Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow

Fermat, Leibniz, Euler, and Cauchy all used one or another form of approximate equality, or the idea of discarding "negligible" terms, so as to obtain a correct analytic answer. Their inferential moves find suitable proxies in the context of modern theories of infinitesimals, and specifically the concept of shadow. We give an application to decreasing rearrangements of real functions.Comment: 35 pages, 2 figures, to appear in Notices of the American Mathematical Society 61 (2014), no.

All null supersymmetric backgrounds of N=2, D=4 gauged supergravity coupled to abelian vector multiplets

The lightlike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to an arbitrary number of abelian vector multiplets are classified using spinorial geometry techniques. The solutions fall into two classes, depending on whether the Killing spinor is constant or not. In both cases, we give explicit examples of supersymmetric backgrounds. Among these BPS solutions, which preserve one quarter of the supersymmetry, there are gravitational waves propagating on domain walls or on bubbles of nothing that asymptote to AdS_4. Furthermore, we obtain the additional constraints obeyed by half-supersymmetric vacua. These are divided into four categories, that include bubbles of nothing which are asymptotically AdS_4, pp-waves on domain walls, AdS_3 x R, and spacetimes conformal to AdS_3 times an interval.Comment: 55 pages, uses JHEP3.cls. v2: Minor errors corrected, small changes in introductio

Time Dependent CP Asymmetries and Branching RatioMeasurements in Charmless Three Body B Decays at BABAR

In this work we presented measurements of CP violation and decay rates of B decays in final states not involving a charm quark in the final state. In particular, the time-dependent CP asymmetries of decays which proceed through b {yields} s elementary transition is a particularly sensitive probe of physics beyond the Standard Model. In fact, even if the precise measurements of CP conserving and CP violating processes show the success of the CKM picture of the flavour physics, the sector of b {yields} s transitions is still not strongly constrained and leaves room for new physics contributions. In particular, we considered the decays which have the cleanest theoretical prediction within the Standard Model: B{sup 0} {yields} {phi}K{sup 0} and B{sup 0} {yields} K{sub s}{sup 0}K{sub s}{sup 0}K{sub s}{sup 0} {beta}{sub eff}{sup SM} = 0.379. We examined the former with a completely new approach with respect to the past: the study of CP violation in the whole K{sup +}K{sup -}K{sup 0} phase space through a time-dependent Dalitz plot analysis. With this approach, we simultaneously measured the CP-violating asymmetries of the {phi}KJ{sup 0}, f{sub 0}(980)K{sup 0} resonant and K{sup +}K{sup -}K{sup 0} non-resonant contributions, avoiding one of the largest uncertainties which affected the previous measurements of B{sup 0} {yields} {phi}K{sup 0}. We find {beta}{sub eff}(B{sup 0} {yields} {phi}K{sup 0}) = 0.06 {+-} 0.16 {+-} 0.05, which is lower than the Standard Model expectation, but it is consistent with it within two standard deviations. Moreover, only a recently developed experimental technique, which allows the determination of the position of B decay vertex when no charged tracks are originating from it, has made possible the measurement of the time-dependent CP asymmetry in B{sup 0} {yields} K{sub s}{sup 0}K{sub s}{sup 0}K{sub s}{sup 0} decays. The mixing-induced CP parameter S in the Standard Model should be equal to sin 2{beta} parameter, which is measured with high precision in B {yields} [c{bar c}]K{sup 0} decays by the B-factories. This statement is true, in the Standard Model, with excellent approximation for the decays studied in this work. The summary of the measurements in the b {yields} s sector is shown in Fig. 9.8 A naive average of the b {yields} s penguins, which does not account for the correlations existing among {phi}K{sup 0}, f{sub 0}(980)K{sup 0} and K{sup +}K{sup -}K{sup 0}, and that includes also modes with larger theoretical uncertainties, shows that -{eta}{sub CP} x S is lower than sin 2{beta}. This is not an evidence of physics beyond the Standard Model, but the systematic deviation from the expected value is an hint that there is room for it. More compelling evidence for new physics could be obtained measuring significant deviation in each decay channel from Standard Model prediction. Currently all the measurement are statistically limited and therefore an increase in accumulated statistics will shed more light into this quest for New Physics

Chapter RoCKIn@Home: Domestic Robots Challenge

Service robots performing complex tasks involving people in houses or public environments are becoming more and more common, and there is a huge interest from both the research and the industrial point of view. The RoCKIn@Home challenge has been designed to compare and evaluate different approaches and solutions to tasks related to the development of domestic and service robots. RoCKIn@Home competitions have been designed and executed according to the benchmarking methodology developed during the project and received very positive feedbacks from the participating teams. Tasks and functionality benchmarks are explained in detail

RoCKIn@Home: Domestic Robots Challenge

Service robots performing complex tasks involving people in houses or public environments are becoming more and more common, and there is a huge interest from both the research and the industrial point of view. The RoCKIn@Home challenge has been designed to compare and evaluate different approaches and solutions to tasks related to the development of domestic and service robots. RoCKIn@Home competitions have been designed and executed according to the benchmarking methodology developed during the project and received very positive feedbacks from the participating teams. Tasks and functionality benchmarks are explained in detail

Prognostic significance of tyrosinase expression in sentinel lymph node biopsy for ultra-thin, thin, and thick melanomas

Abstract. – BACKGROUND: Investigate if the tyrosinase mRNA expression may be predictive of the outcome on ultra-thin, thin, and thick melanoma patients. AIM: In our study, we sought to correlate tyrosinase mRNA expression to the outcome in a group of 71 patients with thick, thin and ultra-thin melanomas. MATERIALS AND METHODS: 71 patients with melanomas underwent a SLNB (sentinel lymph node biopsy) at the “Sapienza” University of Rome. Among these, 38 patients had thin melanomas, while the other 33 patients had thick melanomas. In every patient’s sample histology, immunohistochemistry and reverse transcriptase-polymerase chain reaction (RT-PCR) was completed. We then correlated tyrosinase mRNA expression to the statistical analysis of the outcome of patients. RESULTS: Positivity of histology was found in one patient (1.4%), immunohistochemistry in five patients (7%), and tyrosinase in 52/71 (73.2%). Thickness and tyrosinase positivity were predictive for disease progression (p < 0.05). The median follow-up was 58.24 months. There were recurrences and/or deaths in both groups of patients. CONCLUSIONS: Nodal metastasis in melanoma is uncommon, especially in patients with thin melanomas. In this study, histology and immunohistochemistry were found to be non predictive for the risk of nodal metastases, while instead, tyrosinase m-RNA expression appeared to play a role in highlighting those patients with a risk of disease progression. Moreover, no differences among the thin melanoma groups of patients (0.30-0.75 mm and 0.76-1.00 mm) were observed

Fast and Furious: Shock Heated Gas as the Origin of Spatially Resolved Hard X-ray Emission in the Central 5 kpc of the Galaxy Merger NGC 6240

We have obtained a deep, sub-arcsecond resolution X-ray image of the nuclear region of the luminous galaxy merger NGC 6240 with Chandra, which resolves the X-ray emission from the pair of active nuclei and the diffuse hot gas in great detail. We detect extended hard X-ray emission from kT~6 keV (~70 million K) hot gas over a spatial scale of 5 kpc, indicating the presence of fast shocks with velocity of ~2200 km/s. For the first time we obtain the spatial distribution of this highly ionized gas emitting FeXXV, which shows a remarkable correspondence to the large scale morphology of H_2(1-0) S(1) line emission and H\alpha filaments. Propagation of fast shocks originated in the starburst driven wind into the ambient dense gas can account for this morphological correspondence. With an observed L(0.5-8 keV)=5.3E+41 erg/s, the diffuse hard X-ray emission is 100 times more luminous than that observed in the classic starburst galaxy M82. Assuming a filling factor of 1% for the 70 MK temperature gas, we estimate its total mass (M_{hot}=1.8E+8 Msun) and thermal energy (E_{th}=6.5E+57 ergs). The total iron mass in the highly ionized plasma is M_{Fe}=4.6E+5 Msun. Both the energetics and the iron mass in the hot gas are consistent with the expected injection from the supernovae explosion during the starburst that is commensurate with its high star formation rate. No evidence for fluorescent Fe I emission is found in the CO filament connecting the two nuclei.Comment: Accepted to ApJ. 37 pages, 13 figures. Figures 5 and 6 are rotated for better visualization in prin

Universal nonequilibrium properties of dissipative Rydberg gases

We investigate the out-of-equilibrium behavior of a dissipative gas of Rydberg atoms that features a dynamical transition between two stationary states characterized by different excitation densities. We determine the structure and properties of the phase diagram and identify the universality class of the transition, both for the statics and the dynamics. We show that the proper dynamical order parameter is in fact not the excitation density and find evidence that the dynamical transition is in the “model A” universality class; i.e., it features a nontrivial Z2 symmetry and a dynamics with nonconserved order parameter. This sheds light on some relevant and observable aspects of dynamical transitions in Rydberg gases. In particular it permits a quantitative understanding of a recent experiment [C. Carr, Phys. Rev. Lett. 111, 113901 (2013)] which observed bistable behavior as well as power-law scaling of the relaxation time. The latter emerges not due to critical slowing down in the vicinity of a second order transition, but from the nonequilibrium dynamics near a so-called spinodal line

The obesity paradox: Analysis from the SMAtteo COvid-19 REgistry (SMACORE) cohort

Background and aims: Obesity has been suggested as a possible risk factor for a more severe course of COVID-19; however, conclusive evidence is lacking and few studies have investigated the role of BMI as a risk factor for admission to intensive care unit (ICU) and mortality. We retrospectively analyzed a COVID-19 cohort recruited during the first 40 days of the epidemic in Italy. We examined the association between obesity and 30-day mortality, admission to ICU, mortality and length of hospital stay in patients with COVID-19. Methods and results: Demographic, clinical and outcome data were retrospectively analyzed in 331 patients with COVID-19 admitted to hospital between 21 February and 31 March 2020. The predictive effect of obesity on mortality was assessed using a Cox proportional-hazard regression model, its effect on ICU admission and mortality in the ICU using logistic regressions, and its effect on length of hospital stay using a linear regression. Seventy-four of 331 patients had a BMI ≥30&nbsp;kg/m2. Among obese patients, 21 (28.4%) required admission in ICU and 25 died (33.8%). After controlling for sex, age, comorbidities and clinical data, obesity was not significantly associated with mortality, mortality in ICU and length of hospital stay. The effect of obesity on ICU admission remained significant after controlling for sex, age, interstitial lung disease, heart disease and serum C-reactive protein. Conclusions: Obese patients with COVID-19 were more likely to be admitted to ICU than non-obese patients. However, there were no significant differences in mortality between the two groups