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Global exponential stability of generalized recurrent neural networks with discrete and distributed delays

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2006 Elsevier Ltd.This paper is concerned with analysis problem for the global exponential stability of a class of recurrent neural networks (RNNs) with mixed discrete and distributed delays. We first prove the existence and uniqueness of the equilibrium point under mild conditions, assuming neither differentiability nor strict monotonicity for the activation function. Then, by employing a new Lyapunov–Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the RNNs to be globally exponentially stable. Therefore, the global exponential stability of the delayed RNNs can be easily checked by utilizing the numerically efficient Matlab LMI toolbox, and no tuning of parameters is required. A simulation example is exploited to show the usefulness of the derived LMI-based stability conditions.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2006 Elsevier Ltd.This Letter is concerned with the global asymptotic stability analysis problem for a class of uncertain stochastic Hopfield neural networks with discrete and distributed time-delays. By utilizing a Lyapunov–Krasovskii functional, using the well-known S-procedure and conducting stochastic analysis, we show that the addressed neural networks are robustly, globally, asymptotically stable if a convex optimization problem is feasible. Then, the stability criteria are derived in terms of linear matrix inequalities (LMIs), which can be effectively solved by some standard numerical packages. The main results are also extended to the multiple time-delay case. Two numerical examples are given to demonstrate the usefulness of the proposed global stability condition.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

Azithromycin for community treatment of suspected COVID-19 in people at increased risk of an adverse clinical course in the UK (PRINCIPLE): a randomised, controlled, open-label, adaptive platform trial

Background Azithromycin, an antibiotic with potential antiviral and anti-inflammatory properties, has been used to treat COVID-19, but evidence from community randomised trials is lacking. We aimed to assess the effectiveness of azithromycin to treat suspected COVID-19 among people in the community who had an increased risk of complications. Methods In this UK-based, primary care, open-label, multi-arm, adaptive platform randomised trial of interventions against COVID-19 in people at increased risk of an adverse clinical course (PRINCIPLE), we randomly assigned people aged 65 years and older, or 50 years and older with at least one comorbidity, who had been unwell for 14 days or less with suspected COVID-19, to usual care plus azithromycin 500 mg daily for three days, usual care plus other interventions, or usual care alone. The trial had two coprimary endpoints measured within 28 days from randomisation: time to first self-reported recovery, analysed using a Bayesian piecewise exponential, and hospital admission or death related to COVID-19, analysed using a Bayesian logistic regression model. Eligible participants with outcome data were included in the primary analysis, and those who received the allocated treatment were included in the safety analysis. The trial is registered with ISRCTN, ISRCTN86534580. Findings The first participant was recruited to PRINCIPLE on April 2, 2020. The azithromycin group enrolled participants between May 22 and Nov 30, 2020, by which time 2265 participants had been randomly assigned, 540 to azithromycin plus usual care, 875 to usual care alone, and 850 to other interventions. 2120 (94%) of 2265 participants provided follow-up data and were included in the Bayesian primary analysis, 500 participants in the azithromycin plus usual care group, 823 in the usual care alone group, and 797 in other intervention groups. 402 (80%) of 500 participants in the azithromycin plus usual care group and 631 (77%) of 823 participants in the usual care alone group reported feeling recovered within 28 days. We found little evidence of a meaningful benefit in the azithromycin plus usual care group in time to first reported recovery versus usual care alone (hazard ratio 1·08, 95% Bayesian credibility interval [BCI] 0·95 to 1·23), equating to an estimated benefit in median time to first recovery of 0·94 days (95% BCI −0·56 to 2·43). The probability that there was a clinically meaningful benefit of at least 1·5 days in time to recovery was 0·23. 16 (3%) of 500 participants in the azithromycin plus usual care group and 28 (3%) of 823 participants in the usual care alone group were hospitalised (absolute benefit in percentage 0·3%, 95% BCI −1·7 to 2·2). There were no deaths in either study group. Safety outcomes were similar in both groups. Two (1%) of 455 participants in the azothromycin plus usual care group and four (1%) of 668 participants in the usual care alone group reported admission to hospital during the trial, not related to COVID-19. Interpretation Our findings do not justify the routine use of azithromycin for reducing time to recovery or risk of hospitalisation for people with suspected COVID-19 in the community. These findings have important antibiotic stewardship implications during this pandemic, as inappropriate use of antibiotics leads to increased antimicrobial resistance, and there is evidence that azithromycin use increased during the pandemic in the UK. Funding UK Research and Innovation and UK Department of Health and Social Care

On global asymptotic stability of neural networks with discrete and distributed delays

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2005 Elsevier Ltd.In this Letter, the global asymptotic stability analysis problem is investigated for a class of neural networks with discrete and distributed time-delays. The purpose of the problem is to determine the asymptotic stability by employing some easy-to-test conditions. It is shown, via the Lyapunov–Krasovskii stability theory, that the class of neural networks under consideration is globally asymptotically stable if a quadratic matrix inequality involving several parameters is feasible. Furthermore, a linear matrix inequality (LMI) approach is exploited to transform the addressed stability analysis problem into a convex optimization problem, and sufficient conditions for the neural networks to be globally asymptotically stable are then derived in terms of a linear matrix inequality, which can be readily solved by using the Matlab LMI toolbox. Two numerical examples are provided to show the usefulness of the proposed global stability condition.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

DC Cancellation As a Method of Generating a t^2 Response and of Solving the Radial Nonobservability Problem in a Concentric Free-Falling Two-Sphere Equivalence-Principle Experiment in a Drag-Free Satellite

This paper solves two major problems which have blocked a free-fall Equivalence-Principle (EP) in a satellite for 25 years: a semimajor-axis error between the two proof masses cannot be distinguished from an EP violation and the response to an EP violation only grows as t not t^2. Using the cancellation method described in this paper, the nonobservability problem can be suppressed and a t^2 response can be generated which lasts between 10^4 and 10^6 seconds depending on the cancellation accuracy. t^2 response times between 10^5 and 10^6 seconds are equivalent to a very tall (0.1 to 10 AU) drop tower with a constant gravitational field of 3/7 ge.Comment: 40 pages, 7 figures, Revision 3.0: Reviewer's suggested corrections for journal submissio

Azithromycin for community treatment of suspected COVID-19 in people at increased risk of an adverse clinical course in the UK (PRINCIPLE): a randomised, controlled, open-label, adaptive platform trial

This is the final version. Available on open access from Elsevier via the DOI in this recordData sharing: Data can be shared with qualifying researchers who submit a proposal with a valuable research question as assessed by a committee formed from the Trial Management Group, including senior statistical and clinical representation. A contract should be signed. Requests should be directed to [email protected] Azithromycin, an antibiotic with potential antiviral and anti-inflammatory properties, has been used to treat COVID-19, but evidence from community randomised trials is lacking. We aimed to assess the effectiveness of azithromycin to treat suspected COVID-19 among people in the community who had an increased risk of complications. Methods In this UK-based, primary care, open-label, multi-arm, adaptive platform randomised trial of interventions against COVID-19 in people at increased risk of an adverse clinical course (PRINCIPLE), we randomly assigned people aged 65 years and older, or 50 years and older with at least one comorbidity, who had been unwell for 14 days or less with suspected COVID-19, to usual care plus azithromycin 500 mg daily for three days, usual care plus other interventions, or usual care alone. The trial had two coprimary endpoints measured within 28 days from randomisation: time to first self-reported recovery, analysed using a Bayesian piecewise exponential, and hospital admission or death related to COVID-19, analysed using a Bayesian logistic regression model. Eligible participants with outcome data were included in the primary analysis, and those who received the allocated treatment were included in the safety analysis. The trial is registered with ISRCTN, ISRCTN86534580. Findings The first participant was recruited to PRINCIPLE on April 2, 2020. The azithromycin group enrolled participants between May 22 and Nov 30, 2020, by which time 2265 participants had been randomly assigned, 540 to azithromycin plus usual care, 875 to usual care alone, and 850 to other interventions. 2120 (94%) of 2265 participants provided follow-up data and were included in the Bayesian primary analysis, 500 participants in the azithromycin plus usual care group, 823 in the usual care alone group, and 797 in other intervention groups. 402 (80%) of 500 participants in the azithromycin plus usual care group and 631 (77%) of 823 participants in the usual care alone group reported feeling recovered within 28 days. We found little evidence of a meaningful benefit in the azithromycin plus usual care group in time to first reported recovery versus usual care alone (hazard ratio 1·08, 95% Bayesian credibility interval [BCI] 0·95 to 1·23), equating to an estimated benefit in median time to first recovery of 0·94 days (95% BCI −0·56 to 2·43). The probability that there was a clinically meaningful benefit of at least 1·5 days in time to recovery was 0·23. 16 (3%) of 500 participants in the azithromycin plus usual care group and 28 (3%) of 823 participants in the usual care alone group were hospitalised (absolute benefit in percentage 0·3%, 95% BCI −1·7 to 2·2). There were no deaths in either study group. Safety outcomes were similar in both groups. Two (1%) of 455 participants in the azothromycin plus usual care group and four (1%) of 668 participants in the usual care alone group reported admission to hospital during the trial, not related to COVID-19. Interpretation Our findings do not justify the routine use of azithromycin for reducing time to recovery or risk of hospitalisation for people with suspected COVID-19 in the community. These findings have important antibiotic stewardship implications during this pandemic, as inappropriate use of antibiotics leads to increased antimicrobial resistance, and there is evidence that azithromycin use increased during the pandemic in the UK.UK Research and InnovationUK Department of Health and Social Car

Multi-Collision Resistance: A Paradigm for Keyless Hash Functions

We introduce a new notion of multi-collision resistance for keyless hash functions. This is a natural relaxation of collision resistance where it is hard to find multiple inputs with the same hash in the following sense. The number of colliding inputs that a polynomial-time non-uniform adversary can find is not much larger than its advice. We discuss potential candidates for this notion and study its applications. Assuming the existence of such hash functions, we resolve the long-standing question of the round complexity of zero knowledge protocols --- we construct a 3-message zero knowledge argument against arbitrary polynomial-size non-uniform adversaries. We also improve the round complexity in several other central applications, including a 3-message succinct argument of knowledge for NP, a 4-message zero-knowledge proof, and a 5-message public-coin zero-knowledge argument. Our techniques can also be applied in the keyed setting, where we match the round complexity of known protocols while relaxing the underlying assumption from collision-resistance to keyed multi-collision resistance. The core technical contribution behind our results is a domain extension transformation from multi-collision-resistant hash functions for a fixed input length to ones with an arbitrary input length and a local opening property. The transformation is based on a combination of classical domain extension techniques, together with new information-theoretic tools. In particular, we define and construct a new variant of list-recoverable codes, which may be of independent interest