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Temporal lobe epilepsy (TLE) patients are at risk of memory deficits, which have been linked to functional network disturbances, particularly of integration of the default mode network (DMN). However, the cellular substrates of functional network integration are unknown. We leverage a unique cross-scale dataset of drug-resistant TLE patients (n = 31), who underwent pseudo resting-state functional magnetic resonance imaging (fMRI), resting-state magnetoencephalography (MEG) and/or neuropsychological testing before neurosurgery. fMRI and MEG underwent atlas-based connectivity analyses. Functional network centrality of the lateral middle temporal gyrus, part of the DMN, was used as a measure of local network integration. Subsequently, non-pathological cortical tissue from this region was used for single cell morphological and electrophysiological patch-clamp analysis, assessing integration in terms of total dendritic length and action potential rise speed. As could be hypothesized, greater network centrality related to better memory performance. Moreover, greater network centrality correlated with more integrative properties at the cellular level across patients. We conclude that individual differences in cognitively relevant functional network integration of a DMN region are mirrored by differences in cellular integrative properties of this region in TLE patients. These findings connect previously separate scales of investigation, increasing translational insight into focal pathology and large-scale network disturbances in TLE.

Volume exclusion and single-file diffusion play an important role at very small scales, such as those associated with molecular machines, ion channels, and transport in zeolites, while introducing fundamental differences compared to Brownian motion, such as changes to the power-law relation between the mean square displacement and time. In this work we map the chemical master equation for excluded diffusion onto a Schrödinger equation via annihilation and creation ladder operators with fermionic statistics, together with linear and symbolic algebra with the resulting Fock-space representation to describe the effect of volume-exclusion processes in finite one-dimensional chains. We contrast the dynamics with the nonexclusive (bosonic) diffusion for crowded, intermediate, and dilute particle populations. Motivated by shuttling in molecular machines, we proceed to investigate differences in exit time distributions introduced by volume exclusion, incorporating the presence of transport bias. More generally, this study demonstrates how one can analyze volume-excluded transport for small stochastic systems, without the need for stochastic simulation and ensemble averaging, simply by considering anticommutation relations and fermionic statistics in a Fock-space representation of the stochastic dynamics.

In this work, we investigate the electronic transport properties of curved two-dimensional quantum systems with a position-dependent mass (PDM). We find the Schrodinger equation for a general surface following the da Costa approach, obtaining the geometrical potential for systems with PDM. We obtain expressions for the transmittance and reflectance for a general surface of revolution and, as a first application of the general results obtained here, we investigate the transport properties of deformed nanotubes whose variation of the effective mass with the radius has been disconsidered in previous studies. We find that the inclusion of the position-dependent mass, can induce a significant correction in the transport properties of the system. This reveals that the transport properties of two-dimensional quantum systems are sensitive to the PDM and that, when modeling electronic transport in surfaces, these effects should be considered.

The Hamiltonian mean-field model is investigated in the presence of a field. The self-consistent equations for the magnetization and the energy per particle are derived, and the field effect on the caloric curve is presented. The analytical geometric approach to Hamiltonian dynamics, under the hypothesis of quasi-isotropy, allows us to calculate the field effect on the energy-dependent microcanonical mean Ricci curvature and its fluctuations. Notably, the method proved suitable to identify that stable and metastable solutions of the Lyapunov exponent exhibit intriguing distinct curvature behavior very close to the critical point at extremely low field values. In addition, finite-size molecular dynamics (MD) simulations are used to observe the evolution of the magnetization and their components, including the stability properties of the solutions. Most importantly, comparison of finite-size MD calculations of the Lyapunov exponent and related properties with those via the geometric approach unveil the sensible dependence of these microcanonical quantities on energy, number of particles, and field, before a quasisaturation behavior at high fields. Finally, relaxation properties from out-of-equilibrium initial conditions are discussed in light of MD simulations.

The investigation of curved low-dimensional systems is a topic of great research interest. Such investigations include two-dimensional systems with cylindrical symmetry. In this work, we present a numerical study of the electronic transport properties of metallic nanotubes deviating from the cylindrical form either by having a bump or a depression, and under the influence of a magnetic field. Under these circumstances, it is found that the nanotube may be used as an energy high-pass filter for electrons. It is also shown that the device can be used to tune the angular momentum of transmitted electrons., Comment: The following article has been accepted by J. of Applied Physics

In this work, we use methods and concepts of applied algebraic topology to comprehensively explore topological phase transitions in complex systems. Topological phase transitions are characterized by the zeros of the Euler characteristic (EC) or by singularities of the Euler entropy and also indicates signal changes in the mean node curvature of networks. Here, we provide strong evidence that the zeros of the Euler characteristic can be interpreted as a complex network9s intrinsic fingerprint. We theoretically and empirically illustrate this across different biological networks: We first target our investigation to protein-protein interaction networks (PPIN). To do so, we used methods of topological data analysis to compute the Euler characteristic analytically, and the Betti numbers numerically as a function of the attachment probability for two variants of the Duplication Divergence model, namely the totally asymmetric model and the heterodimerization model. We contrast our theoretical results with experimental data freely available for gene co-expression networks (GCN) of \textit{Saccharomyces cerevisiae}, also known as baker9s yeast, as well as of the nematode \textit{Caenorhabditis elegans}. Supporting our theoretical expectations, we are able to detect topological phase transitions in both networks obtained according to different similarity measures. Later, we theoretically illustrate the emergence of topological phase transitions in three classical network models, namely the Watts-Strogratz model, the Random Geometric Graph, and the Barabasi-Albert model. Given the universality and wide use of those models across disciplines, our results indicate that topological phase transitions may permeate across a wide range of theoretical and empirical networks. Hereby, our paper reinforces the idea of using topological phase transitions to advance the understanding of complex systems more generally.

Living systems are subject to the arrow of time; from birth, they undergo complex transformations (self-organization) in a constant battle for survival, but inevitably ageing and disease trap them to death. Can ageing be understood and eventually reversed? What tools can be employed to further our understanding of ageing? The present article is an invitation for biologists and clinicians to consider key conceptual ideas and computational tools (known to mathematicians and physicists), which potentially may help dissect some of the underlying processes of ageing and disease. Specifically, we first discuss how to classify and analyse complex systems, as well as highlight critical theoretical difficulties that make complex systems hard to study. Subsequently, we introduce Topological Data Analysis - a novel Big Data tool – which may help in the study of complex systems since it extracts knowledge from data in a holistic approach via topological considerations. These conceptual ideas and tools are discussed in a relatively informal way to pave future discussions and collaborations between mathematicians and biologists studying ageing., Basque Government under the grant “Artificial Intelligence in BCAM number EXP. 2019/00432” Inria associated team "NeuroTransSF"

Functional brain networks are shaped and constrained by the underlying structural network. However, functional networks are not merely a one-to-one reflection of the structural network. Several theories have been put forward to understand the relationship between structural and functional networks. However, it remains unclear how these theories can be unified. Two existing recent theories state that 1) functional networks can be explained by all possible walks in the structural network, which we will refer to as the series expansion approach, and 2) functional networks can be explained by a weighted combination of the eigenmodes of the structural network, the so-called eigenmode approach. To elucidate the unique or common explanatory power of these approaches to estimate functional networks from the structural network, we analysed the relationship between these two existing views. Using linear algebra, we first show that the eigenmode approach can be written in terms of the series expansion approach, i.e., walks on the structural network associated with different hop counts correspond to different weightings of the eigenvectors of this network. Second, we provide explicit expressions for the coefficients for both the eigenmode and series expansion approach. These theoretical results were verified by empirical data from Diffusion Tensor Imaging (DTI) and functional Magnetic Resonance Imaging (fMRI), demonstrating a strong correlation between the mappings based on both approaches. Third, we analytically and empirically demonstrate that the fit of the eigenmode approach to measured functional data is always at least as good as the fit of the series expansion approach, and that errors in the structural data lead to large errors of the estimated coefficients for the series expansion approach. Therefore, we argue that the eigenmode approach should be preferred over the series expansion approach. Results hold for eigenmodes of the weighted adjacency matrices as well as eigenmodes of the graph Laplacian. ​Taken together, these results provide an important step towards unification of existing theories regarding the structure-function relationships in brain networks.

BackgroundPublic health recommendations and governmental measures during the COVID-19 pandemic have enforced numerous restrictions on daily living including social distancing, isolation and home confinement. While these measures are imperative to abate the spreading of COVID-19, the impact of these restrictions on health behaviours and lifestyle at home is undefined. Therefore, an international online survey was launched in April 2020 in seven languages to elucidate the behavioral and lifestyle consequences of COVID-19 restrictions. This report presents the preliminary results from the first thousand responders on physical activity (PA) and nutrition behaviours.MethodsThirty-five research organisations from Europe, North-Africa, Western Asia and the Americas promoted the survey through their networks to the general society, in English, German, French, Arabic, Spanish, Portugese, and Slovenian languages. Questions were presented in a differential format with questions related to responses “before” and “during” confinement conditions.Results1047 replies (54% women) from Asia (36%), Africa (40%), Europe (21%) and other (3%) were included into a general analysis. The COVID-19 home confinement had a negative effect on all intensities of PA (vigorous, moderate, walking and overall). Conversely, daily sitting time increased from 5 to 8 hours per day. Additionally, food consumption and meal patterns (the type of food, eating out of control, snacks between meals, number of meals) were more unhealthy during confinement with only alcohol binge drink decreasing significantly.ConclusionWhile isolation is a necessary measure to protect public health, our results indicate that it alters physical activity and eating behaviours in a direction that would compromise health. A more detailed analysis of survey data will allow for a segregation of these responses in different age groups, countries and other subgroups which will help develop bespoke interventions to mitigate the negative lifestyle behaviors manifest during the COVID-19 confinement.

The damage of the novel Coronavirus disease (COVID-19) is reaching unprecedented scales. There are numerous classical epidemiology models trying to quantify epidemiology metrics. Usually, to forecast epidemics, classical approaches need parameter estimations, such as the contagion rate or the basic reproduction number. Here, we propose a data-driven, parameter-free, geometric approach to access the emergence of a pandemic state by studying the Forman-Ricci and Ollivier- Ricci network curvatures. Discrete Ollivier-Ricci curvature has been used successfully to forecast risk in nancial networks and we suggest that those results can provide analogous results for COVID-19 epidemic time-series. We rst compute both curvatures in a toy-model of epidemic time-series with delays, which allows us to create epidemic networks. We also compared our results to classical network metrics. By doing so, we are able to verify that the Ollivier-Ricci and Forman-Ricci curvatures can be a parameter-free estimate for identifying a pandemic state in the simulated epidemic. On this basis, we then compute both Forman-Ricci and Ollivier-Ricci curvatures for real epidemic networks built from COVID-19 epidemic time-series available at the World Health Organization (WHO). This approach allow us to detect early warning signs of the emergence of the pandemic. The advantage of our method lies in providing an early geometrical data marker for the pandemic state, regardless of parameter estimation and stochastic modelling. This work opens the possibility of using discrete geometry to study epidemic networks. Keywords: COVID-19, SARS2, Forman-Ricci Curvature, Ollivier-Ricci curvature, Epidemiology, Topologi- cal Data Analysis

The statistical description of a one-dimensional superdiffusive Lévy flier restricted to a finite domain is well known to be technically involving. For example, in this type of process the probability distribution P(x, t) and survival probability S(t) cannot be obtained from the method of images. Other methods, such as the fractional derivative approach, also find technical difficulties due to the long jumps combined with the presence of absorbing boundaries. Here we revisit this problem through a different point of view. We map the corresponding master equation to a Schrödinger-like equation and then describe the Lévy flier evolution in a Fock space. The system states are assigned to the available positions in the discrete space. The Hamiltonian-like matrix is calculated for any Lévy index α ∈ (0, 2]. For the system sizes studied here the computation of its eigenvalues and eigenvectors are performed using a symbolic computing software. This method allows to build the time evolution operator, the distribution P(x, t) and the survival probability S(t). We compare our results for P(x, t) with direct Monte Carlo simulations and find a good agreement for all α ∈ (0, 2]. Similarly, our results for S(t) nicely agree with the numerical simulations for any time t, including the short-term behavior. In the long-term asymptotic limit we identify the crossover between the power-law and exponential behaviors, which emerge respectively when only one or both boundaries are reached by the Lévy flier. Comparisons with some exact expressions for Lévy flights in the continuous space limit also display good agreement. We conclude our analysis by discussing the possibility of extending the present framework to general bounded random walks and flights.

Functional brain networks are often constructed by quantifying correlations among brain regions. Their topological structure includes nodes, edges, triangles and even higher-dimensional objects. Topological data analysis (TDA) is the emerging framework to process datasets under this perspective. In parallel, topology has proven essential for understanding fundamental questions in physics. Here we report the discovery of topological phase transitions in functional brain networks by merging concepts from TDA, topology, geometry, physics, and network theory. We show that topological phase transitions occur when the Euler entropy has a singularity, which remarkably coincides with the emergence of multidimensional topological holes in the brain network. Our results suggest that a major alteration in the pattern of brain correlations can modify the signature of such transitions, and may point to suboptimal brain functioning. Due to the universal character of phase transitions and noise robustness of TDA, our findings open perspectives towards establishing reliable topological and geometrical biomarkers of individual and group differences in functional brain network organization.

This work proposes bifacial tandem solar panels with MOS cells on the backside aiming at applications in deserts. MOS solar cells were fabricated using Al(200nm)/ Mg(30nm)/SiO 2 (1.73nm)/Si-p structures. The gate oxide was grown by rapid thermal processing (RTP) and the main parameters studied were extracted by means of electric characterization through IxV curves of the MOS solar cells. For the operation temperature of the MOS cell varying from 25°C to 70°C, it was shown that the loss of the conversion efficiency ($\eta$) was at least 25% lower compared to conventional solar modules based on PN junctions and multi-crystalline-Si [9, 12]. As a result, the use of MOS solar cell on the backside of two different generations of CdS_CdTe cells with different conversion efficiencies at 25° C (15.8% and 21.0%), operating at the typical temperature of 70°C in deserts, promotes the increase of the conversion efficiency of 10.0% for CdS_CdTe1 (15.8%) and 6.0% for CdS_CdTe2 (21.0%).

The damage of the novel Coronavirus disease (COVID-19) is reaching an unprecedented scale. There are numerous classical epidemiology models trying to quantify epidemiology metrics. To forecast epidemics, classical approaches usually need parameter estimations, such as the contagion rate or the basic reproduction number. Here, we propose a data-driven, parameter-free, geometric approach to access the emergence of a pandemic state by studying the Forman–Ricci and Ollivier–Ricci network curvatures. Discrete Ollivier–Ricci curvature has been used successfully to forecast risk in financial networks and we suggest that those results can provide analogous results for COVID-19 epidemic time-series. We first compute both curvatures in a toy-model of epidemic time-series with delays, which allows us to create epidemic networks. We also compared our results to classical network metrics. By doing so, we are able to verify that the Ollivier–Ricci and Forman–Ricci curvatures can be a parameter-free estimate for identifying a pandemic state in the simulated epidemic. On this basis, we then compute both Forman–Ricci and Ollivier–Ricci curvatures for real epidemic networks built from COVID-19 epidemic time-series available at the World Health Organization (WHO). This approach allows us to detect early warning signs of the emergence of the pandemic. The advantage of our method lies in providing an early geometrical data marker for the pandemic state, regardless of parameter estimation and stochastic modelling. This work opens the possibility of using discrete geometry to study epidemic networks.

The presence of topological defects in a material can modify its electrical, acoustic or thermal properties. However, when a group of defects is present, the calculations can become quite cumbersome due to the differential equations that can emerge from the modeling. In this work, we express phonons as geodesics of a 2 + 1 spacetime in the presence of a channel of dislocation dipoles in a crystalline environment described analytically in the continuum limit with differential geometry methods. We show that such a simple model of 1D array of topological defects is able to guide phonon waves. The presence of defects indeed distorts the effective metric of the material, leading to an anisotropic landscape of refraction index which curves the path followed by phonons, with focusing/defocusing properties depending on the angle of the incident wave. As a consequence, using Boltzmann transfer equation, we show that the defects may induce an enhancement or a depletion of the elastic energy transport. We comment on the possibility of designing artificial materials through the presence of topological defects., Comment: arXiv admin note: substantial text overlap with arXiv:1601.06584

International audience; We address the problem of quantum particles moving on a manifold characterised by the presence of torsion along a preferential axis. In fact, such a torsion may be taylored by the presence of a single screw dislocation, whose Burgers vector measures the torsion amplitude. The problem, first treated in the relativistic limit describing fermions that couple minimally to torsion, is then analysed in the Pauli limit. We show that torsion induces a geometric potential and also that it couples generically to the phase of the wave function, giving rise to the possibility of using torsion to manipulate spin currents in the case of spinor wave functions. These results emerge as an alternative strategy for using screw dislocations in the design of spintronic-based devices.

We present an alternative solution of the Ising chain in a field under free and periodic boundary conditions, in the microcanonical, canonical, and grand canonical ensembles, from a unified combinatorial and topological perspective. In particular, the computation of the per-site entropy as a function of the energy un- veils a residual value for critical values of the magnetic field, a phenomenon for which we provide a topological interpretation and a connection with the Fibonacci se- quence. We also show that, in the thermodynamic limit, the per-site microcanonical entropy is equal to the loga- rithm of the per-site Euler characteristic. The canonical and grand canonical partition functions are identified as combinatorial generating functions of the micro- canonical problem, which allows us to evaluate them. A detailed analysis of the magnetic field-dependent thermodynamics, including positive and negative tem- peratures, reveals interesting features. Finally, we em- phasize that our combinatorial approach to the canon- ical ensemble allows exact computation of the ther- mally averaged value � χ� of the Euler characteristic associated with the spin configurations of the chain, which is discontinuous at the critical fields, and whose thermal behavior is expected to determine the phase transition of the model. Indeed, our results show that the conjecture � χ� (TC) = 0 ,w hereTC is the critical temperature, is valid for the Ising chain.

International audience; We examine the properties of a family of defects called hyperbolic disclinations, and discuss their possible use for the design of perfect optical absorbers. In hyperbolic metamaterials, the ratio of ordinary and extraordinary permittivities is negative, which leads to an effective metric of Kleinian signature (two timelike coordinates). Considering a disclination in the hyperbolic nematic host matrix, we show that the timelike geodesics are Poinsot spirals, i.e., whatever the impact parameter of an incident light beam, it is confined and whirls about the defect core. The trapping effect does not require light to be coherent. This property also remains in the wave formalism, which may be the sign for many potential applications.

Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.

We propose a topological approach suitable to establish a connection between thermodynamics and topology in the microcanonical ensemble. Indeed, we report on results that point to the possibility of describing {\it interacting classical spin systems} in the thermodynamic limit, including the occurrence of a phase transition, using topology arguments only. Our approach relies on Morse theory, through the determination of the critical points of the potential energy, which is the proper Morse function. Our main finding is to show that, in the context of the studied classical models, the Euler characteristic $\chi(E)$ embeds the necessary features for a correct description of several magnetic thermodynamic quantities of the systems, such as the magnetization, correlation function, susceptibility, and critical temperature. Despite the classical nature of the studied models, such quantities are those that do not violate the laws of thermodynamics [with the proviso that Van der Waals loop states are mean field (MF) artifacts]. We also discuss the subtle connection between our approach using the Euler entropy, defined by the logarithm of the modulus of $\chi(E)$ per site, and that using the {\it Boltzmann} microcanonical entropy. Moreover, the results suggest that the loss of regularity in the Morse function is associated with the occurrence of unstable and metastable thermodynamic solutions in the MF case. The reliability of our approach is tested in two exactly soluble systems: the infinite-range and the short-range $XY$ models in the presence of a magnetic field. In particular, we confirm that the topological hypothesis holds for both the infinite-range ($T_c \neq 0$) and the short-range ($T_c = 0$) $XY$ models. Further studies are very desirable in order to clarify the extension of the validity of our proposal.

Nanotubes are generally not perfectly straight cylinders and the local curvature can influence transport properties. As shown by da Costa [1], charged particles moving on a curved surface experience an effective potential which modifies their dynamics. In this paper, we solve a one-electron Schrodinger equation in a distorted nanotube with open boundary conditions. We find that the deformations may open bandgaps suggesting their use in the design of nanotube- based electronic devices.

We use a topological approach to describe the frustration- and field-induced phase transitions exhibited by the infinite-range $XY$ model on the $A{B}_{2}$ chain, including noncollinear spin structures. For this purpose, we have computed the Morse number and the Euler characteristic, as well as other topological invariants, which are found to behave similarly as a function of the energy level in the context of Morse theory. In particular, we use a method based on an analogy with statistical mechanics to compute the Euler characteristic, which proves to be quite feasible. We also introduce topological energies which help us to clarify several properties of the transitions, both at zero and finite temperatures. In addition, we establish a nontrivial direct connection between the thermodynamics of the systems, which have been solved exactly under the saddle-point approach, and the topology of their configuration space. This connection allows us to identify the nondegeneracy condition under which the divergence of the density of Jacobian's critical points $[{j}_{l}(E)]$ at the critical energy of a topology-induced phase transition, proposed by Kastner and Schnetz [Phys. Rev. Lett. 100, 160601 (2008)] as a necessary criterion, is suppressed. Finally, our findings and those available in the literature suggest that the cusplike singularity exhibited both by the Euler characteristic and the topological contribution for the entropy at the critical energy, put together with the divergence of ${j}_{l}(E)$, and emerge as necessary and sufficient conditions for the occurrence of the finite-temperature topology-induced phase transitions examined in this work. The general character of this proposal should be subject to a more rigorous scrutiny.

parasitic and mycotic infections), malignancy (breast carcinoma) and other causes of granulomatous disease (as sarcoidosis, Wegener’s granulomatosis, giant cell arteritis or polyarteritis nodosum). Case report: A 38-year-old pre-menopausal woman presented with a twoweek history of a left breast mass. She had no particular medical records, there was no history of oral contraceptive use and she breastfed her 3-year-old child for 16 months. Concerning family illness, she had two aunts affected with breast cancer. The woman was apyretic and on physical examination there was a hard and painful mass, with 10cm diameter, on her left breast. The overlying skin showed signs of inflammation, and a 2cm palpable lymph node was present in the ipsilateral axilla. She began therapy with a broad spectrum antibiotic, which showed no success in resolving the lesion. Radiologic data was suggestive of a malignant process. Fine needle aspiration cytology was performed, as well as a skin, breast and lymph node biopsy, but the histopathologic results were inconclusive. Therefore, a wide excision was done, which revealed an inflammatory nonspecific mastitis with all microbiology and serological tests being negative. She was than treated with prednisone 60mg, gradually tapered in 6 weeks, and after 1 year had no recurrence. Conclusion: IGM is a rare and benign inflammatory process, commonly mistaken for malignancy and consequently can lead to unnecessary surgical procedures. Correct diagnosis requires the exclusion of malignancy, other granulomatous disease and infectious etiologies, combined with definitive histopathological confirmation. There is no clear clinical consensus regarding the ideal therapeutic management of IGM, but corticoid therapy should be an option.