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A data-driven study on implicit LES using a spectral difference method
No full textIn this paper, we introduce a data-driven filter to analyze the relationship between Implicit Large-Eddy Simulations (ILES) and Direct Numerical Simulations (DNS) in the context of the Spectral Difference method. The proposed filter is constructed from a linear combination of sharp-modal filters where the weights are given by a convolutional neural network trained to replicate ILES results from filtered DNS data. In order to preserve the compactness of the discretization, the filter is local in time and acts at the elementary cell level. The neural network is trained on the data generated from the Taylor-Green Vortex test-case at Re=1600. In order to mitigate the temporal effects and highlight the influence of the spatial discretization, the ILESs are periodically restarted from DNS data for different time windows. Smaller time windows result in higher cross-correlations between ILES and the filtered DNS snapshots using the data-driven filters. The modal decay of the filter for the smallest time window considered aligns with classical eigenanalysis, showing better energy conservation for higher orders of approximation. Similarly, an analysis of the filter's kernel in the Fourier space confirms that higher polynomial orders are less dissipative compared to lower orders. As large time windows are considered, the trained filter encounters difficulties in representing the data due to significant non-linear effects. Additionally, the impact of the data-driven filter on the resolved kinetic energy has been assessed through the evaluation of the sub-grid production term which results in both direct and inverse cascades with the former being more likely on average. The presence of backscatter suggests that ILESs based on Discontinuous Spectral Element Methods might be equipped with an intrinsic mechanism to transfer energy in both directions with a predominance of direct kinetic energy cascade. Finally, it was shown that the learned filters can be used as test-filters within a self-similarity context for a-posteriori computations. The models have been evaluated at a Reynolds number (Re=5000) and grid resolution not included in the training data
Exploring the impact of SerpinA3n deficiency on prion strains propagation
No full textTransmissible spongiform encephalopathies (TSEs) are a group of devastating neurodegenerative diseases characterized by the conversion of the normal cellular prion protein (PrPC) into its misfolded, pathogenic form, PrPSc. Despite significant research, the exact molecular mechanisms driving PrPC to PrPSc conversion remain elusive and are thought to involve multiple molecules or cofactors. One protein of interest, SERPINA3 (murine SerpinA3n), is an acute-phase protein, a member of the serine protease inhibitor family. Intriguingly, SERPINA3 expression is notably upregulated in the brains of patients with Creutzfeldt-Jakob disease and in mice experimentally infected with prions, suggesting a potential role in prion disease pathology. In this study, we deepened the role of SerpinA3n in prion conversion and propagation by utilizing SerpinA3n-deficient (SerpinA3n−/−) mice intracerebrally injected with the RML, 139A, or ME7 prion strains. Our results showed that the specific absence of SerpinA3n did not significantly affect prion propagation, as evidenced by the lack of notable changes in clinical and neuropathological assessments. Compensatory mechanisms involving other serpins or molecules may mitigate the effects of the specific absence of SerpinA3n, thereby maintaining efficient prion propagation
Deep learning solutions to singular ordinary differential equations: From special functions to spherical accretion
No full textSingular regular points often arise in differential equations describing physical phenomena such as fluid dynamics, electromagnetism, and gravitation. Traditional numerical techniques often fail or become unstable near these points, requiring the use of semianalytical tools, such as series expansions and perturbative methods, in combination with numerical algorithms; or to invoke more sophisticated methods. In this work, we take an alternative route and leverage the power of machine learning to exploit physics informed neural networks (PINNs) as a modern approach to solving ordinary differential equations with singular points. PINNs utilize deep learning architectures to approximate solutions by embedding the differential equations into the loss function of the neural network. We discuss the advantages of PINNs in handling singularities, particularly their ability to bypass traditional grid-based methods and provide smooth approximations across irregular regions. Techniques for enhancing the accuracy of PINNs near singular points, such as adaptive loss weighting, are used in order to achieve high efficiency in the training of the network. We exemplify our results by studying four differential equations of interest in mathematics and gravitation - the Legendre equation, the hypergeometric equation, the solution for black hole space-times in theories of Lorentz violating gravity, and the spherical accretion of a perfect fluid in a Schwarzschild geometry
On the lower bound of the curvature exponent on step-two Carnot groups
No full textIn this work, we show that there exists a step-two Carnot group on which the new lower bound of the curvature exponent given in Golo and Zhang [Anal. Geom. Metr. Spaces 12 (2024), p. 30] can be strictly less than the curvature exponent by studying the convergence of the structure constants of Lie algebra
Unveiling the warm molecular outflow component of type-2 quasars with SINFONI
No full textWe present seeing-limited (0.8′′) near-infrared integral field spectroscopy data of the type-2 quasars, QSO2s, SDSS J135646.10+102609.0 (J1356) and SDSS J143029.89+133912.1 (J1430, the Teacup), both belonging to the Quasar Feedback, QSOFEED, sample. The nuclear K-band spectra (1.95-2.45 μm) of these radio-quiet QSO2s reveal several H2 emission lines, indicative of the presence of a warm molecular gas reservoir (T ≥ 1000 K). We measure nuclear masses of MH2 = 5.9, 4.1, and 1.5 × 103 M⊙ in the inner 0.8′′ diameter region of the Teacup (∼1.3 kpc), J1356 north (J1356N), and south nuclei (∼1.8 kpc), respectively. The total warm H2 mass budget is ∼4.5 × 104 M⊙ in the Teacup and ∼1.3 × 104 M⊙ in J1356N, implying warm-to-cold molecular gas ratios of 10-6. The warm molecular gas kinematics, traced with the H21-0S(1) and S(2) emission lines, is consistent with that of the cold molecular phase, traced by ALMA CO emission at higher angular resolution (0.2′′ and 0.6′′). In J1430, we detect the blue- and red-shifted sides of a compact warm molecular outflow extending up to 1.9 kpc and with velocities of 450 km s-1. In J1356 only the red-shifted side is detected, with a radius of up to 2.0 kpc and velocity of 370 km s-1. The outflow masses are 2.6 and 1.5 × 103 M⊙ for the Teacup and J1356N, and the warm-to-cold gas ratios in the outflows are 0.8 and 1 × 10-4, implying that the cold molecular phase dominates the mass budget. We measure warm molecular mass outflow rates of 6.2 and 2.9 × 10-4 M⊙ yr-1 for the Teacup and J1356N, which are approximately 0.001% of the total mass outflow rate (ionized + cold and warm molecular). We find an enhancement of velocity dispersion in the H21-0S(1) residual dispersion map of the Teacup, both along and perpendicular to the compact radio jet direction. This enhanced turbulence can be reproduced by simulations of jet-ISM interactions
Large-Scale Response Theory for Gapless Lattice Fermi Systems in Low Dimensions
No full textThis thesis develops a rigorous large-scale response theory for gapless lattice Fermi systems in low dimensions, focusing on the mathematical validity of linear response -- the Kubo formula -- for transport in gapless systems, where the absence of a spectral gap prevents the direct use of standard adiabatic theorems.
After reviewing fundamental results on many-body lattice fermions, we first analyse the transport properties of non-interacting, gapless, one-dimensional quantum systems and of the edge modes of two-dimensional topological insulators. We prove the validity of the Kubo formula, in the zero-temperature and infinite-volume limit, for perturbations that are weak and slowly varying in space and time. The proof relies on expressing the real-time Duhamel series in imaginary time, which ensures its convergence uniformly in the scaling parameter and system size, at low temperatures. This representation also reveals a key cancellation in the scaling limit, linked to the emergent anomalous chiral symmetry of relativistic one-dimensional fermions. As a consequence, in the combined low-temperature and scaling limit, the linear response provides the full physical response. In particular, the method yields a dynamical proof of the quantisation of edge conductance in two-dimensional quantum Hall systems.
The analysis is then extended to weakly interacting, gapless one-dimensional fermionic systems, for which we obtain explicit expressions for the response functions in terms of renormalised Fermi velocities. Here, sharp estimates for interacting Euclidean correlation functions are established via rigorous renormalisation-group methods. The asymptotic exactness of linear response persists due to a cancellation in the scaling limit of the correlations -- reminiscent of bosonisation -- derived rigorously from emergent chiral Ward identities
FAIR Data in Practice: Riverine Litter Data Standardization and Nanopore Sequencing Workflow Validation
No full textThis thesis explores the operationalization and challenges to the implementation of the FAIR
(Findable, Accessible, Interoperable, Reusable) data principles in two very different scientific
domains (riverine litter data management; nanopore sequencing data analysis). It responded to a
growing need for structured frameworks for data management in the wake of exponential growth in
scientific data generation, as many earnestly present and operationalized datasets suffer from
fragmentation, no documentation, and are difficult to reuse.
The first project sought to standardize and migrate a large riverine litter dataset from 716 micro
research campaigns, with 12,143 samples, across waterways around the world from a heterogeneous
excel format to a normalized MySQL database. The second project developed an automated Pythonbased tool for validating and analyzing Oxford Nanopore sequencing outputs that improved quality
assessment and metadata extraction from a variety of output file formats.
Both applications showed marked improvements in data utility, despite a series of challenges, which
were data heterogeneity, persistent identifier adoption, and limitations on resources. The riverine
litter database was able to undergo full migration to using more standardized terminology and
hierarchical classification systems enabling cross-continental comparisons. The sequencing analysis
application was able to implement automated quality assessments, context-aware reports, and tiered
metadata extraction activities which shortened the time-to-insight for sequencing run assessments.
Despite the recognition that FAIR principles would require considerable adaptations specific to the
scientific domain, the results showed each time the adaptations were successfully completed the
practical benefits outweighed the adaptations in terms of improved data discoverability, decreased
redundancy, and improved reproducibility. The project delivers economic impact and highlights the
dangers of duplicated, wasted research efforts if FAIR principles are adopted, but stresses the need
for institutional policies, specialized training, and long-lasting supportive technical infrastructure
for further FAIR implementation across science
Gravothermalizing into primordial black holes, boson stars, and cannibal stars
No full textVery little is known about the cosmological history from after the end of inflation until big bang nucleosynthesis. Various well-motivated models predict that the universe could have undergone a period of matter domination in this early epoch. We demonstrate that if the particles causing matter domination have self-interactions, they can form halos that undergo a gravothermal collapse. We thus propose a novel scenario for the formation of primordial black holes, which in particular can lie within the asteroid-mass range. We also find that it is not only black holes that can form in the aftermath of a gravothermal evolution. We show that number-changing annihilations of the particles can create sufficient heat to halt the gravothermal evolution, thus forming a "cannibal star." Likewise, the pressure from the particle's repulsive self-interactions can form a boson star during a gravothermal evolution. These stars can also eventually collapse into black holes. Thus, our study highlights that structure formation in the early universe can have a rich phenomenology
Learning Beyond the Gaussian Approximation: Algorithmic Hardness, Neural Network Dynamics and Independent Components
No full textNeural networks excel at discovering statistical patterns in high-dimensional data sets. In practice, higher-order cumulants, which quantify the non-Gaussian correlations between three or more variables, are particularly important for the performance of neural networks. In this thesis we study the efficiency of neural networks at extracting features from higher-order cumulants.
We first discuss the fundamental statistical and computational limits of recovering a single non-Gaussian direction, by computing the number of samples~n required to reliably distinguish between inputs from the spiked cumulant model and isotropic Gaussian inputs.
Our findings confirm the existence of a wide statistical-to-computational gap: statistical distinguishability requires n > d samples, while distinguishing the two distributions in polynomial time requires n > d^2 samples for the class of algorithms covered by the low degree conjecture.
Numerical experiments show that neural networks do indeed learn to distinguish the two distributions with quadratic sample complexity. Then, to further bridge the gap between theory and practice, we show that correlations between latent variables along the directions encoded in different input cumulants speed up learning from higher-order cumulants, reaching linear sample complexity. We show this effect analytically by deriving nearly sharp thresholds for the number of samples required by a single neuron to weakly-recover these directions using online SGD from a random start in high dimensions. Our analytical results are confirmed in simulations of two-layer neural networks and unveil a new mechanism for hierarchical learning in neural networks.
Finally we connect to feature learning of deep networks via the proxy of independent component analysis (ICA), a simple unsupervised method that seeks the most non-Gaussian projections of its inputs. The motivation is that ICA finds features that are similar to the first-layer filters learned by deep convolutional networks on classification tasks. This similarity suggests that ICA provides a simple, yet principled model for studying feature learning.
Here, we prove that FastICA, the most popular ICA algorithm, requires at least n> d^4 samples to recover a single non-Gaussian direction from d-dimensional inputs on a simple synthetic data model. We show that vanilla online SGD outperforms FastICA, and prove that the optimal sample complexity n > d^2 can be reached by smoothing the loss, albeit in a data-dependent way.
We conclude by discussing how this picture extends to different distributions and architectures, such as generative diffusion models
Existence and blow-up for non-autonomous scalar conservation laws with viscosity
No full textWe consider a question posed in [1], namelytheblow-upofthePDEut+(b(t, x)u1+k)x=uxxwhenbisuniformlybounded,Lipschitzandk=2.WegiveacompleteanswertothebehaviorofsolutionswhenbbelongstotheLorentzspacesb is an element of Lp,infinity,p is an element of(2,infinity],orbx is an element of Lp,infinity,p is an element of(1,infinity].(c) 2024ElsevierInc.Allrightsarereserved,includingthosefortextanddatamining,AItraining,andsimilartechnologies