An Example of Symmetry Exploitation for Energy-related Eigencomputations

One of the most used approaches in simulating materials is the tight-binding approximation. When using this method in a material simulation, it is necessary to compute the eigenvalues and eigenvectors of the Hamiltonian describing the system. In general, the system possesses few explicit symmetries. Due to them, the problem has many degenerate eigenvalues. The ambiguity in choosing a orthonormal basis of the invariant subspaces, associated with degenerate eigenvalues, will result in eigenvectors which are not invariant under the action of the symmetry operators in matrix form. A meaningful computation of the eigenvectors needs to take those symmetries into account. A natural choice is a set of eigenvectors, which simultaneously diagonalizes the Hamiltonian and the symmetry matrices. This is possible because all the matrices commute with each other. The simultaneous eigenvectors and the corresponding eigenvalues will be in a parametrized form in terms of the lattice momentum components. This functional dependence of the eigenvalues is the dispersion relation and describes the band structure of a material. Therefore it is important to find this functional dependence in any numerical computation related to material properties.Comment: To appear in the proceedings of the 7th International Conference on Computational Methods in Science and Engineering (ICCMSE '09

Towards an Efficient Use of the BLAS Library for Multilinear Tensor Contractions

Mathematical operators whose transformation rules constitute the building blocks of a multi-linear algebra are widely used in physics and engineering applications where they are very often represented as tensors. In the last century, thanks to the advances in tensor calculus, it was possible to uncover new research fields and make remarkable progress in the existing ones, from electromagnetism to the dynamics of fluids and from the mechanics of rigid bodies to quantum mechanics of many atoms. By now, the formal mathematical and geometrical properties of tensors are well defined and understood; conversely, in the context of scientific and high-performance computing, many tensor- related problems are still open. In this paper, we address the problem of efficiently computing contractions among two tensors of arbitrary dimension by using kernels from the highly optimized BLAS library. In particular, we establish precise conditions to determine if and when GEMM, the kernel for matrix products, can be used. Such conditions take into consideration both the nature of the operation and the storage scheme of the tensors, and induce a classification of the contractions into three groups. For each group, we provide a recipe to guide the users towards the most effective use of BLAS.Comment: 27 Pages, 7 figures and additional tikz generated diagrams. Submitted to Applied Mathematics and Computatio

Dissecting the FEAST algorithm for generalized eigenproblems

We analyze the FEAST method for computing selected eigenvalues and eigenvectors of large sparse matrix pencils. After establishing the close connection between FEAST and the well-known Rayleigh-Ritz method, we identify several critical issues that influence convergence and accuracy of the solver: the choice of the starting vector space, the stopping criterion, how the inner linear systems impact the quality of the solution, and the use of FEAST for computing eigenpairs from multiple intervals. We complement the study with numerical examples, and hint at possible improvements to overcome the existing problems.Comment: 11 Pages, 5 Figures. Submitted to Journal of Computational and Applied Mathematic

Matrix Structure Exploitation in Generalized Eigenproblems Arising in Density Functional Theory

In this short paper, the authors report a new computational approach in the context of Density Functional Theory (DFT). It is shown how it is possible to speed up the self-consistent cycle (iteration) characterizing one of the most well-known DFT implementations: FLAPW. Generating the Hamiltonian and overlap matrices and solving the associated generalized eigenproblems $Ax = \lambda Bx$ constitute the two most time-consuming fractions of each iteration. Two promising directions, implementing the new methodology, are presented that will ultimately improve the performance of the generalized eigensolver and save computational time.Comment: To appear in the proceedings of 8th International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2010

L'uscita dall'euro e dall'Unione Europea: teoria e pratica del Grexit e del Brexit

Il progetto di integrazione europea, a lungo emblema di pace ed esemplare compromesso tra prosperità ed equità sociale, attraversa oggi tempi duri: crisi economica, rinnovati nazionalismi, spinte xenofobe ed un assetto istituzionale frequentemente in balía della ragion di Stato dei propri membri sottopongono l'Unione Europea a inediti stress tests, tali da metterne in dubbio persino la sopravvivenza: scenari come il recesso dall'UE o l'uscita dall'euro da parte di uno Stato membro, un tempo tanto improbabili da meritare a malapena menzione all'interno dei trattati appaiono oggi come spade di Damocle pendenti sulle sorti dell'Unione. Secondo una struttura idealmente bipartita, i quattro capitoli che compongono il presente lavoro indagano con approccio teorico-pratico le questioni giuridiche sottese al recesso dall'Unione Europea e dall'euro da parte di uno Stato membro. Il Capitolo I si occupa, a fronte del silenzio dei trattati europei, della ricostruzione della disciplina applicabile all'uscita dall'euro: vengono esaminate le principali posizioni dottrinali l'applicabilità, controversa, del Diritto Internazionale, concludendosi per l'indisponibilità – al di fuori del recesso in toto dall'Unione ex art. 50 TUE e, teoricamente, di una revisione ad hoc dei trattati ex art. 48 TUE – di vie in grado di assicurare un recesso pacificamente legittimo dalla moneta unica. Speciale attenzione è riservata, nel Capitolo II, all'ipotesi del Grexit ed agli ingranaggi normativi che muovono tre scenari pratici: Grexit volontario, forzato e accidentale. La seconda parte di questo lavoro, dedicata al recesso dall'Unione, è inaugurata dal Capitolo III attraverso l'analisi della disciplina vigente. Punto focale è la clausola di recesso ex art. 50 TUE, introdotta a Lisbona. L'iter e gli effetti del recesso sono presi in considerazione sia nel caso in cui questo avvenga tramite Withdrawal Agreement tra Unione e Stato interessato, sia ove il recesso avvenga in sua assenza. Il Capitolo IV studia la minaccia del Brexit, dedicando grande attenzione alle problematiche giuridiche sollevate dalle proposte di riforma dell'Unione avanzate dal premier britannico Cameron ed a quelle che l'eventuale recesso britannico potrebbe scatenare. Sono oggetto di studio anche le alternative alla membership UE a disposizione del Regno Unito ed il ruolo che l'Italia potrebbe assumere nelle trattative volte ad impedirne l'addio. Nelle conclusioni è infine lasciato spazio, alla luce degli elementi emersi, ad una riflessione sul complessivo stato di salute dell'Unione Europea e della comunità di destino ad essa sottesa

A New Model for Testing IPv6 Fragment Handling

Since the origins of the Internet, various vulnerabilities exploiting the IP fragmentation process have plagued IPv4 protocol, many leading to a wide range of attacks. IPv6 modified the handling of fragmentations and introduced a specific extension header, not solving the related problems, as proved by extensive literature. One of the primary sources of problems has been the overlapping fragments, which result in unexpected or malicious packets when reassembled. To overcome the problem related to fragmentation, the authors of RFC 5722 decided that IPv6 hosts MUST silently drop overlapping fragments. Since then, several studies have proposed methodologies to check if IPv6 hosts accept overlapping fragments and are still vulnerable to related attacks. However, some of the above methodologies have not been proven complete or need to be more accurate. In this paper we propose a novel model to check IPv6 fragmentation handling specifically suited for the reassembling strategies of modern operating systems. Previous models, indeed, considered OS reassembly policy as byte-based. However, nowadays, reassembly policies are fragment-based, making previous models inadequate. Our model leverages the commutative property of the checksum, simplifying the whole assessing process. Starting with this new model, we were able to better evaluate the RFC-5722 and RFC-9099 compliance of modern operating systems against fragmentation handling. Our results suggest that IPv6 fragmentation can still be considered a threat and that more effort is needed to solve related security issues

Bosentan for digital ulcers prevention does not worsen cardiopulmonary exercise test parameters in SSc patients with interstitial lung disease

Bosentan for digital ulcers prevention does not worsen cardiopulmonary exercise test parameters in SSc patients with interstitial lung diseas

Editorial: high-performance tensor computations in scientific computing and data science

Introduction In the last two decade, tensor computations developed from a small and little known subject to a vast and heterogeneous field with many diverse topics ranging from high-order decomposition and low-rank approximation to optimization and multi-linear contractions. At the same time, several of these operations with tensors are progressively and diversely applied to many, rather distinct domains; from Quantum Chemistry to Deep Learning, and from Condensed Matter Physics to Remote Sensing. These domain-specific applications of tensor computations present a number of particular challenges originating from their high dimensionality, computational cost, and complexity. Usually, because these challenges could be quite diverse among application areas, there is not an homogeneous and uniform approach in the development of software programs tackling tensor operations. On the contrary, very often developers implement domain-specific libraries which compromise their use across disciplines. The end result is a fragmented community where efforts are often replicated and scattered [1]. This Research Topic represents an attempt in bringing together different communities, spearheading the latest cutting-edge results at the frontier of tensor computations, and sharing the lessons learned in domain-specific applications. The issue includes ten research articles written by experts in the field. For the sake of clarity, the articles can be somewhat artificially divided in four main areas: (i) decompositions, (ii) low-rank approximations, (iii) high-performance operations, and (iv) tensor networks. In practice, many of the works in this Research Topic spill over the boundaries of such areas and are interdisciplinary in nature, thus demonstrating how cross-fertilizing the field of tensor computations is

Shape Complementarity Optimization of Antibody-Antigen Interfaces: the Application to SARS-CoV-2 Spike Protein

Many factors influence biomolecules binding, and its assessment constitutes an elusive challenge in computational structural biology. In this respect, the evaluation of shape complementarity at molecular interfaces is one of the main factors to be considered. We focus on the particular case of antibody-antigen complexes to quantify the complementarities occurring at molecular interfaces. We relied on a method we recently developed, which employs the 2D Zernike descriptors, to characterize investigated regions with an ordered set of numbers summarizing the local shape properties. Collected a structural dataset of antibody-antigen complexes, we applied this method and we statistically distinguished, in terms of shape complementarity, pairs of interacting regions from non-interacting ones. Thus, we set up a novel computational strategy based on \textit{in-silico} mutagenesis of antibody binding site residues. We developed a Monte Carlo procedure to increase the shape complementarity between the antibody paratope and a given epitope on a target protein surface. We applied our protocol against several molecular targets in SARS-CoV-2 spike protein, known to be indispensable for viral cell invasion. We, therefore, optimized the shape of template antibodies for the interaction with such regions. As the last step of our procedure, we performed an independent molecular docking validation of the results of our Monte Carlo simulations.Comment: 13 pages, 4 figure

Neuronal desertification after a direct lightning strike: a case report

Background: Lightning strike is a rare but dramatic cause of injury. Patients admitted to intensive care units (ICUs) with lightning strike frequently have a high mortality and significant long-term morbidity related to a direct brain injury or induced cardiac arrest (CA). Case presentation: A 50-year-old Caucasian man was admitted to our hospital after being struck by lightning resulting in immediate CA. Spontaneous circulation was initially restored, and the man was admitted to the ICU, but ultimately died while in hospital due to neurological injury. The computer tomography scan revealed a massive loss of grey-white matter differentiation at the fronto-temporal lobes bilaterally. Somatosensory-evoked potentials demonstrated bilateral absence of the cortical somatosensory N20-potential, and the electroencephalogram recorded minimal cerebral electrical activity. The patient died on day 10 and a post-mortem study revealed a widespread loss of neurons. Conclusion: This case study illustrates severe brain injury caused by a direct lighting strike, with the patient presenting an extraordinary microscopic pattern of neuronal desertification