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Purpose: Several brain complications of SARS-CoV-2 infection have been reported. It has been moreover speculated that this neurotropism could potentially cause a delayed outbreak of neuropsychiatric and neurodegenerative diseases of neuroinflammatory origin. A propagation mechanism has been proposed across the cribriform plate of the ethmoid bone, from the nose to the olfactory epithelium, and possibly afterward to other limbic structures, and deeper parts of the brain including the brainstem. Methods: Review of clinical examination, and whole-brain voxel-based analysis of $^{18}$F-FDG PET metabolism in comparison with healthy subjects (p voxel<0.001, p-cluster<0.05, uncorrected), of two patients with confirmed diagnosis of SARS-CoV-2 explored at the post-viral stage of the disease. Results: Hypometabolism of the olfactory/rectus gyrus was found on the two patients, especially one with 4-week prolonged anosmia. Additional hypometabolisms were found within amygdala, hippocampus, parahippocampus, cingulate cortex, pre-/post-central gyrus, thalamus/hypothalamus, cerebellum, pons, and medulla in the other patient who complained of delayed onset of a painful syndrome. Conclusion: These preliminary findings reinforce the hypotheses of SARS-CoV-2 neurotropism through the olfactory bulb and the possible extension of this impairment to other brain structures. $^{18}$F-FDG PET hypometabolism could constitute a cerebral quantitative biomarker of this involvement. Post-viral cohort studies are required to specify the exact relationship between such hypometabolisms and the possible persistent disorders, especially involving cognitive or emotion disturbances, residual respiratory symptoms, or painful complaints.

Vanadium in silicon carbide is a promising spin photon interface candidate with optical transitions in the telecom range and a long lived electron spin, hosted in an advanced semiconductor platform. In this detailed investigation of the defect's 16-dimensional ground state spin manifold at millikelvin temperatures, a wide range of previously unreported transitions are observed which are accurately described using a theoretical model that includes strain. Using a superconducting microcoil we achieve Rabi frequencies exceeding 20 MHz and perform the first coherent manipulation of a direct hyperfine transition. These insights further underscore the defect's potential for strain engineering and sensing, as well as for fault-tolerant qudit encoding., Comment: 6 pages, 3 figures

Early Solar System (SS) planetesimals constitute the parent bodies of most meteorites investigated today. Nucleosynthetic isotope anomalies of bulk meteorites have revealed a dichotomy between non-carbonaceous (NC) and carbonaceous (CC) groups. Planetesimals sampling NC and CC isotopic signatures are conventionally thought to originate from the "dry" inner disk, and volatile-rich outer disk, respectively, with their segregation enforced by a pressure bump close to the water-ice sublimation line, possibly tied to Jupiter's formation. This framework is challenged by emerging evidence that the oldest NC planetesimals (i.e., the iron meteorites parent bodies; IMPBs) were characterized by far higher oxidation states than previously imagined, suggesting abundant ($\gtrsim$ few wt.%) liquid water in their interiors prior to core differentiation. In this paper, we employ a model for a degassing icy planetesimal (heated by $^{26}$Al decay) to map the conditions for liquid water production therein. Our work culminates in threshold characteristic sizes for pebbles composing the said planetesimal, under which water-ice melting occurs. Adopting a model for a disk evolving under both turbulence and magnetohydrodynamic disk winds, and assuming pebble growth is fragmentation-limited, we self-consistently translate the threshold pebble size to lower limits on early SS turbulence. We find that if NC IMPBs were "wet," their constituent pebbles must have been smaller than a few centimeters, corresponding to typical values of the Shakura-Sunyaev $\alpha_{\nu}$ turbulence parameter in excess of $10^{-3}$. These findings argue against a quiescent SS disk (for <10 AU), are concordant with astronomical constraints on protoplanetary disk turbulence, and suggest pebble accretion played a secondary role in building our rocky planets.

We consider the optimal control of occupied processes which record all positions of the state process. Dynamic programming yields nonlinear equations on the space of positive measures. We develop the viscosity theory for this infinite dimensional parabolic $occupied$ PDE by proving a comparison result between sub and supersolutions, and thus provide a characterization of the value function as the unique viscosity solution. Toward this proof, an extension of the celebrated Crandall-Ishii-Lions (second order) Lemma to this setting, as well as finite-dimensional approximations, is established. Examples including the occupied heat equation, and pricing PDEs of financial derivatives contingent on the occupation measure are also discussed., Comment: 23 pages

A general entanglement generation protocol between remote stationary qubits using single-photon reflection in a photonic network is explored theoretically. The nodes of the network consist of single qubits that are typically represented by the spin of a color center, each localized in a separate optical cavity and linked to other nodes via photonic links such as optical fibers. We derive a model applicable to a wide range of parameters and scenarios to describe the nodes and the local spin-photon interaction accounting for the pulsed (finite bandwidth) nature of flying single photons while optimizing the rate and fidelity. We investigate entanglement generation between remote qubits and tailor protocols to a variety of physical implementations with different properties. Of particular interest is the regime of weak coupling and low cooperativity between spin and cavity which is relevant in the cases of the nitrogen and silicon vacancy centers in diamond. We also take into account the variability of the properties between realistic (stationary) nodes., Comment: 19 pages (incl. Appendices), 8 figures

Optically interfaced solid-state defects are promising candidates for quantum communication technologies. The ideal defect system would feature bright telecom emission, long-lived spin states, and a scalable material platform, simultaneously. Here, we employ one such system, vanadium (V4+) in silicon carbide (SiC), to establish a potential telecom spin-photon interface within a mature semiconductor host. This demonstration of efficient optical spin polarization and readout facilitates all optical measurements of temperature-dependent spin relaxation times (T1). With this technique, we lower the temperature from about 2K to 100 mK to observe a remarkable four-orders-of-magnitude increase in spin T1 from all measured sites, with site-specific values ranging from 57 ms to above 27 s. Furthermore, we identify the underlying relaxation mechanisms, which involve a two-phonon Orbach process, indicating the opportunity for strain-tuning to enable qubit operation at higher temperatures. These results position V4+ in SiC as a prime candidate for scalable quantum nodes in future quantum networks., Comment: 11 pages, 6 figures

Ground-based observations of `Barbarian' L-type asteroids at 1 to 2.5-$\mu$m indicate that their near-infrared spectra are dominated by the mineral spinel, which has been attributed to a high abundance of calcium-aluminum inclusions (CAIs) -- the first solids to condense out of the protoplanetary disk during the formation of the Solar System. However, the spectral properties of these asteroids from 2.5 to 5-$\mu$m, a wavelength region that covers signatures of hydrated minerals, water, and organics, have not yet been explored. Here, we present 2 to 5-$\mu$m reflectance spectra of five spinel-rich asteroids obtained with the NIRSpec instrument on the James Webb Space Telescope. All five targets exhibit a $\sim$ 2.85-$\mu$m absorption feature with a band depth of 3-6$\%$ that appears correlated in strength with that of the 2-$\mu$m spinel absorption feature. The shape and position of the 2.85-$\mu$m feature are not a good match to the 2.7-$\mu$m feature commonly seen in carbonaceous CM meteorites or C-type asteroids. The closest spectral matches are to the Moon and Vesta, suggesting commonalities in aqueous alteration across silicate bodies, infall of hydrated material, and/or space weathering by solar wind H implantation. Lab spectra of CO/CV chondrites, CAIs, as well as the minerals cronstedtite and spinel, also show a similar feature, providing clues into the origin of the 2.85-$\mu$m feature., Comment: 11 pages, 5 figures, and 2 tables. Published in ApjL

Many laboratories routinely cool samples to 10 mK, but relatively few can cool condensed matter below 1 mK. Easy access to the microkelvin range would propel fields such as quantum sensors and quantum materials. Such temperatures are achieved with adiabatic nuclear demagnetization. Existing nuclear demagnetization refrigerators (NDR) are ``single-shot'', and the recycling time is incompatible with some sub-mK experiments. Furthermore, a high cooling power is required to overcome the excess heat load of order nW on NDR pre-cooled by cryogen-free dilution refrigerators. We report the performance of an aluminum NDR designed for powerful cooling when part of a dual stage continuous NDR (CNDR). Its thermal resistance is minimized to maximize the cycling rate of the CNDR and consequently its cooling power. At the same time, its susceptibility to eddy current heating is minimized. A CNDR based on two of the aluminum NDR presented here would achieve a cooling power of approximately 40 nW at 560 $\mu$K less than six days after cooling from room temperature, with a small offset in electronic temperature that decreases as the time-dependent heat load decays.

Quantum communication promises unprecedented communication capabilities enabled by the transmission of quantum states of light. However, current implementations face severe limitations in communication distance due to photon loss. Silicon carbide (SiC) defects have emerged as a promising quantum device platform, offering strong optical transitions, long spin coherence lifetimes and the opportunity for integration with semiconductor devices. Some defects with optical transitions in the telecom range have been identified, allowing to interface with fiber networks without the need for wavelength conversion. These unique properties make SiC an attractive platform for the implementation of quantum nodes for quantum communication networks. We provide an overview of the most prominent defects in SiC and their implementation in spin-photon interfaces. Furthermore, we model a memory-enhanced quantum communication protocol in order to extract the parameters required to surpass a direct point-to-point link performance. Based on these insights, we summarize the key steps required towards the deployment of SiC devices in large-scale quantum communication networks., Comment: 20 pages, 8 figures

As the field of Zr stable isotopes is rapidly expanding from the study of mass-independent to that of mass-dependent isotope effects, a variety of Zr standards have appeared in the literature. While several of these standards have been proposed as the ideal isotope reference material (iRM) against which all data should be reported, none of them have been shown to meet the compositional and/or conflict-of-interest-free distribution requirements put forth by the community. To remedy this situation, we report on a community-led effort to develop and calibrate a scale defining iRM for Zr isotopes: NIST RM 8299. Developed in partnership with the National Institute of Standards and Technology (NIST) from the widely used SRM 3169 Zr Standard Solution, the candidate RM 8299 was calibrated through an inter-laboratory study involving three laboratories. Our data show that RM 8299 meets all requirements of an ideal iRM. It is an isotopically homogeneous, high-purity reference material, that is free of isotope anomalies, and whose composition is identical to that of a major geological reservoir (Ocean Island Basalts). Furthermore, RM 8299 will be curated and distributed by NIST, a neutral, conflict-of-interest free organization, and was produced in sufficient quantities to last multiple decades. We recommend that all Zr isotope data to be reported against RM 8299. Our results also show that SRM 3169 lots #130920 and #071226 have identical composition to RM 8299. Therefore, using RM 8299 as the scale defining iRM will enable direct comparison of all future data with the vast majority of the existing literature data, both for mass-independent and mass-dependent isotope effects. To facilitate conversion of d94/90Zr values reported against other Zr standards, we provide high-precision conversion factors to the RM 8299 scale obtained using the double-spike method.

Recent publications explore AI biases in detecting objects and people in the environment. However, there is no research tackling how AI examines nature. This case study presents a pioneering exploration into the AI attitudes (ecocentric, anthropocentric and antipathetic) toward nature. Experiments with a Large Language Model (LLM) and an image captioning algorithm demonstrate the presence of anthropocentric biases in AI. Moreover, to delve deeper into these biases and Human-Nature-AI interaction, we conducted a real-life experiment in which participants underwent an immersive de-anthropocentric experience in a forest and subsequently engaged with ChatGPT to co-create narratives. By creating fictional AI chatbot characters with ecocentric attributes, emotions and views, we successfully amplified ecocentric exchanges. We encountered some difficulties, mainly that participants deviated from narrative co-creation to short dialogues and questions and answers, possibly due to the novelty of interacting with LLMs. To solve this problem, we recommend providing preliminary guidelines on interacting with LLMs and allowing participants to get familiar with the technology. We plan to repeat this experiment in various countries and forests to expand our corpus of ecocentric materials., Comment: 9 pages, 5 figures, 2 tables

We develop an It\^o calculus for functionals of the "time" spent by a path at arbitrary levels. A Markovian setting is recovered by lifting a process $X$ with its flow of occupation measures $\mathcal{O}$ and call the pair $(\mathcal{O},X)$ the occupied process. While the occupation measure erases the chronology of the path, we show that our framework still includes many relevant problems in stochastic analysis and financial mathematics. The study of occupied processes therefore strikes a middle ground between the path-independent case and Dupire's Functional It\^o Calculus. We extend It\^o's and Feynman-Kac's formula by introducing the occupation derivative, a projection of the functional linear derivative used extensively in mean field games and McKean-Vlasov optimal control. Importantly, we can recast through Feynman-Kac's theorem a large class of path-dependent PDEs as parabolic problems where the occupation measure plays the role of time. We apply the present tools to the optimal stopping of spot local time and discuss financial examples including exotic options, corridor variance swaps, and path-dependent volatility., Comment: 47 pages, 10 figures

Transition metal (TM) defects in silicon carbide (SiC) are a promising platform for applications in quantum technology as some of these defects, e.g. vanadium (V), allow for optical emission in one of the telecom bands. For other defects it was shown that straining the crystal can lead to beneficial effects regarding the emission properties. Motivated by this, we theoretically study the main effects of strain on the electronic level structure and optical electric-dipole transitions of the V defect in SiC. In particular we show how strain can be used to engineer the g-tensor, electronic selection rules, and the hyperfine interaction. Based on these insights we discuss optical Lambda systems and a path forward to initializing the quantum state of strained TM defects in SiC., Comment: 14 pages, 6 figures

Reservoir engineering has become a prominent tool to control quantum systems. Recently, there have been first experiments applying it to many-body systems, especially with a view to engineer particle-conserving dissipation for quantum simulations using bosons. In this work, we explore the dissipative dynamics of these systems in the classical limit. We derive a general equation of motion capturing the effective nonlinear dissipation introduced by the bath and apply it to the special case of a Bose-Hubbard model, where it leads to an unconventional type of dissipative nonlinear Schr\"odinger equation. Building on that, we study the dynamics of one and two solitons in such a dissipative classical field theory., Comment: 14 pages, 6 figures

The aim of this paper is to provide a stochastic version under location uncertainty of the compressible Navier-Stokes equations. The modelling under location uncertainty setting is used here to derive a physically consistent stochastic dynamical system for compressible flows. It relies on an extended stochastic version of the Reynolds transport theorem involving stochastic source terms. In a similar way as in the deterministic case, this conservation theorem is applied to density, momentum and total energy in order to obtain a transport equation of the primitive variables, i.e. density, velocity and temperature. For the modelling of ocean dynamics, the transport of mass fraction of species, such as salinity, is also considered. We show that performing low Mach and Boussinesq approximations to this more general set of equations allows us to recover previous versions of incompressible stochastic Navier-Stokes equations and the stochastic Boussinesq equations, respectively. Finally, we provide some research directions on the use of this general set of equations in the perspective of relaxing the Boussinesq and hydrostatic approximation for ocean modelling.

We study the scaling behaviour of a class of compatible two-well problems for higher order, homogeneous linear differential operators. To this end, we first deduce general lower scaling bounds which are determined by the vanishing order of the symbol of the operator on the unit sphere in direction of the associated element in the wave cone. We complement the lower bound estimates by a detailed analysis of the two-well problem for generalized (tensor-valued) symmetrized derivatives with the help of the (tensor-valued) Saint-Venant compatibility conditions. In two spatial dimensions for highly symmetric boundary data (but arbitrary tensor order $m \in \mathbb{N}$) we provide upper bound constructions matching the lower bound estimates. This illustrates that for the two-well problem for higher order operators new scaling laws emerge which are determined by the Fourier symbol in the direction of the wave cone. The scaling for the symmetrized gradient from \cite{CC15} which was also discussed in \cite{RRT23} provides an example of this family of new scaling laws., Comment: 36 pages, 1 figure, comments welcome; changes in the upper bound construction (Lemmas 4.2, 4.5); restricted to $\lambda = 1/2$ in the upper bound construction

We propose a level-set approach to characterize the region occupied by the solid in Stefan problems with and without surface tension, based on their recent probabilistic reformulation. The level-set function is parameterized by a feed-forward neural network, whose parameters are trained using the probabilistic formulation of the Stefan growth condition. The algorithm can handle Stefan problems where the liquid is supercooled and can capture surface tension effects through the simulation of particles along the moving boundary together with an efficient approximation of the mean curvature. We demonstrate the effectiveness of the method on a variety of examples with and without radial symmetry., Comment: 31 pages, 17 figures

We study boundaries and their hitting times in the context of optimal stopping and Bermudan-style options. We prove the continuity of the map linking the boundary to the value of its associated stopping policy. While the supremum norm is used to compare continuous boundaries, a weaker topology induced by the so-called relaxed $L^{\infty}$ distance is used in the semicontinuous case. Relaxed stopping rules and their properties are also discussed. Incidentally, we provide a convergence analysis for neural stopping boundaries [Reppen, Soner, and Tissot-Daguette, Neural Optimal Stopping Boundary, 2022] entailing the universal approximation capability of neural networks and the notion of inf/sup convolution., Comment: 22 pages, 4 figures

Spin-active quantum emitters have emerged as a leading platform for quantum technologies. However, one of their major limitations is the large spread in optical emission frequencies, which typically extends over tens of GHz. Here, we investigate single V4+ vanadium centres in 4H-SiC, which feature telecom-wavelength emission and a coherent S=1/2 spin state. We perform spectroscopy on single emitters and report the observation of spin-dependent optical transitions, a key requirement for spin-photon interfaces. By engineering the isotopic composition of the SiC matrix, we reduce the inhomogeneous spectral distribution of different emitters down to 100 MHz, significantly smaller than any other single quantum emitter. Additionally, we tailor the dopant concentration to stabilise the telecom-wavelength V4+ charge state, thereby extending its lifetime by at least two orders of magnitude. These results bolster the prospects for single V emitters in SiC as material nodes in scalable telecom quantum networks., Comment: 29 pages, 20 figures, 2 tables

In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind or coming as the feedback of the ocean on the atmosphere and leading in a very fast way to the selection of some wavelength. This interwoven, yet simple, mechanism explains the emergence of typical wavelength associated to near inertial waves. Ensemble-mean waves that are not in phase with the random forcing are damped at an exponential rate, whose magnitude depends on the random forcing variance. Geostrophic adjustment is also interpreted as a statistical homogenization process in which, in order to conserve potential vorticity, the small-scale component tends to align to the velocity fields to form a statistically homogeneous random field., Comment: Submitted for STUOD 2022 conference proceedings