological models is the possibility of species extinctions, which leads to an increased universality of dynamics as the fraction of extinct species increases. We expect that these findings can inform new developments in theoretical ecology as well as for other families of complex systems., Comment: 12 pages, 3 figures

We present NNPDF4.0MC, a variant of the NNPDF4.0 set of parton distributions (PDFs) at LO, NLO and NNLO, with and without inclusion of the photon PDF, suitable for use with Monte Carlo (MC) event generators, which require PDFs to satisfy additional constraints in comparison to standard PDF sets. These requirements include PDF positivity down to a low scale $Q\sim 1$ GeV, smooth extrapolation in the very small and large $x$ regions, and numerically stable results even in extreme regions of phase space for all PDFs. We compare the NNPDF4.0MC PDFs to their baseline NNPDF4.0 counterparts, and to the NNPDF2.3LO set entering the Monash tune of the Pythia8 event generator. We briefly assess the phenomenological impact of these PDFs on the cross-sections for hard and soft QCD processes at the LHC., Comment: 14 pages, 9 figures, PDF sets available from https://nnpdf.mi.infn.it/nnpdf4-0-mc/ ; version to be published in jhep

The student-optimal stable mechanism (DA), the most popular mechanism in school choice, is the only one that is both stable and strategy-proof. However, when DA is implemented, a student can change the schools of others without changing her own. We show that this drawback is limited: a student cannot change her classmates without modifying her school. We refer to this new property as {\it{local non-bossiness}} and use it to provide a new characterization of DA that does not rely on stability. Furthermore, we show that local non-bossiness plays a crucial role in providing incentives to be truthful when students have preferences over their colleagues. As long as students first consider the school to which they are assigned and then their classmates, DA induces the only stable and strategy-proof mechanism. There is limited room to expand this preference domain without compromising the existence of a stable and strategy-proof mechanism.

We extend the existing leading (LO), next-to-leading (NLO), and next-to-next-to-leading order (NNLO) NNPDF4.0 sets of parton distribution functions (PDFs) to approximate next-to-next-to-next-to-leading order (aN$^3$LO). We construct an approximation to the N$^3$LO splitting functions that includes all available partial information from both fixed-order computations and from small and large $x$ resummation, and estimate the uncertainty on this approximation by varying the set of basis functions used to construct the approximation. We include known N$^3$LO corrections to deep-inelastic scattering structure functions and extend the FONLL general-mass scheme to $\mathcal{O}\left( \alpha_s^3\right)$ accuracy. We determine a set of aN$^3$LO PDFs by accounting both for the uncertainty on splitting functions due to the incomplete knowledge of N$^3$LO terms, and to the uncertainty related to missing higher corrections (MHOU), estimated by scale variation, through a theory covariance matrix formalism. We assess the perturbative stability of the resulting PDFs, we study the impact of MHOUs on them, and we compare our results to the aN$^3$LO PDFs from the MSHT group. We examine the phenomenological impact of aN$^3$LO corrections on parton luminosities at the LHC, and give a first assessment of the impact of aN$^3$LO PDFs on the Higgs and Drell-Yan total production cross-sections. We find that the aN$^3$LO NNPDF4.0 PDFs are consistent within uncertainties with their NNLO counterparts, that they improve the description of the global dataset and the perturbative convergence of Higgs and Drell-Yan cross-sections, and that MHOUs on PDFs decrease substantially with the increase of perturbative order., Comment: 63 pages, 41 figures. Final version, as published in EPJC. Various clarifications added. Fig 2.9 and Tab. 4.6, 5.1 and 5.2 added. In particular, comparison to approximate YR4 estimate of PDF uncertainties added (Tab 4.1, 4.2 and associate discussion in sect. 5)

We include uncertainties due to missing higher order corrections to QCD computations (MHOU) used in the determination of parton distributions (PDFs) in the recent NNPDF4.0 set of PDFs. We use our previously published methodology, based on the treatment of MHOUs and their full correlations through a theory covariance matrix determined by scale variation, now fully incorporated in the new NNPDF theory pipeline. We assess the impact of the inclusion of MHOUs on the NNPDF4.0 central values and uncertainties, and specifically show that they lead to improved consistency of the PDF determination with an ensuing moderate reduction of PDF uncertainties at NNLO., Comment: 23 pages, 6 figures. Final version, as published in EPJC. Several small improvements; expanded discussion of the phi indicator in sect 4.2

We construct a set of parton distribution functions (PDFs), based on the recent NNPDF4.0 PDF set, that also include a photon PDF. The photon PDF is constructed using the LuxQED formalism, while QED evolution accounting for O(alpha), O(alpha alphas) and O(alpha^2) corrections is implemented and benchmarked by means of the EKO code. We investigate the impact of QED effects on NNPDF4.0, and compare our results both to our previous NNPDF3.1QED PDF set and to other recent PDF sets that include the photon. We assess the impact of photon-initiated processes and electroweak corrections on a variety of representative LHC processes, and find that they can reach the 5% level in vector boson pair production at large invariant mass., Comment: 32 pages, 19 figures. Final; version, as published on EPJC. Pheno discussion in Sect 4.2 improved, a few typos corrected

We provide a first quantitative indication that the wave function of the proton contains unequal distributions of charm quarks and antiquarks, i.e. a nonvanishing intrinsic valence charm distribution. A significant nonvanishing valence component cannot be perturbatively generated, hence our results reinforce previous evidence that the proton contains an intrinsic (i.e., not radiatively generated) charm quark component. We establish our result through a determination of the parton distribution functions (PDFs) of charm quarks and antiquarks in the proton. We propose two novel experimental probes of this intrinsic charm valence component: D-meson asymmetries in Z+c-jet production at the LHCb experiment, and flavor-tagged structure functions at the Electron-Ion Collider., Comment: 11 pages, 11 figures. PDF files available for download in LHAPDF format from https://nnpdf.mi.infn.it/nnpdf4-0-charm-asymmetry-study/ Final version, to be published in PRD (letters). Figures 2, 6 and 7 added. Fit without imposing the charm valence sum rule added. Various small clarifications

We formulate a one-center non-orthogonal configuration interaction singles (1C-NOCIS) theory for the computation of core excited states of an initial singlet state with two unpaired electrons. This model, which we refer to as 1C-NOCIS two-electron open-shell (2eOS), is appropriate for computing the K-edge near-edge X-ray absorption spectra (NEXAS) of the valence excited states of closed-shell molecules relevant to pump-probe time-resolved (TR) NEXAS experiments. With inclusion of core hole relaxation effects and explicit spin adaptation, 1C-NOCIS 2eOS requires mild shifts to match experiment, is free of artifacts due to spin contamination, and can capture the high-energy region of the spectrum beyond the transitions into the singly occupied molecular orbitals (SOMO). Calculations on water and thymine illustrate the different key features of excited-state NEXAS, namely the core-to-SOMO transition as well as shifts and spin-splittings in the transitions analogous to those of the ground state. Finally, simulations of the TR-NEXAS of acetylacetone after excitation onto its pi to pi-star singlet excited state at the carbon K-edge - an experiment carried out recently - showcases the ability of 1C-NOCIS 2eOS to efficiently simulate NEXAS based on non-adiabatic molecular dynamics simulations., Comment: Manuscript: 42 pages, 6 figures. SI: 48 pages, 10 figures

Wind speed and direction variations across the rotor affect power production. As utility-scale turbines extend higher into the atmospheric boundary layer (ABL) with larger rotor diameters and hub heights, they increasingly encounter more complex wind speed and direction variations. We assess three models for power production that account for wind speed and direction shear. Two are based on actuator disc representations and the third is a blade element representation. We also evaluate the predictions from a standard power curve model that has no knowledge of wind shear. The predictions from each model, driven by wind profile measurements from a profiling LiDAR, are compared to concurrent power measurements from an adjacent utility-scale wind turbine. In the field measurements of the utility-scale turbine, discrete combinations of speed and direction shear induce changes in power production of -19% to +34% relative to the turbine power curve for a given hub height wind speed. Positive speed shear generally corresponds to over-performance and positive direction shear to under-performance, relative to the power curve. Overall, the blade element model produces both higher correlation and lower error relative to the other models, but its quantitative accuracy depends on induction and controller sub-models. To further assess the influence of complex, non-monotonic wind profiles, we also drive the models with best-fit power law wind speed profiles and linear wind direction profiles. These idealized inputs produce qualitative and quantitative differences in power predictions from each model, demonstrating that time-varying, non-monotonic wind shear affects wind power production., Comment: 28 pages, 14 figures in main body, 1 figure in Appendix A, to be published in Wiley Wind Energy

Proton-proton collisions at the LHC generate a high-intensity collimated beam of neutrinos in the forward (beam) direction, characterised by energies of up to several TeV. The recent observation of LHC neutrinos by FASER$\nu$ and SND@LHC signals that this hitherto ignored particle beam is now available for scientific inquiry. Here we quantify the impact that neutrino deep-inelastic scattering (DIS) measurements at the LHC would have on the parton distributions (PDFs) of protons and heavy nuclei. We generate projections for DIS structure functions for FASER$\nu$ and SND@LHC at Run III, as well as for the FASER$\nu$2, AdvSND, and FLArE experiments to be hosted at the proposed Forward Physics Facility (FPF) operating concurrently with the High-Luminosity LHC (HL-LHC). We determine that up to one million electron- and muon-neutrino DIS interactions within detector acceptance can be expected by the end of the HL-LHC, covering a kinematic region in $x$ and $Q^2$ overlapping with that of the Electron-Ion Collider. Including these DIS projections into global (n)PDF analyses, specifically PDF4LHC21, NNPDF4.0, and EPPS21, reveals a significant reduction of PDF uncertainties, in particular for strangeness and the up and down valence PDFs. We show that LHC neutrino data enables improved theoretical predictions for core processes at the HL-LHC, such as Higgs and weak gauge boson production. Our analysis demonstrates that exploiting the LHC neutrino beam effectively provides CERN with a "Neutrino-Ion Collider" without requiring modifications in its accelerator infrastructure., Comment: 42 pages, 22 figures. Added detailed studies on fluxes uncertainties

The quantum chemistry community has developed analytic forces for approximate electronic excited states to enable walking on excited state potential energy surfaces (PES). One can thereby computationally characterize excited state minima and saddle points. Always implicit in using this machinery is the fact that an excited state PES only exists within the realm of the Born-Oppenheimer approximation, where the nuclear and electronic degrees of freedom separate. This work demonstrates through ab initio calculations and simple nonadiabatic dynamics that some excited state minimum structures are fantastical: they appear to exist as stable configurations only as a consequence of the PES construct, rather than being physically observable. One such case is the S2 excited state of phosphine and a second case are local minima of a number of states of tris(bipyridine)ruthenium(II). Each fantastical structure exhibits an unphysically high predicted harmonic frequency and associated force constant. This fact can serve as a valuable diagnostic of when an optimized excited state structure is non-observable. Their origin lies in the coupling between different electronic states, and the resulting avoided crossings. The upper state may exhibit a minimum very close to the crossing, where the force constant relates to the strength of the electronic coupling rather than to any characteristic excited state vibration. Nonadiabatic dynamics results using a Landau-Zener model illustrate that fantastical excited state structures have extremely short lifetimes on the order of a few femtoseconds. Their appearance in a calculation signals the presence of a nearby avoided crossing or conical intersection through which the system will rapidly cross to a lower surface., Comment: 7 pages, 4 figures

In this work we present a novel strategy to evaluate multi-variable integrals with quantum circuits. The procedure first encodes the integration variables into a parametric circuit. The obtained circuit is then derived with respect to the integration variables using the parameter shift rule technique. The observable representing the derivative is then used as the predictor of the target integrand function following a quantum machine learning approach. The integral is then estimated using the fundamental theorem of integral calculus by evaluating the original circuit. Embedding data according to a reuploading strategy, multi-dimensional variables can be easily encoded into the circuit's gates and then individually taken as targets while deriving the circuit. These techniques can be exploited to partially integrate a function or to quickly compute parametric integrands within the training hyperspace., Comment: Code available at https://github.com/qiboteam/QiNNtegrate, version that appeared in journal

Wet chemistry C-S-H precipitation experiments were performed under controlled conditions of solution supersaturation in the presence and absence of gluconate and three hexitol molecules. Characterization of the precipitates with SAXS and cryo-TEM experiments confirmed the presence of a multi-step nucleation pathway. Induction times for the formation of the amorphous C-S-H spheroids were determined from light transmittance. Analysis of those data with the classical nucleation theory revealed a significant increase of the kinetic prefactor in the same order as the complexation constants of calcium and silicate with each of the organics. Finally, two distinct precipitation regimes of the C-S-H amorphous precursor were identified: i) a nucleation regime at low saturation indexes (SI) and ii) a spinodal nucleation regime at high SI where the free energy barrier to the phase transition is found to be of the order of the kinetic energy or less., Comment: Accepted in Cement and Concrete Research. 30 pages plus supplementary materials. arXiv admin note: substantial text overlap with arXiv:2111.02743

Let $G$ be a finite group, let $\pi$ be a set of primes and let $p$ be the smallest prime in $\pi$. In this work, we prove that $G$ possesses a normal and abelian Hall $\pi$-subgroup if and only if the probability that two random $\pi$-elements of $G$ commute is larger than $\frac{p^2+p-1}{p^3}$. We also prove that if $x$ is a $\pi$-element not lying in $O_{\pi}(G)$, then the proportion of $\pi$-elements commuting with $x$ is at most $1/p$., Comment: 18 pages, accepted in Mathematische Nachrichten, Theorem B has been improved

A reliable determination of probability density functions from data samples is still a relevant topic in scientific applications. In this work we investigate the possibility of defining an algorithm for density function estimation using adiabatic quantum computing. Starting from a sample of a one-dimensional distribution, we define a classical-to-quantum data embedding procedure which maps the empirical cumulative distribution function of the sample into time dependent Hamiltonian using adiabatic quantum evolution. The obtained Hamiltonian is then projected into a quantum circuit using the time evolution operator. Finally, the probability density function of the sample is obtained using quantum hardware differentiation through the parameter shift rule algorithm. We present successful numerical results for predefined known distributions and high-energy physics Monte Carlo simulation samples., Comment: 7 pages, 3 figures

Continuously comparing theory predictions to experimental data is a common task in analysis of particle physics such as fitting parton distribution functions (PDFs). However, typically, both the computation of scattering amplitudes and the evolution of candidate PDFs from the fitting scale to the process scale are non-trivial, computing intesive tasks. We develop a new stack of software tools that aim to facilitate the theory predictions by computing FastKernel (FK) tables that reduce the theory computation to a linear algebra operation. Specifically, I present PineAPPL, our workhorse for grid operations, EKO, a new DGLAP solver, and yadism, a new DIS library. Alongside, I review several projects that become available with the new tools., Comment: 5 pages, 2 figures; submitted to ACAT 2022 proceedings

We present a collection of tools automating the efficient computation of large sets of theory predictions for high-energy physics. Calculating predictions for different processes often require dedicated programs. These programs, however, accept inputs and produce outputs that are usually very different from each other. The industrialization of theory predictions is achieved by a framework which harmonizes inputs (runcard, parameter settings), standardizes outputs (in the form of grids), produces reusable intermediate objects, and carefully tracks all meta data required to reproduce the computation. Parameter searches and fitting of non-perturbative objects are exemplary use cases that require a full or partial re-computation of theory predictions and will thus benefit of such a toolset. As an example application we present a study of the impact of replacing NNLO QCD K-factors in a PDF fit with the exact NNLO predictions., Comment: Documentation and code at https://nnpdf.github.io/pineline ; updated to published version

Let $p$ be a prime and let $G$ be a finite group such that the smallest prime that divides $|G|$ is $p$. We find sharp bounds, depending on $p$, for the commuting probability and the average character degree to guarantee that $G$ is nilpotent or supersolvable., Comment: 15 pages

We use physics-informed neural networks (PINNs) to compute the first quasi-normal modes of the Kerr geometry via the Teukolsky equation. This technique allows us to extract the complex frequencies and separation constants of the equation without the need for sophisticated numerical techniques, and with an almost immediate implementation under the \texttt{PyTorch} framework. We are able to compute the oscillation frequencies and damping times for arbitrary black hole spins and masses, with accuracy typically below the percentual level as compared to the accepted values in the literature. We find that PINN-computed quasi-normal modes are indistinguishable from those obtained through existing methods at signal-to-noise ratios (SNRs) larger than 100, making the former reliable for gravitational-wave data analysis in the mid term, before the arrival of third-generation detectors like LISA or the Einstein Telescope, where SNRs of ${\cal O}(1000)$ might be achieved., Comment: 12 pages, 7 figures. v2: Matches published version, minor typos corrected

In this proceedings we demonstrate some advantages of a top-bottom approach in the development of hardware-accelerated code. We start with an autogenerated hardware-agnostic Monte Carlo generator, which is parallelized in the event axis. This allow us to take advantage of the parallelizable nature of Monte Carlo integrals even if we don't have control of the hardware in which the computation will run (i.e., an external cluster). The generic nature of such an implementation can introduce spurious bottlenecks or overheads. Fortunately, said bottlenecks are usually restricted to a subset of operations and not to the whole vectorized program. By identifying the more critical parts of the calculation one can get very efficient code and at the same time minimize the amount of hardware-specific code that needs to be written. We show benchmarks demonstrating how simply reducing the memory footprint of the calculation can increase the performance of a $2 \to 4$ process., Comment: Proceedings ICHEP 2022, 6 pages

We respond to the criticism raised by Courtoy et al., in which the faithfulness of the NNPDF4.0 sampling is questioned and an under-estimate of the NNPDF4.0 PDF uncertainties is implied. We list, correct, and clarify in detail a number of inaccurate or misleading claims that are made in this Reference. Specifically, we explain and explicitly demonstrate why the central value of the PDF distribution does not generally coincide with the absolute minimum of the $\chi^{2}$ to the data. We examine some PDFs that have been constructed in the above study and claimed to be "good solutions": we show that similar PDFs are found with the NNPDF methodology, but with very low probability., Comment: 18 pages, 12 figures

Fitting PDFs requires the integration of a broad range of datasets, both from data and theory side, into a unique framework. While for data the integration mainly consists in the standardization of the data format, for the theory predictions there are multiple ingredients involved. Different providers are developed by separate groups for different processes, with a variety of inputs (runcards) and outputs (interpolation grids). Moreover, since processes are measured at different scales, DGLAP evolution has to be provided for the PDF candidate, or precomputed into the grids. We are working towards the automation of all these steps in a unique framework, that will be useful for any PDF fitting groups, and possibly also for phenomenological studies., Comment: 6 pages, 1 figure. Contribution to the Proceedings of the ICHEP 2022 Conference

The theory of the strong force, quantum chromodynamics, describes the proton in terms of quarks and gluons. The proton is a state of two up quarks and one down quark bound by gluons, but quantum theory predicts that in addition there is an infinite number of quark-antiquark pairs. Both light and heavy quarks, whose mass is respectively smaller or bigger than the mass of the proton, are revealed inside the proton in high-energy collisions. However, it is unclear whether heavy quarks also exist as a part of the proton wavefunction, which is determined by non-perturbative dynamics and accordingly unknown: so-called intrinsic heavy quarks. It has been argued for a long time that the proton could have a sizable intrinsic component of the lightest heavy quark, the charm quark. Innumerable efforts to establish intrinsic charm in the proton have remained inconclusive. Here we provide evidence for intrinsic charm by exploiting a high-precision determination of the quark-gluon content of the nucleon based on machine learning and a large experimental dataset. We disentangle the intrinsic charm component from charm-anticharm pairs arising from high-energy radiation. We establish the existence of intrinsic charm at the 3-standard-deviation level, with a momentum distribution in remarkable agreement with model predictions. We confirm these findings by comparing to very recent data on Z-boson production with charm jets from the LHCb experiment., Comment: 10 pages, 4 figures + Supplementary Information, published version available in https://www.nature.com/articles/s41586-022-04998-2. v2: updated comparison with the MBC model in Fig. 1 right (thanks to Tim Hobbs for the suggestion)

Hybridization of multi-junction concentrator photovoltaics with single-junction flat plate solar cells (CPV/PV) can deliver the highest power output per module area of any PV technology. Conversion efficiencies up to 34.2% have been published under the AM1.5g spectrum at standard test conditions for the EyeCon module which combines Fresnel lenses and III-V four-junction solar cells with bifacial c-Si. We investigate here its energy yield and compare it to conventional CPV as well as flat plate PV. The advantage of the hybrid CPV/PV module is that it converts direct sunlight with the most advanced multi-junction cell technology, while accessing diffuse, lens-scattered and back side irradiance with a Si cell that also serves as the heat distributor for the concentrator cells. This article quantifies that hybrid bifacial CPV/PV modules are expected to generate a 25 - 35% higher energy yield with respect to their closest competitor in regions with a diffuse irradiance fraction around 50%. Additionally, the relative cost of electricity generated by hybrid CPV/PV technology was calculated worldwide under certain economic assumptions. Therefore, this article gives clear guidance towards establishing competitive business cases for the technology.

The particle-hole interaction problem is longstanding within time-dependent density functional theory (TDDFT) and leads to extreme errors in the prediction of K-edge X-ray absorption spectra (XAS). We derive a linear-response formalism that uses optimized orbitals of the n-1-electron system as reference, building orbital relaxation and a proper hole into the initial density. Our approach is an exact generalization of the static-exchange approximation that ameliorates particle-hole interaction error associated with the adiabatic approximation and reduces errors in TDDFT XAS by orders of magnitude. With a statistical performance of just 0.5 eV root-mean-square error and the same computational scaling as TDDFT under the core-valence separation approximation, we anticipate that this approach will be of great utility in XAS calculations of large systems., Comment: 11 pages (main text), 12 pages (supporting information), 9 figures

In this work, we classify all finite groups such that for every field extension F of \mathbb{Q}, F is the field of values of at most 3 irreducible characters., Comment: 18 pages

We investigate the use of orbital-optimized references in conjunction with single-reference coupled-cluster theory with single and double substitutions (CCSD) for the study of core excitations and ionizations of 18 small organic molecules, without any use of response theory or equation-of-motion formalisms. Three schemes are employed to successfully address the convergence difficulties associated with the coupled-cluster equations, and the spin contamination resulting from the use of a spin symmetry-broken reference, in the case of excitations. In order to gauge the inherent potential of the methods studied, an effort is made to provide reasonable basis set limit estimates for the transition energies. Overall, we find that the two best-performing schemes studied here for Delta-CCSD are capable of predicting excitation and ionization energies with errors comparable to experimental accuracies. The proposed Delta-CCSD schemes seem to fare better than the widely used equation-of-motion CCSD (EOM-CCSD) with core-valence separation protocol, with statistical errors being reduced by more than a factor of two when compared to FC-CVS-EOM-CCSD.