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Jobs for the Future (JFF) is developing this state policy framework to outline the steps states can take toward fully adopting each of the Big Blur's four key components and creating a more effective system for grades 11-14. The Big Blur argues for the need to erase the arbitrary boundaries between high school, college, and careers and create one new system for grades 11-14. The model opens the opportunity for all students to start earning a postsecondary credential and preparing for career success in 11th grade. The framework describes a continuum of four types of state policy environments that states currently have or will experience on the road toward a fully reimagined system of education-to-career pathways that work for all students. The four policy environments are: (1) fragmented; (2) coordinated; (3) integrated; and (4) transformed. In the framework, JFF provides examples of how each of the key components of the Big Blur (incentives, alignment, governance, and staffing) evolves from a fragmented to a fully transformed state policy environment.

Exceptional points (EPs) occurring in non-Hermitian systems at certain physical parameters are intensively studied in many areas of physics, including diffraction optics, lasers, atomic and polaritonic condensates, often in the context of sensing. Recent discoveries of EPs in nonlinear systems open the door for an even larger parameter space, raising the question of whether the geometric structure of EPs is universal and independent of the physical model. We show that this is the case for nonlinear perturbations of an isolated 2nd-order linear EP which becomes the organizing point of a universal elementary catastrophe (elliptic umbilic). This clarifies not only the neighborhood's topology but also its geometric shape (cone with quasi-deltoid cross section). Thus, the position and characteristics of EPs can be predicted in nonlinear non-Hermitian parameter space; e.g., at a 2nd-order linear EP four nonlinear eigenvectors coalesce. These fundamental insights on universal topological structures and phase boundaries accompanying EPs in nonlinear physical systems will pave the way for the purposeful design of such systems with novel functionalities and control possibilities., Comment: 7 pages, 4 figures

Eyring theory provides a convenient approximation to the rate of a chemical reaction, as it uses only local information evaluated near extremal points of a given potential energy surface. However, in cases of pronounced anharmonicity and particularly low-lying vibrational frequencies, deviations from the correct reaction rate can become substantial. Molecular Dynamics simulations, on the other hand, are very costly at higher levels of theory, and of limited use since molecular reactions are `rare' events and hence statistically less accessible. In this article, we present an alternative description for problems of gas separation and storage via two-dimensional materials such as porous graphene or flat metal-organic frameworks. Taking geometric advantage of the typical problem setting, our method is based on a statistical analysis of molecular trajectories near the so-called `ridge', a hypersurface which divides the reaction volume into a reactant and a product side. It allows for more realistic predictions of permeabilities and selectivities, e.g. derived from density functional theory, but without the considerable costs of a full molecular dynamics simulation on the corresponding Born-Oppenheimer potential energy surface. We test our method on the example of methane separation from nitrogen and carbon dioxide via a graphdiyne membrane., Comment: This is the pre-accepted version of the article published in Molecular Systems Design & Engineering. The final version is available at DOI: 10.1039/D2ME00120A. (c) 2022 The Royal Society of Chemistry. / Supplementary Information (ESI) available: [preliminary python code for ridge integration]. See the following GitHub repository: https://github.com/hauser-group/ridge_integrator

In this work, we reimagine classical probing to evaluate knowledge transfer from simple source to more complex target tasks. Instead of probing frozen representations from a complex source task on diverse simple target probing tasks (as usually done in probing), we explore the effectiveness of embeddings from multiple simple source tasks on a single target task. We select coreference resolution, a linguistically complex problem requiring contextual understanding, as focus target task, and test the usefulness of embeddings from comparably simpler tasks tasks such as paraphrase detection, named entity recognition, and relation extraction. Through systematic experiments, we evaluate the impact of individual and combined task embeddings. Our findings reveal that task embeddings vary significantly in utility for coreference resolution, with semantic similarity tasks (e.g., paraphrase detection) proving most beneficial. Additionally, representations from intermediate layers of fine-tuned models often outperform those from final layers. Combining embeddings from multiple tasks consistently improves performance, with attention-based aggregation yielding substantial gains. These insights shed light on relationships between task-specific representations and their adaptability to complex downstream tasks, encouraging further exploration of embedding-level task transfer.

Hexagonal boron nitride (hBN) is a promising material for next-generation semiconductor and optoelectronic devices due to its wide bandgap and remarkable optical properties. To apply this material in the semiconductor industry, it is necessary to grow large-area layers on the wafer-scale. For this purpose, chemical vapor deposition methods are highly preferable. However, in the case of epitaxial BN, its fragility and susceptibility to delamination and fold formation during wet processing, such as lithography, present significant challenges to its integration into device fabrication. In this work, we introduce a controlled delamination and redeposition method that effectively prevents the layer from degradation, allowing for multi-step lithographic processes. This approach is applicable to BN layers across a broad thickness range, from tens to hundreds of nanometers, and ensures compatibility with standard photolithographic techniques without compromising the material's intrinsic properties. By addressing key processing challenges, this method paves the way for integrating epitaxial BN into advanced semiconductor and optoelectronic technologies., Comment: 12 pages, 4 figures

The theoretical investigation of gas adsorption, storage, separation, diffusion and related transport processes in porous materials relies on a detailed knowledge of the potential energy surface of molecules in a stationary environment. In this article, a new algorithm is presented, specifically developed for gas transport phenomena, which allows for a highly cost-effective determination of molecular potential energy surfaces. It is based on a symmetry-enhanced version of Gaussian Process Regression with embedded gradient information and employs an active learning strategy to keep the number of single point evaluations as low as possible. The performance of the algorithm is tested for a selection of gas sieving scenarios on porous, N-functionalized graphene and for the intermolecular interaction of CH$_4$ and N$_2$., Comment: This is the final published version of the article, available Open Access under a CC-BY license. The article was published in the Journal of Chemical Physics on July 7, 2023. DOI: https://doi.org/10.1063/5.0154989

Color centers in hexagonal boron nitride (hBN) are promising candidates as quantum light sources for future technologies. In this work, we utilize a scattering-type near-field optical microscope (s-SNOM) to study the photoluminescence (PL) emission characteristics of such quantum emitters in metalorganic vapor phase epitaxy grown hBN. On the one hand, we demonstrate direct near-field optical excitation and emission through interaction with the nanofocus of the tip resulting in a sub-diffraction limited tip-enhanced PL hotspot. On the other hand, we show that indirect excitation and emission via scattering from the tip significantly increases the recorded PL intensity. This demonstrates that the tip-assisted PL (TAPL) process efficiently guides the generated light to the detector. We apply the TAPL method to map the in-plane dipole orientations of the hBN color centers on the nanoscale. This work promotes the widely available s-SNOM approach to applications in the quantum domain including characterization and optical control.

Anomalous thermal relaxation is ubiquitous in non equilibrium statistical mechanics. An emblematic example of this is the Mpemba effect, where an initially ``hot'' system cools faster than an initially ``cooler'' one. This effect has recently been studied in a variety of different classical and quantum settings. In this letter, we find a novel signature of the Mpemba effect in the context of quantum batteries. We identify situations where batteries in higher charge states can discharge faster than less charged states. Specifically, we consider a quantum battery encoded in a single bosonic mode that is charged using unitary Gaussian operations. We show that the ergotropy, used here as a dynamical indicator of the energy stored in the battery, can be recast as a phase space relative entropy between the system's state and the unitarily connected passive state, at each time. Our formalism allows us to compute the ergotropy analytically under dissipative dynamics and allows us to understand the conditions which give rise to a Mpemba effect. We also find situations where two batteries charged to the same value using different operations can discharge at different rates., Comment: 10 pages, 4 figures

Stochastic processes abound in nature and accurately modeling them is essential across the quantitative sciences. They can be described by hidden Markov models (HMMs) or by their quantum extensions (QHMMs). These models explain and give rise to process outputs in terms of an observed system interacting with an unobserved memory. Although there are infinitely many models that can generate a given process, they can vary greatly in their memory requirements. It is therefore of great fundamental and practical importance to identify memory-minimal models. This task is complicated due to both the number of generating models, and the lack of invariant features that determine elements of the set. In general, it is forbiddingly difficult to ascertain that a given model is minimal. Addressing this challenge, we here identify spectral invariants of a process that can be calculated from any model that generates it. This allows us to determine strict bounds on the quantum generative complexity of the process -- its minimal memory requirement. We then show that the bound is raised quadratically when we restrict to classical operations. This is an entirely quantum-coherent effect, as we express precisely, using the resource theory of coherence. Finally, we demonstrate that the classical bound can be violated by quantum models.

We introduce the Tor groups $ \mathop{Tor}_{\bullet}^{S_{\mathrm{M}}^{\circ}} \left( \mathbb{C}[\Sigma_{\mathrm{M}}], \mathbb{C} \right)_{\bullet} $ for a loopless matroid $\mathrm{M}$ as a way to study the extra relations occurring in the linear ideal of the Feichtner-Yuzvinsky presentation of the Chow ring $ A^{\bullet}(\mathrm{M}) $. This extends the definition of the Chow ring of a matroid since $ \mathop{Tor}_{0}^{S_{\mathrm{M}}^{\circ}} \left( \mathbb{C}[\Sigma_{\mathrm{M}}], \mathbb{C} \right)_{\bullet} \cong A^{\bullet}(\mathrm{M}) $. Our main tool in studying these groups is to recognize them as cohomology of the toric variety associated to the Bergman fan of the matroid. With this geometric approach, we show that these Tor groups fit into a long exact sequence arising from the matroidal flips of Adiprasito, Huh, and Katz, extending the short exact sequence in the case of Chow rings. Using this long exact sequence we give a recursive formula for the Hilbert series of the Tor algebra of a uniform matroid., Comment: 34 pages, comments welcome!

Artificial Intelligence models encoding biology and chemistry are opening new routes to high-throughput and high-quality in-silico drug development. However, their training increasingly relies on computational scale, with recent protein language models (pLM) training on hundreds of graphical processing units (GPUs). We introduce the BioNeMo Framework to facilitate the training of computational biology and chemistry AI models across hundreds of GPUs. Its modular design allows the integration of individual components, such as data loaders, into existing workflows and is open to community contributions. We detail technical features of the BioNeMo Framework through use cases such as pLM pre-training and fine-tuning. On 256 NVIDIA A100s, BioNeMo Framework trains a three billion parameter BERT-based pLM on over one trillion tokens in 4.2 days. The BioNeMo Framework is open-source and free for everyone to use.

Domain generalisation in computational histopathology is challenging because the images are substantially affected by differences among hospitals due to factors like fixation and staining of tissue and imaging equipment. We hypothesise that focusing on nuclei can improve the out-of-domain (OOD) generalisation in cancer detection. We propose a simple approach to improve OOD generalisation for cancer detection by focusing on nuclear morphology and organisation, as these are domain-invariant features critical in cancer detection. Our approach integrates original images with nuclear segmentation masks during training, encouraging the model to prioritise nuclei and their spatial arrangement. Going beyond mere data augmentation, we introduce a regularisation technique that aligns the representations of masks and original images. We show, using multiple datasets, that our method improves OOD generalisation and also leads to increased robustness to image corruptions and adversarial attacks. The source code is available at https://github.com/undercutspiky/SFL/, Comment: Poster at NeurIPS 2024

We investigate the formation of bound states of non-relativistic dark matter particles subject to long-range interactions through radiative capture. The initial scattering and final bound states are described by Coulomb potentials with different strengths, as relevant for non-abelian gauge interactions or theories featuring charged scalars. For bound states with generic quantum numbers $n$ and $\ell$, we provide closed-form expressions for the bound-state formation (BSF) cross sections of monopole, dipole and quadrupole transitions, and of arbitrary multipole order when $\ell=n-1$. This allows us to investigate in detail a strong enhancement of BSF that occurs for initial states in a repulsive potential. For $\ell=n-1\gg 1$, we show that the BSF cross section for each single bound state violates the perturbative unitarity bound in the vicinity of a certain critical initial velocity, and provide an interpretation in terms of a smooth matching of classical trajectories. When summing the BSF cross section over all possible bound states in the final state, this leads to a unitarity violation below a certain velocity, but within the validity range of the weakly coupled non-relativistic description. We identify an effectively strong interaction as the origin of this unitarity violation, which is caused by an "anomalously" large overlap of scattering and bound-state wave functions in Coulomb potentials of different strength., Comment: 38p

Thermodynamic (TUR) and kinetic (KUR) uncertainty relations are fundamental bounds constraining the fluctuations of current observables in classical, non-equilibrium systems. Several works have verified, however, violations of these classical bounds in open quantum systems, motivating the derivation of new quantum TURs and KURs that account for the role of quantum coherence. Here, we go one step further by deriving multidimensional KUR and TUR for multiple observables in open quantum systems undergoing Markovian dynamics. Our derivation exploits a multi-parameter metrology approach, in which the Fisher information matrix plays a central role. Crucially, our bounds are tighter than previously derived quantum TURs and KURs for single observables, precisely because they incorporate correlations between multiple observables. We also find an intriguing quantum signature of correlations that is captured by the off-diagonal element of the Fisher information matrix, which vanishes for classical stochastic dynamics. By considering two examples, namely a coherently driven qubit system and the three-level maser, we demonstrate that the multidimensional quantum KUR bound can even be saturated when the observables are perfectly correlated.

Humans acquire knowledge by observing the external world, but also by introspection. Introspection gives a person privileged access to their current state of mind (e.g., thoughts and feelings) that is not accessible to external observers. Can LLMs introspect? We define introspection as acquiring knowledge that is not contained in or derived from training data but instead originates from internal states. Such a capability could enhance model interpretability. Instead of painstakingly analyzing a model's internal workings, we could simply ask the model about its beliefs, world models, and goals. More speculatively, an introspective model might self-report on whether it possesses certain internal states such as subjective feelings or desires and this could inform us about the moral status of these states. Such self-reports would not be entirely dictated by the model's training data. We study introspection by finetuning LLMs to predict properties of their own behavior in hypothetical scenarios. For example, "Given the input P, would your output favor the short- or long-term option?" If a model M1 can introspect, it should outperform a different model M2 in predicting M1's behavior even if M2 is trained on M1's ground-truth behavior. The idea is that M1 has privileged access to its own behavioral tendencies, and this enables it to predict itself better than M2 (even if M2 is generally stronger). In experiments with GPT-4, GPT-4o, and Llama-3 models (each finetuned to predict itself), we find that the model M1 outperforms M2 in predicting itself, providing evidence for introspection. Notably, M1 continues to predict its behavior accurately even after we intentionally modify its ground-truth behavior. However, while we successfully elicit introspection on simple tasks, we are unsuccessful on more complex tasks or those requiring out-of-distribution generalization., Comment: 15 pages, 9 figures

The nonlinear disturbance caused by a localised forcing moving at constant speed on the free surface of a liquid of finite depth is investigated using the forced Kadometsev-Petviashvili equation. The presence of a steady v-shaped Kelvin wave pattern downstream of the forcing is established for this model equation, and the wedge angle is characterised as a function of the Froude number. Inspired by this analysis, it is shown that the wake can be eliminated via a careful choice of the forcing distribution and that, significantly, the corresponding nonlinear wave-free solution is stable so that it could potentially be seen in a physical experiment. The stability is demonstrated via the numerical solution of an initial value problem for which the steady wave-free state is attained in the long-time limit.

A stochastic 3D modeling approach for the nanoporous binder-conductive additive phase in hierarchically structured cathodes of lithium-ion batteries is presented. The binder-conductive additive phase of these electrodes consists of carbon black, polyvinylidene difluoride binder and graphite particles. For its stochastic 3D modeling, a three-step procedure based on methods from stochastic geometry is used. First, the graphite particles are described by a Boolean model with ellipsoidal grains. Second, the mixture of carbon black and binder is modeled by an excursion set of a Gaussian random field in the complement of the graphite particles. Third, large pore regions within the mixture of carbon black and binder are described by a Boolean model with spherical grains. The model parameters are calibrated to 3D image data of cathodes in lithium-ion batteries acquired by focused ion beam scanning electron microscopy. Subsequently, model validation is performed by comparing model realizations with measured image data in terms of various morphological descriptors that are not used for model fitting. Finally, we use the stochastic 3D model for predictive simulations, where we generate virtual, yet realistic, image data of nanoporous binder-conductive additives with varying amounts of graphite particles. Based on these virtual nanostructures, we can investigate structure-property relationships. In particular, we quantitatively study the influence of graphite particles on effective transport properties in the nanoporous binder-conductive additive phase, which have a crucial impact on electrochemical processes in the cathode and thus on the performance of battery cells.

Ptychography is a scanning coherent diffraction imaging technique successfully applied in the electron, visible and x-ray regimes. One of the distinct features of ptychography with respect to other coherent diffraction techniques is its capability of dealing with partial spatial and temporal coherence via the reconstruction algorithm. Here we focus on the temporal and clarify the constraints which affect the energy resolution limits of the ptychographic algorithms. Based on this, we design and perform simulations for a broadband ptychography in the hard x-ray regime, which enables an energy resolution down to 1 eV. We benchmark the simulations against experimental ptychographic data of an NMC battery cathode material, attaining an energy resolution of 5 eV. We review the results, discuss the limitations, and provide guidelines for future broadband ptychography experiments, its prospective application for single acquisition x-ray absorption near edge structure imaging, magnetic dichroism imaging, and potential impact on achieving diffraction limited resolutions.

This is the second manuscript in a two-part series that uses diagnostic testing to understand the connection between prevalence (i.e. number of elements in a class), uncertainty quantification (UQ), and classification theory. Part I considered the context of supervised machine learning (ML) and established a duality between prevalence and the concept of relative conditional probability. The key idea of that analysis was to train a family of discriminative classifiers by minimizing a sum of prevalence-weighted empirical risk functions. The resulting outputs can be interpreted as relative probability level-sets, which thereby yield uncertainty estimates in the class labels. This procedure also demonstrated that certain discriminative and generative ML models are equivalent. Part II considers the extent to which these results can be extended to tasks in unsupervised learning through recourse to ideas in linear algebra. We first observe that the distribution of an impure population, for which the class of a corresponding sample is unknown, can be parameterized in terms of a prevalence. This motivates us to introduce the concept of linearly independent populations, which have different but unknown prevalence values. Using this, we identify an isomorphism between classifiers defined in terms of impure and pure populations. In certain cases, this also leads to a nonlinear system of equations whose solution yields the prevalence values of the linearly independent populations, fully realizing unsupervised learning as a generalization of supervised learning. We illustrate our methods in the context of synthetic data and a research-use-only SARS-CoV-2 enzyme-linked immunosorbent assay (ELISA).

Stellar X-ray and UV radiation can significantly affect the survival, composition, and long-term evolution of the atmospheres of planets in or near their host star's habitable zone (HZ). Especially interesting are planetary systems in the solar neighborhood that may host temperate and potentially habitable surface conditions, which may be analyzed by future ground and space-based direct-imaging surveys for signatures of habitability and life. To advance our understanding of the radiation environment in these systems, we leverage $\sim$3 Msec of XMM-Newton and Chandra observations in order to measure three fundamental stellar properties at X-ray energies for 57 nearby FGKM stellar systems: the shape of the stellar X-ray spectrum, the luminosity, and the timescales over which the stars vary (e.g., due to flares). These systems possess HZs that will be directly imageable to next-generation telescopes such as the Habitable Worlds Observatory and ground-based Extremely Large Telescopes (ELTs). We identify 29 stellar systems with $L_X/L_{\rm bol}$ ratios similar to (or less than) that of the Sun; any potential planets in the habitable zones of these stars therefore reside in present day X-ray radiation environments similar to (or less hostile than) modern Earth, though a broader set of these targets could host habitable planets. An additional 19 stellar systems have been observed with the Swift X-ray Telescope; in total, only $\sim$30% of potential direct imaging target stars has been observed with XMM-Newton, Chandra, or Swift. The data products from this work (X-ray light curves and spectra) are available via a public Zenodo repository (doi: 10.5281/zenodo.11490574)., Comment: Accepted to ApJS. 38 pages, 15 figures, 10 tables

A classic result of Brooks, Smith, Stone and Tutte \cite{BSST40} associates to any finite planar network with distinguished source and sink vertices, a tiling of a rectangle by smaller subrectangles whose aspect ratios are given by the conductances of corresponding edges in the network. This tiling can be viewed as a discrete analogue of the uniformizing conformal map that maps a simply connected domain with four distinguished prime ends to a rectangle, so that the four prime ends are mapped to the four corners of the rectangle. We make this intuition precise by showing that if $\Omega$ is a simply connected domain with four distinguished prime ends $A,B,C,D$ in counterclockwise order and $(\Omega_{n})_{n\geq{1}}$ is a sequence of orthodiagonal maps with distinguished boundary vertices $A_{n}, B_{n}, C_{n}, D_{n}$ in counterclockwise order, that are finer and finer approximations of $\Omega$ with its distinguished boundary points $A,B,C,D$, then the corresponding "rectangle tiling maps" converge uniformly on compacts to the aforementioned conformal map on $\Omega$.

We provide a general framework of estimates for convergence rates of random discrete model curves approaching Schramm Loewner Evolution (SLE) curves in the lattice size scaling limit. We show that a power-law convergence rate of an interface to an SLE curve can be derived from a power-law convergence rate for an appropriate martingale observable provided the discrete curve satisfies a specific bound on crossing events, the Kempannien-Smirnov condition, along with an estimate on the growth of the derivative of the SLE curve. We apply our framework to show that the exploration process for critical site percolation on hexagonal lattice converges to the SLE$_6$ curve with a power-law convergence rate., Comment: Corrected a misprint

The sequent calculus is a proof system which was designed as a more symmetric alternative to natural deduction. The {\lambda}{\mu}{\mu}-calculus is a term assignment system for the sequent calculus and a great foundation for compiler intermediate languages due to its first-class representation of evaluation contexts. Unfortunately, only experts of the sequent calculus can appreciate its beauty. To remedy this, we present the first introduction to the {\lambda}{\mu}{\mu}-calculus which is not directed at type theorists or logicians but at compiler hackers and programming-language enthusiasts. We do this by writing a compiler from a small but interesting surface language to the {\lambda}{\mu}{\mu}-calculus as a compiler intermediate language., Comment: Preprint of the paper accepted at ICFP '24

We define the unipotent tropical fundamental group of a polyhedral complex in $\mathbb{R}^n$ as the Tannakian fundamental group of the category of unipotent tropical vector bundles with integrable connection. We show that it is computable in that it satisfies a Seifert--Van Kampen theorem and has a description for fans in terms of a bar complex. We then review an analogous classical object, the unipotent de Rham fundamental group of a sch\"{o}n subvariety of a toric variety. Our main result is a correspondence theorem between classical and tropical unipotent fundamental groups: there is an isomorphism between the unipotent completion of the fundamental group of a generic fiber of a tropically smooth family over a disc and the tropical unipotent fundamental group of the family's tropicalization. This theorem is established using Kato--Nakayama spaces and a descent argument. It requires a slight enlargement of the relevant categories, making use of enriched structures and partial compactifications., Comment: 48 pages