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This document is comprised of a collection of updated preliminary parameters for the key parts of the muon collider. The updated preliminary parameters follow on from the October 2023 Tentative Parameters Report. Particular attention has been given to regions of the facility that are believed to hold greater technical uncertainty in their design and that have a strong impact on the cost and power consumption of the facility. The data is collected from a collaborative spreadsheet and transferred to overleaf.

We present the study of an end-to-end multi-track reconstruction algorithm for the central drift chamber of the Belle II experiment at the SuperKEKB collider using Graph Neural Networks for an unknown number of particles. The algorithm uses detector hits as inputs without pre-filtering to simultaneously predict the number of track candidates in an event and and their kinematic properties. In a second step, we cluster detector hits for each track candidate to pass to a track fitting algorithm. Using a realistic full detector simulation including beam-induced backgrounds and detector noise taken from actual collision data, we find significant improvements in track finding efficiencies for tracks in a variety of different event topologies compared to the existing baseline algorithm used in Belle II. For events with a hypothetical long-lived massive particle with a mass in the GeV-range decaying uniformly along its flight direction into two charged particles, the GNN achieves a combined track finding and fitting efficiency of 85.4% with a fake rate of 2.5%, compared to 52.2% and 4.1% for the baseline algorithm. This is the first end-to-end multi-track machine learning algorithm for a drift chamber detector that has been utilized in a realistic particle physics environment.

Two-body decays like $K \to \pi a$ rank among the most constraining collider probes for new, low-mass, feebly interacting pseudoscalar particles $a$. We explore an alternative class of kaon decay modes, specifically three-body decays to $\pi \pi a$ or $\mu \mu a$. The former occur at tree level, while the latter is loop-suppressed yet accidentally finite. These modes specifically leverage the accurate tracking capabilities at LHCb. We present an estimation approach for the sensitivity achievable in future searches within these channels. Our argument uses the current uncertainty in leading irreducible backgrounds identified for each channel. Our findings suggest that dedicated searches could probe $f_a$ scales between $10^4$ and $10^6$ TeV, highlighting their strong potential. A direct comparison with actual searches, only available in the $K^+ \to \pi^+ \pi^0 a$ channel, supports this conclusion. Finally, we show that, in these searches, reconstruction efficiency maps are such that large efficiencies are naturally aligned with regions of higher yields in Dalitz plots., Comment: 17 pages, 10 figures

Gaussian states of bosonic quantum systems enjoy numerous technological applications and are ubiquitous in nature. Their significance lies in their simplicity, which in turn rests on the fact that they are uniquely determined by two experimentally accessible quantities, their first and second moments. But what if these moments are only known approximately, as is inevitable in any realistic experiment? What is the resulting error on the Gaussian state itself, as measured by the most operationally meaningful metric for distinguishing quantum states, namely, the trace distance? In this work, we fully resolve this question by demonstrating that if the first and second moments are known up to an error $\varepsilon$, the trace distance error on the state also scales as $\varepsilon$, and this functional dependence is optimal. To prove this, we establish tight bounds on the trace distance between two Gaussian states in terms of the norm distance of their first and second moments. As an application, we improve existing bounds on the sample complexity of tomography of Gaussian states., Comment: 27 pages

While it is very common to model diffusion as a random walk by assuming memorylessness of the trajectory and diffusive step lengths, these assumptions can lead to significant errors. This paper describes the extent to which a physical trajectory of a Brownian particle can be described by a random flight. Analysis of simple timelapses of physical trajectories (calculated over collisional timescales using a velocity autocorrelation function that captures the hydrodynamic and acoustic effects induced by the solvent) gave us two observations: (i) subsampled trajectories become genuinely memoryless only when the time step is ~200 times larger than the relaxation time, and (ii) the distribution of the step lengths has variances that remain significantly smaller than 2Dt (usually by a factor of ~2). This last fact is due to the combination of two effects: diffusional MSD is mathematically superballistic at short timescales and subsampled trajectories are moving averages of the underlying physical trajectory. In other words, the MSD of the physical trajectory at long time intervals asymptotically approaches 2Dt, but the MSD of the subsampled steps does not, even when the associated time interval is several hundred times larger than the relaxation time. I discuss how to best account for this effect in computational approaches., Comment: 6 figures

The accurate modeling of individual movement in cities has significant implications for policy decisions across various sectors. Existing research emphasizes the universality of human mobility, positing that simple models can capture population-level movements. However, population-level accuracy does not guarantee consistent performance across all individuals. By overlooking individual differences, universality laws may accurately describe certain groups while less precisely representing others, resulting in aggregate accuracy from a balance of discrepancies. Using large-scale mobility data, we assess individual-level accuracy of a universal model, the Exploration and Preferential Return (EPR), by examining deviations from expected behavior in two scaling laws - one related to exploration and the other to return patterns. Our findings reveal that, while the model can describe population-wide movement patterns, it displays widespread deviations linked to individuals' behavioral traits, socioeconomic status, and lifestyles, contradicting model assumptions like non-bursty exploration and preferential return. Specifically, individuals poorly represented by the EPR model tend to visit routine locations in sequences, exploring rarely but in a bursty manner when they do. Among socioeconomic factors, income most strongly correlates with significant deviations. Consequently, spatial inhomogeneity emerges in model accuracy, with lower performance concentrated in urbanized, densely populated areas, underscoring policy implications. Our results show that emphasizing population-wide models can propagate socioeconomic inequalities by poorly representing vulnerable population sectors.

We analyze the precision of currents in a generic multi-terminal quantum-transport setting. Employing scattering theory, we show that the precision of the currents is limited by a function of the particle-current noise that can be interpreted as the activity in the classical limit. We thereby establish a kinetic uncertainty relation for quantum transport. In the full quantum limit, we find precision bounds in which we modify the activity constraints depending on whether the system is fermionic or bosonic. We expect these bounds to be guidelines for any transport process aiming at high precision., Comment: 12 pages, 5 figures

We revisit the expected sensitivity of large-scale xenon detectors to Weakly Interacting Massive Particles (WIMPs). Assuming current primary noise sources can be mitigated, we find that with the present discrimination power between nuclear and electron recoils, the experimental sensitivity is limited not only by atmospheric neutrinos' nuclear recoils (''nuclear recoil neutrino fog'') but also by solar neutrinos' electron-recoil events (''electron recoil neutrino fog''). While this is known by experimentalists, it is often missed or misunderstood by theorists, and we therefore emphasize this effect. We set up a realistic detector simulation to quantify the contamination of the WIMP signal from both these neutrino backgrounds. We observe that the electron-recoil background remains significant even for signal rates exceeding those of atmospheric neutrinos, as predicted by most electroweak WIMP candidates. We update the projections for the required exposure to exclude/discover a given electroweak WIMP, streamlining the computation of their signal rates and uncertainties. We show that all of the real WIMPs with zero hypercharge can be excluded (discovered) with a 50 tonne year (300 tonne year) exposure. A similar exposure will allow to probe a large portion of the viable parameter space for complex WIMP with non-zero hypercharge., Comment: 17+6 pages, 9+3 figures, GitHub link for full analysis details

Less than 10 meters deep, shallow landslides are rapidly moving and strongly dangerous slides. In the present work, the probabilistic distribution of the landslide detachment points within a valley is modelled as a spatial Poisson point process, whose intensity depends on geophysical predictors according to a generalized additive model. Modelling the intensity with a generalized additive model jointly allows to obtain good predictive performance and to preserve the interpretability of the effects of the geophysical predictors on the intensity of the process. We propose a novel workflow, based on Random Forests, to select the geophysical predictors entering the model for the intensity. In this context, the statistically significant effects are interpreted as activating or stabilizing factors for landslide detachment. In order to guarantee the transferability of the resulting model, training, validation, and test of the algorithm are performed on mutually disjoint valleys in the Alps of Lombardy (Italy). Finally, the uncertainty around the estimated intensity of the process is quantified via semiparametric bootstrap.

Diffusion-based recommender systems have recently proven to outperform traditional generative recommendation approaches, such as variational autoencoders and generative adversarial networks. Nevertheless, the machine learning literature has raised several concerns regarding the possibility that diffusion models, while learning the distribution of data samples, may inadvertently carry information bias and lead to unfair outcomes. In light of this aspect, and considering the relevance that fairness has held in recommendations over the last few decades, we conduct one of the first fairness investigations in the literature on DiffRec, a pioneer approach in diffusion-based recommendation. First, we propose an experimental setting involving DiffRec (and its variant L-DiffRec) along with nine state-of-the-art recommendation models, two popular recommendation datasets from the fairness-aware literature, and six metrics accounting for accuracy and consumer/provider fairness. Then, we perform a twofold analysis, one assessing models' performance under accuracy and recommendation fairness separately, and the other identifying if and to what extent such metrics can strike a performance trade-off. Experimental results from both studies confirm the initial unfairness warnings but pave the way for how to address them in future research directions.

The Master Stability Function is a robust and useful tool for determining the conditions of synchronization stability in a network of coupled systems. While a comprehensive classification exists in the case in which the nodes are chaotic dynamical systems, its application to periodic systems has been less explored. By studying several well-known periodic systems, we establish a comprehensive framework to understand and classify their properties of synchronizability. This allows us to define five distinct classes of synchronization stability, including some that are unique to periodic systems. Specifically, in periodic systems, the Master Stability Function vanishes at the origin, and it can therefore display behavioral classes that are not achievable in chaotic systems, where it starts, instead, at a strictly positive value. Moreover, our results challenge the widely-held belief that periodic systems are easily put in a stable synchronous state, showing, instead, the common occurrence of a lower threshold for synchronization stability., Comment: 8 pages, 6 figures, plus supplementary material with 5 pages and 6 figures

We study bipartite quantum systems kept at different temperatures where a tunnel coupling between the two subsystems induces transitions. We find two independent constraints on the temperature-bias-dependent, out-of-equilibrium tunneling rates between the two subsystems, which both turn out to be particularly restrictive when the coupled quantum systems are small. These bounds take the form of a thermodynamic and of an energetic constraint, as they are associated with the dissipated heat and with the absorbed energy required to establish and deplete the temperature bias, respectively. The derived constraints apply to a large class of experimentally accessible quantum systems: except for the restriction to the tunneling regime, they hold for arbitrary subsystem Hamiltonians, including interactions or non-linear energy spectra. These results hold for a large class of experimentally relevant systems, ranging from molecular junctions to coupled cavities, and can be tested by, for instance, measuring the out-of-equilibrium tunneling current and its noise.

We show that Frenkel's integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. Our main general result is a dimension-independent semi-continuity relation for the quantum relative entropy with respect to the first argument. Using it, we obtain a number of results: (1) a tight continuity relation for the conditional entropy in the case where the two states have equal marginals on the conditioning system, resolving a conjecture by Wilde in this special case; (2) a stronger version of the Fannes-Audenaert inequality on quantum entropy; (3) better estimates on the quantum capacity of approximately degradable channels; (4) an improved continuity relation for the entanglement cost; (5) general upper bounds on asymptotic transformation rates in infinite-dimensional entanglement theory; and (6) a proof of a conjecture due to Christandl, Ferrara, and Lancien on the continuity of 'filtered' relative entropy distances., Comment: 23 pages. In v2 we removed the claims on continuity of quantum channel capacities, as tighter bounds due to Shirokov are already available

DarkSide-20k (DS-20k) is a dark matter detection experiment under construction at the Laboratori Nazionali del Gran Sasso (LNGS) in Italy. It utilises ~100 t of low radioactivity argon from an underground source (UAr) in its inner detector, with half serving as target in a dual-phase time projection chamber (TPC). The UAr cryogenics system must maintain stable thermodynamic conditions throughout the experiment's lifetime of >10 years. Continuous removal of impurities and radon from the UAr is essential for maximising signal yield and mitigating background. We are developing an efficient and powerful cryogenics system with a gas purification loop with a target circulation rate of 1000 slpm. Central to its design is a condenser operated with liquid nitrogen which is paired with a gas heat exchanger cascade, delivering a combined cooling power of >8 kW. Here we present the design choices in view of the DS-20k requirements, in particular the condenser's working principle and the cooling control, and we show test results obtained with a dedicated benchmarking platform at CERN and LNGS. We find that the thermal efficiency of the recirculation loop, defined in terms of nitrogen consumption per argon flow rate, is 95 % and the pressure in the test cryostat can be maintained within $\pm$(0.1-0.2) mbar. We further detail a 5-day cool-down procedure of the test cryostat, maintaining a cooling rate typically within -2 K/h, as required for the DS-20k inner detector. Additionally, we assess the circuit's flow resistance, and the heat transfer capabilities of two heat exchanger geometries for argon phase change, used to provide gas for recirculation. We conclude by discussing how our findings influence the finalisation of the system design, including necessary modifications to meet requirements and ongoing testing activities., Comment: 45 pages, 24 figures

Recent developments in recommendation have harnessed the collaborative power of graph neural networks (GNNs) in learning users' preferences from user-item networks. Despite emerging regulations addressing fairness of automated systems, unfairness issues in graph collaborative filtering remain underexplored, especially from the consumer's perspective. Despite numerous contributions on consumer unfairness, only a few of these works have delved into GNNs. A notable gap exists in the formalization of the latest mitigation algorithms, as well as in their effectiveness and reliability on cutting-edge models. This paper serves as a solid response to recent research highlighting unfairness issues in graph collaborative filtering by reproducing one of the latest mitigation methods. The reproduced technique adjusts the system fairness level by learning a fair graph augmentation. Under an experimental setup based on 11 GNNs, 5 non-GNN models, and 5 real-world networks across diverse domains, our investigation reveals that fair graph augmentation is consistently effective on high-utility models and large datasets. Experiments on the transferability of the fair augmented graph open new issues for future recommendation studies. Source code: https://github.com/jackmedda/FA4GCF.

The Ricordi archive, a prestigious collection of significant musical manuscripts from renowned opera composers such as Donizetti, Verdi and Puccini, has been digitized. This process has allowed us to automatically extract samples that represent various musical elements depicted on the manuscripts, including notes, staves, clefs, erasures, and composer's annotations, among others. To distinguish between digitization noise and actual music elements, a subset of these images was meticulously grouped and labeled by multiple individuals into several classes. After assessing the consistency of the annotations, we trained multiple neural network-based classifiers to differentiate between the identified music elements. The primary objective of this study was to evaluate the reliability of these classifiers, with the ultimate goal of using them for the automatic categorization of the remaining unannotated data set. The dataset, complemented by manual annotations, models, and source code used in these experiments are publicly accessible for replication purposes., Comment: Accepted at AudioMostly 2024

Despite the central importance of quantum entanglement in fueling many quantum technologies, the understanding of the optimal ways to exploit it is still beyond our reach, and even measuring entanglement in an operationally meaningful way is prohibitively difficult. This is due to the need to precisely characterise many-copy, asymptotic protocols for entanglement processing. Here we overcome these issues by introducing a new way of benchmarking the fundamental protocol of entanglement distillation (purification), where instead of measuring its asymptotic yield, we focus on the best achievable error. We connect this formulation of the task with an information-theoretic problem in composite quantum hypothesis testing known as generalised Sanov's theorem. By solving the latter problem -- which had no previously known solution even in classical information theory -- we thus compute the optimal asymptotic error exponent of entanglement distillation. We show this asymptotic solution to be given by the reverse relative entropy of entanglement, a single-letter quantity that can be evaluated using only a single copy of a quantum state, which is a unique feature among operational measures of entanglement. Altogether, we thus demonstrate a measure of entanglement that admits a direct operational interpretation as the optimal asymptotic rate of an important entanglement manipulation protocol while enjoying an exact, single-letter formula., Comment: 18+18 pages

We solve the generalised quantum Stein's lemma, proving that the Stein exponent associated with entanglement testing, namely, the quantum hypothesis testing task of distinguishing between $n$ copies of an entangled state $\rho_{AB}$ and a generic separable state $\sigma_{A^n:B^n}$, equals the regularised relative entropy of entanglement. Not only does this determine the ultimate performance of entanglement testing, but it also establishes the reversibility of all quantum resource theories under asymptotically resource non-generating operations, with the regularised relative entropy of resource governing the asymptotic transformation rate between any two quantum states. As a by-product, we prove that the same Stein exponent can also be achieved when the null hypothesis is only approximately i.i.d., in the sense that it can be modelled by an "almost power state". To solve the problem we introduce two techniques. The first is a procedure that we call "blurring", which, informally, transforms a permutationally symmetric state by making it more evenly spread across nearby type classes. Blurring alone suffices to prove the generalised Stein's lemma in the fully classical case, but not in the quantum case. Our second technical innovation, therefore, is to perform a second quantisation step to lift the problem to an infinite-dimensional bosonic quantum system; we then solve it there by using techniques from continuous-variable quantum information. Rather remarkably, the second-quantised action of the blurring map corresponds to a pure loss channel. A careful examination of this second quantisation step is the core of our quantum solution., Comment: 59 pages, 2 figures. In v2 I corrected several typos and added the new Section VI, where the generalised quantum Stein's lemma is extended to almost power states

Reactions in solution require "contact" between the reagents. We can predict the rate at which reagents come into "contact" (at least in dilute conditions), but if the initial collision does not lead to reaction, what happens then? The collision rates in solution-phase reactions are generally described (explicitly or implicitly) with the Smoluchowski equation. Unfortunately, that model describes coagulations in gases, not reactions in solutions. The model is memory-less, i.e., collisions are treated as random processes, unaware of each other in space and time. The reality is that unreactive collisions create memory: particles (even molecules) "remember" they just collided, i.e, the probability of collision depends on how far back in time their prior collision happened. As we show here, this purely geometric and statistical fact is valid as long as their size is larger than the Kuhn length of their Brownian motion in solution. Under these conditions, particles in solution form, even in the absence of attractive interactions, relatively long-lived "clusters" kept together by the statistical unlikeliness of separating. We show here through Brownian dynamics simulations that, as a result of this memory, the collision rates and the lifetimes of these clusters, differently from what predicted by Smoluchowski's model, are proportional to the ratio between the radius of the colliders and the Kuhn length of their path in solution, with a coefficient close to unity!, Comment: 4 figures + 3 supporting information figures

In computational practice, we often encounter situations where only measurements at equally spaced points are available. Using standard polynomial interpolation in such cases can lead to highly inaccurate results due to numerical ill-conditioning of the problem. Several techniques have been developed to mitigate this issue, such as the mock-Chebyshev subset interpolation and the constrained mock-Chebyshev least-squares approximation. The high accuracy and the numerical stability achieved by these techniques motivate us to extend these methods to histopolation, a polynomial interpolation method based on segmental function averages. While classical polynomial interpolation relies on function evaluations at specific nodes, histopolation leverages averages of the function over subintervals. In this work, we introduce three types of mock-Chebyshev approaches for segmental interpolation and theoretically analyse the stability of their Lebesgue constants, which measure the numerical conditioning of the histopolation problem under small perturbations of the segments. We demonstrate that these segmental mock-Chebyshev approaches yield a quasi-optimal logarithmic growth of the Lebesgue constant in relevant scenarios. Additionally, we compare the performance of these new approximation techniques through various numerical experiments., Comment: 20 pages, 7 figure, 1 table

Travel Recommender Systems TRSs have been proposed to ease the burden of choice in the travel domain by providing valuable suggestions based on user preferences Despite the broad similarities in functionalities and data provided by TRSs these systems are significantly influenced by the diverse and heterogeneous contexts in which they operate This plays a crucial role in determining the accuracy and appropriateness of the travel recommendations they deliver For instance in contexts like smart cities and natural parks diverse runtime informationsuch as traffic conditions and trail status respectivelyshould be utilized to ensure the delivery of pertinent recommendations aligned with user preferences within the specific context However there is a trend to build TRSs from scratch for different contexts rather than supporting developers with configuration approaches that promote reuse minimize errors and accelerate timetomarket To illustrate this gap in this paper we conduct a systematic mapping study to examine the extent to which existing TRSs are configurable for different contexts The conducted analysis reveals the lack of configuration support assisting TRSs providers in developing TRSs closely tied to their operational context Our findings shed light on uncovered challenges in the domain thus fostering future research focused on providing new methodologies enabling providers to handle TRSs configurations, Comment: Accepted at the 50th Euromicro Conference Series on Software Engineering and Advanced Applications (SEAA) 2024

The dual-phase liquid argon time projection chamber is presently one of the leading technologies to search for dark matter particles with masses below 10 GeV/c$^2$. This was demonstrated by the DarkSide-50 experiment with approximately 50 kg of low-radioactivity liquid argon as target material. The next generation experiment DarkSide-20k, currently under construction, will use 1,000 times more argon and is expected to start operation in 2027. Based on the DarkSide-50 experience, here we assess the DarkSide-20k sensitivity to models predicting light dark matter particles, including Weakly Interacting Massive Particles (WIMPs) and sub-GeV/c$^2$ particles interacting with electrons in argon atoms. With one year of data, a sensitivity improvement to dark matter interaction cross-sections by at least one order of magnitude with respect to DarkSide-50 is expected for all these models. A sensitivity to WIMP--nucleon interaction cross-sections below $1\times10^{-42}$ cm$^2$ is achievable for WIMP masses above 800 MeV/c$^2$. With 10 years exposure, the neutrino fog can be reached for WIMP masses around 5 GeV/c$^2$., Comment: submitted to Nature Communications

Light activated local stimulation and sensing of biological cells offers enormous potential for minimally invasive bioelectronic interfaces. Organic semiconductors are a promising material class to achieve this kind of transduction due to their optoelectronic properties and biocompatibility. Here we investigate which material properties are necessary to keep the optical excitation localized. This is critical to single cell transduction with high spatial resolution. As a model system we use organic photocapacitors for cell stimulation made of the small molecule semiconductors H2Pc and PTCDI. We investigate the spatial broadening of the localized optical excitation with photovoltage microscopy measurements. Our experimental data combined with modelling show that resolution losses due to the broadening of the excitation are directly related to the effective diffusion length of charge carriers generated at the heterojunction. With additional transient photovoltage measurements we find that the H2Pc/PTCDI heterojunction offers a small diffusion length of lambda = 1.5 +/- 0.1 um due to the small mobility of charge carriers along the heterojunction. Instead covering the heterojunction with a layer of PEDOT:PSS improves the photocapacitor performance but increases the carrier diffusion length to lambda = 7.0 +/- 0.3 um due to longer lifetime and higher carrier mobility. Furthermore, we introduce electrochemical photocurrent microscopy experiments to demonstrate micrometric resolution with the pn-junction under realistic aqueous operation conditions. This work offers valuable insights into the physical mechanisms governing the excitation and transduction profile and provide design principles for future organic semiconductor junctions, aiming to achieve high efficiency and high spatial resolution.

Model-Driven Engineering (MDE) is a software engineering methodology focusing on models as primary artifacts. In the last years, the emergence of Web technologies has led to the development of Web-based modeling tools and model-based approaches for the Web that offer a web-based environment to create and edit models or model-based low-code solutions. A common requirement when developing Web-based modeling tools is to provide a fast and efficient way for model management, and this is particularly a hot topic in model-based system engineering. However, the number of approaches offering RESTful services for model management is still limited. Among the alternatives for developing distributed services, there is a growing interest in the use of RESTful services. In this paper, we present an approach to provide RESTful services for model management that can be used to interact with any kind of model and can be used to build a modeling platform providing modeling-as-a-service. The approach follows the REST principles to provide a stateless and scalable service., Comment: 3 pages, 1 figure, 1 table

Alternative routing is crucial to minimize the environmental impact of urban transportation while enhancing road network efficiency and reducing traffic congestion. Existing methods neglect information about road popularity, possibly leading to unintended consequences such as increasing emissions and congestion. This paper introduces Polaris, an alternative routing algorithm that exploits road popularity to optimize traffic distribution and reduce CO2 emissions. Polaris leverages the novel concept of K-road layers, which mitigates the feedback loop effect where redirecting vehicles to less popular roads could increase their popularity in the future. We conduct experiments in three cities to evaluate Polaris against state-of-the-art alternative routing algorithms. Our results demonstrate that Polaris significantly reduces the overuse of highly popular road edges and traversed regulated intersections, showcasing its ability to generate efficient routes and distribute traffic more evenly. Furthermore, Polaris achieves substantial CO2 reductions, outperforming existing alternative routing strategies. Finally, we compare Polaris to an algorithm that coordinates vehicles centrally to distribute them more evenly on the road network. Our findings reveal that Polaris performs comparably well, even with much less information, highlighting its potential as an efficient and sustainable solution for urban traffic management.

We discuss numerical aspects of instantons in two- and three-dimensional $\phi^4$ theories with an internal $O(N)$ symmetry group, the so-called $N$-vector model. Combining asymptotic transseries expansions for large argument with convergence acceleration techniques, we obtain high-precision values for certain integrals of the instanton that naturally occur in loop corrections around instanton configurations. Knowledge of these numerical properties are necessary in order to evaluate corrections to the large-order factorial growth of perturbation theory in $\phi^4$ theories. The results contribute to the understanding of the mathematical structures underlying the instanton configurations., Comment: 11 pages; RevTeX

Observing and understanding the origin of the very-high-energy (VHE) spectral component in gamma-ray bursts (GRBs) has been challenging because of the lack of sensitivity in MeV-GeV observations, so far. The majestic GRB 221009A, known as the brightest of all times (BOAT), offers a unique opportunity to identify spectral components during the prompt and early afterglow phases and probe their origin. Analyzing simultaneous observations spanning from keV to TeV energies, we identified two distinct spectral components during the initial 20 minutes of the burst. The second spectral component peaks between $10-300$ GeV, and the bolometric fluence (10 MeV-10 TeV) is estimated to be greater than 2$\times10^{-3}$ erg/ cm$^{2}$. Performing broad-band spectral modeling, we provide constraints on the magnetic field and the energies of electrons accelerated in the external relativistic shock. We interpret the VHE component as an afterglow emission that is affected by luminous prompt MeV radiation at early times., Comment: Comments and suggestions are welcome

Quantum information theory is plagued by the problem of regularisations, which require the evaluation of formidable asymptotic quantities. This makes it computationally intractable to gain a precise quantitative understanding of the ultimate efficiency of key operational tasks such as entanglement manipulation. Here we consider the problem of computing the asymptotic entanglement cost of preparing noisy quantum states under quantum operations with positive partial transpose (PPT). A previously claimed solution to this problem is shown to be incorrect. We construct instead an alternative solution in the form of two hierarchies of semi-definite programs that converge to the true asymptotic value of the entanglement cost from above and from below. Our main result establishes that this convergence happens exponentially fast, thus yielding an efficient algorithm that approximates the cost up to an additive error $\varepsilon$ in time $\mathrm{poly}\big(D,\,\log(1/\varepsilon)\big)$, where $D$ is the underlying Hilbert space dimension. To our knowledge, this is the first time that an asymptotic entanglement measure is shown to be efficiently computable despite no closed-form formula being available., Comment: 7+24 pages, no figures