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Efficiently distributing secret keys over long distances remains a critical challenge in the development of quantum networks. "First-generation" quantum repeater chains distribute entanglement by executing protocols composed of probabilistic entanglement generation, swapping and distillation operations. However, finding the protocol that maximizes the secret-key rate is difficult for two reasons. First, calculating the secretkey rate for a given protocol is non-trivial due to experimental imperfections and the probabilistic nature of the operations. Second, the protocol space rapidly grows with the number of nodes, and lacks any clear structure for efficient exploration. To address the first challenge, we build upon the efficient machinery developed by Li et al. [1] and we extend it, enabling numerical calculation of the secret-key rate for heterogeneous repeater chains with an arbitrary number of nodes. For navigating the large, unstructured space of repeater protocols, we implement a Bayesian optimization algorithm, which we find consistently returns the optimal result. Whenever comparisons are feasible, we validate its accuracy against results obtained through brute-force methods. Further, we use our framework to extract insight on how to maximize the efficiency of repeater protocols across varying node configurations and hardware conditions. Our results highlight the effectiveness of Bayesian optimization in exploring the potential of near-term quantum repeater chains., Comment: 8 pages, 8 figures

The Ion Beam Induced Charge (IBIC) technique is widely used to characterize the electronic properties of semiconductor materials and devices. Its main advantage over other charge collection microscopies stems in the use of MeV ion probes, which provide both measurable induced charge signals from single ions, and high spatial resolution, which is maintained along the ion range. It is a fact, however, that the use of low-energy ions in the keV range can provide the IBIC technique with complementary analytical capabilities, that are not available with MeV ions, for example the higher sensitivity to the status, contamination and morphology of the surface and the fact that the induced signal depends on the transport of only one type of charge carrier. This paper outlines the upgrade that was made at the 100 kV ion implanter of the University of Torino, originally installed for material and surface modification, to explore the rather unexplored keV-IBIC field and to assess its potential to characterize semiconductor devices. Finally, we report the first IBIC application of our apparatus, which regards the assessment of the radiation damage of a commercially available silicon photodiode, adopting the IAEA experimental protocol and the relevant interpretative model., Comment: 15 pages, 9 figures

In a sequence $S=\{(X,f_n)\}_{n\in\mathbb{N}}$ of dynamical systems sharing a common ambient space, the point $f^k_n(x)$ visited by a certain $x\in X$ depends on the iteration order $k$ and on the index $n$ specifying the system in $S$. If the sequence of maps $\{f_n\}_{n\in\mathbb{N}}$ is eventually constant at every point, the $f_n$-orbits show an emergent poset structure. A maximal initial segment of this poset is isomorphic to a certain countable ordinal $\ge\omega$. We study this transfinite emergent structure from the point of view of topological dynamics, investigating orbits, recurrence, limit sets, attractors and conjugacy.

In this study, we inspect and analyze the effect of Al implantation into AlN by conducting confocal microscopy on the ion implanted regions, before and after implantation, followed by an annealing step. The independent effect of annealing is studied in an unimplanted control region, which showed that annealing alone does not produce new emitters. We observed that point-like emitters are created in the implanted regions after annealing by tracking individual locations in a lithographically patterned sample. The newly created quantum emitters show anti-bunching under ambient conditions and are spectrally similar to the previously discovered emitters in as-grown AlN.

Among solar system objects, comets coming from the Oort Cloud are an elusive population, intrinsically rare and difficult to detect. Nonetheless, as the more pristine objects we can observe, they encapsulate critical cues on the formation of planetary systems and are the focus of many scientific investigations and science missions. The Legacy Survey of Space and Time (LSST), which will start to operate from the Vera C. Rubin Observatory in 2025, is expected to dramatically improve our detection ability of these comets by performing regular monitoring of the Southern sky deep down to magnitude 24.5 with excellent astrometry. However, making straightforward predictions on future LSST detection rates is challenging due to our biased knowledge of the underlying population. This is because identifications to date have been conducted by various surveys or individual observers, often without detailed information on their respective selection functions. Recent efforts to predict incoming flux of Long Period Comets still suffer of the lack of systematic, well-characterized, homogeneous cometary surveys. Here, we adopt a different point of view by asking how much earlier~on known comets on long-period or hyperbolic orbits would have been discovered by a LSST-like survey if it was already in place 10 years prior to their perihelion epoch. In this case, we are not simulating a real flux of incoming comet, as all comets in our sample reach the perihelion simultaneously, but we can analyze the impact of a LSST-like survey on individual objects. We find that LSST would have found about 40% of comets in our sample at least 5 years prior to their perihelion epoch, and at double (at least) the distance at which they were actually discovered. Based on this approach, we find that LSST has the potentiality to at least twofold the current discovery rate of long-period and hyperbolic comets., Comment: 14 pages, 7 figures. Accepted for publication on Icarus

This paper is concerned with a comparison principle for viscosity solutions to Hamilton-Jacobi (HJ), -Bellman (HJB), and -Isaacs (HJI) equations for general classes of partial integro-differential operators. Our approach innovates in three ways: (1) We reinterpret the classical doubling-of-variables method in the context of second-order equations by casting the Ishii-Crandall Lemma into a test function framework. This adaptation allows us to effectively handle non-local integral operators, such as those associated with L\'evy processes. (2) We translate the key estimate on the difference of Hamiltonians in terms of an adaptation of the probabilistic notion of couplings, providing a unified approach that applies to differential, difference, and integral operators. (3) We strengthen the sup-norm contractivity resulting from the comparison principle to one that encodes continuity in the strict topology. We apply our theory to a variety of examples, in particular, to second-order differential operators and, more generally, generators of spatially inhomogeneous L\'evy processes.

Visual scene understanding is a fundamental task in computer vision that aims to extract meaningful information from visual data. It traditionally involves disjoint and specialized algorithms for different tasks that are tailored for specific application scenarios. This can be cumbersome when designing complex systems that include processing of visual and semantic data extracted from visual scenes, which is even more noticeable nowadays with the influx of applications for virtual or augmented reality. When designing a system that employs automatic visual scene understanding to enable a precise and semantically coherent description of the underlying scene, which can be used to fuel a visualization component with 3D virtual synthesis, the lack of flexibility and unified frameworks become more prominent. To alleviate this issue and its inherent problems, we propose an architecture that addresses the challenges of visual scene understanding and description towards a 3D virtual synthesis that enables an adaptable, unified and coherent solution. Furthermore, we expose how our proposition can be of use into multiple application areas. Additionally, we also present a proof of concept system that employs our architecture to further prove its usability in practice.

We first give a cleaner and more direct approach to the derivation of the Fast model of the Kummer surface. We show how to construct efficient (N,N)-isogenies, for any odd N, both on the general Kummer surface and on the Fast model., Comment: 38 pages, 2 figures. To appear in Mathematics of Computation

Split-vacancy color centers in diamond are promising solid state platforms for the implementation of photonic quantum technologies. These luminescent defects are commonly fabricated upon low energy ion implantation and subsequent thermal annealing. Their technological uptake will require the availability of reliable methods for the controlled, large scale production of localized individual photon emitters. This task is partially achieved by controlled ion implantation to introduce selected impurities in the host material, and requires the development of challenging beam focusing or collimation procedures coupled with single-ion detection techniques. We report on protocol for the direct optical activation of split-vacancy color centers in diamond via localized processing with continuous wave laser at mW optical powers. We demonstrate the activation of photoluminescent Mg- and Sn-related centers at both the ensemble and single-photon emitter level in ion-implanted, high-purity diamond crystals without further thermal processing. The proposed lithographic method enables the activation of individual color centers at specific positions of a large area sample by means of a relatively inexpensive equipment offering the real-time, in situ monitoring of the process., Comment: 17 pages, 7 figures

We give a new perspective on the existence of viscosity solutions for a stationary and a time-dependent first order Hamilton-Jacobi equation. Following recent comparison principles, we work in a framework in which we consider a subsolution and a supersolution for two equations in terms of two Hamiltonians that can be seen as an upper and lower bound of our original Hamiltonian respectively. The upper and lower bound are formulated in terms of a relaxed Lyapunov function which allows us to restrict part of the analysis to compact sets and to work with almost optimizers of the considered control problems. For this reason, we can relax assumptions on the control problem: most notably, we do not need completeness of set of controlled paths. Moreover, our strategy avoids a-priori analysis on the regularity of the candidate solutions. We then explore the context of Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Isaacs equations to verify our assumptions in a convex and non-convex setting respectively.

In the last years the attention towards topological dynamical properties of highly discontinuous maps has increased significantly. In [D.Corona, A. Della Corte. The critical exponent functions. Comptes Rendus Math\'ematique, 360(G4), 315-332, 2022], a class of densely discontinuous interval maps, called "critical exponent maps", was introduced. These maps are defined through the word-combinatorics concept of critical exponent applied to the binary expansion of reals and show highly chaotically properties as well as some challenging problems. In this paper we identify an error in the proof of Theorem 7 in [D.Corona, A. Della Corte. The critical exponent functions. Comptes Rendus Math\'ematique, 360(G4), 315-332, 2022], a purely combinatorial result which in fact does not hold. We show that most of the results in [D.Corona, A. Della Corte. The critical exponent functions. Comptes Rendus Math\'ematique, 360(G4), 315-332, 2022], obtained there through Theorem 7, can be recovered. Moreover, we propose as a conjecture a weaker form of Theorem 7.

Despite considerable progress in developing artificial intelligence (AI) algorithms for prostate cancer detection from whole slide images, the clinical applicability of these models remains limited due to variability in pathological annotations and existing dataset limitations. This article proposes a novel approach to overcome these challenges by leveraging a Bayesian framework to seamlessly integrate new data, and present results as a panel of annotations. The framework is demonstrated by integrating a Bayesian prior with one trained AI model to generate a distribution of Gleason patterns for each pixel of an image. It is shown that using this distribution of Gleason patterns rather than a ground-truth label can improve model applicability, mitigate errors, and highlight areas of interest for pathologists. Additionally, we present a high-quality, hand-curated dataset of prostate histopathological images annotated at the gland level by trained pre-medical students and verified by an expert pathologist. We highlight the potential of this adaptive and uncertainty-aware framework for developing clinically deployable AI tools that can support pathologists in accurate prostate cancer grading, improve diagnostic accuracy, and create positive patient outcomes., Comment: 5 pages, 3 figures, one table. Accepted for presentation at the 22nd International Conference on Artificial Intelligence in Medicine (AIME 2024)

Point cloud matching, a crucial technique in computer vision, medical and robotics fields, is primarily concerned with finding correspondences between pairs of point clouds or voxels. In some practical scenarios, emphasizing local differences is crucial for accurately identifying a correct match, thereby enhancing the overall robustness and reliability of the matching process. Commonly used shape descriptors have several limitations and often fail to provide meaningful local insights about the paired geometries. In this work, we propose a new technique, based on graph Laplacian eigenmaps, to match point clouds by taking into account fine local structures. To deal with the order and sign ambiguity of Laplacian eigenmaps, we introduce a new operator, called Coupled Laplacian (https://github.com/matteo-bastico/CoupLap), that allows to easily generate aligned eigenspaces for multiple registered geometries. We show that the similarity between those aligned high-dimensional spaces provides a locally meaningful score to match shapes. We firstly evaluate the performance of the proposed technique in a point-wise manner, focusing on the task of object anomaly localization on the MVTec 3D-AD dataset. Additionally, we define a new medical task, called automatic Bone Side Estimation (BSE), which we address through a global similarity score derived from coupled eigenspaces. In order to test it, we propose a benchmark collecting bone surface structures from various public datasets. Our matching technique, based on Coupled Laplacian, outperforms other methods by reaching an impressive accuracy on both tasks., Comment: This paper has been accepted at Computer Vision and Patter Recognition (CVPR) 2024

We give an alternative derivation of $(N,N)$-isogenies between fast Kummer surfaces which complements existing works based on the theory oftheta functions. We use this framework to produce explicit formulae for the case of $N = 3$, and show that the resulting algorithms are more efficient than all prior $(3, 3)$-isogeny algorithms.

Nanodiamonds (NDs) gained increasing attention in multiple research areas due to the possibility of tuning their physical and chemical features by functionalizing their surface. This has a crucial impact on their electrical properties, which are essential in applications such as the development of innovative sensors and in the biomedical field. The great interest in electrical conduction in NDs has driven the scientific community to its extensive investigation. The role of various functionalities has been considered and different conduction mechanisms have been proposed. In this work, we reported on a systematic study of the modification of the electrical properties of differently sized NDs, as a function of different thermal treatments in air, hydrogen or inert atmosphere. Samples were electrically characterized in controlled humidity conditions to consider the influence of water on conductivity. NDs electrical properties were interpreted in connection with their surface chemistry and structural features, probed with infrared and Raman spectroscopies. The presence of surface graphite, hydrogen terminations or water adsorbed on hydrophilic oxygen-containing functional groups rendered NDs more conductive. These moieties indeed enabled different conduction mechanisms, which were respectively graphite-mediated conduction, water-induced transfer doping and Grotthus mechanism in surface-adsorbed water. The effect of particles size on conductivity has also been evaluated and discussed. Our experimental findings shed light on the link between surface modifications and electrical properties of NDs, providing at the same time an interpretative key to understanding the effect of particles dimensions.

Nitrogen-Vacancy (NV) centers in diamond are promising systems for quantum technologies, including quantum metrology and sensing. A promising strategy for the achievement of high sensitivity to external fields relies on the exploitation of large ensembles of NV centers, whose fabrication by ion implantation is upper limited by the amount of radiation damage introduced in the diamond lattice. In this works we demonstrate an approach to increase the density of NV centers upon the high-fluence implantation of MeV N2+ ions on a hot target substrate (>550 {\deg}C). Our results show that, with respect to room-temperature implantation, the high-temperature process increases the vacancy density threshold required for the irreversible conversion of diamond to a graphitic phase, thus enabling to achieve higher density ensembles. Furthermore, the formation efficiency of color centers was investigated on diamond substrates implanted at varying temperatures with MeV N2+ and Mg+ ions revealing that the formation efficiency of both NV centers and magnesium-vacancy (MgV) centers increases with the implantation temperature., Comment: 12 pages, 5 figures

We prove comparison principle for viscosity solutions of a Hamilton-Jacobi-Bellman equation in a strong coupling regime considering a stationary and a time-dependent version of the equation. We consider a Hamiltonian that has a representation as the supremum of a difference of two functions: an internal Hamiltonian depending on a control variable and a function interpreted as a cost of applying the controls. Our major innovation lies in the use of a cost function that can be discontinuous, unbounded and depending on momenta, enabling us to address previously unexplored scenarios such as cases arising from the theory of large deviations and homogenisation. For completeness, we also state the existence of viscosity solutions and we verify the assumptions for an example arising from biochemistry.

When it comes to clinical images, automatic segmentation has a wide variety of applications and a considerable diversity of input domains, such as different types of Magnetic Resonance Images (MRIs) and Computerized Tomography (CT) scans. This heterogeneity is a challenge for cross-modality algorithms that should equally perform independently of the input image type fed to them. Often, segmentation models are trained using a single modality, preventing generalization to other types of input data without resorting to transfer learning techniques. Furthermore, the multi-modal or cross-modality architectures proposed in the literature frequently require registered images, which are not easy to collect in clinical environments, or need additional processing steps, such as synthetic image generation. In this work, we propose a simple framework to achieve fair image segmentation of multiple modalities using a single conditional model that adapts its normalization layers based on the input type, trained with non-registered interleaved mixed data. We show that our framework outperforms other cross-modality segmentation methods, when applied to the same 3D UNet baseline model, on the Multi-Modality Whole Heart Segmentation Challenge. Furthermore, we define the Conditional Vision Transformer (C-ViT) encoder, based on the proposed cross-modality framework, and we show that it brings significant improvements to the resulting segmentation, up to 6.87\% of Dice accuracy, with respect to its baseline reference. The code to reproduce our experiments and the trained model weights are available at https://github.com/matteo-bastico/MI-Seg., Comment: This paper has been accepted in International Conference on Computer Vision Workshops (ICCVW) 2023

We investigate the quantification of demographic risk in a framework consistent with the market-consistent valuation imposed by Solvency II. We provide compact formulas for evaluating inflows and outflows of a portfolio of insurance policies based on a cohort approach. In this context, we maintain the highest level of generality in order to consider both traditional policies and equity-linked policies: therefore, we propose a market-consistent valuation of the liabilities. In the second step we evaluate the Solvency Capital Requirement of the idiosyncratic risk, linked to accidental mortality, and the systematic risk one, also known as trend risk, proposing a formal closed formula for the former and an algorithm for the latter. We show that accidental volatility depends on the intrinsic characteristics of the policies of the cohort (Sums-at-Risk), on the age of the policyholders and on the variability of the sums insured; trend risk depends both on accidental volatility and on the longevity forecasting model used.