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Quantum many-body systems undergoing phase transitions have been proposed as probes enabling beyond-classical enhancement of sensing precision. However, this enhancement is usually limited to a very narrow region around the critical point. Here, we systematically develop a modular approach for introducing multiple phase transitions in a many-body system. This naturally allows us to enlarge the region of quantum-enhanced precision by encompassing the newly created phase boundaries. Our approach is general and can be applied to both symmetry-breaking and topological quantum sensors. In symmetry-breaking sensors, we show that the newly created critical points inherit the original universality class and a simple total magnetization measurement already suffices to locate them. In topological sensors, our modular construction creates multiple bands which leads to a rich phase diagram. In both cases, Heisenberg scaling for Hamiltonian parameter estimation is achieved at all the phase boundaries. This can be exploited to create a global sensor which significantly outperforms a uniform probe., Comment: 4+6 pages, 6+4 figures, accepted for publication in Physical Review Letters

Optimal choice of spin polarization enables electron injection into the helical edge state at a precise position, despite the uncertainty principle, permitting access to specific nonlocal Green's functions. We show, within 1D effective description, that this fact facilitates a direct identification of odd-frequency pairing through parity measurement (under frequency reversal) of the nonlocal differential conductance in a setup comprising the Josephson junction on the helical edge state of a 2D topological insulator with two spin-polarized probes tunnel-coupled to the junction region. A 2D numerical simulation has also been conducted to confirm theoretical predictions as well as to demonstrate the experimental feasibility of the proposal., Comment: 11 pages, 3 figures

In this article, universally optimal multivariate crossover designs are studied. The multiple response crossover design is motivated by a $3 \times 3$ crossover setup, where the effect of $3$ doses of an oral drug are studied on gene expressions related to mucosal inflammation. Subjects are assigned to three treatment sequences and response measurements on $5$ different gene expressions are taken from each subject in each of the $3$ time periods. To model multiple or $g$ responses, where $g>1$, in a crossover setup, a multivariate fixed effect model with both direct and carryover treatment effects is considered. It is assumed that there are non zero within response correlations, while between response correlations are taken to be zero. The information matrix corresponding to the direct effects is obtained and some results are studied. The information matrix in the multivariate case is shown to differ from the univariate case, particularly in the completely symmetric property. For the $g>1$ case, with $t$ treatments and $p$ periods, for $p=t \geq 3$, the design represented by a Type $\rm{I}$ orthogonal array of strength $2$ is proved to be universally optimal over the class of binary designs, for the direct treatment effects., Comment: 18 Pages, 2 Figures

In-beam $ \gamma $-ray spectroscopy of $^{131}$Xe has been carried out to study the structure of the intruder $ \nu h_{11/2} $ band. Excited states were populated via an $ \alpha $-induced fusion-evaporation reaction at E$ _{\alpha} = 38 $ MeV. Inspection of $ \gamma \gamma $-coincidence data resulted in the identification of a new rotational sequence. Based on the systematics of excitation energy, assigned spin-parity, decay pattern, and the electromagnetic character of the inter-band $ \Delta I = 1 $ $ \gamma $-transitions, this sequence is proposed as the unfavoured signature partner of the $ \nu h_{11/2} $ band. The structure of this band is further illuminated in the light of the triaxial particle rotor model (TPRM). The possibility of wobbling excitation in $ N = 77 $ Xe-Ba-Ce isotones has been explored in a systematic manner.

The radiative decay of the Hoyle state is the doorway to the production of heavier elements in stellar environment. Here we report, an exclusive measurement of electric quadruple (E$_2$) transitions of the Hoyle state to the ground state of $^{12}$C through the $^{12}$C(p, p$^\prime$$\gamma$$\gamma$)$^{12}$C reaction. Triple coincidence measurement yields a value of radiative branching ratio $\Gamma_{rad}$/$\Gamma$ = 4.01 (30) $\times$ 10$^{-4}$. The result has been corroborated by an independent experiment based on the complete kinematical measurement $via.$ $^{12}$C(p, p$^\prime$)$^{12}$C reaction ($\Gamma_{rad}$/$\Gamma$ = 4.04 (30) $\times$ 10$^{-4}$). Using our results together with the currently adopted values of $\Gamma_{\pi}$(E$_0$)/$\Gamma$ and $\Gamma_{\pi}$($E_0$), the radiative width of the Hoyle state is found to be 3.75 (40) $\times$ 10$^{-3}$ eV. We emphasize here that our result is not in agreement with 34 $\%$ increase in the radiative decay width of the Hoyle state measured recently but consistent with the currently adopted value., Comment: 7 pages, 5 figures Submitted to Phys. Rev. Lett

MoEDAL's Apparatus for Penetrating Particles (MAPP) Experiment is designed to expand the search for new physics at the LHC, significantly extending the physics program of the baseline MoEDAL Experiment. The Phase-1 MAPP detector (MAPP-1) is currently undergoing installation at the LHC's UA83 gallery adjacent to the LHCb/MoEDAL region at Interaction Point 8 and will begin data-taking in early 2024. The focus of the MAPP experiment is on the quest for new feebly interacting particles$\unicode{x2014}$avatars of new physics with extremely small Standard Model couplings, such as minicharged particles (mCPs). In this study, we present the results of a comprehensive analysis of MAPP-1's sensitivity to mCPs arising in the canonical model involving the kinetic mixing of a massless dark $U(1)$ gauge field with the Standard Model hypercharge gauge field. We focus on several dominant production mechanisms of mCPs at the LHC across the mass$\unicode{x2013}$mixing parameter space of interest to MAPP: Drell$\unicode{x2013}$Yan pair production, direct decays of heavy quarkonia and light vector mesons, and single Dalitz decays of pseudoscalar mesons. The $95\%$ confidence level background-free sensitivity of MAPP-1 for mCPs produced at the LHC's Run 3 and the HL-LHC through these mechanisms, along with projected constraints on the minicharged strongly interacting dark matter window, are reported. Our results indicate that MAPP-1 exhibits sensitivity to sizable regions of unconstrained parameter space and can probe effective charges as low as $8 \times 10^{-4}\:e$ and $6 \times 10^{-4}\:e$ for Run 3 and the HL-LHC, respectively., Comment: 11 pages, 7 figures

The densities in the cores of the neutron stars (NSs) can reach several times that of the nuclear saturation density. The exact nature of matter at these densities is still virtually unknown. We consider a number of proposed, phenomenological relativistic mean-field equations of state to construct theoretical models of NSs. We find that, based on our selected set of models, the emergence of exotic matter at these high densities restricts the mass of NSs to $\simeq 2.2 M_\odot$. However, the presence of magnetic fields and a model anisotropy significantly increases the star's mass, placing it within the observational mass gap that separates the heaviest NSs from the lightest black holes. Therefore, we propose that gravitational wave observations, like GW190814, and other potential candidates within this mass gap, may actually represent massive, magnetized NSs., Comment: 18 pages including 26 figures and 12 tables; this version published in Phys. Rev. D

Continual learning (CL) methods designed for natural image classification often fail to reach basic quality standards for medical image segmentation. Atlas-based segmentation, a well-established approach in medical imaging, incorporates domain knowledge on the region of interest, leading to semantically coherent predictions. This is especially promising for CL, as it allows us to leverage structural information and strike an optimal balance between model rigidity and plasticity over time. When combined with privacy-preserving prototypes, this process offers the advantages of rehearsal-based CL without compromising patient privacy. We propose Atlas Replay, an atlas-based segmentation approach that uses prototypes to generate high-quality segmentation masks through image registration that maintain consistency even as the training distribution changes. We explore how our proposed method performs compared to state-of-the-art CL methods in terms of knowledge transferability across seven publicly available prostate segmentation datasets. Prostate segmentation plays a vital role in diagnosing prostate cancer, however, it poses challenges due to substantial anatomical variations, benign structural differences in older age groups, and fluctuating acquisition parameters. Our results show that Atlas Replay is both robust and generalizes well to yet-unseen domains while being able to maintain knowledge, unlike end-to-end segmentation methods. Our code base is available under https://github.com/MECLabTUDA/Atlas-Replay.

The next generation gravitational wave (GW) detectors -- Einstein Telescope (ET) and Cosmic Explorer (CE) will have distance horizons up to $\mathcal{O}(10)$ Gpc for detecting binary neutron star (BNS) mergers. This will make them ideal for triggering high-energy neutrino searches from BNS mergers at the next generation neutrino detectors, such as IceCube-Gen2. We calculate the distance limits as a function of the time window of neutrino analysis, up to which meaningful triggers from the GW detectors can be used to minimize backgrounds and collect a good sample of high-energy neutrino events at the neutrino detectors, using the sky localization capabilities of the GW detectors. We then discuss the prospects of the next generation detectors to work in synergy to facilitate coincident neutrino detections or to constrain the parameter space in the case of non-detection of neutrinos. We show that good localization of GW events, which can be achieved by multiple third generation GW detectors, is necessary to detect a GW-associated neutrino event or put a meaningful constraint ($\sim 3\sigma$ confidence level) on neutrino emission models. Such an analysis can also help constrain physical models and hence provide insights into neutrino production mechanisms in binary neutron star mergers., Comment: 15 pages, 4 figures, published version

Traditional initialisation methods, e.g. He and Xavier, have been effective in avoiding the problem of vanishing or exploding gradients in neural networks. However, they only use simple pointwise distributions, which model one-dimensional variables. Moreover, they ignore most information about the architecture and disregard past training experiences. These limitations can be overcome by employing generative models for initialisation. In this paper, we introduce two groups of new initialisation methods. First, we locally initialise weight groups by employing variational autoencoders. Secondly, we globally initialise full weight sets by employing graph hypernetworks. We thoroughly evaluate the impact of the employed generative models on state-of-the-art neural networks in terms of accuracy, convergence speed and ensembling. Our results show that global initialisations result in higher accuracy and faster initial convergence speed. However, the implementation through graph hypernetworks leads to diminished ensemble performance on out of distribution data. To counteract, we propose a modification called noise graph hypernetwork, which encourages diversity in the produced ensemble members. Furthermore, our approach might be able to transfer learned knowledge to different image distributions. Our work provides insights into the potential, the trade-offs and possible modifications of these new initialisation methods.

When a number of similar tasks have to be learned simultaneously, multi-task learning (MTL) models can attain significantly higher accuracy than single-task learning (STL) models. However, the advantage of MTL depends on various factors, such as the similarity of the tasks, the sizes of the datasets, and so on; in fact, some tasks might not benefit from MTL and may even incur a loss of accuracy compared to STL. Hence, the question arises: which tasks should be learned together? Domain experts can attempt to group tasks together following intuition, experience, and best practices, but manual grouping can be labor-intensive and far from optimal. In this paper, we propose a novel automated approach for task grouping. First, we study the affinity of tasks for MTL using four benchmark datasets that have been used extensively in the MTL literature, focusing on neural network-based MTL models. We identify inherent task features and STL characteristics that can help us to predict whether a group of tasks should be learned together using MTL or if they should be learned independently using STL. Building on this predictor, we introduce a randomized search algorithm, which employs the predictor to minimize the number of MTL trainings performed during the search for task groups. We demonstrate on the four benchmark datasets that our predictor-driven search approach can find better task groupings than existing baseline approaches.

The future of quantum information processing hinges on chip-scale nanophotonics, specifically cavity QED and waveguide QED. One of the foremost processes underpinning quantum photonic technologies is the phenomenon of Rabi oscillations, which manifests when a qubit is irradiated by an intense laser source. Departing from the conventional semiclassical framework, we expound on the more general, quantum-theoretic case where the optical excitation takes the form of a multiphoton Fock state, and the qubit couples to a continuum of radiation modes. By employing the real-space formalism, we analytically explore the scattering dynamics of the photonic Fock state as it interfaces with a two-level emitter. The resulting amplitude for atomic excitation features a linear superposition of various independent scattering events that are triggered by the potential of sequential photon absorptions and emissions. The lowest-order excitation event, initiated by the stochastic scattering of one of the several photons, aptly characterizes the dynamics in a weak-field environment. This is complemented by a multitude of higher-order scattering events ensuing from repeated atom-photon interactions. The temporal evolution of the qubit excitation in our configuration closely mirrors the semiclassical predictions, particularly in the strong-pumping limit where Rabi oscillations unfold. Notably, this compatibility with the semiclassical paradigm applies both to the weak-driving and large-detuning limits. Our analysis, therefore, extends the existing results on quantum Rabi oscillations pertinent to single-mode cavity QED, to the multimode, waveguide-QED configurations wherein flying photons are the information carriers. Finally, we explore the scattering dynamics of pulsed wave packets, highlighting the potential to substantially enhance excitation efficiency, even in scenarios involving just a few photons.

Given ideals $I,J$ of a noetherian local ring $(R, \mathfrak m)$ such that $I+J$ is $\mathfrak m$-primary and a finitely generated $R$-module $M$, we associate an invariant of $(M,R,I,J)$ called the $h$-function. Our results on $h$-functions allow extensions of the theories of Frobenius-Poincar\'e functions and Hilbert-Kunz density functions from the known graded case to the local case, answering a question of V.Trivedi. When $J$ is $\mathfrak m$-primary, we describe the support of the corresponding density function in terms of other invariants of $(R, I,J)$. We show that the support captures the $F$-threshold: $c^J(I)$, under mild assumptions, extending results of V. Trivedi and Watanabe. The $h$-function encodes Hilbert-Samuel, Hilbert-Kunz multiplicity and $F$-threshold of the ideal pair involved. Using this feature of $h$-functions, we provide an equivalent formulation of a conjecture of Huneke, Musta\c{t}\u{a}, Takagi, Watanabe; recover a result of Smirnov and Betancourt; prove that a result of Hanes comparing multiplicities, is equivalent to an a priori weaker containment condition on ideals. We also point out that a conjecture of Smirnov-Betancourt as stated is false and suggest a correction which we relate to the conjecture of Huneke et al. We develop the theory of $h$-functions in a more general setting which yields a density function for $F$-signature. A key to many results on $h$-functions is a `convexity technique' that we introduce, which in particular proves differentiability of Hilbert-Kunz density functions almost everywhere on $(0,\infty)$, thus contributing to another question of Trivedi., Comment: v2: substantial changes: applications added, results improved

In this article, we examine the Poissonian pair correlation (PPC) statistic for higher-dimensional real sequences. Specifically, we demonstrate that for $d\geq 3$, almost all $(\alpha_1,\ldots,\alpha_d) \in \mathbb{R}^d$, the sequence $\big(\{x_n\alpha_1\},\dots,\{x_n\alpha_d\}\big)$ in $[0,1)^d$ has PPC conditionally on the additive energy bound of $(x_n).$ This bound is more relaxed compared to the additive energy bound for one dimension as discussed in [1]. More generally, we derive the PPC for $\big(\{x_n^{(1)}\alpha_1\},\dots,\{x_n^{(d)}\alpha_d\}\big) \in [0,1)^d$ for almost all $(\alpha_1,\ldots,\alpha_d) \in \mathbb{R}^d.$ As a consequence we establish the metric PPC for $(n^{\theta_1},\ldots,n^{\theta_d})$ provided that all of the $\theta_i$'s are greater than two.