Statistical properties of Lorenz like flows, recent developments and perspectives

We comment on mathematical results about the statistical behavior of Lorenz equations an its attractor, and more generally to the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be surprisingly difficult. It is remarkable that a rigorous proof of the existence of the Lorenz attractor was presented only around the year 2000 with a computer assisted proof together with an extension of the hyperbolic theory developed to encompass attractors robustly containing equilibria. We present some of the main results on the statisitcal behavior of such systems. We show that for attractors of three-dimensional flows, robust chaotic behavior is equivalent to the existence of certain hyperbolic structures, known as singular-hyperbolicity. These structures, in turn, are associated to the existence of physical measures: \emph{in low dimensions, robust chaotic behavior for flows ensures the existence of a physical measure}. We then give more details on recent results on the dynamics of singular-hyperbolic (Lorenz-like) attractors.Comment: 40 pages; 10 figures; Keywords: sensitive dependence on initial conditions, physical measure, singular-hyperbolicity, expansiveness, robust attractor, robust chaotic flow, positive Lyapunov exponent, large deviations, hitting and recurrence times. Minor typos corrected and precise acknowledgments of financial support added. To appear in Int J of Bif and Chaos in App Sciences and Engineerin

Isolated Testicular Metastasis from Prostate Cancer

Prostatic adenocarcinoma is the most frequently diagnosed carcinoma in the male population; the most common sites of secondary lesions are nodes, bones, and lungs. We report the clinical case of a 58-year-old man presenting with a single metastasis in the left testis after a radical prostatectomy/lymphadenectomy for prostate cancer. CASE REPORT This clinical report focuses on a 58-year-old man with prostate cancer who developed an uncommon single metastasis in the left testis after radical surgery and adjuvant pelvic radiation therapy. CONCLUSIONS Prostate-specific antigen (PSA) levels are important in the follow-up of prostate cancer. At the same time, physical examination of all possible sites of metastasis and proper evaluation of all signs/symptoms are indispensable in the process of identifying recurrence and for the selection of patients undergoing adjuvant therapy

Implant-Prosthetic rehabilitation in bilateral agenesis of maxillary lateral incisors with a mini split crest

The reported clinical case describes the surgical procedure of ridge augmentation by using a "split crest" technique with a partial thickness flap and a subsequent implant-prosthetic rehabilitation aimed at treating a bilateral agenesis of the upper lateral incisors. In such cases with vestibule-palatal and mesial-distal scarce bone thicknesses associated with the need of a proper functional and aesthetic rehabilitation, the split crest technique is particularly suitable. In the case we reported, because of the poor bone thicknesses, we performed a minimally invasive split crest which allowed a correct insertion of the fixtures. This technique allowed us to achieve an optimal functional and aesthetic rehabilitation; moreover, we obtained a good emergency profile, ensuring the vitality of the close teeth and ensuring a good primary stability and the following osseointegration of dental implants

Analysis of sightings of white sharks in Gansbaai (South Africa)

In Gansbaai (South Africa), at Dyer Island Nature Reserve, a large White shark population is present and can be observed due to the support of local ecotourism operators authorised to reach the field observation sites. Between 2009 and 2019, it was possible to create a database including information about each individual observed. In total, 423 white sharks were sighted during 462 direct observation hours from the boat, that included 220 hours from the diving "cage". The mean sighting rate was 0.91 (range 0.18-1.53) sharks per hour and sighting rates dramatically declined in the last three years of the study period. Ninety-nine unique Photo-Ids of the dorsal fin were collected and only five re-sightings occurred, which indicate a transient behaviour for the Gansbaai White shark population. The sex ratio showed that females were always prevalent over males throughout the duration of the observations: the ratios were 1:2.2:0.8 for males, females, and unsexed sharks, respectively, and showed the prevalence of immature female individuals (immature: 51 males, 201 females, and 40 unsexed; adults: 49 males, 14 females, and 1 unsexed; undefined maturity: 5 males, 19 females, and 43 unsexed sharks). The predominance of immatures only applies to the females; there were as many immature males (51) as mature (49). The total length for all the individuals was between 150 cm and 500 cm (mean 308 cm, n = 423) with few young-of-the-year and adults recorded, indicating that Gansbaai Area is not a nursery area nor an adult aggregation site, but a seasonal feeding ground. The interannual sighting trend showed a consistent long-term increasing peak (ca. 4-5 years) and this could confirm that, in Gansbaai, the White shark frequency is not affected by ecotourism but, since 2017, a consistent loss of sightings was also due to recorded transient killer whales' unusual fatal attacks

New oxaliplatin-pyrophosphato analogs with improved in vitro cytotoxicity

Two new Pt(II)-pyrophosphato complexes containing the carrier ligands cis-1,3- diaminocyclohexane (cis-1,3-DACH) and trans-1,2-diamine-4-cyclohexene (1,2-DACHEX), variants of the 1R,2R-diaminocyclohexane ligand present in the clinically used Pt-drug oxaliplatin, have been synthesized with the aim of developing new potential antitumor drugs with high bone tropism. The complexes are more stable at physiological pH than in acid conditions, with Na2[Pt(pyrophosphato)(cis-1,3-DACH)] (1) slightly more stable than Pt(dihydrogenpyrophosphato)(1,2-DACHEX)] (2). The greater reactivity at acidic pH ensures a greater efficacy at the tumor site. Preliminary NMR studies indicate that 1 and 2 react slowly with 5’-GMP (used as a model of nucleic acids), releasing the pyrophosphate ligand and affording the bis 5’-GMP adduct. In vitro cytotoxicity assays performed against a panel of four human cancer cell lines have shown that both compounds are more active than oxaliplatin. Flow cytometry studies on HCT116 cells showed that the pyrophosphato compounds with the non-classical 1,3- and 1,4- diaminocyclohexane ligands (1 and 4) are the most capable to induce cells’ death by apoptosis and necrosis

A protective role for autophagy in vitiligo

A growing number of studies supports the existence of a dynamic interplay between energetic metabolism and autophagy, whose induction represents an adaptive response against several stress conditions. Autophagy is an evolutionarily conserved and a highly orchestrated catabolic recycling process that guarantees cellular homeostasis. To date, the exact role of autophagy in vitiligo pathogenesis is still not clear. Here, we provide the first evidence that autophagy occurs in melanocytes and fibroblasts from non-lesional skin of vitiligo patients, as a result of metabolic surveillance response. More precisely, this study is the first to reveal that induction of autophagy exerts a protective role against the intrinsic metabolic stress and attempts to antagonize degenerative processes in normal appearing vitiligo skin, where melanocytes and fibroblasts are already prone to premature senescence

Gut microbiota and nutrient interactions with skin in psoriasis : a comprehensive review of animal and human studies

The intestinal tract (i.e., the gut), is where the body's nutrients are absorbed, and is simultaneously inhabited by numerous microbes. An increasing body of literature suggests a crucial role for the gut microbiome in modulating systemic inflammatory disease. Psoriasis is a chronic systemic inflammatory disease and its pathogenesis is related to the interaction between genetic susceptibility, immune response and environmental triggers. The omics era has allowed physicians to assess different aspects of psoriasis pathogenesis such as the microbiome, infectome, and autoinfectome. Furthermore, diet appears to play an important role in modulating disease activity, perhaps by influencing gut microbes. Given these observations, we aimed to summarize the current knowledge regarding skin-microbiome-gut-nutrients and psoriasis

Tetracyclines in COVID-19 patients quarantined at home: Literature evidence supporting real-world data from a multicenter observational study targeting inflammatory and infectious dermatoses

Tetracyclines (TetraC) are widely used in dermatology for both inflammatory and infectious dermatoses; recently both in vivo and in vitro studies started to suggest also a potential antiviral effect. During COVID-19 outbreak, several dermatological patients contracted SARS-CoV-2 experiencing only mild symptoms, but no protocol were approved. A multicenter prospective observational study that enrolled COVID-19 patients visited with teledermatology and undergoing TetraC was performed. About 38 adult outpatients (M/F: 20/18, age 42.6 years [21-67]) were enrolled. During the TetraC treatment, symptoms resolved in all patients within 10 days. Remarkably, ageusia and anosmia disappeared in the first week of TetraC treatment. TetraC seem a promising drug to treat COVID-19 outpatients with mild symptoms

The Impact of Intermittent Fasting (Ramadan Fasting) on Psoriatic Arthritis Disease Activity, Enthesitis, and Dactylitis: A Multicentre Study

Intermittent circadian fasting, namely Ramadan, is a common worldwide practice. Such fasting has a positive impact on psoriasis, but no data exist on its role in psoriatic arthritis (PsA)—a disease that is clearly linked to body mass index. We enrolled 37 patients (23 females and 14 males) with a mean age 43.32 ± 7.81 and they fasted for 17 h for one month in 2016. The baseline PsA characteristics were collected and 12 (32.4%) patients had peripheral arthritis, 13 (35.1%) had axial involvement, 24 (64.9%) had enthesitis, and 13 (35.1%) had dactylitis. Three patients (8.1%) were treated with methotrexate, 28 (75.7%) with TNF-α blockers, and 6 (16.2%) with IL-17 blockers. After a month of intermittent fasting, C-reactive protein (CRP) levels decreased from 14.08 ± 4.65 to 12.16 ± 4.46 (p < 0.0001), Bath Ankylosing Spondylitis Disease Activity Index (BASDAI) decreased from 2.83 ± 1.03 to 2.08 ± 0.67 (p = 0.0078), Psoriasis Area Severity Index (PASI) decreased from 7.46 ± 2.43 to 5.86 ± 2.37 (p < 0.0001), and Disease Activity index for PSoriatic Arthritis (DAPSA) decreased from 28.11 ± 4.51 to 25.76 ± 4.48 (p < 0.0001). Similarly, enthesitis improved after fasting, with Leeds Enthesitis Index (LEI) decreasing from 2.25 ± 1.11 to 1.71 ± 0.86 (p < 0.0001) and dactylitis severity score (DSS) decreasing from 9.92 ± 2.93 to 8.54 ± 2.79 (p = 0.0001). Fasting was found to be a predictor of a decrease in PsA disease activity scores (DAPSA, BASDAI, LEI, DSS) even after adjustment for weight loss. IL-17 therapy was found to be an independent predictor of decreases in LEI after fasting. These preliminary data may support the use of chronomedicine in the context of rheumatic diseases, namely PsA. Further studies are needed to support our findings