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This set of tables introduces new data for national and state-level public elementary and secondary revenues and expenditures for fiscal year (FY) 2021. Specifically, these tables include the following school finance data: (1) revenue and expenditure totals; (2) revenues by source; (3) expenditures by function and object; (4) current expenditures; (5) revenues and current expenditures per pupil; (6) expenditures from Title I funds; and (7) revenues and expenditures from COVID-19 Federal Assistance Funds. The tables chosen for this report demonstrate the range of information available when using the National Public Education Financial Survey (NPEFS). [For "Revenues and Expenditures for Public Elementary and Secondary Education: FY 20. Finance Tables. NCES 2022-301," see ED619372.]

This work investigates the coverage control problem over a static, compact, and convex workspace and develops a hybrid extension of the continuous-time Lloyd algorithm. Each agent in a multi-agent system (MAS) is equipped with a timer mechanism that generates intermittent measurement and control update events, which may occur asynchronously between agents. Between consecutive event times, as determined by the corresponding timer mechanism, the controller of each agent is held constant. These controllers are shown to drive the configuration of the MAS into a neighborhood of the set of centroidal Voronoi configurations, i.e., the minimizers of the standard locational cost. The combination of continuous-time dynamics with intermittently updated control inputs is modeled as a hybrid system. The coverage objective is posed as a set attractivity problem for hybrid systems, where an invariance-based convergence analysis yields sufficient conditions that ensure maximal solutions of the hybrid system asymptotically converge to a desired set. A brief simulation example is included to showcase the result.

Ultracold atomic gases hold unique promise for space science by capitalizing on quantum advantages and extended freefall, afforded in a microgravity environment, to enable next-generation precision sensors. Atom interferometers are a class of quantum sensors which can use freely falling gases of atoms cooled to sub-photon-recoil temperatures to provide unprecedented sensitivities to accelerations, rotations, and gravitational forces, and are currently being developed for space-based applications in gravitational, earth, and planetary sciences, as well as to search for subtle forces that could signify physics beyond General Relativity and the Standard Model. NASA's Cold Atom Lab (CAL) operates onboard the International Space Station as a multi-user facility for studies of ultracold atoms and to mature quantum technologies, including atom interferometry, in persistent microgravity. In this paper, we report on path-finding experiments utilizing ultracold $^{87}$Rb atoms in the CAL atom interferometer, which was enabled by an on-orbit upgrade of the CAL science module: A three-pulse Mach-Zehnder interferometer was studied to understand limitations from the influence of ISS vibrations. Additionally, Ramsey shear-wave interferometry was used to manifest interference patterns in a single run that were observable for over 150 ms free-expansion time. Finally, the CAL atom interferometer was used to remotely measure the photon recoil from the atom interferometer laser as a demonstration of the first quantum sensor using matter-wave interferometry in space., Comment: 14 pages, 5 figures

We test the BUQEYE model of correlated effective field theory (EFT) truncation errors on Reinert, Krebs, and Epelbaum's semi-local momentum-space implementation of the chiral EFT ($\chi$EFT) expansion of the nucleon-nucleon (NN) potential. This Bayesian model hypothesizes that dimensionless coefficient functions extracted from the order-by-order corrections to NN observables can be treated as draws from a Gaussian process (GP). We combine a variety of graphical and statistical diagnostics to assess when predicted observables have a $\chi$EFT convergence pattern consistent with the hypothesized GP statistical model. Our conclusions are: First, the BUQEYE model is generally applicable to the potential investigated here, which enables statistically principled estimates of the impact of higher EFT orders on observables. Second, parameters defining the extracted coefficients such as the expansion parameter $Q$ must be well chosen for the coefficients to exhibit a regular convergence pattern -- a property we exploit to obtain posterior distributions for such quantities. Third, the assumption of GP stationarity across lab energy and scattering angle is not generally met; this necessitates adjustments in future work. We provide a workflow and interpretive guide for our analysis framework, and show what can be inferred about probability distributions for $Q$, the EFT breakdown scale $\Lambda_b$, the scale associated with soft physics in the $\chi$EFT potential $m_{\rm eff}$, and the GP hyperparameters. All our results can be reproduced using a publicly available Jupyter notebook, which can be straightforwardly modified to analyze other $\chi$EFT NN potentials., Comment: 29 pages, 33 figures

We consider the setting of repeated fair division between two players, denoted Alice and Bob, with private valuations over a cake. In each round, a new cake arrives, which is identical to the ones in previous rounds. Alice cuts the cake at a point of her choice, while Bob chooses the left piece or the right piece, leaving the remainder for Alice. We consider two versions: sequential, where Bob observes Alice's cut point before choosing left/right, and simultaneous, where he only observes her cut point after making his choice. The simultaneous version was first considered by Aumann and Maschler (1995). We observe that if Bob is almost myopic and chooses his favorite piece too often, then he can be systematically exploited by Alice through a strategy akin to a binary search. This strategy allows Alice to approximate Bob's preferences with increasing precision, thereby securing a disproportionate share of the resource over time. We analyze the limits of how much a player can exploit the other one and show that fair utility profiles are in fact achievable. Specifically, the players can enforce the equitable utility profile of $(1/2, 1/2)$ in the limit on every trajectory of play, by keeping the other player's utility to approximately $1/2$ on average while guaranteeing they themselves get at least approximately $1/2$ on average. We show this theorem using a connection with Blackwell approachability. Finally, we analyze a natural dynamic known as fictitious play, where players best respond to the empirical distribution of the other player. We show that fictitious play converges to the equitable utility profile of $(1/2, 1/2)$ at a rate of $O(1/\sqrt{T})$.

The emergence of correlated phenomena arising from the combination of 1$\mathrm{T}$ and 1$\mathrm{H}$ van der Waals layers is the focus of intense research. Here, we synthesize a novel self-stacked 6$\mathrm{R}$ phase in NbSeTe, showing a perfect alternating 1T and 1H layers that grow coherently along the c-direction, as revealed by scanning transmission electron microscopy. Angle resolved photoemission spectroscopy shows a mixed contribution of the trigonal and octahedral Nb bands to the Fermi level. Diffuse scattering reveals temperature-independent short-range charge fluctuations with propagation vector $\mathrm{q_{CO}}$=(0.25,0), derived from the condensation of a longitudinal mode in the 1T layer. We observe that ligand disorder quenches the formation of a charge density wave. Magnetization measurements suggest the presence of an inhomogeneous, short-range magnetic order, further supported by the absence of a clear phase transition in the specific heat. These experimental analyses in combination with \textit{ab initio} calculations indicate that the ground state of 6$\mathrm{R}$-NbSeTe is described by a statistical distribution of short-range charge-modulated and spin-correlated regions driven by ligand disorder. Our results devise a route to synthesize 1$\mathrm{T}$-1$\mathrm{H}$ self-stacked bulk heterostructures to study emergent phases of matter., Comment: 12 pages, including Supplementary Information. 4 figures + 6 supplementary figures

Denoising diffusion models have become ubiquitous for generative modeling. The core idea is to transport the data distribution to a Gaussian by using a diffusion. Approximate samples from the data distribution are then obtained by estimating the time-reversal of this diffusion using score matching ideas. We follow here a similar strategy to sample from unnormalized probability densities and compute their normalizing constants. However, the time-reversed diffusion is here simulated by using an original iterative particle scheme relying on a novel score matching loss. Contrary to standard denoising diffusion models, the resulting Particle Denoising Diffusion Sampler (PDDS) provides asymptotically consistent estimates under mild assumptions. We demonstrate PDDS on multimodal and high dimensional sampling tasks., Comment: To be published in ICML 2024. 37 pages, 20 figures, 3 tables, 5 algorithms

We refine and generalize what is known about coresets for classification problems via the sensitivity sampling framework. Such coresets seek the smallest possible subsets of input data, so one can optimize a loss function on the coreset and ensure approximation guarantees with respect to the original data. Our analysis provides the first no dimensional coresets, so the size does not depend on the dimension. Moreover, our results are general, apply for distributional input and can use iid samples, so provide sample complexity bounds, and work for a variety of loss functions. A key tool we develop is a Radamacher complexity version of the main sensitivity sampling approach, which can be of independent interest., Comment: 42 Pages

A longstanding belief holds that Bayesian Optimization (BO) with standard Gaussian processes (GP) -- referred to as standard BO -- underperforms in high-dimensional optimization problems. While this belief seems plausible, it lacks both robust empirical evidence and theoretical justification. To address this gap, we present a systematic investigation. First, through a comprehensive evaluation across eleven widely used benchmarks, we found that while the popular Square Exponential (SE) kernel often leads to poor performance, using Matern kernels enables standard BO to consistently achieve top-tier results, frequently surpassing methods specifically designed for high-dimensional optimization. Second, our theoretical analysis reveals that the SE kernels failure primarily stems from improper initialization of the length-scale parameters, which are commonly used in practice but can cause gradient vanishing in training. We provide a probabilistic bound to characterize this issue, showing that Matern kernels are less susceptible and can robustly handle much higher dimensions. Third, we propose a simple robust initialization strategy that dramatically improves the performance of the SE kernel, bringing it close to state of the art methods, without requiring any additional priors or regularization. We prove another probabilistic bound that demonstrates how the gradient vanishing issue can be effectively mitigated with our method. Our findings advocate for a re-evaluation of standard BOs potential in high-dimensional settings.

Artificially generated induced pluripotent stem cells (iPSCs) from somatic cells play an important role for disease modeling and drug screening of neurodegenerative diseases. Astrocytes differentiated from iPSCs are important targets to investigate neuronal metabolism. The astrocyte differentiation progress can be monitored through the variations of morphology observed from microscopy images at different differentiation stages, then determined by molecular biology techniques upon maturation. However, the astrocytes usually ``perfectly'' blend into the background and some of them are covered by interference information (i.e., dead cells, media sediments, and cell debris), which makes astrocytes difficult to observe. Due to the lack of annotated datasets, the existing state-of-the-art deep learning approaches cannot be used to address this issue. In this paper, we introduce a new task named astrocyte segmentation with a novel dataset, called IAI704, which contains 704 images and their corresponding pixel-level annotation masks. Moreover, a novel frequency domain denoising network, named FDNet, is proposed for astrocyte segmentation. In detail, our FDNet consists of a contextual information fusion module (CIF), an attention block (AB), and a Fourier transform block (FTB). CIF and AB fuse multi-scale feature embeddings to localize the astrocytes. FTB transforms feature embeddings into the frequency domain and conducts a high-pass filter to eliminate interference information. Experimental results demonstrate the superiority of our proposed FDNet over the state-of-the-art substitutes in astrocyte segmentation, shedding insights for iPSC differentiation progress prediction., Comment: Accepted by The IEEE International Symposium on Biomedical Imaging (ISBI) 2024

Theoretical physics suffered a major loss with the death of my dear friend Jan Zaanen on January 18. This note is my remembrance of him.

We reiterate the contribution made by Harrow, Hassidim, and Llyod to the quantum matrix equation solver with the emphasis on the algorithm description and the error analysis derivation details. Moreover, the behavior of the amplitudes of the phase register on the completion of the Quantum Phase Estimation is studied. This study is beneficial for the comprehension of the choice of the phase register size and its interrelation with the Hamiltonian simulation duration in the algorithm setup phase.

We present the first \emph{ab initio} calculation of elastic Compton scattering from 4He. It is carried out to $\mathcal{O}(e^2 \delta^3)$ [N3LO] in the $\delta$ expansion of $\chi$EFT. At this order and for this target, the only free parameters are the scalar-isoscalar electric and magnetic dipole polarisabilities of the nucleon. Adopting current values for these yields a parameter-free prediction. This compares favourably with the world data from HI$\gamma$S, Illinois and Lund for photon energies $50\;\mathrm{MeV}\lesssim\omega\lesssim120\;\mathrm{MeV}$ within our theoretical uncertainties of $\pm10\%$. We predict a cross section up to 7 times that for deuterium. As in 3He, this emphasises and tests the key role of meson-exchange currents between np pairs in Compton scattering on light nuclei. We assess the sensitivity of the cross section and beam asymmetry to the nucleon polarisabilities, providing clear guidance to future experiments seeking to further constrain them. The calculation becomes tractable by use of the Transition Density Method. The one- and two-body densities generated from 5 chiral potentials and the AV18$+$UIX potential are available using the python package provided at \url{https://pypi.org/project/nucdens/}., Comment: 38 pages LaTeX2e (pdflatex) including 13 figures as 14 .pdf files using includegraphics. Minor grammatical/typographical changes, figures 3, 4 and 7 typographically corrected without changes of substance. Text- and figure-identical to published version

The Hunting Outbursting Young Stars (HOYS) project performs long-term, optical, multi-filter, high cadence monitoring of 25 nearby young clusters and star forming regions. Utilising Gaia DR3 data we have identified about 17000 potential young stellar members in 45 coherent astrometric groups in these fields. Twenty one of them are clear young groups or clusters of stars within one kiloparsec and they contain 9143 Gaia selected potential members. The cluster distances, proper motions and membership numbers are determined. We analyse long term (about 7yr) V, R, and I-band light curves from HOYS for 1687 of the potential cluster members. One quarter of the stars are variable in all three optical filters, and two thirds of these have light curves that are symmetric around the mean. Light curves affected by obscuration from circumstellar materials are more common than those affected by accretion bursts, by a factor of 2-4. The variability fraction in the clusters ranges from 10 to almost 100 percent, and correlates positively with the fraction of stars with detectable inner disks, indicating that a lot of variability is driven by the disk. About one in six variables shows detectable periodicity, mostly caused by magnetic spots. Two thirds of the periodic variables with disk excess emission are slow rotators, and amongst the stars without disk excess two thirds are fast rotators - in agreement with rotation being slowed down by the presence of a disk., Comment: accepted for publication in MNRAS, 1 table, 9 figures

This study examines the use of embedded tweets in online news media. In particular, we add to the previous literature by exploring embedded tweets across reliable and unreliable news outlets. We use a mixed-method analysis to examine how the function and frequency of embedded tweets change across outlet reliability and news topic. We find that, no matter the outlet reliability, embedded tweets are most often used to relay the opinions of elites, to syndicate information from another news source, or to self-cite information an outlet previously produced. Our results also show some notable differences between reliable media and fringe media's use of tweets. Namely, fringe media embed tweets more and use those tweets as the source of news more than reliable media. Our work adds to the literature on hybrid media systems and the normalization of social media in journalism., Comment: MeLa Lab Preliminary Findings Report

For the vast majority of genes in sequenced genomes, there is limited understanding of how they are regulated. Without such knowledge, it is not possible to perform a quantitative theory-experiment dialogue on how such genes give rise to physiological and evolutionary adaptation. One category of high-throughput experiments used to understand the sequence-phenotype relationship of the transcriptome is massively parallel reporter assays (MPRAs). However, to improve the versatility and scalability of MPRA pipelines, we need a "theory of the experiment" to help us better understand the impact of various biological and experimental parameters on the interpretation of experimental data. To that end, in this paper we create tens of thousands of synthetic single-cell gene expression outputs using both equilibrium and out-of-equilibrium models. These models make it possible to imitate the summary statistics (information footprints and expression shift matrices) used to characterize the output of MPRAs and from this summary statistic to infer the underlying regulatory architecture. Specifically, we use a more refined implementation of the so-called thermodynamic models in which the binding energies of each sequence variant are derived from energy matrices. Our simulations reveal important effects of the parameters on MPRA data and we demonstrate our ability to optimize MPRA experimental designs with the goal of generating thermodynamic models of the transcriptome with base-pair specificity. Further, this approach makes it possible to carefully examine the mapping between mutations in binding sites and their corresponding expression profiles, a tool useful not only for better designing MPRAs, but also for exploring regulatory evolution.

The method and results of the first theory description of 4He Compton scattering at nuclear energies is presented, with a focus on figures. An upcoming publication [1] contains details and a comprehensive list of references., Comment: 6 pages LaTeX2e (pdflatex) including 4 figures as 6 .pdf files using includegraphics and webofc class. Contribution to the Proceedings of the 16th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU 2023), Mainz 16-20 October 2023

We present JWST spectral and photometric observations of the Type IIP supernova (SN) 2022acko at ~50 days past explosion. These data are the first JWST spectral observations of a core-collapse SN. We identify ~30 different H I features, other features associated with products produced from the CNO cycle, and s-process elements such as Sc II and Ba II. By combining the JWST spectra with ground-based optical and NIR spectra, we construct a full Spectral Energy Distribution from 0.4 to 25 microns and find that the JWST spectra are fully consistent with the simultaneous JWST photometry. The data lack signatures of CO formation and we estimate a limit on the CO mass of < 10^{-8} solar mass. We demonstrate how the CO fundamental band limits can be used to probe underlying physics during stellar evolution, explosion, and the environment. The observations indicate little mixing between the H envelope and C/O core in the ejecta and show no evidence of dust. The data presented here set a critical baseline for future JWST observations, where possible molecular and dust formation may be seen.

As deep neural networks become adopted in high-stakes domains, it is crucial to identify when inference inputs are Out-of-Distribution (OOD) so that users can be alerted of likely drops in performance and calibration despite high confidence -- ultimately to know when networks' decisions (and their uncertainty in those decisions) should be trusted. In this paper we introduce Ablated Learned Temperature Energy (or "AbeT" for short), an OOD detection method which lowers the False Positive Rate at 95\% True Positive Rate (FPR@95) by $43.43\%$ in classification compared to state of the art without training networks in multiple stages or requiring hyperparameters or test-time backward passes. We additionally provide empirical insights as to why our model learns to distinguish between In-Distribution (ID) and OOD samples while only being explicitly trained on ID samples via exposure to misclassified ID examples at training time. Lastly, we show the efficacy of our method in identifying predicted bounding boxes and pixels corresponding to OOD objects in object detection and semantic segmentation, respectively -- with an AUROC increase of $5.15\%$ in object detection and both a decrease in FPR@95 of $41.48\%$ and an increase in AUPRC of $34.20\%$ in semantic segmentation compared to previous state of the art.

Sleep behavior significantly impacts health and acts as an indicator of physical and mental well-being. Monitoring and predicting sleep behavior with ubiquitous sensors may therefore assist in both sleep management and tracking of related health conditions. While sleep behavior depends on, and is reflected in the physiology of a person, it is also impacted by external factors such as digital media usage, social network contagion, and the surrounding weather. In this work, we propose SleepNet, a system that exploits social contagion in sleep behavior through graph networks and integrates it with physiological and phone data extracted from ubiquitous mobile and wearable devices for predicting next-day sleep labels about sleep duration. Our architecture overcomes the limitations of large-scale graphs containing connections irrelevant to sleep behavior by devising an attention mechanism. The extensive experimental evaluation highlights the improvement provided by incorporating social networks in the model. Additionally, we conduct robustness analysis to demonstrate the system's performance in real-life conditions. The outcomes affirm the stability of SleepNet against perturbations in input data. Further analyses emphasize the significance of network topology in prediction performance revealing that users with higher eigenvalue centrality are more vulnerable to data perturbations., Comment: Accepted for publication in Proceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies (IMWUT), 8 (March 2024)

We present the $n$-orbital extension of the Hatsugai-Kohmoto (HK) model to the orbital HK (OHK) model which obtains by covering the Brillouin zone with $N/n$ Hubbard clusters each containing $n$-sites all connected via twisted boundary conditions. We show that this defines a systematic computational scheme to go from $n=1$ ``band'' HK to the full Hubbard model. Further, through powerful scaling arguments, we show that the convergence to Hubbard goes as $1/n^{2d}$ for $n^d$-orbital HK on a $d$-dimensional system implying that all the fluctuations vanish in $d=\infty$. As evidence for the above, we employ exact diagonalization and DMRG to show that the OHK model matches the exact (from Bethe ansatz) ground state energy of the 1d Hubbard model within 1$\%$ with just $n=10$ orbitals. For a square lattice, we recover an insulating state regardless of the strength of the interactions, double occupancy in agreement with state of the art simulations, dynamical spectral weight transfer, short-range antiferromagnetic correlations and charge neutral excitations leading to the algebraic temperature dependence of the specific heat, all with a fraction of the computational time of more advanced cluster methods and making it possible to obtain analytical insights. The success of OHK and its rapid convergence to the Hubbard model reiterates that a fixed point controls the physics. Consequently, the $n$-orbital HK model offers a new tool for strongly correlated quantum matter., Comment: 7 pages + supplement (greatly expanded revision)

In biological systems, molecular-scale forces and motions are pivotal for enabling processes like motility, shape change, and replication. These forces and motions are organized, amplified, and transmitted across macroscopic scales by active materials such as the cytoskeleton, which drives micron-scale cellular movement and re-organization. Despite the integral role of active materials, understanding how molecular-scale interactions alter macroscopic structure and force propagation remains elusive. This knowledge gap presents challenges to the harnessing and regulation of such dynamics across diverse length scales. Here, we demonstrate how mediating the bundling of microtubules can shift active matter between a global force-transmitting phase and a local force-dissipating phase. A fivefold increase in microtubule effective length results in the transition from local to global phase with a hundredfold increase in velocity autocorrelation. Through theory and simulation, we identify signatures of a percolation-driven transition between the two phases. This provides evidence for how force propagation can be generated when local molecular interactions reach a sufficient length scale. We show that force propagation in the active matter system enables material transport. Consequently, we demonstrate that the global phase is capable of facilitating millimeter-scale human cell transport and manipulation, as well as powering the movement of aqueous droplets. These findings underscore the potential for designing active materials capable of force organization and transmission. Our results lay the foundation for further exploration into the organization and propagation of forces/stresses in biological systems, thereby paving the way for the engineering of active materials in synthetic biology and soft robotics., Comment: 15 pages, 4 figrues

We show here that numerous examples abound where changing topology does not necessarily close the bulk insulating charge gap as demanded in the standard non-interacting picture. From extensive determinantal and dynamical cluster quantum Monte Carlo simulations of the half-filled and quarter-filled Kane-Mele-Hubbard model, we show that for sufficiently strong interactions at either half- or quarter-filling, a transition between topological and trivial insulators occurs without the closing of a charge gap. To shed light on this behavior, we illustrate that an exactly solvable model reveals that while the single-particle gap remains, the many-body gap does in fact close. These two gaps are the same in the non-interacting system but depart from each other as the interaction turns on. We purport that for interacting systems, the proper probe of topological phase transitions is the closing of the many-body rather than the single-particle gap.

The paper provides an elementary proof establishing a sharp universal bound on the $(d-1)$-Hausdorff measure of the zeros of any nontrivial multivariable polynomial $p:\mathbb{R}^d\to\mathbb{R}$ within a $d$-dimensional cube of size $r$. This bound depends solely on the parameter $r$, the dimension $d$, and the degrees of $p$.

We report the formation of Mn-rich regions at the interface of Co2FexMn1-xSi thin films grown on GaAs substrates by molecular beam epitaxy (MBE). Scanning transmission electron microscopy (STEM) with electron energy loss (EEL) spectrum imaging reveals that each interfacial region: (1) is 1-2 nm wide, (2) occurs irrespective of the Fe/Mn composition ratio and in both Co-rich and Co-poor films, and (3) displaces both Co and Fe indiscriminately. We also observe a Mn-depleted region in each film directly above each Mn-rich interfacial layer, roughly 3 nm in width in the x = 0 and x = 0.3 films, and 1 nm in the x = 0.7 (less Mn) film. We posit that growth energetics favor Mn diffusion to the interface even when there is no significant Ga interdiffusion into the epitaxial film. Element-specific X-ray magnetic circular dichroism (XMCD) measurements show larger Co, Fe, and Mn orbital to spin magnetic moment ratios compared to bulk values across the Co2FexMn1-xSi compositional range. The values lie between reported values for pure bulk and nanostructured Co, Fe, and Mn materials, corroborating the non-uniform, layered nature of the material on the nanoscale. Finally, SQUID magnetometry demonstrates that the films deviate from the Slater-Pauling rule for uniform films of both the expected and the measured composition. The results inform a need for care and increased scrutiny when forming Mn-based magnetic thin films on III-V semiconductors like GaAs, particularly when films are on the order of 5 nm or when interface composition is critical to spin transport or other device applications.

We construct an uncountable family of pairwise nonisomorphic AH algebras with the same Elliott invariant and same radius of comparison. They can be distinguished by a local radius of comparison function, naturally defined on the positive cone of the K_0 group., Comment: 34 pages; added some details and corrected misprints

We study loops which are universal (that is, isotopically invariant) with respect to the property of flexibility ($xy\cdot x = x\cdot yx$). We also weaken this to semi-universality, that is, loops in which every left and right isotope is flexible, but not necessarily every isotope. One of our main results is that universally flexible, inverse property loops are Moufang loops. On the other hand, semi-universally flexible, inverse property loops are diassociative. We also examine the relationship between universally flexible loops and middle Bol loops. The paper concludes with some open problems., Comment: 13pp