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With the growth of computer vision applications, deep learning, and edge computing contribute to ensuring practical collaborative intelligence (CI) by distributing the workload among edge devices and the cloud. However, running separate single-task models on edge devices is inefficient regarding the required computational resource and time. In this context, multi-task learning allows leveraging a single deep learning model for performing multiple tasks, such as semantic segmentation and depth estimation on incoming video frames. This single processing pipeline generates common deep features that are shared among multi-task modules. However, in a collaborative intelligence scenario, generating common deep features has two major issues. First, the deep features may inadvertently contain input information exposed to the downstream modules (violating input privacy). Second, the generated universal features expose a piece of collective information than what is intended for a certain task, in which features for one task can be utilized to perform another task (violating task privacy). This paper proposes a novel deep learning-based privacy-cognizant feature generation process called MetaMorphosis that limits inference capability to specific tasks at hand. To achieve this, we propose a channel squeeze-excitation based feature metamorphosis module, Cross-SEC, to achieve distinct attention of all tasks and a de-correlation loss function with differential-privacy to train a deep learning model that produces distinct privacy-aware features as an output for the respective tasks. With extensive experimentation on four datasets consisting of diverse images related to scene understanding and facial attributes, we show that MetaMorphosis outperforms recent adversarial learning and universal feature generation methods by guaranteeing privacy requirements in an efficient way for image and video analytics., Comment: Preprint version, 22 pages. Keywords: Multi-task learning, neural networks, collaborative intelligence, differential privacy, task privacy

Quantum entanglement distribution between remote nodes is key to many promising quantum applications. Existing mechanisms have mainly focused on improving throughput and fidelity via entanglement routing or single-node scheduling. This paper considers entanglement scheduling and distribution among many source-destination pairs with different requests over an entire quantum network topology. Two practical scenarios are considered. When requests do not have deadlines, we seek to minimize the average completion time of the communication requests. If deadlines are specified, we seek to maximize the number of requests whose deadlines are met. Inspired by optimal scheduling disciplines in conventional single-queue scenarios, we design a general optimization framework for entanglement scheduling and distribution called ESDI, and develop a probabilistic protocol to implement the optimized solutions in a general buffered quantum network. We develop a discrete-time quantum network simulator for evaluation. Results show the superior performance of ESDI compared to existing solutions.

The paper concerns the weak differentiability of weak solutions to two kinds of nonuniform nonlinear degenerate elliptic systems under the $p,q$-growth condition on the Heisenberg Group. We use the iteration to fractional difference quotients on the Heisenberg Group to get the weak differentiability of weak solution $u$ in the vertical direction (i.e., ${L^p}$($1

A quantum network distributes quantum entanglements between remote nodes, and is key to many applications in secure communication, quantum sensing and distributed quantum computing. This paper explores the fundamental trade-off between the throughput and the quality of entanglement distribution in a multi-hop quantum repeater network. Compared to existing work which aims to heuristically maximize the entanglement distribution rate (EDR) and/or entanglement fidelity, our goal is to characterize the maximum achievable worst-case fidelity, while satisfying a bound on the maximum achievable expected EDR between an arbitrary pair of quantum nodes. This characterization will provide fundamental bounds on the achievable performance region of a quantum network, which can assist with the design of quantum network topology, protocols and applications. However, the task is highly non-trivial and is NP-hard as we shall prove. Our main contribution is a fully polynomial-time approximation scheme to approximate the achievable worst-case fidelity subject to a strict expected EDR bound, combining an optimal fidelity-agnostic EDR-maximizing formulation and a worst-case isotropic noise model. The EDR and fidelity guarantees can be implemented by a post-selection-and-storage protocol with quantum memories. By developing a discrete-time quantum network simulator, we conduct simulations to show the characterized performance region (the approximate Pareto frontier) of a network, and demonstrate that the designed protocol can achieve the performance region while existing protocols exhibit a substantial gap., Comment: Currently under review at IEEE/ACM Transactions on Networking

This paper is concerned with the Liouville type theorems for the 3D stationary incompressible Hall-MHD equations. We establish that under some sufficient conditions in local Morrey spaces, solutions of the stationary Hall-MHD equations are identically zero. In particular, we also prove Liouville type results for the stationary incompressible MHD equations on $\mathbb{R}^3$. Our theorems extend and generalize the classical results for the stationary incompressible Navier-Stokes equations.

In this paper, we consider the global well-posedness of the incompressible Hall-MHD equations in $\mathbb{R}^3$. We prove that the solution of this system is globally regular if the initial data is axisymmetric and the swirl components of the velocity and magnetic vorticity are trivial. It should be pointed out that the initial data without any smallness and in low regularity spaces. This improves a previous result established in \cite{Fan2013}.

The purpose of this paper is to study the incompressible non-resistive MHD equations in $\mathbb{R}^3$. We establish the global well-posedness of classical solutions if the initial data is axially symmetric and the swirl components of the velocity and magnetic vorticity vanish. In particular, the special axially symmetric initial data can be arbitrarily large and satisfy low regularity assumptions.

In this paper, we investigate the three dimensional stationary compressible Navier-Stokes equations, and obtain Liouville type theorems if a smooth solution $(\rho, \mathbf{u})$ satisfies some suitable conditions. In particular, our results improve and generalize the corresponding result of Li and Yu (2014) [8].

Let $(u, \pi)$ with $u=(u_1,u_2,u_3)$ be a suitable weak solution of the three dimensional Navier-Stokes equations in $\mathbb{R}^3\times [0, T]$. Denote by $\dot{\mathcal{B}}^{-1}_{\infty,\infty}$ the closure of $C_0^\infty$ in $\dot{B}^{-1}_{\infty,\infty}$. We prove that if $u\in L^\infty(0, T; \dot{B}^{-1}_{\infty,\infty})$, $u(x, T)\in \dot{\mathcal{B}}^{-1}_{\infty,\infty})$, and $u_3\in L^\infty(0, T; L^{3, \infty})$ or $u_3\in L^\infty(0, T; \dot{B}^{-1+3/p}_{p, q})$ with $3

We prove several Liouville type results for the stationary MHD and Hall-MHD equations. In particular, we show that the velocity and magnetic field, belonging to some Lorentz spaces or satisfying a priori decay assumption, must be zero., Comment: Our proof is incomplete. We need to check it

This paper is concerned with the Cauchy problem of the two-dimensional MHD system with magnetic diffusion. It was proved that the MHD equations have a unique global strong solution around the equilibrium state $(0, e_1)$. Furthermore, the $L^2$ decay rate of the velocity and magnetic field is obtained., Comment: Our proof is incomplete. We need to check it

This paper is concerned with the Cauchy problem of the one-dimensional free surface equation of shallow water wave, we obtain local well-posedness of the free surface equation of shallow water wave in Sobolev spaces. In addition, we also derive a wave-breaking mechanism for strong solutions., Comment: arXiv admin note: text overlap with arXiv:0709.0905 by other authors

We prove several Liouville type results for the stationary Hall-MHD and MHD equations. In particular, we show that the velocity and magnetic field, belonging to some Lorentz spaces, must be zero., Comment: There is a key error in our proofs