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We determine the A(1)-homotopy of the topological cyclic homology of the connective real K-theory spectrum ko. The answer has an associated graded that is a free F_2[v_2^4]-module of rank 52, on explicit generators in stems -1 \le * \le 30. The calculation is achieved by using prismatic and syntomic cohomology of ko as introduced by Hahn-Raksit-Wilson, extending work of Bhatt-Morrow-Scholze from the case of classical commutative rings to E_\infty rings. A new feature in our case is that there are nonzero differentials in the motivic spectral sequence from syntomic cohomology to topological cyclic homology., Comment: 52 pages, 12 figures, 1 table. Conjecture B from v1 is proved in v2, along with other improvements

Is Stochastic Gradient Descent (SGD) substantially different from Metropolis Monte Carlo dynamics? This is a fundamental question at the time of understanding the most used training algorithm in the field of Machine Learning, but it received no answer until now. Here we show that in discrete optimization and inference problems, the dynamics of an SGD-like algorithm resemble very closely that of Metropolis Monte Carlo with a properly chosen temperature, which depends on the mini-batch size. This quantitative matching holds both at equilibrium and in the out-of-equilibrium regime, despite the two algorithms having fundamental differences (e.g.\ SGD does not satisfy detailed balance). Such equivalence allows us to use results about performances and limits of Monte Carlo algorithms to optimize the mini-batch size in the SGD-like algorithm and make it efficient at recovering the signal in hard inference problems., Comment: 19 pages, 9 figures

The microscopic dynamics of spontaneously aged and rejuvenated glassy Laponite is investigated through X-ray photon correlation spectroscopy. Two different behaviours of the intensity autocorrelation functions are observed depending on the history of the sample: stretched for spontaneously aged samples and samples rejuvenated from a Wigner glass and compressed, typical of anomalous dynamics, for samples rejuvenated from a DHOC glass. The relaxation time behaviour in the three cases indicates a non-diffusive dynamics of the particles. The present system offers therefore an overview of various dynamical behaviours previously observed individually in several systems and the possibility to pass from one to the other choosing ad hoc the time parameter., Comment: 5 pages, 4 figures

The localization length r_{loc} associated with a fast secondary relaxation in glassy Laponite is determined by X-ray photon correlation spectroscopy (XPCS) through a Debye-Waller fit of the non-ergodicity parameter. Quantitative differences are observed between the time dependence (aging) of r_{loc} in spontaneously aged and rejuvenated samples. This behavior is also reflected in the calculated shear modulus which matches well with data obtained by rheological measurements., Comment: 6 pages, 5 figures

The aging dynamics of a colloidal glass has been studied by multiangle Dynamic Light Scattering, Neutron Spin Echo, X-ray Photon Correlation Spectroscopy and Molecular Dynamics simulations. The two relaxation processes, microscopic (fast) and structural (slow), have been investigated in an unprecedentedly wide range of time and length scales covering both ergodic and nonergodic regimes. The microscopic relaxation time remains diffusive at all length scales across the glass transition scaling with wavevector Q as Q^{-2}. The length-scale dependence of structural relaxation time changes from diffusive, characterized by a Q^{-2}-dependence in the early stages of aging, to Q^{-1}- dependence in the full aging regime which marks a discontinuous hopping dynamics. Both regimes are associated with a stretched behaviour of the correlation functions. We expect these findings to provide a general description of both relaxations across the glass transition., Comment: 6 pages, 4 figures

An unexpected dichotomic long time aging behaviour is observed in a glassy colloidal clay suspension investigated by X-Ray Photon Correlation Spectroscopy and Dynamic Light Scattering. In the long time aging regime the intensity autocorrelations are non-exponential, following the Kohlrausch-Williams-Watts functional form with exponent bQ. We show that for spontaneously aged samples a stretched behaviour (\beta_Q < 1) is always found. Surprisingly a compressed exponent (\beta_Q > 1) appears only when the system is rejuvenated by application of a shear field. In both cases the relaxation times scale as Q^{-1}. These observations shed light on the origin of compressed exponential behaviour and helps in classifying previous results in the literature on anomalous dynamics., Comment: 5 pages, 5 figures

The high frequency collective dynamics of liquid hydrogen fluoride is studied by inelastic x-ray scattering on the coexistence curve at T = 239 K. The comparison with existing molecular dynamics simulations shows the existence of two active relaxation processes with characteristic time scales in the subpicosecond range. The observed scenario is very similar to that found in liquid water. This suggests that hydrogen bonded liquids behave similarly to other very different systems as simple and glass forming liquids, thus indicating that these two relaxation processes are universal features of the liquid state., Comment: 6 pages, 5 figures

Deep Neural Networks (DNNs) deployed to the real world are regularly subject to out-of-distribution (OoD) data, various types of noise, and shifting conceptual objectives. This paper proposes a framework for adapting to data distribution drift modeled by benchmark Continual Learning datasets. We develop and evaluate a method of Continual Learning that leverages uncertainty quantification from Bayesian Inference to mitigate catastrophic forgetting. We expand on previous approaches by removing the need for Monte Carlo sampling of the model weights to sample the predictive distribution. We optimize a closed-form Evidence Lower Bound (ELBO) objective approximating the predictive distribution by propagating the first two moments of a distribution, i.e. mean and covariance, through all network layers. Catastrophic forgetting is mitigated by using the closed-form ELBO to approximate the Minimum Description Length (MDL) Principle, inherently penalizing changes in the model likelihood by minimizing the KL Divergence between the variational posterior for the current task and the previous task's variational posterior acting as the prior. Leveraging the approximation of the MDL principle, we aim to initially learn a sparse variational posterior and then minimize additional model complexity learned for subsequent tasks. Our approach is evaluated for the task incremental learning scenario using density propagated versions of fully-connected and convolutional neural networks across multiple sequential benchmark datasets with varying task sequence lengths. Ultimately, this procedure produces a minimally complex network over a series of tasks mitigating catastrophic forgetting., Comment: 6 pages, 13th Int'l Symposium on Image and Signal Processing and Analysis

We present a device that exploits spatial and spectral correlations in parametric downconversion at once. By using a ghost imaging arrangement, we have been able to reconstruct remotely the frequency profile of a composite system. The presence of distinct spectral regions is corroborated by a model-independent statistical analysis that constitutes an intriguing possibility also in the low count regime.

We describe a deformation of the $\infty$-category of Borel $G$-spectra for a finite group $G$. This provides a new presentation of the $a$-complete real Artin--Tate motivic stable homotopy category when $G=C_2$ and gives a new interpretation of the $a$-completed $C_2$-effective slice spectral sequence. As a new computational tool, we present a modified Adams--Novikov spectral sequence which computes the $RO(G)$-graded Mackey functor valued homotopy of Borel $G$-spectra., Comment: updated introduction and references; 49 pages, comments welcome!

Segment anything model (SAM) has emerged as the leading approach for zero-shot learning in segmentation tasks, offering the advantage of avoiding pixel-wise annotations. It is particularly appealing in medical image segmentation, where the annotation process is laborious and expertise-demanding. However, the direct application of SAM often yields inferior results compared to conventional fully supervised segmentation networks. An alternative approach is to use SAM as the initial stage to generate pseudo labels for further network training. However, the performance is limited by the quality of pseudo labels. In this paper, we propose a novel label correction framework to push the boundary of SAM-based segmentation. Our model utilizes a label quality evaluation module to distinguish between noisy labels and clean labels. This enables the correction of the noisy labels using an uncertainty-based self-correction module, thereby enriching the clean training set. Finally, we retrain the segmentation network with updated labels to optimize its weights for future predictions. One key advantage of our model is its ability to train deep networks using SAM-generated pseudo labels without relying on a set of expert-level annotations while attaining good segmentation performance. We demonstrate the effectiveness of our proposed model on three public datasets, indicating its ability to improve segmentation accuracy and outperform baseline methods in label correction.

Many macroeconomic time series are characterised by nonlinearity both in the conditional mean and in the conditional variance and, in practice, it is important to investigate separately these two aspects. Here we address the issue of testing for threshold nonlinearity in the conditional mean, in the presence of conditional heteroskedasticity. We propose a supremum Lagrange Multiplier approach to test a linear ARMA-GARCH model against the alternative of a TARMA-GARCH model. We derive the asymptotic null distribution of the test statistic and this requires novel results since the difficulties of working with nuisance parameters, absent under the null hypothesis, are amplified by the non-linear moving average, combined with GARCH-type innovations. We show that tests that do not account for heteroskedasticity fail to achieve the correct size even for large sample sizes. Moreover, we show that the TARMA specification naturally accounts for the ubiquitous presence of measurement error that affects macroeconomic data. We apply the results to analyse the time series of Italian strikes and we show that the TARMA-GARCH specification is consistent with the relevant macroeconomic theory while capturing the main features of the Italian strikes dynamics, such as asymmetric cycles and regime-switching., Comment: 61 pages, 19 figures, 10 tables

Dynamic Light Scattering (DLS) and Small-Angle Neutron Scattering (SANS) are two key tools with which to probe the dynamic and static structure factor, respectively, in soft matter. Usually DLS and SANS measurements are performed separately, in different laboratories, on different samples and at different times. However, this methodology has particular disadvantages for a large variety of soft materials which exhibit high sensitivity to small changes in fundamental parameters such as waiting times, concentration, pH, ionic strength, etc. Here we report on a new portable DLS-SANS apparatus that allows one to simultaneously measure both the microscopic dynamics (through DLS) and the static structure (through SANS) on the same sample. The apparatus has been constructed as a collaboration between two laboratories, each an expert in one of the scattering methods, and was commissioned on the \textit{LOQ} and \textit{ZOOM} SANS instruments at the ISIS Pulsed Neutron \& Muon Source, U.K.

Coronal mass ejections (CMEs) can create significant disruption to human activities and systems on Earth, much of which can be mitigated with prior warning of the upstream solar wind conditions. However, it is currently extremely challenging to accurately predict the arrival time and internal structure of a CME from coronagraph images alone. In this study, we take advantage of a rare opportunity to use Solar Orbiter, at 0.5\,AU upstream of Earth, as an upstream solar wind monitor. We were able to use real time science quality magnetic field measurements, taken only 12 minutes earlier, to predict the arrival time of a CME prior to reaching Earth. We used measurements at Solar Orbiter to constrain an ensemble of simulation runs from the ELEvoHI model, reducing the uncertainty in arrival time from 10.4\,hours to 2.5\,hours. There was also an excellent agreement in the $B_z$ profile between Solar Orbiter and Wind spacecraft, despite being separated by 0.5\,AU and 10$^{\circ}$ longitude. Therefore, we show that it is possible to predict not only the arrival time of a CME, but the sub-structure of the magnetic field within it, over a day in advance. The opportunity to use Solar Orbiter as an upstream solar wind monitor will repeat once a year, which should further help assess the efficacy upstream in-situ measurements in real time space weather forecasting.