2063 research outputs found
Sort by
A mathematical, computational and experimental study of neuronal excitability
Get PDFNeuronal excitability refers to the ability of neurons to generate electrical signals, called action
potentials, in response to stimuli. This concept can be studied through different aspects (math-
ematical, computational and experimental). In this thesis, we will be interested in studying this
concept by overlapping, when necessary, these different aspects in order to extract new results,
and this through five different projects. In the first project, we will first mathematically study the
behavioral transition between integrator neurons (type-I neuron models) and resonator neurons
(type-II neuron models) in mathematical models of neurons while retaining the properties that
make the model an integrator neuron. In a second project, we will analyze neuronal data obtained
from patch-clamp recordings of Granule cells (GC) during their development. During a transient
period of maturation, new GCs intrinsic and synaptic properties exhibit distinct from mature GCs,
potentially underlying the contribution of neurogenesis to memory encoding. We will produce a
model adapted to this behavior. In two related projects, we will focus on obtaining bifurcation
diagrams from noisy experiments, with methods inspired by digital continuation, called Control
Based Continuation in Experiments (CBCE). The idea is apply closed-loop control to an exper-
iment and iteratively bring the control to being noninvasive, which reveals the attractor of the
uncontrolled experiment. In the last project, we will analyze calcium imaging data from the ol-
factory bulb of several mice to which different chemicals were presented. Our main objective was
to highlight neural reaction patterns to stimuli, but also to develop a pipeline allowing to compare
the activity of different subjects, through odotopic maps
QUANTITATIVE HARDY INEQUALITY FOR MAGNETIC HAMILTONIANS
No full textIn this paper we present a new method of proof of Hardy type inequalities for two-
dimensional quantum Hamiltonians with a magnetic field of finite flux. Our approach gives a quanti-
tative lower bound on the best constant in these inequalities both for Schr¨odinger and Pauli operators.
Pauli operators with Aharonov-Bohm magnetic field are discussed as well
The theory of F-rational signature
No full textF-signature is an important numeric invariant of singularities in positive characteristic that can be used to detect strong F-regularity. One would like to have a variant that rather detects F-rationality, and there are two theories that aim to fill this gap: F-rational signature of Hochster and Yao and dual F-signature of Sannai. Unfortunately, several important properties of the original F-signature are unknown for these invariants. We find a modification of the Hochster–Yao definition that agrees with Sannai’s dual F-signature and push further the united theory to achieve a complete generalization of F-signature.EUR2023-143443
RYC2020-028976-
Uniform resolvent estimates and absence of eigenvalues of biharmonic operators with complex potentials
No full textWe quantify the subcriticality of the bilaplacian in dimensions greater than four by providing explicit repulsivity/smallness conditions on complex additive perturbations under which the spectrum remains stable. Our assumptions cover critical Rellich-type potentials too. As a byproduct we obtain uniform resolvent estimates in weighted spaces. Some of the results are new also in the self-adjoint setting
Adaptive Deep Fourier Residual method via overlapping domain decomposition
Get PDFThe Deep Fourier Residual (DFR) method is a specific type of variational physics-informed neural network (VPINN). It provides a robust neural network-based solution to partial differential equations (PDEs). The DFR strategy is based on minimizing the dual norm of the weak residual of a PDE, which is equivalent to minimizing the energy norm of the error. To compute the dual norm of the weak residual, the DFR method employs an orthonormal spectral basis of the test space, known for rectangles or cuboids for multiple function spaces.
In this work, we extend the DFR method with ideas of traditional domain decomposition (DD). This enables two improvements: (a) to solve problems in more general polygonal domains and (b) to develop an adaptive refinement technique in the test space using a Döfler marking algorithm. In the former case, we retain the desirable equivalence between the employed loss function and the H1 error under non-restrictive assumptions, numerically demonstrating adherence to explicit bounds in the case of the L-shaped domain problem. In the latter, we show how refinement strategies lead to potentially significant improvements against a reference, classical DFR implementation with a test function space of significantly lower dimensionality, allowing us to better approximate singular solutions at a more reasonable computational cost.PDC2021-121093-I00 (MCIN/AEI/10.13039/501100011033/Next Generation EU)
Consolidated Research Group MATHMODE (IT1456-22
Relevance of comorbidities for main outcomes during different periods of the COVID-19 pandemic
Get PDFBackground: Throughout the evolution of the COVID-19 pandemic, the severity of the disease has varied. The aim of this study was to determine how patients' comorbidities affected and were related to, different outcomes during this time. Methods: Retrospective cohort study of all patients testing positive for SARS-CoV-2 infection between March 1, 2020, and January 9, 2022. We extracted sociodemographic, basal comorbidities, prescribed treatments, COVID-19 vaccination data, and outcomes such as death and admission to hospital and intensive care unit (ICU) during the different periods of the pandemic. We used logistic regression to quantify the effect of each covariate in each outcome variable and a random forest algorithm to select the most relevant comorbidities. Results: Predictors of death included having dementia, heart failure, kidney disease, or cancer, while arterial hypertension, diabetes, ischemic heart, cerebrovascular, peripheral vascular diseases, and leukemia were also relevant. Heart failure, dementia, kidney disease, diabetes, and cancer were predictors of adverse evolution (death or ICU admission) with arterial hypertension, ischemic heart, cerebrovascular, peripheral vascular diseases, and leukemia also relevant. Arterial hypertension, heart failure, diabetes, kidney, ischemic heart diseases, and cancer were predictors of hospitalization, while dyslipidemia and respiratory, cerebrovascular, and peripheral vascular diseases were also relevant. Conclusions: Preexisting comorbidities such as dementia, cardiovascular and renal diseases, and cancers were those most related to adverse outcomes. Of particular note were the discrepancies between predictors of adverse outcomes and predictors of hospitalization and the fact that patients with dementia had a lower probability of being admitted in the first wave
Combining general and personal models for epilepsy detection with hyperdimensional computing
Get PDFEpilepsy is a highly prevalent chronic neurological disorder with great negative impact on patients’ daily lives. Despite this there is still no adequate technological support to enable epilepsy detection and continuous outpatient monitoring in everyday life. Hyperdimensional (HD) computing is a promising method for epilepsy detection via wearable devices, characterized by a simpler learning process and lower memory requirements compared to other methods. In this work, we demonstrate additional avenues in which HD computing and the manner in which its models are built and stored can be used to better understand, compare and create more advanced machine learning models for epilepsy detection. These possibilities are not feasible with other state-of-the-art models, such as random forests or neural networks. We compare inter-subject model similarity of different classes (seizure and non-seizure), study the process of creating general models from personal ones, and finally posit a method of combining personal and general models to create hybrid models. This results in an improved epilepsy detection performance. We also tested knowledge transfer between models trained on two different datasets. The attained insights are highly interesting not only from an engineering perspective, to create better models for wearables, but also from a neurological perspective, to better understand individual epilepsy patterns.RYC2021-032853-
r-Adaptive deep learning method for solving partial di erential equations
Get PDFWe introduce a Deep Neural Network (DNN) method for solving Partial Di erential
Equations (PDEs) that simultaneously: (a) constructs an optimal radapted mesh, i.e.,
given an initial mesh, it provides optimal node locations, and (b) solves the PDE over
the constructed r-adaptive mesh. The node locations are optimized over a set of 1D
boundary nodes, and the corresponding 2D quadrilateral meshes are built using tensor
product. The method supports the definition of fixed interfaces to create conforming
meshes and allows nodes to jump across them, permitting topological variations. To
numerically illustrate the performance of our novel radaptive deep learning method,
we apply it in combination with other numerical methods including collocation, Least
Squares, and the Deep Ritz method. We solve one- and two-dimensional problems
whose solutions are smooth, singular, and/or exhibit strong gradients. Results consistently
show the outperformance of employing radaptivity, while in some cases the
improvement is limited by the tensor-product structure of the mesh.IA4TES (MIA.2021.M04.008 / NextGenerationEU PRTR);
PDC2021-121093-I00 (MCIN/ AEI / 10.13039/501100011033/Next Generation EU
Scenarios for the appearance of strange attractors in a model of three interacting microbubble contrast agents
Get PDFWe study nonlinear dynamics in a model of three interacting encapsulated gas bubbles in a liquid. The model is a system of three coupled nonlinear oscillators with an external periodic force. Such bubbles have numerous applications, for instance, they are used as contrast agents in ultrasound visualization. Certain types of bubbles oscillations may be beneficial or undesirable depending on a given application and, hence, the dependence of the regimes of bubbles oscillations on the control parameters is worth studying. We demonstrate that there is a wide variety of types of dynamics in the model by constructing a chart of dynamical regimes in the control parameters space. Here we focus on hyperchaotic attractors characterized by three positive Lyapunov exponents and strange attractors with one or two positive Lyapunov exponents possessing an additional zero Lyapunov exponent, which have not been observed previously in the context of bubbles oscillations. We also believe that we provide a first example of a hyperchaotic attractor with additional zero Lyapunov exponent. Furthermore, the mechanisms of the onset of these types of attractors are still not well studied. We identify two-parametric regions in the control parameter space where these hyperchaotic and chaotic attractors appear and study one-parametric routes leading to them. We associate the appearance of hyperchaotic attractors with three positive Lyapunov exponents with the inclusion of a periodic orbit with a three-dimensional unstable manifold, while the onset of chaotic oscillations with an additional zero Lyapunov exponent is connected to the partial synchronization of bubbles oscillations. We propose several underlying bifurcation mechanisms that explain the emergence of these regimes. We believe that these bifurcation scenarios are universal and can be observed in other systems of coupled oscillators.RSF Grant No. 19-71-10048, RSFGrant No. 19-71-1000