A discrete Laplace-Beltrami operator for simplicial surfaces

We define a discrete Laplace-Beltrami operator for simplicial surfaces. It depends only on the intrinsic geometry of the surface and its edge weights are positive. Our Laplace operator is similar to the well known finite-elements Laplacian (the so called ``cotan formula'') except that it is based on the intrinsic Delaunay triangulation of the simplicial surface. This leads to new definitions of discrete harmonic functions, discrete mean curvature, and discrete minimal surfaces. The definition of the discrete Laplace-Beltrami operator depends on the existence and uniqueness of Delaunay tessellations in piecewise flat surfaces. While the existence is known, we prove the uniqueness. Using Rippa's Theorem we show that, as claimed, Musin's harmonic index provides an optimality criterion for Delaunay triangulations, and this can be used to prove that the edge flipping algorithm terminates also in the setting of piecewise flat surfaces.Comment: 18 pages, 6 vector graphics figures. v2: Section 2 on Delaunay triangulations of piecewise flat surfaces revised and expanded. References added. Some minor changes, typos corrected. v3: fixed inaccuracies in discussion of flip algorithm, corrected attributions, added references, some minor revision to improve expositio

An alternative procedure for selecting a good value for the parameter c in RBF-interpolation

The impact of the scaling parameter c on the accuracy of interpolation schemes using radial basis functions (RBFs) has been pointed out by several authors. Rippa (Adv Comput Math 11:193-210, 1999) proposes an algorithm based on the idea of cross validation for selecting a good such parameter value. In this paper we present an alternative procedure, that can be interpreted as a refinement of Rippa's algorithm for a cost function based on the euclidean norm. We point out how this method is related to the procedure of maximum likelihood estimation, which is used for identifying covariance parameters of stochastic processes in spatial statistics. Using the same test functions as Rippa we show that our algorithm compares favorably with cross validation in many cases and discuss its limitations. Finally we present some computational aspects of our algorithm

The effect of carnitine on Arabidopsis development and recovery in salt stress conditions

Carnitine exists in all living organisms where it plays diverse roles. In animals and yeast, it is implicated in lipid metabolism and is also associated with oxidative stress tolerance. In bacteria, it is a major player in osmotic stress tolerance. We investigate the carnitine function in plants and our present work shows that carnitine enhances the development and recovery of Arabidopsis thaliana seedlings subjected to salt stress. Biological data show that exogenous carnitine supplies improve the germination and survival rates of seedlings grown on salt-enriched medium, in a manner comparable to proline. Both compounds are shown to improve seedling survival under oxidative constraint meaning that they may act on salt stress through antioxidant properties. A transcriptome analysis of seedlings treated with exogenous carnitine reveals that it modulates the expression of genes involved in water stress and abscisic acid responses. Analyses of the abscisic acid mutants, aba1-1 and abi1-1, indicate that carnitine and proline may act through a modulation of the ABA pathway

Fungal volatile organic compounds: emphasis on their plant growth-promoting

Fungal volatile organic compounds (VOCs) commonly formed bioactive interface between plants and countless of microorganisms on the above- and below-ground plant-fungus interactions. Fungal-plant interactions symbolize intriguingly biochemical complex and challenging scenarios that are discovered by metabolomic approaches. Remarkably secondary metabolites (SMs) played a significant role in the virulence and existence with plant-fungal pathogen interaction; only 25% of the fungal gene clusters have been functionally identified, even though these numbers are too low as compared with plant secondary metabolites. The current insights on fungal VOCs are conducted under lab environments and to apply small numbers of microbes; its molecules have significant effects on growth, development, and defense system of plants. Many fungal VOCs supported dynamic processes, leading to countless interactions between plants, antagonists, and mutualistic symbionts. The fundamental role of fungal VOCs at field level is required for better understanding, so more studies will offer further constructive scientific evidences that can show the cost-effectiveness of ecofriendly and ecologically produced fungal VOCs for crop welfare

Flavin-Induced Oligomerization in Escherichia coli Adaptive Response Protein AidB

The process known as “adaptive response” allows Escherichia coli to respond to small doses of DNA-methylating agents by upregulating the expression of four proteins. While the role of three of these proteins in mitigating DNA damage is well understood, the function of AidB is less clear. Although AidB is a flavoprotein, no catalytic role has been established for the bound cofactor. Here we investigate the possibility that flavin plays a structural role in the assembly of the AidB tetramer. We report the generation and biophysical characterization of deflavinated AidB and of an AidB mutant that has greatly reduced affinity for flavin adenine dinucleotide (FAD). Using fluorescence quenching and analytical ultracentrifugation, we find that apo AidB has a high affinity for FAD, as indicated by an apparent dissociation constant of 402.1 ± 35.1 nM, and that binding of substoichiometric amounts of FAD triggers a transition in the AidB oligomeric state. In particular, deflavinated AidB is dimeric, whereas the addition of FAD yields a tetramer. We further investigate the dimerization and tetramerization interfaces of AidB by determining a 2.8 Å resolution crystal structure in space group P32 that contains three intact tetramers in the asymmetric unit. Taken together, our findings provide strong evidence that FAD plays a structural role in the formation of tetrameric AidB.National Institutes of Health (U.S.) (grant R01-GM0272663)National Institutes of Health (U.S.) (grant P30-ES002109)National Science Foundation (U.S.) (grant MCB-0543833

Novel hybrid organic/inorganic 2D quasiperiodic PC: from diffraction pattern to vertical light extraction

Recently, important efforts have been dedicated to the realization of a fascinating class of new photonic materials or metamaterials, known as photonic quasicrystals (PQCs), in which the lack of the translational symmetry is compensated by rotational symmetries not achievable by the conventional periodic crystals. As ever, more advanced functionality is demanded and one strategy is the introduction of non-linear and/or active functionality in photonic materials. In this view, core/shell nanorods (NRs) are a promising active material for light-emitting applications. In this article a two-dimensional (2D) hybrid a 2D octagonal PQC which consists of air rods in an organic/inorganic nanocomposite is proposed and experimentally demonstrated. The nanocomposite was prepared by incorporating CdSe/CdS core/shell NRs into a polymer matrix. The PQC was realized by electron beam lithography (EBL) technique. Scanning electron microscopy, far field diffraction and spectra measurements are used to characterize the experimental structure. The vertical extraction of the light, by the coupling of the modes guided by the PQC slab to the free radiation via Bragg scattering, consists of a narrow red emissions band at 690 nm with a full width at half-maximum (FWHM) of 21.5 nm. The original characteristics of hybrid materials based on polymers and colloidal NRs, able to combine the unique optical properties of the inorganic moiety with the processability of the host matrix, are extremely appealing in view of their technological impact on the development of new high performing optical devices such as organic light-emitting diodes, ultra-low threshold lasers, and non-linear devices

Sex differences in schizophrenia spectrum disorders: insights from the DiAPAson study using a data-driven approach

Purpose Schizophrenia Spectrum Disorders (SSD) display notable sex differences: males have an earlier onset and more severe negative symptoms, while females exhibit affective symptoms, better verbal abilities, and a more favourable prognosis. Despite extensive research, areas such as time perception and positivity remain underexplored, and machine learning has not yet been adequately utilised. This study aims to address these gaps by examining sex differences in a sample of Italian patients with SSD using a data-driven approach. Methods As part of the DiAPAson project, 619 Italian patients with SSD (198 females; 421 males) were assessed using standardised clinical tools. Data on socio-demographics, clinical characteristics, symptom severity, functioning, positivity, quality of life (QoL), and time perspective were collected. Descriptive and regression analyses were conducted. Principal Component Analysis (PCA) and the Gaussian Mixture Model (GMM) was used to define data-driven clusters. A leave-one-group-out validation was performed. Results Males were more likely to be single (p < 0.001) and less educated (p = 0.006), while females smoked more tobacco (p = 0.011). Males were more frequently prescribed antipsychotics (p = 0.022) and exhibited more severe psychiatric (p = 0.004) and negative symptoms (p = 0.013). They also had a less negative perception of past events (p = 0.047) and a better view of their psychological condition (p = 0.004). Females showed better interpersonal functioning (p = 0.008). PCA and GMM revealed two main clusters with significant sex differences (p = 0.027). Conclusion This study identifies sex differences in SSD, suggesting tailored treatments such as enhancing interpersonal skills for females and maintaining positive self-assessment for males. Using machine learning, we highlight distinct SSD phenotypes, emphasising the need for sex-specific interventions to improve outcomes and QoL. Our findings stress the importance of a multifaceted, interdisciplinary approach to address sex-based disparities in SSD. Trial registration ISRCTN registry ID ISRCTN21141466