The Benefits of Port Liberalization: A Case Study from India

In contrast to the rest of India, where it is the government that predominantly owns and manages ports, the Indian state of Gujarat has implemented various forms of port liberalization since the 1990s. This has helped it become the country's fastest growing state. Gujarat's economy has grown at an average of 10.14 percent per year from fiscal year 2001 to fiscal year 2006, the last five years for which data are available. This is comparable with China's average growth rate since 1978, and is distinctly faster than the growth of the other Asian tigers in the 15 years before the Asian financial crisis of 1997. Gujarat has broken new ground with different forms of privatization, ranging from private provision of port services to completely private ownership of new ports. The process started in the 1980s and gathered momentum rapidly after the central government in New Delhi enacted major economic reforms in the early 1990s. Gujarat has taken advantage of a constitutional loophole to convert its minor ports into some of the biggest ports in the country, vastly improved the availability and efficiency of port infrastructure, and facilitated the development of industrial centers that otherwise would not have existed. Gujarat's port liberalization, along with its status as one of the economically freest states in India, should serve as a model for the rest of India and other developing countries, which can also benefit from the dynamic gains of port privatization

A novel user-centered design for personalized video summarization

In the past, several automatic video summarization systems had been proposed to generate video summary. However, a generic video summary that is generated based only on audio, visual and textual saliencies will not satisfy every user. This paper proposes a novel system for generating semantically meaningful personalized video summaries, which are tailored to the individual user's preferences over video semantics. Each video shot is represented using a semantic multinomial which is a vector of posterior semantic concept probabilities. The proposed system stitches video summary based on summary time span and top-ranked shots that are semantically relevant to the user's preferences. The proposed summarization system is evaluated using both quantitative and subjective evaluation metrics. The experimental results on the performance of the proposed video summarization system are encouraging

Elliptic Curve Variants of the Least Quadratic Nonresidue Problem and Linnik's Theorem

Let $E_1$ and $E_2$ be $\overline{\mathbb{Q}}$-nonisogenous, semistable elliptic curves over $\mathbb{Q}$, having respective conductors $N_{E_1}$ and $N_{E_2}$ and both without complex multiplication. For each prime $p$, denote by $a_{E_i}(p) := p+1-\#E_i(\mathbb{F}_p)$ the trace of Frobenius. Under the assumption of the Generalized Riemann Hypothesis (GRH) for the convolved symmetric power $L$-functions $L(s, \mathrm{Sym}^i E_1\otimes\mathrm{Sym}^j E_2)$ where $i,j\in\{0,1,2\}$, we prove an explicit result that can be stated succinctly as follows: there exists a prime $p\nmid N_{E_1}N_{E_2}$ such that $a_{E_1}(p)a_{E_2}(p)<0$ and $$p < \big( (32+o(1))\cdot \log N_{E_1} N_{E_2}\big)^2.$$ This improves and makes explicit a result of Bucur and Kedlaya. Now, if $I\subset[-1,1]$ is a subinterval with Sato-Tate measure $\mu$ and if the symmetric power $L$-functions $L(s, \mathrm{Sym}^k E_1)$ are functorial and satisfy GRH for all $k \le 8/\mu$, we employ similar techniques to prove an explicit result that can be stated succinctly as follows: there exists a prime $p\nmid N_{E_1}$ such that $a_{E_1}(p)/(2\sqrt{p})\in I$ and $$p < \left((21+o(1)) \cdot \mu^{-2}\log (N_{E_1}/\mu)\right)^2.$$Comment: 30 page

On Logarithmically Benford Sequences

Let $\mathcal{I} \subset \mathbb{N}$ be an infinite subset, and let $\{a_i\}_{i \in \mathcal{I}}$ be a sequence of nonzero real numbers indexed by $\mathcal{I}$ such that there exist positive constants $m, C_1$ for which $|a_i| \leq C_1 \cdot i^m$ for all $i \in \mathcal{I}$. Furthermore, let $c_i \in [-1,1]$ be defined by $c_i = \frac{a_i}{C_1 \cdot i^m}$ for each $i \in \mathcal{I}$, and suppose the $c_i$'s are equidistributed in $[-1,1]$ with respect to a continuous, symmetric probability measure $\mu$. In this paper, we show that if $\mathcal{I} \subset \mathbb{N}$ is not too sparse, then the sequence $\{a_i\}_{i \in \mathcal{I}}$ fails to obey Benford's Law with respect to arithmetic density in any sufficiently large base, and in fact in any base when $\mu([0,t])$ is a strictly convex function of $t \in (0,1)$. Nonetheless, we also provide conditions on the density of $\mathcal{I} \subset \mathbb{N}$ under which the sequence $\{a_i\}_{i \in \mathcal{I}}$ satisfies Benford's Law with respect to logarithmic density in every base. As an application, we apply our general result to study Benford's Law-type behavior in the leading digits of Frobenius traces of newforms of positive, even weight. Our methods of proof build on the work of Jameson, Thorner, and Ye, who studied the particular case of newforms without complex multiplication.Comment: 10 page

Linnik's Theorem for Sato-Tate Laws on Elliptic Curves with Complex Multiplication

Let $E/\mathbb{Q}$ be an elliptic curve with complex multiplication (CM), and for each prime $p$ of good reduction, let $a_E(p) = p + 1 - \#E(\mathbb{F}_p)$ denote the trace of Frobenius. By the Hasse bound, $a_E(p) = 2\sqrt{p} \cos \theta_p$ for a unique $\theta_p \in [0, \pi]$. In this paper, we prove that the least prime $p$ such that $\theta_p \in [\alpha, \beta] \subset [0, \pi]$ satisfies $$p \ll \left(\frac{N_E}{\beta - \alpha}\right)^A,$$ where $N_E$ is the conductor of $E$ and the implied constant and exponent $A > 2$ are absolute and effectively computable. Our result is an analogue for CM elliptic curves of Linnik's Theorem for arithmetic progressions, which states that the least prime $p \equiv a \pmod q$ for $(a,q)=1$ satisfies $p \ll q^L$ for an absolute constant $L > 0$.Comment: 11 pages; made minor modification

Tuberculosis and the immune response in children

Tuberculosis is one of the major killers in the world today and has been described as a “global emergency” by WHO. I n I n d i a t h e r e a r e approximately 1 million new cases every year and 500,000 deaths. Tuberculosis also affects children who get the infection from adults. It is important to study the natural history, clinical manifestations and immunological profile of children in order to diagnose them earlier and treat them effectively

Treatment of Tuberculosis

Early diagnosis and prompt treatment of tuberculosis is important in order to minimise complications and sequale. It is important to select the proper regimen and ensure that hte patient is getting adeuqate number of drugs for adequate duration. The principles of short course chemotherapy and the rationale behidn the currently recommended regimens are outlined in this article. Standard (daily or intermittent) 6-month short course regimens are sufficient to cure most forms of tuberculosis in children and only severe form slike miliary, meningitis and neurotuberculosis require a longer duration of treatment. Worldwide, the DOTS strategy is now recommended in order to ensure cure and cut down the transmission of disease in the community and wherever possible, should be employed in the treatment of tuberculosis in children also

Pulmonary Function Testing in Office Practice

With the wide availability of simple to operate pulmonary function equipment, these tests can now be performed in the office or clinic setting. The use of pulmonary function tests in the assessment of patients with pulmonary diseases has thus expanded. These simple tests rely on data generated from a forced expiratory vital capacity maneuver which can be performed reliably by most children over the age of 6 or 7 years. Pulmonary function tests provide both diagnostic and prognostic information and help in the management of a number of respiratory diseases. The number of tests available vary with the level of sophistication of the pulmonary function laboratory; in most situations simple spirometry is adequate. Several new and inexpensive peak flow meters are now available for home use; these are very useful for home monitoring of asthma patients. Physicians caring for patients with asthma or other chronic respiratory diseases should be encouraged to use these tests routinely in the management of these children

Dynamics of circular arrangements of vorticity in two dimensions

The merger of two like-signed vortices is a well-studied problem, but in a turbulent flow, we may often have more than two like-signed vortices interacting. We study the merger of three or more identical co-rotating vortices initially arranged on the vertices of a regular polygon. At low to moderate Reynolds numbers, we find an additional stage in the merger process, absent in the merger of two vortices, where an annular vortical structure is formed and is long-lived. Vortex merger is slowed down significantly due to this. Such annular vortices are known at far higher Reynolds numbers in studies of tropical cyclones, which have been noticed to a break down into individual vortices. In the pre-annular stage, vortical structures in a viscous flow are found here to tilt and realign in a manner similar to the inviscid case, but the pronounced filaments visible in the latter are practically absent in the former. Interestingly at higher Reynolds numbers, the merger of an odd number of vortices is found to proceed very differently from that of an even number. The former process is rapid and chaotic whereas the latter proceeds more slowly via pairing events. The annular vortex takes the form of a generalised Lamb-Oseen vortex (GLO), and diffuses inwards until it forms a standard Lamb-Oseen vortex. For lower Reynolds number, the numerical (fully nonlinear) evolution of the GLO vortex follows exactly the analytical evolution until merger. At higher Reynolds numbers, the annulus goes through instabilities whose nonlinear stages show a pronounced difference between even and odd mode disturbances. It is hoped that the present findings, that multiple vortex merger is qualitatively different from the merger of two vortices, will motivate studies on how multiple vortex interactions affect the inverse cascade in two-dimensional turbulence.Comment: Abstract truncated. Paper to appear in Physical Review