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We propose a novel framework for the statistical analysis of genus-zero 4D surfaces, i.e., 3D surfaces that deform and evolve over time. This problem is particularly challenging due to the arbitrary parameterizations of these surfaces and their varying deformation speeds, necessitating effective spatiotemporal registration. Traditionally, 4D surfaces are discretized, in space and time, before computing their spatiotemporal registrations, geodesics, and statistics. However, this approach may result in suboptimal solutions and, as we demonstrate in this paper, is not necessary. In contrast, we treat 4D surfaces as continuous functions in both space and time. We introduce Dynamic Spherical Neural Surfaces (D-SNS), an efficient smooth and continuous spatiotemporal representation for genus-0 4D surfaces. We then demonstrate how to perform core 4D shape analysis tasks such as spatiotemporal registration, geodesics computation, and mean 4D shape estimation, directly on these continuous representations without upfront discretization and meshing. By integrating neural representations with classical Riemannian geometry and statistical shape analysis techniques, we provide the building blocks for enabling full functional shape analysis. We demonstrate the efficiency of the framework on 4D human and face datasets. The source code and additional results are available at https://4d-dsns.github.io/DSNS/. 

This work proposes a class of differentially private mechanisms for linear queries, in par- ticular range queries, that leverages corre- lated input perturbation to simultaneously achieve unbiasedness, consistency, statisti- cal transparency, and control over utility re- quirements in terms of accuracy targets ex- pressed either in certain query margins or as implied by the hierarchical database struc- ture. The proposed Cascade Sampling al- gorithm instantiates the mechanism exactly and efficiently. Our theoretical and empir- ical analysis demonstrates that we achieve near-optimal utility, effectively compete with other methods, and retain all the favorable statistical properties discussed earlier. 

We present results of a search for spin-independent dark matter-nucleus interactions in a $1{\mathrm{cm}}^2$by 1 mm thick (0.233 g) high-resolution silicon athermal phonon detector operated above ground. For interactions in the substrate, this detector achieves an rms baseline energy resolution of $361.5\left(4\right)\mathrm{m}\mathrm{eV}$(statistical error), the best for any athermal phonon detector to date. With an exposure of $0.233\mathrm{g}\times 12$hours, we place the most stringent constraints on dark matter masses between 44 and $87\mathrm{M}\mathrm{eV}/{\mathrm{c}}^2$, with the lowest unexplored cross section of $4\times {10}^{-32}{\mathrm{c}\mathrm{m}}^2$at $87\mathrm{M}\mathrm{eV}/{\mathrm{c}}^2$. We employ a conservative salting technique to reach the lowest dark matter mass ever probed via direct detection experiment. This constraint is enabled by two-channel rejection of low energy backgrounds that are coupled to individual sensors. 

Abstract This study explores the dynamics of charge transport within a cryogenic P-type Ge particle detector, fabricated from a crystal cultivated at the University of South Dakota. By subjecting the detector to cryogenic temperatures and an Am-241 source, we observe evolving charge dynamics and the emergence of cluster dipole states, leading to the impact ionization process at 40 mK. Our analysis focuses on crucial parameters: the zero-field cross-section of cluster dipole states and the binding energy of these states. For the Ge detector in our investigation, the zero-field cross-section of cluster dipole states is determined to be 8.45 × 10⁻¹¹± 4.22 × 10⁻¹²cm². Examination of the binding energy associated with cluster dipole states, formed by charge trapping onto dipole states during the freeze-out process, reveals a value of 0.034 ± 0.0017 meV. These findings shed light on the intricate charge states influenced by the interplay of temperature and electric field, with potential implications for the sensitivity in detecting low-mass dark matter. 

Abstract Cryogenic calorimetric experiments to search for neutrinoless double-beta decay ($$0\nu \beta \beta $$ $0\nu \beta \beta$) are highly competitive, scalable and versatile in isotope. The largest planned detector array, CUPID, is comprised of about 1500 individual Li$$_{2}$$ $_2^{}$$$^{100}$$ $_{}^{100}$MoO$$_4$$ $_4^{}$detector modules with a further scale up envisioned for a follow up experiment (CUPID-1T). In this article, we present a novel detector concept targeting this second stage with a low impedance TES based readout for the Li$$_2$$ $_2^{}$MoO$$_4$$ $_4^{}$absorber that is easily mass-produced and lends itself to a multiplexed readout. We present the detector design and results from a first prototype detector operated at the NEXUS shallow underground facility at Fermilab. The detector is a 2-cm-side cube with 21 g mass that is strongly thermally coupled to its readout chip to allow rise-times of$$\sim $$ $\sim$0.5 ms. This design is more than one order of magnitude faster than present NTD based detectors and is hence expected to effectively mitigate backgrounds generated through the pile-up of two independent two neutrino decay events coinciding close in time. Together with a baseline resolution of 1.95 keV (FWHM) these performance parameters extrapolate to a background index from pile-up as low as$$5\cdot 10^{-6}$$ $5·{10}^{-6}$ counts/keV/kg/yr in CUPID size crystals. The detector was calibrated up to the MeV region showing sufficient dynamic range for$$0\nu \beta \beta $$ $0\nu \beta \beta$searches. In combination with a SuperCDMS HVeV detector this setup also allowed us to perform a precision measurement of the scintillation time constants of Li$$_2$$ $_2^{}$MoO$$_4$$ $_4^{}$, which showed a primary component with a fast O(20 $$\upmu $$ $\mu$s) time scale.