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Objective: This study explores a semi-supervised learning (SSL), pseudo-labeled strategy using diverse datasets to enhance lung cancer (LCa) survival predictions, analyzing Handcrafted and Deep Radiomic Features (HRF/DRF) from PET/CT scans with Hybrid Machine Learning Systems (HMLS). Methods: We collected 199 LCa patients with both PET & CT images, obtained from The Cancer Imaging Archive (TCIA) and our local database, alongside 408 head&neck cancer (HNCa) PET/CT images from TCIA. We extracted 215 HRFs and 1024 DRFs by PySERA and a 3D-Autoencoder, respectively, within the ViSERA software, from segmented primary tumors. The supervised strategy (SL) employed a HMLSs: PCA connected with 4 classifiers on both HRF and DRFs. SSL strategy expanded the datasets by adding 408 pseudo-labeled HNCa cases (labeled by Random Forest algorithm) to 199 LCa cases, using the same HMLSs techniques. Furthermore, Principal Component Analysis (PCA) linked with 4 survival prediction algorithms were utilized in survival hazard ratio analysis. Results: SSL strategy outperformed SL method (p-value<0.05), achieving an average accuracy of 0.85 with DRFs from PET and PCA+ Multi-Layer Perceptron (MLP), compared to 0.65 for SL strategy using DRFs from CT and PCA+ K-Nearest Neighbor (KNN). Additionally, PCA linked with Component-wise Gradient Boosting Survival Analysis on both HRFs and DRFs, as extracted from CT, had an average c-index of 0.80 with a Log Rank p-value<<0.001, confirmed by external testing. Conclusions: Shifting from HRFs and SL to DRFs and SSL strategies, particularly in contexts with limited data points, enabling CT or PET alone to significantly achieve high predictive performance., Comment: 12 pages and 7 figures

Many numerical algorithms and learning tasks rest on solution of the Monge-Kantorovich problem and corresponding Wasserstein distances. While the natural approach is to treat the problem as an infinite-dimensional linear programming, such a methodology severely limits the computational performance due to the polynomial scaling with respect to the sample size along with intensive memory requirements. We propose a novel alternative framework to address the Monge-Kantorovich problem based on a projection type gradient descent scheme. The micro-dynamics is built on the notion of the conditional expectation, where the connection with the opinion dynamics is explored and leveraged to build compact numerical schemes. We demonstrate that the devised dynamics recovers random maps with favourable computational performance. Along with the theoretical insight, the provided dynamics paves the way for innovative approaches to construct numerical schemes for computing optimal transport maps as well as Wasserstein distances.

SHAP values are a popular local feature-attribution method widely used in interpretable and explainable AI. We tackle the problem of efficiently computing these values. We cover both the model-agnostic (black-box) setting, where one only has query access to the model and also the case of (ensembles of) trees where one has access to the structure of the tree. For both the black-box and the tree setting we propose a two-stage approach for estimating SHAP values. Our algorithm's first step harnesses recent results showing that many real-world predictors have a spectral bias that allows us to either exactly represent (in the case of ensembles of decision trees), or efficiently approximate them (in the case of neural networks) using a compact Fourier representation. In the second step of the algorithm, we use the Fourier representation to exactly compute SHAP values. The second step is computationally very cheap because firstly, the representation is compact and secondly, we prove that there exists a closed-form expression for SHAP values for the Fourier basis functions. Furthermore, the expression we derive effectively linearizes the computation into a simple summation and is amenable to parallelization on multiple cores or a GPU. Since the function approximation (first step) is only done once, it allows us to produce Shapley values in an amortized way. We show speedups compared to relevant baseline methods equal levels of accuracy for both the tree and black-box settings. Moreover, this approach introduces a reliable and fine-grained continuous trade-off between computation and accuracy through the sparsity of the Fourier approximation, a feature previously unavailable in all black-box methods., Comment: Submitted as a conference paper to ICLR 2025

The visual cortex is a vital part of the brain, responsible for hierarchically identifying objects. Understanding the role of the lateral geniculate nucleus (LGN) as a prior region of the visual cortex is crucial when processing visual information in both bottom-up and top-down pathways. When visual stimuli reach the retina, they are transmitted to the LGN area for initial processing before being sent to the visual cortex for further processing. In this study, we introduce a deep convolutional model that closely approximates human visual information processing. We aim to approximate the function for the LGN area using a trained shallow convolutional model which is designed based on a pruned autoencoder (pAE) architecture. The pAE model attempts to integrate feed forward and feedback streams from/to the V1 area into the problem. This modeling framework encompasses both temporal and non-temporal data feeding modes of the visual stimuli dataset containing natural images captured by a fixed camera in consecutive frames, featuring two categories: images with animals (in motion), and images without animals. Subsequently, we compare the results of our proposed deep-tuned model with wavelet filter bank methods employing Gabor and biorthogonal wavelet functions. Our experiments reveal that the proposed method based on the deep-tuned model not only achieves results with high similarity in comparison with human benchmarks but also performs significantly better than other models. The pAE model achieves the final 99.26% prediction performance and demonstrates a notable improvement of around 28% over human results in the temporal mode., Comment: 14 pages, 14 figures, and 1 table

We study the cosmic microwave background (CMB) radiation in the unified description of the effective field theory (EFT) of dark energy that accommodates both scalar-tensor and vector-tensor theories. The boundaries of different classes of theories are universally parameterised by a new EFT parameter $\alpha_V$ characterising the vectorial nature of dark energy and a set of consistency relations associated with the global/local shift symmetry. After implementing the equations of motion in a Boltzmann code, as a demonstration, we compute the CMB power spectrum based on the $w$CDM background with the EFT parameterisation of perturbations and a concrete Horndeski/generalised Proca theory. We show that the vectorial nature generically prevents modifications of gravity in the CMB spectrum. On the other hand, while the shift symmetry is less significant in the perturbation equations unless the background is close to the $\Lambda$CDM, it requires that the effective equation of state of dark energy is in the phantom region $w_{\rm DE}<-1$. The latter is particularly interesting in light of the latest result of the DESI+CMB combination as the observational verification of $w_{\rm DE}>-1$ can rule out shift-symmetric theories including vector-tensor theories in one shot., Comment: 21 pages, 4 figures, 1 table

Contrary to conformal transformations, disformal transformations can change the principal null directions of a spacetime geometry. Thus, depending on the frame a gravitational wave (GW) detector minimally couples to, the properties of GWs may change under a disformal transformation. In this paper, we provide \textit{necessary} and \textit{sufficient} conditions which determine whether GWs change under disformal transformations or not. Our argument is coordinate-independent and can be applied to any spacetime geometry at the fully non-linear level. As an example, we show that an exact radiative solution of massless Einstein-scalar gravity which admits only shear-free parallel transported frame is mapped to a disformed geometry which does not possess any shear-free parallel transported frame. This radiative geometry and its disformed counterpart provide a concrete example of the possibility to generate tensorial GWs from a disformal transformation at the fully non-linear level. This type of non-linear effect can be completely overlooked in the usual linear perturbation theory., Comment: 12 pages, 1 figure

We present and analyze a new non-perturbative radiative solution of Horndeski gravity. This exact solution is constructed by a disformal mapping of a seed solution of the shift-symmetric Einstein-Scalar system belonging to the Robinson-Trautman geometry describing the gravitational radiation emitted by a time-dependent scalar monopole. After analyzing in detail the properties of the seed, we show that while the general relativity solution allows for shear-free parallel transported null frames, the disformed solution can only admit parallel transported null frames with a non-vanishing shear. This result shows that, at the nonlinear level, the scalar-tensor mixing descending from the higher-order terms in Horndeski dynamics can generate shear out of a pure scalar monopole. We further confirm this analysis by identifying the spin-0 and spin-2 polarizations in the disformed solution using the Penrose limit of our radiative solution. Finally, we compute the geodesic motion and the memory effects experienced by two null test particles with vanishing initial relative velocity after the passage of the pulse. This exact radiative solution offers a simple framework to witness nonlinear consequences of the scalar-tensor mixing in higher-order scalar-tensor theories., Comment: 31 pages, 9 figures

We formulate the effective field theory (EFT) of vector-tensor gravity for perturbations around an arbitrary background with a ${\it timelike}$ vector profile, which can be applied to study black hole perturbations. The vector profile spontaneously breaks both the time diffeomorphism and the $U(1)$ symmetry, leaving their combination and the spatial diffeomorphism as the residual symmetries in the unitary gauge. We derive two sets of consistency relations which guarantee the residual symmetries of the EFT. Also, we provide the dictionary between our EFT coefficients and those of generalized Proca (GP) theories, which enables us to identify a simple subclass of the EFT that includes the GP theories as a special case. For this subclass, we consider the stealth Schwarzschild(-de Sitter) background solution with a constant temporal component of the vector field and study the decoupling limit of the longitudinal mode of the vector field, explicitly showing that the strong coupling problem arises due to vanishing sound speeds. This is in sharp contrast to the case of gauged ghost condensate, in which perturbations are weakly coupled thanks to certain higher-derivative terms, i.e., the scordatura terms. This implies that, in order to consistently describe this type of stealth solutions within the EFT, the scordatura terms must necessarily be taken into account in addition to those already included in the simple subclass., Comment: 33 pages. Matches JCAP version

This study investigates the influence of varying illumination levels on architectural experiences by employing a comprehensive approach that combines self-reported assessments and neurophysiological measurements. Thirty participants were exposed to nine distinct illumination conditions in a controlled virtual reality environment. Subjective assessments, collected through questionnaires in which participants were asked to rate how pleasant, interesting, exciting, calming, complex, bright and spacious they found the space. Objective measurements of brain activity were collected by electroencephalogram (EEG). Data analysis demonstrated that illumination levels significantly influenced cognitive engagement and different architectural experience indicators. This alignment between subjective assessment and EEG data underscores the relationship between illuminance and architectural experiences. The study bridges the gap between quantitative and qualitative assessments, providing a deeper understanding of the intricate connection between lighting conditions and human responses. These findings contribute to the enhancement of environmental design based on neuroscientific insights, emphasizing the critical role of well-considered daylighting design in positively influencing occupants' cognitive and emotional states within built environments.

We formulate cosmological perturbation theory around the spatially curved FLRW background in the context of metric-affine gauge theory of gravity which includes torsion and nonmetricity. Performing scalar-vector-tensor decomposition of the spatial perturbations, we find that the theory displays a rich perturbation spectrum with helicities 0, 1, 2 and 3, on top of the usual scalar, vector and tensor metric perturbations arising from Riemannian geometry. Accordingly, the theory provides a diverse phenomenology, e.g. the helicity-2 modes of the torsion and/or nonmetricity tensors source helicity-2 metric tensor perturbation at the linear level leading to the production of gravitational waves. As an immediate application, we study linear perturbation of the nonmetricity helicity-3 modes for a general parity-preserving action of metric-affine gravity which includes quadratic terms in curvature, torsion, and nonmetricity. We then find the conditions to avoid possible instabilities in the helicity-3 modes of the spin-3 field., Comment: Matches published version in PRD. 23+20 pages, 5 appendices

Maximum-Entropy Distributions offer an attractive family of probability densities suitable for moment closure problems. Yet finding the Lagrange multipliers which parametrize these distributions, turns out to be a computational bottleneck for practical closure settings. Motivated by recent success of Gaussian processes, we investigate the suitability of Gaussian priors to approximate the Lagrange multipliers as a map of a given set of moments. Examining various kernel functions, the hyperparameters are optimized by maximizing the log-likelihood. The performance of the devised data-driven Maximum-Entropy closure is studied for couple of test cases including relaxation of non-equilibrium distributions governed by Bhatnagar-Gross-Krook and Boltzmann kinetic equations.

The kinetic theory of rarefied gases and numerical schemes based on the Boltzmann equation have evolved to the cornerstone of non-equilibrium gas dynamics. However, their counterparts in the dense regime remain rather exotic for practical non-continuum scenarios. This problem is partly due to the fact that long-range interactions arising from the attractive tail of molecular potentials, lead to a computationally demanding Vlasov integral. This study focuses on numerical remedies for efficient stochastic particle simulations based on the Enskog-Vlasov kinetic equation. In particular, we devise a Poisson-type elliptic equation that governs the underlying long-range interactions. The idea comes through fitting a Green function to the molecular potential, and hence deriving an elliptic equation for the associated fundamental solution. Through this transformation of the Vlasov integral, efficient Poisson-type solvers can be readily employed in order to compute the mean field forces. Besides the technical aspects of different numerical schemes for the treatment of the Vlasov integral, simulation results for the evaporation of a liquid slab into the vacuum are presented. It is shown that the proposed formulation leads to accurate predictions with a reasonable computational cost.

An important class of multi-scale flow scenarios deals with an interplay between kinetic and continuum phenomena. While hybrid solvers provide a natural way to cope with these settings, two issues restrict their performance. Foremost, the inverse problem implied by estimating distributions has to be addressed, to provide boundary conditions for the kinetic solver. The next issue comes from defining a robust yet accurate switching criterion between the two solvers. This study introduces a data-driven kinetic-continuum coupling, where the Maximum-Entropy-Distribution (MED) is employed to parametrize distributions arising from continuum field variables. Two regression methodologies of Gaussian-Processes (GPs) and Artificial-Neural-Networks (ANNs) are utilized to predict MEDs efficiently. Hence the MED estimates are employed to carry out the coupling, besides providing a switching criterion. To achieve the latter, a continuum breakdown parameter is defined by means of the Fisher information distance computed from the MED estimates. We test the performance of our devised MED estimators by recovering bi-modal densities. Next, MED estimates are integrated into a hybrid kinetic-continuum solution algorithm. Here Direct Simulation Monte-Carlo (DSMC) and Smoothed-Particle Hydrodynamics (SPH) are chosen as kinetic and continuum solvers, respectively. The problem of monatomic gas inside Sod's shock tube is investigated, where DSMC-SPH coupling is realized by applying the devised MED estimates. Very good agreements with respect to benchmark solutions along with a promising speed-up are observed in our reported test cases.

Multi-phase phenomena remain at the heart of many challenging fluid dynamics problems. Molecular fluxes at the interface determine the fate of neighboring phases, yet their closure far from the continuum needs to be modeled. Along the hierarchy of kinetic approaches, a multi-phase particle method is devised in this study. This approach is built closely upon the previous studies on the kinetic method development for dense gasses [Phys. Fluids, 29 (12), 2017] and long-range interactions [J. Comput. Phys, 378, 2019]. It is on this background that the current work on Fokker-Planck-Poisson modeling of multi-phase phenomena is initiated. Molecular interactions are expressed via stochastic forces driven by the white noise, coupled with long-range attractions. The former is local and pursues diffusive approximation of molecular collisions, whereas the latter takes a global feature owing to mean-field forces. The obtained Fokker-Planck-Poisson combination provides an efficient workflow for physics-driven simulations suitable for multi-phase phenomena far from the equilibrium. Besides highlighting the computational efficiency of the method, various archetypical and complex problems ranging from inverted-temperature-gradient between droplets to spinodal decomposition are explored. Detailed discussions are provided on different characteristics of the droplets dispersed in low/high density background gases; including the departure of heat fluxes from Fourier's law as well as droplets growth in spinodal phases.