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The Transformer Cookbook
Item type: Journal Article
Yang A.; Watson C.; Xue A.; et al. (2026)
We present the transformer cookbook: a collection of techniques for directly encoding algorithms into a transformer’s parameters. This work addresses the steep learning curve of such endeavors, a problem exacerbated by a fragmented literature where key results are scattered across numerous papers. In particular, we synthesize this disparate body of findings into a curated set of recipes that demonstrate how to implement everything from basic arithmetic in feed-forward layers to complex data routing via self-attention. Our mise en place of formulations is for both newcomers seeking an accessible entry point and experts in need of a systematic reference. This unified presentation of transformer constructions provides a foundation for future work spanning theoretical research in computational complexity to empirical investigations in architecture design and interpretability. We provide code implementations of each construction in numpy alongside a suite of generative unit tests.
Bridging hospital and community pharmacy at transition of care: Improving the management of drug-related problems at discharge through hospital pharmacy hotlines
Item type: Journal Article
Garin P.; Boeni F.; Stämpfli D.; et al. (2026)
Background Hospital discharge is a critical step in transitions of care, exposing patients to adverse drug events. Community pharmacists play a key role in post-discharge medication management. However, they often face challenges clarifying hospital discharge prescriptions due to limited access to relevant information and communication gaps between hospital and ambulatory care. Objectives This study aims to investigate how hospital pharmacy hotlines can improve communication and support community pharmacists in resolving drug-related problems (DRPs) on hospital discharge prescriptions. Methods Pharmaceutical hotlines answered by hospital pharmacists were implemented in three regional hospitals. Community pharmacists could use the hotline when facing DRPs or to obtain additional information about the hospital discharge prescriptions. For each query, the rate of resolution without physician involvement and the type of DRP were documented. Satisfaction was assessed through online questionnaires at the end of the study. Results The hotlines were implemented during 2 months in two hospitals and 6 months in the third. Community pharmacists raised 185 questions using the hotlines, 54 % of which were resolved without the need to contact the physician. The most common DRPs were unclear or incomplete prescriptions (n = 60, 32 %), medication unavailability (n = 29, 16 %), and drug-drug interactions (n = 22, 12 %). Of the 95 community pharmacies surveyed, 46 responded, with 87 % expressing satisfaction with the hospital pharmacy hotlines. Conclusion The hospital pharmacy hotlines proved to be an effective tool to improve intraprofessional collaboration and support community pharmacists in managing hospital discharge prescriptions, with more than half of DRPs resolved without the need to contact the physician.
The chemical habitability of Earth and rocky planets prescribed by core formation
Item type: Journal Article
Walton C.R.; Rogers L.K.; Bonsor A.; et al. (2026)
A crucial factor governing the habitability of exoplanets is the availability of bioessential elements such as nitrogen (N) and phosphorous (P), which foster prebiotic chemistry and sustain life after its emergence. However, concentrations of P and N in planetary mantles vary, owing to initial availability and oxidation conditions during planet formation, and thus their characterization and availability in planetary environments are challenging. Here we use a core-formation model to show that moderate oxygen fugacity during core formation is the key parameter to the availability of these two elements, with the existence of a narrow ‘chemical Goldilocks zone’ that allows both P and N to be present with the right abundances in the mantle. Earth falls within this zone, whereas planets with more reducing/oxidizing conditions will sequester P/N into the core, hindering their availability for life. Future observations refining estimates of the oxygen fugacity prevalent during exoplanet core formation will be crucial to properly evaluate exoplanetary habitability and correctly interpret possible biosignatures.
Entanglement and optimization within autoregressive neural quantum states
Item type: Journal Article
Jreissaty A.; Zhang H.; Quijano J.C.; et al. (2026)
Neural quantum states (NQSs) are powerful variational ansätze capable of representing highly entangled quantum many-body wavefunctions. While the average entanglement properties of ensembles of restricted Boltzmann machines are well understood, the entanglement structure of autoregressive NQSs such as recurrent neural networks and transformers remains largely unexplored. We perform large-scale simulations of ensembles of random autoregressive wavefunctions for chains of up to 256 spins and uncover signatures of transitions in their average entanglement scaling, entanglement spectra, and correlation functions. We show that the standard softmax normalization of the wavefunction suppresses entanglement and fluctuations, and introduce a square modulus normalization function that restores them. Finally, we connect the insights gained from our entanglement and activation function analysis to initialization strategies for finding the ground states of strongly correlated Hamiltonians via variational Monte Carlo.
Impact of static disorder on quasiparticle spectra: Debye-Waller, mean free path, and potential fluctuation effects
Item type: Journal Article
Della Valle E.; Constantinou P.; Schmitt T.; et al. (2026)
Angle-resolved photoemission spectroscopy (ARPES) is a widely used characterization technique in condensed matter physics, providing direct access to the single-electron spectral function of crystals, including their electronic band structure and Fermi surface. Measuring the band structure of novel quantum materials has been fundamentally important for determining, for example, nontrivial band topology, as in topological insulators, Weyl semimetals, and Dirac semimetals, or for identifying new classes of materials, such as altermagnets. A key challenge with these emerging quantum materials is that their initial crystalline quality is rarely optimized, which directly affects the spectra measured by ARPES. Here, we present a theoretical framework and experimental evidence addressing two common consequences of static disorder in photoemission experiments: the loss of coherent spectral weight and the broadening of spectral features. ARPES spectra can be understood as a sum of coherent and incoherent intensities, with their relative contributions controlled by atomic disorder and electron correlation effects. For disorder caused by phonons, the coherent intensity is exponentially suppressed as temperature increases, a phenomenon analogous to the Debye-Waller factor in diffraction, where Bragg peaks diminish in favor of diffuse scattering as disorder increases. In this work, we report a soft-x-ray study of the deliberately disordered (via Ar ion sputtering) InAs(110) surface, characterized by scanning tunneling microscopy, scanning tunneling spectroscopy, and low-energy electron diffraction. We introduce a framework that enables quantification of coherent photoemission intensity loss with increasing disorder, allowing both thermal and static disorder to be treated within a unified approach. Additionally, we identify a second major effect of disorder beyond lifetime broadening: inhomogeneous spectral broadening arising from local potential fluctuations. We show that such fluctuations increase the linewidths of the spectra of localized and delocalized states and contribute to the suppression of ARPES intensity from states near the Fermi level. The concepts and analysis methods presented should make ARPES useful for direct diagnosis of disorder effects on electronic states, for science as well as engineering.