The Submillimeter Array Polarimeter

We describe the Submillimeter Array (SMA) Polarimeter, a polarization converter and feed multiplexer installed on the SMA. The polarimeter uses narrow-band quarter-wave plates to generate circular polarization sensitivity from the linearly-polarized SMA feeds. The wave plates are mounted in rotation stages under computer control so that the polarization handedness of each antenna is rapidly selectable. Positioning of the wave plates is found to be highly repeatable, better than 0.2 degrees. Although only a single polarization is detected at any time, all four cross correlations of left- and right-circular polarization are efficiently sampled on each baseline through coordinated switching of the antenna polarizations in Walsh function patterns. The initial set of anti-reflection coated quartz and sapphire wave plates allows polarimetry near 345 GHz; these plates have been have been used in observations between 325 and 350 GHz. The frequency-dependent cross-polarization of each antenna, largely due to the variation with frequency of the retardation phase of the single-element wave plates, can be measured precisely through observations of bright point sources. Such measurements indicate that the cross-polarization of each antenna is a few percent or smaller and stable, consistent with the expected frequency dependence and very small alignment errors. The polarimeter is now available for general use as a facility instrument of the SMA.Comment: To appear in Proc. SPIE 7020, 'Millimeter and Submillimeter Detectors and Instrumentation'. Uses spie.cl

Health damage cost of automotive air pollution: Cost benefit analysis of fuel quality upgradation for Indian cities.

The paper has analysed the economic implication of judicial activism of the apex court of India in the regulation of automotive air pollution. It estimates the health damage cost of urban air pollution for 35 major urban agglomerations of India arising from automotive emissions and the savings that can be achieved by the regulation of fuel quality so as to conform to the Euro norms. It has used the results of some US based study and has applied the transfer of benefit method from the US to the Indian situation for the purpose. The paper finally makes a benefit cost analysis of refinery upgradation for such improvement of fuel quality.Urban air pollution ; Health damage cost ; Benefit-cost comparison

Near-optimal Bootstrapping of Hitting Sets for Algebraic Models

The classical lemma of Ore-DeMillo-Lipton-Schwartz-Zippel [Ore22,DL78,Zip79,Sch80] states that any nonzero polynomial $f(x_1,\ldots, x_n)$ of degree at most $s$ will evaluate to a nonzero value at some point on a grid $S^n \subseteq \mathbb{F}^n$ with $|S| > s$. Thus, there is an explicit hitting set for all $n$-variate degree $s$, size $s$ algebraic circuits of size $(s+1)^n$. In this paper, we prove the following results: - Let $\epsilon > 0$ be a constant. For a sufficiently large constant $n$ and all $s > n$, if we have an explicit hitting set of size $(s+1)^{n-\epsilon}$ for the class of $n$-variate degree $s$ polynomials that are computable by algebraic circuits of size $s$, then for all $s$, we have an explicit hitting set of size $s^{\exp \circ \exp (O(\log^\ast s))}$ for $s$-variate circuits of degree $s$ and size $s$. That is, if we can obtain a barely non-trivial exponent compared to the trivial $(s+1)^{n}$ sized hitting set even for constant variate circuits, we can get an almost complete derandomization of PIT. - The above result holds when "circuits" are replaced by "formulas" or "algebraic branching programs". This extends a recent surprising result of Agrawal, Ghosh and Saxena [AGS18] who proved the same conclusion for the class of algebraic circuits, if the hypothesis provided a hitting set of size at most $(s^{n^{0.5 - \delta}})$ (where $\delta>0$ is any constant). Hence, our work significantly weakens the hypothesis of Agrawal, Ghosh and Saxena to only require a slightly non-trivial saving over the trivial hitting set, and also presents the first such result for algebraic branching programs and formulas.Comment: The main result has been strengthened significantly, compared to the older version of the paper. Additionally, the stronger theorem now holds even for subclasses of algebraic circuits, such as algebraic formulas and algebraic branching program

Functional lower bounds for arithmetic circuits and connections to boolean circuit complexity

We say that a circuit $C$ over a field $F$ functionally computes an $n$-variate polynomial $P$ if for every $x \in \{0,1\}^n$ we have that $C(x) = P(x)$. This is in contrast to syntactically computing $P$, when $C \equiv P$ as formal polynomials. In this paper, we study the question of proving lower bounds for homogeneous depth-$3$ and depth-$4$ arithmetic circuits for functional computation. We prove the following results : 1. Exponential lower bounds homogeneous depth-$3$ arithmetic circuits for a polynomial in $VNP$. 2. Exponential lower bounds for homogeneous depth-$4$ arithmetic circuits with bounded individual degree for a polynomial in $VNP$. Our main motivation for this line of research comes from our observation that strong enough functional lower bounds for even very special depth-$4$ arithmetic circuits for the Permanent imply a separation between ${\#}P$ and $ACC$. Thus, improving the second result to get rid of the bounded individual degree condition could lead to substantial progress in boolean circuit complexity. Besides, it is known from a recent result of Kumar and Saptharishi [KS15] that over constant sized finite fields, strong enough average case functional lower bounds for homogeneous depth-$4$ circuits imply superpolynomial lower bounds for homogeneous depth-$5$ circuits. Our proofs are based on a family of new complexity measures called shifted evaluation dimension, and might be of independent interest

Regime-Shifts & Post-Float Inflation Dynamics In Australia

Australia’s inflation rate and inflation uncertainty during the post-float era 1983Q3-2006Q4 have acted as important barometers of Australia’s macroeconomic performance. The conceptualisation and measurement of the nexus between inflation and inflation uncertainty is subject to complex dynamics. We use Markov regime switching heteroscedasticity (MRSH) model to capture long-run stochastic trend and short-run noisy components. This allows us to conclude that in post-float Australia the results deviate significantly from the mainstream Friedman paradigm on inflation and its uncertainty. We also critically review the plausibility of rival paradigm explaining this paradoxical behaviour. The regime shifts detected in the inflation dynamics appear to be linked to the macroeconomic policies pursued to achieve external and internal balance as implied by Keynesian Mundell-Fleming model.