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? 2022 Elsevier Inc.We consider the Cauchy problem for the nonlocal (derivative) NLS in super-critical function spaces Eσs for which the norms are defined by ‖f‖Eσs=‖〈ξ〉σ2s|ξ|f?(ξ)‖L2,s<0,σ∈R. Any Sobolev space Hr is a subspace of Eσs, i.e., Hr?Eσs for any r,σ∈R and s<0. Let s<0 and σ>?1/2 (σ>0) for the nonlocal NLS ...
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? 2022 Elsevier Inc.We consider the Cauchy problem for the nonlocal (derivative) NLS in super-critical function spaces Eσs for which the norms are defined by ‖f‖Eσs=‖〈ξ〉σ2s|ξ|f?(ξ)‖L2,s<0,σ∈R. Any Sobolev space Hr is a subspace of Eσs, i.e., Hr?Eσs for any r,σ∈R and s<0. Let s<0 and σ>?1/2 (σ>0) for the nonlocal NLS (for the nonlocal derivative NLS). We show the global existence and uniqueness of the solutions if the initial data belong to Eσs and their Fourier transforms are supported in (0,∞), the smallness conditions on the initial data in Eσs are not required for the global solutions.
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Intuitive context-aware algorithms called "Next Basket recommender systems" improve consumers' decision-making by offering suggestions for potential products they might like to buy next based on their past behaviour. Even though i...
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Intuitive context-aware algorithms called "Next Basket recommender systems" improve consumers' decision-making by offering suggestions for potential products they might like to buy next based on their past behaviour. Even though it is now well-known, this field is still young. Many different industries, such as e-commerce and healthcare, employ recommender systems. Even though these datasets frequently contain sensitive data, most recommender systems place a greater emphasis on the models' accuracy than on their security and privacy. We investigate this concept in the context of the sequential recommendation job known as Next Basket Recommendation (NBR), whose objective is to provide a user with a selection of goods based on their purchasing behaviour. A recent state-of-the-art technology is blockchain. Blockchain creates a trusted environment without the involvement of a third party, thus ensuring privacy and security. It is designed in such a way that it is enough in itself to create trust. In this paper, we propose and assimilate an authentic blockchain privacy system for a fortified user recommendation system for the Next Basket Recommendation. With next basket proposals based on blockchain for safe transactions and distributed context-based processing, this suggested system enables the development of decentralized RSs. Through the use of atomic swaps on the blockchain, this effort aims to provide viable solutions that can lead to fair procedures. It places a focus on effective data deletion procedures that preserve user privacy and transfers the issue of decremental learning to the Next Basket system, a more secure and wise recommendation. By incorporating blockchain into recommender systems (RSs), which contain smart contracts in the main blockchain-based RS protocol, it is feasible to create safe trust-based systems with the benefit of multi-party computation backed by blockchain. Additionally, it aids in protecting user information since blockchain enables the secure processing of customer data in online portals.
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Distributed target tracking is an important problem in sensor networks (SNs). In this paper, the problem of distributed target tracking is addressed under cyber-attacks for targets with discrete-time and continuous-time nonlinear ...
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Distributed target tracking is an important problem in sensor networks (SNs). In this paper, the problem of distributed target tracking is addressed under cyber-attacks for targets with discrete-time and continuous-time nonlinear dynamics. Two distributed filters are obtained for every node of the SN to estimate the states of a general class of nonlinear targets which can be seen in many practical applications. Compared with the existing results in the literature, the network topology of the SN is assumed to be subjected to the denial-of-service attack such that the communication links among sensor nodes are paralyzed or destroyed by this kind of attack. Moreover, the proposed algorithms are designed based on an event-triggered communication strategy that means the frequency of information transmission and unnecessary resource consumption are significantly reduced. The presented algorithms’ stability is also analyzed in the presence of noise to achieve secure event-triggered target tracking in mean-square. Two simulation examples are utilized to demonstrate the efficiency of the proposed event-triggered algorithms.
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? 2021 The Author(s)Although classically known as an endocrine signal produced by the ovary, 17β-estradiol (E2) is also a neurosteroid produced in neurons and astrocytes in the brain of many different species. In this review, we ...
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? 2021 The Author(s)Although classically known as an endocrine signal produced by the ovary, 17β-estradiol (E2) is also a neurosteroid produced in neurons and astrocytes in the brain of many different species. In this review, we provide a comprehensive overview of the localization, regulation, sex differences, and physiological/pathological roles of brain-derived E2 (BDE2). Much of what we know regarding the functional roles of BDE2 has come from studies using specific inhibitors of the E2 synthesis enzyme, aromatase, as well as the recent development of conditional forebrain neuron-specific and astrocyte-specific aromatase knockout mouse models. The evidence from these studies support a critical role for neuron-derived E2 (NDE2) in the regulation of synaptic plasticity, memory, socio-sexual behavior, sexual differentiation, reproduction, injury-induced reactive gliosis, and neuroprotection. Furthermore, we review evidence that astrocyte-derived E2 (ADE2) is induced following brain injury/ischemia, and plays a key role in reactive gliosis, neuroprotection, and cognitive preservation. Finally, we conclude by discussing the key controversies and challenges in this area, as well as potential future directions for the field.
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