The forward approximation as a mean field approximation for the Anderson and Many Body Localization transitions

In this paper we analyze the predictions of the forward approximation in some models which exhibit an Anderson (single-) or many-body localized phase. This approximation, which consists in summing over the amplitudes of only the shortest paths in the locator expansion, is known to over-estimate the critical value of the disorder which determines the onset of the localized phase. Nevertheless, the results provided by the approximation become more and more accurate as the local coordination (dimensionality) of the graph, defined by the hopping matrix, is made larger. In this sense, the forward approximation can be regarded as a mean field theory for the Anderson transition in infinite dimensions. The sum can be efficiently computed using transfer matrix techniques, and the results are compared with the most precise exact diagonalization results available. For the Anderson problem, we find a critical value of the disorder which is $0.9\%$ off the most precise available numerical value already in 5 spatial dimensions, while for the many-body localized phase of the Heisenberg model with random fields the critical disorder $h_c=4.0\pm 0.3$ is strikingly close to the most recent results obtained by exact diagonalization. In both cases we obtain a critical exponent $\nu=1$. In the Anderson case, the latter does not show dependence on the dimensionality, as it is common within mean field approximations. We discuss the relevance of the correlations between the shortest paths for both the single- and many-body problems, and comment on the connections of our results with the problem of directed polymers in random medium

Regulation of maize Ac/Ds transposition by replication and DNA methylation

In maize the transposable elements Activator/Dissociation (Ac/Ds) transpose shortly after replication from one of the two resulting chromatids ("chromatid selectivity"). A model was suggested that explains this phenomenon as a consequence of different Ac transposase binding to holo-, hemi- and unmethylated transposon ends (Wang et al., 1996). It assumes that before replication the element is holomethylated and does not transpose because TPase can not bind to the transposon ends. Shortly after replication one of the two differentially hemimethylated daughter transposons should become transposition competent. However, DNA methylation-mediated replication dependence does not completely explain the behavior of Ac/Ds transposition. In several studies performed in monocot hosts, it was found that in a transient assay Ac/Ds element excision from extrachromosomal geminivirus vectors occurs only during vector replication, although the transfected DNAs were not Cmethylated. In this work the correlation between Ds transposition, DNA replication and DNA methylation in the dicot species Petunia hybrida was studied. Ds reporter vectors harboring TYLCV (Tomato Yellow Leaf Curl Virus) geminivirus replicon sequences and replicating in transfected petunia cells were constructed. It has been shown that the transposition of a Ds element from an extrachromosomal vector in petunia cells is regulated by DNA replication in a methylation-dependent and -independent mode. Holomethylation completely inhibits Ds excision from a non-replicating plasmid, whereas Ds transposition is restored by replication. Moreover, Ds elements that are hemimethylated on one DNA strand transpose in the absence of replication, whereas methylation on the complementary DNA strand results in at least 6.3-fold reduced excision frequencies. These data strongly support the transposition model of Wang et al. (1996). Beyond that, Ds transposition is strongly promoted by replication also in the absence of methylation. It has been shown that in petunia cells, unlike monocot hosts, replication is not a prerequisite for Ds transposition, nevertheless it enhances Ds transposition by at least a factor of 7.5. Moreover, replication promotes the formation of a predominant excision footprint. Implications on the mechanism and regulation of Ac/Ds transposition are discussed

Anderson transition on the Bethe lattice: an approach with real energies

We study the Anderson model on the Bethe lattice by working directly with propagators at real energies $E$. We introduce a novel criterion for the localization-delocalization transition based on the stability of the population of the propagators, and show that it is consistent with the one obtained through the study of the imaginary part of the self-energy. We present an accurate numerical estimate of the transition point, as well as a concise proof of the asymptotic formula for the critical disorder on lattices of large connectivity, as given in [P.W. Anderson 1958]. We discuss how the forward approximation used in analytic treatments of localization problems fits into this scenario and how one can interpolate between it and the correct asymptotic analysis.Comment: Close to published versio

Understanding Mathematics Anxiety: Investigating the experiences of UK primary and secondary school students

The project investigated individuals’ attitudes towards mathematics because of what could be referred to as a “mathematics crisis” in the UK. Evidence suggests that functional literacy skills amongst working-age adults are steadily increasing but the proportion of adults with functional maths skills equivalent to a GCSE grade C has dropped from 26% in 2003 to only 22% in 2011 (National Numeracy, 2014). This number is strikingly low compared with the 57% who achieved the equivalent in functional literacy skills (National Numeracy, 2014)

Prediction of polyspecificity from antibody sequence data by machine learning

Antibodies are generated with great diversity in nature resulting in a set of molecules, each optimized to bind a specific target. Taking advantage of their diversity and specificity, antibodies make up for a large part of recently developed biologic drugs. For therapeutic use antibodies need to fulfill several criteria to be safe and efficient. Polyspecific antibodies can bind structurally unrelated molecules in addition to their main target, which can lead to side effects and decreased efficacy in a therapeutic setting, for example via reduction of effective drug levels. Therefore, we created a neural-network-based model to predict polyspecificity of antibodies using the heavy chain variable region sequence as input. We devised a strategy for enriching antibodies from an immunization campaign either for antigen-specific or polyspecific binding properties, followed by generation of a large sequencing data set for training and cross-validation of the model. We identified important physico-chemical features influencing polyspecificity by investigating the behaviour of this model. This work is a machine-learning-based approach to polyspecificity prediction and, besides increasing our understanding of polyspecificity, it might contribute to therapeutic antibody development

Association of immune-related adverse events with the outcomes of immune checkpoint inhibitors in patients with dMMR/MSI-H metastatic colorectal cancer

Neoplàsies gastrointestinals; Immunoteràpia; Biomarcadors tumoralsNeoplasias gastrointestinales; Inmunoterapia; Biomarcadores tumoralesGastrointestinal neoplasms; Immunotherapy; Tumor biomarkersBackground Immune checkpoint inhibitors (ICIs) show a tremendous activity in microsatellite instability-high (MSI-H) metastatic colorectal cancer (mCRC), but a consistent fraction of patients does not respond. Prognostic/predictive markers are needed. Despite previous investigations in other tumor types, immune-related adverse events (irAEs) have not been well evaluated in patients with MSI-H cancers treated with ICIs. Methods We conducted an international cohort study at tertiary cancer centers collecting clinic-pathological features from 331 patients with MSI-H mCRC treated with ICIs. Of note, the irAEs were summarized using a ‘burden score’ constructed in a way that the same score value could be obtained by cumulating many low-grade irAEs or few high-grade irAEs; as a result, the lower the burden the better. Clearly, the irAE burden is not a baseline information, thus it was modeled as a time-dependent variable in univariable and multivariable Cox models. Results Among 331 patients, irAEs were reported in 144 (43.5%) patients. After a median follow-up time of 29.7 months, patients with higher burden of skin, endocrine and musculoskeletal irAEs (the latter two’s effect was confirmed at multivariable analysis) had longer overall survival (OS), as opposed to gastrointestinal, pneumonitis, neurological, liver, renal and other irAEs, which showed an harmful effect. Similar results were observed for progression-free survival (PFS). Based on the results retrieved from organ-specific irAEs, ‘aggregated’ burden scores were developed to distinguish ‘protective’ (endocrine and musculoskeletal) and ‘harmful’ (gastrointestinal, pneumonitis, neurological, hepatic) irAEs showing prognostic effects on OS and PFS. Conclusions Our results demonstrate that not all irAEs could exert a protective effect on oncologic outcome. An easy-to-use model for ICIs toxicity (burden score of protective and harmful irAEs) may be used as surrogate marker of response

Nomogram to predict the outcomes of patients with microsatellite instability-high metastatic colorectal cancer receiving immune checkpoint inhibitors

Neoplasias gastrointestinales; InmunoterapiaNeoplàsies gastrointestinals; ImmunoteràpiaGastrointestinal neoplasms; ImmunotherapyBackground The efficacy of immune checkpoint inhibitors (ICIs) in patients with microsatellite instability (MSI)-high metastatic colorectal cancer (mCRC) is unprecedented. A relevant proportion of subjects achieving durable disease control may be considered potentially ‘cured’, as opposed to patients experiencing primary ICI refractoriness or short-term clinical benefit. We developed and externally validated a nomogram to estimate the progression-free survival (PFS) and the time-independent event-free probability (EFP) in patients with MSI-high mCRC receiving ICIs. Methods The PFS and EFP were estimated using a cure model fitted on a developing set of 163 patients and validated on a set of 146 patients with MSI-high mCRC receiving anti-programmed death (ligand)1 (PD-(L)1) ± anticytotoxic T-lymphocyte antigen 4 (CTLA-4) agents. A total of 23 putative prognostic factors were chosen and then selected using a random survival forest (RSF). The model performance in estimating PFS probability was evaluated by assessing calibration (internally—developing set and externally—validating set) and quantifying the discriminative ability (Harrell C index). Results RFS selected five variables: ICI type (anti-PD-(L)1 monotherapy vs anti-CTLA-4 combo), ECOG PS (0 vs >0), neutrophil-to-lymphocyte ratio (≤3 vs >3), platelet count, and prior treatment lines. As both in the developing and validation series most PFS events occurred within 12 months, this was chosen as cut-point for PFS prediction. The combination of the selected variables allowed estimation of the 12-month PFS (focused on patients with low chance of being cured) and the EFP (focused on patients likely to be event-free at a certain point of their follow-up). ICI type was significantly associated with disease control, as patients receiving the anti-CTLA-4-combination experienced the best outcomes. The calibration of PFS predictions was good both in the developing and validating sets. The median value of the EFP (46%) allowed segregation of two prognostic groups in both the developing (PFS HR=3.73, 95% CI 2.25 to 6.18; p<0.0001) and validating (PFS HR=1.86, 95% CI 1.07 to 3.23; p=0.0269) sets. Conclusions A nomogram based on five easily assessable variables including ICI treatment was built to estimate the outcomes of patients with MSI-high mCRC, with the potential to assist clinicians in their clinical practice. The web-based system ‘MSI mCRC Cure’ was released.The authors have not declared a specific grant for this research from any funding agency in the public, commercial or not-for-profit sectors

A case study of management and disposal of TENORMs: radiological risk estimation by TSD Dose and RESRAD-ONSITE

Naturally Occurring Radioactive Materials (NORMs) and Technologically Enhanced NORMs (TENORMs) are among the principal sources of radiation exposure for humans and for the environment. Therefore, the assessment of the impact of NORMs and TENORMs waste on human health is a key issue for their management and for acceptance of disposal sites. The radiological doses to workers and public due to TENORMs disposal depend on the waste inventory, on the usage of the site during operational activities and post closure phase and on the presence of dwelling areas in the vicinity of the disposal site. In the present study it is presented a methodology to preliminary assess the feasibility of a disposal of TENORMs, mainly constituted by phosphate sludges, originated from phosphoric acid industry activities. The hypothetical case study here presented is inspired by a real case study. Different possible scenarios have been considered. The potential doses to workers and to the public on-site have been estimated by the use of the TSD Dose and the RESRAD on-site codes both during the production life cycle of the site and once it ended. Sensitivity analyses were conducted to evaluate the impact of some key parameters, such the coverage thickness and wind velocity, on potential risk for workers and public. </abstract