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Let $(\mathcal{A,B})$ be a GP-admissible pair and $(\mathcal{Z,W})$ be a GI-admissible pair of classes of objects in an abelian category $\mathcal{C}$, and consider the class $\pi\mathcal{GP}_{(\omega,\mathcal{B},1)}$ of $1$-periodic $(\omega,\mathcal{B})$-Gorenstein projective objects, where $\omega := \mathcal{A} \cap \mathcal{B}$ and $\nu := \mathcal{Z} \cap \mathcal{W}$. We claimed in \cite[Lem. 8.1]{HMP2023m} that the $(\mathcal{Z,W})$-Gorenstein injective dimension of $\pi\mathcal{GP}_{(\omega,\mathcal{B},1)}$ is bounded by the $(\mathcal{Z,W})$-Gorenstein injective dimension of $\omega$, provided that: (1) $\omega$ is closed under direct summands, (2) $\mathrm{Ext}^1(\pi\mathcal{GP}_{(\omega,\mathcal{B},1)},\nu) = 0$, and (3) every object in $\pi\mathcal{GP}_{(\omega,\mathcal{B},1)}$ admits a $\mathrm{Hom}(-,\nu)$-acyclic $\nu$-coresolution. These conditions are their duals are part of what we called ``Setup 1''. Moreover, if we replace $\pi\mathcal{GP}_{(\omega,\mathcal{B},1)}$ by the class $\mathcal{GP}_{(\mathcal{A,B})}$ of $(\mathcal{A,B})$-Gorenstein projective objects, the resulting inequality is claimed to be true under a set of conditions named ``Setup 2''. The proof we gave for the claims $\mathrm{Gid}_{(\mathcal{Z,W})}(\pi\mathcal{GP}_{(\omega,\mathcal{B},1)}) \leq \mathrm{Gid}_{(\mathcal{Z,W})}(\omega)$ and $\mathrm{Gid}_{(\mathcal{Z,W})}(\mathcal{GP}_{(\mathcal{A,B})}) \leq \mathrm{Gid}_{(\mathcal{Z,W})}(\omega)$ is incorrect, and the purpose of this note is to exhibit a corrected proof of the first inequality, under the additional assumption that every object in $\pi\mathcal{GP}_{(\omega,\mathcal{B},1)}$ has finite injective dimension relative to $\mathcal{Z}$. Setup 2 is no longer required, and as a result the second inequality was removed. We also fix those results in \S \ 8 of \cite{HMP2023m} affected by Lemma 8.1, and comment some applications and examples., Comment: 10 pages. arXiv admin note: text overlap with arXiv:2207.00075

In flavor models the vacuum alignment of flavons is typically achieved via the $F$-terms of certain fields in the supersymmetric limit. We propose a method for preserving such alignments, up to a rescaling of the vacuum expectation values, even after supersymmetry (and the flavor symmetry) are softly broken, facilitating the vacuum alignment in models which are non-supersymmetric at low energies. Examples of models with different flavor groups, namely $A_4$, $T_7$, $S_4$ and $\Delta(27)$, are discussed., Comment: 28 pages + references

Putnam and Finkelstein can be read as providing an answer to Kripke's skeptical argument by appealing to the way mathematics is commonly pursued. Nowadays, the debate surrounding pluralism has questioned the postulation of a unique way of developing mathematical activity. In this paper, we wish to reformulate Kripke's argument as a challenge for the conjunction of 'ifthenism' and a reasonable form of pluralism (which we have called '$V$-pluralism') and, at the same time, propose a reading of some passages of the 'Philosophical Investigations' as a solution. Our conclusion is that, in order for pluralism to be preserved, we need to clarify both the fact that we make definite 'decisions' and the philosophical value that they, as we argue, bear. To investigate the nature of this value is one of the further tasks want to cover in this article.

Lattice simulations of Yang-Mills theories coupled with $N_f$ flavours of fermions in the adjoint representation provide a way to probe the non-perturbative regime of a plethora of different physical scenarios, such as Supersymmetric Yang-Mills theory to BSM models. We are interested in the large-$N_c$ limit of these theories, for which standard lattice techniques are limited by high-computational costs. Our approach makes use of the well-established twisted volume reduction, which allows one to simulate these theories on a $1^4$ lattice. In this talk, we are going to present a detailed study of the scale setting of these theories, performed with Wilson flow techniques, but endowed with a procedure that allowed us to reduce finite-volume (finite $N_c$) systematic effects. We will apply this procedure to our configurations for $N_f=0,\frac{1}{2},1,2$ and analyze the dependence of the scale on the coupling, the adjoint fermion mass and the number of flavours. For the cases in which enough couplings are available we compared the resulting $\beta$-function with the predictions of perturbation theory, finding very good agreement.

Controlled integration of metallic nanoparticles (NPs) onto photonic nanostructures enables realization of complex devices for extreme light confinement and enhanced light-matter interaction. This can be achieved combining Nanoparticle-on-Mirror (NPoM) nanocavities with the light manipulation capabilities of micron-scale metallic antennas and/or photonic integrated waveguides. However, metallic nanoparticles are usually deposited via drop-casting, which prevents their accurate positioning. Here we present a methodology for precise transfer and positioning of individual NPs onto different photonic nanostructures. The method is based on soft lithography printing that employs elastomeric stamp-assisted transfer of individual NPs onto a single nanostructure. It can also parallel imprint many individual NPs with high throughput and accuracy in a single step. Raman spectroscopy confirms enhanced light-matter interactions in the resulting NPoM-based devices. Our method mixes top-down and bottom-up nanofabrication techniques and shows the potential of building complex photonic nanodevices for applications ranging from enhanced sensing and spectroscopy to signal processing., Comment: 13 pages, 6 figures

The World Health Organisation (WHO) presents an upper limit for lead in drinking water of 10 parts per billion ppb. Typically, to reach this level of sensitivity, expensive metrology is required. To increase the sensitivity of low cost devices, this paper explores the prospects of using a volume reduction technique of a boiled water sample doped with Lead-210 ($^{210}Pb$), as a means to increase the solute's concentration. $^{210}$Pb is a radioactive lead isotope and its concentration in a water sample can be measured with e.g. High Purity Germanium (HPGe) detectors at the Boulby Underground Germanium Suite. Concentrations close to the WHO limit have not been examined. This paper presents a measurement of the volume reduction technique retaining $99\pm(9)\%$ of $^{210}$Pb starting from a concentration of $1.9\times10^{-6}$ ppb before reduction and resulting in $2.63\times10^{-4}$ ppb after reduction. This work also applies the volume reduction technique to London tap water and reports the radioassay results from gamma counting in HPGe detectors. Among other radio-isotopes, $^{40}$K, $^{210}$Pb, $^{131}$I and $^{177}$Lu were identified at measured concentrations of $2.83\times10^{3}$ ppb, $2.55\times10^{-7}$ ppb, $5.06\times10^{-10}$ ppb and $5.84\times10^{-10}$ ppb in the London tap water sample. This technique retained $90\pm50\%$ of $^{40}$K. Stable lead was inferred from the same water sample at a measured concentration of 0.012 ppb, prior to reduction.

In superconducting quantum circuits, aluminum is one of the most widely used materials. It is currently also the superconductor of choice for the development of topological qubits. In this application, however, aluminum-based devices suffer from poor magnetic field compatibility. In this article, we resolve this limitation by showing that adatoms of heavy elements (e.g. platinum) increase the critical field of thin aluminum films by more than a factor of two. Using tunnel junctions, we show that the increased field resilience originates from spin-orbit scattering introduced by Pt. We exploit this property in the context of the superconducting proximity effect in semiconductor-superconductor hybrids, where we show that InSb nanowires strongly coupled to Al/Pt films can maintain superconductivity up to 7T. The two-electron charging effect, a fundamental requirement for topological quantum computation, is shown to be robust against the presence of heavy adatoms. Additionally, we use non-local spectroscopy in a three-terminal geometry to probe the bulk of hybrid devices, showing that it remains free of sub-gap states. Finally, we demonstrate that semiconductor states which are proximitized by Al/Pt films maintain their ability to Zeeman-split in an applied magnetic field. Combined with the chemical stability and well-known fabrication routes of aluminum, Al/Pt emerges as the natural successor to Al-based systems and is a compelling alternative to other superconductors, whenever high-field resilience is required.

Minimum Bayes factors are commonly used to transform two-sided p-values to lower bounds on the posterior probability of the null hypothesis, as in Pericchi et al. (2017). In this article, we show posterior probabilities of hypothesis by transforming the commonly used -eplog(p), proposed by Vovk (1993) and Sellke et al. (2001). This is achieved after adjusting this minimum Bayes factor with the information to approximate it to an exact Bayes factor, not only when p is a p-value but also when p is a pseudo p-value in the sense of Casella and Berger (2001). Additionally, we show the fit to a refined version to linear models., Comment: 19 pages,5 figures

In this paper we present a method for obtention of neutron images with Commercial-Off-The-Shelf (COTS) CMOS image sensors through the activation of indium foils. This detection method has been designed specifically for the acquisition of thermal and epitermal neutron images in mixed beams with a high gamma flux, and also for the study of high radioactive samples that are usually placed into research reactor pools. We also present a technique to obtain multi-spectral neutron images taking advantage of the high neutron absorption cross-section of this material in the thermal energy range, as well as around the 1.45 eV resonance. Measurements performed in a neutron beam of the RA6 nuclear research reactor located in Bariloche, Argentina, confirm the capability of the proposed technique., Comment: 17 pages, 9 figures, accepted for publication in the Journal of Instrumentation

The International Fusion Materials Irradiation Facility (IFMIF), presently in its Engineering Validation and Engineering Design Activities (EVEDA) phase under the frame of the Broader Approach Agreement between Europe and Japan, accomplished in summer 2013, on schedule, its EDA phase with the release of the engineering design report of the IFMIF plant, which is here described. Many improvements of the design from former phases are implemented, particularly a reduction of beam losses and operational costs thanks to the superconducting accelerator concept, the re-location of the quench tank outside the test cell (TC) with a reduction of tritium inventory and a simplification on its replacement in case of failure, the separation of the irradiation modules from the shielding block gaining irradiation flexibility and enhancement of the remote handling equipment reliability and cost reduction, and the water cooling of the liner and biological shielding of the TC, enhancing the efficiency and economy of the related sub-systems. In addition, the maintenance strategy has been modified to allow a shorter yearly stop of the irradiation operations and a more careful management of the irradiated samples. The design of the IFMIF plant is intimately linked with the EVA phase carried out since the entry into force of IFMIF/EVEDA in June 2007.

We present here two concrete examples of models where a sub-TeV scale breaking of their respective $\mathcal{T}_{13}$ and $A_5$ flavor symmetries is able to account for the recently observed discrepancy in the muon anomalous magnetic moment, $(g-2)_\mu$. Similarities in the flavor structures of the charged-lepton Yukawa matrix and dipole matrix yielding $(g-2)_\mu$ give rise to strong constraints on low-scale flavor models when bounds from lepton flavor violation (LFV) are imposed. These constraints place stringent limits on the off-diagonal Yukawa structure, suggesting a mostly (quasi-)diagonal texture for models with a low flavor breaking scale $\Lambda_f$. We argue that many of the popular flavor models in the literature designed to explain the fermion masses and mixings are not suitable for reproducing the observed discrepancy in $(g-2)_\mu$, which requires a delicate balance of maintaining a low flavor scale while simultaneously satisfying strong LFV constraints., Comment: 22+12 pages, 5 figures, minor changes to match published version

$\mathcal{N}=1$ SUSY Yang-Mills theory is an appealing theoretical framework that has been studied in the literature using different methods, including standard lattice simulations. Among these, the volume-reduced twisted Eguchi-Kawai model, endowed with one adjoint Majorana fermion, could play an important role in studying its large-$N$ limit via the Curci-Veneziano prescription. In this talk, we present our results on the analysis of the scale of the theory, performed via different methods based on purely gluonic observables as well as (quenched) fundamental mesons in the chiral limit. These lattice results will be used as a scale setting for the analysis of the spectrum of the theory., Comment: 9 pages, 4 figures, 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021 Zoom/Gather@Massachusetts Institute of Technology