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We show that the braid group associated to the complex reflection group $G(d,d,n)$ is an index $d$ subgroup of the braid group of the orbifold quotient of the complex numbers by a cyclic group of order $d$. We also give a compatible presentation of $G(d,d,n)$ and its braid group for each tagged triangulation of the disk with $n$ marked points on its boundary and an interior marked point (interpreted as a cone point of degree $d$) in such a way that the presentations of Brou\'{e}-Malle-Rouquier correspond to a special tagged triangulation., Comment: 50 pages

The primary focus of this work is to investigate how the most emblematic classical probability density, namely a Gaussian, can be mapped to a valid quantum states. To explore this issue, we consider a Gaussian whose squared variance depends on a parameter $\lambda$. Specifically, depending on the value of $\lambda$, we study what happens in the classical-quantum correspondence as we change the indeterminacy of the classical particle. Furthermore, finding a correspondence between a classical state and a quantum state is not a trivial task. Quantum observables, described by Hermitian operators, do not generally commute, so a precise ordering must be introduced to resolve this ambiguity. In this work, we study two different arbitrary orderings: the first is an arbitrary ordering of the position and momentum observables; the second, which is the main focus of the present work, is an arbitrary ordering of the annihilation and creation operators. In this latter case, we find the interesting result that even a $\delta$-function, which in general has no quantum correspondence, can be mapped into a valid quantum state for a particular ordering, specifically the antinormal one (all creation operators are to the right of all annihilation operators in the product). This means that the Gaussian probability density corresponds to a valid quantum state, regardless of how localized classical particles are in phase space., Comment: 16 Pages, one figure. Typos corrected

Artificial intelligence (AI) advancements over the past few years have had an unprecedented and revolutionary impact across everyday application areas. Its significance also extends to technical challenges within science and engineering, including the nascent field of quantum computing (QC). The counterintuitive nature and high-dimensional mathematics of QC make it a prime candidate for AI's data-driven learning capabilities, and in fact, many of QC's biggest scaling challenges may ultimately rest on developments in AI. However, bringing leading techniques from AI to QC requires drawing on disparate expertise from arguably two of the most advanced and esoteric areas of computer science. Here we aim to encourage this cross-pollination by reviewing how state-of-the-art AI techniques are already advancing challenges across the hardware and software stack needed to develop useful QC - from device design to applications. We then close by examining its future opportunities and obstacles in this space., Comment: 42 pages, 7 figures, 2 tables

In this paper we study the bounds that can be inferred on New Physics couplings to heavy sterile neutrinos $N$ from the recent measurements performed by the Belle collaboration of the angular analysis of $B\to D^*\ell\bar\nu_\ell$ decays, with $\ell=e,\mu$. Indeed, a sterile neutrino $N$ may lead to competing $B\to D^*\ell\bar N$ decays and Belle might have measured an incoherent sum of these two independent channels. After reviewing the theoretical formalism required to describe this phenomenon in full generality, we first perform a bump hunt in the $M_{\rm miss}^2$ Belle distribution to search for evidences of an additional massive neutrino. We found in such a way a small hint at $M_{\rm miss}^2 \sim (350\ {\rm MeV})^2$. However, the Belle angular analysis is sensitive to $N$ masses up to $\mathcal{O}$(50 MeV), preventing us to further inspect this hint. Nevertheless, we study the potential impact of this additional channel in the allowed mass range on the measured angular distributions and extract model-independent bounds on the new-physics couplings which could mediate such an interaction. In particular, in the mass window here inspected, we obtain the most stringent bounds for vector and left-handed scalar operators to date., Comment: 23 pages, 6 figures, 2 tables. Matching published version to appear on JHEP

The energy cost of erasing a bit of information was fundamentally lower bounded by Landauer, in terms of the temperature of its environment: $W\geq k_\mathrm{B} T \ln 2$. However, in real electronic devices, the information-bearing system is usually in contact with two or more electrodes, with different temperatures and chemical potentials. It is not clear what sets the cost of erasure in such nonequilibrium situations. One promising technology for testing the thermodynamic limits of information processing is quantum dots, in which a bit is encoded in the presence or absence of a single electron. We here develop a thermodynamic description of devices of this type and find that, in addition to the electrode temperatures, the potential difference across the quantum dot and lifetime broadening of its energy level contribute to the minimum work cost of erasure. In practical contexts, these contributions may significantly outweigh the cost due to temperature alone., Comment: 6 pages plus 8-page supplemental material. 3 figures

The reduced-complexity models developed by Edward Lorenz are widely used in atmospheric and climate sciences to study nonlinear aspect of dynamics and to demonstrate new methods for numerical weather prediction. A set of inviscid Lorenz models describing the dynamics of a single variable in a zonally-periodic domain, without dissipation and forcing, conserve energy but are not Hamiltonian. In this paper, we start from a general continuous parent fluid model, from which we derive a family of Hamiltonian Lorenz-like models through a symplectic discretization of the associated Poisson bracket that preserves the Jacobi identity. A symplectic-split integrator is also formulated. These Hamiltonian models conserve energy and maintain the nearest-neighbor couplings inherent in the original Lorenz model. As a corollary, we find that the Lorenz-96 model can be seen as a result of a poor discretization of a Poisson bracket. Hamiltonian Lorenz-like models offer promising alternatives to the original Lorenz models, especially for the qualitative representation of non-Gaussian weather extremes and wave interactions, which are key factors in understanding many phenomena of the climate system.

When the planet formation process begins in the disks surrounding young stars is still an open question. Annular substructures such as rings and gaps in disks are intertwined with planet formation, and thus their presence or absence is commonly used to investigate the onset of this process. Current observations show a limited number of disks surrounding protostars exhibiting annular substructures, all of them in the Class I stage. The lack of observed features in most of these sources may indicate a late emergence of substructures, but it could also be an artifact of these disks being optically thick. To mitigate the problem of optical depth, we investigate substructures within a very young Class 0 disk characterized by a low inclination using observations at longer wavelengths. We use 3 mm ALMA observations tracing dust emission at a resolution of 7 au to search for evidence of annular substructures in the disk around the deeply embedded Class 0 protostar Oph A SM1. The observations reveal a nearly face-on disk (i$\sim$16$^{\circ}$) extending up to 40 au. The radial intensity profile shows a clear deviation from a smooth profile near 30 au, which we interpret as the presence of either a gap at 28 au or a ring at 34 au with Gaussian widths of $\sigma=1.4^{+2.3}_{-1.2}$ au and $\sigma=3.9^{+2.0}_{-1.9}$ au, respectively. The 3 mm emission at the location of the possible gap or ring is determined to be optically thin, precluding the possibility that this feature in the intensity profile is due to the emission being optically thick. Annular substructures resembling those in the more evolved Class I and II disks could indeed be present in the Class 0 stage, earlier than previous observations suggested. Similar observations of embedded disks in which the high optical depth problem can be mitigated are clearly needed to better constrain the onset of substructures in the embedded stages., Comment: 12 pages, 7 figures, 2 tables. Accepted for publication in A&A Letters

The Extremely Large Telescopes (ELTs), thanks to their large apertures and cutting-edge Multi-Conjugate Adaptive Optics (MCAO) systems, promise to deliver sharper and deeper data even than the JWST. SHARP is a concept study for a near-IR (0.95-2.45 $\mu$m) spectrograph conceived to fully exploit the collecting area and the angular resolution of the upcoming generation of ELTs. In particular, SHARP is designed for the 2nd port of MORFEO@ELT. Composed of a Multi-Object Spectrograph, NEXUS, and a multi-Integral Field Unit, VESPER, MORFEO-SHARP will deliver high angular ($\sim$30 mas) and spectral (R$\simeq$300, 2000, 6000, 17000) resolution, outperforming NIRSpec@JWST (100 mas). SHARP will enable studies of the nearby Universe and the early Universe in unprecedented detail. NEXUS is fed by a configurable slit system deploying up to 30 slits with $\sim$2.4 arcsec length and adjustable width, over a field of about 1.2"$\times$1.2" (35 mas/pix). Each slit is fed by an inversion prism able to rotate by an arbitrary angle the field that can be seen by the slit. VESPER is composed of 12 probes of 1.7"$\times$1.5" each (spaxel 31 mas) probing a field 24"$\times$70". SHARP is conceived to exploit the ELTs apertures reaching the faintest flux and the sharpest angular resolution by joining the sensitivity of NEXUS and the high spatial sampling of VESPER to MORFEO capabilities. This article provides an overview of the scientific design drivers, their solutions, and the resulting optical design of the instrument achieving the required optical performance., Comment: Proceedings of the SPIE Astronomical Telescopes and Instrumentation 2024, Volume 13096, Paper No. 130965I, 11 pp, 11 figs

Recent observations suggest that planets formation starts early, in protostellar disks of $\le10^5$ yrs, which are characterized by strong interactions with the environment, e.g., through accretion streamers and molecular outflows. To investigate the impact of such phenomena on disk physical and chemical properties it is key to understand what chemistry planets inherit from their natal environment. In the context of the ALMA Large Program Fifty AU STudy of the chemistry in the disk/envelope system of Solar-like protostars (FAUST), we present observations on scales from ~1500 au to ~60 au of H$_2$CO, HDCO, and D$_2$CO towards the young planet-forming disk IRS~63. H$_2$CO probes the gas in the disk as well as in a large scale streamer (~1500 au) impacting onto the South-East (SE) disk side. We detect for the first time deuterated formaldehyde, HDCO and D$_2$CO, in a planet-forming disk, and HDCO in the streamer that is feeding it. This allows us to estimate the deuterium fractionation of H$_2$CO in the disk: [HDCO]/[H$_2$CO]$\sim0.1-0.3$ and [D$_2$CO]/[H$_2$CO]$\sim0.1$. Interestingly, while HDCO follows the H$_2$CO distribution in the disk and in the streamer, the distribution of D$_2$CO is highly asymmetric, with a peak of the emission (and [D]/[H] ratio) in the SE disk side, where the streamer crashes onto the disk. In addition, D$_2$CO is detected in two spots along the blue- and red-shifted outflow. This suggests that: (i) in the disk, HDCO formation is dominated by gas-phase reactions similarly to H$_2$CO, while (ii) D$_2$CO was mainly formed on the grain mantles during the prestellar phase and/or in the disk itself, and is at present released in the gas-phase in the shocks driven by the streamer and the outflow. These findings testify on the key role of streamers in the build-up of the disk both concerning the final mass available for planet formation and its chemical composition., Comment: 12 pages, 10 figures, accepted for publication on A&A

Starting from its original definition in module categories with respect to projective modules, the index has played an important role in various aspects of homological algebra, categorification of cluster algebras and $K$-theory. In the last few years, the notion of index has been generalised to several different contexts in (higher) homological algebra, typically with respect to a (higher) cluster-tilting subcategory $\mathcal{X}$ of the relevant ambient category $\mathcal{C}$. The recent tools of extriangulated and higher-exangulated categories have permitted some conditions on the subcategory $\mathcal{X}$ to be relaxed. In this paper, we introduce the index with respect to a generating, contravariantly finite subcategory of a $d$-exact category that has $d$-kernels. We show that our index has the important property of being additive on $d$-exact sequences up to an error term., Comment: 17 pages. Comments welcome!

The exploration of outflows in protobinary systems presents a challenging yet crucial endeavour, offering valuable insights into the dynamic interplay between protostars and their evolution. In this study, we examine the morphology and dynamics of jets and outflows within the IRAS\,4A protobinary system. This analysis is based on ALMA observations of SiO(5--4), H$_2$CO(3$_{0,3}$--2$_{0,3}$), and HDCO(4$_{1,4}$--3$_{1,3}$) with a spatial resolution of $\sim$150\,au. Leveraging an astrochemical approach involving the use of diverse tracers beyond traditional ones has enabled the identification of novel features and a comprehensive understanding of the broader outflow dynamics. Our analysis reveals the presence of two jets in the redshifted emission, emanating from IRAS\,4A1 and IRAS\,4A2, respectively. Furthermore, we identify four distinct outflows in the region for the first time, with each protostar, 4A1 and 4A2, contributing to two of them. We characterise the morphology and orientation of each outflow, challenging previous suggestions of bends in their trajectories. The outflow cavities of IRAS\,4A1 exhibit extensions of 10$''$ and 13$''$ with position angles (PA) of 0$^{\circ}$ and -12$^{\circ}$, respectively, while those of IRAS\,4A2 are more extended, spanning 18$''$ and 25$''$ with PAs of 29$^{\circ}$ and 26$^{\circ}$. We propose that the misalignment of the cavities is due to a jet precession in each protostar, a notion supported by the observation that the more extended cavities of the same source exhibit lower velocities, indicating they may stem from older ejection events.

In a XOR-based alternating block cipher the plaintext is masked by a sequence of layers each performing distinct actions: a highly nonlinear permutation, a linear transformation, and the bitwise key addition. When assessing resistance against classical differential attacks (where differences are computed with respect to XOR), the cryptanalysts must only take into account differential probabilities introduced by the nonlinear layer, this being the only one whose differential transitions are not deterministic. The temptation of computing differentials with respect to another difference operation runs into the difficulty of understanding how differentials propagate through the XOR-affine levels of the cipher. In this paper we introduce a special family of braces that enable the derivation of a set of differences whose interaction with every layer of an XOR-based alternating block cipher can be understood. We show that such braces can be described also in terms of alternating binary algebras of nilpotency class two. Additionally, we present a method to compute the automorphism group of these structures through an equivalence between bilinear maps. By doing so, we characterise the XOR-linear permutations for which the differential transitions with respect to the new difference are deterministic, facilitating an alternative differential attack.

Environmental fluctuations degrade the performance of solid-state qubits but can in principle be mitigated by real-time Hamiltonian estimation down to time scales set by the estimation efficiency. We implement a physics-informed and an adaptive Bayesian estimation strategy and apply them in real time to a semiconductor spin qubit. The physics-informed strategy propagates a probability distribution inside the quantum controller according to the Fokker-Planck equation, appropriate for describing the effects of nuclear spin diffusion in gallium-arsenide. Evaluating and narrowing the anticipated distribution by a predetermined qubit probe sequence enables improved dynamical tracking of the uncontrolled magnetic field gradient within the singlet-triplet qubit. The adaptive strategy replaces the probe sequence by a small number of qubit probe cycles, with each probe time conditioned on the previous measurement outcomes, thereby further increasing the estimation efficiency. The combined real-time estimation strategy efficiently tracks low-frequency nuclear spin fluctuations in solid-state qubits, and can be applied to other qubit platforms by tailoring the appropriate update equation to capture their distinct noise sources., Comment: 21 pages, 10 figures, including 11-page 6-figure Supplemental Material

We present the first results of the JWST program PROJECT-J (PROtostellar JEts Cradle Tested with JWST ), designed to study the Class I source HH46 IRS and its outflow through NIRSpec and MIRI spectroscopy (1.66 to 28 micron). The data provide line-images (~ 6.6" in length with NIRSpec, and up to 20" with MIRI) revealing unprecedented details within the jet, the molecular outflow and the cavity. We detect, for the first time, the red-shifted jet within ~ 90 au from the source. Dozens of shock-excited forbidden lines are observed, including highly ionized species such as [Ne III] 15.5 micron, suggesting that the gas is excited by high velocity (> 80 km/s) shocks in a relatively high density medium. Images of H2 lines at different excitations outline a complex molecular flow, where a bright cavity, molecular shells, and a jet-driven bow-shock interact with and are shaped by the ambient conditions. Additional NIRCam 2 micron images resolve the HH46 IRS ~ 110 au binary system and suggest that the large asymmetries observed between the jet and the H2 wide angle emission could be due to two separate outflows being driven by the two sources. The spectra of the unresolved binary show deep ice bands and plenty of gaseous lines in absorption, likely originating in a cold envelope or disk. In conclusion, JWST has unraveled for the first time the origin of the HH46 IRS complex outflow demonstrating its capability to investigate embedded regions around young stars, which remain elusive even at near-IR wavelengths., Comment: 28 pages, 15 figures, Accepted for publication on The Astrophysical Journal (9 April 2024)

Semiconductor quantum dot arrays are a leading architecture for the development of quantum technologies. Over the years, the constant capacitance model has served as a fundamental framework for simulating, understanding, and navigating the charge stability diagrams of small quantum dot arrays. However, while the size of the arrays keeps growing, solving the constant capacitance model becomes computationally prohibitive. This paper presents an open-source software package able to compute a $100 \times 100$ pixels charge stability diagram of a 16-dot array in less than a second. Smaller arrays can be simulated in milliseconds - faster than they could be measured experimentally, enabling the creation of diverse datasets for training machine learning models and the creation of digital twins that can interface with quantum dot devices in real-time. Our software package implements its core functionalities in the systems programming language Rust and the high-performance numerical computing library JAX. The Rust implementation benefits from advanced optimisations and parallelisation, enabling the users to take full advantage of multi-core processors. The JAX implementation allows for GPU acceleration.

Motivated by the recent theoretical and experimental developments in $b \to c \ell\nu$ transitions, the aim of these proceedings is to critically analyse the current situation in this sector. In particular, we will inspect the possibility of explaining the current anomalous pattern by means of New Physics effects coupled with light charged leptons, motivated both by the measurement of the LFUV ratio ${\cal R}(\Lambda_c)$ and by the recent application of the Dispersive Matrix approach to estimate Form Factors in $B \to D^*$ transitions. These proceedings are based on Refs.~\cite{Fedele:2022iib,Fedele:2023ewe}., Comment: Presented at the 12th Workshop on the CKM Unitarity Triangle, 18-22 September 2023, Santiago de Compostela

The origin of the chemical diversity observed around low-mass protostars probably resides in the earliest history of these systems. We aim to investigate the impact of protostellar feedback on the chemistry and grain growth in the circumstellar medium of multiple stellar systems. In the context of the ALMA Large Program FAUST, we present high-resolution (50 au) observations of CH$_3$OH, H$_2$CO, and SiO and continuum emission at 1.3 mm and 3 mm towards the Corona Australis star cluster. Methanol emission reveals an arc-like structure at $\sim$1800 au from the protostellar system IRS7B along the direction perpendicular to the major axis of the disc. The arc is located at the edge of two elongated continuum structures that define a cone emerging from IRS7B. The region inside the cone is probed by H$_2$CO, while the eastern wall of the arc shows bright emission in SiO, a typical shock tracer. Taking into account the association with a previously detected radio jet imaged with JVLA at 6 cm, the molecular arc reveals for the first time a bow shock driven by IRS7B and a two-sided dust cavity opened by the mass-loss process. For each cavity wall, we derive an average H$_2$ column density of $\sim$7$\times$10$^{21}$ cm$^{-2}$, a mass of $\sim$9$\times$10$^{-3}$ M$_\odot$, and a lower limit on the dust spectral index of $1.4$. These observations provide the first evidence of a shock and a conical dust cavity opened by the jet driven by IRS7B, with important implications for the chemical enrichment and grain growth in the envelope of Solar System analogues., Comment: 12 pages, 8 figures, 3 tables. Accepted Letter in Astronomy & Astrophysics

This paper presents a new software framework for HRI experimentation with the sixth version of the common NAO robot produced by the United Robotics Group. Embracing the common demand of researchers for better performance and new features for NAO, the authors took advantage of the ability to run ROS2 onboard on the NAO to develop a framework independent of the APIs provided by the manufacturer. Such a system provides NAO with not only the basic skills of a humanoid robot such as walking and reproducing movements of interest but also features often used in HRI such as: speech recognition/synthesis, face and object detention, and the use of Generative Pre-trained Transformer (GPT) models for conversation. The developed code is therefore configured as a ready-to-use but also highly expandable and improvable tool thanks to the possibilities provided by the ROS community., Comment: 7 pages, 3 figures

Coupling a single spin to high-frequency mechanical motion is a fundamental bottleneck of applications such as quantum sensing, intermediate and long-distance spin-spin coupling, and classical and quantum information processing. Previous experiments have only shown single spin coupling to low-frequency mechanical resonators, such as diamond cantilevers. High-frequency mechanical resonators, having the ability to access the quantum regime, open a range of possibilities when coupled to single spins, including readout and storage of quantum states. Here we report the first experimental demonstration of spin-mechanical coupling to a high-frequency resonator. We achieve this all-electrically on a fully suspended carbon nanotube device. A new mechanism gives rise to this coupling, which stems from spin-orbit coupling, and it is not mediated by strain. We observe both resonant and off-resonant coupling as a shift and broadening of the electric dipole spin resonance (EDSR), respectively. We develop a complete theoretical model taking into account the tensor form of the coupling and non-linearity in the motion. Our results propel spin-mechanical platforms to an uncharted regime. The interaction we reveal provides the full toolbox for promising applications ranging from the demonstration of macroscopic superpositions, to the operation of fully quantum engines, to quantum simulators., Comment: Comments welcome

One can explicitly compute the generators of a surface cluster algebra either combinatorially, through dimer covers of snake graphs, or homologically, through the CC-map applied to indecomposable modules over the appropriate algebra. Recent work by Musiker, Ovenhouse and Zhang used Penner and Zeitlin's decorated super Teichm{\"u}ller theory to define a super version of the cluster algebra of type $A$ and gave a combinatorial formula to compute the even generators. We extend this theory by giving a homological way of explicitly computing these generators by defining a super CC-map for type $A$., Comment: 43 pages, 19 figures, This work originates as part of the WINART3 Workshop: Women in Noncommutative Algebra and Representation Theory

This report provides an overview of the challenge hosted at the OpenSUN3D Workshop on Open-Vocabulary 3D Scene Understanding held in conjunction with ICCV 2023. The goal of this workshop series is to provide a platform for exploration and discussion of open-vocabulary 3D scene understanding tasks, including but not limited to segmentation, detection and mapping. We provide an overview of the challenge hosted at the workshop, present the challenge dataset, the evaluation methodology, and brief descriptions of the winning methods. For additional details, please see https://opensun3d.github.io/index_iccv23.html., Comment: Our OpenSUN3D workshop website for ICCV 2023: https://opensun3d.github.io/index_iccv23.html

The ALMA interferometer has played a key role in revealing a new component of the Sun-like star forming process: the molecular streamers, i.e. structures up to thousands of au long funneling material non-axisymmetrically to disks. In the context of the FAUST ALMA LP, the archetypical VLA1623-2417 protostellar cluster has been imaged at 1.3 mm in the SO(5$_6$--4$_5$), SO(6$_6$--5$_5$), and SiO(5--4) line emission at the spatial resolution of 50 au. We detect extended SO emission, peaking towards the A and B protostars. Emission blue-shifted down to 6.6 km s$^{-1}$ reveals for the first time a long ($\sim$ 2000 au) accelerating streamer plausibly feeding the VLA1623 B protostar. Using SO, we derive for the first time an estimate of the excitation temperature of an accreting streamer: 33$\pm$9 K. The SO column density is $\sim$ 10$^{14}$ cm$^{-2}$, and the SO/H$_2$ abundance ratio is $\sim$ 10$^{-8}$. The total mass of the streamer is 3 $\times$ 10$^{-3}$ $Msun$, while its accretion rate is 3--5 $\times$ 10$^{-7}$ Msun yr$^{-1}$. This is close to the mass accretion rate of VLA1623 B, in the 0.6--3 $\times$ 10$^{-7}$ Msun yr$^{-1}$ range, showing the importance of the streamer in contributing to the mass of protostellar disks. The highest blue- and red-shifted SO velocities behave as the SiO(5--4) emission, the latter species detected for the first time in VLA1623-2417: the emission is compact (100-200 au), and associated only with the B protostar. The SO excitation temperature is $\sim$ 100 K, supporting the occurrence of shocks associated with the jet, traced by SiO., Comment: accepted by MNRAS

Spanning over two decades, the study of qubits in semiconductors for quantum computing has yielded significant breakthroughs. However, the development of large-scale semiconductor quantum circuits is still limited by challenges in efficiently tuning and operating these circuits. Identifying optimal operating conditions for these qubits is complex, involving the exploration of vast parameter spaces. This presents a real 'needle in the haystack' problem, which, until now, has resisted complete automation due to device variability and fabrication imperfections. In this study, we present the first fully autonomous tuning of a semiconductor qubit, from a grounded device to Rabi oscillations, a clear indication of successful qubit operation. We demonstrate this automation, achieved without human intervention, in a Ge/Si core/shell nanowire device. Our approach integrates deep learning, Bayesian optimization, and computer vision techniques. We expect this automation algorithm to apply to a wide range of semiconductor qubit devices, allowing for statistical studies of qubit quality metrics. As a demonstration of the potential of full automation, we characterise how the Rabi frequency and g-factor depend on barrier gate voltages for one of the qubits found by the algorithm. Twenty years after the initial demonstrations of spin qubit operation, this significant advancement is poised to finally catalyze the operation of large, previously unexplored quantum circuits.

In this proceeding we will review the current theoretical status of rare $B$ decays. These decays are indeed excellent indirect probes for New Physics searches, and in the current situation where no new states have been directly observed at collider, they provide a fundamental and alternative approach in the quest for Physics beyond the Standard Model. We will focus on the following classes of decays: $B_q\to\tau\nu$, $B_q\to\mu\mu$, $B\to K^{(*)}\nu\bar\nu$, $B\to K^{(*)}\ell\ell$, $B_s\to\phi\ell\ell$ and $b\to s\gamma$. The most updated Standard Model predictions will be provided, highlighting which are the main sources of uncertainty, and what is the possibility for New Physics effects when confronting the theory numbers to current experimental results., Comment: 9 pages. Prepared for the Proceedings for the "Workshop Italiano sulla Fisica ad Alta Intensit\`a (WIFAI2023)", 8-10 November 2023, Rome, Italy

Cluster algebras are categorified by cluster categories, and $g$-vectors are categorified by the classic index with respect to cluster tilting subcategories. However, the recently introduced completed discrete cluster categories of Dynkin type $\mathbb{A}$ have a very limited supply of cluster tilting subcategories, so we define the index with respect to additive, contravariantly finite subcategories of which there are many more. This permits us to extend several strong results from the classic theory to completed discrete cluster categories of Dynkin type $\mathbb{A}$. Notably, the index with respect to the subcategory generated by a fan triangulation distinguishes between rigid objects. We also prove that our index is additive on triangles up to an error term. This extends the key property which permits the classic index to be used in the categorification of cluster algebras., Comment: v2: 27 pages; sections 3 and 4 are new; introduction re-written

Nanomachines are often interpreted as autonomous Maxwell's demons or information engines. This interpretation is appealing from a conceptual viewpoint but sometimes lacks a rigorous and precise formulation. Moreover, it is unclear whether this interpretation is truly useful for analyzing the performance of nanomachines or designing more efficient ones. The concepts of mutual information and information flows provide a quantitative and rigorous account of the role of information in physical systems. In this chapter, we present a pedagogical review of these concepts and apply them to a specific energy transducer at the nanoscale, which couples the tunnel transport of electrons through a carbon nanotube with its mechanical oscillations., Comment: 32 pages, 12 figures