Tideglusib: The Miracle Molecule for Tooth Repair

Guest Comment by Sahil Gupta titled "Tideglusib: The Miracle Molecule for Tooth Repair

FDI in India and Other Asian Countries

The Sub-continent has become the prime target for foreign direct investment. The economic policies of India have been tailor made to specifically attract substantial inflow of capital into the Indian market and to sustain such inflows of capital. The Indian Government is constantly innovating to make the country an investor friendly destination and this attitude is reaping good results. The economic policies and economic reforms initiated by the Government had resulted in India being ranked the second position in attracting foreign direct investments (FDI). This ranking was conferred in 2010 by the United Nations Conference on Trade and Development (UNCTAD). The ranking was published in a report of UNCTAD titled: “World Investment Prospects Survey 2009-2012”. The said report has made the investment climate in India more favourable than ever before. The report also forecast that soon the country is going to feature among the top 5 investment destinations for investor from the world in the period 2010 to 2012. In May 2011 the inflow of FDI was more than hundred percent at US $4.66 billion. This amount has been the highest monthly investment in a single month for the last thirty nine months. Cumulatively, the total amount of FDI in India for the period April-May 2011 stands at around US$ 205.96 billion. This figure is according to the latest data released by the Department of Industrial Policy and Promotion (DIPP). Of all the sectors that drew FDI during the latest year, the highest FDI was drawn by the services sectors which included both the financial as well as non-financial sectors. The amount of FDI was US$910 million. Of the flow of FDI from countries, Mauritius topped the investment, investing close to US$ 56.31 billion while Singapore was the second largest foreign investor at US$13.25 billion. The US stood at the third place in investment, investing about US$ 9.71 billion. The period of the above said investment was between April 2000 to May 2011. The Forex reserves which are also known as foreign exchange reserves have increased significantly by US$2.29 billion. This amount is for the week that ended on 22nd July 2011. The above data was released by the Reserve Bank of India which is also known as RBI in it’s weekly statistical report. Similarly the foreign currency assets stood at US$ 284.53 billion from US$ 2.23 billion for the same period. It is also predicted that India might become the largest market of the US Export-Import Bank in the coming year and a half or so. This paper analysis the structure of economic reforms during the pre- independence and post independence era in the context of growth of foreign direct investment and the risks posed by the political, economic and social conditions for foreign investors. Essentially, this paper seeks to analyse and understand the politico-economic dynamics in relation to the country’s progressive integration with other major economies of the world which has put India on the global economic map

Robust Algorithms for the Secretary Problem

In classical secretary problems, a sequence of n elements arrive in a uniformly random order, and we want to choose a single item, or a set of size K. The random order model allows us to escape from the strong lower bounds for the adversarial order setting, and excellent algorithms are known in this setting. However, one worrying aspect of these results is that the algorithms overfit to the model: they are not very robust. Indeed, if a few "outlier" arrivals are adversarially placed in the arrival sequence, the algorithms perform poorly. E.g., Dynkin’s popular 1/e-secretary algorithm is sensitive to even a single adversarial arrival: if the adversary gives one large bid at the beginning of the stream, the algorithm does not select any element at all. We investigate a robust version of the secretary problem. In the Byzantine Secretary model, we have two kinds of elements: green (good) and red (rogue). The values of all elements are chosen by the adversary. The green elements arrive at times uniformly randomly drawn from [0,1]. The red elements, however, arrive at adversarially chosen times. Naturally, the algorithm does not see these colors: how well can it solve secretary problems? We show that selecting the highest value red set, or the single largest green element is not possible with even a small fraction of red items. However, on the positive side, we show that these are the only bad cases, by giving algorithms which get value comparable to the value of the optimal green set minus the largest green item. (This benchmark reminds us of regret minimization and digital auctions, where we subtract an additive term depending on the "scale" of the problem.) Specifically, we give an algorithm to pick K elements, which gets within (1-ε) factor of the above benchmark, as long as K ≥ poly(ε^{-1} log n). We extend this to the knapsack secretary problem, for large knapsack size K. For the single-item case, an analogous benchmark is the value of the second-largest green item. For value-maximization, we give a poly log^* n-competitive algorithm, using a multi-layered bucketing scheme that adaptively refines our estimates of second-max over time. For probability-maximization, we show the existence of a good randomized algorithm, using the minimax principle. We hope that this work will spur further research on robust algorithms for the secretary problem, and for other problems in sequential decision-making, where the existing algorithms are not robust and often tend to overfit to the model.ISSN:1868-896

Dietary Habits of Patients with Chronic Medical Conditions During COVID-19

Over the past two years, the COVID-19 pandemic has forced drastic changes in various aspects of normal life for millions world-wide. As of April 2022, there have been over reported 80.8 million cases and 989,000 reported deaths. At the start of the COVID-19 pandemic, there were numerous societal changes occurred such as social distancing protocols, mask recommendations and restrictions in public spaces. With such drastic changes to normal life, investigators began examining how dietary habits in the general population could have been affected, but not investigated the impacts on patients with chronic medical conditions (CMC). Prior to major vaccination efforts, in February of 2021, the CDC noted that of the 548,971 confirmed deaths, 96.1% of those deaths where among individuals with pre-existing chronic medical conditions. Patients with chronic medical conditions, have strict regimented dietary patterns and nutritional needs. GOAL: Gather information and use it to help address the needs of patients with chronic medical conditions and address factors that can influence dietary habits

Proximinality and co-proximinality in metric linear spaces

As a counterpart to best approximation, the concept of best coapproximation was introduced in normed linear spaces by C. Franchetti and M. Furi in 1972. Subsequently, this study was taken up by many researchers. In this paper, we discuss some results on the existence and uniqueness of best approximation and best coapproximation when the underlying spaces are metric linear spaces

On strong proximinality in normed linear spaces

The paper deals with strong proximinality in normed linear spaces. It is proved that in  a compactly locally uniformly rotund Banach space, proximinality, strong proximinality, weak approximative compactness and  approximative compactness are all equivalent for closed convex sets. How strong proximinality can be transmitted to and from quotient spaces has also been discussed