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We introduce a simple definition of the weight of any given Slater determinant in the coupled-cluster state, namely as the expectation value of the projection operator onto that determinant. The definition can be applied to any coupled-cluster formulation, including conventional coupled-cluster theory, nonorthogonal orbital-optimized coupled-cluster theory, and extended coupled-cluster theory. Numerical experiments show that for single-reference systems the coupled-cluster weights are in excellent agreement with those obtained from the full configuration-interaction wave function. Moreover, the well-known insensitivity of the total energy obtained from truncated coupled-cluster models to the choice of orbital basis is clearly exposed by weights computed in the $\hat{T}_1$-transformed determinant basis. We demonstrate that the inseparability of the conventional linear parameterization of the bra (left state) for systems composed of noninteracting subsystems may lead to ill-behaved (negative or greater than unity) weights, an issue that can only be fully remedied by switching to extended coupled-cluster theory. The latter is corroborated by results obtained with quadratic coupled-cluster theory, which is shown numerically to yield a significant improvement., Comment: 35 pages, 4 figures

In this paper, we study normal forms of analytic saddle-nodes in $\mathbb C^n$ with any Poincar\'e rank $k\in \mathbb N$. The approach and the results generalize those of Bonchaert and De Maesschalck from 2008 that considered $k=1$. In particular, we introduce a Banach convolutional algebra that is tailored to study differential equations in the Borel plane of order $k$. We anticipate that our approach can stimulate new research and be used to study different normal forms in future work.

We study a class of solutions within the context of modified gravity theories, characterized by a non-trivial field that does not generate any back-reaction on the metric. These stealth configurations are effectively defined by the stealth conditions, which correspond to a vanishing stress-energy tensor. In this work, we introduce a novel approach to constructing this class of solutions. In contrast to the standard procedure, the starting point requires satisfying the stealth conditions for a given ansatz independently of the gravitational dynamics. This approach simultaneously determines the non-trivial field and the geometries capable of supporting it as a stealth configuration. Consequently, a gravity model can accommodate a stealth field only if its vacuum solution falls within the geometries permissible under stealth conditions. By applying this reverse procedure in the non-minimal $R\phi^2$ coupling, we recover all previously known stealth configurations and present new solutions. Although it seems intuitive to assume that this ``gravitationally undetectable'' scalar field leaves no physical traces, it remarkably reveals thermodynamic imprints, as its presence screens the black hole mass and modifies the entropy according to the first law.

In this paper, we show that the coefficients $\phi_n$ of the formal series expansions $y=\sum_{n=1}^\infty \phi_n x^n\in x\mathbb C[[x]]$ of center manifolds of planar analytic saddle-nodes grow like $\Gamma(n+a)$ (after rescaling $x$) as $n\rightarrow \infty$. Here the quantity $a$ is the formal analytic invariant associated with the saddle node (following the work of J. Martinet and J.-P. Ramis). This growth property of $\phi_n$, which cannot be improved when the center manifold is nonanalytic, was recently (2024) described for a restricted class of nonlinearities by the present author in collaboration with P. Szmolyan. This joint work was in turn inspired by the work of Merle, Rapha\"{e}l, Rodnianski, and Szeftel (2022), which described the growth of the coefficients for a system related to self-similar solutions of the compressible Euler. In the present paper, we combine the previous approaches with a Borel-Laplace approach. Specifically, we adapt the Banach norm of Bonckaert and De Maesschalck (2008) in order to capture the singularity in the complex plane., Comment: Comments are welcomed

We have discovered a triply eclipsing triple-star system, TIC 290061484, with the shortest known outer period, Pout, of only 24.5 days. This "eclipses" the previous record set by lambda Tauri at 33.02 days, which held for 68 yr. The inner binary, with an orbital period of Pin = 1.8 days, produces primary and secondary eclipses and exhibits prominent eclipse timing variations with the same periodicity as the outer orbit. The tertiary star eclipses, and is eclipsed by, the inner binary with pronounced asymmetric profiles. The inclinations of both orbits evolve on observable timescales such that the third-body eclipses exhibit dramatic depth variations in TESS data. A photodynamical model provides a complete solution for all orbital and physical parameters of the triple system, showing that the three stars have masses of 6.85, 6.11, and 7.90 MSun, radii near those corresponding to the main sequence, and Teff in the range of 21,000-23,700 K. Remarkably, the model shows that the triple is in fact a subsystem of a hierarchical 2+1+1 quadruple with a distant fourth star. The outermost star has a period of ~3200 days and a mass comparable to the stars in the inner triple. In ~20 Myr, all three components of the triple subsystem will merge, undergo a Type II supernova explosion, and leave a single remnant neutron star. At the time of writing, TIC 290061484 is the most compact triple system and one of the tighter known compact triples (i.e., Pout/Pin = 13.7)., Comment: 27 pages, 13 figures, 6 tables

A data-driven model (DDM) suitable for regional weather forecasting applications is presented. The model extends the Artificial Intelligence Forecasting System by introducing a stretched-grid architecture that dedicates higher resolution over a regional area of interest and maintains a lower resolution elsewhere on the globe. The model is based on graph neural networks, which naturally affords arbitrary multi-resolution grid configurations. The model is applied to short-range weather prediction for the Nordics, producing forecasts at 2.5 km spatial and 6 h temporal resolution. The model is pre-trained on 43 years of global ERA5 data at 31 km resolution and is further refined using 3.3 years of 2.5 km resolution operational analyses from the MetCoOp Ensemble Prediction System (MEPS). The performance of the model is evaluated using surface observations from measurement stations across Norway and is compared to short-range weather forecasts from MEPS. The DDM outperforms both the control run and the ensemble mean of MEPS for 2 m temperature. The model also produces competitive precipitation and wind speed forecasts, but is shown to underestimate extreme events.

In modern deep learning, the models are learned by applying gradient updates using an optimizer, which transforms the updates based on various statistics. Optimizers are often hand-designed and tuning their hyperparameters is a big part of the training process. Learned optimizers have shown some initial promise, but are generally unsuccessful as a general optimization mechanism applicable to every problem. In this work we explore a different direction: instead of learning general optimizers, we instead specialize them to a specific training environment. We propose a novel optimizer technique that learns a layer-specific linear combination of update directions provided by a set of base optimizers, effectively adapting its strategy to the specific model and dataset. When evaluated on image classification tasks, this specialized optimizer significantly outperforms both traditional off-the-shelf methods such as Adam, as well as existing general learned optimizers. Moreover, it demonstrates robust generalization with respect to model initialization, evaluating on unseen datasets, and training durations beyond its meta-training horizon.

The formalism of real-time (RT) methods has been well-established during recent years, while no inclusion beyond the double excitation has been discussed. In this article, we introduce an implementation of real-time coupled cluster singles, doubles and approximate triples (CC3) method to explore the potential of a high excitation level. The CC3 method is well-known for its advantages in calculating dynamic properties and combining with the response theory. It is a well-qualified candidate for handling the interaction between the system and the applied field, and therefore suitable for a RT implementation. The derivation and implementation are first demonstrated following applications on calculating frequency-dependent properties. Terms with triples are calculated and added upon the existing CCSD equations, giving the method a formally $N^{7}$ scaling. The Graphics Processing Unit (GPU) accelerated implementation is utilized to reduce the computational cost. It is been verified that the GPU implementation can speed up the calculation by up to a factor of 17 for water cluster test cases. Additionally, the single-precision arithmetic is used and compared to the conventional double-precision arithmetic. No significant difference is found in the polarizabilities and $G'$ tensor results, but a higher percentage error for the first hyperpolarizabilities is observed. Compared to the linear response (LR) CC3 results, the percentage errors of RT-CC3 polarizabilities and RT-CC3 first hyperpolarizabilities are under 0.1% and 1%, respectively for the $H_2O$/cc-pVDZ test case. Furthermore, a discussion on the calculation of polarizabilities is included, which compares RT-CC3 with RT-CCSD and time-dependent nonorthogonal orbital-optimized coupled cluster doubles (TDNOCCD), in order to examine the performance of RT-CC3 and the orbital-optimization effect using a group of ten-electron systems., Comment: 56 pages, 5 figures, 10 tables

A novel method to reconstruct the energy of hadronic showers in the CMS High Granularity Calorimeter (HGCAL) is presented. The HGCAL is a sampling calorimeter with very fine transverse and longitudinal granularity. The active media are silicon sensors and scintillator tiles readout by SiPMs and the absorbers are a combination of lead and Cu/CuW in the electromagnetic section, and steel in the hadronic section. The shower reconstruction method is based on graph neural networks and it makes use of a dynamic reduction network architecture. It is shown that the algorithm is able to capture and mitigate the main effects that normally hinder the reconstruction of hadronic showers using classical reconstruction methods, by compensating for fluctuations in the multiplicity, energy, and spatial distributions of the shower's constituents. The performance of the algorithm is evaluated using test beam data collected in 2018 prototype of the CMS HGCAL accompanied by a section of the CALICE AHCAL prototype. The capability of the method to mitigate the impact of energy leakage from the calorimeter is also demonstrated., Comment: Prepared for submission to JINST

In this work, we use optimal control to change the behavior of a deep reinforcement learning policy by optimizing directly in the policy's latent space. We hypothesize that distinct behavioral patterns, termed behavioral modes, can be identified within certain regions of a deep reinforcement learning policy's latent space, meaning that specific actions or strategies are preferred within these regions. We identify these behavioral modes using latent space dimension-reduction with \ac*{pacmap}. Using the actions generated by the optimal control procedure, we move the system from one behavioral mode to another. We subsequently utilize these actions as a filter for interpreting the neural network policy. The results show that this approach can impose desired behavioral modes in the policy, demonstrated by showing how a failed episode can be made successful and vice versa using the lunar lander reinforcement learning environment., Comment: Published in the proceedings of the 32nd Mediterranean Conference on Control and Automation [MED2024]

NASA's Transiting Exoplanet Survey Satellite (TESS) has identified over 7,000 candidate exoplanets via the transit method, with gas giants among the most readily detected due to their large radii. Even so, long intervals between TESS observations for much of the sky lead to candidates for which only a single transit is detected in one TESS sector, leaving those candidate exoplanets with unconstrained orbital periods. Here, we confirm the planetary nature of TIC 393818343 b, originally identified via a single TESS transit, using radial velocity data and ground-based photometric observations from citizen scientists with the Unistellar Network and Exoplanet Watch. We determine a period of $P$ = 16.24921 $\substack{+0.00010 \\ -0.00011}$ days, a mass $M_{P}$ = 4.34 $\pm$ 0.15 $M_{J}$, and semi-major axis $a$ = 0.1291 $\substack{+0.0021 \\ -0.0022}$ au, placing TIC 393818343 b in the "warm Jupiter" population of exoplanets. With an eccentricity $e$ = 0.6058 $\pm$ 0.0023, TIC 393818343 b is the most eccentric warm Jupiter to be discovered by TESS orbiting less than 0.15 au from its host star and therefore an excellent candidate for follow-up, as it may inform our future understanding of how hot and warm Jupiter populations are linked., Comment: 13 pages, 4 figures, 3 tables. Accepted for publication in AJ

We prove the existence of a family of travelling wave solutions in a variant of the $\textit{Zeldovich-Frank-Kamenetskii (ZFK) equation}$, a reaction-diffusion equation which models the propagation of planar laminar premixed flames in combustion theory. Our results are valid in an asymptotic regime which corresponds to a reaction with high activation energy, and provide a rigorous and geometrically informative counterpart to formal asymptotic results that have been obtained for similar problems using $\textit{high activation energy asymptotics}$. We also go beyond the existing results by (i) proving smoothness of the minimum wave speed function $\overline c(\epsilon)$, where $0< \epsilon \ll 1$ is the small parameter, and (ii) providing an asymptotic series for a flat slow manifold which plays a role in the construction of travelling wave solutions for non-minimal wave speeds $c > \overline c(\epsilon)$. The analysis is complicated by the presence of an exponential nonlinearity which leads to two different scaling regimes as $\epsilon \to 0$, which we refer to herein as the $\textit{convective-diffusive}$ and $\textit{diffusive-reactive}$ zones. The main idea of the proof is to use the geometric blow-up method to identify and characterise a $(c,\epsilon)$-family of heteroclinic orbits which traverse both of these regimes, and correspond to travelling waves in the original ZFK equation. More generally, our analysis contributes to a growing number of studies which demonstrate the utility of geometric blow-up approaches to the study dynamical systems with singular exponential nonlinearities., Comment: Accepted version, to appear in SIADS

Recent advances in attosecond science have made it increasingly important to develop stable, reliable and accurate algorithms and methods to model the time evolution of atoms and molecules in intense laser fields. A key process in attosecond science is high-harmonic generation, which is challenging to model with fixed Gaussian basis sets, as it produces high-energy electrons, with a resulting rapidly varying and highly oscillatory wave function that extends over dozens of {\aa}ngstr\"om. Recently, Rothe's method, where time evolution is rephrased as an optimization problem, has been applied to the one-dimensional Schr\"odinger equation. Here, we apply Rothe's method to the hydrogen wave function and demonstrate that complex-valued Gaussian wave packets with time-dependent width, center, and momentum parameters are able to reproduce spectra obtained from essentially exact grid calculations for high-harmonic generation with only 50-181 Gaussians for field strengths up to $5\times 10^{14}$W/cm$^2$. This paves the way for the inclusion of continuum contributions into real-time, time-dependent electronic-structure theory with Gaussian basis sets for strong fields, and eventually accurate simulations of the time evolution of molecules without the Born-Oppenheimer approximation., Comment: 20 pages, 10 figures

The purpose of this document is to describe the solution and implementation of the time-independent and time-dependent Schr\"odinger using pseudospectral methods. Currently, the description is for single particle systems interacting with a classical electromagnetic field in spherical coordinates.

We have identified nearly a hundred close triply eclipsing hierarchical triple star systems from data taken with the space telescope TESS. These systems are noteworthy in that we can potentially determine their dynamical and astrophysical parameters with a high precision. In the present paper, we report the comprehensive study of seven new compact triply eclipsing triple star systems taken from this larger sample: TICs 133771812, 176713425, 185615681, 287756035, 321978218, 323486857, and 650024463. Most of the data for this study come from TESS observations, but two of them have Gaia measurements of their outer orbits, and we obtained supplemental radial velocity (RV) measurements for three of the systems. The eclipse timing variation curves extracted from the TESS data, the photometric light curves, the RV points, and the spectral energy distribution (SED) are combined in a complex photodynamical analysis to yield the stellar and orbital parameters of all seven systems. Four of the systems are quite compact with outer periods in the range of 41-56 days. All of the systems are substantially flat, with mutual inclination angles of < ~2 degrees. Including the systems reported in this work, we have now studied in considerable detail some 30 triply eclipsing triples with TESS, and are accumulating a meaningful census of these systems., Comment: 33 pages, 23 figures, and 19 tables; accepted for publication in Astronomy & Astrophysics

Any attracting, hyperbolic and proper node of a two-dimensional analytic vector-field has a unique strong-stable manifold. This manifold is analytic. The corresponding weak-stable manifolds are, on the other hand, not unique, but in the nonresonant case there is a unique weak-stable manifold that is analytic. As the system approaches a saddle-node (under parameter variation), a sequence of resonances (of increasing order) occur. In this paper, we give a detailed description of the analytic weak-stable manifolds during this process. In particular, we relate a ``flapping-mechanism'', corresponding to a dramatic change of the position of the analytic weak-stable manifold as the parameter passes through the infinitely many resonances, to the lack of analyticity of the center manifold at the saddle-node. Our work is motivated and inspired by the work of Merle, Rapha\"{e}l, Rodnianski, and Szeftel, where this flapping mechanism is the crucial ingredient in the construction of $C^\infty$-smooth self-similar solutions of the compressible Euler equations., Comment: Typos have been corrected, the introduction has been rewritten and certain statements (including Theorem 3.1, see also App B) have been improved

We introduce a first-order theory $\mathsf{Seq}$ which is mutually interpretable with Robinson's $\mathsf{Q}$. The universe of a standard model for $\mathsf{Seq}$ consists of sequences. We prove that $\mathsf{Seq}$ directly interprets the adjuctive set theory $\mathsf{AST}$, and we prove that $\mathsf{Seq}$ interprets the tree theory $\mathsf{T}$ and the set theory $\mathsf{AST + EXT}$., Comment: 24 pages

This work introduces a novel family of boundary conditions for AdS$_3$ General Relativity, constructed through a polynomial expansion in negative integer powers of the Brown-Henneaux central charge. The associated dynamics is governed by the Dym hierarchy of integrable equations. It is shown that the infinite set of Dym conserved charges generates an abelian asymptotic symmetry group. Additionally, these boundary conditions encompass black hole solutions, whose thermodynamic properties are examined., Comment: 41 pages, 1 figure, matches published version

A reliable and cost-effective interconnect technology is required for the development of hybrid pixel detectors. The interconnect technology needs to be adapted for the pitch and die sizes of the respective applications. For small-scale applications and during the ASIC and sensor development phase, interconnect technologies must also be suitable for the assembly of single-dies typically available from Multi-Project-Wafer submissions. Within the CERN EP R&D program and the AIDAinnova collaboration, innovative and scalable hybridization concepts are under development for pixel-detector applications in future colliders. This contribution presents recent results of a newly developed in-house single-die interconnection process based on Anisotropic Conductive Adhesives (ACA). The ACA interconnect technology replaces solder bumps with conductive micro-particles embedded in an epoxy layer applied as either film or paste. The electro-mechanical connection between the sensor and ASIC is achieved via thermocompression of the ACA using a flip-chip device bonder. A specific pixel-pad topology is required to enable the connection via micro-particles and create cavities into which excess epoxy can flow. This pixel-pad topology is achieved with an in-house Electroless Nickel Immersion Gold process that is also under development within the project. The ENIG and ACA processes are qualified with a variety of different ASICs, sensors, and dedicated test structures, with pad diameters ranging from 12 {\mu}m to 140 {\mu}m and pitches between 20 {\mu}m and 1.3 mm. The produced assemblies are characterized electrically, with radioactive-source exposures, and in tests with high-momentum particle beams. A focus is placed on recent optimization of the plating and interconnect processes, resulting in an improved plating uniformity and interconnect yield., Comment: Procceding to IPRD23 conference in Siena 2023

In this paper, we revisit the damped Kepler problem within a general family of nonlinear damping forces with magnitude $\delta \vert u\vert^{\beta}\vert \dot u\vert^{\alpha+1}$, depending on three parameters $\delta>0,\alpha\ge 0$ and $\beta\ge 0$, and address the general question of circularization whereby orbits tend to become more circular as they approach the sun. Our approach is based on dynamical systems theory, using blowup and desingularization as our main technical tools. We find that $\gamma=\alpha+2\beta-3$ is an important quantity, with the special case $\gamma=0$ separating circularization ($-3<\gamma<0$) where the eccentricity converges to zero, i.e. $e(t)\rightarrow 0$ as $u(t)\rightarrow 0$, from cases ($\gamma>0$) where $e(t)\rightarrow 1$ as $u(t)\rightarrow 0$, both on open sets of initial conditions. We find that circularization for $-3<\gamma<0$ occurs due to asymptotic stability of a zero-Hopf equilibrium point (i.e., the eigenvalues are $\pm i \omega,0$) of a three-dimensional reduced problem (which is analytic in the blowup coordinates). The attraction is therefore not hyperbolic and in particular not covered by standard dynamical systems theory. Instead we use recent results on normal forms of the zero-Hopf to locally bring the system into a form where the stability can be addressed directly. We believe that our approach can be used to describe unbounded solutions.

We report the discovery of two TESS sub-Neptunes orbiting the early M dwarf TOI-904 (TIC 261257684). Both exoplanets, TOI-904 b and c, were initially observed in TESS sector 12 with twin sizes of 2.49R$_\oplus$ and 2.31R$_\oplus$, respectively. Through observations in five additional sectors in the TESS primary mission and the first and second extended missions, the orbital periods of both planets were measured to be 10.887$\pm$0.001 and 83.999$\pm$0.001 days, respectively. Reconnaissance radial velocity measurements (taken with EULER/CORALIE) and high resolution speckle imaging with adaptive optics (obtained from SOAR/HRCAM and Gemini South/ZORRO) show no evidence of an eclipsing binary or a nearby companion, which together with the low false positive probabilities calculated with the statistical validation software TRICERATOPS establish the planetary nature of these candidates. The outer planet, TOI-904 c, is the longest-period M dwarf exoplanet found by TESS, with an estimated equilibrium temperature of 217K. As the three other validated planets with comparable host stars and orbital periods were observed by Kepler around much dimmer stars (J$_{mag}$ $>$ 12), TOI-904 c, orbiting a brighter star (J$_{mag}$ $=$ 9.6), is the coldest M dwarf planet easily accessible for atmospheric follow-up. Future mass measurements and transmission spectroscopy of the similar sized planets in this system could determine whether they are also similar in density and composition, suggesting a common formation pathway, or whether they have distinct origins., Comment: 18 pages, 6 figures, Accepted by the Astrophysical Journal Letters

The goal of this paper is to study the number of sliding limit cycles of a regularized piecewise linear $VI_3$ two-fold using the notion of slow divergence integral. We focus on limit cycles produced by canard cycles located in the half-plane with an invisible fold point. We prove that the integral has at most $1$ zero counting multiplicity (when it is not identically zero). This will imply that the canard cycles can produce at most $2$ limit cycles. Moreover, we detect regions in the parameter space with $2$ limit cycles.

In this paper we define the notion of slow divergence integral along sliding segments in regularized planar piecewise smooth systems. The boundary of such segments may contain diverse tangency points. We show that the slow divergence integral is invariant under smooth equivalences. This is a natural generalization of the notion of slow divergence integral along normally hyperbolic portions of curve of singularities in smooth planar slow-fast systems. We give an interesting application of the integral in a model with visible-invisible two-fold of type $VI_3$. It is related to a connection between so-called Minkowski dimension of bounded and monotone "entry-exit" sequences and the number of sliding limit cycles produced by so-called canard cycles.

The generation and evolution of entanglement in quantum many-body systems is an active area of research that spans multiple fields, from quantum information science to the simulation of quantum many-body systems encountered in condensed matter, subatomic physics, and quantum chemistry. Motivated by recent experiments exploring quantum information processing systems with electrons trapped above the surface of cryogenic noble gas substrates, we theoretically investigate the generation of \emph{motional} entanglement between two electrons via their unscreened Coulomb interaction. The model system consists of two electrons confined in separate electrostatic traps which establish microwave frequency quantized states of their motion. We compute the motional energy spectra of the electrons, as well as their entanglement, by diagonalizing the model Hamiltonian with respect to a single-particle Hartree product basis. This computational procedure can in turn be employed for device design and guidance of experimental implementations. In particular, the theoretical tools developed here can be used for fine tuning and optimization of control parameters in future experiments with electrons trapped above the surface of superfluid helium or solid neon., Comment: Revised figures and discussions

Ensuring quality human-AI interaction (HAII) in safety-critical industries is essential. Failure to do so can lead to catastrophic and deadly consequences. Despite this urgency, existing research on HAII is limited, fragmented, and inconsistent. We present here a survey of that literature and recommendations for research best practices that should improve the field. We divided our investigation into the following areas: 1) terms used to describe HAII, 2) primary roles of AI-enabled systems, 3) factors that influence HAII, and 4) how HAII is measured. Additionally, we described the capabilities and maturity of the AI-enabled systems used in safety-critical industries discussed in these articles. We found that no single term is used across the literature to describe HAII and some terms have multiple meanings. According to our literature, seven factors influence HAII: user characteristics (e.g., user personality), user perceptions and attitudes (e.g., user biases), user expectations and experience (e.g., mismatched user expectations and experience), AI interface and features (e.g., interactive design), AI output (e.g., perceived accuracy), explainability and interpretability (e.g., level of detail, user understanding), and usage of AI (e.g., heterogeneity of environments). HAII is most measured with user-related subjective metrics (e.g., user perceptions, trust, and attitudes), and AI-assisted decision-making is the most common primary role of AI-enabled systems. Based on this review, we conclude that there are substantial research gaps in HAII. Researchers and developers need to codify HAII terminology, involve users throughout the AI lifecycle (especially during development), and tailor HAII in safety-critical industries to the users and environments., Comment: Accepted for publication in IEEE Access