The Hadamard product of hypergeometric series

AbstractTypically a hypergeometric function is a multi-valued analytic function with algebraic singularities. In this paper we give a complete description of the Newton polytope of the polynomial whose zero set naturally contains the singular locus of a nonconfluent double hypergeometric series. We show in particular that the Hadamard multiplication of such series corresponds to the Minkowski sum of the Newton polytopes of polynomials which define their singularities

Direct Numerical Simulation of 3D Salt Fingers: From Secondary Instability to Chaotic Convection

The amplification and equilibration of three-dimensional salt fingers in unbounded uniform vertical gradients of temperature and salinity is modeled with a Direct Numerical Simulation in a triply periodic computational domain. A fluid dynamics video of the simulation shows that the secondary instability of the fastest growing square-planform finger mode is a combination of the well-known vertical shear instability of two-dimensional fingers [Holyer, 1984] and a new horizontal shear mode.Comment: APS DFD Gallery of Fluid Motion 200

A mechanism for establishment and maintenance of the meridional overturning in the upper ocean

A two-dimensional analytical residual-mean model of the meridional overturning in the upper ocean is presented which illustrates dynamics of the interaction between the Northern and Southern hemispheres. The theory is based on the semi-adiabatic approximation in which all diabatic processes are confined to the upper mixed layer. The overturning circulation is driven directly by the wind forcing which, in our model, is affected by the sea-surface temperature distribution. The surface boundary conditions are symmetric with respect to the equator, and therefore one of the steady state solutions represents a symmetric flow characterized by the absence of the inter-hemispheric buoyancy fluxes. However, linear stability analysis, which takes into account both mechanical and thermodynamic forcing at the sea surface, indicates that the symmetric configuration such as this is unstable. The instability results in transition to the asymmetric regime with finite cross-equatorial exchange flows and heat transfer. Weakly nonlinear instability theory makes it possible to estimate the equilibrium fluxes in the new asymmetric steady states; for the oceanographically relevant range of parameters our model predicts the meridional overturning of about 10 Sv. While earlier studies considered the role of salt advection in spontaneous symmetry breaking, our study relies on a positive feedback between atmospheric winds and the oceanic meridional circulation

Vortices in Fermi gases with spin-dependent rotation potentials

The rotation of two-component Fermi gases and the subsequent appearance of vortices have been the subject of numerous experimental and theoretical studies. Recent experimental advances in hyperfine state-dependent potentials and highly degenerate heteronuclear Fermi gases suggest that it would be feasible to create component-dependent rotation potentials in future experiments. In this study we use an effective field theory for Fermi gases to consider the effects of rotating only one component of the Fermi gas. We find that the superfluid band gap in bulk exists up to higher rotation frequencies because the superfluid at rest, far away from the vortex, has to resist only half of the rotational effects. The vortex remains the energetically favorable state above a critical frequency but exhibits a larger core size.Comment: 15 pages, 2 figure

DP-BART for Privatized Text Rewriting under Local Differential Privacy

Privatized text rewriting with local differential privacy (LDP) is a recent approach that enables sharing of sensitive textual documents while formally guaranteeing privacy protection to individuals. However, existing systems face several issues, such as formal mathematical flaws, unrealistic privacy guarantees, privatization of only individual words, as well as a lack of transparency and reproducibility. In this paper, we propose a new system 'DP-BART' that largely outperforms existing LDP systems. Our approach uses a novel clipping method, iterative pruning, and further training of internal representations which drastically reduces the amount of noise required for DP guarantees. We run experiments on five textual datasets of varying sizes, rewriting them at different privacy guarantees and evaluating the rewritten texts on downstream text classification tasks. Finally, we thoroughly discuss the privatized text rewriting approach and its limitations, including the problem of the strict text adjacency constraint in the LDP paradigm that leads to the high noise requirement

Hydrodynamically-based Detection of the Surface and Subsurface Wakes

NPS NRP Executive SummaryHydrodynamically-based Detection of the Surface and Subsurface WakesN2/N6 - Information WarfareThis research is supported by funding from the Naval Postgraduate School, Naval Research Program (PE 0605853N/2098). https://nps.edu/nrpChief of Naval Operations (CNO)Approved for public release. Distribution is unlimited.

Privacy-Preserving Graph Convolutional Networks for Text Classification

Graph convolutional networks (GCNs) are a powerful architecture for representation learning on documents that naturally occur as graphs, e.g., citation or social networks. However, sensitive personal information, such as documents with people's profiles or relationships as edges, are prone to privacy leaks, as the trained model might reveal the original input. Although differential privacy (DP) offers a well-founded privacy-preserving framework, GCNs pose theoretical and practical challenges due to their training specifics. We address these challenges by adapting differentially-private gradient-based training to GCNs and conduct experiments using two optimizers on five NLP datasets in two languages. We propose a simple yet efficient method based on random graph splits that not only improves the baseline privacy bounds by a factor of 2.7 while retaining competitive F1 scores, but also provides strong privacy guarantees of epsilon = 1.0. We show that, under certain modeling choices, privacy-preserving GCNs perform up to 90% of their non-private variants, while formally guaranteeing strong privacy measures

Stabilization of Isolated Vortices in a Rotating Stratified Fluid

The key element of Geophysical Fluid Dynamics—reorganization of potential vorticity (PV) by nonlinear processes—is studied numerically for isolated vortices in a uniform environment. Many theoretical studies and laboratory experiments suggest that axisymmetric vortices with a Gaussian shape are not able to remain circular owing to the growth of small perturbations in the typical parameter range of abundant long-lived vortices. An example of vortex destabilization and the eventual formation of more intense self-propagating structures is presented using a 3D rotating stratified Boussinesq numerical model. The peak vorticity growth found during the stages of strong elongation and fragmentation is related to the transfer of available potential energy into kinetic energy of vortices. In order to develop a theoretical model of a stable circular vortex with a small Burger number compatible with observations, we suggest a simple stabilizing procedure involving the modification of peripheral PV gradients. The results have important implications for better understanding of real-ocean eddies

The salt finger amplitude in unbounded T-S gradient layers

Finite amplitude numerical calculations are made for a completely unbounded salt finger domain whose overall vertical property gradients (Tz and Sz) are uniform and remain unaltered in time. For diffusivity ratio τ = κS/κT = O (1), Prandtl number ν/κT \u3e\u3e 1, and density ratio R = Tz/Sz \u3e 1 this regime corresponds to a double gradient sugar (S)—salt (T) experiment. Two-dimensional pseudo-spectral calculations are made in the vicinity of the minimum critical condition for salt finger instability, viz., small ε ≡ (Rτ)-1 - 1 \u3e 0; the allowed spectrum includes the fastest growing wave of linear theory. When the vertical wavelength of the fundamental Fourier component is systematically increased the solution changes from a single steady vertical mode to a multi-modal statistically steady chaotic state. Each of the long vertical modes can be amplified by the (unchanging overall) gradient Sz, and can be stabilized by the induced vertical T, S gradients on the same scale as the modes; nonlinear triad interactions in the T - S equations can also lead to amplitude equilibration even though ε, κT/ν, and the Reynolds number are extremely small. When subharmonics of the horizonal wavelength of maximum growth are introduced into the numerical calculations the new wave amplifies (via Sz) and produces a quantitative change in the time average fluxes. Experimentally testable values of heat flux and rms horizontal T-fluctuations are computed in the range 2.8 \u3e R \u3e1.6 for τ = 1/3. Asymptotic similarity laws ε → 0 are also presented