Deformations of overconvergent isocrystals on the projective line

Let $k$ be a perfect field of positive characteristic and $Z$ an effective Cartier divisor in the projective line over $k$ with complement $U$. In this note, we establish some results about the formal deformation theory of overconvergent isocrystals on $U$ with fixed "local monodromy" along $Z$. En route, we show that a Hochschild cochain complex governs deformations of a module over an arbitrary associative algebra. We also relate this Hochschild cochain complex to a de Rham complex in order to understand the deformation theory of a differential module over a differential ring.Comment: 59 pages; fixed typos, improved exposition; comments welcome

Correlation of serum androgen and gonadotropin with anti-mullerian hormone in polycystic ovarian syndrome in Eastern Indian population

Background: Ovarian steroidogenesis requires gonadotropin stimulation, Luteinizing Hormone (LH) is a key factor in the hyperandrogenaemia of the polycystic ovary syndrome. Progesterone is the primary regulator of Gonadotropin-Releasing Hormone (GnRH) pulse frequency; however, in the polycystic ovary syndrome, the GnRH pulse generator is relatively resistant to the negative feedback effects of progesterone.  Study aims to evaluate the association of Anti-mullerian hormone with serum androgen and gonadotropin level in adolescents and young women of Polycystic Ovary Syndrome (PCOS).Methods: This was a single centre observational Cross-sectional study carried out in the department of Endocrinology and metabolism, Medical College, Kolkata from March 2017 to January 2019. Total number of study subjects were 207 out of which 138 were cases.Results: The AMH had strong positive correlation with serum testosterone in both case and control groups (r 0.542, p<0.001 and r 0.57, p<0.001) respectively .After the adjustment of age and BMI , the AMH moderately positive  but extremely significant correlation with serum testosterone as compare to control.Conclusions: Hyperandrogenaemia and higher ratio of LH and FSH associated with higher serum AMH level is associated with the higher serum AMH in polycystic ovarian syndrome

Silicone sleeve of extrusion cannula as an intraocular foreign body

An unusual intraocular foreign body - the silicone sleeve of a soft-tipped extrusion cannula left behind accidentally in the vitreous cavity following a vitreoretinal surgical procedure for complex retinal detachment - is reported. The silicone sleeve remained within the eye for a year without causing any proble

Formation control of differential-drive robots with input saturation and constraints on formation size

&lt;p&gt;Cooperative control involves developing control strategies for individual robots that guarantee synchronized behavior of the states of all the robots in a team in some prescribed sense. In this work, we present a novel controller that achieves formation control for a group of differential-drive robots. First, we propose a nonlinear feedback control law that guarantees stable tracking of a reference trajectory for a single robot without exceeding the velocity limits of the robot. Using Lyapunov analysis, we obtain the necessary conditions on the control parameters and establish ultimate boundedness on error terms. Next, we formulate the formation control problem as a trajectory tracking problem for the multi-robot system and solve it using the proposed controller. Additionally, we provide constraints on formation size for given reference trajectory which ensures smooth turning of multi-robot formation without exceeding actuation limits.   &lt;/p&gt;</jats:p