Sparse Convolution for Approximate Sparse Instance

Computing the convolution $A \star B$ of two vectors of dimension $n$ is one of the most important computational primitives in many fields. For the non-negative convolution scenario, the classical solution is to leverage the Fast Fourier Transform whose time complexity is $O(n \log n)$. However, the vectors $A$ and $B$ could be very sparse and we can exploit such property to accelerate the computation to obtain the result. In this paper, we show that when $\|A \star B\|_{\geq c_1} = k$ and $\|A \star B\|_{\leq c_2} = n-k$ holds, we can approximately recover the all index in $\mathrm{supp}_{\geq c_1}(A \star B)$ with point-wise error of $o(1)$ in $O(k \log (n) \log(k)\log(k/\delta))$ time. We further show that we can iteratively correct the error and recover all index in $\mathrm{supp}_{\geq c_1}(A \star B)$ correctly in $O(k \log(n) \log^2(k) (\log(1/\delta) + \log\log(k)))$ time

A Convergence Theory for Federated Average: Beyond Smoothness

Federated learning enables a large amount of edge computing devices to learn a model without data sharing jointly. As a leading algorithm in this setting, Federated Average FedAvg, which runs Stochastic Gradient Descent (SGD) in parallel on local devices and averages the sequences only once in a while, have been widely used due to their simplicity and low communication cost. However, despite recent research efforts, it lacks theoretical analysis under assumptions beyond smoothness. In this paper, we analyze the convergence of FedAvg. Different from the existing work, we relax the assumption of strong smoothness. More specifically, we assume the semi-smoothness and semi-Lipschitz properties for the loss function, which have an additional first-order term in assumption definitions. In addition, we also assume bound on the gradient, which is weaker than the commonly used bounded gradient assumption in the convergence analysis scheme. As a solution, this paper provides a theoretical convergence study on Federated Learning.Comment: BigData 202

An Approximate Algorithm Combining P Systems and Active Evolutionary Algorithms for Traveling Salesman Problems

An approximate algorithm combining P systems and active evolutionary algorithms (AEAPS) to solve traveling salesman problems (TSPs) is proposed in this paper. The novel algorithm uses the same membrane structure, subalgorithms and transporting mechanisms as Nishida’s algorithm, but adopts two classes of active evolution operators and a good initial solution generating method. Computer experiments show that the AEAPS produces better solutions than Nishida’s shrink membrane algorithm and similar solutions with an approximate optimization algorithm integrating P systems and ant colony optimization techniques (ACOPS) in solving TSPs. But the necessary number of iterations using AEAPS is less than both of them

The impact of gratitude interventions on patients with cardiovascular disease: a systematic review

Positive psychological factors play a pivotal role in improving cardiovascular outcomes. Gratitude interventions are among the most effective positive psychological interventions, with potential clinical applications in cardiology practice. To better understand the potential clinical effects of gratitude interventions in cardiovascular disease, four databases (Web of Science, Scopus, PubMed, and PsycArticles) were searched from 2005 to 2023 for relevant studies. Randomized controlled trials of gratitude interventions as the intervention and that reported physiological or psychosocial outcomes were eligible for inclusion. In total, 19 studies were identified, reporting results from 2951 participants from 19 to 71 years old from both healthy populations and those with clinical diagnoses. The studies showed that gratitude not only promotes mental health and adherence to healthy behaviors but also improves cardiovascular outcomes. Gratitude may have a positive impact on biomarkers of cardiovascular disease risk, especially asymptomatic heart failure, cardiovascular function, and autonomic nervous system activity

Asynchronous Spiking Neural P Systems with Multiple Channels and Symbols

Spiking neural P systems (SNP systems, in short) are a class of distributed parallel computation systems, inspired from the way that the neurons process and communicate information by means of spikes. A new variant of SNP systems, which works in asynchronous mode, asynchronous spiking neural P systems with multiple channels and symbols (ASNP-MCS systems, in short), is investigated in this paper. There are two interesting features in ASNP-MCS systems: multiple channels and multiple symbols. That is, every neuron has more than one synaptic channels to connect its subsequent neurons, and every neuron can deal with more than one type of spikes. The variant works in asynchronous mode: in every step, each neuron can be free to fire or not when its rules can be applied. The computational completeness of ASNP-MCS systems is investigated. It is proved that ASNP-MCS systems as number generating and accepting devices are Turing universal. Moreover, we obtain a small universal function computing device that is an ASNP-MCS system with 67 neurons. Specially, a new idea that can solve ``block'' problems is proposed in INPUT modules

Interactions between aerosol organic components and liquid water content during haze episodes in Beijing

Aerosol liquid water (ALW) is ubiquitous in ambient aerosol and plays an important role in the formation of both aerosol organics and inorganics. To investigate the interactions between ALW and aerosol organics during haze formation and evolution, ALW was modelled based on long-term measurement of submicron aerosol composition in different seasons in Beijing. ALW contributed by aerosol inorganics (ALW(inorg)) was modelled by ISORROPIA II, and ALW contributed by organics (ALW(org)) was estimated with kappa-Kohler theory, where the real-time hygroscopicity parameter of the organics (kappa(org)) was calculated from the real-time organic oxygen-to-carbon ratio (O/C). Overall particle hygroscopicity (kappa(total)) was computed by weighting component hygroscopicity parameters based on their volume fractions in the mixture. We found that ALW(org), which is often neglected in traditional ALW modelling, contributes a significant fraction (18 %-32 %) to the total ALW in Beijing. The ALW(org) fraction is largest on the cleanest days when both the organic fraction and kappa(org) are relatively high. The large variation in O/C, from 0.2 to 1.3, indicates the wide variety of organic components. This emphasizes the necessity of using real-time kappa(org), instead of fixed kappa(org), to calculate ALW(org) in Beijing. The significant variation in K org (calculated from O/C), together with highly variable organic or inorganic volume fractions, leads to a wide range of kappa(total) (between 0.20 and 0.45), which has a great impact on water uptake. The variation in organic O/C, or derived K org , was found to be influenced by temperature (T), ALW, and aerosol mass concentrations, among which T and ALW both have promoting effects on O/C. During high-ALW haze episodes, although the organic fraction decreases rapidly, O/C and derived K org increase with the increase in ALW, suggesting the formation of more soluble organics via heterogeneous uptake or aqueous processes. A positive feedback loop is thus formed: during high-ALW episodes, increasing kappa(org), together with decreasing particle organic fraction (or increasing particle inorganic fraction), increases kappa(total), and thus further promotes the ability of particles to uptake water.Peer reviewe