Non-stationary Stochastic Optimization

We consider a non-stationary variant of a sequential stochastic optimization problem, in which the underlying cost functions may change along the horizon. We propose a measure, termed variation budget, that controls the extent of said change, and study how restrictions on this budget impact achievable performance. We identify sharp conditions under which it is possible to achieve long-run-average optimality and more refined performance measures such as rate optimality that fully characterize the complexity of such problems. In doing so, we also establish a strong connection between two rather disparate strands of literature: adversarial online convex optimization; and the more traditional stochastic approximation paradigm (couched in a non-stationary setting). This connection is the key to deriving well performing policies in the latter, by leveraging structure of optimal policies in the former. Finally, tight bounds on the minimax regret allow us to quantify the "price of non-stationarity," which mathematically captures the added complexity embedded in a temporally changing environment versus a stationary one

Three-Prong Distribution of Massive Narrow QCD Jets

We study the planar-flow distributions of narrow, highly boosted, massive QCD jets. Using the factorization properties of QCD in the collinear limit, we compute the planar-flow jet function from the one-to-three splitting function at tree-level. We derive the leading-log behavior of the jet function analytically. We also compare our semi-analytic jet function with parton-shower predictions using various generators.Comment: 59 pages, 9 figure

Kepler Studies of Low-Mass Eclipsing Binaries I. Parameters of the Long-Period Binary KIC 6131659

KIC 6131659 is a long-period (17.5 days) eclipsing binary discovered by the Kepler mission. We analyzed six quarters of Kepler data along with supporting ground-based photometric and spectroscopic data to obtain accurate values for the mass and radius of both stars, namely M_1=0.922 +/- 0.007 M_sun, R_1=0.8800 +/- 0.0028 R_sun, and M_2=0.685 +/- 0.005 M_sun, R_2=0.6395 +/- 0.0061 R_sun. There is a well-known issue with low mass (M <<0.8 M_sun) stars (in cases where the mass and radius measurement uncertainties are smaller than two or three percent) where the measured radii are almost always 5 to 15 percent larger than expected from evolutionary models, i.e. the measured radii are all above the model isochrones in a mass-radius plane. In contrast, the two stars in KIC 6131659 were found to sit on the same theoretical isochrone in the mass-radius plane. Until recently, all of the well-studied eclipsing binaries with low-mass stars had periods less than about three days. The stars in such systems may have been inflated by high levels of stellar activity induced by tidal effects in these close binaries. KIC 6131659 shows essentially no evidence of enhanced stellar activity, and our measurements support the hypothesis that the unusual mass-radius relationship observed in most low-mass stars is influenced by strong magnetic activity created by the rapid rotation of the stars in tidally-locked, short-period systems. Finally, using short cadence data, we show that KIC 6131657 has one of the smallest measured non-zero eccentricities of a binary with two main sequence stars, where e cos omega=(4.57 +/-0.02)*10^-5

Deciphering M-T diagram of shape memory Heusler alloys: reentrance, plateau and beyond

We present our recent results on temperature behaviour of magnetization observed in Ni_47Mn_39In_14 Heusler alloys. Three regions can be distinguished in the M-T diagram: (I) low temperature martensitic phase (with the Curie temperature T_CM = 140 K), (II) intermediate mixed phase (with the critical temperature T_MS = 230 K) exhibiting a reentrant like behavior (between T_CM and T_MS) and (III) high temperature austenitic phase (with the Curie temperature T_CA = 320 K) exhibiting a rather wide plateau region (between T_MS and T_CA). By arguing that powerful structural transformations, causing drastic modifications of the domain structure in alloys, would also trigger strong fluctuations of the order parameters throughout the entire M-T diagram, we were able to successfully fit all the data by incorporating Gaussian fluctuations (both above and below the above three critical temperatures) into the Ginzburg-Landau scenario