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The 2D toric code is a prototypical example that exhibits non-trivial topological properties and a ground state possessing a non-trivial topological order. Until now, all the cases studied in the literature have been in the stable equilibrium regime, leaving the relaxation towards this state unexplored. In the present work, the dynamics of the toric code towards stable equilibrium is explored within the steepest-entropy-ascent quantum thermodynamic (SEAQT) framework. Under these dynamics, information correlations such as the relative entropy, logarithmic negativity, magnetization, coherent information, and geometric entropy are described out of equilibrium, permitting a connection to be made between the out-of-equilibrium dynamics and these information measures., Comment: 31 pages, 15 figures

We utilize the now substantial amount of astrophysical observations of neutron stars (NSs), along with perturbative Quantum Chromodynamics (pQCD) calculations at high density, to directly constrain the NS Equation of State (EoS). To this end, we construct non-parametric EoS priors by using Gaussian processes trained on 75 EoSs, which includes models with either hadrons, hyperons or quarks at high densities. We create a prior using the full EoS sample (model-agnostic), and one prior for each EoS family to test model discrimination. These are then utilized in a Bayesian updating scheme by first performing a complete analysis of the binary NS merger event GW170817 with minimal assumptions, and sequentially adding information from X-ray and radio NS observations, along with pQCD calculations. Besides providing standard constraints, such as the pressure at twice nuclear saturation density $p(2\rho_\text{sat})=4.3^{+0.6}_{-0.6}\,\times 10^{34}\text{dyne/cm}^{2}$, at $95\%$ confidence level, for the model agnostic prior, our methodology also allows the constraining of EoS properties such as phase transitions and differentiation among quark, hyperonic or hadronic models., Comment: 22 pages, 11 figures, 4 tables, 5 appendices

The self-dual double copy is further explored. In previous work, it has been shown that Hyper-Hermitian manifolds also have associated the self-dual gauge theories via Kerr-Schild double copy. The self-dual double copy is generalized in the structure of the kinematic algebra by changing the area-preserving diffeomorphisms algebra by the diffeomorphisms on a surface algebra. This gave rise to the hyper-Hermitian double copy in the Kerr-Schild approach. In the present article, we further study the hyper-Hermitian case using the Weyl double copy formalism. In particular, we have found solutions within this formalism for different hyper-Hermitian metrics. One of the main features is that there will be two Maxwell spinors and one of them is source-free and the other has a source current. This is compatible with the fact that in general the hyper-Hermitian spaces are not Ricci-flat., Comment: 28 pages, 7 figures

Scanning tunneling microscope data from a dinuclear Co(II) complex adsorbed on Au(111) are analysed using density functional theory calculations. We find that the interaction with the substrate substantially changes the geometry of the non-planar molecule. Its electronic states, however, remain fairly similar to those calculated for a gas-phase molecule. The calculations reproduce intriguing contrasts observed in experimental maps of the differential conductance dI/dV and reveal the relative importance of geometric and electronic factors that impinge on the image contrasts. For a meaningful comparison, it is important that the calculations closely mimic the experimental mode of measurement., Comment: 9 pages, 7 figures

This paper formulates the completion time $\tau$ of a project network as $ \tau =\|\mathbf{R} \mathbf{t} \|_\infty $ where the rows of $\mathbf{R}$ are simple paths of the network and $\mathbf{t}$ is a column vector representing the duration of the activities. Considering this product as a linear transformation leads to interesting findings on the topological relevance of both paths and activities using singular value decomposition. The notion of spectral networks is introduced to condense the fundamental structure of the project network. A definition of project stress is introduced to establish a comparison index between two alternatives in terms of slack. Additionally, the Moore-Penrose inverse of $\mathbf{R}$ is presented to find the configuration of the durations of the activities resulting in a given simple path duration vector. Then, the systematic mapping review process carried out to assess our claims' novelty is reported. Finally, we reflect on the notion of relevance for paths and activities and the relationship of the incidence matrix with the proposed approach., Comment: 20 pages, 2 figures

The steepest-entropy-ascent quantum thermodynamics (SEAQT) framework is employed to describe the adsorption process of arsenic (V) onto graphene oxide both in and out of equilibrium. The steepest-entropy-ascent principle is used to derive a non-equilibrium equation of motion applicable to a system composed of five species: water, arsenic, two functional groups of graphene oxide, and hydrogen ions. The equation of motion is solved using the system's energy eigenstructure. This eigenstructure is constructed with the Replica-Exchange Wang-Landau algorithm and used to train an artificial neural network that predicts the energy eigenstructure for dilute arsenic concentrations in the range of groundwater contamination. For a specified initial pH and specified initial concentrations of Ar and graphene oxide, the framework predicts arsenic adsorption capacity and the stable equilibrium arsenic concentration. Equilibrium results match well with equilibrium experimental data, demonstrating the efficacy of this framework for describing the adsorption process. Finally, the model is used to predict non-equilibrium adsorption behavior and the influence of solution pH upon arsenic removal efficiency., Comment: 17 pages, 13 figures

This work outlines the foundations for being able to do a first-principle study of the adsorption process using the steepest-entropy-ascent quantum thermodynamic (SEAQT) framework, a framework able to predict the unique non-equilibrium path taken by a system from some initial state to stable equilibrium. To account for the process of multi-component adsorption, the SEAQT framework incorporates the particle number operator for each absorbed species directly into its equation of motion. The theoretical models developed are validated via some initial comparisons with experimental data found in the literature, demonstrating good agreement. The findings reveal that this framework can be an effective tool for describing the adsorption process out of equilibrium. It is able to do so without $a \; priori$ knowledge of the specific adsorption mechanism(s) involved. It also aligns well with the anticipated predictions of equilibrium models. In addition, within this framework, all intensive thermodynamic properties are characterized by out-of-equilibrium fluctuations, highlighting the significance of non-equilibrium thermodynamics in predicting measurable physical quantities., Comment: 13 pages, 3 figures

The United Nations 2030 Agenda for Sustainable Development outlines 17 goals to address global challenges. However, progress has been slower than expected and, consequently, there is a need to investigate the reasons behind this fact. In this study, we used a novel data-driven methodology to analyze data from 107 countries (2000$-$2022) using unsupervised machine learning techniques. Our analysis reveals strong positive and negative correlations between certain SDGs. The findings show that progress toward the SDGs is heavily influenced by geographical, cultural and socioeconomic factors, with no country on track to achieve all goals by 2030. This highlights the need for a region specific, systemic approach to sustainable development that acknowledges the complex interdependencies of the goals and the diverse capacities of nations. Our approach provides a robust framework for developing efficient and data-informed strategies, to promote cooperative and targeted initiatives for sustainable progress.

Exploring the limits of the microscopic reversibility principle, we investigated the interplay between thermal and electron tunneling excitations for the unidirectional rotation of a molecule-rotor on the Au(111) surface. We identified a range of moderate voltages and temperatures where heating the surface enhances the unidirectional rotational rate of a chemisorbed DMNI-P rotor. At higher voltage, inelastic tunneling effects dominate while at higher temperature the process becomes stochastic. At each electron transfer event during tunneling, the quantum mixing of ground and excited electronic states brings part of the surface thermal energy in the excited electronic states of the molecule-rotor. Thermal energy contributes therefore to the semi-classical unidirectional rotation without contradicting the microscopic reversibility principle.

The influence of hydrogen on magnetization is of significant interest to spintronics. Understanding and controlling this phenomenon at the atomic scale, particularly in nanoscale systems, is crucial. In this study, we utilized scanning tunneling microscopy (STM) combined with a nickelocene molecule to sense the spin of a hydrogen-loaded nanoscale Co island grown on Cu(111). Magnetic exchange maps obtained from the molecular tip revealed the presence of a hydrogen superstructure and a 90$^{\circ}$ rotation of the magnetization compared to the pristine island. \textit{Ab initio} calculations corroborate these observations, indicating that hydrogen hybridization with Co atoms on the island surface drives the spin reorientation of the island. This reorientation is further reinforced by hydrogen penetration into the island that locates at the Co/Cu interface. However, the subsurface sensitivity of the magnetic exchange maps indicate that this effect is limited. Our study provides valuable microscopic insights into the chemical control of magnetism at the nanoscale.

The interplay between the $^{22}$Ne$(\alpha,\gamma)^{26}$Mg and the competing $^{22}$Ne$(\alpha,n)^{25}$Mg reactions determines the efficiency of the latter as a neutron source at the temperatures of stellar helium burning. In both cases, the rates are dominated by the $\alpha$-cluster resonance at 830 keV. This resonance plays a particularly important role in determining the strength of the neutron flux for both the weak and main $s$-process as well as the $n$-process. Recent experimental studies based on transfer reactions suggest that the neutron and $\gamma$-ray strengths for this resonance are approximately equal. In this study, the $^{22}$Ne$(\alpha,n)^{25}$Mg resonance strength has been remeasured and found to be similar to the previous direct studies. This reinforces an 830 keV resonance strength that is approximately a factor of three larger for the $^{22}$Ne$(\alpha,n)^{25}$Mg reaction than for the $^{22}$Ne$(\alpha,\gamma)^{26}$Mg reaction.

We developed SaludConectaMX as a comprehensive system to track and understand the determinants of complications throughout chemotherapy treatment for children with cancer in Mexico. SaludConectaMX is unique in that it integrates patient clinical indicators with social determinants and caregiver mental health, forming a social-clinical perspective of the patient's evolving health trajectory. The system is composed of a web application (for hospital staff) and a mobile application (for family caregivers), providing the opportunity for cooperative patient monitoring in both hospital and home settings. This paper presents the system's preliminary design and usability evaluation results from a 1.5-year pilot study. Our findings indicate that while the hospital web app demonstrates high completion rates and user satisfaction, the family mobile app requires additional improvements for optimal accessibility; statistical and qualitative data analysis illuminate pathways for system improvement. Based on this evidence, we formalize suggestions for health system development in LMICs, which HCI researchers may leverage in future work.

The BCJ duality between color and kinematics brings two advantages to calculating multi-loop scattering amplitudes. First the number of ordered cuts that need to be performed to fix the integrand to a gauge theory is minimal -- reducing the factorially-growing number of diagrams to a single-digit basis in all known cases. Second is the trivial generation of related gravitational amplitudes from gauge theory amplitudes via double-copy. Mounting evidence suggests there are some cases where no local color-dual representations exist, even when the semi-classical theory is color-dual. Can we still simplify the calculations without making the duality manifest at the level of the integrand? Here we take a non-trivial step in this direction by showing that the satisfaction of tree-level BCJ relations is sufficient to dramatically reduce the number of explicit cuts that must be performed, even when the loop-level relations are not explicitly satisfied. We introduce an agglomerative algorithm, color-dual cut tiling, that identifies and builds the entire integrand from the simplest on-shell conditions applied to a seed of off-shell integrand information. Specifically, we demonstrate that for two-to-two scattering at three loops in the maximally supersymmetric gauge theory there is sufficient information contained in planar cuts -- completely determined by positivity constraints -- to generate all of the non-planar sector. Additionally, we make use of the generalized double copy to generate a representation of maximally supersymmetric gravity as a functional of the planar SYM input. We discuss how the process might generalize, and then close by commenting on the applicability of this method for additional cases of interest where performing explicit unitarity cuts is expensive., Comment: 8 pages, 5 figures

Python, one of the most prevalent programming languages today, is widely utilized in various domains, including web development, data science, machine learning, and DevOps. Recent scholarly efforts have proposed a methodology to assess Python competence levels, similar to how proficiency in natural languages is evaluated. This method involves assigning levels of competence to Python constructs, for instance, placing simple 'print' statements at the most basic level and abstract base classes at the most advanced. The aim is to gauge the level of proficiency a developer must have to understand a piece of source code. This is particularly crucial for software maintenance and evolution tasks, such as debugging or adding new features. For example, in a code review process, this method could determine the competence level required for reviewers. However, categorizing Python constructs by proficiency levels poses significant challenges. Prior attempts, which relied heavily on expert opinions and developer surveys, have led to considerable discrepancies. In response, this paper presents a new approach to identifying Python competency levels through the systematic analysis of introductory Python programming textbooks. By comparing the sequence in which Python constructs are introduced in these textbooks with the current state of the art, we have uncovered notable discrepancies in the order of introduction of Python constructs. Our study underscores a misalignment in the sequences, demonstrating that pinpointing proficiency levels is not trivial. Insights from the study serve as pivotal steps toward reinforcing the idea that textbooks serve as a valuable source for evaluating developers' proficiency, and particularly in terms of their ability to undertake maintenance and evolution tasks., Comment: 12 pages, 7 figures, 6 tables, ICSME2024

The United States Food and Drug Administration's (FDA's) Premarket Notification 510(K) pathway allows manufacturers to gain approval for a medical device by demonstrating its substantial equivalence to another legally marketed device. However, the inherent ambiguity of this regulatory procedure has led to high recall rates for many devices cleared through this pathway. This trend has raised significant concerns regarding the efficacy of the FDA's current approach, prompting a reassessment of the 510(K) regulatory framework. In this paper, we develop a combined human-algorithm approach to assist the FDA in improving its 510(k) medical device clearance process by reducing the risk of potential recalls and the workload imposed on the FDA. We first develop machine learning methods to estimate the risk of recall of 510(k) medical devices based on the information available at the time of submission. We then propose a data-driven clearance policy that recommends acceptance, rejection, or deferral to FDA's committees for in-depth evaluation. We conduct an empirical study using a unique large-scale dataset of over 31,000 medical devices and 12,000 national and international manufacturers from over 65 countries that we assembled based on data sources from the FDA and Centers for Medicare and Medicaid Service (CMS). A conservative evaluation of our proposed policy based on this data shows a 38.9% improvement in the recall rate and a 43.0% reduction in the FDA's workload. Our analyses also indicate that implementing our policy could result in significant annual cost-savings ranging between \$2.4 billion and \$2.7 billion, which highlights the value of using a holistic and data-driven approach to improve the FDA's current 510(K) medical device evaluation pathway.

We present a study of a general spin Hamiltonian with terms up to fourth order. With the coherent states the semiclassical potential is obtained and with catastrophe theory its parameter space is constructed. When the fourth order parameters are large enough the parameter space has regions where the semiclassical potential has three wells. By applying an oscillating magnetic field a trajectory in parameter space crosses the Maxwell set multiple times resulting in many ground state quantum phase transitions. Using the coherent states we are able to visualize the localization of the ground state on the Bloch sphere as the magnetic field is varied., Comment: 18 pages, 6 figures

The diffusionless martensitic phase transition from a hexagonal close-packed (hcp) arrangement to the face-centered close-packed (fcc) and subsequently the body-centered cubic (bcc) lattice is discussed for a Lennard-Jones solid. The associated lattice vectors to construct the underlying bi-lattice for a Burgers-Bain-type of transformation require a minimum of four parameters $(a,\alpha,\beta,\gamma=c/a)$ describing, beside the change in the base lattice parameters $a$ and $c$, the shear force acting on the hexagonal base plane through the parameter $\alpha$, and the sliding force of the middle layer in the original AB hexagonal packing arrangement through the parameter $\beta$. By optimizing the lattice parameters $a$ and $\beta$ for a $(n,m)$-Lennard-Jones potential, we obtain a simple two-dimensional picture for the complete Burgers-Bain-type hcp$\leftrightarrow$fcc$\leftrightarrow$bcc phase transition. From the generalized lattice vectors we were able to construct the corresponding lattice sums in terms of inverse power potentials applying fast converging Bessel function expansions using a Terras decomposition of the Epstein zeta function combined with a Van der Hoff-Benson expansion for the lattice sums. This allows the cohesive energy to be determined to computer precision for a Lennard-Jones solid. For six different combinations of $(n,m)$-Lennard-Jones potentials the energy $(\alpha,\gamma)$ hypersurface was then mapped out and studied in more detail. We show that for a Lennard-Jones model the minimum energy path is found to be a two-step hcp$\rightarrow$fcc$\rightarrow$bcc transition process. The lowest transition state in each case can be regarded as an upper limit to a hypothetical true minimum energy path out of the many possibilities in a hcp$\leftrightarrow$fcc$\leftrightarrow$bcc phase transition.

The What Works Clearinghouse (WWC) released a report that applies two methodological approaches new to the WWC that together aim to improve researchers' understanding of how early literacy interventions may work to improve outcomes for students in grades K-3. First, this report pilots a new taxonomy developed by early literacy experts and intervention developers as part of a larger effort to develop standard nomenclature for the components of literacy interventions. Then, the WWC uses Bayesian meta-analysis--a statistical method to systematically summarize evidence across multiple studies--to estimate the associations between intervention components and intervention impacts. Twenty-nine studies of 25 early literacy interventions that were previously reviewed by the WWC and met the WWC's rigorous research standards were included in the analysis. This method found that the components examined in this synthesis appear to have a limited role in explaining variation in intervention impacts on alphabetics outcomes, including phonics, phonemic awareness, phonological awareness, and letter identification. This method also identified positive associations between intervention impacts on alphabetics outcomes and components related to using student assessment data to drive decisions, including about how to group students for instruction, and components related to non-academic student supports, including efforts to teach social-emotional learning strategies and outreach to parents and families. This report is exploratory because this synthesis cannot conclude that specific components caused improved alphabetics outcomes. [For the appendices to this report, see ED630496.]

Surface-adsorbed rare-earth nanostructures are ideal platforms to investigate the interplay between intra-atomic interactions and multi-orbital spin configurations. However, addressing these properties has posed severe experimental and theoretical challenges. Here, we use the orbital selectivity offered by X-ray absorption spectroscopy to quantify the Coulomb integrals of Nd atoms on conductive surfaces, as well as the variation of individual orbital occupation upon cluster nucleation. Using X-ray magnetic circular dichroism we identify magnetic moments of the order of \MK{few tens of}~$\mu_{\rm{B}}$ at the $5d$ orbitals and their magnetic coupling with the $4f$ spins. Our results validate orbital-resolved X-ray spectroscopy as a reliable method for quantifying complex multi-orbital interactions in surface-adsorbed lanthanides.

This article, written in Spanish, provides a comprehensive review of the Fargues-Fontaine curve, a cornerstone in $p$-adic Hodge theory, and its pivotal role in classifying $p$-adic Galois representations. We synthesize key developments surrounding this curve, emphasizing its connection between advanced concepts in arithmetic geometry and the practical theory of representations. We offer a detailed analysis of the Fontaine period rings ($B_{cris}, B_{st}, B_{dR}$), exploring their crucial algebraic and arithmetic properties and their contribution to the curve's construction and definition. Furthermore, we delve into the theory of admissible $p$-adic Galois representations, discussing how the curve, once defined, integrates with Harder-Narasimhan theory., Comment: The article is a review comprising 14 pages, including references and two illustrations. In Spanish language

Point cloud filtering is a fundamental 3D vision task, which aims to remove noise while recovering the underlying clean surfaces. State-of-the-art methods remove noise by moving noisy points along stochastic trajectories to the clean surfaces. These methods often require regularization within the training objective and/or during post-processing, to ensure fidelity. In this paper, we introduce StraightPCF, a new deep learning based method for point cloud filtering. It works by moving noisy points along straight paths, thus reducing discretization errors while ensuring faster convergence to the clean surfaces. We model noisy patches as intermediate states between high noise patch variants and their clean counterparts, and design the VelocityModule to infer a constant flow velocity from the former to the latter. This constant flow leads to straight filtering trajectories. In addition, we introduce a DistanceModule that scales the straight trajectory using an estimated distance scalar to attain convergence near the clean surface. Our network is lightweight and only has $\sim530K$ parameters, being 17% of IterativePFN (a most recent point cloud filtering network). Extensive experiments on both synthetic and real-world data show our method achieves state-of-the-art results. Our method also demonstrates nice distributions of filtered points without the need for regularization. The implementation code can be found at: https://github.com/ddsediri/StraightPCF., Comment: This paper has been accepted to the IEEE/CVF CVPR Conference, 2024

This paper investigates the relationships between hyperparameters of machine learning and fairness. Data-driven solutions are increasingly used in critical socio-technical applications where ensuring fairness is important. Rather than explicitly encoding decision logic via control and data structures, the ML developers provide input data, perform some pre-processing, choose ML algorithms, and tune hyperparameters (HPs) to infer a program that encodes the decision logic. Prior works report that the selection of HPs can significantly influence fairness. However, tuning HPs to find an ideal trade-off between accuracy, precision, and fairness has remained an expensive and tedious task. Can we predict fairness of HP configuration for a given dataset? Are the predictions robust to distribution shifts? We focus on group fairness notions and investigate the HP space of 5 training algorithms. We first find that tree regressors and XGBoots significantly outperformed deep neural networks and support vector machines in accurately predicting the fairness of HPs. When predicting the fairness of ML hyperparameters under temporal distribution shift, the tree regressors outperforms the other algorithms with reasonable accuracy. However, the precision depends on the ML training algorithm, dataset, and protected attributes. For example, the tree regressor model was robust for training data shift from 2014 to 2018 on logistic regression and discriminant analysis HPs with sex as the protected attribute; but not for race and other training algorithms. Our method provides a sound framework to efficiently perform fine-tuning of ML training algorithms and understand the relationships between HPs and fairness., Comment: To Appear in the 20th International Conference on Predictive Models and Data Analytics in Software Engineering (PROMISE'24)

We present an improved treatment for the scattering of heavy dark matter from the ion constituents of a white dwarf. In the heavy dark matter regime, multiple collisions are required for the dark matter to become gravitationally captured. Our treatment incorporates all relevant physical effects including the dark matter trajectories, nuclear form factors, and radial profiles for the white dwarf escape velocity and target number densities. Our capture rates differ by orders of magnitude from previous estimates, which have typically used approximations developed for dark matter scattering in the Earth. We also compute the time for the dark matter to thermalize in the center of the white dwarf, including in-medium effects such as phonon emission and absorption from the ionic lattice in the case where the star has a crystallized core. We find much shorter thermalization timescales than previously estimated, especially if the white dwarf core has crystallized. We illustrate the importance of our improved approach by determining the cross section required for accumulated asymmetric dark matter to self-gravitate., Comment: 32 pages, 7 figures, 2 tables, 1 appendix. Discussion extended, matches published version

At the current pace of technological advancements, Generative AI models, including both Large Language Models and Large Multi-modal Models, are becoming integral to the developer workspace. However, challenges emerge due to the 'black box' nature of many of these models, where the processes behind their outputs are not transparent. This position paper advocates for a 'white box' approach to these generative models, emphasizing the necessity of transparency and understanding in AI-generated code to match the proficiency levels of human developers and better enable software maintenance and evolution. We outline a research agenda aimed at investigating the alignment between AI-generated code and developer skills, highlighting the importance of responsibility, security, legal compliance, creativity, and social value in software development. The proposed research questions explore the potential of white-box methodologies to ensure that software remains an inspectable, adaptable, and trustworthy asset in the face of rapid AI integration, setting a course for research that could shape the role of code proficiency into 2030 and beyond., Comment: submitted to Software Engineering 2030

Electron beam shaping allows the control of the temporal properties of x-ray free-electron laser pulses from femtosecond to attosecond timescales. Here we demonstrate the use of a laser heater to shape electron bunches and enable the generation of attosecond x-ray pulses. We demonstrate that this method can be applied in a selective way, shaping a targeted subset of bunches while leaving the remaining bunches unchanged. This experiment enables the delivery of shaped x-ray pulses to multiple undulator beamlines, with pulse properties tailored to specialized scientific applications.

The baryon mass operator is studied within a combined expansion in $1/N_c$ and perturbative $SU(3)$ flavor symmetry breaking, where $N_c$ denotes the number of quark charges. Flavor projection operators are used to classify the baryon operators involved in the expansion, which fall into the flavor representations $1$, $8$, $10+\overline{10}$, $27$, $35+\overline{35}$ and $64$. This approach allows one to incorporate up to third-order flavor symmetry breaking in the baryon mass operator in a rigorous and systematic way. Previous work on the subject is considered to validate the approach. A fit to data is performed to evaluate the free parameters in the theory and to produce some numerical values of baryon masses. Results are consistent and reaffirm the striking success of the $1/N_c$ expansion., Comment: 34 pages, 3 tables, 2 figures

The properties of 2D materials are strongly influenced by their substrate, leading to a variety of "proximity effects" like screening, charge transfer, and hybridization. Surprisingly, there is a dearth of theoretical studies on these effects. Particularly, previous theoretical research on the Star of David (SOD) structure in 1T-NbSe$_2$ has focused on single-layer configurations or stacking with the same 1T phase without any real substrate. Here, we depart from these approaches and explore how these proximity effects shape the electronic and magnetic properties of the 1T-NbSe$_2$ phase when it is grown on the metallic 1H-NbSe$_2$ substrate. Using Density Functional Calculations, we establish a common framework to define the key characteristics of both free-standning 1T-NbSe$_2$ and 1H-NbSe$_2$. We then identify the optimal stacking arrangement for these two layers, revealing a transfer from the 1T to the 1H phase and a reorganization of charge within each layer. Our findings indicate that the magnetic moment of the SOD structure is still robust; however, is diminished due to a reduction in the on-site Coulomb interaction of the Hubbard bands. Additionally, the interlayer coupling induces metallicity in the 1T phase and increases the decoupling of the lower Hubbard band from the valence band.

We propose a scheme for coherently shaping attosecond x-ray pulses at free-electron lasers. We show that by seeding an FEL with a short coherent seed that overfills the amplification bandwidth, one can shape the wigner function of the pulse by controlling the undulator taper profile. The examples of controllable coherent pulse pairs and trains, as well as isolated spectrotemporally shaped pulses with very broad coherent bandwidths are examined in detail. Existing attosecond XFELs can achieve these experimental conditions in a two-stage cascade, in which the coherent seed is generated by a short current spike in an electron bunch and shaped in an unspoiled region within the same bunch. We experimentally demonstrate the production of pulse pairs using this method at the Linac Coherent Light Source.

The soliton-like superradiant regime of free-electron lasers (FEL) offers a promising path towards ultrashort pulses, beyond the natural limit dictated by the bandwidth of the high-gain FEL instability. In this work we present a three-dimensional theory of the superradiant regime, including the effects of beam emittance and energy spread. Our work takes advantage of recent developments in non-linear FEL theory to provide a fully analytical description of soliton-like superradiance. Our theory proves the existence of a diffraction-dominated steady-state regime in which the superradiant peak power grows indefinitely while leaving the pulse duration and on-axis intensity almost unchanged. These results are in excellent agreement with three-dimensional simulations and are supported by recent experimental results at the Linac Coherent Light Source. This work advances non-linear FEL theory and provides a theoretical framework for the next generation of attosecond x-ray FELs.