Dark energy-matter equivalence by the evolution of cosmic equation of state

We consider a model-independent approach to constrain the equivalence redshift, $z_{eq}$, at which dark energy and the total matter (cold dark matter and baryonic) equate their magnitudes. To this aim, in the context of a homogeneous and isotropic universe, we first consider a generic model where the dark energy contribution is provided by an unknown function of barotropic fluids. Afterwards, we compute the deceleration and jerk parameters, evaluating at our epoch, namely $z=0$, and at $z=z_{eq}$. Thus, by Taylor expanding around current time the Hubble rate, luminosity and angular distances, we substitute the theoretical expressions obtained from the aforementioned generic dark energy model, defining a correspondence between quantities evaluated at $z=0$ and $z=z_{eq}$. In so doing, we directly fit these quantities by means of current data sets, involving the most recent Pantheon type Ia supernovae, baryonic acoustic oscillation and Hubble rate points. We consider two hierarchies in our fitting procedures and compare our findings in the spatially-flat universe first and including spatial curvature, later. We assess constraints on the overall equation of state of the universe and its first derivative. We compare our results with those predicted by the standard $\Lambda$CDM paradigm. Specifically, our findings are in agreement at the 2$\sigma$ confidence level, assuming a constant dark energy term. However, our analysis does not rule out the possibility of a slight evolution of dark energy, indicating a small deviation from the scenario of a pure cosmological constant. In particular, the possible departures appear consistent with a phenomenological $\omega$CDM model, rather than more complicated dark energy parameterizations.Comment: 28 pages, 8 figures, 3 table

On orthogonal projections for dimension reduction and applications in augmented target loss functions for learning problems

The use of orthogonal projections on high-dimensional input and target data in learning frameworks is studied. First, we investigate the relations between two standard objectives in dimension reduction, preservation of variance and of pairwise relative distances. Investigations of their asymptotic correlation as well as numerical experiments show that a projection does usually not satisfy both objectives at once. In a standard classification problem we determine projections on the input data that balance the objectives and compare subsequent results. Next, we extend our application of orthogonal projections to deep learning tasks and introduce a general framework of augmented target loss functions. These loss functions integrate additional information via transformations and projections of the target data. In two supervised learning problems, clinical image segmentation and music information classification, the application of our proposed augmented target loss functions increase the accuracy

D’Annunzio traduttore: i quattro Inni Omerici di Primo Vere

**

Il greco di Calabria: un esempio di bilinguismo nell’Europa antica

**

A Sulfonated All-Aromatic Polyamide for Heavy Metal Capture: A Model Study with Pb(II)

Polyelectrolytes are widely used in heavy metal removal, finding applications as coagulants and flocculants. We compare the heavy metal removal capability of a water-soluble sulfonated semirigid polyamide, poly(2,2'-disulfonyl-4,4'-benzidine isophthalamide) (PBDI), with that of a well-known random-coil polymer, poly(sodium 4-styrenesulfonate) (PSS). Using lead (Pb(II)) as a model contaminant, both polymers precipitate out from solution at ~500 mg/L Pb(II) in water. The ability to remove Pb(II) from water was quantified using adsorption isotherms and fitted with Langmuir and Freundlich adsorption models. The sorption of Pb(II) by PSS fit the Langmuir model with a high degree of correlation (0.976 R2), but the sorption of Pb(II) by PBDI could not be accurately predicted using the Langmuir or Freundlich model. The sorption of Pb(II) by PBDI and PSS was compared by normalizing sorption by the number of sulfonate groups of each polymer and the ion exchange capacity (IEC), found by titration. We find that PBDI removes a greater amount of Pb(II) per gram of sorbent compared to PSS, 410 mg/g vs 260 mg/g, respectively, which cannot be accounted for by differences in IEC or number of sulfonate groups. Our findings confirm that the positioning of the sulfonate groups and the rigidity of the polymer backbone play an important role in how Pb(II) coordinates to the polymer prior to precipitating out from solution