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If $\mathscr A$ is a set of natural numbers of exponential density $\delta$, then the exponential density of all numbers of the form $x^3+a$ with $x\in\mathbb N$ and $a\in\mathscr A$ is at least $\min(1, \frac 13+\frac 56 \delta)$. This is a considerable improvement on the previous best lower bounds for this problem, obtained by Davenport more than 80 years ago. The result is the best possible for $\delta\ge \frac 45$., Comment: 27 pages, 16 references

Atmospheres above lava-ocean planets (LOPs) hold clues as to the properties of their interiors, owing to the expectation that the two reservoirs are in chemical equilibrium. Here we consider `mineral' atmospheres produced in equilibrium with silicate liquids. We treat oxygen fugacity ($f$O$_2$) as an independent variable, together with temperature ($T$) and composition ($X$), to compute equilibrium partial pressures ($p$) of stable gas species at the liquid-gas interface. Above this boundary, the atmospheric speciation and the pressure-temperature structure are computed self-consistently to yield emission spectra. We explore a wide array of plausible compositions, oxygen fugacities (between 6 log$_{10}$ units below- and above the iron-w\"ustite buffer, IW) and irradiation temperatures (2000, 2500, 3000 and 3500 K) relevant to LOPs. We find that SiO(g), Fe(g) and Mg(g) are the major species below $\sim$IW, ceding to O$_2$(g) and O(g) in more oxidised atmospheres. The transition between the two regimes demarcates a minimum in total pressure ($P$). Because $p$ scales linearly with $X$, emission spectra are only modest functions of composition. By contrast, $f$O$_2$ can vary over orders of magnitude, thus causing commensurate changes in $p$. Reducing atmospheres show intense SiO emission, creating a temperature inversion in the upper atmosphere. Conversely, oxidised atmospheres have lower $p$SiO and lack thermal inversions, with resulting emission spectra that mimic that of a black body. Consequently, the intensity of SiO emission relative to the background, generated by MgO(g), can be used to quantify the $f$O$_2$ of the atmosphere. Depending on the emission spectroscopy metric of the target, deriving the $f$O$_2$ of known nearby LOPs is possible with a few secondary occultations observed by JWST.

We consider a downlink (DL) massive multiple-input multiple-output (MIMO) system, where different users have different mobility profiles. To support this system, we categorize the users into two disjoint groups according to their mobility profile and implement a hybrid orthogonal time frequency space (OTFS)/orthogonal frequency division multiplexing (OFDM) modulation scheme. Building upon this framework, two precoding designs, namely full-pilot zero-forcing (FZF) precoding and partial zero-forcing (PZF) precoding are considered. To shed light on the system performance, the spectral efficiency (SE) with a minimum-mean-square-error (MMSE)-successive interference cancellation (SIC) detector is investigated. Closed-form expressions for the SE are obtained using some tight mathematical approximations. To improve fairness among different users, we consider max-min power control for both precoding schemes based on the closed-form SE expression. However, by noting the large performance gap for different groups of users with PZF precoding, the per-user SE will be compromised when pursuing overall fairness. Therefore, we propose a weighted max-min power control scheme. By introducing a weighting coefficient, the trade-off between the per-user performance and fairness can be enhanced. Our numerical results confirm the theoretical analysis and reveal that with mobility-based grouping, the proposed hybrid OTFS/OFDM modulation significantly outperforms the conventional OFDM modulation for high-mobility users.

Realising quantum control and entanglement of particles is crucial for advancing both quantum technologies and fundamental science. Significant developments in this domain have been achieved in a variety of systems. In this context, ultracold polar molecules offer new and unique opportunities due to their more complex internal structure associated with vibration and rotation, coupled to the existence of long-range interactions. However, the same properties make molecules highly sensitive to their environment, impacting their coherence and utility in some applications. Here we show that by engineering an exceptionally controlled environment using rotationally-magic optical tweezers, we can achieve long-lived entanglement between pairs of molecules using hertz-scale interactions. We demonstrate the highest reported fidelity to date for a two-molecule Bell state ($0.976^{+0.014}_{-0.016}$) and present the first realisation of a microwave-driven entangling gate between two molecules, preparing the molecules in a decoherence-free subspace. We show that the magic-wavelength trap preserves the entanglement, with no measurable decay over 0.5 s, opening new avenues for quantum-enhanced metrology, ultracold chemistry and the use of rotational states for quantum simulation, quantum computation and as quantum memories. The extension of precise quantum control to complex molecular systems will allow their additional degrees of freedom to be exploited across many domains of quantum science., Comment: 15 pages, 6 figures

Many experimental platforms for quantum science depend on state control via laser fields. Frequently, however, the control fidelity is limited by optical phase noise. This is exacerbated in stabilized laser systems where high-frequency phase noise is an unavoidable consequence of feedback. Here we implement an optical feedforward technique to suppress laser phase noise in the STIRAP state transfer of ultracold RbCs molecules, across 114 THz, from a weakly bound Feshbach state to the rovibrational ground state. By performing over 100 state transfers on single molecules, we measure a significantly enhanced transfer efficiency of 98.7(1)% limited only by available laser intensity.

In pulmonary tracheal segmentation, the scarcity of annotated data is a prevalent issue in medical segmentation. Additionally, Deep Learning (DL) methods face challenges: the opacity of 'black box' models and the need for performance enhancement. Our Human-Computer Interaction (HCI) based models (RS_UNet, LC_UNet, UUNet, and WD_UNet) address these challenges by combining diverse query strategies with various DL models. We train four HCI models and repeat these steps: (1) Query Strategy: The HCI models select samples that provide the most additional representative information when labeled in each iteration and identify unlabeled samples with the greatest predictive disparity using Wasserstein Distance, Least Confidence, Entropy Sampling, and Random Sampling. (2) Central line correction: Selected samples are used for expert correction of system-generated tracheal central lines in each training round. (3) Update training dataset: Experts update the training dataset after each DL model's training epoch, enhancing the trustworthiness and performance of the models. (4) Model training: The HCI model is trained using the updated dataset and an enhanced UNet version. Experimental results confirm the effectiveness of these HCI-based approaches, showing that WD-UNet, LC-UNet, UUNet, and RS-UNet achieve comparable or superior performance to state-of-the-art DL models. Notably, WD-UNet achieves this with only 15%-35% of the training data, reducing physician annotation time by 65%-85%.

Past studies show that coupled model biases in European blocking and North Atlantic eddy-driven jet variability decrease as one increases the horizontal resolution in the atmospheric and oceanic model components. This has commonly been argued to be related to an alleviation of sea surface temperature (SST) biases due to increased oceanic resolution in particular, with a physical pathway via changes to surface baroclinicity. On the other hand, many studies have now highlighted the key role of diabatic processes in the Gulf Stream region on blocking formation and maintenance. Here, following recent work by Schemm, we leverage a large multi-model ensemble to show that Gulf Stream precipitation variability in coupled models is tightly linked to the simulated frequency of European blocking and northern jet excursions. Furthermore, the reduced biases in blocking and jet variability are consistent with greater precipitation variability as a result of increased atmospheric horizontal resolution. By contrast, typical North Atlantic SST biases are found to share only a weak or negligible relationship with blocking and jet biases. Finally, while previous studies have used a comparison between coupled models and models run with prescribed SSTs to argue for the role of ocean resolution, we emphasise here that models run with prescribed SSTs experience greatly reduced precipitation variability due to their excessive thermal damping, making it unclear if such a comparison is meaningful. Instead, we speculate that most of the reduction in coupled model biases may actually be due to increased atmospheric resolution., Comment: Submitted for review

Distributed acoustic sensing through fiber-optical cables can contribute to traffic monitoring systems. Using data from a day of field testing on a 50 km long fiber-optic cable along a railroad track in Norway, we detect and track cars and trains along a segment of the fiber-optic cable where the road runs parallel to the railroad tracks. We develop a method for automatic detection of events and then use these in a Kalman filter variant known as joint probabilistic data association for object tracking and classification. Model parameters are specified using in-situ log data along with the fiber-optic signals. Running the algorithm over an entire day, we highlight results of counting cars and trains over time and their estimated velocities.

We report on the discovery and validation of a transiting long-period mini-Neptune orbiting a bright (V = 9.0 mag) G dwarf (TOI 4633; R = 1.05 RSun, M = 1.10 MSun). The planet was identified in data from the Transiting Exoplanet Survey Satellite by citizen scientists taking part in the Planet Hunters TESS project. Modeling of the transit events yields an orbital period of 271.9445 +/- 0.0040 days and radius of 3.2 +/- 0.20 REarth. The Earth-like orbital period and an incident flux of 1.56 +/- 0.2 places it in the optimistic habitable zone around the star. Doppler spectroscopy of the system allowed us to place an upper mass limit on the transiting planet and revealed a non-transiting planet candidate in the system with a period of 34.15 +/- 0.15 days. Furthermore, the combination of archival data dating back to 1905 with new high angular resolution imaging revealed a stellar companion orbiting the primary star with an orbital period of around 230 years and an eccentricity of about 0.9. The long period of the transiting planet, combined with the high eccentricity and close approach of the companion star makes this a valuable system for testing the formation and stability of planets in binary systems., Comment: 24 pages, 16 figures, 4 tables

Avian-informed drones feature morphing wing and tail surfaces, enhancing agility and adaptability in flight. Despite their large potential, realising their full capabilities remains challenging due to the lack of generalized control strategies accommodating their large degrees of freedom and cross-coupling effects between their control surfaces. Here we propose a new body-rate controller for avian-informed drones that uses all available actuators to control the motion of the drone. The method exhibits robustness against physical perturbations, turbulent airflow, and even loss of certain actuators mid-flight. Furthermore, wing and tail morphing is leveraged to enhance energy efficiency at 8m/s, 10m/s and 12m/s using in-flight Bayesian optimization. The resulting morphing configurations yield significant gains across all three speeds of up to 11.5% compared to non-morphing configurations and display a strong resemblance to avian flight at different speeds. This research lays the groundwork for the development of autonomous avian-informed drones that operate under diverse wind conditions, emphasizing the role of morphing in improving energy efficiency., Comment: 22 pages, 9 figures

Each medical segmentation task should be considered with a specific AI algorithm based on its scenario so that the most accurate prediction model can be obtained. The most popular algorithms in medical segmentation, 3D U-Net and its variants, can directly implement the task of lung trachea segmentation, but its failure to consider the special tree-like structure of the trachea suggests that there is much room for improvement in its segmentation accuracy. Therefore, a research gap exists because a great amount of state-of-the-art DL algorithms are vanilla 3D U-Net structures, which do not introduce the various performance-enhancing modules that come with special natural image modality in lung airway segmentation. In this paper, we proposed two different network structures Branch-Level U-Net (B-UNet) and Branch-Level CE-UNet (B-CE-UNet) which are based on U-Net structure and compared the prediction results with the same dataset. Specially, both of the two networks add branch loss and central line loss to learn the feature of fine branch endings of the airways. Uncertainty estimation algorithms are also included to attain confident predictions and thereby, increase the overall trustworthiness of our whole model. In addition, predictions of the lung trachea based on the maximum connectivity rate were calculated and extracted during post-processing for segmentation refinement and pruning.

Control over the quantum states of individual molecules is crucial in the quest to harness their rich internal structure and dipolar interactions for applications in quantum science. In this paper, we develop a toolbox of techniques for the control and readout of individually trapped polar molecules in an array of optical tweezers. Starting with arrays of up to eight Rb and eight Cs atoms, we assemble arrays of RbCs molecules in their rovibrational and hyperfine ground state with an overall efficiency of 48(2)%. We demonstrate global microwave control of multiple rotational states of the molecules and use an auxiliary tweezer array to implement site-resolved addressing and state control. We show how the rotational state of the molecule can be mapped onto the position of Rb atoms and use this capability to readout multiple rotational states in a single experimental run. Further, using a scheme for the mid-sequence detection of molecule formation errors, we perform rearrangement of assembled molecules to prepare small defect-free arrays. Finally, we discuss a feasible route to scaling to larger arrays of molecules., Comment: 18 pages, 8 figures. Updated bibliography

Ultracold molecules confined in optical lattices or tweezer traps can be used to process quantum information and simulate the behaviour of many-body quantum systems. Molecules offer several advantages for these applications. They have a large set of stable states with strong transitions between them and long coherence times. They can be prepared in a chosen state with high fidelity, and the state populations can be measured efficiently. They have controllable long-range dipole-dipole interactions that can be used to entangle pairs of molecules and generate interesting many-body states. We review the advances that have been made and the challenges still to overcome, and describe the new ideas that will unlock the full potential of the field., Comment: 15 pages, 4 figures. Comments welcome

We report on a study of modulation transfer spectroscopy of the $4\textrm{S}_{1/2}\rightarrow 4\textrm{P}_{1/2}$ ($D_{1}$) transition of naturally abundant potassium in a room-temperature vapour cell. This transition is critical for laser cooling and optical pumping of potassium and our study is therefore motivated by the need for robust laser frequency stabilisation. Despite the absence of a closed transition, the small ground-state hyperfine splitting in potassium results in strong crossover features in the $D_{1}$ modulation transfer spectrum. To emphasise this we compare the $D_{1}$ and $D_{2}$ spectra of potassium with those of rubidium. Further, we compare our experimental results with a detailed theoretical simulation, examining different pump-probe polarization configurations to identify the optimal signals for laser frequency stabilisation. We find good agreement between the experiment and the theory, especially for the $\textrm{lin} \parallel \textrm{lin}$ polarization configuration.

In this paper, we consider a downlink (DL) massive multiple-input multiple-output (MIMO) system, where different users have different mobility profiles. To support this system, we propose to use a hybrid orthogonal time frequency space (OTFS)/orthogonal frequency division multiplexing (OFDM) modulation scheme, where OTFS is applied for high-mobility users and OFDM is used for low-mobility users. Two precoding designs, namely full zero-forcing (FZF) precoding and partial zero-forcing (PZF) precoding, are considered and analyzed in terms of per-user spectral efficiency (SE). With FZF, interference among users is totally eliminated at the cost of high computational complexity, while PZF can be used to provide a trade-off between complexity and performance. To apply PZF precoding, users are grouped into two disjoint groups according to their mobility profile or channel gain. Then, zero-forcing (ZF) is utilized for high-mobility or strong channel gain users to completely cancel the inter-group interference, while maximum ratio transmission (MRT) is applied for low-mobility users or users with weak channel gain. To shed light on the system performance, the SE for high-mobility and low-mobility users with a minimum-mean-square-error (MMSE)-successive interference cancellation (SIC) detector is investigated. Our numerical results reveal that the PZF precoding with channel gain grouping can guarantee a similar quality of service for all users. In addition, with mobility-based grouping, the hybrid OTFS/OFDM modulation outperforms the conventional OFDM modulation for high-mobility users.

Ultra-hot Jupiters are tidally locked with their host stars dividing their atmospheres into a hot dayside and a colder nightside. As the planet moves through transit, different regions of the atmosphere rotate into view revealing different chemical regimes. High-resolution spectrographs can observe asymmetries and velocity shifts, and offer the possibility for time-resolved spectroscopy. In this study, we search for other atoms and molecules in the planet`s transmission spectrum and investigate asymmetric signals. We analyse and combine eight transits of the ultra-hot Jupiter WASP-189 b taken with the HARPS, HARPS-N, ESPRESSO and MAROON-X high-resolution spectrographs. Using the cross-correlation technique, we search for neutral and ionised atoms, and oxides and compare the obtained signals to model predictions. We report significant detections for H, Na, Mg, Ca, Ca+, Ti, Ti+, TiO, V, Cr, Mn, Fe, Fe+, Ni, Sr, Sr+, and Ba+. Of these, Sr, Sr+, and Ba+ are detected for the first time in the transmission spectrum of WASP-189 b. In addition, we robustly confirm the detection of titanium oxide based on observations with HARPS and HARPS-N using the follow-up observations performed with MAROON-X and ESPRESSO. By fitting the orbital traces of the detected species by means of time-resolved spectroscopy using a Bayesian framework, we infer posterior distributions for orbital parameters as well as lineshapes. Our results indicate that different species must originate from different regions of the atmosphere to be able to explain the observed time dependence of the signals. Throughout the course of the transit, most signal strengths are expected to increase due to the larger atmospheric scale height at the hotter trailing terminator. For some species, however, the signals are instead observed to weaken due to ionisation for atoms and their ions, or the dissociation of molecules on the dayside., Comment: 38 pages, 34 figures, published in A&A on October 24, 2023

We report on the transport of ultracold cesium and rubidium atoms over $37.2\,$cm in under $25\,$ms using an optical conveyor belt formed by two counter-propagating beams with a controllable frequency difference that generate a movable optical lattice. By carefully selecting the waists and focus positions, we are able to use two static Gaussian beams for the transport, avoiding the need for a Bessel beam or vari-focus lenses. We characterize the transport efficiency for both species, including a comparison of different transport trajectories, gaining insight into the loss mechanisms and finding the minimum jerk trajectory to be optimum. Using the optimized parameters, we are able to transport up to $7 \times 10^6$ cesium or rubidium atoms with an efficiency up to $75\,$%. To demonstrate the viability of our transport scheme for experiments employing quantum gas microscopy, we produce Bose-Einstein condensates of either species after transport and present measurements of the simultaneous transport of both species., Comment: 15 pages, 10 figures

Let E be an elliptic curve defined by a Weierstrass equation with integer coefficients. Any rational point on E other than the identity is of the form $ ( x(P) / z(P)^2 , y(P) / z(P)^3 ) $ where $ x(P), y(P) \in \mathbb Z $ and $ z(P) \in \mathbb N $ and in addition both $ \gcd( x(P) , z(P) ) = 1 $ and $ \gcd( y(P) , z(P) ) = 1 $ hold. The question is: how often is $ z(P) $ a prime number?, Comment: 3 pages. This is a slightly edited version of an open question I submitted to the problem session of the JA2023 conference, where it was communicated by Michel Waldschmidt

Ultracold polar molecules uniquely combine a rich structure of long-lived internal states with access to controllable long-range, anisotropic dipole-dipole interactions. In particular, the rotational states of polar molecules confined in optical tweezers or optical lattices may be used to encode interacting qubits for quantum computation or pseudo-spins for simulating quantum magnetism. As with all quantum platforms, the engineering of robust coherent superpositions of states is vital. However, for optically trapped molecules, the coherence time between rotational states is typically limited by inhomogeneous light shifts. Here we demonstrate a rotationally-magic optical trap for RbCs molecules that supports a Ramsey coherence time of 0.78(4) seconds in the absence of dipole-dipole interactions. This extends to >1.4 seconds at the 95% confidence level using a single spin-echo pulse. In our magic trap, dipolar interactions become the dominant mechanism by which Ramsey contrast is lost for superpositions that generate oscillating dipoles. By changing the states forming the superposition, we tune the effective dipole moment and show that the coherence time is inversely proportional to the strength of the dipolar interaction. Our work unlocks the full potential of the rotational degree of freedom in molecules for quantum computation and quantum simulation., Comment: 12 pages, 7 figures (main text and supplementary information combined)

We identify a route for the production of $^{87}$Rb$^{133}$Cs molecules in the $\textrm{X} \, ^1\Sigma^+$ rovibronic ground state that is compatible with efficient mixing of the atoms in optical lattices. We first construct a model for the excited-state structure using constants found by fitting to spectroscopy of the relevant $\textrm{a} \, ^3\Sigma^+ \rightarrow \textrm{b} \, ^3\Pi_1$ transitions at 181.5 G and 217.1 G. We then compare the predicted transition dipole matrix elements from this model to those found for the transitions that have been successfully used for STIRAP at 181.5 G. We form molecules by magnetoassociation on a broad interspecies Feshbach resonance at 352.7 G and explore the pattern of Feshbach states near 305 G. This allows us to navigate to a suitable initial state for STIRAP by jumping across an avoided crossing with radiofrequency radiation. We identify suitable transitions for STIRAP at 305 G. We characterize these transitions experimentally and demonstrate STIRAP to a single hyperfine level of the ground state with a one-way efficiency of 85(4)%., Comment: 21 pages, 8 figures

We demonstrate Rydberg blockade due to the charge-dipole interaction between a single Rb atom and a single RbCs molecule confined in optical tweezers. The molecule is formed by magnetoassociation of a Rb+Cs atom pair and subsequently transferred to the rovibrational ground state with an efficiency of 91(1)\%. Species-specific tweezers are used to control the separation between the atom and molecule. The charge-dipole interaction causes blockade of the transition to the Rb(52s) Rydberg state, when the atom-molecule separation is set to $310(40)$~nm. The observed excitation dynamics are in good agreement with simulations using calculated interaction potentials. Our results open up the prospect of a hybrid platform where quantum information is transferred between individually trapped molecules using Rydberg atoms., Comment: Main text contains 8 pages, 4 figures. Supplementary material is 13 pages containing 10 figures

We examine to what extent disk and outflow models can reproduce observations of H I gas within a few virial radii of galaxies in pairs and groups. Using highly-sensitive HST/COS and FOS spectra of the Q0107 quasar triplet covering Ly$\alpha$ for z$\lesssim$1, as well as a deep galaxy redshift survey including VIMOS, DEIMOS, GMOS and MUSE data, we test simple disk and outflow models against the H I absorption along three lines-of-sight (separated by 200-500 kpc) through nine galaxy groups in this field. These can be compared with our previous results in which these models can often be fit to the absorption around isolated galaxies. Our models can reproduce $\approx$ 75$\%$ of the 28 identified absorption components within 500 km/s of a group galaxy, so most of the H I around groups is consistent with a superposition of the CGM of the individual galaxies. Gas stripped in interactions between galaxies may be a plausible explanation for some of the remaining absorption, but neither the galaxy images nor the galaxy and absorber kinematics provide clear evidence of such stripped material, and these unexplained absorbers do not preferentially occur around close pairs of galaxies. We find H I column densities typically higher than at similar impact parameters around isolated galaxies ($\approx$ 2.5$\sigma$), as well as more frequent detections of O VI than around isolated galaxies (30$\%$ of sightlines to 7$\%$)., Comment: 33 pages, 15 figures (main text 22 pages, 9 figures). Accepted for publication in MNRAS

We demonstrate the formation of a single RbCs molecule during the merging of two optical tweezers, one containing a single Rb atom and the other a single Cs atom. Both atoms are initially predominantly in the motional ground states of their respective tweezers. We confirm molecule formation and establish the state of the molecule formed by measuring its binding energy. We find that the probability of molecule formation can be controlled by tuning the confinement of the traps during the merging process, in good agreement with coupled-channel calculations. We show that the conversion efficiency from atoms to molecules using this technique is comparable to magnetoassociation., Comment: 14 pages, 10 figures

We present extremely deep Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) observations of the MUSE Ultra Deep Field (MUDF). This unique region of the sky contains two quasars at $z \approx$ 3.22 that are separated by only $\sim$500 kpc, providing a stereoscopic view of gas and galaxies in emission and absorption across $\sim$10 billion years of cosmic time. We have obtained 90 orbits of HST WFC3 G141 near-infrared grism spectroscopy of this field in a single pointing, as well as 142 hours of optical spectroscopy with the Very Large Telescope (VLT) Multi Unit Spectroscopic Explorer (MUSE). The WFC3 (F140W, F125W, and F336W) and archival WFPC2 (F702W and F450W) imaging provides five-filter photometry that we use to detect 3,375 sources between $z \approx$ 0 - 6, including 1,536 objects in a deep central pointing with both spectroscopic and photometric coverage. The F140W and F336W mosaics reach exceptional depths of $m_\mathrm{AB}\approx$ 28 and 29, respectively, providing near-infrared and rest-frame ultraviolet information for 1,580 sources, and we reach 5$\sigma$ continuum detections for objects as faint as $m_\mathrm{AB}\approx$ 27 in the grism spectra. The extensive wavelength coverage of MUSE and WFC3 allows us to measure spectroscopic redshifts for 419 sources, down to galaxy stellar masses of log(M/M$_{\odot}$) $\approx$ 7 at $z \approx$ 1 - 2. In this publication, we provide the calibrated HST data and source catalogs as High Level Science Products for use by the community, which includes photometry, morphology, and redshift measurements that enable a variety of studies aimed at advancing our models of galaxy formation and evolution in different environments., Comment: Accepted for publication in ApJS on February 1, 2023. The paper has 25 pages, 13 figures, and 7 tables. Version two includes minor corrections to match the journal publication. The calibrated data are available through MAST at: https://archive.stsci.edu/hlsp/mudf

We present a simple motorised rotation mount for a half-wave plate that can be used to rapidly change the polarization of light. We use the device to switch a high power laser beam between different optical dipole traps in an ultracold atom experiment. The device uses a stepper motor with a hollow shaft, which allows a beam to propagate along the axis of the motor shaft, minimising inertia and mechanical complexity. A simple machined adapter is used to mount the wave plate. We characterise the performance of the device, focusing on its capability to switch a beam between the output ports of a polarizing beamsplitter cube. We demonstrate a switching time of 15.9(3) ms, limited by the torque of the motor. The mount has a reaction time of 0.52(3) ms, and a rotational resolution of 0.45 degrees. The rotation is highly reproducible, with the stepper motor not missing a step in 2000 repeated tests over 11 hours., Comment: 5 pages, 4 figures, Submitted to Review of Scientific Instruments

We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. Under such an assumption, this work builds upon a recently introduced multi-index Sequential Monte Carlo (SMC) ratio estimator, which provably enjoys the complexity improvements of multi-index Monte Carlo (MIMC) and the efficiency of SMC for inference. The present work leverages a randomization strategy to remove bias entirely, which simplifies estimation substantially, particularly in the MIMC context, where the choice of index set is otherwise important. Under reasonable assumptions, the proposed method provably achieves the same canonical complexity of MSE$^{-1}$ as the original method (where MSE is mean squared error), but without discretization bias. It is illustrated on examples of Bayesian inverse and spatial statistics problems., Comment: 27 pages 8 figures

Sleep plays a crucial role in the well-being of human lives. Traditional sleep studies using Polysomnography are associated with discomfort and often lower sleep quality caused by the acquisition setup. Previous works have focused on developing less obtrusive methods to conduct high-quality sleep studies, and ear-EEG is among popular alternatives. However, the performance of sleep staging based on ear-EEG is still inferior to scalp-EEG based sleep staging. In order to address the performance gap between scalp-EEG and ear-EEG based sleep staging, we propose a cross-modal knowledge distillation strategy, which is a domain adaptation approach. Our experiments and analysis validate the effectiveness of the proposed approach with existing architectures, where it enhances the accuracy of the ear-EEG based sleep staging by 3.46% and Cohen's kappa coefficient by a margin of 0.038., Comment: Code available at : https://github.com/Mithunjha/EarEEG_KnowledgeDistillation

Bayesian Optimisation (BO) methods seek to find global optima of objective functions which are only available as a black-box or are expensive to evaluate. Such methods construct a surrogate model for the objective function, quantifying the uncertainty in that surrogate through Bayesian inference. Objective evaluations are sequentially determined by maximising an acquisition function at each step. However, this ancilliary optimisation problem can be highly non-trivial to solve, due to the non-convexity of the acquisition function, particularly in the case of batch Bayesian optimisation, where multiple points are selected in every step. In this work we reformulate batch BO as an optimisation problem over the space of probability measures. We construct a new acquisition function based on multipoint expected improvement which is convex over the space of probability measures. Practical schemes for solving this `inner' optimisation problem arise naturally as gradient flows of this objective function. We demonstrate the efficacy of this new method on different benchmark functions and compare with state-of-the-art batch BO methods.