Bounce and cyclic cosmology in extended nonlinear massive gravity

We investigate non-singular bounce and cyclic cosmological evolutions in a universe governed by the extended nonlinear massive gravity, in which the graviton mass is promoted to a scalar-field potential. The extra freedom of the theory can lead to certain energy conditions violations and drive cyclicity with two different mechanisms: either with a suitably chosen scalar-field potential under a given Stuckelberg-scalar function, or with a suitably chosen Stuckelberg-scalar function under a given scalar-field potential. Our analysis shows that extended nonlinear massive gravity can alter significantly the evolution of the universe at both early and late times.Comment: 20 pages, 5 figures, version published at JCA

Phase-Space analysis of Teleparallel Dark Energy

We perform a detailed dynamical analysis of the teleparallel dark energy scenario, which is based on the teleparallel equivalent of General Relativity, in which one adds a canonical scalar field, allowing also for a nonminimal coupling with gravity. We find that the universe can result in the quintessence-like, dark-energy-dominated solution, or to the stiff dark-energy late-time attractor, similarly to standard quintessence. However, teleparallel dark energy possesses an additional late-time solution, in which dark energy behaves like a cosmological constant, independently of the specific values of the model parameters. Finally, during the evolution the dark energy equation-of-state parameter can be either above or below -1, offering a good description for its observed dynamical behavior and its stabilization close to the cosmological-constant value.Comment: 23 pages, 4 figures, 5 tables, version published at JCA

Aspects of Horava-Lifshitz cosmology

We review some general aspects of Horava-Lifshitz cosmology. Formulating it in its basic version, we extract the cosmological equations and we use observational data in order to constrain the parameters of the theory. Through a phase-space analysis we extract the late-time stable solutions, and we show that eternal expansion, and bouncing and cyclic behavior can arise naturally. Concerning the effective dark energy sector we show that it can describe the phantom phase without the use of a phantom field. However, performing a detailed perturbation analysis, we see that Horava-Lifshitz gravity in its basic version suffers from instabilities. Therefore, suitable generalizations are required in order for this novel theory to be a candidate for the description of nature.Comment: 10 pages, 4 figures, invited talk given at the 2nd International Workshop on Dark Matter, Dark Energy and Matter-Antimatter Assymetry, National Tsing Hua University, Hsinchu, Taiwan, November 5-6, 201

A note on Friedmann equation of FRW universe in deformed Horava-Lifshitz gravity from entropic force

With entropic interpretation of gravity proposed by Verlinde, we obtain the Friedmann equation of the Friedmann-Robertson-Walker universe for the deformed Ho\v{r}ava-Lifshitz gravity. It is shown that, when the parameter of Ho\v{r}ava-Lifshitz gravity $\omega\rightarrow \infty$, the modified Friedmann equation will go back to the one in Einstein gravity. This results may imply that the entropic interpretation of gravity is effective for the deformed Ho\v{r}ava-Lifshitz gravity.Comment: 9 pages, no figure

Notes on Matter in Horava-Lifshitz Gravity

We investigate the dynamics of a scalar field governed by the Lifshitz-type action which should appear naturally in Horava-Lifshitz gravity. The wave of the scalar field may propagate with any speed without an upper bound. To preserve the causality, the action cannot have a generic form. Due to the superluminal propagation, a formation of a singularity may cause the breakdown of the predictability of the theory. To check whether such a catastrophe could occur in Horava-Lifshitz gravity, we investigate the dynamics of a dust. It turns out that the dust does not collapse completely to form a singularity in a generic situation, but expands again after it attains a maximum energy density.Comment: 14 pages, references adde

A Unified Single-stage Learning Model for Estimating Fiber Orientation Distribution Functions on Heterogeneous Multi-shell Diffusion-weighted MRI

Diffusion-weighted (DW) MRI measures the direction and scale of the local diffusion process in every voxel through its spectrum in q-space, typically acquired in one or more shells. Recent developments in micro-structure imaging and multi-tissue decomposition have sparked renewed attention to the radial b-value dependence of the signal. Applications in tissue classification and micro-architecture estimation, therefore, require a signal representation that extends over the radial as well as angular domain. Multiple approaches have been proposed that can model the non-linear relationship between the DW-MRI signal and biological microstructure. In the past few years, many deep learning-based methods have been developed towards faster inference speed and higher inter-scan consistency compared with traditional model-based methods (e.g., multi-shell multi-tissue constrained spherical deconvolution). However, a multi-stage learning strategy is typically required since the learning process relied on various middle representations, such as simple harmonic oscillator reconstruction (SHORE) representation. In this work, we present a unified dynamic network with a single-stage spherical convolutional neural network, which allows efficient fiber orientation distribution function (fODF) estimation through heterogeneous multi-shell diffusion MRI sequences. We study the Human Connectome Project (HCP) young adults with test-retest scans. From the experimental results, the proposed single-stage method outperforms prior multi-stage approaches in repeated fODF estimation with shell dropoff and single-shell DW-MRI sequences

Particle Kinematics in Horava-Lifshitz Gravity

We study the deformed kinematics of point particles in the Horava theory of gravity. This is achieved by considering particles as the optical limit of fields with a generalized Klein-Gordon action. We derive the deformed geodesic equation and study in detail the cases of flat and spherically symmetric (Schwarzschild-like) spacetimes. As the theory is not invariant under local Lorenz transformations, deviations from standard kinematics become evident even for flat manifolds, supporting superluminal as well as massive luminal particles. These deviations from standard behavior could be used for experimental tests of this modified theory of gravity.Comment: Added references, corrected a typing erro

Fluctuations in a Ho\v{r}ava-Lifshitz Bouncing Cosmology

Ho\v{r}ava-Lifshitz gravity is a potentially UV complete theory with important implications for the very early universe. In particular, in the presence of spatial curvature it is possible to obtain a non-singular bouncing cosmology. The bounce is realized as a consequence of higher order spatial curvature terms in the gravitational action. Here, we extend the study of linear cosmological perturbations in Ho\v{r}ava-Lifshitz gravity coupled to matter in the case when spatial curvature is present. As in the case without spatial curvature, we find that there is no extra dynamical degree of freedom for scalar metric perturbations. We study the evolution of fluctuations through the bounce and show that the solutions remain non-singular throughout. If we start with quantum vacuum fluctuations on sub-Hubble scales in the contracting phase, and if the contracting phase is dominated by pressure-less matter, then for $\lambda = 1$ and in the infrared limit the perturbations at late times are scale invariant. Thus, Ho\v{r}ava-Lifshitz gravity can provide a realization of the ``matter bounce'' scenario of structure formation.Comment: 19 page

Scaling Up 3D Kernels with Bayesian Frequency Re-parameterization for Medical Image Segmentation

With the inspiration of vision transformers, the concept of depth-wise convolution revisits to provide a large Effective Receptive Field (ERF) using Large Kernel (LK) sizes for medical image segmentation. However, the segmentation performance might be saturated and even degraded as the kernel sizes scaled up (e.g., $21\times 21\times 21$) in a Convolutional Neural Network (CNN). We hypothesize that convolution with LK sizes is limited to maintain an optimal convergence for locality learning. While Structural Re-parameterization (SR) enhances the local convergence with small kernels in parallel, optimal small kernel branches may hinder the computational efficiency for training. In this work, we propose RepUX-Net, a pure CNN architecture with a simple large kernel block design, which competes favorably with current network state-of-the-art (SOTA) (e.g., 3D UX-Net, SwinUNETR) using 6 challenging public datasets. We derive an equivalency between kernel re-parameterization and the branch-wise variation in kernel convergence. Inspired by the spatial frequency in the human visual system, we extend to vary the kernel convergence into element-wise setting and model the spatial frequency as a Bayesian prior to re-parameterize convolutional weights during training. Specifically, a reciprocal function is leveraged to estimate a frequency-weighted value, which rescales the corresponding kernel element for stochastic gradient descent. From the experimental results, RepUX-Net consistently outperforms 3D SOTA benchmarks with internal validation (FLARE: 0.929 to 0.944), external validation (MSD: 0.901 to 0.932, KiTS: 0.815 to 0.847, LiTS: 0.933 to 0.949, TCIA: 0.736 to 0.779) and transfer learning (AMOS: 0.880 to 0.911) scenarios in Dice Score.Comment: Both codes and pretrained models are available at: https://github.com/MASILab/RepUX-Ne