Perturbation Theory in the Complex Plane: Exceptional Points and Where to Find Them

We explore the non-Hermitian extension of quantum chemistry in the complex plane and its link with perturbation theory. We observe that the physics of a quantum system is intimately connected to the position of complex-valued energy singularities, known as exceptional points. After presenting the fundamental concepts of non-Hermitian quantum chemistry in the complex plane, including the mean-field Hartree--Fock approximation and Rayleigh--Schr\"odinger perturbation theory, we provide a historical overview of the various research activities that have been performed on the physics of singularities. In particular, we highlight seminal work on the convergence behaviour of perturbative series obtained within M{\o}ller--Plesset perturbation theory, and its links with quantum phase transitions. We also discuss several resummation techniques (such as Pad\'e and quadratic approximants) that can improve the overall accuracy of the M{\o}ller--Plesset perturbative series in both convergent and divergent cases. Each of these points is illustrated using the Hubbard dimer at half filling, which proves to be a versatile model for understanding the subtlety of analytically-continued perturbation theory in the complex plane.Comment: 22 page, 14 figures, 4 table

Some remarks on quasi-Hermitian operators

A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze the structure generated by unbounded metric operators in a Hilbert space. Following our previous work, we introduce several generalizations of the notion of similarity between operators. Then we explore systematically the various types of quasi-Hermitian operators, bounded or not. Finally we discuss their application in the so-called pseudo-Hermitian quantum mechanics.Comment: 18page

Propagation dynamics on networks featuring complex topologies

Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently couple the dynamics of the network elements (nodes, vertices, individuals...) on the one hand and their recurrent topological patterns (subgraphs, groups...) on the other hand. In a SIS model of epidemic spread on social networks with community structure, this approach yields a set of ODEs for the time evolution of the system, as well as analytical solutions for the epidemic threshold and equilibria. The results obtained are in good agreement with numerical simulations and reproduce random networks behavior in the appropriate limits which highlights the influence of topology on the processes. Finally, it is demonstrated that our model predicts higher epidemic thresholds for clustered structures than for equivalent random topologies in the case of networks with zero degree correlation.Comment: 10 pages, 5 figures, 1 Appendix. Published in Phys. Rev. E (mistakes in the PRE version are corrected here

Missions religieuses dans le monde ibérique moderne

Pierre-Antoine Fabre, directeur d’étudesInes G. Županov, chargée de recherche au CNRS Missions et cultures à l’époque moderne Avec Charlotte de Castelnau-l’Estoile, maître de conférences à l’Université Paris-Ouest/Nanterre La Défense, Marie Lucie Copete, maître de conférences à l’Université de Rouen et Aliocha Maldavsky, maître de conférences à l’Université Paris-Ouest/Nanterre La Défense. Dans la continuation de notre séminaire sur les missions catholiques (XVIe-XVIIIe siècle), nous avons ou..

A new perspective on permafrost boundaries in France during the Last Glacial Maximum

During the Last Glacial Maximum (LGM), a very cold and dry period around 26.5–19 kyr BP, permafrost was widespread across Europe. In this work, we explore the possible benefit of using regional climate model data to improve the permafrost representation in France, decipher how the atmospheric circulation affects the permafrost boundaries in the models, and test the role of ground thermal contraction cracking in edge development during the LGM. With these aims, criteria for possible thermal contraction cracking of the ground are applied to climate model data for the first time. Our results show that the permafrost extent and ground cracking regions deviate from proxy evidence when the simulated large-scale circulation in both global and re-gional climate models favours prevailing westerly winds. A colder and, with regard to proxy data, more realistic version of the LGM climate is achieved given more frequent easterly winds conditions. Given the appropriate forcing, an added value of the regional climate model simulation can be achieved in representing permafrost and ground thermal contraction cracking. Furthermore, the model data provide evidence that thermal contraction cracking occurred in Europe during the LGM in a wide latitudinal band south of the probable permafrost border, in agreement with field data analysis. This enables the reconsideration of the role of sand-wedge casts to identify past permafrost regions

A robust and reliable methodology to perform GECI-based multi-time point neuronal calcium imaging within mixed cultures of human iPSC-derived cortical neurons

IntroductionHuman induced pluripotent stem cells (iPSCs), with their ability to generate human neural cells (astrocytes and neurons) from patients, hold great promise for understanding the pathophysiology of major neuropsychiatric diseases such as schizophrenia and bipolar disorders, which includes alterations in cerebral development. Indeed, the in vitro neurodifferentiation of iPSCs, while recapitulating certain major stages of neurodevelopment in vivo, makes it possible to obtain networks of living human neurons. The culture model presented is particularly attractive within this framework since it involves iPSC-derived neural cells, which more specifically differentiate into cortical neurons of diverse types (in particular glutamatergic and GABAergic) and astrocytes. However, these in vitro neuronal networks, which may be heterogeneous in their degree of differentiation, remain challenging to bring to an appropriate level of maturation. It is therefore necessary to develop tools capable of analyzing a large number of cells to assess this maturation process. Calcium (Ca2+) imaging, which has been extensively developed, undoubtedly offers an incredibly good approach, particularly in its versions using genetically encoded calcium indicators. However, in the context of these iPSC-derived neural cell cultures, there is a lack of studies that propose Ca2+ imaging methods that can finely characterize the evolution of neuronal maturation during the neurodifferentiation process.MethodsIn this study, we propose a robust and reliable method for specifically measuring neuronal activity at two different time points of the neurodifferentiation process in such human neural cultures. To this end, we have developed a specific Ca2+ signal analysis procedure and tested a series of different AAV serotypes to obtain expression levels of GCaMP6f under the control of the neuron-specific human synapsin1 (hSyn) promoter.ResultsThe retro serotype has been found to be the most efficient in driving the expression of the GCaMP6f and is compatible with multi-time point neuronal Ca2+ imaging in our human iPSC-derived neural cultures. An AAV2/retro carrying GCaMP6f under the hSyn promoter (AAV2/retro-hSyn-GCaMP6f) is an efficient vector that we have identified. To establish the method, calcium measurements were carried out at two time points in the neurodifferentiation process with both hSyn and CAG promoters, the latter being known to provide high transient gene expression across various cell types.DiscussionOur results stress that this methodology involving AAV2/retro-hSyn-GCaMP6f is suitable for specifically measuring neuronal calcium activities over multiple time points and is compatible with the neurodifferentiation process in our mixed human neural cultures

Neural network-based emulation of interstellar medium models

The interpretation of observations of atomic and molecular tracers in the galactic and extragalactic interstellar medium (ISM) requires comparisons with state-of-the-art astrophysical models to infer some physical conditions. Usually, ISM models are too time-consuming for such inference procedures, as they call for numerous model evaluations. As a result, they are often replaced by an interpolation of a grid of precomputed models. We propose a new general method to derive faster, lighter, and more accurate approximations of the model from a grid of precomputed models. These emulators are defined with artificial neural networks (ANNs) designed and trained to address the specificities inherent in ISM models. Indeed, such models often predict many observables (e.g., line intensities) from just a few input physical parameters and can yield outliers due to numerical instabilities or physical bistabilities. We propose applying five strategies to address these characteristics: 1) an outlier removal procedure; 2) a clustering method that yields homogeneous subsets of lines that are simpler to predict with different ANNs; 3) a dimension reduction technique that enables to adequately size the network architecture; 4) the physical inputs are augmented with a polynomial transform to ease the learning of nonlinearities; and 5) a dense architecture to ease the learning of simple relations. We compare the proposed ANNs with standard classes of interpolation methods to emulate the Meudon PDR code, a representative ISM numerical model. Combinations of the proposed strategies outperform all interpolation methods by a factor of 2 on the average error, reaching 4.5% on the Meudon PDR code. These networks are also 1000 times faster than accurate interpolation methods and require ten to forty times less memory. This work will enable efficient inferences on wide-field multiline observations of the ISM

A SILAC-Based Screen for Methyl-CpG Binding Proteins Identifies RBP-J as a DNA Methylation and Sequence-Specific Binding Protein

Contains fulltext : 91489.pdf (publisher's version ) (Open Access)10 p

Marburg hemorrhagic fever in Durba and Watsa, Democratic Republic of the Congo: clinical documentation, features of illness, and treatment

The objective of the present study was to describe day of onset and duration of symptoms of Marburg hemorrhagic fever (MHF), to summarize the treatments applied, and to assess the quality of clinical documentation. Surveillance and clinical records of 77 patients with MHF cases were reviewed. Initial symptoms included fever, headache, general pain, nausea, vomiting, and anorexia (median day of onset, day 1-2), followed by hemorrhagic manifestations (day 5-8+), and terminal symptoms included confusion, agitation, coma, anuria, and shock. Treatment in isolation wards was acceptable, but the quality of clinical documentation was unsatisfactory. Improved clinical documentation is necessary for a basic evaluation of supportive treatment

Structural preferential attachment: Network organization beyond the link

We introduce a mechanism which models the emergence of the universal properties of complex networks, such as scale independence, modularity and self-similarity, and unifies them under a scale-free organization beyond the link. This brings a new perspective on network organization where communities, instead of links, are the fundamental building blocks of complex systems. We show how our simple model can reproduce social and information networks by predicting their community structure and more importantly, how their nodes or communities are interconnected, often in a self-similar manner.Comment: 4 pages, 3 figures, 1 tabl