We propose a scalable, cloud-native architecture designed for Transcriptomics Atlas Pipeline, using a resource-intensive STAR aligner and processing tens or hundreds of terabytes of RNA-seq data. We implement the pipeline using AWS cloud services, introduce performance optimizations and perform experimental evaluation in the cloud. Our optimization techniques result in computational savings thanks to the "early stopping" approach, selection of right-sized resources, and using newer version of Ensembl genome.

We show the existence of Arnold diffusion in the planar full three-body problem, which is expressed as a perturbation of a Kepler problem and a planar circular restricted three-body problem, with the perturbation parameter being the mass of the smallest body. In this context, we obtain Arnold diffusion in terms of a transfer of energy, in an amount independent of the perturbation parameter, between the Kepler problem and the restricted three-body problem. Our argument is based on a topological method based on correctly aligned windows which is implemented into a computer assisted proof. This approach can be applied to physically relevant masses of the bodies, such as those in a Neptune-Triton-asteroid system. In this case, we obtain explicit estimates for the range of the perturbation parameter and for the diffusion time.

In this paper, we propose a novel approach to address the problem of camera and radar sensor fusion for 3D object detection in autonomous vehicle perception systems. Our approach builds on recent advances in deep learning and leverages the strengths of both sensors to improve object detection performance. Precisely, we extract 2D features from camera images using a state-of-the-art deep learning architecture and then apply a novel Cross-Domain Spatial Matching (CDSM) transformation method to convert these features into 3D space. We then fuse them with extracted radar data using a complementary fusion strategy to produce a final 3D object representation. To demonstrate the effectiveness of our approach, we evaluate it on the NuScenes dataset. We compare our approach to both single-sensor performance and current state-of-the-art fusion methods. Our results show that the proposed approach achieves superior performance over single-sensor solutions and could directly compete with other top-level fusion methods.

Relativistic heavy-ion beams at the LHC are accompanied by a large flux of equivalent photons, leading to multiple photon-induced processes. This proceeding presents searches for physics beyond the Standard Model enabled by photon-photon processes in both di-tau and diphoton final states. The tau-pair production measurements can constrain the tau lepton's anomalous magnetic dipole moment (g-2), and a recent ATLAS measurement using muonic decays of tau leptons in association with electrons and tracks provides one of the most stringent limits available to date. Similarly, light-by-light scattering proceeds via loop diagrams, which can contain particles not yet directly observed. Thus, high statistics measurements of light-by-light scattering provide a precise and unique opportunity to investigate extensions of the Standard Model, such as the presence of axion-like particles.

Modelling the diffusion-relaxation magnetic resonance (MR) signal obtained from multi-parametric sequences has recently gained immense interest in the community due to new techniques significantly reducing data acquisition time. A preferred approach for examining the diffusion-relaxation MR data is to follow the continuum modelling principle that employs kernels to represent the tissue features, such as the relaxations or diffusion properties. However, constructing reasonable dictionaries with predefined signal components depends on the sampling density of model parameter space, thus leading to a geometrical increase in the number of atoms per extra tissue parameter considered in the model. That makes estimating the contributions from each atom in the signal challenging, especially considering diffusion features beyond the mono-exponential decay. This paper presents a new Multi-Compartment diffusion-relaxation MR signal representation based on the Simple Harmonic Oscillator-based Reconstruction and Estimation (MC-SHORE) representation, compatible with scattered acquisitions. The proposed technique imposes sparsity constraint on the solution via the $\ell_1$ norm and enables the estimation of the microstructural measures, such as the return-to-the-origin probability, and the orientation distribution function, depending on the compartments considered in a single voxel. The procedure has been verified with in silico and in vivo data and enabled the approximation of the diffusion-relaxation MR signal more accurately than single-compartment non-Gaussian representations and multi-compartment mono-exponential decay techniques, maintaining a low number of atoms in the dictionary. Ultimately, the MC-SHORE procedure allows for separating intra-/extra-axonal and free water contributions from the signal, thus reducing the partial volume effect observable in the boundaries of the tissues.

In this paper, we investigate the following nonlinear Schr\"odinger equation with Neumann boundary conditions: \begin{equation*} \begin{cases} -\Delta u+ \lambda u= f(u) & {\rm in} \,~ \Omega,\\ \displaystyle\frac{\partial u}{\partial \nu}=0 \, &{\rm on}\,~\partial \Omega \end{cases} \end{equation*} coupled with a constraint condition: \begin{equation*} \int_{\Omega}|u|^2 dx=c, \end{equation*} where $\Omega\subset \mathbb{R}^N(N\ge3)$ denotes a smooth bounded domain, $\nu$ represents the unit outer normal vector to $\partial \Omega$,$c$is a positive constant, and$\lambda$ acts as a Lagrange multiplier. When the nonlinearity $f$ exhibits a general mass supercritical growth at infinity, we establish the existence of normalized solutions, which are not necessarily positive solutions and can be characterized as mountain pass type critical points of the associated constraint functional. Our approach provides a uniform treatment of various nonlinearities, including cases such as $f(u)=|u|^{p-2}u$, $|u|^{q-2}u+ |u|^{p-2}u$, and $-|u|^{q-2}u+|u|^{p-2}u$, where $2

The Restricted Planar Circular 3-Body Problem models the motion of a body of negligible mass under the gravitational influence of two massive bodies, called the primaries, which perform circular orbits coplanar with that of the massless body. In rotating coordinates, it can be modelled by a two degrees of freedom Hamiltonian system, which has five critical points called the Lagrange points. Among them, the point L3 is a saddle-center which is collinear with the primaries and beyond the largest of the two. The papers arXiv:2107.09942 and arXiv:2107.09941 provide an asymptotic formula for the distance between the one dimensional stable and unstable manifolds of L3 in a transverse section for small values of the mass ratio $\mu$. This distance is exponentially small with respect to $\mu$ and its first order depends on what is usually called a Stokes constant. The non-vanishing of this constant implies that the distance between the invariant manifolds at the section is not zero. In this paper, we prove that the Stokes constant is non-zero. The proof is computer assisted.