Nonlinear stability of continuously stratified quasi-geostrophic flow

Nonlinear stability theorems analogous to Arnol'd's second stability theorem are established for continuously stratified quasi-geostrophic flow with general nonlinear boundary conditions in a vertically and horizontally confined domain. Both the standard quasi-geostrophic model and the modified quasi-geostrophic model (incorporating effects of hydrostatic compressibility) are treated. The results establish explicit upper bounds on the disturbance energy, the disturbance potential enstrophy, and the disturbance available potential energy on the horizontal boundaries, in terms of the initial disturbance fields. Nonlinear stability in the sense of Liapunov is also established

Visualizing Convolutional Networks for MRI-based Diagnosis of Alzheimer's Disease

Visualizing and interpreting convolutional neural networks (CNNs) is an important task to increase trust in automatic medical decision making systems. In this study, we train a 3D CNN to detect Alzheimer's disease based on structural MRI scans of the brain. Then, we apply four different gradient-based and occlusion-based visualization methods that explain the network's classification decisions by highlighting relevant areas in the input image. We compare the methods qualitatively and quantitatively. We find that all four methods focus on brain regions known to be involved in Alzheimer's disease, such as inferior and middle temporal gyrus. While the occlusion-based methods focus more on specific regions, the gradient-based methods pick up distributed relevance patterns. Additionally, we find that the distribution of relevance varies across patients, with some having a stronger focus on the temporal lobe, whereas for others more cortical areas are relevant. In summary, we show that applying different visualization methods is important to understand the decisions of a CNN, a step that is crucial to increase clinical impact and trust in computer-based decision support systems.Comment: MLCN 201

Nonlinear stability of multilayer quasi-geostrophic flow

New nonlinear stability theorems are derived for disturbances to steady basic flows in the context of the multilayer quasi-geostrophic equations. These theorems are analogues of Arnol’d's second stability theorem, the latter applying to the two-dimensional Euler equations. Explicit upper bounds are obtained on both the disturbance energy and disturbance potential enstrophy in terms of the initial disturbance fields. An important feature of the present analysis is that the disturbances are allowed to have non-zero circulation. While Arnol’d's stability method relies on the energy–Casimir invariant being sign-definite, the new criteria can be applied to cases where it is sign-indefinite because of the disturbance circulations. A version of Andrews’ theorem is established for this problem, and uniform potential vorticity flow is shown to be nonlinearly stable. The special case of two-layer flow is treated in detail, with particular attention paid to the Phillips model of baroclinic instability. It is found that the short-wave portion of the marginal stability curve found in linear theory is precisely captured by the new nonlinear stability criteria

Chiral Perturbation Theory and U(3)_L\times U(3)_R Chiral Theory of Mesons

We examine low energy limit of $U(3)_L\times U(3)_R$ chiral theory of mesons through integrating out fields of vector and axial-vector mesons. The effective lagrangian for pseudoscalar mesons at $O(p^4)$ has been obtained, and five low energy coupling constants $L_i(i=1,2,3,9,10)$ have been revealed. They are in good agreement with the results of CHPT's at $\mu \sim m_\rho$.Comment: 20 pages, Standard LaTex file, no finger

Nonlinearly combined impacts of initial perturbation from human activities and parameter perturbation from climate change on the grassland ecosystem

Human activities and climate change are important factors that affect grassland ecosystems. A new optimization approach, the approach of conditional nonlinear optimal perturbation (CNOP) related to initial and parameter perturbations, is employed to explore the nonlinearly combined impacts of human activities and climate change on a grassland ecosystem using a theoretical grassland model. In our study, it is assumed that the initial perturbations and parameter perturbations are regarded as human activities and climate change, respectively. Numerical results indicate that the climate changes causing the maximum effect in the grassland ecosystem are different under disparate intensities of human activities. This implies the pattern of climate change is very critical to the maintenance or degradation of grassland ecosystem in light of high intensity of human activities and that the grassland ecosystem should be rationally managed when the moisture index decreases. The grassland ecosystem influenced by the nonlinear combination of human activities and climate change undergoes abrupt change, while the grassland ecosystem affected by other types of human activities and climate change fails to show the abrupt change under a certain range of perturbations with the theoretical model. The further numerical analyses also indicate that the growth of living biomass and the evaporation from soil surface shaded by the wilted biomass may be crucial factors contributing to the abrupt change of the grassland equilibrium state within the theoretical model

Low Scale Non-universal, Non-anomalous U(1)'_F in a Minimal Supersymmetric Standard Model

We propose a non-universal U(1)'_F symmetry combined with the Minimal Supersymmetric Standard Model. All anomaly cancellation conditions are satisfied without exotic fields other than three right-handed neutrinos. Because our model allows all three generations of chiral superfields to have different U(1)'_F charges, upon the breaking of the U(1)'_F symmetry at a low scale, realistic masses and mixing angles in both the quark and lepton sectors are obtained. In our model, neutrinos are predicted to be Dirac fermions and their mass ordering is of the inverted hierarchy type. The U(1)'_F charges of the chiral super-fields also naturally suppress the mu term and automatically forbid baryon number and lepton number violating operators. While all flavor-changing neutral current constraints in the down quark and charged lepton sectors can be satisfied, we find that constraint from D0-D0bar turns out to be much more stringent than the constraints from the precision electroweak data.Comment: 21 pages, 2 figures; v2: discussion on sparticle mass spectrum included, 27 pages, 2 figure