2063 research outputs found
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Importance of methodological choices in data manipulation for validating epileptic seizure detection models
Get PDFEpilepsy is a chronic neurological disorder that affects a significant portion of the human population and imposes serious risks in the daily life. Despite advances in machine learning and IoT, small, non-stigmatizing wearable devices for continuous monitoring and detection in outpatient environments are not yet widely available. Part of the reason is the complexity of epilepsy itself, including highly imbalanced data, multimodal nature, and very subject-specific signatures. However, another problem is the heterogeneity of methodological approaches in research, leading to slower progress, difficulty in comparing results, and low reproducibility. Therefore, this article identifies a wide range of methodological decisions that must be made and reported when training and evaluating the performance of epilepsy detection systems. We characterize the influence of individual choices using a typical ensemble random-forest model and the publicly available CHB-MIT database, providing a broader picture of each decision and giving good-practice recommendations, based on our experience, where possible.RYC2021-032853-
ON THE TRIPLE JUNCTION PROBLEM ON THE PLANE WITHOUT SYMMETRY HYPOTHESES
No full textWe investigate the Allen-Cahn system
∆u− Wu(u) = 0, u : R2 → R2
,
where W ∈ C2(R2
, [0, +∞)) is a potential with three global minima. We establish the existence of
an entire solution u which possesses a triple junction structure. The main strategy is to study the
global minimizer uε of the variational problem
min ˆB
ε
2 |∇u|2 +
1
ε
W (u) dz, u= gε on ∂B1.
The point of departure is an energy lower bound that plays a crucial role in estimating the location
and size of the diffuse interface. We do not impose any symmetry hypothesis on the solution
Invariants for neural automata
Get PDFComputational modeling of neurodynamical systems often deploys neural networks and symbolic dynamics. One particular way for combining these approaches within a framework called vector symbolic architectures leads to neural automata. Specifically, neural automata result from the assignment of symbols and symbol strings to numbers, known as Gödel encoding. Under this assignment, symbolic computation becomes represented by trajectories of state vectors in a real phase space, that allows for statistical correlation analyses with real-world measurements and experimental data. However, these assignments are usually completely arbitrary. Hence, it makes sense to address the problem which aspects of the dynamics observed under a Gödel representation is intrinsic to the dynamics and which are not. In this study, we develop a formally rigorous mathematical framework for the investigation of symmetries and invariants of neural automata under different encodings. As a central concept we define patterns of equality for such systems. We consider different macroscopic observables, such as the mean activation level of the neural network, and ask for their invariance properties. Our main result shows that only step functions that are defined over those patterns of equality are invariant under symbolic recodings, while the mean activation, e.g., is not. Our work could be of substantial importance for related regression studies of real-world measurements with neurosymbolic processors for avoiding confounding results that are dependant on a particular encoding and not intrinsic to the dynamics.RTI2018-093860-BC21 funded by (AEI/FEDER, UE) and acronym MathNEURO
PID2020-117281GB-I00
PID2019-107444GA-I00
European Regional Development Fund (ERDF)
Basque Government, grant IT1483-2
Slow–fast dynamics in a neurotransmitter release model: Delayed response to a time-dependent input signal
Get PDFWe propose a generalization of the neurotransmitter release model proposed in Rodrigues et al. (2016). We increase the complexity of the underlying slow–fast system by considering a degree-four polynomial as parametrization of the critical manifold. We focus on the possible transient and asymptotic dynamics, exploiting the so-called entry–exit function to describe slow parts of the dynamics. We provide extensive numerical simulations, complemented by numerical bifurcation analysis.Italian Ministry for University and Research (MUR) through the PRIN 2020 project ‘‘Integrated Mathematical Approaches to Socio-Epidemiological Dynamics’’ (No. 2020JLWP23);
Elkartek project ‘‘Onbody’’ code KK-2023/00070;
Inria Associated Team NeuroTransS
Fast Computation of Cluster Validity Measures for Bregman Divergences and Benefits
Get PDFPartitional clustering is one of the most relevant unsupervised learning and pattern recognition techniques. Unfortunately, one of the main drawbacks of these methodologies refer to the fact that the number of clusters is generally assumed to be known beforehand and automating its selection is not straightforward. On the same token, internal validity measures, such as the Silhouette index, Davies-Bouldin and Caliski-Harabasz measures have emerged as the standard techniques to be used when comparing the goodness of clustering results obtained via different clustering methods. These measures take into consideration both the inter and intra-cluster simmilarities and can be adapted to different metrics. Unfortunately, their used has been hindered due to their large computational complexities, which are commonly quadratic with respect to the number of instances of the data set. In this work, we show that the time complexity of computing the most popular internal validity measures can be utterly reduced by making used of the within-cluster errors and different properties of the Bregman divergences. This contribution ultimately allows us to massively speed-up the selection of an adequate number of clusters for a given data set as verified with extensive empirical comparisons.TIN2017-82626-
Non-affine motion and selection of slip coefficient in constitutive modeling of polymeric solutions using a mixed derivative
Get PDFConstitutive models for the dynamics of polymer solutions traditionally rely on closure relations for the extra stress or related microstructural variables (e.g., conformation tensor) linking them to flow history. In this work, we study the eigendynamics of the conformation tensor within the GENERIC framework in mesoscopic computer simulations of polymer solutions to separate the effects of nonaffine motion from other sources of non-Newtonian behavior. We observe that nonaffine motion or slip increases with both the polymer concentration and the polymer chain length. Our analysis allows to uniquely calibrate a mixed derivative of the Gordon-Schowalter type in macroscopic models based on a micro-macromapping of the dynamics of the polymeric system. The presented approach paves the way for better polymer constitutive modeling in multiscale simulations of polymer solutions, where different sources of non-Newtonian behavior are modelled independently
Modelling the behavior of human crowds as coupled active-passive dynamics of interacting particle systems
Get PDFThe modelling of human crowd behaviors offers many challenging questions to science in general.
Specifically, the social human behavior consists of many physiological and psychological processes
which are still largely unknown. To model reliably such human crowd systems with complex social
interactions, stochastic tools play an important role for the setting of mathematical formulations
of the problems. In this work, using the description based on an exclusion principle, we study
a statistical-mechanics-based lattice gas model for active-passive population dynamics with an
application to human crowd behaviors. We provide representative numerical examples for the
evacuation dynamics of human crowds, where the main focus in our considerations is given to
an interacting particle system of active and passive human groups. Furthermore, our numerical
results show that the communication between active and passive humans strongly influences the
evacuation time of the whole population even when the “faster-is-slower” phenomenon is taken
into account. To provide an additional inside into the problem, a stationary state of our model is
analyzed via current representations and heat map techniques. Finally, future extensions of the
proposed models are discussed in the context of coupled data-driven modelling of human crowds
and traffic flows, vital for the design strategies in developing intelligent transportation systems
Supervised Learning in Time-dependent Environments with Performance Guarantees
Get PDFIn practical scenarios, it is common to learn from a sequence of related problems (tasks).
Such tasks are usually time-dependent in the sense that consecutive tasks are often
significantly more similar. Time-dependency is common in multiple applications such
as load forecasting, spam main filtering, and face emotion recognition. For instance, in
the problem of load forecasting, the consumption patterns in consecutive time periods
are significantly more similar since human habits and weather factors change gradually
over time. Learning from a sequence tasks holds promise to enable accurate performance
even with few samples per task by leveraging information from different tasks. However,
harnessing the benefits of learning from a sequence of tasks is challenging since tasks
are characterized by different underlying distributions.
Most existing techniques are designed for situations where the tasks’ similarities
do not depend on their order in the sequence. Existing techniques designed for timedependent
tasks adapt to changes between consecutive tasks accounting for a scalar
rate of change by using a carefully chosen parameter such as a learning rate or a weight
factor. However, the tasks’ changes are commonly multidimensional, i.e., the timedependency
often varies across different statistical characteristics describing the tasks.
For instance, in the problem of load forecasting, the statistical characteristics related
to weather factors often change differently from those related to generation.
In this dissertation, we establish methodologies for supervised learning from a sequence
of time-dependent tasks that effectively exploit information from all tasks,
provide multidimensional adaptation to tasks’ changes, and provide computable tight
performance guarantees. We develop methods for supervised learning settings where
tasks arrive over time including techniques for supervised classification under concept
drift (SCD) and techniques for continual learning (CL). In addition, we present techniques
for load forecasting that can adapt to time changes in consumption patterns
and assess intrinsic uncertainties in load demand. The numerical results show that the
proposed methodologies can significantly improve the performance of existing methods
using multiple benchmark datasets. This dissertation makes theoretical contributions
leading to efficient algorithms for multiple machine learning scenarios that provide computable
performance guarantees and superior performance than state-of-the-art techniques
Physics-guided deep-learning inversion method for the interpretation of noisy logging-while-drilling resistivity measurements
Get PDFDeep learning (DL) inversion is a promising method for real-Time interpretation of logging-while-drilling (LWD) resistivity measurements for well-navigation applications. In this context, measurement noise may significantly affect inversion results. Existing publications examining the effects of measurement noise on DL inversion results are scarce. We develop a method to generate training data sets and construct DL architectures that enhance the robustness of DL inversion methods in the presence of noisy LWD resistivity measurements. We use two synthetic resistivity models to test the three approaches that explicitly consider the presence of noise: (1) adding noise to the measurements in the training set, (2) augmenting the training set by replicating it and adding varying noise realizations and (3) adding a noise layer in the DL architecture. Numerical results confirm that each of the three approaches enhances the noise-robustness of the trained DL inversion modules, yielding better inversion results-in both the predicted earth model and measurements-compared to the basic DL inversion and also to traditional gradient-based inversion results. A combination of the second and third approaches delivers the best results
Morning naps architecture and mentation recall complexity
Get PDFMentation reports were collected after spontaneous awakenings from morning naps in 18 healthy participants, and associations between sleep stages duration and complexity of recalled mentation were investigated. Participants were continuously recorded with polysomnography and allowed to sleep for a maximum of 2 hr. Mentation reports were classified according to both their complexity (1–6 scale) and their perceived timing of occurrence (Recent or Previous Mentation with respect to the final awakening). The results showed a good level of mentation recall, including different types of mentation with lab-related stimuli. N1 + N2 duration was positively related to the complexity of Previous Mentation recall, while rapid eye movement sleep duration was negatively related. This suggests that the recall of complex mentation, such as dreaming with a plot, occurring far from awakening may depend on the length of N1 + N2. However, the duration of sleep stages did not predict the complexity of Recent Mentation recall. Nevertheless, 80% of participants who recalled Recent Mentation had a rapid eye movement sleep episode. Half of the participants reported incorporating lab-related stimuli in their mentation, which positively correlated with both N1 + N2 and rapid eye movement duration. In conclusion, nap sleep architecture is informative about the complexity of dreams perceived as having occurred early during the sleep episode, but not about those perceived as recent