In this article, we study deformations of conjugate self-dual Galois representations. The study has two folds. First, we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field, satisfying a certa
in property called rigid. Second, we study the rigidity property for the family of residue Galois representations attached to a symmetric power of an elliptic curve, as well as to a regular algebraic conjugate self-dual cuspidal representation.
Unitary learning is a backpropagation that serves to unitary weights update in deep complex-valued neural network with full connections, meeting a physical unitary prior in diffractive deep neural network ([DN]2). However, the square matrix property
of unitary weights induces that the function signal has a limited dimension that could not generalize well. To address the overfitting problem that comes from the small samples loaded to [DN]2, an optical phase dropout trick is implemented. Phase dropout in unitary space that is evolved from a complex dropout and has a statistical inference is formulated for the first time. A synthetic mask recreated from random point apertures with random phase-shifting and its smothered modulation tailors the redundant links through incompletely sampling the input optical field at each diffractive layer. The physical features about the synthetic mask using different nonlinear activations are elucidated in detail. The equivalence between digital and diffractive model determines compound modulations that could successfully circumvent the nonlinear activations physically implemented in [DN]2. The numerical experiments verify the superiority of optical phase dropout in [DN]2 to enhance accuracy in 2D classification and recognition tasks-oriented.
Realization of deep learning with coherent diffraction has achieved remarkable development nowadays, which benefits on the fact that matrix multiplication can be optically executed in parallel as well as with little power consumption. Coherent optica
l field propagated in the form of complex-value entity can be manipulated into a task-oriented output with statistical inference. In this paper, we present a unitary learning protocol on deep diffractive neural network, meeting the physical unitary prior in coherent diffraction. Unitary learning is a backpropagation serving to unitary weights update through the gradient translation between Euclidean and Riemannian space. The temporal-space evolution characteristic in unitary learning is formulated and elucidated. Particularly a compatible condition on how to select the nonlinear activations in complex space is unveiled, encapsulating the fundamental sigmoid, tanh and quasi-ReLu in complex space. As a preliminary application, deep diffractive neural network with unitary learning is tentatively implemented on the 2D classification and verification tasks.
Narrowband internet-of-things (NB-IoT) is a competitive 5G technology for massive machine-type communication scenarios, but meanwhile introduces narrowband interference (NBI) to existing broadband transmission such as the long term evolution (LTE) sy
stems in enhanced mobile broadband (eMBB) scenarios. In order to facilitate the harmonic and fair coexistence in wireless heterogeneous networks, it is important to eliminate NB-IoT interference to LTE systems. In this paper, a novel sparse machine learning based framework and a sparse combinatorial optimization problem is formulated for accurate NBI recovery, which can be efficiently solved using the proposed iterative sparse learning algorithm called sparse cross-entropy minimization (SCEM). To further improve the recovery accuracy and convergence rate, regularization is introduced to the loss function in the enhanced algorithm called regularized SCEM. Moreover, exploiting the spatial correlation of NBI, the framework is extended to multiple-input multiple-output systems. Simulation results demonstrate that the proposed methods are effective in eliminating NB-IoT interference to LTE systems, and significantly outperform the state-of-the-art methods.
Realization of deep learning with coherent optical field has attracted remarkably attentions presently, which benefits on the fact that optical matrix manipulation can be executed at speed of light with inherent parallel computation as well as low la
tency. Photonic neural network has a significant potential for prediction-oriented tasks. Yet, real-value Backpropagation behaves somewhat intractably for coherent photonic intelligent training. We develop a compatible learning protocol in complex space, of which nonlinear activation could be selected efficiently depending on the unveiled compatible condition. Compatibility indicates that matrix representation in complex space covers its real counterpart, which could enable a single channel mingled training in real and complex space as a unified model. The phase logical XOR gate with Mach-Zehnder interferometers and diffractive neural network with optical modulation mechanism, implementing intelligent weight learned from compatible learning, are presented to prove the availability. Compatible learning opens an envisaged window for deep photonic neural network.
In this article, we study the Beilinson-Bloch-Kato conjecture for motives corresponding to the Rankin-Selberg product of conjugate self-dual automorphic representations, within the framework of the Gan-Gross-Prasad conjecture. We show that if the cen
tral critical value of the Rankin-Selberg $L$-function does not vanish, then the Bloch-Kato Selmer group with coefficients in a favorable field of the corresponding motive vanishes. We also show that if the class in the Bloch-Kato Selmer group constructed from certain diagonal cycle does not vanish, which is conjecturally equivalent to the nonvanishing of the central critical first derivative of the Rankin-Selberg $L$-function, then the Bloch-Kato Selmer group is of rank one.
We study the space of vector-valued (twisted) conjugate invariant functions on a connected reductive group.
Internet of things (IoT) that integrate a variety of devices into networks to provide advanced and intelligent services have to protect user privacy and address attacks such as spoofing attacks, denial of service attacks, jamming and eavesdropping. I
n this article, we investigate the attack model for IoT systems, and review the IoT security solutions based on machine learning techniques including supervised learning, unsupervised learning and reinforcement learning. We focus on the machine learning based IoT authentication, access control, secure offloading and malware detection schemes to protect data privacy. In this article, we discuss the challenges that need to be addressed to implement these machine learning based security schemes in practical IoT systems.
By using smart radio devices, a jammer can dynamically change its jamming policy based on opposing security mechanisms; it can even induce the mobile device to enter a specific communication mode and then launch the jamming policy accordingly. On the
other hand, mobile devices can exploit spread spectrum and user mobility to address both jamming and interference. In this paper, a two-dimensional anti-jamming mobile communication scheme is proposed in which a mobile device leaves a heavily jammed/interfered-with frequency or area. It is shown that, by applying reinforcement learning techniques, a mobile device can achieve an optimal communication policy without the need to know the jamming and interference model and the radio channel model in a dynamic game framework. More specifically, a hotbooting deep Q-network based two-dimensional mobile communication scheme is proposed that exploits experiences in similar scenarios to reduce the exploration time at the beginning of the game, and applies deep convolutional neural network and macro-action techniques to accelerate the learning speed in dynamic situations. Several real-world scenarios are simulated to evaluate the proposed method. These simulation results show that our proposed scheme can improve both the signal-to-interference-plus-noise ratio of the signals and the utility of the mobile devices against cooperative jamming compared with benchmark schemes.
We study a kind of generalized porous medium equation with fractional Laplacian and abstract pressure term. For a large class of equations corresponding to the form: $u_t+ u Lambda^{beta}u= ablacdot(u abla Pu)$, we get their local well-posedness in F
ourier-Besov spaces for large initial data. If the initial data is small, then the solution becomes global. Furthermore, we prove a blowup criterion for the solutions.
