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关键词： Neural ODE   Adversarial defense   Hopfield-type network   Image classification  

摘要： Neural networks are vulnerable to adversarial input perturbations imperceptible to human, which calls for robust machine learning for safety-critical applications. In this paper, we propose a new neural ODE layer which is inspired by Hopfield-type neural networks. We prove that the proposed ODE layer has global asymptotic stability on the projected space, which implies the existence and uniqueness of its steady state. We further show that the proposed layer satisfies the local stability condition such that the output is Lipschitz continuous in the ODE layer input, guaranteeing that the norm of perturbation on the hidden state does not grow over time. By experiments we show that an appropriate level of stability constraints imposed on the proposed ODE layer can improve the adversarial robustness of ODE layers, and present a heuristic method for finding good hyperparameters for stability constraints. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Fractional stochastic systems   Controllability   Optimal control  

摘要： In this paper, we study the controllability and optimal control for a class of time-delayed fractional stochastic integro-differential system with Poisson jumps. A set of sufficient conditions is established for complete and approximate controllability by assuming non-Lipschitz conditions and pth mean square norm. We also give an existence of optimal control for Bolza problem. Our result is valid for fractional order alpha > p-1/p, p >= 2. Finally, an example is provided to illustrate the efficiency of the obtained theoretical results.

关键词： Pulmonary TB   Helminth coinfection   Tregs   TGF-beta plus tregs   TB disease Severity  

摘要： Helminth induced expansion of regulatory T cells (Tregs) may take part in suppressing protective host responses during tuberculosis (TB), although Tregs functionality and link to TB disease severity remains unexplored. We investigated the species-specific effect of helminths on frequency and TGF-beta producing capacity of Tregs, and possible connection to TB disease severity. 89 pulmonary TB patients (PTB) and 69 community controls (CCs) from Gondar, Ethiopia, were included. Clinical disease severity was graded by TB score, and flow cytometry used to characterize Treg frequency and functionality measured as their TGF-beta-producing capacity. In helminth positive PTB patients (Helminth+PTB+) compared to helminth negative PTB or CCs, TGF-beta(+) Tregs were significantly increased mainly in hookworm coinfection whereas S. mansoni increased TGF-beta(+) Tregs in CCs. Treatment of TB and helminths decreased TGF-beta(+) Tregs in Helminth+PTB+ at 2 months follow-up. There were no overall differences in the frequency of Tregs in CCs or PTB unless stratification on TB disease severity was performed. At inclusion Helminth+PTB+ had increased frequency of Tregs already at low disease severity, and TGF-beta(+) Tregs correlated to intermediate-to-high disease severity. In conclusion, helminth specific increase of TGF-beta(+) Tregs in PTB patients was correlated to TB disease severity and was restored following anti-helminth treatment.

关键词： Receivers   Transmitters   Encryption   Wireless communication   Public key   Complexity   differential frequency hopping (DFH)   encryption algorithm   G-function   hybrid encryption   security  

摘要： Differential frequency hopping (DFH) technique is widely used in wireless communications by exploiting its capabilities of mitigating tracking interference and confidentiality. However, electronic attacks in wireless systems become more and more rigorous, which imposes a lot of challenges on the DFH sequences designed based on the linear congruence theory, fuzzy and chaotic theory, etc. In this article, we investigate the sequence design in DFH systems by exploiting the equivalence principle between the G-function algorithm and the encryption algorithm, in order to achieve high security. In more details, first, the novel G-function is proposed with the aid of the Government Standard algorithm and the Rivest-Shamir-Adleman algorithm. Then, two sequence design algorithms are proposed, namely, the G-function-assisted sequence generation algorithm, which takes the full advantages of the symmetric and asymmetric encryption algorithms, and the high-order G-function-aided sequence generation algorithm, which is capable of enhancing the correlation of the elements in a DFH sequence. Moreover, the security and ergodicity performance of the proposed algorithms are analyzed. Our studies and results show that the DFH sequences generated by the proposed algorithms significantly outperform the sequences generated by the reversible hash algorithm and affine transformation in terms of the uniformity, randomness, complexity, and the security.

关键词： fractional differential equations   ulam stabilities   numerical approximations   infectious diseases  

摘要： The Zika virus is considered to be one of the dangerous virus, which spread in the community through small insect so-called mosquitoes. Some of the other will known methods by which the consider virus may transform are: pregnant mother can pass it to her baby during the pregnancy or birth time, it can also spread through sexual intercourse. Therefore, the world health organization (WHO) declares the Zika infection with clusters of microcephaly and other neurological disorders constitutes a public health emergency of international concern. To understand the dynamics of Zika infectious virus, we investigate the fractional order mathematical model for the transference of Zika infectious disease. The proposed model is divided into seven compartments. Particularly, the author's used the results of fixed point theory to discuss the existence and uniqueness of the solution and stability analysis for the proposed model. Furthermore, we have calculated the equilibrium points, basic reproduction number and stability of the basic reproduction number. In addition, for the numerical solution of the said model, the author's used two steps fractional Adam's Bashforth method (FABm). Finally, numerical simulation and discussion of the graphical representation of the solutions obtained via FABm are given.

关键词： Cognition   Heterogeneity   Functional disability  

摘要： Bipolar disorder (BD) is a complex illness with variability at the level of symptom presentation, clinical course, cognitive capacity, and everyday function. Cognition is a key predictor of functional disability in BD, however, much remains unknown about the development and presentation of cognitive dysfunction in BD. Studies have shown that 30-50% of affectively stable people with BD are indistinguishable from healthy individuals in terms of cognitive presentation. In contrast, many people with BD have moderate to severe cognitive deficits, in some cases on par with what is typically observed in schizophrenia (SZ). Recent research efforts have aimed to parse this cognitive heterogeneity using unsupervised statistical techniques, resulting in more homogeneous subgroups. This method has provided new insights into the clinical and biological predictors of a potentially - neuroprogressive - declinin - gcognitive course in BD. Future studies that include detailed longitudinal follow-up in large BD cohorts hold promise for guiding the development of novel treatments that reach beyond the primary affective symptoms and target functionally relevant outcomes to promote full recovery. (C) 2021 Elsevier B.V. and ECNP. All rights reserved.

关键词： Impulsive delay differential equations   Floquet multipliers   Chebyshev series   Rigorous numerics   Computer-assisted proofs  

摘要： We develop validated numerical methods for the computation of Floquet multipliers of equilibria and periodic solutions of delay differential equations, as well as impulsive delay differential equations. Using our methods, one can rigorously count the number of Floquet multipliers outside a closed disc centered at zero or the number of multipliers contained in a compact set bounded away from zero. We consider systems with a single delay where the period is at most equal to the delay, and the latter two are commensurate. We first represent the monodromy operator (period map) as an operator acting on a product of sequence spaces that represent the Chebyshev coefficients of the state-space vectors. Truncation of the number of modes yields the numerical method, and by carefully bounding the truncation error in addition to some other technical operator norms, this leads to the method being suitable to computer-assisted proofs of Floquet multiplier location. We demonstrate the computer-assisted proofs on two example problems. We also test our discretization scheme in floating point arithmetic on a gamut of randomly-generated high-dimensional examples with both periodic and constant coefficients to inspect the precision of the spectral radius estimation of the monodromy operator (i.e. stability/instability check for periodic systems) for increasing numbers of Chebyshev modes.

关键词： differential geometry   quaternion  

摘要： This paper describes the foundations of a differential geometry of a quaternionic curves. The Frenet-Serret equations and the evolutes and evolvents of a particular quaternionic curve are accordingly determined. This new formulation takes benefit of the quaternionic structure, and the results are much simpler than the present formulations of quaternionic curves.

关键词： Analog front end   Inverter-based   Chopper stabilization   Fully differential difference amplifier   Low noise amplifier   Programmable gain amplifier  

摘要： In this paper, a low power and low noise analog front end (AFE) is designed for biosignal acquisition. The first stage is a low noise amplifier (LNA) that is designed by combining the fully differential difference amplifier (FDDA) structure with inverter-based to achieve the optimal power, noise, CMRR, and input impedance simultaneously. Also, to increase the output resistance of the LNA, and subsequently increase the gain without reducing the output voltage swing, the gain boosting technique has been used. To use this structure for biosignals, the second stage is designed as a programmable gain amplifier (PGA). This AFE is reconfigurable for electroencephalography (EEG), electrocardiogram (ECG), and surface electromyography (sEMG) biosignals with variable gain of 71 dB, 56 dB, and 44 dB and bandwidth of (0.9-100 Hz), (1-560 Hz) and (12 Hz-1.5 kHz), respectively. The AFE consumes only 303 nW at 0.8 V supply voltage and confers excellent input impedance of 250 G Omega and 5.2 G Omega when the chopper is "off' and "on" respectively. The chopper method has been used and the total integrated input-referred noise is obtained, 1.4 mu V-rms. The proposed AFE is simulated in TSMC 65 nm CMOS technology and occupies an area of 0.16mm(2).

关键词： phase contrast microscopy   polarisation-resolved imaging   quantitative phase imaging  

摘要： We present a robust, low-cost single-shot implementation of differential phase microscopy utilising a polarisation-sensitive camera to simultaneously acquire four images from which phase contrast images can be calculated. This polarisation-resolved differential phase contrast (pDPC) microscopy technique can be easily integrated with fluorescence microscopy.