Primitive abundant and weird numbers with many prime factors

We give an algorithm to enumerate all primitive abundant numbers (briefly, PANs) with a fixed $\Omega$ (the number of prime factors counted with their multiplicity), and explicitly find all PANs up to $\Omega=6$, count all PANs and square-free PANs up to $\Omega=7$ and count all odd PANs and odd square-free PANs up to $\Omega=8$. We find primitive weird numbers (briefly, PWNs) with up to 16 prime factors, improving the previous results of [Amato-Hasler-Melfi-Parton] where PWNs with up to 6 prime factors have been given. The largest PWN we find has 14712 digits: as far as we know, this is the largest example existing, the previous one being 5328 digits long [Melfi]. We find hundreds of PWNs with exactly one square odd prime factor: as far as we know, only five were known before. We find all PWNs with at least one odd prime factor with multiplicity greater than one and $\Omega = 7$ and prove that there are none with $\Omega < 7$. Regarding PWNs with a cubic (or higher) odd prime factor, we prove that there are none with $\Omega\le 7$, and we did not find any with larger $\Omega$. Finally, we find several PWNs with 2 square odd prime factors, and one with 3 square odd prime factors. These are the first such examples.Comment: New section on open problems. A mistake in table 2 corrected (# odd PAN with Omega=8). New PWN in table 5, last line, 2 squared prime factors, Omega=15. Updated bibliograph

SAI, a Sensible Artificial Intelligence that plays Go

We propose a multiple-komi modification of the AlphaGo Zero/Leela Zero paradigm. The winrate as a function of the komi is modeled with a two-parameters sigmoid function, so that the neural network must predict just one more variable to assess the winrate for all komi values. A second novel feature is that training is based on self-play games that occasionally branch -- with changed komi -- when the position is uneven. With this setting, reinforcement learning is showed to work on 7x7 Go, obtaining very strong playing agents. As a useful byproduct, the sigmoid parameters given by the network allow to estimate the score difference on the board, and to evaluate how much the game is decided.Comment: Updated for IJCNN 2019 conferenc

Progetto del sistema di bloccaggio opto-meccanico di un prisma ottico per un telescopio spaziale operante a temperatura criogenica

Progetto del sistema di bloccaggio opto-meccanico di un prisma ottico facente parte degli elementi dell'Assemblato Opto-Meccanico dello Spettrometro di Velocità Radiale (RVS-OMA) montato sul telescopio del satellite GAIA, e quindi operante a temperatura criogenica

Nuclear Magnetic Resonance Reveals Molecular Species in Carbon Nanodot Samples Disclosing Flaws

Carbon nanodots are currently one of the hot topics in the nanomaterials world, due to their accessible synthesis and promising features. However, the purification of these materials is still a critical aspect, especially for syntheses involving molecular precursors. Indeed, the presence of unreacted species or small organic molecules formed during solvothermal treatments can affect the properties of the synthesized nanomaterials. To illustrate the extreme importance of this issue, we present two case studies in which insufficient purification results in misleading conclusions regarding the chiral and fluorescent properties of the investigated materials. Key to identify molecular species is the use of nuclear magnetic resonance, which proves to be an effective tool. Our work highlights the need to include nuclear magnetic resonance as a standard characterization technique for carbon-based nanomaterials, to minimize the risk of observing properties that arise from molecular species, rather than the target carbon nanodots

The β3 adrenoceptor in proliferative retinopathies: "Cinderella" steps out of its family shadow

: In the retina, hypoxic condition leads to overgrowing leaky vessels resulting in altered metabolic supply that may cause impaired visual function. Hypoxia-inducible factor-1 (HIF-1) is a central regulator of the retinal response to hypoxia by activating the transcription of numerous target genes, including vascular endothelium growth factor, which acts as a major player in retinal angiogenesis. In the present review, oxygen urge by the retina and its oxygen sensing systems including HIF-1 are discussed in respect to the role of the beta-adrenergic receptors (β-ARs) and their pharmacologic manipulation in the vascular response to hypoxia. In the β-AR family, β1- and β2-AR have long been attracting attention because their pharmacology is intensely used for human health, while β3-AR, the third and last cloned receptor is no longer increasingly emerging as an attractive target for drug discovery. Here, β3-AR, a main character in several organs including the heart, the adipose tissue and the urinary bladder, but so far a supporting actor in the retina, has been thoroughly examined in respect to its function in retinal response to hypoxia. In particular, its oxygen dependence has been taken as a key indicator of β3-AR involvement in HIF-1-mediated responses to oxygen. Hence, the possibility of β3-AR transcription by HIF-1 has been discussed from early circumstantial evidence to the recent demonstration that β3-AR acts as a novel HIF-1 target gene by playing like a putative intermediary between oxygen levels and retinal vessel proliferation. Thus, targeting β3-AR may implement the therapeutic armamentarium against neovascular pathologies of the eye

VEGF as a survival factor in ex vivo models of early diabetic retinopathy

PURPOSE: Growing evidence indicates neuroprotection as a therapeutic target in diabetic retinopathy (DR). We tested the hypothesis that VEGF is released and acts as a survival factor in the retina in early DR. METHODS: Ex vivo mouse retinal explants were exposed to stressors similar to those characterizing DR, that is, high glucose (HG), oxidative stress (OS), or advanced glycation end-products (AGE). Neuroprotection was provided using octreotide (OCT), a somatostatin analog, and pituitary adenylate cyclase activating peptide (PACAP), two well-documented neuroprotectants. Data were obtained with real-time RT-PCR, Western blot, ELISA, and immunohistochemistry. RESULTS: Apoptosis was induced in the retinal explants by HG, OS, or AGE treatments. At the same time, explants also showed increased VEGF expression and release. The data revealed that VEGF is released shortly after exposure of the explants to stressors and before the level of cell death reaches its maximum. Retinal cell apoptosis was inhibited by OCT and PACAP. At the same time, OCT and PACAP also reduced VEGF expression and release. Vascular endothelial growth factor turned out to be a protective factor for the stressed retinal explants, because inhibiting VEGF with a VEGF trap further increased cell death. CONCLUSIONS: These data show that protecting retinal neurons from diabetic stress also reduces VEGF expression and release, while inhibiting VEGF leads to exacerbation of apoptosis. These observations suggest that the retina in early DR releases VEGF as a prosurvival factor. Neuroprotective agents may decrease the need of VEGF production by the retina, therefore limiting the risk, in the long term, of pathologic angiogenesis