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2025 EN
Carlo Alberto De Bernardi · Alessandro Preti · Jacopo Somaglia
We prove that every separable infinite-dimensional Banach space admits aG\^ateaux smooth and rotund norm which is not midpoint locally uniformlyrotund. Moreover, by using a similar technique, we provide in everyinfinite-dimensional Banach space with separable dual a Fr\'echet smooth andweakly uniformly rotund norm which is not midpoint locally uniformly rotund.These two results provide a positive answer to some open problems by A. J.Guirao, V. Montesinos, and V. Zizler.
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2025 EN
Olivier Bernardi · Éric Fusy · Shizhe Liang
We present two graph drawing algorithms based on the recently defined"grand-Schnyder woods", which are a far-reaching generalization of theclassical Schnyder woods. The first is a straight-line drawing algorithm forplane graphs with faces of degree 3 and 4 with no separating 3-cycle, while thesecond is a rectangular drawing algorithm for the dual of such plane graphs. In our algorithms, the coordinates of the vertices are defined in a globalmanner, based on the underlying grand-Schnyder woods. The grand-Schnyder woodsand drawings are computed in linear time. When specializing our algorithms to special classes of plane graphs, werecover the following known algorithms: (1) He's algorithm for rectangulardrawing of 3-valent plane graphs, based on transversal structures, (2) Fusy'salgorithm for the straight-line drawing of triangulations of the square, basedon transversal structures, (3) Bernardi and Fusy's algorithm for the orthogonaldrawing of 4-valent plane graphs, based on 2-orientations, (4) Barriere andHuemer's algorithm for the straight-line drawing of quadrangulations, based onseparating decompositions. Our contributions therefore provide a unifying perspective on a large familyof graph drawing algorithms that were originally defined on different classesof plane graphs and were based on seemingly different combinatorial structures.
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2025 EN
Jamie Bernardi · Gabriel Mukobi · Hilary Greaves
+2 more
Existing strategies for managing risks from advanced AI systems often focuson affecting what AI systems are developed and how they diffuse. However, thisapproach becomes less feasible as the number of developers of advanced AIgrows, and impedes beneficial use-cases as well as harmful ones. In response,we urge a complementary approach: increasing societal adaptation to advancedAI, that is, reducing the expected negative impacts from a given level ofdiffusion of a given AI capability. We introduce a conceptual framework whichhelps identify adaptive interventions that avoid, defend against and remedypotentially harmful uses of AI systems, illustrated with examples in electionmanipulation, cyberterrorism, and loss of control to AI decision-makers. Wediscuss a three-step cycle that society can implement to adapt to AI.Increasing society's ability to implement this cycle builds its resilience toadvanced AI. We conclude with concrete recommendations for governments,industry, and third-parties.
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2025 EN
Andrii Semenov · Niall Murphy · Simone Patscheider
+2 more
Entanglement is one of the fundamental properties of a quantum state and is acrucial differentiator between classical and quantum computation. There aremany ways to define entanglement and its measure, depending on the problem orapplication under consideration. Each of these measures may be computed orapproximated by multiple methods. However, hardly any of these methods can berun on near-term quantum hardware. This work presents a quantum adaptation ofthe iterative higher-order power method for estimating the geometric measure ofentanglement of multi-qubit pure states using rank-1 tensor approximation. Thismethod is executable on current (hybrid) quantum hardware and does not dependon quantum memory. We study the effect of noise on the algorithm using a simpletheoretical model based on the standard depolarising channel. This model allowsus to post hoc mitigate the effects of noise on the results of the computation.
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2025 EN
Lívia P. Matte · Maximilian Jaugstetter · Alisson S. Thill
+6 more
Hydrogen holds great promise as a cleaner alternative to fossil fuels, butits efficient and affordable storage remains a significant challenge.Bimetallic systems, such as Pd-Ni, present a promising option for storinghydrogen. In this study, using the combination of different cuttingedge X-rayand electron techniques, we observed the transformations of Pd-Ninanoparticles, which initially consist of a NiO-rich shell surrounding aPd-rich core but undergo a major transformation when interacting with hydrogen.During the hydrogen exposure, the Pd core breaks into smaller pockets,dramatically increasing its surface area and enhancing the hydrogen storagecapacity, especially in nanoparticles with lower Pd content. The findingsprovide deep understanding of the morphological changes at the atomic levelduring hydrogen storage and contribute for designing cost-effective hydrogenstorage using multi-metallic systems.
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2025 EN
Laura Pierson
The chromatic symmetric $X_G$ function is a symmetric function generalizationof the chromatic polynomial of a graph, introduced by Stanley (1995). Stanleygave an expansion formula for $X_G$ in terms of the power sum symmetricfunctions $p_\lambda$ using the principle of inclusion-exclusion, and inarXiv:1904.01262, Bernardi and Nadeau gave an alternate $p$-expansion for $X_G$in terms of acyclic orientations. In arXiv:2301.02177, Crew, Pechenik, andSpirkl defined the Kromatic symmetric function $\overline{X}_G$ as a$K$-theoretic analogue of $X_G$, constructed in the same way except that eachvertex is assigned a nonempty set of colors such that adjacent vertices havenonoverlapping color sets. They defined a $K$-analogue $\overline{p}_\lambda$of the power sum basis and computed the first few coefficients of the$\overline{p}$-expansion of $\overline{X}_G$ for some small graphs $G$. Theyconjectured that the $\overline{p}$-expansion always has integer coefficientsand asked whether there is an explicit formula for these coefficients. In thisnote, we give a formula for the $\overline{p}$-expansion of $\overline{X}_G$,show two ways to compute the coefficients recursively (along with examples),and prove that the coefficients are indeed always integers. In a more recentpaper arXiv:2502.21285, we use our formula from this note to give acombinatorial description of the $\overline{p}$-coefficients$[\overline{p}_\lambda]\overline{X}_G$ and a simple characterization of theirsigns in the case of unweighted graphs.
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2025 EN
G. Zanelli · E. Moreva · E. Bernardi
+7 more
The Nitrogen-Vacancy (NV) center in diamond is an intriguing electronic spinsystem with applications in quantum radiometry, sensing and computation. Inthose experiments, a bias magnetic field is commonly applied along the NVsymmetry axis to eliminate the triplet ground state manifold's degeneracy(S=1). In this configuration, the eigenvectors of the NV spin's projectionalong its axis are called strong-axial field states. Conversely, in someexperiments a weak magnetic field is applied orthogonal to the NV symmetryaxis, leading to eigenstates that are balanced linear superpositions ofstrong-axial field states, referred to as dressed states. The latter aresensitive to environmental magnetic noise at the second order, allowing toperform magnetic field protected measurements while providing increasedcoherence times. However, if a small axial magnetic field is added in thisregime, the linear superposition of strong-axial field states becomesunbalanced. This paper presents a comprehensive study of Free Induction Decay(FID) measurements performed on a NV center ensemble in the presence of strainand weak orthogonal magnetic field, as a function of a small magnetic fieldapplied along the NV symmetry axis. The simultaneous detection of dressedstates and unbalanced superpositions of strong-axial field states in a singleFID measurement is shown, gaining insight about coherence time, nuclear spinand the interplay between temperature and magnetic field sensitivity. Thediscussion concludes by describing how the simultaneous presence ofmagnetically-sensitive and -insensitive states opens up appealing possibilitiesfor both sensing and quantum computation applications.
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2025 EN
Giovanni Bernardi · Ilaria Castellani · Paul Laforgue
+1 more
De Nicola and Hennessy's must-preorder is a contextual refinement whichstates that a server q refines a server p if all clients satisfied by p arealso satisfied by q. Owing to the universal quantification over clients, thisdefinition does not yield a practical proof method for the must-preorder, andalternative characterisations are necessary to reason over it. Finding thesecharacterisations for asynchronous semantics, i.e. where outputs arenon-blocking, has thus far proven to be a challenge, usually tackled via ad-hocdefinitions. We show that the standard characterisations of the must-preordercarry over as they stand to asynchronous communication, if servers are enhancedto act as forwarders, i.e. they can input any message as long as they store itback into the shared buffer. Our development is constructive, is completelymechanised in Coq, and is independent of any calculus: our results pertain toSelinger output-buffered agents with feedback. This is a class of LabelledTransition Systems that captures programs that communicate via a sharedunordered buffer, as in asynchronous CCS or the asynchronous pi-calculus. Weshow that the standard coinductive characterisation lets us prove in Coq thatconcrete programs are related by the must-preorder. Finally, our proofs showthat Brouwer's bar induction principle is a useful technique to reason onliveness preserving program transformations.
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2025 EN
Khoa B. Le · Ali Esquembre-Kucukalic · Hsiao-Yi Chen
+5 more
Modeling spin-wave (magnon) dynamics in novel materials is important toadvance spintronics and spin-based quantum technologies. The interactionsbetween magnons and lattice vibrations (phonons) limit the length scale formagnon transport. However, quantifying these interactions remains challenging.Here we show many-body calculations of magnon-phonon (mag-ph) coupling based onthe ab initio Bethe-Salpeter equation. We derive expressions for mag-phcoupling matrices and compute them in 2D ferromagnets, focusing on hydrogenatedgraphene and monolayer CrI3. Our analysis shows that electron-phonon (e-ph) andmag-ph interactions differ significantly, where modes with weak e-ph couplingcan exhibit strong mag-ph coupling (and vice versa), and reveals which phononmodes couple more strongly with magnons. In both materials studied here, theinelastic magnon relaxation time is found to decrease abruptly above thethreshold for emission of strongly coupled phonons, thereby defining alow-energy window for efficient magnon transport. By averaging in this window,we compute the temperature-dependent magnon mean-free path, a key figure ofmerit for spintronics, entirely from first principles. The theory andcomputational tools shown in this work enable studies of magnon interactions,scattering, and dynamics in generic materials, advancing the design of magneticsystems and magnon- and spin-based devices.
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2025 EN
Ali Esquembre-Kučukalić · Khoa B. Le · Alberto García-Cristóbal
+3 more
Chromium trihalides (CrX$_3$, with $\rm{X=I,Br,Cl}$) are layeredferromagnetic materials with rich physics and possible applications. Theirstructure consists of magnetic Cr atoms positioned between two layers of halideatoms. The choice of halide results in distinct magnetic properties, but theireffect on spin-wave (magnon) excitations is not fully understood. Here wepresent first-principles calculations of magnon dispersions and wave functionsfor monolayer Cr trihalides using the finite-momentum Bethe-Salpeter equation(BSE) to describe collective spin-flip excitations. % We study the dependenceof magnon dispersions on the halide species and resolve the small topologicalgap at the Dirac point in the magnon spectrum by including spin-orbit coupling.Analysis of magnon wave functions reveals that magnons are made up ofelectronic transitions with a wider energy range than excitons in CrX$_3$monolayers, providing insight into magnon states in real and reciprocal space.We discuss Heisenberg exchange parameters extracted from the BSE and discussthe convergence of BSE magnon calculations. Our work advances the quantitativemodeling of magnons in two-dimensional materials, providing the starting pointfor studying magnon interactions in a first-principles BSE framework.