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Nonlinear dynamics have long been exploited in order to damp vibrations in solid mechanics. The phenomenon of irreversible energy transfer from a linear primary system to a nonlinear absorber has driven great attention to the optimal design of vibration absorbers both for stationary and transient regimes. Recently, the same principle has also been targeted in acoustics for the absorption of sound waves at high excitation amplitudes. Meanwhile, acoustic absorption by electro-active means has found great success for noise reduction in the linear regime. This study uses a method allowing the design of nonlinear resonators at amplitudes that typically induce linear behaviors. This research proposes an analytical study of the implementation of the duffing equation as a nonlinear electroacoustic resonator coupled to an acoustic mode of a tube. Experiments are carried out and compared to the analytical results. The experimental implementation is done using a real-time-based algorithm retrieving the measured pressure from a microphone and giving the electrical current to send to a loudspeaker as an output thanks to a Runge-Kutta-like algorithm., Comment: Preprint of a submitted article

We consider the problem of allocating indivisible resources to players so as to maximize the minimum total value any player receives. This problem is sometimes dubbed the Santa Claus problem and its different variants have been subject to extensive research towards approximation algorithms over the past two decades. In the case where each player has a potentially different additive valuation function, Chakrabarty, Chuzhoy, and Khanna [FOCS'09] gave an $O(n^{\epsilon})$-approximation algorithm with polynomial running time for any constant $\epsilon > 0$ and a polylogarithmic approximation algorithm in quasi-polynomial time. We show that the same can be achieved for monotone submodular valuation functions, improving over the previously best algorithm due to Goemans, Harvey, Iwata, and Mirrokni [SODA'09], which has an approximation ratio of more than $\sqrt{n}$. Our result builds up on a sophisticated LP relaxation, which has a recursive block structure that allows us to solve it despite having exponentially many variables and constraints.

We investigate the relation between galaxy structure and star formation rate (SFR) in a sample of $\sim2.9\times10^{4}$ central galaxies with $z<0.0674$ and axial ratios $b/a>0.5$. The star-forming main sequence (SFMS) shows a bend around the stellar mass of $M_\ast\leq{}M_c=2\times10^{10}{}M_{\odot}$. At $M_\ast\leq{}M_c$ the SFMS follows a power-law $\text{SFR}\propto{}M_\ast^{0.85}$, while at higher masses it flattens. $M_c$ corresponds to a dark matter halo mass of $M_\text{vir}\sim{}10^{11.8}M_{\odot}$ where virial shocks occurs. Some galaxy structure (e.g., half-light radius, $R_e$) exhibits a non-monotonic dependence across the SFMS at a fixed $M_\ast$. We find $\text{SFR}\propto{R_e^{-0.28}}$ at fixed $M_\ast$, consistent with the global Kennicutt-Schmidt (KS) law. This finding suggests that galaxy sizes contribute to the scatter of the SFMS. However, at $M_\ast>M_c$ the relationship between SFR and $R_e$ diminishes. Low-mass galaxies above the mean of the SFMS have smaller radii, exhibit compact and centrally concentrated profiles resembling green valley (GV) and quiescent galaxies at the same mass, and have higher $M_{\text{H}_2}/M_\text{HI}$. Conversely, those below the SFMS exhibit larger radii, lower densities, have no GV or quiescent counterparts at their mass and have lower $M_{\text{H}_2}/M_\text{HI}$. The above data suggest two pathways for quenching low-mass galaxies, $M_\ast\leq{}M_c$: a fast one that changes the morphology on the SFMS and a slow one that does not. Above $M_c$, galaxies below the SFMS resemble GV and quiescent galaxies structurally, implying that they undergo a structural transformation already within the SFMS. For these massive galaxies, CG are strongly bimodal, with SFMS galaxies exhibiting negative color gradients, suggesting most star formation occurs in their outskirts, maintaining them within the SFMS., Comment: 30 pages, 28 figures, submitted to MNRAS

Consider an $M$-th order linear differential operator, $M\geq 2$, $$ \mathcal{L}^{(M)}=\sum_{k=0}^{M}\rho_{k}(z)\frac{d^k}{dz^k}, $$ where $\rho_M $ is a monic complex polynomial such that $degree[\rho_M]=M$ and $(\rho_k)_{k=0}^{M-1}$ are complex polynomials such that $degree[ \rho_k ]\leq k, 0\leq k \leq M-1$. It is known that the zero counting measure of its eigenpolynomials converges in the weak star sense to a measure $\mu$. We obtain an asymptotic expansion of the eigenpolynomials of $\mathcal{L}^{(M)}$ in compact subsets out the support of $\mu$. In particular, we solve a conjecture posed in G.~Masson and B.~Shapiro, ``On polynomial eigenfunctions of a hypergeometric type operator,'' Exper. Math., vol.~10, pp.~609--618, 2001.

Below we study a linear differential equation $\MM (v(z,\eta))=\eta^M{v(z,\eta)}$, where $\eta>0$ is a large spectral parameter and $\MM=\sum_{k=1}^{M}\rho_{k}(z)\frac{d^k}{dz^k},\; M\ge 2$ is a differential operator with polynomial coefficients such that the leading coefficient $\rho_M(z)$ is a monic complex-valued polynomial with $\dgr{\rho_M }=M$ and other $\rho_k(z)$'s are complex-valued polynomials with $\dgr{\rho_k }\leq k$. We prove the Borel summability of its WKB-solutions in the Stokes regions. For $M=3$ under the assumption that $\rho_M$ has simple zeros, we give the full description of the Stokes complex (i.e. the union of all Stokes curves) of this equation. Finally, we show that for the Euler-Cauchy equations, their WKB-solutions converge in the usual sense.

We study a sample of 936 early-type galaxies located in 48 low-z regular galaxy clusters with $M_{200}\geq 10^{14}~ M_\odot$ at $z< 0.1$. We examine variations in the Kormendy relation (KR) according to their location in the projected phase space (PPS) of the clusters. We have used a combination of Bayesian statistical methods to identify possible differences between the fitted relations. Our results indicate that the overall KR is better fitted when we take into account the information about PPS regions. We also find that objects with time since infall $\geq 6.5$ Gyr have a significant statistical difference of the KR coefficients relative to objects that are more recent in the cluster environment. We show that giant central ellipticals are responsible for tilting the KR relation towards smaller slopes. These galaxies present a late growth probably due to cumulative preprocessing during infall, plus cannibalism and accretion of smaller stripped objects near the center of the clusters., Comment: 8 pages, 8 figures, appendix, published in MNRAS. arXiv admin note: text overlap with arXiv:2302.04287

We revisit the Next-to-Leading Order (two-loop) contributions to the Anomalous Dimensions of $\Delta F = 1$ four-quark operators in QCD. We devise a test for anomalous dimensions, that we regard as of general interest, and by means of which we detect a problem in the results available in the literature. Deconstructing the steps leading to the available result, we identify the source of the problem, which is related to the operator known as $Q_{11}$. We show how to fix the problem and provide the corrected anomalous dimensions. With the insight of our findings, we propose an alternative approach to the one used in the literature which does not suffer from the identified disease, and which confirms our corrected results. We assess the numerical impact of our corrections, which happens to be in the ballpark of $5\%$ in certain entries of the evolution matrix. Our results are important for the correct resummation of Next-to-Leading Logarithms in analyses of physics beyond the Standard Model in $\Delta F = 1$ processes, such as the decays of Kaons and $B$-mesons., Comment: 32 pages. Published version

This paper introduces a novel multimodal and high-resolution human brain cerebellum lobule segmentation method. Unlike current tools that operate at standard resolution ($1 \text{ mm}^{3}$) or using mono-modal data, the proposed method improves cerebellum lobule segmentation through the use of a multimodal and ultra-high resolution ($0.125 \text{ mm}^{3}$) training dataset. To develop the method, first, a database of semi-automatically labelled cerebellum lobules was created to train the proposed method with ultra-high resolution T1 and T2 MR images. Then, an ensemble of deep networks has been designed and developed, allowing the proposed method to excel in the complex cerebellum lobule segmentation task, improving precision while being memory efficient. Notably, our approach deviates from the traditional U-Net model by exploring alternative architectures. We have also integrated deep learning with classical machine learning methods incorporating a priori knowledge from multi-atlas segmentation, which improved precision and robustness. Finally, a new online pipeline, named DeepCERES, has been developed to make available the proposed method to the scientific community requiring as input only a single T1 MR image at standard resolution., Comment: 20 pages

Ferroics based on transition-metal (TM) substituted SrTiO$_{3}$ have called much attention as magnetism and/or ferroelectricity can be tuned by using cations substitution and defects, strain and/or oxygen deficiency. C. A. Ross et al. [Phys. Rev. Applied 7, 024006 (2017)] demonstrated the SrTi$_{1-x}$Fe$_{x}$O$_{3-\delta}$ (STF) magnetization behavior for different deposition oxygen-pressures, substrates and magnetic fields. The relation between oxygen deficiency and ferroic orders is yet to be well understood, for which the full potential of oxygen-stoichiometry engineered materials remain an open question. Here, we use hybrid-DFT to calculate different oxygen vacancy ($v_{o}$) states in STF with a variety of TM distributions. The resulting cations' magnetic states and alignments associated to the $v_{o}$ ground-states for $x=\{0.125,0.25\}$ are used within a Monte Carlo scope for collinear magnetism to simulate the spontaneous magnetization. Our model captures several experimental STF features i.e., display a maximum of the magnetization at intermediate number of vacancies, a monotonous quenching from $\sim{0.35}\mu{_{B}}$ for small ${\delta}$, and a slower decreasing of such saturation for larger number of vacancies. Moreover, our approach gives a further insight into the relations between defects stabilization and magnetization, vacancy density and the oxygen pressure required to maximize such ferroic order, and sets guidelines for future Machine Learning based computational synthesis of multiferroic oxides.

We study a sample of 936 early-type galaxies (ETGs) located in 48 low-z regular galaxy clusters with $M_{200}\geq 10^{14}~ M_\odot$ at $z< 0.1$. We examine variations in the concentration index, radius, and color gradient of ETGs as a function of their stellar mass and loci in the projected phase space (PPS) of the clusters. We aim to understand the environmental influence on the growth of ETGs according to the time since infall into their host clusters. Our analysis indicates a significant change in the behavior of the concentration index $C$ and color gradient around $M_{\ast} \approx 2\times 10^{11} ~M_\odot \equiv \tilde{M}_{\ast}$. Objects less massive than $ \tilde{M}_{\ast}$ present a slight growth of $C$ with $M_{\ast}$ with negative and approximately constant color gradients in all regions of the PPS. Objects more massive than $ \tilde{M}_{\ast}$ present a slight decrease of $C$ with $M_{\ast}$ with color gradients becoming less negative and approaching zero. We also find that objects more massive than $ \tilde{M}_{\ast}$, in all PPS regions, have smaller $R_{90}$ for a given $R_{50}$, suggesting a smaller external growth in these objects or even a shrinkage possibly due to tidal stripping. Finally, we estimate different dark matter fractions for galaxies in different regions of the PPS, with the ancient satellites having the largest fractions, $f_{DM}\approx$ 65%. These results favor a scenario where cluster ETGs experience environmental influence the longer they remain and the deeper into the gravitational potential they lie, indicating a combination of tidal stripping + harassment, which predominate during infall, followed by mergers + feedback effects affecting the late growth of ancient satellites and BCGs., Comment: 14 pages, 9 figures, accepted for publication in MNRAS; Appendix = 2 figures

Recently, many causal estimators for Conditional Average Treatment Effect (CATE) and instrumental variable (IV) problems have been published and open sourced, allowing to estimate granular impact of both randomized treatments (such as A/B tests) and of user choices on the outcomes of interest. However, the practical application of such models has ben hampered by the lack of a valid way to score the performance of such models out of sample, in order to select the best one for a given application. We address that gap by proposing novel scoring approaches for both the CATE case and an important subset of instrumental variable problems, namely those where the instrumental variable is customer acces to a product feature, and the treatment is the customer's choice to use that feature. Being able to score model performance out of sample allows us to apply hyperparameter optimization methods to causal model selection and tuning. We implement that in an open source package that relies on DoWhy and EconML libraries for implementation of causal inference models (and also includes a Transformed Outcome model implementation), and on FLAML for hyperparameter optimization and for component models used in the causal models. We demonstrate on synthetic data that optimizing the proposed scores is a reliable method for choosing the model and its hyperparameter values, whose estimates are close to the true impact, in the randomized CATE and IV cases. Further, we provide examles of applying these methods to real customer data from Wise., Comment: 9 pages, 6 figures

We report the existence of moir\'e patterns and magic angle physics in all families of chiral collapsed carbon nanotubes. A detailed study of the electronic structure of all types of chiral nanotubes, previously collapsed via molecular dynamics, has been performed. We find that each family possesses a unique geometry and moir\'e disposition, as well as a characteristic number of flat bands. Remarkably, all kinds of nanotubes behave the same with respect to magic angle tuning, showing a monotonic behavior that gives rise to magic angles in full agreement with those of twisted bilayer graphene. Therefore, magic angle behavior is universally found in chiral collapsed nanotubes with a small chiral angle, giving rise to moir\'e patterns. Our approach comprises first-principles and semi-empirical calculations of the band structure, density of states and spatial distribution of the localized states signaled by flat bands.

From monolayers composed of different atoms, we can build structures with spontaneous vertical polarization by conveniently stacking multiple layers. We have studied, using first-principles methods and based on modern polarization theory, a system composed of three layers of hexagonal Boron-Nitride(h-BN) in all possible stackings. We obtain for each of the configurations how charge transfers between the layers and how it impacts on the polarization of the system. In addition, we studied a system of three layers, one of them rotated, and we found that not only did the magnitude of the polarization increase comparing with the bilayer but also, depending on the initial stacking and the rotated layer, we can create a variety of mosaic-like polarization arrangements, which are composed of regions with either triangular or hexagonal symmetry., Comment: 14 Pages

We consider orthogonal polynomials with respect to a linear differential operator $$\mathcal{L}^{(M)}=\sum_{k=0}^{M}\rho_{k}(z)\frac{d^k}{dz^k}, $$ where $\{\rho_k\}_{k=0}^{M}$ are complex polynomials such that $deg[\rho_k]\leq k, 0\leq k \leq M$, with equality for at least one index. We analyze the uniqueness and zero location of these polynomials. An interesting phenomenon occurring in this kind of orthogonality is the existence of operators for which the associated sequence of orthogonal polynomials reduces to a finite set. For a given operator, we find a classification of the measures for which it is possible to guarantee the existence of an infinite sequence of orthogonal polynomials, in terms of a linear system of difference equations with varying coefficients. Also, for the case of a first-order differential operator, we locate the zeros and establish the strong asymptotic behavior of these polynomials.