A novel, simple interpretation of Nesterov’s accelerated method as a combination of gradient and mirror descent

First-order methods play a central role in large-scale convex optimization. Despite their various forms of descriptions and many applications, such methods mostly and fundamentally rely on two basic types of analyses: gradient-descent analysis, which yields primal progress, and mirror-descent analysis, which yields dual progress. In this paper, we observe that the performances of these two analyses are complementary, so that faster algorithms can be designed by coupling the two analyses, and their corresponding descent steps. In particular, we show in this paper how to obtain a conceptually simple reinterpretation of Nesterov's accelerated gradient method [Nes83, Nes04, Nes05]. Nesterov's method is the optimal first-order method for the class of smooth convex optimization problems. However, the proof of the fast convergence of Nesterov's method has no clear interpretation and is regarded by some as relying on an "algebraic trick". We apply our novel insights to express Nesterov's algorithm as a coupling of gradient descent and mirror descent, and as a result, the convergence proof can be understood as some natural combination of the two underlying convergence analyses. We believe that this complementary view of the two types of analysis may not only facilitate the study of Nesterov's method in a white-box manner so as to apply it to problems outside its original scope, but also let us design better first-order methods in a conceptually easier way

Distributed Edge Connectivity in Sublinear Time

We present the first sublinear-time algorithm for a distributed message-passing network sto compute its edge connectivity $\lambda$ exactly in the CONGEST model, as long as there are no parallel edges. Our algorithm takes $\tilde O(n^{1-1/353}D^{1/353}+n^{1-1/706})$ time to compute $\lambda$ and a cut of cardinality $\lambda$ with high probability, where $n$ and $D$ are the number of nodes and the diameter of the network, respectively, and $\tilde O$ hides polylogarithmic factors. This running time is sublinear in $n$ (i.e. $\tilde O(n^{1-\epsilon})$) whenever $D$ is. Previous sublinear-time distributed algorithms can solve this problem either (i) exactly only when $\lambda=O(n^{1/8-\epsilon})$ [Thurimella PODC'95; Pritchard, Thurimella, ACM Trans. Algorithms'11; Nanongkai, Su, DISC'14] or (ii) approximately [Ghaffari, Kuhn, DISC'13; Nanongkai, Su, DISC'14]. To achieve this we develop and combine several new techniques. First, we design the first distributed algorithm that can compute a $k$-edge connectivity certificate for any $k=O(n^{1-\epsilon})$ in time $\tilde O(\sqrt{nk}+D)$. Second, we show that by combining the recent distributed expander decomposition technique of [Chang, Pettie, Zhang, SODA'19] with techniques from the sequential deterministic edge connectivity algorithm of [Kawarabayashi, Thorup, STOC'15], we can decompose the network into a sublinear number of clusters with small average diameter and without any mincut separating a cluster (except the `trivial' ones). Finally, by extending the tree packing technique from [Karger STOC'96], we can find the minimum cut in time proportional to the number of components. As a byproduct of this technique, we obtain an $\tilde O(n)$-time algorithm for computing exact minimum cut for weighted graphs.Comment: Accepted at 51st ACM Symposium on Theory of Computing (STOC 2019

Spectral Sparsification and Regret Minimization Beyond Matrix Multiplicative Updates

In this paper, we provide a novel construction of the linear-sized spectral sparsifiers of Batson, Spielman and Srivastava [BSS14]. While previous constructions required $\Omega(n^4)$ running time [BSS14, Zou12], our sparsification routine can be implemented in almost-quadratic running time $O(n^{2+\varepsilon})$. The fundamental conceptual novelty of our work is the leveraging of a strong connection between sparsification and a regret minimization problem over density matrices. This connection was known to provide an interpretation of the randomized sparsifiers of Spielman and Srivastava [SS11] via the application of matrix multiplicative weight updates (MWU) [CHS11, Vis14]. In this paper, we explain how matrix MWU naturally arises as an instance of the Follow-the-Regularized-Leader framework and generalize this approach to yield a larger class of updates. This new class allows us to accelerate the construction of linear-sized spectral sparsifiers, and give novel insights on the motivation behind Batson, Spielman and Srivastava [BSS14]

Fonti orali e teatro. Memoria, storia e performance

The book has its roots in a seminar held in 2015 in the University Centre of Imperia. The seminar was devoted to oral sources and theatre. It was a first, important opportunity for (Italian and French) theatre historians and oral historians to meet and have a debate. After a first part centred on interdisciplinary considerations (Oral history, memory, theatre), the book collects essays organized into two conceptual subdivisions. Oral sources for the theatre deals with oral sources as documentary resources for theatre history and for a polyphonic memory of theatre, by exploring methodological questions and offering some concrete examples. Oral sources in the theatre focuses on theatre performances where oral sources are used as dramaturgy materials. The book doesn\u2019t offer unequivocal answers, but it confirms the countless and possible exchanges of views between orality and theatre scholars. This result is a dynamic and open research of new tools and knowledge

Three-times daily radiotherapy after chemotherapy in stage III non-small cell lung cancer. Single-institution prospective study

Aim: A prospective study for stage IIIA-B non-small cell lung cancer (NSCLC), with three-times daily (3td) radiotherapy (RT), after induction chemotherapy (iCT), with or without surgery. Patients and Methods: Induction cisplatin and gemcitabine chemotherapy was delivered. Surgery and postoperative (post-op) radiotherapy were planned for responsive stage IIIA patients; definitive irradiation was performed in unresectable III A and IIIB patients. Doses of 54.4 and 64.6 Gy were delivered for the post-op and definitive treatments, respectively. Results: Out of 52 patients (pts), 37 received 3tdRT as definitive (18 pts) or post-op treatment (19 pts). Overall, the failures were similar between post-op and definitive 3tdRT (78.9% vs. 77.8%). In the post-op treatment, metastases and local failures were 52.6% and 10.5%, respectively and in the definitive radiotherapy, the incidence was similar (local 33.3% vs. systemic 44.4%). The five-year overall survival (OS) was 25% for the post-op and 21% for the definitive patients (p=0.87). Conclusion: Three-times daily postoperative radiotherapy did not improve the outcome in NSCLC, but for unresectable patients, this approach may have a role in selected cases

Prevalence and genotyping of human isolates of Giardia duodenalis from Albania

Microscopical and PCR-based techniques were performed in order to investigate the prevalence of infection and the genotypes of Giardia duodenalis from 125 stool samples collected from children living in the urban and the rural areas of Tirana (Albania) and hospitalized with acute gastroenteritis. 7 out of 125 samples resulted positive for Giardia at the microscopic examination (5.6%). In 50 selected samples including the 7 samples positive for Giardia by microscopy, 3 and 15 additional positive samples were detected by immunofluorescence and PCR, respectively. Seasonality appeared as an important parameter to be evaluated in order to better understand the prevalence of infection. Sequence analysis revealed both human Assemblage A and B. This result represents the first data on G. duodenalis genotypes in Albania. (c) 2006 Elsevier Ireland Ltd. All rights reserved

po 237 the pro oncogenic transcription factor stat3 regulates ca2 release and apoptosis from the endoplasmic reticulum via interaction with the ca2 channel ip3r3

Introduction Signal Transducer and Activator of Transcription (STAT) 3 is an oncogenic transcription factor found constitutively activated in several tumours, where it exerts its functions both as a canonical transcription factor and as a non-canonical regulator of energy metabolism and mitochondrial functions. These two activities rely on different post-translational activating events; the phosphorylation on Y705 is involved in nuclear activities, while that on S727 is relevant for mitochondrial functions. Mitochondrial STAT3 increases aerobic glycolysis and decreases ROS production, partly by interacting with the Electron Transfer Complexes (ETC). Material and methods By means of cell fractionations, we tested STAT3 localization to the Endoplasmic Reticulum (ER) in breast cancer cell lines dependent or not on STAT3 activity. We then measured Ca2+ release and apoptotic response in the same cells. The physical interaction between inositol 1,4,5-trisphosphate receptor type 3 (IP3R3) and STAT3 was demonstrated by co-IP either of the endogenous proteins or of their truncated/mutated forms, while STAT3 role in the degradation of IP3R3 was tested by serum starvation and refeeding experiments, followed by WB. Results and discussions We describe here the previously undetected abundant localization of STAT3 also to the ER. In this cellular compartment IP3R3, a Ca2+ channel that allows Ca2+ release from the ER and the mitochondrial associated membranes (MAMs) in response to IP3, regulates the balance between mitochondrial activation and Ca2+-triggered apoptosis. We observed that STAT3 within the ER physically interacts with IP3R3 and, via its phosphorylation on S727, it down-regulates Ca2+ release and apoptosis. Indeed, STAT3 silencing enhances both ER Ca2+ release and sensitivity to apoptosis following oxidative stress in STAT3-dependent mammary tumour cells, correlating with increased IP3R3 levels. In line with this, basal-like breast tumours, which frequently display constitutively active STAT3, show an inverse correlation between IP3R3 and STAT3 protein levels. Conclusion Our results indicate that S727-phosphorylated STAT3 contribute to mammary tumour aggressiveness, also by localising to the ER and regulating Ca2+ fluxes. STAT3-mediated enhanced IP3R3 degradation leads to decreased Ca2+ release and thus to resistance to apoptosis. This new non-canonical STAT3 role appears to be particularly relevant in basal-like breast cancers, adding a new mechanisms through which STAT3 exerts its well established pro-oncogenic anti-apoptotic role