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In this letter, we demonstrate for the first time the creation of Josephson-like superconducting nanojunctions using a thermal scanning probe to directly inscribe weak links into microstrips of YBa2Cu3O7-x (YBCO). Our method effectively reduces the critical current (Ic) over an order of magnitude. The resulting nanobridges exhibit clear evidence of Josephson effects, of SNS-type junctions, as shown by both the DC and AC Josephson effects. This approach provides a novel and flexible method for scaling up quantum mechanical circuits that operate at liquid nitrogen temperatures. Additionally, it offers a promising pathway for modifying properties of the junctions in-situ and post fabrication., Comment: 14 pages, 4 figures

Diffusion-weighted MRI is increasingly used to study the normal and abnormal development of fetal brain in-utero. Recent studies have shown that dMRI can offer invaluable insights into the neurodevelopmental processes in the fetal stage. However, because of the low data quality and rapid brain development, reliable analysis of fetal dMRI data requires dedicated computational methods that are currently unavailable. The lack of automated methods for fast, accurate, and reproducible data analysis has seriously limited our ability to tap the potential of fetal brain dMRI for medical and scientific applications. In this work, we developed and validated a unified computational framework to (1) segment the brain tissue into white matter, cortical/subcortical gray matter, and cerebrospinal fluid, (2) segment 31 distinct white matter tracts, and (3) parcellate the brain's cortex and delineate the deep gray nuclei and white matter structures into 96 anatomically meaningful regions. We utilized a set of manual, semi-automatic, and automatic approaches to annotate 97 fetal brains. Using these labels, we developed and validated a multi-task deep learning method to perform the three computations. Our evaluations show that the new method can accurately carry out all three tasks, achieving a mean Dice similarity coefficient of 0.865 on tissue segmentation, 0.825 on white matter tract segmentation, and 0.819 on parcellation. The proposed method can greatly advance the field of fetal neuroimaging as it can lead to substantial improvements in fetal brain tractography, tract-specific analysis, and structural connectivity assessment.

Diffusion-weighted magnetic resonance imaging (dMRI) is the only non-invasive tool for studying white matter tracts and structural connectivity of the brain. These assessments rely heavily on tractography techniques, which reconstruct virtual streamlines representing white matter fibers. Much effort has been devoted to improving tractography methodology for adult brains, while tractography of the fetal brain has been largely neglected. Fetal tractography faces unique difficulties due to low dMRI signal quality, immature and rapidly developing brain structures, and paucity of reference data. This work presents the first machine learning model for fetal tractography. The model input consists of five sources of information: (1) Fiber orientation, inferred from a diffusion tensor fit to the dMRI signal; (2) Directions of recent propagation steps; (3) Global spatial information, encoded as distances to keypoints in the brain cortex; (4) Tissue segmentation information; and (5) Prior information about the expected local fiber orientations supplied with an atlas. In order to mitigate the local tensor estimation error, a large spatial context around the current point in the diffusion tensor image is encoded using convolutional and attention neural network modules. Moreover, the diffusion tensor information at a hypothetical next point is included in the model input. Filtering rules based on anatomically constrained tractography are applied to prune implausible streamlines. We trained the model on manually-refined whole-brain fetal tractograms and validated the trained model on an independent set of 11 test scans with gestational ages between 23 and 36 weeks. Results show that our proposed method achieves superior performance across all evaluated tracts. The new method can significantly advance the capabilities of dMRI for studying normal and abnormal brain development in utero.

There is a growing interest in using diffusion MRI to study the white matter tracts and structural connectivity of the fetal brain. Recent progress in data acquisition and processing suggests that this imaging modality has a unique role in elucidating the normal and abnormal patterns of neurodevelopment in utero. However, there have been no efforts to quantify the prevalence of crossing tracts and bottleneck regions, important issues that have been extensively researched for adult brains. In this work, we determined the brain regions with crossing tracts and bottlenecks between 23 and 36 gestational weeks. We performed probabilistic tractography on 59 fetal brain scans and extracted a set of 51 distinct white tracts, which we grouped into 10 major tract bundle groups. We analyzed the results to determine the patterns of tract crossings and bottlenecks. Our results showed that 20-25% of the white matter voxels included two or three crossing tracts. Bottlenecks were more prevalent. Between 75-80% of the voxels were characterized as bottlenecks, with more than 40% of the voxels involving four or more tracts. The results of this study highlight the challenge of fetal brain tractography and structural connectivity assessment and call for innovative image acquisition and analysis methods to mitigate these problems.

Measurement estimation bounds for local quantum multiparameter estimation, which provide lower bounds on possible measurement uncertainties, have so far been formulated in two ways: by extending the classical Cram\'er--Rao bound (e.g., the quantum Cram\'er--Rao bound and the Nagaoka Cram'er--Rao bound) and by incorporating the parameter estimation framework with the uncertainty principle, as in the Lu--Wang uncertainty relation. In this work, we present a general framework that allows a direct comparison between these different types of estimation limits. Specifically, we compare the attainability of the Nagaoka Cram\'er--Rao bound and the Lu--Wang uncertainty relation, using analytical and numerical techniques. We show that these two limits can provide different information about the physically attainable precision. We present an example where both limits provide the same attainable precision and an example where the Lu--Wang uncertainty relation is not attainable even for pure states. We further demonstrate that the unattainability in the latter case arises because the figure of merit underpinning the Lu--Wang uncertainty relation (the difference between the quantum and classical Fisher information matrices) does not necessarily agree with the conventionally used figure of merit (mean squared error). The results offer insights into the general attainability and applicability of the Lu--Wang uncertainty relation. Furthermore, our proposed framework for comparing bounds of different types may prove useful in other settings., Comment: 13 pages, 7 figures

Accurate segmentation of prostate tumours from PET images presents a formidable challenge in medical image analysis. Despite considerable work and improvement in delineating organs from CT and MR modalities, the existing standards do not transfer well and produce quality results in PET related tasks. Particularly, contemporary methods fail to accurately consider the intensity-based scaling applied by the physicians during manual annotation of tumour contours. In this paper, we observe that the prostate-localised uptake threshold ranges are beneficial for suppressing outliers. Therefore, we utilize the intensity threshold values, to implement a new custom-feature-clipping normalisation technique. We evaluate multiple, established U-Net variants under different normalisation schemes, using the nnU-Net framework. All models were trained and tested on multiple datasets, obtained with two radioactive tracers: [68-Ga]Ga-PSMA-11 and [18-F]PSMA-1007. Our results show that the U-Net models achieve much better performance when the PET scans are preprocessed with our novel clipping technique.

Faced with a dangerous epidemic humans will spontaneously social distance to reduce their risk of infection at a socio-economic cost. Compartmentalised epidemic models have been extended to include this endogenous decision making: Individuals choose their behaviour to optimise a utility function, self-consistently giving rise to population behaviour. Here we study the properties of the resulting Nash equilibria, in which no member of the population can gain an advantage by unilaterally adopting different behaviour. We leverage a new analytic solution to obtain, (1) a simple relationship between rational social distancing behaviour and the current number of infections; (2) new scaling results for how the infection peak and number of total cases depend on the cost of contracting the disease; (3) characteristic infection costs that divide regimes of strong and weak behavioural response and depend only on the basic reproduction number of the disease; (4) a closed form expression for the value of the utility. We discuss how these analytic results provide a deep and intuitive understanding into the disease dynamics, useful for both individuals and policymakers. In particular the relationship between social distancing and infections represents a heuristic that could be communicated to the population to encourage, or "bootstrap", rational behaviour.

Analyzing the motion of multiple biological agents, be it cells or individual animals, is pivotal for the understanding of complex collective behaviors. With the advent of advanced microscopy, detailed images of complex tissue formations involving multiple cell types have become more accessible in recent years. However, deciphering the underlying rules that govern cell movements is far from trivial. Here, we present a novel deep learning framework to estimate the underlying equations of motion from observed trajectories, a pivotal step in decoding such complex dynamics. Our framework integrates graph neural networks with neural differential equations, enabling effective prediction of two-body interactions based on the states of the interacting entities. We demonstrate the efficacy of our approach through two numerical experiments. First, we used a simulated data from a toy model to tune the hyperparameters. Based on the obtained hyperparameters, we then applied this approach to a more complex model that describes interacting cells of cellular slime molds. Our results show that the proposed method can accurately estimate the function of two-body interactions, thereby precisely replicating both individual and collective behaviors within these systems., Comment: 14 pages, 4 figures

In multi-parameter quantum metrology, the resource of entanglement can lead to an increase in efficiency of the estimation process. Entanglement can be used in the state preparation stage, or the measurement stage, or both, to harness this advantage; here we focus on the role of entangling measurements. Specifically, entangling or collective measurements over multiple identical copies of a probe state are known to be superior to measuring each probe individually, but the extent of this improvement is an open problem. It is also known that such entangling measurements, though resource-intensive, are required to attain the ultimate limits in multi-parameter quantum metrology and quantum information processing tasks. In this work we investigate the maximum precision improvement that collective quantum measurements can offer over individual measurements for estimating parameters of qudit states, calling this the 'collective quantum enhancement'. We show that, whereas the maximum enhancement can, in principle, be a factor of $n$ for estimating $n$ parameters, this bound is not tight for large $n$. Instead, our results prove an enhancement linear in dimension of the qudit is possible using collective measurements and lead us to conjecture that this is the maximum collective quantum enhancement in any local estimation scenario., Comment: 22 pages, 9 figures, 10 appendices; presented at AIP Summer Meeting 2023

Functional Magnetic Resonance Imaging (fMRI) is vital in neuroscience, enabling investigations into brain disorders, treatment monitoring, and brain function mapping. However, head motion during fMRI scans, occurring between shots of slice acquisition, can result in distortion, biased analyses, and increased costs due to the need for scan repetitions. Therefore, retrospective slice-level motion correction through slice-to-volume registration (SVR) is crucial. Previous studies have utilized deep learning (DL) based models to address the SVR task; however, they overlooked the uncertainty stemming from the input stack of slices and did not assign weighting or scoring to each slice. In this work, we introduce an end-to-end SVR model for aligning 2D fMRI slices with a 3D reference volume, incorporating a self-attention mechanism to enhance robustness against input data variations and uncertainties. It utilizes independent slice and volume encoders and a self-attention module to assign pixel-wise scores for each slice. We conducted evaluation experiments on 200 images involving synthetic rigid motion generated from 27 subjects belonging to the test set, from the publicly available Healthy Brain Network (HBN) dataset. Our experimental results demonstrate that our model achieves competitive performance in terms of alignment accuracy compared to state-of-the-art deep learning-based methods (Euclidean distance of $0.93$ [mm] vs. $1.86$ [mm]). Furthermore, our approach exhibits significantly faster registration speed compared to conventional iterative methods ($0.096$ sec. vs. $1.17$ sec.). Our end-to-end SVR model facilitates real-time head motion tracking during fMRI acquisition, ensuring reliability and robustness against uncertainties in inputs. source code, which includes the training and evaluations, will be available soon., Comment: Currently under review

Diffusion-weighted Magnetic Resonance Imaging (dMRI) is increasingly used to study the fetal brain in utero. An important computation enabled by dMRI is streamline tractography, which has unique applications such as tract-specific analysis of the brain white matter and structural connectivity assessment. However, due to the low fetal dMRI data quality and the challenging nature of tractography, existing methods tend to produce highly inaccurate results. They generate many false streamlines while failing to reconstruct streamlines that constitute the major white matter tracts. In this paper, we advocate for anatomically constrained tractography based on an accurate segmentation of the fetal brain tissue directly in the dMRI space. We develop a deep learning method to compute the segmentation automatically. Experiments on independent test data show that this method can accurately segment the fetal brain tissue and drastically improve tractography results. It enables the reconstruction of highly curved tracts such as optic radiations. Importantly, our method infers the tissue segmentation and streamline propagation direction from a diffusion tensor fit to the dMRI data, making it applicable to routine fetal dMRI scans. The proposed method can lead to significant improvements in the accuracy and reproducibility of quantitative assessment of the fetal brain with dMRI.

We present cross sections for the formation of positronium chloride (PsCl) in its ground state from the charge exchange between positronium (Ps) and chloride (Cl$^-$) in the range of 10 meV - 100 eV Ps energy. We have used theoretical models based on the first Born approximation in its three-body formulation. We simulated the collisions between Ps and Cl$^-$ using ab-initio methods at both mean-field and correlated levels extrapolated to the complete basis set limit. We have investigated Ps excited states up to ${n=4}$. The results suggest that the channel Ps(${n=2}$) is of particular interest for the production of PsCl in the ground state, and shows that an accurate treatment of the electronic correlation leads to a significant change in the global shape of the PsCl production cross section with respect to the mean-field level., Comment: 13 Pages, 7 Figures, 3 Tables

During epidemics people may reduce their social and economic activity to lower their risk of infection. Such social distancing strategies will depend on information about the course of the epidemic but also on when they expect the epidemic to end, for instance due to vaccination. Typically it is difficult to make optimal decisions, because the available information is incomplete and uncertain. Here, we show how optimal decision-making depends on information about vaccination timing in a differential game in which individual decision-making gives rise to Nash equilibria, and the arrival of the vaccine is described by a probability distribution. We predict stronger social distancing the earlier the vaccination is expected and also the more sharply peaked its probability distribution. In particular, equilibrium social distancing only meaningfully deviates from the no-vaccination equilibrium course if the vaccine is expected to arrive before the epidemic would have run its course. We demonstrate how the probability distribution of the vaccination time acts as a generalised form of discounting, with the special case of an exponential vaccination time distribution directly corresponding to regular exponential discounting.

Magnetic resonance imaging (MRI) is critically important for brain mapping in both scientific research and clinical studies. Precise segmentation of brain tumors facilitates clinical diagnosis, evaluations, and surgical planning. Deep learning has recently emerged to improve brain tumor segmentation and achieved impressive results. Convolutional architectures are widely used to implement those neural networks. By the nature of limited receptive fields, however, those architectures are subject to representing long-range spatial dependencies of the voxel intensities in MRI images. Transformers have been leveraged recently to address the above limitations of convolutional networks. Unfortunately, the majority of current Transformers-based methods in segmentation are performed with 2D MRI slices, instead of 3D volumes. Moreover, it is difficult to incorporate the structures between layers because each head is calculated independently in the Multi-Head Self-Attention mechanism (MHSA). In this work, we proposed a 3D Transformer-based segmentation approach. We developed a Fusion-Head Self-Attention mechanism (FHSA) to combine each attention head through attention logic and weight mapping, for the exploration of the long-range spatial dependencies in 3D MRI images. We implemented a plug-and-play self-attention module, named the Infinite Deformable Fusion Transformer Module (IDFTM), to extract features on any deformable feature maps. We applied our approach to the task of brain tumor segmentation, and assessed it on the public BRATS datasets. The experimental results demonstrated that our proposed approach achieved superior performance, in comparison to several state-of-the-art segmentation methods., Comment: 10 pages, 4 figures

We consider iterated function systems on the real line that consist of continuous, piecewise linear functions. Under a mild separation condition, we show that the Hausdorff and box dimensions of the attractor are equal to the minimum of 1 and the exponent which comes from the most natural system of covers of the attractor.