Search

We discuss a recently introduced strategy to study non-perturbatively thermal QCD up to temperatures of the order of the electro-weak scale, combining step scaling techniques and shifted boundary conditions. The former allow to renormalize the theory for a range of scales which spans several orders of magnitude with a moderate computational cost. Shifted boundary conditions remove the need for the zero temperature subtraction in the Equation of State. As a consequence, the simulated lattices do not have to accommodate two very different scales, the pion mass and the temperature, at the very same spacing. Effective field theory arguments guarantee that finite volume effects can be kept under control safely. With this strategy the first computation of the hadronic screening spectrum has been carried out over more than two orders of magnitude in the temperature, from $T\sim 1$ GeV up to $\sim 160$ GeV. This study is complemented with the first quantitative computation of the baryonic screening mass at next-to-leading order in the three-dimensional effective theory describing QCD at high temperatures. Both for the mesonic and the baryonic screening masses, the known leading behaviour in the coupling constant is found to be not sufficient to explain the non-perturbative data over the entire range of temperatures. These findings shed further light on the limited applicability of the perturbative approach at finite temperature, even at the electro-weak scale., Comment: arXiv admin note: substantial text overlap with arXiv:2410.12626

CHANCES, the CHileAN Cluster galaxy Evolution Survey, will study the evolution of galaxies in and around ${\sim}$150 massive galaxy clusters, from the local universe out to z=0.45. CHANCES will use the new 4MOST Spectroscopic Survey Facility on the VISTA 4m telescope to obtain spectra for ${\sim}$500,000 galaxies with magnitudes $r_\mathrm{AB} < 20.5$, providing comprehensive spectroscopic coverage of each cluster out to $5r_{200}$. Its wide and deep scope will trace massive and dwarf galaxies from the surrounding filaments and groups to the cores of galaxy clusters, enabling the study of galaxy pre-processing and the role of the evolving environment on galaxy evolution. In this paper we present and characterize the sample of clusters and superclusters to be targeted by CHANCES. We used literature catalogues based on X-ray emission and Sunyaev-Zel'dovich effect to define the cluster sample in a homogeneous way, with attention to cluster mass and redshift, as well as the availability of ancillary data. We calibrated literature mass estimates from various surveys against each other and provide an initial mass estimate for each cluster, which we used to define the radial extent of the 4MOST coverage. We also present an initial assessment of the structure surrounding these clusters based on the redMaPPer red-sequence algorithm as a preview of some of the science CHANCES will enable., Comment: 11 pages, 9 figures, plus references and appendix containing catalog tables, submitted to A&A

We present a recently introduced strategy to study non-perturbatively thermal QCD up to temperatures of the order of the electro-weak scale, combining step scaling techniques and shifted boundary conditions. The former allow to renormalize the theory for a range of scales which spans several orders of magnitude with a moderate computational cost. Shifted boundary conditions avoid the need for the zero temperature subtraction in the Equation of State. As a consequence, the simulated lattices do not have to accommodate two very different scales, the pion mass and the temperature. Effective field theory arguments guarantee that finite volume effects can be kept under control safely. As a first application of this strategy, we present the results of the computation of the hadronic screening spectrum in QCD with $N_f=3$ flavours of massless quarks for temperatures from $T\sim 1$ GeV up to $\sim 160$ GeV., Comment: 6 pages, 3 figures, Proceedings of the 42nd International Conference on High Energy Physics (ICHEP2024)

In this paper, we provide an efficient algorithm to construct almost optimal $(k,n,d)$-superimposed codes with runlength constraints. A $(k,n,d)$-superimposed code of length $t$ is a $t \times n$ binary matrix such that any two 1's in each column are separated by a run of at least $d$ 0's, and such that for any column $\mathbf{c}$ and any other $k-1$ columns, there exists a row where $\mathbf{c}$ has $1$ and all the remaining $k-1$ columns have $0$. These combinatorial structures were introduced by Agarwal et al. [1], in the context of Non-Adaptive Group Testing algorithms with runlength constraints. By using Moser and Tardos' constructive version of the Lov\'asz Local Lemma, we provide an efficient randomized Las Vegas algorithm of complexity $\Theta(t n^2)$ for the construction of $(k,n,d)$-superimposed codes of length $t=O(dk\log n +k^2\log n)$. We also show that the length of our codes is shorter, for $n$ sufficiently large, than that of the codes whose existence was proved in [1]., Comment: Accepted for publication in Discrete Applied Mathematics

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

The Minimum Branch Vertices Spanning Tree problem aims to find a spanning tree $T$ in a given graph $G$ with the fewest branch vertices, defined as vertices with a degree three or more in $T$. This problem, known to be NP-hard, has attracted significant attention due to its importance in network design and optimization. Extensive research has been conducted on the algorithmic and combinatorial aspects of this problem, with recent studies delving into its fixed-parameter tractability. In this paper, we focus primarily on the parameter modular-width. We demonstrate that finding a spanning tree with the minimum number of branch vertices is Fixed-Parameter Tractable (FPT) when considered with respect to modular-width. Additionally, in cases where each vertex in the input graph has an associated cost for serving as a branch vertex, we prove that the problem of finding a spanning tree with the minimum branch cost (i.e., minimizing the sum of the costs of branch vertices) is FPT with respect to neighborhood diversity.

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

This work focuses on the analysis of the mean longitudinal magnetic field as a stellar activity tracer in the context of small exoplanet detection and characterisation in radial-velocity (RV) surveys. We use SDO/HMI filtergrams to derive Sun-as-a-star magnetic field measurements, and show that the mean longitudinal magnetic field is an excellent rotational period detector and a useful tracer of the solar magnetic cycle. To put these results into context, we compare the mean longitudinal magnetic field to three common activity proxies derived from HARPS-N Sun-as-a-star data: the full-width at half-maximum, the bisector span and the S-index. The mean longitudinal magnetic field does not correlate with the RVs and therefore cannot be used as a one-to-one proxy. However, with high cadence and a long baseline, the mean longitudinal magnetic field outperforms all other considered proxies as a solar rotational period detector, and can be used to inform our understanding of the physical processes happening on the surface of the Sun. We also test the mean longitudinal magnetic field as a "stellar proxy" on a reduced solar dataset to simulate stellar-like observational sampling. With a Gaussian Process regression analysis, we confirm that the solar mean longitudinal magnetic field is the most effective of the considered indicators, and is the most efficient rotational period indicator over different levels of stellar activity. This work highlights the need for polarimetric time series observations of stars., Comment: 23 pages, 27 figures

Hydrogen hydrates present a rich phase diagram influenced by both pressure and temperature, with the so-called C$_2$ phase emerging prominently above 2.5 GPa. In this phase, hydrogen molecules are densely packed within a cubic ice-like lattice and the interaction with the surrounding water molecules profoundly affects their quantum rotational dynamics. Herein, we delve into this intricate interplay by directly solving the Schr\"{o}dinger's equation for a quantum H$_2$ rotor in the C$_2$ crystal field at finite temperature, generated through Density Functional Theory. Our calculations reveal a giant energy splitting relative to the magnetic quantum number of $\pm$3.2 meV for $l=1$. Employing inelastic neutron scattering, we experimentally measure the energy levels of H$_2$ within the C$_2$ phase at 6.0 and 3.4 GPa and low temperatures, finding remarkable agreement with our theoretical predictions. These findings underscore the pivotal role of hydrogen--water interactions in dictating the rotational behavior of the hydrogen molecules within the C$_2$ phase and indicate heightened induced-dipole interactions compared to other hydrogen hydrates., Comment: 4 Figures

Stellar magnetic activity induces both distortions and Doppler-shifts in the absorption line profiles of Sun-like stars. Those effects produce apparent radial velocity (RV) signals which greatly hamper the search for potentially habitable, Earth-like planets. In this work, we investigate these distortions in the Sun using cross-correlation functions (CCFs), derived from intensive monitoring with the high-precision spectrograph HARPS-N. We show that the RV signal arising from line-shape variations on time-scales associated with the solar rotation and activity cycle can be robustly extracted from the data, reducing the RV dispersion by half. Once these have been corrected, activity-induced Doppler-shifts remain, that are modulated at the solar rotation period, and that are most effectively modelled in the time domain, using Gaussian Processes (GPs). Planet signatures are still best retrieved with multi-dimensonal GPs, when activity is jointly modelled from the raw RVs and indicators of the line width or of the Ca II H and K emission. After GP modelling, the residual RVs exhibit a dispersion of 0.6-0.8 m/s, likely to be dominated by signals induced by super-granulation. Finally, we find that the statistical properties of the RVs evolve significantly over time, and that this evolution is primarily driven by sunspots, which control the smoothness of the signal. Such evolution, which reduces the sensitivity to long-period planet signatures, is no longer seen in the activity-induced Doppler-shifts, which is promising for long term RV monitoring surveys such as the Terra Hunting Experiment or the PLATO follow-up campaign., Comment: Accepted by MNRAS on the 2024 May 20. 17 pages, 14 figures (plus 8 pages of Appendix, 9 Appendix figures)

We compute the baryonic screening masses with nucleon quantum numbers and its negative parity partner in thermal QCD with $N_f=3$ massless quarks for a wide range of temperatures, from $T \sim 1$ GeV up to $\sim 160$ GeV. The computation is performed by Monte Carlo simulations of lattice QCD with $O(a)$-improved Wilson fermions by exploiting a recently proposed strategy to study non-perturbatively QCD at very high temperature. Very large spatial extensions are considered in order to have negligible finite volume effects. For each temperature we have simulated $3$ or $4$ values of the lattice spacing, so as to perform the continuum limit extrapolation with confidence at a few permille accuracy. The degeneracy of the positive and negative parity-state screening masses, expected from Ward identities associated to non-singlet axial transformations, provides further evidence for the restoration of chiral symmetry in the high temperature regime of QCD. In the entire range of temperatures explored, the baryonic masses deviate from the free theory result, $3 \pi T$, by $4$-$8\%$. The contribution due to the interactions is clearly visible up to the highest temperature considered, and cannot be explained by the expected leading behavior in the QCD coupling constant $g$ over the entire range of temperatures explored., Comment: 8 pages, 4 tables and 4 figures. arXiv admin note: substantial text overlap with arXiv:2112.05427

We determine the resummed 1-loop correction to a baryonic thermal screening mass. The calculation is carried out in the framework of a dimensionally reduced effective theory, where quarks are heavy fields due to their non-zero Matsubara frequencies. The correction due to interactions is computed at O($g^2_{ }$) in the coupling constant. In order to solve a 3-body Schr\"odinger equation, we exploit a two-dimensional generalization of the hyperspherical harmonics method. At electroweak scale temperatures, the NLO correction represents a $\sim 4.6 \%$ increase of the free-theory value $3\pi T$ of the screening mass., Comment: 22 pages. v2: minor updates

Experiments aimed at direct searches for WIMP dark matter require highly effective reduction of backgrounds and control of any residual radioactive contamination. In particular, neutrons interacting with atomic nuclei represent an important class of backgrounds due to the expected similarity of a WIMP-nucleon interaction, so that such experiments often feature a dedicated neutron detector surrounding the active target volume. In the context of the development of DarkSide-20k detector at INFN Gran Sasso National Laboratory (LNGS), several R&D projects were conceived and developed for the creation of a new hybrid material rich in both hydrogen and gadolinium nuclei to be employed as an essential element of the neutron detector. Thanks to its very high cross-section for neutron capture, gadolinium is one of the most widely used elements in neutron detectors, while the hydrogen-rich material is instrumental in efficiently moderating the neutrons. In this paper results from one of the R&Ds are presented. In this effort the new hybrid material was obtained as a poly(methyl methacrylate) (PMMA) matrix, loaded with gadolinium oxide in the form of nanoparticles. We describe its realization, including all phases of design, purification, construction, characterization, and determination of mechanical properties of the new material.

We consider models of accidental dark matter, namely models in which the dark matter is a composite state that is stable thanks to an accidental symmetry of the theory. The fundamental constituents are vectorlike fermions, taken to be fragments of representations of the grand unifying gauge group $SU(5)$, as well as a scalar singlet. All the new fields are charged under a new confining gauge group, which we take to be $SU(N)$, leading to models with complex dark matter. We analyse the models in the context of $SU(5)$ grand unification with a non-standard approach recently proposed in the literature. The advantage of including the scalar mainly resides in the fact that it allows several undesired accidental symmetries to be broken, leading to a larger set of viable models with respect to previous literature, in which only fermions (or only scalars) were considered. Moreover these models present distinct novelties, namely dark states with non-zero baryon and lepton number and the existence of composite hybrid states of fermions and scalars. We identify phenomena that are specific to the inclusion of the scalar and discuss possibilities to test this setup., Comment: 27 pages + appendices

Attosecond photoemission or photoionization delays are a unique probe of the structure and the electronic dynamics of matter. However, spectral congestion and spatial delocalization of valence electron wave functions set fundamental limits to the complexity of systems that can be studied and the information that can be retrieved, respectively. Using attosecond X-ray pulses from LCLS, we demonstrate the key advantages of measuring core-level delays: the photoelectron spectra remain atom-like, the measurements become element specific and the observed scattering dynamics originate from a point-like source. We exploit these unique features to reveal the effects of electronegativity and symmetry on attosecond scattering dynamics by measuring the photoionization delays between N-1s and C-1s core shells of a series of aromatic azabenzene molecules. Remarkably, the delays systematically increase with the number of nitrogen atoms in the molecule and reveal multiple resonances. We identify two previously unknown mechanisms regulating the associated attosecond dynamics, namely the enhanced confinement of the trapped wavefunction with increasing electronegativity of the atoms and the decrease of the coupling strength among the photoemitted partial waves with increasing symmetry. This study demonstrates the unique opportunities opened by measurements of core-level photoionization delays for unravelling attosecond electron dynamics in complex matter.

Many quiescent galaxies discovered in the early Universe by \textit{JWST} raise fundamental questions on when and how these galaxies became and stayed quenched. Making use of the latest version of the semi-analytic model GAEA that provides good agreement with the observed quenched fractions up to $z\sim 3$, we make predictions for the expected fractions of quiescent galaxies up to $z\sim 7$ and analyze the main quenching mechanism. We find that in a simulated box of $685~{\rm Mpc}$ on a side, the first quenched massive ($M_{\star} \sim 10^{11} {\rm M}_{\odot}$), Milky Way mass, and low mass ($M_{\star} \sim 10^{9.5} {\rm M}_{\odot}$ ) galaxies appear at $z\sim 4.5$, $z\sim 6.2$, and before $z = 7$. Most quenched galaxies identified at early redshifts remain quenched for more than 1 Gyr. Independently of galaxy stellar mass, the dominant quenching mechanism at high redshift is accretion disk feedback (quasar winds) from a central massive black hole, which is triggered by mergers in massive and MW-mass galaxies, and by disk instabilities in low-mass galaxies. Environmental stripping becomes increasingly more important at lower redshift., Comment: 8 pages, 3 figures, Accepted publication in APJL

The stability of a dark matter detector on the timescale of a few years is a key requirement due to the large exposure needed to achieve a competitive sensitivity. It is especially crucial to enable the detector to potentially detect any annual event rate modulation, an expected dark matter signature. In this work, we present the performance history of the DarkSide-50 dual-phase argon time projection chamber over its almost three-year low-radioactivity argon run. In particular, we focus on the electroluminescence signal that enables sensitivity to sub-keV energy depositions. The stability of the electroluminescence yield is found to be better than 0.5%. Finally, we show the temporal evolution of the observed event rate around the sub-keV region being consistent to the background prediction., Comment: 13 pages, 5 figures

We present the characterisation of an inner mini-Neptune in a 9.2292005$\pm$0.0000063 day orbit and an outer mono-transiting sub-Saturn planet in a 95.50$^{+0.36}_{-0.25}$ day orbit around the moderately active, bright (mv=8.9 mag) K5V star TOI-2134. Based on our analysis of five sectors of TESS data, we determine the radii of TOI-2134b and c to be 2.69$\pm$0.16 R$_{e}$ for the inner planet and 7.27$\pm$0.42 R$_{e}$ for the outer one. We acquired 111 radial-velocity spectra with HARPS-N and 108 radial-velocity spectra with SOPHIE. After careful periodogram analysis, we derive masses for both planets via Gaussian Process regression: 9.13$^{+0.78}_{-0.76}$ M$_{e}$ for TOI-2134b and 41.86$^{+7.69}_{-7.83}$ M$_{e}$ for TOI-2134c. We analysed the photometric and radial-velocity data first separately, then jointly. The inner planet is a mini-Neptune with density consistent with either a water-world or a rocky core planet with a low-mass H/He envelope. The outer planet has a bulk density similar to Saturn's. The outer planet is derived to have a significant eccentricity of 0.67$^{+0.05}_{-0.06}$ from a combination of photometry and RVs. We compute the irradiation of TOI-2134c as 1.45$\pm$0.10 times the bolometric flux received by Earth, positioning it for part of its orbit in the habitable sone of its system. We recommend further RV observations to fully constrain the orbit of TOI-2134c. With an expected Rossiter-McLaughlin (RM) effect amplitude of 7.2$\pm$1.3 m/s, we recommend TOI-2134c for follow-up RM analysis to study the spin-orbit architecture of the system. We calculate the Transmission Spectroscopy Metric, and both planets are suitable for bright-mode NIRCam atmospheric characterisation., Comment: 24 pages, 7 tables, 14 figures

Is the population of close-in planets orbiting M dwarfs sculpted by thermally driven escape or is it a direct outcome of the planet formation process? A number of recent empirical results strongly suggest the latter. However, the unique architecture of the TOI-1266 system presents a challenge to models of planet formation and atmospheric escape given its seemingly "inverted" architecture of a large sub-Neptune ($P_b=10.9$ days, $R_{p,b}=2.62\pm 0.11\, \mathrm{R}_{\oplus}$) orbiting interior to that of the system's smaller planet ($P_c=18.8$ days, $R_{p,c}=2.13\pm 0.12\, \mathrm{R}_{\oplus}$). Here we present revised planetary radii based on new TESS and diffuser-assisted ground-based transit observations, and characterize both planetary masses using a set of 145 radial velocity measurements from HARPS-N ($M_{p,b}=4.23\pm 0.69\, \mathrm{M}_{\oplus}, M_{p,c}=2.88\pm 0.80\, \mathrm{M}_{\oplus}$). Our analysis also reveals a third planet candidate ($P_d=32.3$ days, $M_{p,d}\sin{i} = 4.59^{+0.96}_{-0.94}\, \mathrm{M}_{\oplus}$), which if real, would form a chain of near 5:3 period ratios, although the system is likely not in a mean motion resonance. Our results indicate that TOI-1266 b and c are among the lowest density sub-Neptunes around M dwarfs and likely exhibit distinct bulk compositions of a gas-enveloped terrestrial ($X_{\mathrm{env},b}=5.5\pm 0.7$%) and a water-rich world (WMF$_c=59\pm 14$%), which is supported by hydrodynamic escape models. If distinct bulk compositions are confirmed through atmospheric characterization, the system's unique architecture would represent an interesting test case of inside-out sub-Neptune formation at pebble traps., Comment: Accepted for publication in MNRAS. 21 pages. Our spectroscopic time series are included in the arXiv source files as table6.csv

We announce the detection of escaping helium from TOI 2134b, a mini-Neptune a few Gyr old. The average in-transit absorption spectrum shows a peak of 0.37 +- 0.05% and an equivalent width of $W_{\rm avg}=3.3 \pm 0.3$ m$\r{A}$. Among all planets with helium detections, TOI 2134b is the only mature mini-Neptune, has the smallest helium signal, and experiences the lowest XUV flux. Putting TOI 2134b in the context of all other helium detections, we report the detection of a strong (p=3.0e-5) and theoretically expected correlation between $F_{\rm XUV}/\rho_{\rm XUV}$ (proportional to the energy-limited mass loss rate) and $R_* W_{\rm avg}$ (roughly proportional to the observationally inferred mass loss rate). Here, $W_{\rm avg}$ is the equivalent width of the helium absorption and $\rho_{\rm XUV}$ is the density of the planet within the XUV photosphere, but the correlation is similarly strong if we use the optical photosphere. TOI 2134b anchors the relation, having the lowest value on both axes. We encourage further observations to fill in missing regions of this parameter space and improve estimates of $F_{\rm XUV}$., Comment: Accepted by ApJL

The direct search for dark matter in the form of weakly interacting massive particles (WIMP) is performed by detecting nuclear recoils (NR) produced in a target material from the WIMP elastic scattering. A promising experimental strategy for direct dark matter search employs argon dual-phase time projection chambers (TPC). One of the advantages of the TPC is the capability to detect both the scintillation and charge signals produced by NRs. Furthermore, the existence of a drift electric field in the TPC breaks the rotational symmetry: the angle between the drift field and the momentum of the recoiling nucleus can potentially affect the charge recombination probability in liquid argon and then the relative balance between the two signal channels. This fact could make the detector sensitive to the directionality of the WIMP-induced signal, enabling unmistakable annual and daily modulation signatures for future searches aiming for discovery. The Recoil Directionality (ReD) experiment was designed to probe for such directional sensitivity. The TPC of ReD was irradiated with neutrons at the INFN Laboratori Nazionali del Sud, and data were taken with 72 keV NRs of known recoil directions. The direction-dependent liquid argon charge recombination model by Cataudella et al. was adopted and a likelihood statistical analysis was performed, which gave no indications of significant dependence of the detector response to the recoil direction. The aspect ratio R of the initial ionization cloud is estimated to be 1.037 +/- 0.027 and the upper limit is R < 1.072 with 90% confidence level, Comment: 20 pages, 10 figures, submitted to Eur. Phys. J. C

Dark matter induced event rate in an Earth-based detector is predicted to show an annual modulation as a result of the Earth's orbital motion around the Sun. We searched for this modulation signature using the ionization signal of the DarkSide-50 liquid argon time projection chamber. No significant signature compatible with dark matter is observed in the electron recoil equivalent energy range above $40~{\rm eV_{ee}}$, the lowest threshold ever achieved in such a search., Comment: 10 pages, 5 figures

In this paper, we study upper bounds on the minimum length of frameproof codes introduced by Boneh and Shaw to protect copyrighted materials. A $q$-ary $(k,n)$-frameproof code of length $t$ is a $t \times n$ matrix having entries in $\{0,1,\ldots, q-1\}$ and with the property that for any column $\mathbf{c}$ and any other $k$ columns, there exists a row where the symbols of the $k$ columns are all different from the corresponding symbol (in the same row) of the column $\mathbf{c}$. In this paper, we show the existence of $q$-ary $(k,n)$-frameproof codes of length $t = O(\frac{k^2}{q} \log n)$ for $q \leq k$, using the Lov\'asz Local Lemma, and of length $t = O(\frac{k}{\log(q/k)}\log(n/k))$ for $q > k$ using the expurgation method. Remarkably, for the practical case of $q \leq k$ our findings give codes whose length almost matches the lower bound $\Omega(\frac{k^2}{q\log k} \log n)$ on the length of any $q$-ary $(k,n)$-frameproof code and, more importantly, allow us to derive an algorithm of complexity $O(t n^2)$ for the construction of such codes., Comment: 5 pages plus extra one reference page, accepted to the IEEE Information Theory Workshop (ITW 2023)

We present a novel approach for the search of dark matter in the DarkSide-50 experiment, relying on Bayesian Networks. This method incorporates the detector response model into the likelihood function, explicitly maintaining the connection with the quantity of interest. No assumptions about the linearity of the problem or the shape of the probability distribution functions are required, and there is no need to morph signal and background spectra as a function of nuisance parameters. By expressing the problem in terms of Bayesian Networks, we have developed an inference algorithm based on a Markov Chain Monte Carlo to calculate the posterior probability. A clever description of the detector response model in terms of parametric matrices allows us to study the impact of systematic variations of any parameter on the final results. Our approach not only provides the desired information on the parameter of interest, but also potential constraints on the response model. Our results are consistent with recent published analyses and further refine the parameters of the detector response model., Comment: 24 pages, 12 figures, 1 table