On the Convergence of Decentralized Gradient Descent

Consider the consensus problem of minimizing $f(x)=\sum_{i=1}^n f_i(x)$ where each $f_i$ is only known to one individual agent $i$ out of a connected network of $n$ agents. All the agents shall collaboratively solve this problem and obtain the solution subject to data exchanges restricted to between neighboring agents. Such algorithms avoid the need of a fusion center, offer better network load balance, and improve data privacy. We study the decentralized gradient descent method in which each agent $i$ updates its variable $x_{(i)}$, which is a local approximate to the unknown variable $x$, by combining the average of its neighbors' with the negative gradient step $-\alpha \nabla f_i(x_{(i)})$. The iteration is $$x_{(i)}(k+1) \gets \sum_{\text{neighbor} j \text{of} i} w_{ij} x_{(j)}(k) - \alpha \nabla f_i(x_{(i)}(k)),\quad\text{for each agent} i,$$ where the averaging coefficients form a symmetric doubly stochastic matrix $W=[w_{ij}] \in \mathbb{R}^{n \times n}$. We analyze the convergence of this iteration and derive its converge rate, assuming that each $f_i$ is proper closed convex and lower bounded, $\nabla f_i$ is Lipschitz continuous with constant $L_{f_i}$, and stepsize $\alpha$ is fixed. Provided that $\alpha < O(1/L_h)$ where $L_h=\max_i\{L_{f_i}\}$, the objective error at the averaged solution, $f(\frac{1}{n}\sum_i x_{(i)}(k))-f^*$, reduces at a speed of $O(1/k)$ until it reaches $O(\alpha)$. If $f_i$ are further (restricted) strongly convex, then both $\frac{1}{n}\sum_i x_{(i)}(k)$ and each $x_{(i)}(k)$ converge to the global minimizer $x^*$ at a linear rate until reaching an $O(\alpha)$-neighborhood of $x^*$. We also develop an iteration for decentralized basis pursuit and establish its linear convergence to an $O(\alpha)$-neighborhood of the true unknown sparse signal

On the Linear Convergence of the ADMM in Decentralized Consensus Optimization

In decentralized consensus optimization, a connected network of agents collaboratively minimize the sum of their local objective functions over a common decision variable, where their information exchange is restricted between the neighbors. To this end, one can first obtain a problem reformulation and then apply the alternating direction method of multipliers (ADMM). The method applies iterative computation at the individual agents and information exchange between the neighbors. This approach has been observed to converge quickly and deemed powerful. This paper establishes its linear convergence rate for decentralized consensus optimization problem with strongly convex local objective functions. The theoretical convergence rate is explicitly given in terms of the network topology, the properties of local objective functions, and the algorithm parameter. This result is not only a performance guarantee but also a guideline toward accelerating the ADMM convergence.Comment: 11 figures, IEEE Transactions on Signal Processing, 201

Cortical responses correlate with speech performance in pre-lingually deaf cochlear implant children

IntroductionCochlear implantation is currently the most successful intervention for severe-to-profound sensorineural hearing loss, particularly in deaf infants and children. Nonetheless, there remains a significant degree of variability in the outcomes of CI post-implantation. The purpose of this study was to understand the cortical correlates of the variability in speech outcomes with a cochlear implant in pre-lingually deaf children using functional near-infrared spectroscopy (fNIRS), an emerging brain-imaging technique.MethodsIn this experiment, cortical activities when processing visual speech and two levels of auditory speech, including auditory speech in quiet and in noise with signal-to-noise ratios of 10 dB, were examined in 38 CI recipients with pre-lingual deafness and 36 normally hearing children whose age and sex matched CI users. The HOPE corpus (a corpus of Mandarin sentences) was used to generate speech stimuli. The regions of interest (ROIs) for the fNIRS measurements were fronto-temporal-parietal networks involved in language processing, including bilateral superior temporal gyrus, left inferior frontal gyrus, and bilateral inferior parietal lobes.ResultsThe fNIRS results confirmed and extended findings previously reported in the neuroimaging literature. Firstly, cortical responses of superior temporal gyrus to both auditory and visual speech in CI users were directly correlated to auditory speech perception scores, with the strongest positive association between the levels of cross-modal reorganization and CI outcome. Secondly, compared to NH controls, CI users, particularly those with good speech perception, showed larger cortical activation in the left inferior frontal gyrus in response to all speech stimuli used in the experiment.DiscussionIn conclusion, cross-modal activation to visual speech in the auditory cortex of pre-lingually deaf CI children may be at least one of the neural bases of highly variable CI performance due to its beneficial effects for speech understanding, thus supporting the prediction and assessment of CI outcomes in clinic. Additionally, cortical activation of the left inferior frontal gyrus may be a cortical marker for effortful listening

Generation of Oligodendrocyte Progenitor Cells From Mouse Bone Marrow Cells.

Oligodendrocyte progenitor cells (OPCs) are a subtype of glial cells responsible for myelin regeneration. Oligodendrocytes (OLGs) originate from OPCs and are the myelinating cells in the central nervous system (CNS). OLGs play an important role in the context of lesions in which myelin loss occurs. Even though many protocols for isolating OPCs have been published, their cellular yield remains a limit for clinical application. The protocol proposed here is novel and has practical value; in fact, OPCs can be generated from a source of autologous cells without gene manipulation. Our method represents a rapid, and high-efficiency differentiation protocol for generating mouse OLGs from bone marrow-derived cells using growth-factor defined media. With this protocol, it is possible to obtain mature OLGs in 7-8 weeks. Within 2-3 weeks from bone marrow (BM) isolation, after neurospheres formed, the cells differentiate into Nestin+ Sox2+ neural stem cells (NSCs), around 30 days. OPCs specific markers start to be expressed around day 38, followed by RIP+O4+ around day 42. CNPase+ mature OLGs are finally obtained around 7-8 weeks. Further, bone marrow-derived OPCs exhibited therapeutic effect in shiverer (Shi) mice, promoting myelin regeneration and reducing the tremor. Here, we propose a method by which OLGs can be generated starting from BM cells and have similar abilities to subventricular zone (SVZ)-derived cells. This protocol significantly decreases the timing and costs of the OLGs differentiation within 2 months of culture

2-Chloro-5-(chloro­meth­yl)pyridine

The title compound, C6H5Cl2N, is almost planar, with an r.m.s. deviation of 0.0146 Å for all atoms except for the 5-choloromethyl Cl atom. The offset Cl atom lies above this plane with a Cl—C—C angle of 111.11 (17)°. In the crystal, mol­ecules are connected via inter­molecular C—H⋯N hydrogen bonds, forming dimers

Safety and efficacy of etomidate and propofol anesthesia in elderly patients undergoing gastroscopy: A double-blind randomized clinical study

The aim of the present study is to compare the safety, efficacy and cost effectiveness of anesthetic regimens by compound, using etomidate and propofol in elderly patients undergoing gastroscopy. A total of 200 volunteers (65–79 years of age) scheduled for gastroscopy under anesthesia were randomly divided into the following groups: P, propofol (1.5–2.0 mg/kg); E, etomidate (0.15-0.2 mg/kg); P+E, propofol (0.75–1 mg/kg) followed by etomidate (0.075-0.1 mg/kg); and E+P, etomidate (0.075-0.01 mg/kg) followed by propofol (0.75–1 mg/kg). Vital signs and bispectral index were monitored at different time points. Complications, induction and examination time, anesthesia duration, and recovery and discharge time were recorded. At the end of the procedure, the satisfaction of patients, endoscopists and the anesthetist were evaluated. The recovery (6.1±1.2 h) and discharge times (24.8±2.8 h) in group E were significantly longer compared with groups P, P+E and E+P (P<0.05). The occurrence of injection pain in group P+E was significantly higher compared with the other three groups (P<0.05). In addition, the incidence of myoclonus and post-operative nausea and vomiting were significantly higher in group P+E compared with the other three groups (P<0.05). There was no statistical difference among the four groups with regards to the patients' immediate, post-procedure satisfaction (P>0.05). Furthermore, there was no difference in the satisfaction of anesthesia, as evaluated by the anesthetist and endoscopist, among the four groups (P>0.05). The present study demonstrates that anesthesia for gastroscopy in elderly patients can be safely and effectively accomplished using a drug regimen that combines propofol with etomidate. The combined use of propofol and etomidate has unique characteristics which improve hemodynamic stability, cause minimal respiratory depression and less side effects, provide rapid return to full activity and result in high levels of satisfaction

Phosphocreatine Preconditioning Attenuates Apoptosis in Ischemia-Reperfusion Injury of Rat Brain

Phosphocreatine (PCr) is an endogenous compound containing high-energy phosphate bonds. It has been confirmed that PCr is effective in preventing and treating cardiac and renal ischemia-reperfusion injury. In this study, rat cerebral ischemia-reperfusion injury models were constructed. Apoptotic cells in the cortex region were measured by TUNEL method. Malondialdehyde (MDA) content was detected by chromatometry, and calmodulin (CaM) activity was detected by ELISA. Compared with sham-operated group (sham group), TUNEL-positive cells, MDA, and level of CaM activity increased in ischemia-reperfusion group (I/R group) and PCr preconditioning group (PCr group); compared with I/R group, TUNEL-positive cells, MDA content, and level of CaM activity decreased in PCr group. This study indicated that PCr can decrease the morphological damage and the neuron apoptosis of the ischemia-reperfusion injury brain through attenuating abnormalities of calcium balance and production of oxygen free radicals

Predictors for Smoking Cessation with Acupuncture in a Hong Kong Population

Background. Observational studies of smoking cessation with acupuncture have been reported widely; however, few researchers have focused on its predictors. Objective. This paper attempts to explore the predictors for smoking cessation with acupuncture in a Hong Kong population, aiming to provide references for clinical treatment in the future. Methods. We performed a secondary analysis of data from our observational study “Acupuncture for Smoking Cessation (2011–2014)” in Hong Kong. A total of 23 indexes were selected as possible predictors, and study participants with complete information of 23 indexes were included. By taking 8-week and 52-week smoking cessation results as dependent variables, binary logistic regression method was used to identify the predictors. Additionally, based on an M5P decision-tree algorithm, an equation of “successful rate of smoking cessation with acupuncture” was calculated. Results. (1) 2,051 study participants were included in total. (2) According to the results of binary logistic regression, variables including treatment location, total number of acupuncture sessions received, and whether the study participants received at least 6 sessions of acupuncture were taken as the short-term predictors; gender, treatment location, Fagerstrom Test for Nicotine Dependence (FTND), and total number of acupuncture sessions received were taken as the long-term predictors. (3) According to study participants’ FTND, treatment location, and number of cigarettes smoked/day, the equation of “successful rate of smoking cessation with acupuncture” was established. Conclusion. Receiving sufficient and qualified acupuncture is the leading factor for short-term smoking cessation with acupuncture, whereas individual factors and smoking background play a more important role in long-term smoking cessation with acupuncture