Cluster tilting modules for mesh algebras

We study cluster tilting modules in mesh algebras of Dynkin type, providing a new proof for their existence. In all but one case, we show that these are precisely the maximal rigid modules, and that they are equivariant for a certain automorphism. We further study their mutation, providing an example of mutation in an abelian category which is not stably 2-Calabi-Yau, and explicitly describe the combinatorics.Comment: comments appreciated; the third version includes a discussion on the combinatorics of the mutation

Higher-order interactions in fitness landscapes are sparse

Biological fitness arises from interactions between molecules, genes, and organisms. To discover the causative mechanisms of this complexity, we must differentiate the significant interactions from a large number of possibilities. Epistasis is the standard way to identify interactions in fitness landscapes. However, this intuitive approach breaks down in higher dimensions for example because the sign of epistasis takes on an arbitrary meaning, and the false discovery rate becomes high. These limitations make it difficult to evaluate the role of epistasis in higher dimensions. Here we develop epistatic filtrations, a dimensionally-normalized approach to define fitness landscape topography for higher dimensional spaces. We apply the method to higher-dimensional datasets from genetics and the gut microbiome. This reveals a sparse higher-order structure that often arises from lower-order. Despite sparsity, these higher-order effects carry significant effects on biological fitness and are consequential for ecology and evolution.Comment: 71 pages, various figure

Repetitive higher cluster categories of type A_n

We show that the repetitive higher cluster category of type A_n, defined as the orbit category D^b(mod kA_n)/(tau^{-1}[m])^p, is equivalent to a category defined on a subset of diagonals in a regular p(nm+1)-gon. This generalizes the construction of Caldero-Chapoton-Schiffler, which we recover when p=m=1, and the work of Baur-Marsh, treating the case p=1, m>1. Our approach also leads to a geometric model of the bounded derived category D^b(mod kA_n)

Prospective Evaluation of MGMT-Promoter Methylation Status and Correlations with Outcomes to Temozolomide-Based Chemotherapy in Well-Differentiated Neuroendocrine Tumors

Temozolomide (TEM) as a single agent or in combination with capecitabine (CAPTEM) is active in well-differentiated advanced neuroendocrine tumors (NETs) of gastro-entero-pancreatic and thoracic origin. The predictive role of MGMT-promoter methylation in this setting is controversial. We sought to prospectively evaluate the MGMT-promoter methylation status ability to predict outcomes to TEM-based chemotherapy in patients with NET. A single-center, prospective, observational study has been conducted at the ENETS Center-of-Excellence Outpatient Clinic of the IRCCS Policlinico Sant’Orsola-Malpighi in Bologna, Italy. Patients with advanced, gastro-entero-pancreatic or lung well-differentiated NETs candidate to TEM-based chemotherapy and with available tumor samples for MGMT-promoter methylation assessment were included. The MGMT-promoter methylation status was analyzed by using pyrosequencing. The primary endpoint was progression-free survival (PFS) by the MGMT-promoter methylation status. Secondary endpoints included overall survival (OS), objective response rate (ORR), disease control rate (DCR), and safety. Survival outcomes were compared by restricted mean survival time (RMST) difference. Of 26 screened patients, 22 were finally enrolled in the study. The most frequent NET primary sites were the pancreas (64%) and the lung (23%). MGMT promoter was methylated in five tumors (23%). At a median follow-up time of 47.2 months (95%CI 29.3–89.7), the median PFS was 32.8 months (95%CI 17.2–NA), while the median OS was not reached. Patients in the methylated MGMT group, when compared to those in the unmethylated MGMT group, had longer PFS (median not reached [95%CI NA–NA] vs. 30.2 months [95%CI 15.2–NA], respectively; RMST p = 0.005) and OS (median not reached [95%CI NA–NA] vs. not reached [40.1–NA], respectively; RMST p = 0.019). After adjusting for confounding factors, the MGMT-promoter methylation status was independently associated to the PFS. Numerically higher ORR (60% vs. 24%; p = 0.274) and DCR (100% vs. 88%; p = 1.00) were observed in the methylated vs. unmethylated MGMT group. TEM-based chemotherapy was well-tolerated (adverse events grade ≥3 < 10%). In this prospective study, MGMT-promoter methylation predicted better outcomes to TEM-based chemotherapy in patients with NET

Energy efficiency engagement training in SMEs: A case study in the automotive sector

Energy efficiency requirements in Europe are set by the Energy Efficiency Directive, considering energy audits as a systematic procedure to determine the savings in energy costs. These kinds of tools provide useful information for companies to identify opportunities for the improvement of their energy performance. However, the regulation is only applied for non-SMEs in Europe, which make up only 0.2% of the total number of European companies. Compared in terms of the value added or the number of employees, these companies are still at a lower percentage than small and medium enterprises. The wide versatility of small companies, however, makes it difficult to de-termine a regulation that promotes the objective of the Directive in a uniform way. For this reason, one aspect that is being worked on with small companies is raising awareness and training in energy aspects, encouraging them to carry out activities to improve their energy performance based on their own initiative. In this regard, within the framework of an H2020 research project based on the automotive sector, the E2DRIVER project, a collaborative–cooperative training methodology has been designed to motivate and empower the key actors within a company. This paper describes the methodology and its implementation in different companies in European countries, providing some representative results

Master regulators of biological systems in higher dimensions

A longstanding goal of biology is to identify the key genes and species that critically impact evolution, ecology, and health. Network analysis has revealed keystone species that regulate ecosystems and master regulators that regulate cellular genetic networks. Yet these studies have focused on pairwise biological interactions, which can be affected by the context of genetic background and other species present, generating higher-order interactions. The important regulators of higher-order interactions are unstudied. To address this, we applied a high-dimensional geometry approach that quantifies epistasis in a fitness landscape to ask how individual genes and species influence the interactions in the rest of the biological network. We then generated and also reanalyzed 5-dimensional datasets (two genetic, two microbiome). We identified key genes (e.g., the rbs locus and pykF) and species (e.g., Lactobacilli) that control the interactions of many other genes and species. These higher-order master regulators can induce or suppress evolutionary and ecological diversification by controlling the topography of the fitness landscape. Thus, we provide a method and mathematical justification for exploration of biological networks in higher dimensions.ISSN:0027-8424ISSN:1091-649

The geometry of partial fitness orders and an efficient method for detecting genetic interactions

We present an efficient computational approach for detecting genetic interactions from fitness comparison data together with a geometric interpretation using polyhedral cones associated to partial orderings. Genetic interactions are defined by linear forms with integer coefficients in the fitness variables assigned to genotypes. These forms generalize several popular approaches to study interactions, including Fourier–Walsh coefficients, interaction coordinates, and circuits. We assume that fitness measurements come with high uncertainty or are even unavailable, as is the case for many empirical studies, and derive interactions only from comparisons of genotypes with respect to their fitness, i.e. from partial fitness orders. We present a characterization of the class of partial fitness orders that imply interactions, using a graph-theoretic approach. Our characterization then yields an efficient algorithm for testing the condition when certain genetic interactions, such as sign epistasis, are implied. This provides an exponential improvement of the best previously known method. We also present a geometric interpretation of our characterization, which provides the basis for statistical analysis of partial fitness orders and genetic interactions.ISSN:1432-1416ISSN:0303-681