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Dipolar-octupolar (DO) pyrochlore systems Ce$_2$(Zr,Sn,Hf)$_2$O$_7$ have garnered much attention as recent investigations suggest that they may stabilize a novel quantum spin ice (QSI), a quantum spin liquid (QSL) with an emergent $U(1)$ gauge field. In particular, the experimentally estimated microscopic exchange parameters place Ce$_2$Zr$_2$O$_7$ in the $\pi$-flux QSI regime, and recent neutron scattering experiments have corroborated some key theoretical predictions. On the other hand, to make a definitive conclusion, more multifaceted experimental signatures are desirable. In this regard, recent neutron scattering investigation of the magnetic field dependence of the spin correlations in Ce$_2$Zr$_2$O$_7$ may provide valuable information. However, there have not been any comprehensive theoretical studies for comparison. In this work, we provide such information using gauge mean-field theory (GMFT), allowing for theoretical investigation beyond the perturbative regime. In particular, we construct the phase diagrams for the [110], [111], and [001] field directions. Furthermore, we demonstrate the distinctive evolution of the equal-time and dynamical spin structure factors as a function of the magnetic field for each field direction. These predictions will help future experiments confirm the true nature of the DO-QSI., Comment: 14+11 pages, 11+7 figures

A quantum spin liquid (QSL) arises from a highly entangled superposition of many degenerate classical ground states in a frustrated magnet, and is characterized by emergent gauge fields and deconfined fractionalized excitations (spinons). Because such a novel phase of matter is relevant to high-transition-temperature superconductivity and quantum computation, the microscopic understanding of QSL states is a long-sought goal in condensed matter physics. The 3D pyrochlore lattice of corner-sharing tetrahedra can host a QSL with U(1) gauge fields called quantum spin ice (QSI), which is a quantum (with effective $S=1/2$) analog of the classical (with large effective moment) spin ice. A key difference between QSI and classical spin ice is the predicted presence of the linearly dispersing collective excitations near zero energy, dubbed the "photons", arising from emergent quantum electrodynamics, in addition to the spinons at higher energies. Recently, 3D pyrochlore systems Ce2M2O7 (M = Sn, Zr, Hf) have been suggested as effective $S=1/2$ QSI candidates, but there has been no evidence of quasielastic magnetic scattering signals from photons, a key signature for a QSI. Here, we use polarized neutron scattering experiments on single crystals of Ce2Zr2O7 to conclusively demonstrate the presence of magnetic excitations near zero energy at 50 mK in addition to signatures of spinons at higher energies. By comparing the energy (E), wave vector (Q), and polarization dependence of the magnetic excitations with theoretical calculations, we conclude that Ce2Zr2O7 is the first example of a dipolar-octupolar $\pi$ flux QSI with dominant dipolar Ising interactions, therefore identifying a microscopic Hamiltonian responsible for a QSL.

Early efforts to realize exotic quantum ground states in frustrated magnets focused on frustration arising from the lattice geometry alone. Attention has shifted to bond-dependent anisotropic interactions, as well as further-neighbor interactions, on non-geometrically-frustrated lattices due to their greater versatility. The honeycomb magnet BaCo$_2$(AsO$_4$)$_2$ recently emerged as a candidate host for both bond-dependent (e.g. Kitaev) and third-neighbor ($J_3$) interactions, and has become a model experimental system due to its relatively low levels of disorder. Understanding the relative importance of different exchange interactions holds the key to achieving novel ground states, such as quantum spin liquids. Here, we use the magnetotropic susceptibility to map out the intermediate and high-field phase diagram of BaCo$_2$(AsO$_4$)$_2$ as a function of the out-of-plane magnetic field direction at $T = 1.6$ K. We show that the experimental data are qualitatively consistent with classical Monte Carlo results of the XXZ-$J_1$-$J_3$ model with small Kitaev and off-diagonal exchange couplings included. However, the calculated critical fields are systematically larger than the experimental values. Infinite-DMRG computations on the quantum model reveal that quantum corrections from a nearby ferromagnetic state are likely responsible for the suppressed critical fields. Together, our experiment and theory analyses demonstrate that, while quantum fluctuations play an important role in determining the phase diagram, most of the physics of BaCo$_2$(AsO$_4$)$_2$ can be understood in terms of the classical dynamics of long-range ordered states, leaving little room for the possibility of a quantum spin liquid., Comment: 16 pages, 12 figures

Quantum spin ice (QSI) is an emblematic three-dimensional $U(1)$ quantum spin liquid (QSL) on the pyrochlore lattice that hosts gapless photon-like modes and spinon excitations. Despite its notable status and the current rise of strong material candidates Ce$_2$(Zr, Sn, Hf)$_2$O$_7$, there are still only a few analytical approaches to model the low-energy behavior of QSI. These analytical methods are essential to gain insight into the physical interpretation of measurements. We here introduce the self-consistent exclusive boson representation (SCEBR) to model emergent spinon excitations in QSI. By treating the presence of other emergent charges in an average way, the SCEBR extends the range of validity of the exclusive boson representation previously introduced by Hao, Day, and Gingras [Hao, Day, and Gingras, Physical Review B, 90, 214430 (2014)] to numerous cases of physical relevance. We extensively benchmark the approach and provide detailed analytical expressions for the spinon dispersion, the Bogoliubov transformation that diagonalizes the system, and the dynamical spin structure factor for 0- and $\pi$-flux QSI. Finite temperature properties are further investigated to highlight essential differences between the thermodynamic behavior of the 0- and $\pi$-flux phases. We notably show that the SCEBR predicts a reduction of the spinon bandwidth with increasing temperature, consistent with previous quantum Monte-Carlo results, through suppression of spinon hopping by thermal occupation. The SCEBR thus provides a powerful analytical tool to interpret experiments on current and future candidate material that has several advantages over other widely used methods., Comment: 13+9 pages, 8 figures

Motivated by recent experiments on Ce$_2$Zr$_2$O$_7$ that reveal a dynamic, liquid-like ground state, we study the nearest neighbor XYZ Hamiltonian of dipolar-octupolar pyrochlore magnets with the pseudofermion functional renormalization group (PFFRG), which is numerically implemented by the SpinParser software. Taking the interaction between the octupolar components to be dominant and antiferromagnetic, we map out the phase diagram demarcating the quantum disordered and magnetically ordered states. We identify four distinct phases, namely the $0$-flux and $\pi$-flux quantum spin ices, and the all-in-all-out magnetic orders along the local $z$ and $x$ axes. We further use the static two-spin correlations output by the PFFRG algorithm to compute the polarized neutron scattering cross-sections, which are able to capture several qualitative features observed experimentally, in the materially relevant parameter regime that stabilizes the $\pi$-flux quantum spin ice. Our results provide support for a quantum spin liquid ground state in Ce$_2$Zr$_2$O$_7$., Comment: 10+6 pages, 6+5 figures

The triangular lattice Hubbard model at strong coupling, whose effective spin model contains both Heisenberg and ring exchange interactions, exhibits a rich phase diagram as the ratio of the hopping $t$ to onsite Coulomb repulsion $U$ is tuned. This includes a chiral spin liquid (CSL) phase. Nevertheless, this exotic phase remains challenging to realize experimentally because a given material has a fixed value of $t/U$ that can difficultly be tuned with external stimuli. One approach to address this problem is applying a DC electric field, which renormalizes the exchange interactions as electrons undergo virtual hopping processes; in addition to creating virtual doubly occupied sites, electrons must overcome electric potential energy differences. Performing a small $t/U$ expansion to fourth order, we derive the ring exchange model in the presence of an electric field and find that it not only introduces spatial anisotropy but also tends to enhance the ring exchange term compared to the dominant nearest-neighbor Heisenberg interaction. Thus, increasing the electric field serves as a way to increase the importance of the ring exchange at constant $t/U$. Through density matrix renormalization group calculations, we compute the ground state phase diagram of the ring exchange model for two different electric field directions. In both cases, we find that the electric field shifts the phase boundary of the CSL towards a smaller ratio of $t/U$. Therefore, the electric field can drive a magnetically ordered state into the CSL. This explicit demonstration opens the door to tuning other quantum spin systems into spin liquid phases via the application of an electric field., Comment: 9 + 17 pages, 10 + 13 figures

Understanding non-Fermi liquids in dimensions higher than one remains one of the most formidable challenges in modern condensed matter physics. These systems, characterized by an abundance of gapless degrees of freedom and the absence of well-defined quasiparticles, defy conventional analytical frameworks. Inspired by recent work [Delacretaz, Du, Mehta, and Son, Physical Review Research, 4, 033131 (2022)], we present a procedure for bosonizing Fermi surfaces that does not rely on the existence of sharp excitation and is thus directly applicable to non-Fermi liquids. Our method involves parameterizing the generalized fermionic distribution function through a bosonic field that describes frequency-dependent local variations of the chemical potential in momentum space. We propose an effective action that produces the collisionless quantum Boltzmann equation as its equation of motion and can be used for any dimension and Fermi surface of interest. Even at the quadratic order, this action reproduces non-trivial results obtainable only through involved analysis with alternative means. By offering an alternative method directly applicable to studying the low-energy physics of Fermi and non-Fermi liquids, our work potentially stands as an important building block in advancing the comprehension of strange metals and associated phenomena., Comment: 13+15 pages, 4 figure; the first two authors contributed equally to this work

Electronic spins can form long-range entangled phases of condensed matter named quantum spin liquids. Their existence is conceptualized in models of two- or three-dimensional frustrated magnets that evade symmetry-breaking order down to zero temperature. Quantum spin ice (QSI) is a theoretically well-established example described by an emergent quantum electrodynamics, with excitations behaving like photon and matter quasiparticles. The latter are fractionally charged and equivalent to the `spinons' emerging from coherent phases of singlets in one dimension, where clear experimental proofs of fractionalization exist. However, in frustrated magnets it remains difficult to establish consensual evidence for quantum spin liquid ground states and their fractional excitations. Here, we use backscattering neutron spectroscopy to achieve extremely high resolution of the time-dependent magnetic response of the candidate QSI material Ce$_2$Sn$_2$O$_7$. We find a gapped spectrum featuring a threshold and peaks that match theories for pair production and propagation of fractional matter excitations (spinons) strongly coupled to a background gauge field. The multiple peaks are a specific signature of the $\pi$-flux phase of QSI, providing spectroscopic evidence for fractionalization in a three-dimensional quantum spin liquid., Comment: 19 pages, 6 figures, fixes in references

Understanding historical forest dynamics, specifically changes in forest biomass and carbon stocks, has become critical for assessing current forest climate benefits and projecting future benefits under various policy, regulatory, and stewardship scenarios. Carbon accounting frameworks based exclusively on national forest inventories are limited to broad-scale estimates, but model-based approaches that combine these inventories with remotely sensed data can yield contiguous fine-resolution maps of forest biomass and carbon stocks across landscapes over time. Here we describe a fundamental step in building a map-based stock-change framework: mapping historical forest biomass at fine temporal and spatial resolution (annual, 30m) across all of New York State (USA) from 1990 to 2019, using freely available data and open-source tools. Using Landsat imagery, US Forest Service Forest Inventory and Analysis (FIA) data, and off-the-shelf LiDAR collections we developed three modeling approaches for mapping historical forest aboveground biomass (AGB): training on FIA plot-level AGB estimates (direct), training on LiDAR-derived AGB maps (indirect), and an ensemble averaging predictions from the direct and indirect models. Model prediction surfaces (maps) were tested against FIA estimates at multiple scales. All three approaches produced viable outputs, yet tradeoffs were evident in terms of model complexity, map accuracy, saturation, and fine-scale pattern representation. The resulting map products can help identify where, when, and how forest carbon stocks are changing as a result of both anthropogenic and natural drivers alike. These products can thus serve as inputs to a wide range of applications including stock-change assessments, monitoring reporting and verification frameworks, and prioritizing parcels for protection or enrollment in improved management programs., Comment: Manuscript: 24 pages, 7 figures; Supplements: 12 pages, 5 figures; Submitted to Forest Ecology and Management

Recent investigations on the dipolar-octupolar compounds Ce$_2$Zr$_2$O$_7$ and Ce$_2$Sn$_2$O$_7$ suggest that they may stabilize so-called $\pi$-flux octupolar quantum spin ice ($\pi$-O-QSI), a novel three-dimensional quantum spin liquid hosting emergent photons. Confirmation of such an exotic phase would require the prediction of a distinctive signature and its subsequent experimental observation. So far, however, theoretical predictions for any such sharp smoking-gun signatures are lacking. In this Letter, we thoroughly investigate O-QSI using an extension of gauge mean-field theory. This framework produces a phase diagram consistent with previous studies and an energy-integrated neutron scattering signal with intensity-modulated rod motifs, as reported in experiments and numerical studies. We predict that the dynamical spin structure factor of $\pi$-O-QSI is characterized by a broad continuum with three distinctive peaks as a consequence of the two mostly flat spinon bands. These three peaks should be measurable by high-resolution inelastic neutron scattering. Such spectroscopic signatures would be clear evidence for the realization of $\pi$-flux quantum spin ice., Comment: 7+25 pages, 4+11 figures

The efferent and afferent effects of the vagus nerve on the developing brain have remained enigmatic. Here we review the evidence of such effects on microglial plasticity in the sheep model of human fetal development, one of the most recognized and deployed models of human fetal physiology. We show that vagotomy alters microglial phenotype and that this effect is hormetic under conditions of mild systemic inflammation, as may occur antepartum with chorioamnionitis. We present the methodology to assess not only biomarker-based microglial activation but also the morphometric features of the microglia. Together, these assessments provide a more comprehensive toolbox of glial phenotypical characterizations, especially in the context of investigating the locoregional vagal control of glial function. The presented findings support the earlier discoveries in preclinical and clinical models of adult physiology whereby vagotomy appeared neuroprotective for Parkinson disease, explained, at least in part, by the effects on microglia. In addition, we present the approach to measure and the findings on regional cerebral blood flow changes in relation to vagus nerve manipulation. In summary, the body of evidence underscores the importance of both the efferent and the afferent vagal pathways, via the vagus nerve, in the programming of microglial phenotype in the developing brain. The significance of these relationships for developing and treating early susceptibility to neuroinflammatory and neurodegenerative disorders in later life requires further studies.

Symmetry fractionalization is a ubiquitous feature of topologically ordered states that can be used to classify different symmetry-enriched topological phases and reveal some of their unique experimental signatures. Despite its vast popularity, there is currently no available framework to study symmetry fractionalization of quantum spin ice (QSI) -- a $U(1)$ quantum spin liquid (QSL) on the pyrochlore lattice supporting emergent photons -- within the most widely used theoretical framework to describe it, gauge mean-field theory (GMFT). In this work, we provide an extension of GMFT that allows for the classification of space-time symmetry fractionalization. The construction classifies all GMFT Ans\"atze that yield physical wavefunctions invariant under given symmetries and a specific low-energy gauge structure. As an application of the framework, we first show that the only two Ans\"atze with emergent $U(1)$ gauge fields that respect all space-group symmetries are the well-known 0- and $\pi$-flux states. We then showcase how the framework may describe QSLs beyond the currently known ones by classifying chiral $U(1)$ QSI. We find two new states described by $\pi/2$- and $3\pi/2$-fluxes of the emergent gauge field threading the hexagonal plaquettes of the pyrochlore lattice. We finally discuss how the different ways translation symmetries fractionalize for all these states lead to unique experimentally relevant signatures and compute their respective inelastic neutron scattering cross-section to illustrate the argument., Comment: 12+10 pages, 4+1 figures

Recently, Co-based honeycomb magnets have been proposed as promising candidate materials to host the Kitaev spin liquid state. One of the front-runners is BaCo$_2$(AsO$_4$)$_2$ (BCAO), where it was suggested that the exchange processes between Co$^{2+}$ ions via the surrounding edge-sharing oxygen octahedra could give rise to bond-dependent Kitaev interactions. In this work, we present and analyze comprehensive inelastic neutron scattering studies of BCAO with fields in the honeycomb plane. Combining the constraints from the magnon excitations in the high-field polarized state and the inelastic spin structure factor measured in zero magnetic field, we examine two leading theoretical models: the Kitaev-type \JKG model and the \XXZ model. We show that the existing experimental data can be consistently accounted for by the \XXZ model but not by the \JKG model, and we discuss the implications of these results for the realization of a spin liquid phase in BCAO and more generally for the realization of the Kitaev model in cobaltates., Comment: 15 pages, 10 figures

The contribution of the vagus nerve to inflammation and glucosensing in the fetus is not understood. We hypothesized that vagotomy (Vx) will trigger a rise in systemic glucose levels and this will be enhanced during systemic and organ-specific inflammation. Efferent vagus nerve stimulation (VNS) should reverse this phenotype. Near-term fetal sheep (n=57) were surgically prepared with vascular catheters and ECG electrodes as control and treatment groups (lipopolysaccharide (LPS), Vx+LPS, Vx+LPS+selective efferent VNS). Fetal arterial blood samples were drawn for 7 days to profile inflammation (IL-6), insulin, blood gas and metabolism (glucose). At 54 h, a necropsy was performed; terminal ileum macrophages; CD11c (M1 phenotype) immunofluorescence was quantified to detect inflammation. Across the treatment groups, blood gas and cardiovascular changes indicated mild septicemia. At 3 h, in the LPS group IL-6 peaked; that peak was decreased in Vx+LPS400 and doubled in Vx+LPS800 group; the efferent VNS sped up the reduction of the inflammatory response profile over 54 h. M1 macrophage activity was increased in the LPS and Vx+LPS800 groups only. Glucose and insulin levels in the Vx+LPS group were respectively 1.3-fold and 2.3-fold higher vs. control at 3 h, and the efferent VNS normalized glucose levels. Complete withdrawal of vagal innervation results in a 72h delayed onset of sustained increase in glucose levels for at least 54h and intermittent hyperinsulinemia. Under conditions of moderate fetal inflammation, this is related to higher levels of gut inflammation; the efferent VNS reduces the systemic inflammatory response as well as restores both the levels of glucose and terminal ileum inflammation, but not the insulin levels. Our findings reveal a novel regulatory, hormetic, role of the vagus nerve in the immunometabolic response to endotoxin in near-term fetuses.

We prove a positive characteristic analogue of the classical result that the centralizer of a nonconstant differential operator in one variable is commutative. This leads to a new, short proof of that classical characteristic zero result, by reduction modulo $p.$, Comment: Added a description of the fraction field of the centralizer in positive characteristic. Accepted for publication in International Mathematics Research Notices

Recent experiments on the dipolar-octupolar pyrochlore compound Ce$_2$Zr$_2$O$_7$ indicate that it may realize a three-dimensional quantum spin liquid (QSL). In particular, the analyses of available data suggest that the system is in a region of parameter space, where the so-called $\pi$-flux $U(1)$ octupolar quantum spin ice (QSI) with an emergent photon could be realized. On the other hand, because the system is far from the perturbative classical spin ice regime, it is unclear whether the quantum ground state is primarily a coherent superposition of 2-in-2-out configurations as in the canonical QSI phases. In this work, we explore other possible competing quantum spin liquid states beyond QSI using the Schwinger boson parton construction of the dipolar-octupolar pseudospin-1/2 model. After classifying all symmetric $U(1)$ and $\mathbb{Z}_2$ QSLs using the projective symmetry group (PSG), we construct a mean-field phase diagram that possesses a number of important features observed in an earlier exact diagonalization study. In the experimentally relevant frustrated region of the phase diagram, we find two closely competing gapped $\mathbb{Z}_2$ QSLs with a narrow spinon dispersion. The equal-time and dynamical spin structure factors of these states show key features similar to what was reported in neutron scattering experiments. Hence, these QSLs are closely competing ground states in addition to the $\pi$-flux $U(1)$ QSI, and they should be taken into account on equal footing for the interpretation of experiments on Ce$_2$Zr$_2$O$_7$., Comment: 11+15 pages, 7+3 figures

When implementing a non-continuous controller for a cyber-physical system, it may happen that the evolution of the closed-loop system is not anymore piecewise differentiable along the trajectory, mainly due to conditional statements inside the controller. This may lead to some unwanted chattering effects than may damage the system. This behavior is difficult to observe even in simulation. In this paper, we propose an interval approach to characterize the sliding surface which corresponds to the set of all states such that the state trajectory may jump indefinitely between two distinct behaviors. We show that the recent notion of thick sets will allows us to compute efficiently an outer approximation of the sliding surface of a given class of hybrid system taking into account all set-membership uncertainties. An application to the verification of the controller of a child swing is considered to illustrate the principle of the approach., Comment: In Proceedings SNR 2020, arXiv:2101.05256

Background: The chronically instrumented pregnant sheep has been used as a model of human fetal development and responses to pathophysiologic stimuli. This is due to the unique amenability of the unanesthetized fetal sheep to the surgical placement and maintenance of catheters and electrodes, allowing repetitive blood sampling, substance injection, recording of bioelectrical activity, application of electric stimulation and in vivo organ imaging. Recently, there has been growing interest in pleiotropic effects of vagus nerve stimulation (VNS) on various organ systems such as innate immunity, metabolism, and appetite control. There is no approach to study this in utero and corresponding physiological understanding is scarce. New Method: Based on our previous presentation of a stable chronically instrumented unanesthetized fetal sheep model, here we describe the surgical instrumentation procedure allowing successful implantation of a cervical uni- or bilateral VNS probe with or without vagotomy. Results: In a cohort of 53 animals, we present the changes in blood gas, metabolic, and inflammatory markers during the postoperative period. We detail the design of a VNS probe which also allows recording from the nerve. We also present an example of vagus electroneurogram (VENG) recorded from the VNS probe and an analytical approach to the data. Comparison with Existing Methods: This method represents the first implementation of VENG/VNS in a large pregnant mammalian organism. Conclusions: This study describes a new surgical procedure allowing to record and manipulate chronically the vagus nerve activity in an animal model of human pregnancy., Comment: Accompanying data repository: https://doi.org/10.6084/m9.figshare.7228307.v2

Primates display a marked ability to learn habits in uncertain and dynamic environments. The associated perceptions and actions of such habits engage distributed neural circuits. Yet, precisely how such circuits support the computations necessary for habit learning remain far from understood. Here we construct a formal theory of network energetics to account for how changes in brain state produce changes in sequential behavior. We exercise the theory in the context of multi-unit recordings spanning the caudate nucleus, prefrontal cortex, and frontal eyefields of female macaque monkeys engaged in 60-180 sessions of a free scan task that induces motor habits. The theory relies on the determination of effective connectivity between recording channels, and on the stipulation that a brain state is taken to be the trial-specific firing rate across those channels. The theory then predicts how much energy will be required to transition from one state into another, given the constraint that activity can spread solely through effective connections. Consistent with the theory's predictions, we observed smaller energy requirements for transitions between more similar and more complex trial saccade patterns, and for sessions characterized by less entropic selection of saccade patterns. Using a virtual lesioning approach, we demonstrate the resilience of the observed relationships between minimum control energy and behavior to significant disruptions in the inferred effective connectivity. Our theoretically principled approach to the study of habit learning paves the way for future efforts examining how behavior arises from changing patterns of activity in distributed neural circuitry., Comment: Main Text: 17 pages and 6 figures; Supplement Text: 9 pages and 8 figures

An electrocardiogram (ECG)-derived heart rate variability (HRV) index reliably tracks the inflammatory response induced by low-dose lipopolysaccharide (LPS) in near-term sheep fetuses. We evaluated the effect of vagus nerve stimulation (VNS) on vagus nerve electroneurogram (VENG) and the systemic inflammatory response induced by a high dose of LPS in neonatal piglets to mimic late-onset neonatal sepsis. We tested if our HRV inflammatory index tracks inflammation in piglets and its relationship to VENG. Following anesthesia, electrodes were attached to the left vagal nerve; ECG and blood pressure (BP) were recorded throughout the experiment. Following baseline, the piglets were administered LPS as 2mg/kg IV bolus. In the VNS treated piglet, the vagus nerve was stimulated for 10 minutes prior to and 10 min after the injection of LPS. In both groups, every 15 min post LPS, the arterial blood sample was drawn for blood gas, metabolites, and inflammatory cytokines. At the end of the experiment, the piglets were euthanized. BP and HRV measures were calculated. The piglets developed a potent inflammatory response to the LPS injection with TNF-alpha, IL-1beta, IL-6 and IL-8 peaking between 45 and 90 min post-injection. VNS diminished the LPS-induced systemic inflammatory response varying across the measured cytokines from two to ten-fold. The HRV index tracked accurately the temporal profile of cytokines and VENG changes. This novel model allows manipulating and tracking neonatal sepsis: The HRV inflammatory index 1) applies across species pre- and postnatally and 2) performs well at different degrees of sepsis (i.e., nanogram and milligram doses of LPS); 3) the present VNS paradigm effectively suppresses LPS-induced inflammation, even at high doses of LPS. The potential of early postnatal VNS to counteract sepsis and of HRV monitoring to early detect and track it deserve further study., Comment: updated manuscript with VENG analyses

Following some work done by Komjath and Schmerl, we extend the definition of a cloud to $\mathbb{R}^N$ for $N \geq 2$ and show that $k$ clouds cover $\mathbb{R}^2$ if and only if $k$ clouds cover $\mathbb{R}^N$. We also show that countably many clouds cover $\mathbb{R}^N$., Comment: 8 pages, 2 figures

Fetal heart rate variability (fHRV) is an important indicator of health and disease, yet its physiological origins, neural contributions in particular, are not well understood. We aimed to develop novel experimental and data analytical approaches to identify fHRV measures reflecting the vagus nerve contributions to fHRV. In near-term ovine fetuses, a comprehensive set of 46 fHRV measures was computed from fetal pre-cordial electrocardiogram recorded during surgery and 72 hours later without (n=24) and with intra-surgical bilateral cervical vagotomy (n=15). The fetal heart rate did not change due to vagotomy. We identify fHRV measures specific to the vagal modulation of fHRV: Multiscale time irreversibility asymmetry index (AsymI), Detrended fluctuation analysis (DFA) alpha1, Kullback-Leibler permutation entropy (KLPE) and Scale dependent Lyapunov exponent slope (SDLE alpha). We provide a systematic delineation of vagal contributions to fHRV across signal-analytical domains which should be relevant for the emerging field of bioelectronic medicine and the deciphering of the vagus code. Our findings also have clinical significance for in utero monitoring of fetal health during surgery.