A universal bound on the variations of bounded convex functions

Given a convex set $C$ in a real vector space $E$ and two points $x,y\in C$, we investivate which are the possible values for the variation $f(y)-f(x)$, where $f:C\longrightarrow [m,M]$ is a bounded convex function. We then rewrite the bounds in terms of the Funk weak metric, which will imply that a bounded convex function is Lipschitz-continuous with respect to the Thompson and Hilbert metrics. The bounds are also proved to be optimal. We also exhibit the maximal subdifferential of a bounded convex function at a given point $x\in C$

Gains and Losses are Fundamentally Different in Regret Minimization: The Sparse Case

We demonstrate that, in the classical non-stochastic regret minimization problem with $d$ decisions, gains and losses to be respectively maximized or minimized are fundamentally different. Indeed, by considering the additional sparsity assumption (at each stage, at most $s$ decisions incur a nonzero outcome), we derive optimal regret bounds of different orders. Specifically, with gains, we obtain an optimal regret guarantee after $T$ stages of order $\sqrt{T\log s}$, so the classical dependency in the dimension is replaced by the sparsity size. With losses, we provide matching upper and lower bounds of order $\sqrt{Ts\log(d)/d}$, which is decreasing in $d$. Eventually, we also study the bandit setting, and obtain an upper bound of order $\sqrt{Ts\log (d/s)}$ when outcomes are losses. This bound is proven to be optimal up to the logarithmic factor $\sqrt{\log(d/s)}$

Sparse Stochastic Bandits

In the classical multi-armed bandit problem, d arms are available to the decision maker who pulls them sequentially in order to maximize his cumulative reward. Guarantees can be obtained on a relative quantity called regret, which scales linearly with d (or with sqrt(d) in the minimax sense). We here consider the sparse case of this classical problem in the sense that only a small number of arms, namely s < d, have a positive expected reward. We are able to leverage this additional assumption to provide an algorithm whose regret scales with s instead of d. Moreover, we prove that this algorithm is optimal by providing a matching lower bound - at least for a wide and pertinent range of parameters that we determine - and by evaluating its performance on simulated data

Regionalism as a new motif for regional planning in Korea

Regional development in Korea today is a political necessity. It is to secure continuing political supports for further national economic development on one hamd and on the other, to meet the ever increasing demands for more equitable shares of the development pie. In a society like Korea where 76% of the population believe that they have now achieved "middle class" status, support for futher growth and demand for equitable share are of two sides of a coin. The societal context of persuasion for development ,planning is being shifted from mere rationality -the most efficient means to unquestioned ends- to participatory opportunities. Under such circumstances, "support generally takes the form of agreement not to resist implementation if a plan recognizes or furthers the ends of the affected groups." (Richard Warren Smith, 1973, pp.277-278) And therefore, the scope and strength of political support and the equity of distribution are mutually reinforcing. If indeed regional development is to be effective as a means to manage the distribution process in Korea, it must now be organized as a process of participatory planning. Politicizing development process is often resisted for a very tenable reason of maintaining economic and technical efficiency of development programs, especially so in an early stage when growth is deemed urgent. Sooner or later, however, time comes when the gap between the growing modern sector and the forgotten traditional sector of economy becomes starkly visible and it is no longer tolerated as mere "growing pain" but begins to settle in as structural pattern of the society. The conventional response to such a disparity has been merely to geographically decentralize "industrial locations" of the growing modern sectors over a wider surface of the nation. And yet, since the technology of. modern sector industries is becoming more "footloose" and even "internationalizing," physical locations of new factories and plants do not necessarily guarantee "communalization" of distributive process. (Friedmann and Weaver, 1977, p.358

Cytochrome P450 aromatase (CYP19) and sex differentiation in the Nile tilapia Oreochromis niloticus

Sex steroids are generally considered as natural sex inducers in fish. Aromatase (cytochrome P450 aromatase) catalyses androgens into oestrogens in the steroidogenic pathway. Three different approaches were taken to elucidate the action of aromatase in relation to sex differentiation in the Nile tilapia Oreochromis niloticus. The first was treatment with Fadrozole TM,a non-steroidal aromatase inhibitor (Al), by incorporating it in the diet or by immersing fish in a solution containing Al during the sex differentiation period. The Al treatment masculinised genetic females, indicating the importance of aromatase in sex differentiation. The result revealed that the most sensitive time to Al lies between 11-18 dpf (days post fertilisation). A partial brain type aromatase cDNA (1707bp) was identified from a brain cDNA library of O. niloticus. The amino acid sequence (that corresponds to exon 2-9) derived from this showed 63.7% identity to a previously reported ovarian aromatase gene of this species, and 96.7% identity to the brain type aromatase gene of a closely related species O. mossambicus. A semi-quantitative RT-PCR method was established to investigate expression of brain and ovarian aromatase genes during ontogeny. No sexually dimorphic expression of brain aromatase mRNA was detected. However, expression of ovarian aromatase was down-regulated from 15 to 23 dpf in genetic males but upregulated in genetic females. This period overlaps closely with the most sensitive period to Al. The pattern of temperature-dependent sex determination (TSD) was examined using three different genotypes (XX, XY, YY) at two temperatures (28 and 36°C). The results showed a bidirectional pattern of TSD. YY groups showed a significant percentage of feminisation at the higher temperature, which was suppressed by the Al treatment, implying that aromatisation is mechanistically associated with TSD in this species.All of these data consistently suggest that aromatase plays a crucial role in sex differentiation, and that the decisive aromatisation takes place between 13-25 dpf in this species. Considering the timing (26-30 dpf) of the first appearance of steroid producing cells in the gonadal area, the decisive aromatisation is not likely to take place there. The brain could be the primary aromatisation site in fish sex differentiation

Role of thermal friction in relaxation of turbulent Bose-Einstein condensates

In recent experiments, the relaxation dynamics of highly oblate, turbulent Bose-Einstein condensates (BECs) was investigated by measuring the vortex decay rates in various sample conditions [Phys. Rev. A $\bf 90$, 063627 (2014)] and, separately, the thermal friction coefficient $\alpha$ for vortex motion was measured from the long-time evolution of a corotating vortex pair in a BEC [Phys. Rev. A $\bf 92$, 051601(R) (2015)]. We present a comparative analysis of the experimental results, and find that the vortex decay rate $\Gamma$ is almost linearly proportional to $\alpha$. We perform numerical simulations of the time evolution of a turbulent BEC using a point-vortex model equipped with longitudinal friction and vortex-antivortex pair annihilation, and observe that the linear dependence of $\Gamma$ on $\alpha$ is quantitatively accounted for in the dissipative point-vortex model. The numerical simulations reveal that thermal friction in the experiment was too strong to allow for the emergence of a vortex-clustered state out of decaying turbulence.Comment: 7 pages, 5 figure

Predicting wind turbine blade loads using vorticity transport and RANS methodologies

Two computational methods, one based on the solution of the vorticity transport equation, and a second based on the solution of the Reynolds-Averaged Navier-Stokes equations, have been used to simulate the aerodynamic performance of a horizontal axis wind turbine. Comparisons have been made against data obtained during Phase VI of the NREL Unsteady Aerodynamics Experimental and against existing numerical data for a range of wind conditions. The Reynolds-Averaged Navier-Stokes method demonstrates the potential to predict accurately the flow around the blades and the distribution of aerodynamic loads developed on them. The Vorticity Transport Model possesses a considerable advantage in those situtations where the accurate, but computationally efficient, modelling of the structure of the wake and the associated induced velocity is critical, but where the prediction of blade loads can be achieved with sufficient accuracy using a lifting-line model augmented by incorporating a semi-empirical stall delay model. The largest benefits can be extracted when the two methods are used to complement each other in order to understand better the physical mechanisms governing the aerodynamic performance of wind turbines