Quantitative Equality in Substructural Logic via Lipschitz Doctrines

Substructural logics naturally support a quantitative interpretation of formulas, as they are seen as consumable resources. Distances are the quantitative counterpart of equivalence relations: they measure how much two objects are similar, rather than just saying whether they are equivalent or not. Hence, they provide the natural choice for modelling equality in a substructural setting. In this paper, we develop this idea, using the categorical language of Lawvere's doctrines. We work in a minimal fragment of Linear Logic enriched by graded modalities, which are needed to write a resource sensitive substitution rule for equality, enabling its quantitative interpretation as a distance. We introduce both a deductive calculus and the notion of Lipschitz doctrine to give it a sound and complete categorical semantics. The study of 2-categorical properties of Lipschitz doctrines provides us with a universal construction, which generates examples based for instance on metric spaces and quantitative realisability. Finally, we show how to smoothly extend our results to richer substructural logics, up to full Linear Logic with quantifiers

The Influence of Galaxy Environment on the Stellar Initial Mass Function of Early-Type Galaxies

In this paper we investigate whether the stellar initial mass function of early-type galaxies depends on their host environment. To this purpose, we have selected a sample of early-type galaxies from the SPIDER catalogue, characterized their environment through the group catalogue of Wang et al. and used their optical SDSS spectra to constrain the IMF slope, through the analysis of IMF-sensitive spectral indices. To reach a high enough signal-to-noise ratio, we have stacked spectra in velocity dispersion ($\sigma_0$) bins, on top of separating the sample by galaxy hierarchy and host halo mass, as proxies for galaxy environment. In order to constrain the IMF, we have compared observed line strengths to predictions of MIUSCAT/EMILES synthetic stellar population models, with varying age, metallicity, and "bimodal" (low-mass tapered) IMF slope ($\rm \Gamma_b$). Consistent with previous studies, we find that $\rm \Gamma_b$ increases with $\sigma_0$, becoming bottom-heavy (i.e. an excess of low-mass stars with respect to the Milky-Way-like IMF) at high $\sigma_0$. We find that this result is robust against the set of isochrones used in the stellar population models, as well as the way the effect of elemental abundance ratios is taken into account. We thus conclude that it is possible to use currently state-of-the-art stellar population models and intermediate resolution spectra to consistently probe IMF variations. For the first time, we show that there is no dependence of $\Gamma_b$ on environment or galaxy hierarchy, as measured within the $3"$ SDSS fibre, thus leaving the IMF as an intrinsic galaxy property, possibly set already at high redshift

On the shape and evolution of a cosmic ray regulated galaxy-wide stellar initial mass function

In this paper, we present a new derivation of the shape and evolution of the integrated galaxy-wide initial mass function (IGIMF), incorporating explicitly the effects of cosmic rays (CRs) as regulators of the chemical and thermal state of the gas in the dense cores of molecular clouds. We predict the shape of the IGIMF as a function of star formation rate (SFR) and CR density, and show that it can be significantly different with respect to local estimates. In particular, we focus on the physical conditions corresponding to IGIMF shapes that are simultaneously shallower at high-mass end and steeper at the low-mass end than a Kroupa IMF. These solutions can explain both the levels of $\alpha$-enrichment and the excess of low-mass stars as a function of stellar mass, observed for local spheroidal galaxies. As a preliminary test of our scenario, we use idealized star formation histories to estimate the mean IMF shape for galaxies of different $z=0$ stellar mass. We show that the fraction of low-mass stars as a function of galaxy stellar mass predicted by these mean IMFs agrees with the values derived from high-resolution spectroscopic surveys.Comment: 8 pages, 5 figures, MNRAS accepte

Convective Excitation of Inertial Modes in Binary Neutron Star Mergers

We present the first very long-term simulations (extending up to ~140 ms after merger) of binary neutron star mergers with piecewise polytropic equations of state and in full general relativity. Our simulations reveal that at a time of 30-50 ms after merger, parts of the star become convectively unstable, which triggers the excitation of inertial modes. The excited inertial modes are sustained up to several tens of milliseconds and are potentially observable by the planned third-generation gravitational-wave detectors at frequencies of a few kilohertz. Since inertial modes depend on the rotation rate of the star and they are triggered by a convective instability in the postmerger remnant, their detection in gravitational waves will provide a unique opportunity to probe the rotational and thermal state of the merger remnant. In addition, our findings have implications for the long-term evolution and stability of binary neutron star remnantsComment: 6 pages, 4 figure

Comparative genomic hybridization on microarray (a-CGH) in constitutional and acquired mosaicism may detect as low as 8% abnormal cells

<p>Abstract</p> <p>Background</p> <p>The results of cytogenetic investigations on unbalanced chromosome anomalies, both constitutional and acquired, were largely improved by comparative genomic hybridization on microarray (a-CGH), but in mosaicism the ability of a-CGH to reliably detect imbalances is not yet well established. This problem of sensitivity is even more relevant in acquired mosaicism in neoplastic diseases, where cells carrying acquired imbalances coexist with normal cells, in particular when the proportion of abnormal cells may be low.</p> <p>We constructed a synthetic mosaicism by mixing the DNA of three patients carrying altogether seven chromosome imbalances with normal sex-matched DNA. Dilutions were prepared mimicking 5%, 6%, 7%, 8%, 10% and 15% levels of mosaicism. Oligomer-based a-CGH (244 K whole-genome system) was applied on the patients' DNA and customized slides designed around the regions of imbalance were used for the synthetic mosaics.</p> <p>Results and conclusions</p> <p>The a-CGH on the synthetic mosaics proved to be able to detect as low as 8% abnormal cells in the tissue examined. Although in our experiment some regions of imbalances escaped to be revealed at this level, and were detected only at 10-15% level, it should be remarked that these ones were the smallest analyzed, and that the imbalances recurrent as clonal anomalies in cancer and leukaemia are similar in size to those revealed at 8% level.</p

Different Real Time PCR Approaches for the Fine Quantification of SNP's Alleles in DNA Pools: Assays Development, Characterization and Pre-validation

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Can a robot catch you lying? A machine learning system to detect lies during interactions.

Deception is a complex social skill present in human interactions. Many social professions such as teachers, therapists and law enforcement officers leverage on deception detection techniques to support their working activities. Robots with the ability to autonomously detect deception could provide an important aid to human-human and human-robot interactions. The objective of this work is to demonstrate that it is possible to develop a lie detection system that could be implemented on robots. To this goal, we focus on human human and human robot interaction to understand if there is a difference in the behavior of the participants when lying to a robot or to a human. Participants were shown short movies of robberies and then interrogated by a human and by a humanoid robot "detectives". According to the instructions, subjects provided veridical responses to half of the question and false replies to the other half. Behavioral variables such as eye movements, time to respond and eloquence were measured during the task, while personality traits were assessed before experiment initiation. Participant's behavior showed strong similarities during the interaction with the human and the humanoid. Moreover, the behavioral features were used to train and test a lie detection algorithm. The results show that the selected behavioral variables are valid markers of deception both in human-human and in human-robot interactions and could be exploited to effectively enable robots to detect lies.

Review of the clinical evidence for interferon β 1a (Rebif®) in the treatment of multiple sclerosis

Interferon (INF) β 1a 22 or 44 μg (Rebif®) administered s.c. 3 times a week (t.i.w) is a well established immunomodulating treatment for relapsing remitting multiple sclerosis (RRMS). This review focuses on its mechanisms of action, evidence of efficacy, safety, and tolerability. Several pharmacodynamic properties explain the immunomodulatory actions of INF β 1a 22 or 44 μg s.c. t.i.w. Pivotal trials and post-marketing studies proved that the drug is effective in reducing disease activity and likely in slowing disease progression. Head-to-head comparative studies with other marketed INFs β in RRMS suggested a better therapeutic response associated with higher doses and frequency of administration of Rebif®. Additional evidence indicated a beneficial effect of INF β 1a in patients with clinically isolated syndromes (CIS) suggestive of MS, as treatment reduced time to conversion to clinically definite (CD) disease. Further, although the drug did not prove to slow time to progression there were benefits on relapse- and MRI-related secondary outcome measures in secondary progressive (SP) MS. Pivotal trials, their cross-over extensions, and post-marketing studies consistently showed that INF β 1a 22 or 44 μg s.c. t.i.w. is safe and well tolerated, as adverse drug reactions are usually mild and manageable

Novel recurrent chromosome anomalies in Shwachman Diamond syndrome

Clonal chromosome anomalies are frequently acquired in the bone marrow (BM) of patients with Shwachman-Diamond syndrome (SDS), and two are the most frequent: an isochromosome of the long arm of chromosome 7, i(7)(q10), and an interstitial deletion of the long arm of chromosome 20, del(20)(q). Patients with SDS have a risk of developing myelodysplasia (MDS) and/or acute myeloid leukaemia (AML), and the presence of chromosome changes was studied in relation with this risk. Starting in 1999 we have monitored the cytogenetic picture of a cohort of 92 Italian patients with SDS by all suitable cytogenetic and molecular methods. Clonal anomalies in BM were present in 41/92 patients. The i(7)(q10) was observed in 16 patients, and the del(20)(q) in 15, both these changes in four, but in independent clones. So, the most frequent clonal anomalies were found in 35 patients. Other, different, clonal anomalies were found in the BM of 13 patients, in eight cases in the absence of i(7)(q10) or del(20)(q), in five cases in association with one of these changes. In these less common clonal anomalies, the distribution of the chromosomes involved was markedly disparate, and some of them were novel and recurrent: - structural rearrangements of chromosome 7, mainly unbalanced (deletions, inversions or translocations), were present in five of our 13 patients, three of whom developed MDS/AML. - a further complex rearrangement of the more common del(20)(q), leading to duplicated and deleted portions, was identical in two patients, with almost identical a-CGH profiles, neither developed MDS/AML. - an unbalanced translocation t(3;6), with partial trisomy of the long arm of chromosome 3 and partial monosomy of the long arm of chromosome 6, was not identical but very similar in two patients, one of whom developed MDS/AML