2063 research outputs found
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THE INITIAL-TO-FINAL-STATE INVERSE PROBLEM WITH TIME-INDEPENDENT POTENTIALS
No full textThe initial-to-final-state inverse problem consists in determining a quantum Hamiltonian
assuming the knowledge of the state of the system at some fixed time, for every initial state. This
problem was formulated by Caro and Ruiz and motivated by the data-driven prediction problem in
quantum mechanics. Caro and Ruiz analysed the question of uniqueness for Hamiltonians of the form
´∆ ` V with an electric potential V“ Vpt,xq that depends on the time and space variables. In this
context, they proved that uniqueness holds in dimension n ě 2 whenever the potentials are bounded
and have super-exponential decay at infinity. Although their result does not seem to be optimal, one
would expect at least some degree of exponential decay to be necessary for the potentials. However,
in this paper, we show that by restricting the analysis to Hamiltonians with time-independent electric
potentials, namely V“ Vpxq, uniqueness can be established for bounded integrable potentials exhibiting
only super-linear decay at infinity, in any dimension n ě 2. This surprising improvement is possible
because, unlike Caro and Ruiz’s approach, our argument avoids the use of complex geometrical optics
(CGO). Instead, we rely on the construction of stationary states at different energies—this is possible
because the potential does not depend on time. These states will have an explicit leading term, given
by a Herglotz wave, plus a correction term that will vanish as the energy grows. Besides the significant
relaxation of decay assumptions on the potential, the avoidance of CGO solutions is important in its
own right, since such solutions are not readily available in more complicated geometric settings
Strengths and Pitfalls of classical interatomic potentials for the modelling of hydrogen embrittlement in BCC-Fe: A benchmarking analysis
Full text linkThe rational design of cost-effective, hydrogen-resistant structural materials is essential for establishing hydrogen as a competitive alternative to other emission-free storage technologies. To this end, atomistic models based on empirical interatomic potentials (IPs) provide valuable insights on the interplay between H diffusion and micromechanics at a fraction of the cost of electronic calculations. For the BCC-Fe – H system, several such IPs have been proposed and deployed under a wide variety of conditions. However, IP validation has largely been conducted in the infinite dilution limit and on the basis of thermodynamic metrics, leaving doubts on their accuracy under realistic hydrogen loads in dynamic settings. To address this shortcoming, we provide a comprehensive assessment of seven widely used IPs for the BCC-Fe–H system, encompassing the popular embedded atom (EAM), Modified EAM (MEAM) and bond-order (BOP) potential models. Our analysis incorporates critical metrics, including mechanical behavior under volumetric and uniaxial deformation, hydrogen distribution and kinetics, and grain boundary segregation at both moderate and high hydrogen concentrations. Our findings reveal significant discrepancies in predictive accuracy, along with system-size and simulation-length artifacts that are easily overlooked in the application of these IPs. Additionally, we identify an inherent failure of EAM-type IPs (the most frequently used IP type) to both prevent unrealistic H clustering and accurately estimate its transport properties. Lastly, we present a detailed ranking of the evaluated IPs and assess the overall-best performing model on a large polycrystal system, enabling researchers to make informed choices based on the specific requirements of their studies.MODEL2RESIST (6/12/TT/2024/00003
Bourgain’s Counterexample in the Sequential Convergence Problem for the Schrödinger Equation
Full text linkWe study the problem of pointwise convergence for the Schrödinger operator on along time sequences. We show that the sharp counterexample to the sequential Schrödinger maximal estimate given recently by Li, Wang and Yan based in the construction by Lucà and Rogers can also be achieved with the construction of Bourgain, and we extend it to the fractal setting
Biphasic changes in hippocampal granule cells after traumatic brain injury
Full text linkTraumatic brain injury (TBI) leads to a wide range of long-lasting physical and cognitive impairments. Changes in neuronal excitability and synaptic functions in the hippocampus have been proposed to underlie cognitive alterations. The dentate gyrus (DG) acts as a “gatekeeper” of hippocampal information processing and as a filter of excessive or aberrant input activity. In this study, we investigated the effects of controlled cortical impact, a model of TBI, on the excitability of granule cells (GCs) and spontaneous excitatory postsynaptic currents (sEPSCs) in the DG at three time points, 3 days, 15 days and 4 months after the injury in male and female mice. Our results indicate that changes in the short term are related to intrinsic properties, while changes in the long term are more related to input and synaptic activity, in agreement with the notion that TBI-related pathology courses with an acute phase and a later long-term secondary phase. A biphasic response, a reduction in the shorter term and an increase in the long term, was found in TBI neurons in the frequency of sEPSCs. These changes correlated with a loss of complexity in the pattern of the synaptic input, an alteration that could therefore play a role in the chronic and recurrent TBI-associated hyperexcitation.PID2023-146683OB-100 funded by MCIN/
AEI/10.13039/50110001103
Deep Fourier Residual method for solving time-harmonic Maxwell’s equations
Full text linkSolving PDEs with machine learning techniques has become a popular alternative to conventional
methods. In this context, Neural networks (NNs) are among the most commonly used machine learning
tools, and in those models, the choice of an appropriate loss function is critical. In general, the main
goal is to guarantee that minimizing the loss during training translates to minimizing the error in the
solution at the same rate. In this work, we focus on the time-harmonic Maxwell’s equations, whose weak
formulation takes H0(curl,Omega) as the space of test functions. We propose a NN in which the loss function
is a computable approximation of the dual norm of the weak-form PDE residual. To that end, we employ
the Helmholtz decomposition of the space H0(curl,Omega) and construct an orthonormal basis for this space
in two and three spatial dimensions. Here, we use the Discrete Sine/Cosine Transform to accurately
and efficiently compute the discrete version of our proposed loss function. Moreover, in the numerical
examples we show a high correlation between the proposed loss function and the H(curl)-norm of the
error, even in problems with low-regularity solutions.PDC2021-121093-I0
Supervised Learning with Evolving Tasks and Performance Guarantees
Full text linkMultiple supervised learning scenarios are composed by a sequence of classification tasks. For instance, multi-task learning and continual learning aim to learn a sequence of tasks that is either fixed or grows over time. Existing techniques for learning tasks that are in a sequence are tailored to specific scenarios, lacking adaptability to others. In addition, most of existing techniques consider situations in which the order of the tasks in the sequence is not relevant. However, it is common that tasks in a sequence are evolving in the sense that consecutive tasks often have a higher similarity. This paper presents a learning methodology that is applicable to multiple supervised learning scenarios and adapts to evolving tasks. Differently from existing techniques, we provide computable tight performance guarantees and analytically characterize the increase in the effective sample size. Experiments on benchmark datasets show the performance improvement of the proposed methodology in multiple scenarios and the reliability of the presented performance guarantees.PID2022-137063NBI00
PID2022-137442NB-I00
CNS2022-135203
CEX2021-001142-S
IT1504-2
Topology of Empirical Models
Full text linkAbramsky and Branderburger put forth a sheaf based interpretation of non-locality and contextuality as obstructions in inter-knitting local sections together to form a compatible global section. The synergistic interaction of a local function(s) in a global topological space unfolds novel behaviour emerging as a locally consistent but globally inconsistent pattern in data characterising this empirical phenomenon. We explore a general method to associate an explicit approximation of a topological space represented as a simplicial complex to the empirical models, witness- ing different strengths of contextuality; alongside their polyhedral description whose symmetries are subject to this structural constraint akin to sheafification based on information of tabular representation of these models. A local consistency corresponds to any possible polyhedral symmetry whereas a global consistency characterises symmetries that take a polyhedron back to itself subject to spatial constraints whose discrete representation quantifies contex- tuality through strong collapse as (non)existence of critical simplices and virtual loops using discrete Morse theory. The transient virtual loops characterise contextuality as a topological phase transition – a change in homotopy class – that turns relations locally consistent for an observer but globally non-extendable. We apply the framework on several empirical models in the foundation of quantum physics. The framework could provide a practical way to propose new models for witnessing higher dimensional contextuality in guiding physical experiments and linking the phenomenon to the evolution of geometric structures on 3-manifold theory. We provide two new basic models as examples to conceptualise the reverse of our framework of reproducing possibly higher dimensional tables from a given space and associated polyhedron that could lead to observation of new strength of hyper-contextual scenarios. A seven dimensional Mermin-Ardehali-Belinskii-Klyshko model with its graph-based description could be a first step to discover new structures on 3-manifolds for higher dimensional contextuality
The Bundle-Theoretic Structure and Computational Modeling of Quantum Contextuality
No full textWe propose a novel mathematical framework, rooted in fiber bundle theory, to quantify the phenomenon of quantum contextuality—a fundamental aspect of quantum entanglement. To demonstrate its utility, we first apply the formalism to quantum models in the foundations of quantum physics that both capture and differentiate varying strengths of contextuality. By revealing the intrinsic geometric structure of contextuality, the framework establishes a direct link to its computational foundations, facilitating the formulation of a topology-based model of computation that encapsulates the semantics inherent to contextuality. The framework delivers a rigorous and potentially more profound mathematical characterization of quantum contextuality, while offering new modeling methodologies for quantum cognition.PID2023-146683OB-100 funded by MICIU/AEI /10.13039/501100011033 and by ERDF, E
Accelerated and fast magnetic reconnection through enhanced resistive dissipation for MHD equations
No full textAbstract. We study the emergence of magnetic reconnection, understood as a change in the
topology of magnetic field lines, for sufficiently regular solutions of the three-dimensional periodic
magnetohydrodynamic (MHD) equations. We construct initial data for which reconnection takes
place on time scales strictly shorter than the resistive one, due to enhanced dissipation effects
driven by the advective dynamics. This provides, to our knowledge, the first rigorous examples
where the advection term plays a genuinely active role in the reconnection process. A key aspect of
our argument is a quantitative propagation of enhanced dissipation to Sobolev norms, which may
be of independent interest beyond its application to the MHD equations
On the Three Balls Inequality for Discrete Schr{ö}dinger Operators on Certain Periodic Graphs
No full textWe investigate quantitative unique continuation properties
for discrete magnetic Schrödinger operators in certain periodic
graphs. This unique continuation property will be quantified through
what is known in the literature as a Three Balls Inequality. We are able
to extend this inequality to another family of periodic graph which
contains the Hexagonal lattice. We also give a sketch of the proof for
general star periodic graph. Our proofs are based on Carleman estimates