Last-Iterate Convergence: Zero-Sum Games and Constrained Min-Max Optimization

Motivated by applications in Game Theory, Optimization, and Generative Adversarial Networks, recent work of Daskalakis et al [Daskalakis et al., ICLR, 2018] and follow-up work of Liang and Stokes [Liang and Stokes, 2018] have established that a variant of the widely used Gradient Descent/Ascent procedure, called "Optimistic Gradient Descent/Ascent (OGDA)", exhibits last-iterate convergence to saddle points in unconstrained convex-concave min-max optimization problems. We show that the same holds true in the more general problem of constrained min-max optimization under a variant of the no-regret Multiplicative-Weights-Update method called "Optimistic Multiplicative-Weights Update (OMWU)". This answers an open question of Syrgkanis et al [Syrgkanis et al., NIPS, 2015]. The proof of our result requires fundamentally different techniques from those that exist in no-regret learning literature and the aforementioned papers. We show that OMWU monotonically improves the Kullback-Leibler divergence of the current iterate to the (appropriately normalized) min-max solution until it enters a neighborhood of the solution. Inside that neighborhood we show that OMWU becomes a contracting map converging to the exact solution. We believe that our techniques will be useful in the analysis of the last iterate of other learning algorithms

A New Measurement Model to Estimate the Intensity of Acrotony on the Latent Buds of Grapevine Canes (Vitis vinifera L.)

In warm regions, such as in southern Greece, the climate change can lead to prolonged dormancy as well as to problems in bud dormancy (delay in breaking time, reduce the rate of budbreak, intensity of the phenomenon of acrotony, grapevine bud fall, disorders in bloom with intense blossom dropping, etc.), with a significant impact on the production of the vines. In these areas, it is necessary to apply chemical substances in order to break the dormancy and advance budbreak, especially when it comes to new table grape varieties, most of which are seedless. Another phenomenon which is observed on grapevines and is directly associated with budbreak is acrotony, where the apical buds of the cane break first compared to the middle and basal ones. Acrotony can constitute a problem because it can cause irregular grape ripening, different timing of various activities in the vineyard, which brings about higher cultivation costs. In this research, a new method to measure and evaluate the acrotony and its intensity on the latent buds of grapevine canes was described. The results of two chemical substances applied on table grape variety ‘Prime’ in order to advance budbreak were presented

Stretching Method-Based Operational Modal Analysis of An Old Masonry Lighthouse.

We present in this paper a structural health monitoring study of the Egyptian lighthouse of Rethymnon in Crete, Greece. Using structural vibration data collected on a limited number of sensors during a 3-month period, we illustrate the potential of the stretching method for monitoring variations in the natural frequencies of the structure. The stretching method compares two signals, the current that refers to the actual state of the structure, with the reference one that characterizes the structure at a reference healthy condition. For the structure under study, an 8-day time interval is used for the reference quantity while the current quantity is computed using a time window of 24 h. Our results indicate that frequency shifts of 1% can be detected with high accuracy allowing for early damage assessment. We also provide a simple numerical model that is calibrated to match the natural frequencies estimated using the stretching method. The model is used to produce possible damage scenarios that correspond to 1% shift in the first natural frequencies. Although simple in nature, this model seems to deliver a realistic response of the structure. This is shown by comparing the response at the top of the structure to the actual measurement during a small earthquake. This is a preliminary study indicating the potential of the stretching method for structural health monitoring of historical monuments. The results are very promising. Further analysis is necessary requiring the deployment of the instrumentation (possibly with additional instruments) for a longer period of time

Near-Optimal No-Regret Learning for Correlated Equilibria in Multi-Player General-Sum Games

Recently, Daskalakis, Fishelson, and Golowich (DFG) (NeurIPS`21) showed that if all agents in a multi-player general-sum normal-form game employ Optimistic Multiplicative Weights Update (OMWU), the external regret of every player is $O(\textrm{polylog}(T))$ after $T$ repetitions of the game. We extend their result from external regret to internal regret and swap regret, thereby establishing uncoupled learning dynamics that converge to an approximate correlated equilibrium at the rate of $\tilde{O}(T^{-1})$. This substantially improves over the prior best rate of convergence for correlated equilibria of $O(T^{-3/4})$ due to Chen and Peng (NeurIPS`20), and it is optimal -- within the no-regret framework -- up to polylogarithmic factors in $T$. To obtain these results, we develop new techniques for establishing higher-order smoothness for learning dynamics involving fixed point operations. Specifically, we establish that the no-internal-regret learning dynamics of Stoltz and Lugosi (Mach Learn`05) are equivalently simulated by no-external-regret dynamics on a combinatorial space. This allows us to trade the computation of the stationary distribution on a polynomial-sized Markov chain for a (much more well-behaved) linear transformation on an exponential-sized set, enabling us to leverage similar techniques as DGF to near-optimally bound the internal regret. Moreover, we establish an $O(\textrm{polylog}(T))$ no-swap-regret bound for the classic algorithm of Blum and Mansour (BM) (JMLR`07). We do so by introducing a technique based on the Cauchy Integral Formula that circumvents the more limited combinatorial arguments of DFG. In addition to shedding clarity on the near-optimal regret guarantees of BM, our arguments provide insights into the various ways in which the techniques by DFG can be extended and leveraged in the analysis of more involved learning algorithms.Comment: Appeared at STOC 202

Assessment of the qualitative and quantitative characteristics of the grapes of grapevine cultivar Fokiano (Vitis vinifera L.) in Ikaria Island, under vineyard conditions

This study aimed at assessing the phenolic potential of indigenous Greek red grapevine cultivar Fokiano under different cultivation systems and altitudes, during the cultivation season 2019-2020, which could explore different approaches yielding better results in the same viticultural area, as is Ikaria Island. The samples of the present study were collected from productive (commercial) vineyards in the island of Ikaria, in the region of the North Aegean Sea. Samples of grapes were collected from 7 different vineyards at the northern part of Ikaria with different characteristics: (i) difference in the altitude of the vineyards and (ii) difference in the cultivation system (conventional or organic). The vineyards in question are located at an altitude of 200 m, 400 m, 600 m and 800 m. The samples were collected during the dates of harvest, which were determined according to the technological maturation of the grapes in combination with the biodynamic calendar. In all samples, the mechanical analyses of the grapes and berries took place and the characters of the must as well as the qualitative characters of the berries (must, skins, seeds) were studied. Total soluble solids of the must were calculated using a refractometer, the active acidity (pH) using a pH meter and the total acidity using a sodium hydroxide solution (NaOH). The mechanical analyses that were performed involved the weight of thirty (30) berries, the weight of the grape and the length and width of the berries and the grapes of each sample. The content of grape's skin in total anthocyanins, total phenolics, condensed tannins, total ortho-diphenols, total flavonoids, total flavanols, total flavonols and flavones and their antioxidant capacity with the use of FRAP and DPPH methods were determined using a spectrophotometer. The most important acids found in grapes were identified using High-Performance Liquid Chromatography (HPLC). The measurements in the grape seeds were made on the same compounds as the skins, except for total anthocyanins. The results of the present study showed that the altitude does not seem to have a significant effect on most of the qualitative and quantitative characters of the cultivar in Ikaria, however, in future studies, other factors that affect the qualitative characters of the grapes need to be taken into consideration and further evaluated. The microclimate of the highest altitude (800 m) had a positive effect regarding total phenolics, anthocyanins, tannins, flavonols, o-diphenol content and the antioxidant capacity of the skins according to FRAP method, but with opposite results in the case of the seeds. At the same time, it should be noted that no accurate conclusion can be drawn regarding the cultivation system (conventional or organic), since between the two pairs of conventional and organic vineyards (samples from conventional and organic vineyards at an altitude of 200 m - samples from conventional and organic vineyard at an altitude of 600 m), the measurements exhibit a variation in their results. The antioxidant capacity that was determined in the samples of Fokiano is also remarkable, when also compared with other indigenous red grapevine cultivars. In view of climate change, the exploitation of indigenous varieties under different soil and climatic conditions or even in the same viticultural region, like the one of the current experiment (different cultivation system, different altitude in the island of Ikaria) could unlock and highlight the full potential of such local varieties, depending on the final style of the wine produced

p-cymene impairs SARS-CoV-2 and Influenza A (H1N1) viral replication: In silico predicted interaction with SARS-CoV-2 nucleocapsid protein and H1N1 nucleoprotein

Therapeutic regimens for the COVID-19 pandemics remain unmet. In this line, repurposing of existing drugs against known or predicted SARS-CoV-2 protein actions have been advanced, while natural products have also been tested. Here, we propose that p-cymene, a natural monoterpene, can act as a potential novel agent for the treatment of SARS-CoV-2-induced COVID-19 and other RNA-virus-induced diseases (influenza, rabies, Ebola). We show by extensive molecular simulations that SARS-CoV-2 C-terminal structured domain contains a nuclear localization signal (NLS), like SARS-CoV, on which p-cymene binds with low micromolar affinity, impairing nuclear translocation of this protein and inhibiting viral replication, as verified by preliminary in vitro experiments. A similar mechanism may occur in other RNA-viruses (influenza, rabies and Ebola), also verified in vitro for influenza, by interaction of p-cymene with viral nucleoproteins, and structural modification of their NLS site, weakening its interaction with importin A. This common mechanism of action renders therefore p-cymene as a possible antiviral, alone, or in combination with other agents, in a broad spectrum of RNA viruses, from SARS-CoV-2 to influenza A infections

Energy Resolution Performance of the CMS Electromagnetic Calorimeter

The energy resolution performance of the CMS lead tungstate crystal electromagnetic calorimeter is presented. Measurements were made with an electron beam using a fully equipped supermodule of the calorimeter barrel. Results are given both for electrons incident on the centre of crystals and for electrons distributed uniformly over the calorimeter surface. The electron energy is reconstructed in matrices of 3 times 3 or 5 times 5 crystals centred on the crystal containing the maximum energy. Corrections for variations in the shower containment are applied in the case of uniform incidence. The resolution measured is consistent with the design goals