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In this article, we provide a comprehensive analysis of the asymptotic behavior of Bell numbers, enhancing and unifying various results previously dispersed in the literature. We establish several explicit lower and upper bounds. The main results correspond to two asymptotic forms expressed by means of the Lambert $W$ function. As an application, some straightforward elementary bounds are derived. Additionally, an absolute convergence rate of the ratio of the consecutive Bell numbers is derived. The main challenge was to obtain satisfactory constants, as the Bell numbers grow rapidly, while the convergence rates are rather slow.

A non-uniform and inhomogeneous random hypergraph model is considered, which is a straightforward extension of the celebrated binomial random graph model $\mathbb G(n, p)$. We establish necessary and sufficient conditions for small hypergraph count to be asymptotically normal, and complement them with convergence rate in both the Wasserstein and Kolmogorov distances. Next we narrow our attention to the homogeneous model and relate the obtained results to the fourth moment phenomenon. Additionally, a short proof of necessity of aforementioned conditions is presented, which seems to be absent in the literature even in the context of the model $\mathbb G(n, p)$.

Advances in analytical scanning transmission electron microscopy (STEM) and microelectronic mechanical systems (MEMS) based microheaters have enabled in-situ materials characterization at the nanometer scale at elevated temperature. In addition to resolving the structural information at elevated temperatures, detailed knowledge of the local temperature distribution inside the sample is essential to reveal thermally induced phenomena and processes. Here, we investigate the accuracy of plasmon energy expansion thermometry (PEET) as a method to map the local temperature in a tungsten (W) lamella in a range between room temperature and 700 degC. In particular, we address the influence of sample thickness in the range of a typical electron-transparent TEM sample (from 30 nm to 70 nm) on the temperature-dependent plasmon energy. The shift in plasmon energy, used to determine the local sample temperature, is not only temperature-dependent, but in case of W also thickness-dependent in sample thicknesses below approximately 60 nm. The results highlight the importance of considering sample thickness (and especially thickness variations) when analyzing the local bulk plasmon energy for temperature measurement using PEET. However, in case of W, an increasing beam broadening (FWHM) of the bulk plasmon peak with decreasing sample thickness can be used to improve the accuracy of PEET in TEM lamellae with varying sample thickness.

We extend the classical Baire category approach, used in proving the finite generator theorem of Krieger, the homomorphism theorem of Sinai and the isomorphism theorem of Ornstein, applying a similar reasoning to the case of actions of countably infinite amenable groups. In principle we follow the lines of the paper by Burton, Keane and Serafin (\cite{BKS}), showing that measures defining homomorphisms or isomorphisms form residual subsets in suitably chosen spaces of joinings.

Social welfare orders seek to combine the disparate preferences of an infinite sequence of generations into a single, societal preference order in some reasonably-equitable way. In [2] Dubey and Laguzzi study a type of social welfare order which they call SEA, for strongly equitable and (finitely) anonymous. They prove that the existence of a SEA order implies the existence of a set of reals which does not have the Baire property, and observe that a nonprincipal ultrafilter on $\mathbb{N}$ can be used to construct a SEA order. Questions arising in their work include whether the existence of a SEA order implies the existence of either a set of real numbers which is not Lebesgue-measurable or of a nonprincipal ultrafilter on $\mathbb{N}$. We answer both these questions, the solution to the second using the techniques of geometric set theory as set out by Larson and Zapletal in [11]. The outcome is that the existence of a SEA order does imply the existence of a set of reals which is not Lebesgue-measurable, and does not imply the existence of a nonprincipal ultrafilter on $\mathbb{N}$., Comment: 15 pages; comments welcome

Solute segregation in materials with grain boundaries (GBs) has emerged as a popular method to thermodynamically stabilize nanocrystalline structures. However, the impact of varied GB crystallographic character on solute segregation has never been thoroughly examined. This work examines Co solute segregation in a dataset of 7272 Al bicrystal GBs that span the 5D space of GB crystallographic character. Considerable attention is paid to verification of the calculations in the diverse and large set of GBs. In addition, the results of this work are favorably validated against similar bicrystal and polycrystal simulations. As with other work, we show that Co atoms exhibit strong segregation to sites in Al GBs and that segregation correlates strongly with GB energy and GB excess volume. Segregation varies smoothly in the 5D crystallographic space but has a complex landscape without an obvious functional form., Comment: 15 pages, 10 figures, and supplemental materials

We study how experience with asset price bubbles changes the trading strategies of reinforcement learning (RL) traders and ask whether the change in trading strategies helps to prevent future bubbles. We train the RL traders in a multi-agent market simulation platform, ABIDES, and compare the strategies of traders trained with and without bubble experience. We find that RL traders without bubble experience behave like short-term momentum traders, whereas traders with bubble experience behave like value traders. Therefore, RL traders without bubble experience amplify bubbles, whereas RL traders with bubble experience tend to suppress and sometimes prevent them. This finding suggests that learning from experience is a mechanism for a boom and bust cycle where the experience of a collapsing bubble makes future bubbles less likely for a period of time until the memory fades and bubbles become more likely to form again.

Research on deep learning-powered voice conversion (VC) in speech-to-speech scenarios is getting increasingly popular. Although many of the works in the field of voice conversion share a common global pipeline, there is a considerable diversity in the underlying structures, methods, and neural sub-blocks used across research efforts. Thus, obtaining a comprehensive understanding of the reasons behind the choice of the different methods in the voice conversion pipeline can be challenging, and the actual hurdles in the proposed solutions are often unclear. To shed light on these aspects, this paper presents a scoping review that explores the use of deep learning in speech analysis, synthesis, and disentangled speech representation learning within modern voice conversion systems. We screened 621 publications from more than 38 different venues between the years 2017 and 2023, followed by an in-depth review of a final database consisting of 123 eligible studies. Based on the review, we summarise the most frequently used approaches to voice conversion based on deep learning and highlight common pitfalls within the community. Lastly, we condense the knowledge gathered, identify main challenges and provide recommendations for future research directions.

Geschke, Lubarsky, and Rahn in ``Choice and the Hat Game''~\cite{choice-and-the-hat-game} generalize the classic hat game puzzle to infinitely-many players and ask whether every model of set theory without choice in which the optimal solution can be carried out contains either a nonprincipal ultrafilter on $\mathbb N$ or else a Vitali set. A negative answer is obtained here by constructing a model in which there is an optimal solution to the hat game puzzle but no nonprincipal ultrafilter on $\mathbb N$ and no Vitali set. This is accomplished in a more general setting, establishing that for any Borel bipartite graph $\Gamma$ not embedding some $K_{n,\omega_1}$ and with countable colouring number there is a model of $\mbox{ZF} + \mbox{DC}$ in which $\Gamma$ has a $2$-colouring but there is no ultrafilter as above or Vitali set. The same conclusion applies to the natural generalization of the hat game to an arbitrary finite number of hat colours., Comment: 11 pages

Using archival data from the 42 foot telescope at the Jodrell Bank Observatory, we produce daily stacks of aligned giant pulses for the Crab pulsar, to study changes to the daily profiles between April 2012 to December 2016. From these, we identify echoes, where intervening material away from the line of sight causes pulsed emission to be redirected towards the observer, with delay corresponding to the increased distance of travel, resulting in additional profile components. These observations show that such echoes may be far more common than implied by the previous rate of detections. All the observed echoes are consistent with approaching zero-delay at their closest approach to the normal giant pulse emission. This indicates that the structures responsible for producing these events must be highly anisotropic, with typical lengths greater than $\sim 4\textrm{AU}$, typical widths on the sky of $\sim 0.1 \textrm{AU}$ and typical depths of $\sim 5\textrm{AU}$, given the previously observed electron densities of the nebular filaments, on the order of 1000 cm$^{-3}$. This suggests that these inhomogeneities are likely to be offshoot substructure from the larger nebular filaments of the Crab nebula., Comment: 11 pages, 7 figures, accepted for publication in The Astrophysical Journal

This paper concerns a method of describing hadrons that starts with the canonical front form Hamiltonian of QCD. The method is developed in the relatively simple context of QCD with only heavy quarks. We regulate its canonical Hamiltonian by introducing a vanishingly small gluon mass $m_g$. For positive $m_g$, the small-$x$ gluon divergences become ultraviolet and hence they are renormalized in the same way the ultraviolet transverse divergences are. This is done using the renormalization group procedure for effective particles. Up to the second order of expansion of the renormalized Hamiltonian in powers of the quark-gluon coupling constant $g$, only the quark mass-squared and gluon-exchange divergences require counter terms. In these circumstances, we calculate an effective potential between quarks in heavy quarkonia in an elementary way, replacing all the quarkonium-state components with gluons of mass $m_g$ by only one component with just one gluon that is assigned a mass $m_G$, comparable to or exceeding the scale of typical relative momenta of bound quarks. In the limit of $m_g \to 0$ and large $m_G$ two results are obtained. (1) While the color-singlet quarkonium mass eigenvalue stays finite and physically reasonable in that limit, the eigenvalues for single quarks and octet quarkonia are infinite. (2) The effective quark-antiquark potential is quadratic as a function of the distance and spherically symmetric for typical separations between quarks but becomes logarithmic and no longer spherically symmetric for large separations. Our conclusion indicates how to systematically improve upon the approximations made in this paper., Comment: 31 pages, 4 figures

Human tissue and its constituent cells form a microenvironment that is fundamentally three-dimensional (3D). However, the standard-of-care in pathologic diagnosis involves selecting a few two-dimensional (2D) sections for microscopic evaluation, risking sampling bias and misdiagnosis. Diverse methods for capturing 3D tissue morphologies have been developed, but they have yet had little translation to clinical practice; manual and computational evaluations of such large 3D data have so far been impractical and/or unable to provide patient-level clinical insights. Here we present Modality-Agnostic Multiple instance learning for volumetric Block Analysis (MAMBA), a deep-learning-based platform for processing 3D tissue images from diverse imaging modalities and predicting patient outcomes. Archived prostate cancer specimens were imaged with open-top light-sheet microscopy or microcomputed tomography and the resulting 3D datasets were used to train risk-stratification networks based on 5-year biochemical recurrence outcomes via MAMBA. With the 3D block-based approach, MAMBA achieves an area under the receiver operating characteristic curve (AUC) of 0.86 and 0.74, superior to 2D traditional single-slice-based prognostication (AUC of 0.79 and 0.57), suggesting superior prognostication with 3D morphological features. Further analyses reveal that the incorporation of greater tissue volume improves prognostic performance and mitigates risk prediction variability from sampling bias, suggesting the value of capturing larger extents of heterogeneous 3D morphology. With the rapid growth and adoption of 3D spatial biology and pathology techniques by researchers and clinicians, MAMBA provides a general and efficient framework for 3D weakly supervised learning for clinical decision support and can help to reveal novel 3D morphological biomarkers for prognosis and therapeutic response.

It is generally accepted that the phonon gas of a superfluid always enters a weak coupling regime at sufficiently low temperatures, whatever the strength of the interactions between the underlying particles (constitutive of the superfluid). Thus, in this limit, we should always be able to calculate the damping rate of thermal phonons by applying Fermi's golden rule to the Hamiltonian $H_3$ of cubic phonon-phonon coupling taken from quantum hydrodynamics, at least in the case of a convex acoustic branch and in the collisionless regime (where the eigenfrequency of the considered phonons remains much greater than the gas thermalization rate). Using the many-body Green's function method, we predict that, unexpectedly, this is not true in two dimensions, contrary to the three-dimensional case. We confirm this prediction with classical phonon-field simulations and a non-perturbative theory in $H_3$, where the fourth order is regularized by hand, giving a complex energy to the virtual phonons of the four-phonon collisional processes. For a weakly interacting fluid and a phonon mode in the long-wavelength limit, we predict a damping rate about three times lower than that of the golden rule., Comment: In French (43 pages) and in English (42 pages) (published version)

The SPICE/HeRALD collaboration is performing R&D to enable studies of sub-GeV dark matter models using a variety of target materials. Here we report our recent progress on instrumenting a superfluid $^4$He target mass with a transition-edge sensor based calorimeter to detect both atomic signals (e.g. scintillation) and $^4$He quasiparticle (phonon and roton) excitations. The sensitivity of HeRALD to the critical "quantum evaporation" signal from $^4$He quasiparticles requires us to block the superfluid film flow to the calorimeter. We have developed a heat-free film-blocking method employing an unoxidized Cs film, which we implemented in a prototype "HeRALD v0.1" detector of $\sim$10~g target mass. This article reports initial studies of the atomic and quasiparticle signal channels. A key result of this work is the measurement of the quantum evaporation channel's gain of $0.15 \pm 0.012$, which will enable $^4$He-based dark matter experiments in the near term. With this gain the HeRALD detector reported here has an energy threshold of 145~eV at 5 sigma, which would be sensitive to dark matter masses down to 220~MeV/c$^2$., Comment: 14 pages, 9 figures

Using the proof of Willmore's conjecture by Marques and Neves, we conjecture that the free energy of tensionless fluid membranes of arbitrary genus has an upper bound. This implies that the average genus of such a membrane, in equilibrium, is finite, regardless of external constraints. We propose that the Gaussian rigidity may be determined by measuring the relative frequencies of large-genus configurations at low temperature., Comment: v2: new results; 5 pages, 2 figures. v1: 4 pages, 1 figure

Virtual analog (VA) audio effects are increasingly based on neural networks and deep learning frameworks. Due to the underlying black-box methodology, a successful model will learn to approximate the data it is presented, including potential errors such as latency and audio dropouts as well as non-linear characteristics and frequency-dependent phase shifts produced by the hardware. The latter is of particular interest as the learned phase-response might cause unwanted audible artifacts when the effect is used for creative processing techniques such as dry-wet mixing or parallel compression. To overcome these artifacts we propose differentiable signal processing tools and deep optimization structures for automatically tuning all-pass filters to predict the phase response of different VA simulations, and align processed signals that are out of phase. The approaches are assessed using objective metrics while listening tests evaluate their ability to enhance the quality of parallel path processing techniques. Ultimately, an over-parameterized, BiasNet-based, all-pass model is proposed for the optimization problem under consideration, resulting in models that can estimate all-pass filter coefficients to align a dry signal with its affected, wet, equivalent., Comment: Collaboration done while interning/employed at Native Instruments. Accepted for publication in Proc. DAFX'23, Copenhagen, Denmark, September 2023. Sound examples at https://abargum.github.io v2: 10 pages, LaTeX; figures resized, pdf optimized

We apply the renormalization group procedure for effective particles (RGPEP) to the QCD eigenvalue problem for only heavy quarks. We derive the effective Hamiltonian that acts on the Fock space by solving the RGPEP equation up to second order in powers of the coupling constant. The eigenstates that contain three quarks and two or more gluons are eliminated by inserting a gluon-mass term in the component with one gluon and formulate the eigenvalue problem for baryons. We estimate masses for $bbb$ and $ccc$ states and find that the results match the estimates obtained in lattice QCD and in quark models., Comment: Presented by Mar{\'i}a G\'omez-Rocha at the International Conference on the Structure of Baryons, November 7-11th, Universidad Pablo de Olavide, Sevilla, Spain. 11 pages, 2 figures, 2 tables

This paper presents a novel approach for constructing probabilistic forecasts, which combines both the Quantile Regression Averaging (QRA) method and the Principal Component Analysis (PCA) averaging scheme. The performance of the approach is evaluated on datasets from two European energy markets - the German EPEX SPOT and the Polish Power Exchange (TGE). The results indicate that newly proposed solutions yield results, which are more accurate than the literature benchmarks. Additionally, empirical evidence indicates that the proposed method outperforms its competitors in terms of the empirical coverage and the Christoffersen test. In addition, the economic value of the probabilistic forecast is evaluated on the basis of financial metrics. We test the performance of forecasting models taking into account a day-ahead market trading strategy that utilizes probabilistic price predictions and an energy storage system. The results indicate that profits of up to 10 EUR per 1 MWh transaction can be obtained when predictions are generated using the novel approach.

This paper presents the results of a needs analysis survey for Reverse Engineering (RE). The need for reverse engineers in digital forensics, continues to grow as malware analysis becomes more complicated. The survey was created to investigate tools used in the cybersecurity industry, the methods for teaching RE and educational resources related to RE. Ninety-three (n=93) people responded to our 58 question survey. Participants did not respond to all survey questions as they were optional. The data showed that the majority of 24/71 (33.8%) responses either strongly agreed and 22/71 (30.99%) of responses somewhat agreed that there is a shortage in RE resources. Furthermore, a majority of 17/72 (23.61%) responses indicated that they strongly disagree and that 27/72 (37.5%) somewhat disagree to the statement that graduates are leaving college with adequate RE knowledge. When asked if there is a shortage of adequate RE candidates, the majority of 33/71 (46.48%) responses strongly agreed and 20/71 (28.17%) somewhat agreed. In order to determine if this was a result of the tools at their disposal, a series of questions in regards to the two most popular RE tools were also asked.