The density of numbers nn having a prescribed G.C.D. with the nnth Fibonacci number

For each positive integer $k$, let $\mathscr{A}_k$ be the set of all positive integers $n$ such that $\gcd(n, F_n) = k$, where $F_n$ denotes the $n$th Fibonacci number. We prove that the asymptotic density of $\mathscr{A}_k$ exists and is equal to $$\sum_{d = 1}^\infty \frac{\mu(d)}{\operatorname{lcm}(dk, z(dk))}$$ where $\mu$ is the M\"obius function and $z(m)$ denotes the least positive integer $n$ such that $m$ divides $F_n$. We also give an effective criterion to establish when the asymptotic density of $\mathscr{A}_k$ is zero and we show that this is the case if and only if $\mathscr{A}_k$ is empty

Intra-source provenance study on Monte Arci (Sardinia) obsidian by pXRF: Role of the data acquisition and analysis tools

In this work, a detailed study of Monte Arci obsidian sub-sources using the increasingly accessible technique of pXRF is presented based upon a large dataset of 68 geological samples, for the development of X-ray fluorescence-based analytical standardless procedure. In addition, a non-conventional (for obsidian provenance study) direct application of multivariate analysis on XRF spectra (continuous variables), rather than absolute concentrations or intensity ratios (discrete variables) is proposed. Results from different softwares and data analysis approaches (bi-/trivariate versus multivariate) were compared. In a blind test, the bi-/trivariate approach led to the correct assignment for the main SA, SB, and SC sub-sources, taking into account averaged values of intensity ratios with their standard deviation obtained from three independent measurements. A high intra-source variability for the SB subgroups was detected (almost 13% of error in the assignment, 9 samples out of 68). A non-conventional application of multivariate analysis was carried out directly on the XRF spectra and correct assignments were obtained for SA, SB1, SC groups, while 71% of the SB2 samples were correctly identified. The non-destructive analysis on 14 archaeological samples from Su Carroppu (Carbonia, southwestern Sardinia) rockshelter and from the Middle Neolithic (MN) 422 structure of the open-air dwelling site at Cuccuru is Arrius (Cabras, central-western Sardinia) permitted to test the method and hypothesise their provenance. The comparison with visual characterization or previous analyses by Particle Induced X-Ray Emission (PIXE) permitted to verify the correct provenance assignment of all artifacts for the bi-/trivariate method, and for 12/14 samples in the case of the multivariate one. The standardless analytical approach proposed in this work can represent a more general method exploitable for other obsidian sources, other glassy materials, besides other materials of archaeological interest

Regional and sex inequalities of avoidable mortality in Italy: A time trend analysis

Objectives: This study provides a comprehensive analysis of avoidable mortality (AM), treatable mortality (TM), and preventable mortality (PM) across Italy, focusing on region- and gender-specific inequalities over a 14-year period. Study design: Time-trend analysis (2006–2019). Methods: The study was conducted using mortality data from the Italian Institute of Statistics to evaluate the extent and patterns of AM, TM, and PM in Italy. Biennial age-standardized mortality rates were calculated by gender and region using the joint OECD/Eurostat list. Results: The overall AM rates showed a large reduction from 2006/7 (221.0 per 100,000) to 2018/9 (166.4 per 100,000). Notably, females consistently displayed lower AM rates than males. Furthermore, both gender differences and the North–South gap of AM decreased during the period studied. The regions with the highest AM rates fluctuated throughout the study period. The highest percentage decrease in AM from 2006/7 to 2018/9, for both males (−41.3 %) and females (−34.2 %), was registered in the autonomous province of Trento, while the lowest reduction was observed in Molise for males (−17.4 %) and in Marche for females (−10.0 %). Conclusions: Remarkable gender and regional differences in AM between 2006 and 2019 have been recorded in Italy, although they have decreased over years. Continuous monitoring of AM and the implementation of region- and gender-specific interventions is essential to provide valuable insights for both policy and public health practice. This study contributes to the efforts to improve health equity between Italian regions

First Phase Space Portrait of a Hierarchical Stellar Structure in the Milky Way

We present the first detailed observational picture of a possible ongoing massive cluster hierarchical assembly in the Galactic disk as revealed by the analysis of the stellar full phase-space (3D positions and kinematics and spectro-photometric properties) of an extended area ($6^{\circ}$ diameter) surrounding the well-known $\it h$ and $\chi$ Persei double stellar cluster in the Perseus Arm. Gaia-EDR3 shows that the area is populated by seven co-moving clusters, three of which were previously unknown, and by an extended and quite massive ($M\sim10^5 M_{\odot}$) halo. All stars and clusters define a complex structure with evidence of possible mutual interactions in the form of intra-cluster over-densities and/or bridges. They share the same chemical abundances (half-solar metallicity) and age ($t\sim20$ Myr) within a small confidence interval and the stellar density distribution of the surrounding diffuse stellar halo resembles that of a cluster-like stellar system. The combination of these evidences suggests that stars distributed within a few degrees from $\it h$ and $\chi$ Persei are part of a common, sub-structured stellar complex that we named LISCA I. Comparison with results obtained through direct $N$-body simulations suggest that LISCA I may be at an intermediate stage of an ongoing cluster assembly that can eventually evolve in a relatively massive (a few $10^5 M_{\odot}$) stellar system. We argue that such cluster formation mechanism may be quite efficient in the Milky Way and disk-like galaxies and, as a consequence, it has a relevant impact on our understanding of cluster formation efficiency as a function of the environment and redshift.Comment: 19 pages, 8 figures, 1 table; accepted for publication in Ap

MiRitH: Efficient Post-Quantum Signatures from MinRank in the Head

Since 2016’s NIST call for standardization of post-quantum cryptographic primitives, developing efficient post-quantum secure digital signature schemes has become a highly active area of research. The difficulty in constructing such schemes is evidenced by NIST reopening the call in 2022 for digital signature schemes, because of missing diversity in existing proposals. In this work, we introduce the new postquantum digital signature scheme MiRitH. As direct successor of a scheme recently developed by Adj, Rivera-Zamarripa and Verbel (Africacrypt ’23), it is based on the hardness of the MinRank problem and follows the MPC-in-the-Head paradigm. We revisit the initial proposal, incorporate design-level improvements and provide more efficient parameter sets. We also provide the missing justification for the quantum security of all parameter sets following NIST metrics. In this context we design a novel Grover-amplified quantum search algorithm for solving the MinRank problem that outperforms a naive quantum brute-force search for the solution. MiRitH obtains signatures of size 5.7 kB for NIST category I security and therefore competes for the smallest signatures among any post-quantum signature following the MPCitH paradigm. At the same time MiRitH offers competitive signing and verification timings compared to the state of the art. To substantiate those claims we provide extensive implementations. This includes a reference implementation as well as optimized constant-time implementations for Intel processors (AVX2), and for the ARM (NEON) architecture. The speedup of our optimized AVX2 implementation relies mostly on a redesign of the finite field arithmetic, improving over existing implementations as well as an improved memory management

MiRitH: Efficient Post-Quantum Signatures from MinRank in the Head

Since 2016’s NIST call for standardization of post-quantum cryptographic primitives, developing efficient post-quantum secure digital signature schemes has become a highly active area of research. The difficulty in constructing such schemes is evidenced by NIST reopening the call in 2022 for digital signature schemes, because of missing diversity in existing proposals. In this work, we introduce the new post-quantum digital signature scheme MiRitH. As direct successor of a scheme recently developed by Adj, Rivera-Zamarripa and Verbel (Africacrypt ’23), it is based on the hardness of the MinRank problem and follows the MPC-in-the-Head paradigm. We revisit the initial proposal, incorporate design-level improvements and provide more efficient parameter sets. We also provide the missing justification for the quantum security of all parameter sets following NIST metrics. In this context we design a novel Grover-amplified quantum search algorithm for solving the MinRank problem that outperforms a naive quantum brute-force search for the solution. MiRitH obtains signatures of size 5.7 kB for NIST category I security and therefore competes for the smallest signatures among any post-quantum signature following the MPCitH paradigm. At the same time MiRitH offers competitive signing and verification timings compared to the state of the art. To substantiate those claims we provide extensive implementations. This includes a reference implementation as well as optimized constant-time implementations for Intel processors (AVX2), and for the ARM (NEON) architecture. The speed-up of our optimized AVX2 implementation relies mostly on a redesign of the finite field arithmetic, improving over existing implementations as well as an improved memory management

Activation of the aryl hydrocarbon receptor and risk of lymphoma subtypes

The aryl hydrocarbon receptor (AhR) is a transcription factor implicated in several pathways known to be relevant in lymphomagenesis. Aim of our study was to explore the link between AhR activation and risk of lymphoma subtypes. We used a Dual-Luciferase Assay® and a luminometer to detect the activation of the luciferase gene, in HepG2 cells transfected with a specific reporter systems, by a 50 ml serum aliquot of cases of diffuse large B cell lymphoma (N = 108), follicular lymphoma (N = 85), chronic lymphocytic leukemia (N = 72), multiple myeloma (N = 80), and Hodgkin lymphoma (N = 94) and 357 controls who participated in the multicentre Italian study on gene-environment interactions in lymphoma etiology (ItGxE). Risk of each lymphoma subtype associated with AhR activation was calculated with polytomous logistic regression adjusting by age, gender, and study centre. The overall prevalence of AhR activation ranged 13.9-23.6% by subtype, and it varied by study area (8-39%). Risk associated with AhR activation was moderately elevated for follicular lymphoma (OR = 1.56, 95% CI 0.86, 2.80) and chronic lymphocytic leukemia (OR = 1.56, 95% CI 0.83, 2.96). Despite our inconclusive findings about the association with risk of lymphoma subtypes, we showed that the Dual-Luciferase Assay can be reliably and easily applied in population-based studies to detect AhR activation

Open data, Science and Society: launching Oasis, the flagship initiative of the Istituto Italiano di Antropologia

The Open Data philosophy has gained considerable momentum in recent years, both in society and the scientific community. The accessibility via web of open data from the public sector has remarkably increased in the last decade, although there are substantial differences among nations (http://datacatalogs.org/). The expectation of many citizens, organizations and pressure groups (the so called “open government” movement) is that the free release of data from public administrations may help increase government transparency and accountability