The Ultra-Violet Imaging Telescope (UVIT) is one of the payloads in AS-TROSAT, the first Indian Space Observatory. The UVIT instrument has two 375 mm telescopes: one for the far-ultraviolet (FUV) channel (1300-1800Å), and the other for the near-ultraviolet (NUV) channel (2000-3000Å) and the visible (VIS) channel (3200-5500Å). UVIT is primarily designed for simultaneous imaging in the two ultraviolet channels with spatial resolution better than 1.8 , along with provision for slit-less spectroscopy in the NUV and FUV channels.The results of in-orbit calibrations of UVIT are presented in this paper.

Results of the initial calibration of the Ultra-Violet Imaging Telescope (UVIT) were reported earlier by Tandon et al. (2017a). The results reported earlier were based on the ground calibration as well as the first observations in orbit. Some additional data from the ground calibration and data from more in-orbit observations have been used to improve the results. In particular, extensive new data from in-orbit observations have been used to obtain (a) new photometric calibration which includes (i) zero-points (ii) flat fields (iii) saturation, (b) sensitivity variations (c) spectral calibration for the near Ultra-Violet (NUV; 2000−3000Å) and far Ultra-Violet (FUV; 1300−1800Å) gratings, (d) point spread function and (e) astrometric calibration which includes distortion. Data acquired over the last three years show continued good performance of UVIT with no reduction in sensitivity in both the UV channels.

We show that, over Q, if an n-variate polynomial of degree d = n O(1) is computable by an arithmetic circuit of size s (respectively by an arithmetic branching program of size s) then it can also be computed by a depth three circuit (i.e. a ΣΠΣ-circuit) of size expIt also means that if we can prove a lower bound of exp(ω( √ d · log d)) on the size of any ΣΠΣ-circuit computing the d × d permanent Perm d then we get superpolynomial lower bounds for the size of any arithmetic branching program computing Perm d . We then give some further results pertaining to derandomizing polynomial identity testing and circuit lower bounds.The ΣΠΣ circuits that we construct have the property that (some of) the intermediate polynomials have degree much higher than d. Indeed such a counterintuitive construction is unavoidable -it is known that in any ΣΠΣ circuit C computing either Det d or Perm d , if every multiplication gate has fanin at most d (or any constant multiple thereof) then C must have size at least exp(Ω(d)).

Agrawal-Vinay [AV08], Koiran [Koi12] and Tavenas [Tav13] have recently shown that an exp(ω( √ n log n)) lower bound for depth four homogeneous circuits computing the permanent with bottom layer of × gates having fanin bounded by √ n translates to super-polynomial lower bound for general arithmetic circuits computing the permanent. Motivated by this, we examine the complexity of computing the permanent and determinant via such homogeneous depth four circuits with bounded bottom fanin.We show here that any homogeneous depth four arithmetic circuit with bottom fanin bounded by √ n computing the permanent (or the determinant) must be of size exp(Ω( √ n)).

Unlike compressive sensing where the measurement outputs are assumed to be real-valued and have infinite precision, in one-bit compressive sensing, measurements are quantized to one bit, their signs. In this work, we show how to recover the support of sparse high-dimensional vectors in the one-bit compressive sensing framework with an asymptotically near-optimal number of measurements. We also improve the bounds on the number of measurements for approximately recovering vectors from one-bit compressive sensing measurements. Our results are universal, namely the same measurement scheme works simultaneously for all sparse vectors.Our proof of optimality for support recovery is obtained by showing an equivalence between the task of support recovery using 1-bit compressive sensing and a well-studied combinatorial object known as Union Free Families.