Alternative structures and bi-Hamiltonian systems on a Hilbert space

We discuss transformations generated by dynamical quantum systems which are bi-unitary, i.e. unitary with respect to a pair of Hermitian structures on an infinite-dimensional complex Hilbert space. We introduce the notion of Hermitian structures in generic relative position. We provide few necessary and sufficient conditions for two Hermitian structures to be in generic relative position to better illustrate the relevance of this notion. The group of bi-unitary transformations is considered in both the generic and non-generic case. Finally, we generalize the analysis to real Hilbert spaces and extend to infinite dimensions results already available in the framework of finite-dimensional linear bi-Hamiltonian systems.Comment: 11 page

Homodyne extimation of quantum states purity by exploiting covariant uncertainty relation

We experimentally verify uncertainty relations for mixed states in the tomographic representation by measuring the radiation field tomograms, i.e. homodyne distributions. Thermal states of single-mode radiation field are discussed in details as paradigm of mixed quantum state. By considering the connection between generalised uncertainty relations and optical tomograms is seen that the purity of the states can be retrieved by statistical analysis of the homodyne data. The purity parameter assumes a relevant role in quantum information where the effective fidelities of protocols depend critically on the purity of the information carrier states. In this contest the homodyne detector becomes an easy to handle purity-meter for the state on-line with a running quantum information protocol.Comment: accepted for publication into Physica Script

Quantum response of dephasing open systems

We develop a theory of adiabatic response for open systems governed by Lindblad evolutions. The theory determines the dependence of the response coefficients on the dephasing rates and allows for residual dissipation even when the ground state is protected by a spectral gap. We give quantum response a geometric interpretation in terms of Hilbert space projections: For a two level system and, more generally, for systems with suitable functional form of the dephasing, the dissipative and non-dissipative parts of the response are linked to a metric and to a symplectic form. The metric is the Fubini-Study metric and the symplectic form is the adiabatic curvature. When the metric and symplectic structures are compatible the non-dissipative part of the inverse matrix of response coefficients turns out to be immune to dephasing. We give three examples of physical systems whose quantum states induce compatible metric and symplectic structures on control space: The qubit, coherent states and a model of the integer quantum Hall effect.Comment: Article rewritten, two appendices added. 16 pages, 2 figure

Ceruloplasmin/Transferrin Ratio Changes in Alzheimer's Disease

The link between iron and Alzheimer's disease (AD) has been mainly investigated with a focus on the local accumulation of this metal in specific areas of the brain that are critical for AD. In the present study, we have instead looked at systemic variations of markers of iron metabolism. We measured serum levels of iron, ceruloplasmin, and transferrin and calculated the transferrin saturation and the ceruloplasmin to transferrin ratio (Cp/Tf). Cp/Tf and transferrin saturation increased in AD patients. Cp/Tf ratios also correlated positively with peroxide levels and negatively with serum iron concentrations. Elevated values of ceruloplasmin, peroxides, and Cp/Tf inversely correlated with MMSE scores. Isolated medial temporal lobe atrophy positively correlated with Cp/Tf and negatively with serum iron. All these findings indicate that the local iron accumulation found in brain areas critical for AD should be viewed in the frame of iron systemic alterations

Pancreatic cancer molecular classifications: From bulk genomics to single cell analysis

Pancreatic cancer represents one of the most lethal disease worldwide but still orphan of a molecularly driven therapeutic approach, although many genomic and transcriptomic classifications have been proposed over the years. Clinical heterogeneity is a hallmark of this disease, as different patients show different responses to the same therapeutic regimens. However, genomic analyses revealed quite a homogeneous disease picture, with very common mutations in four genes only (KRAS, TP53, CDKN2A, and SMAD4) and a long tail of other mutated genes, with doubtful pathogenic meaning. Even bulk transcriptomic classifications could not resolve this great heterogeneity, as many informations related to small cell populations within cancer tissue could be lost. At the same time, single cell analysis has emerged as a powerful tool to dissect intratumoral heterogeneity like never before, with possibility of generating a new disease taxonomy at unprecedented molecular resolution. In this review, we summarize the most relevant genomic, bulk and single-cell transcriptomic classifications of pancreatic cancer, and try to understand how novel technologies, like single cell analysis, could lead to novel therapeutic strategies for this highly lethal disease

Optical tomography of Fock state superpositions

We consider optical tomography of photon Fock state superpositions in connection with recent experimental achievements. The emphasis is put on the fact that it suffices to represent the measured tomogram as a main result of the experiment. We suggest a test for checking the correctness of experimental data. Explicit expressions for optical tomograms of Fock state superpositions are given in terms of Hermite polynomials. Particular cases of vacuum and low photon-number state superposition are considered as well as influence of thermal noise on state purity is studied.Comment: 5 pages, 2 figure

Histochemical analysis of glycoconjugates in the domestic cat testis

The localization and characterization of oligosaccharide sequences in the cat testis was investigated using 12 lectins in combination with the ßelimination reaction, N-Glycosidase F and sialidase digestion. Leydig cells expressed O-linked glycans with terminal aGalNAc (HPA reactivity) and N-glycans with terminal/internal aMan (Con A affinity). The basement membrane showed terminal Neu5Aca2,6Gal/GalNAc, Galß1,3GalNAc, a/ßGalNAc, and GlcNAc (SNA, PNA, HPA, SBA, GSA II reactivity) in O-linked oligosaccharides, terminal Galß1,4GlcNAc (RCA120 staining) and aMan in N-linked oligosaccharides; in addition, terminal Neu5Aca2,3Galß1,4GlcNac, Forssman pentasaccharide, aGal, aL-Fuc and internal GlcNAc (MAL II, DBA, GSA I-B4, UEA I, KOH-sialidase-WGA affinity) formed both O- and N-linked oligosaccharides. The Sertoli cells cytoplasm contained terminal Neu5Ac- Galß1,4GlcNAc, Neu5Ac-ßGalNAc as well as internal GlcNAc in O-linked glycans, aMan in N-linked glycoproteins and terminal Neu5Aca2,6Gal/ GalNAc in both O- and N-linked oligosaccharides. Spermatogonia exhibited cytoplasmic N-linked glycoproteins with aMan residues. The spermatocytes cytoplasm expressed terminal Neu5Aca2,3Galß1,4 GlcNAc and Galß1,3GalNAc in O-linked oligosaccharides, terminal Galß1,4GlcNAc and a/ßGalNAc in N-linked glycoconjugates. The Golgi region showed terminal Neu5aca2,3Galß1,4GlcNac, Galß1,4GlcNAc, Forssman pentasaccharide, and aGalNAc in O-linked oligosaccharides, aMan and terminal ßGal in N-linked oligosaccharides. The acrosomes of Golgi-phase spermatids expressed terminal Galß1,3GalNAc, Galß1,4GlcNAc, Forssmann pentasaccharide, a/ßGalNAc, aGal and internal GlcNAc in O-linked oligosaccharides, terminal a/ßGalNAc, aGal and terminal/internal aMan in N-linked glycoproteins. The acrosomes of cap-phase spermatids lacked internal Forssman pentasaccharide and aGal, while having increased a/ßGalNAc. The acrosomes of elongated spermatids did not show terminal Galß1,3GalNAc, displayed terminal Galß1,4GlcNAc and a/ßGalNAc in N-glycans and Neu5Ac-Galß1,3GalNAc in O-linked oligosaccharides

Cross-sectional survey on BNT162b2 mRNA COVID-19 vaccine serious adverse events in children 5 to 11 years of age. A monocentric experience

Objective: Our aim was to evaluate the safety of COVID-19 vaccine in children resident in the Latina Local Health Authority. Methods: We conducted a telephone survey among children aged 5–11 years receiving BNT162b2 mRNA COVID-19 vaccine between December 15 and 21. The main outcomes included the presence of allergic reactions or anaphylaxis, adverse events after 24–48 h, 7 and 20 days of taking the first and second doses of medications, and documented SARS-CoV-2 infection after vaccination. The information obtained was automatically linked to a spreadsheet and analyzed. Results: 569 children were enrolled. The mean age was 114 ± 4.24 months; there were 251 males in the study. The vaccine showed a favorable safety profile; no anaphylaxis or serious adverse events were reported. The most common symptoms both after the first and second dose were injection site reactions, asthenia, and headache. Injection site reactions were more frequent after the first dose (p = 0.01), while systemic symptoms were more frequent after the second dose (p = 0.022). These symptoms were more frequent in patients with comorbidities (p = 0.0159). Conclusion: Our findings confirm the safety of COVID-19 vaccine in children younger 11 years and could be useful to promote its diffusion in pediatric ages in order to achieve “herd immunity” and prevent the virus’s circulation