Amalgams of inverse semigroups and reversible two-counter machines

We show that the word problem for an amalgam $[S_1,S_2;U,\omega_1,\omega_2]$ of inverse semigroups may be undecidable even if we assume $S_1$ and $S_2$ (and therefore $U$) to have finite $\mathcal{R}$-classes and $\omega_1,\omega_2$ to be computable functions, interrupting a series of positive decidability results on the subject. This is achieved by encoding into an appropriate amalgam of inverse semigroups 2-counter machines with sufficient universality, and relating the nature of certain \sch graphs to sequences of computations in the machine

Xylem plasticity in Pinus pinaster and Quercus ilex growing at sites with different water availability in the Mediterranean region: relations between Intra-Annual Density Fluctuations and environmental conditions.

Fluctuations in climatic conditions during the growing season are recorded in Mediterranean tree-rings and often result in intra-annual density fluctuations (IADFs). Dendroecology and quantitative wood anatomy analyses were used to characterize the relations between the variability of IADF traits and climatic drivers in Pinus pinaster Aiton and Quercus ilex L. growing at sites with different water availability on the Elba island in Central Italy. Our results showed that both species present high xylem plasticity resulting in the formation of L-type IADFs (L-IADFs), consisting of earlywood-like cells in latewood. The occurrence of such IADFs was linked to rain events following periods of summer drought. The formation of L-IADFs in both species increased the hydraulic conductivity late in the growing season, due to their larger lumen area in comparison to "true latewood". The two species expressed greater similarity under arid conditions, as unfavorable climates constrained trait variation. Wood density, measured as the percentage of cell walls over total xylem area, IADF frequency, as well as conduit lumen area and vessel frequency, specifically in the hardwood species, proved to be efficient proxies to encode climate signals recorded in the xylem. The response of these anatomical traits to climatic variations was found to be species- and site-specific

Neutrino current in a gravitational plane wave collision background

The behaviour of a massless Dirac field on a general spacetime background representing two colliding gravitational plane waves is discussed in the Newman-Penrose formalism. The geometrical properties of the neutrino current are analysed and explicit results are given for the special Ferrari-Ibanez solution.Comment: 17 pages, 6 Postscript figures, accepted by International Journal of Modern Physics

The Speciality Index as invariant indicator in the BKL Mixmaster Dynamics

The speciality index, which has been mainly used in Numerical Relativity for studying gravitational waves phenomena as an indicator of the special or non-special Petrov type character of a spacetime, is applied here in the context of Mixmaster cosmology, using the Belinski-Khalatnikov-Lifshitz map. Possible applications for the associated chaotic dynamics are discussed

Nonlinear diffusion & thermo-electric coupling in a two-variable model of cardiac action potential

This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion nonlinearities. As customary in excitable media, the common Q10 and Moore factors are used to describe thermo-electric feedback in a 10-degrees range. Motivated by the porous nature of the cardiac tissue, in this study we also propose a nonlinear Fickian flux formulated by Taylor expanding the voltage dependent diffusion coefficient up to quadratic terms. A fine tuning of the diffusive parameters is performed a priori to match the conduction velocity of the equivalent cable model. The resulting combined effects are then studied by numerically simulating different stimulation protocols on a one-dimensional cable. Model features are compared in terms of action potential morphology, restitution curves, frequency spectra and spatio-temporal phase differences. Two-dimensional long-run simulations are finally performed to characterize spiral breakup during sustained fibrillation at different thermal states. Temperature and nonlinear diffusion effects are found to impact the repolarization phase of the action potential wave with non-monotone patterns and to increase the propensity of arrhythmogenesis

Molecular Structures in T=1 states of 10B

Multi-center (molecular) structures can play an important role in light nuclei. The highly deformed rotational band in 10Be with band head at 6.179 MeV has been observed recently and suggested to have an exotic alpha:2n:alpha configuration. A search for states with alpha:pn:alpha two-center molecular configurations in 10B that are analogous to the states with alpha:2n:alpha structure in 10Be has been performed. The T=1 isobaric analog states in 10B were studied in the excitation energy range of E=8.7-12.1 MeV using the reaction 1H(9Be,alpha)6Li*(T=1, 0+, 3.56 MeV). An R-matrix analysis was used to extract parameters for the states observed in the (p,alpha) excitation function. Five T=1 states in 10B have been identified. The known 2+ and 3- states at 8.9 MeV have been observed and their partial widths have been measured. The spin-parities and partial widths for three higher lying states were determined. Our data support theoretical predictions that the 2+ state at 8.9 MeV (isobaric analog of the 7.54 MeV state in 10Be) is a highly clustered state and can be identified as a member of the alpha:np:alpha rotational band. The next member of this band, the 4+ state, has not been found. A very broad 0+ state at 11 MeV that corresponds to pure alpha+6Li(0+,T=1) configuration is suggested and it might be related to similar structures found in 12C, 18O and 20Ne.Comment: 10 pages, 10 figures, accepted in Physical Review

On the Number of Synchronizing Colorings of Digraphs

We deal with $k$-out-regular directed multigraphs with loops (called simply \emph{digraphs}). The edges of such a digraph can be colored by elements of some fixed $k$-element set in such a way that outgoing edges of every vertex have different colors. Such a coloring corresponds naturally to an automaton. The road coloring theorem states that every primitive digraph has a synchronizing coloring. In the present paper we study how many synchronizing colorings can exist for a digraph with $n$ vertices. We performed an extensive experimental investigation of digraphs with small number of vertices. This was done by using our dedicated algorithm exhaustively enumerating all small digraphs. We also present a series of digraphs whose fraction of synchronizing colorings is equal to $1-1/k^d$, for every $d \ge 1$ and the number of vertices large enough. On the basis of our results we state several conjectures and open problems. In particular, we conjecture that $1-1/k$ is the smallest possible fraction of synchronizing colorings, except for a single exceptional example on 6 vertices for $k=2$.Comment: CIAA 2015. The final publication is available at http://link.springer.com/chapter/10.1007/978-3-319-22360-5_1

Children and youth with diabetes are not at increased risk for hospitalization due to COVID-19

The severe acute respiratory syndrome coronavirus 2 (SARS-Cov-2), responsible for the coronavirus disease COVID-19, was first identified in Wuhan, China in December 2019. Diabetes, as well as other cardiovascular comorbidities, has been recognized as a major risk factor for outcomes and mortality in adults with COVID-19, particularly in the elderly with type 2 diabetes. Based on these conclusions, COVID-19 data on adults have been generalized to youth with diabetes. Nevertheless, experience from pediatric diabetes practices in China (Wuhan), Italy, Spain (Catalonia), and the United States (San Francisco Bay Area) consistently report only a single severe case of COVID-19 in a 20-year-old female youth with type 1 diabetes (T1D) that was hospitalized for bilateral pneumonia and was subsequently discharged without complications. In Italy, information on COVID-19 in all children with diabetes is collected on a weekly basis and those with positive swab test or infection-related symptoms reported to a dedicated national registry. Of a total of 15 500 children tested, 11 subjects with T1D (age 8-17y) tested positive for COVID-19; 6/11 were asymptomatic and the rest presented with mild symptoms. In the rest of locations, youths with T1D diagnosed with COVID-19 were based on clinical suspicion and a confirmatory PCR test (Wuhan:0; Catalonia-HSJD:3; California-Stanford:2). All of them were asymptomatic or had a mild course. We suggest that COVID-19 data from adults should not be generalized to children, adolescents, and youth with diabetes as their outcomes and prognosis seem to be similar to their non-diabetic-peers and consistently milder than adults with diabetes

PrPC Controls via Protein Kinase A the Direction of Synaptic Plasticity in the Immature Hippocampus

The cellular form of prion protein PrPC is highly expressed in the brain, where it can be converted into its abnormally folded isoform PrPSc to cause neurodegenerative diseases. Its predominant synaptic localization suggests a crucial role in synaptic signaling. Interestingly, PrPC is developmentally regulated and its high expression in the immature brain could be instrumental in regulating neurogenesis and cell proliferation. Here, PrPC-deficient (Prnp0/0) mice were used to assess whether the prion protein is involved in synaptic plasticity processes in the neonatal hippocampus. To this aim, calcium transients associated with giant depolarizing potentials, a hallmark of developmental networks, were transiently paired with mossy fiber activation in such a way that the two events were coincident. While this procedure caused long-term potentiation (LTP) in wild-type (WT) animals, it caused long-term depression (LTD) in Prnp0/0 mice. Induction of LTP was postsynaptic and required the activation of cAMP-dependent protein kinase A (PKA) signaling. The induction of LTD was presynaptic and relied on G-protein-coupled GluK1 receptor and protein lipase C. In addition, at emerging CA3-CA1 synapses in WT mice, but not in Prnp0/0 mice, pairing Schaffer collateral stimulation with depolarization of CA1 principal cells induced LTP, known to be PKA dependent. Postsynaptic infusion of a constitutively active isoform of PKA catalytic subunit C\u3b1 into CA1 and CA3 principal cells in the hippocampus of Prnp0/0 mice caused a persistent synaptic facilitation that was occluded by subsequent pairing. These data suggest that PrPC plays a crucial role in regulating via PKA synaptic plasticity in the developing hippocampus. \ua9 2013 the authors