Classification of Humans into Ayurvedic Prakruti Types using Computer Vision

Ayurveda, a 5000 years old Indian medical science, believes that the universe and hence humans are made up of five elements namely ether, fire, water, earth, and air. The three Doshas (Tridosha) Vata, Pitta, and Kapha originated from the combinations of these elements. Every person has a unique combination of Tridosha elements contributing to a person’s ‘Prakruti’. Prakruti governs the physiological and psychological tendencies in all living beings as well as the way they interact with the environment. This balance influences their physiological features like the texture and colour of skin, hair, eyes, length of fingers, the shape of the palm, body frame, strength of digestion and many more as well as the psychological features like their nature (introverted, extroverted, calm, excitable, intense, laidback), and their reaction to stress and diseases. All these features are coded in the constituents at the time of a person’s creation and do not change throughout their lifetime. Ayurvedic doctors analyze the Prakruti of a person either by assessing the physical features manually and/or by examining the nature of their heartbeat (pulse). Based on this analysis, they diagnose, prevent and cure the disease in patients by prescribing precision medicine. This project focuses on identifying Prakruti of a person by analysing his facial features like hair, eyes, nose, lips and skin colour using facial recognition techniques in computer vision. This is the first of its kind research in this problem area that attempts to bring image processing into the domain of Ayurveda

Partial sums of excursions along random geodesics and volume asymptotics for thin parts of moduli spaces of quadratic differentials

For a non-uniform lattice in SL(2, R), we consider excursions of a random geodesic in cusp neighborhoods of the quotient finite area hyperbolic surface or orbifold. We prove a strong law for a certain partial sum involving these excursions. This generalizes a theorem of Diamond and Vaaler for continued fractions. In the Teichmuller setting, we consider invariant measures for the SL(2, R) action on the moduli spaces of quadratic differentials. By the work of Eskin and Mirzakhani, these measures are supported on affine invariant submanifolds of a stratum of quadratic differentials. For a Teichmuller geodesic random with respect to a SL(2,R)-invariant measure, we study its excursions in thin parts of the associated submanifold. Under a regularity hypothesis for the invariant measure, we prove similar strong laws for certain partial sums involving these excursions. The limits in these laws are related to the volume asymptotic of the thin parts. By Siegel-Veech theory, these are given by Siegel-Veech constants. As a direct consequence, we show that the word metric of mapping classes that approximate a Teichmuller geodesic ray that is random with respect to the Masur-Veech measure, grows faster than T log T

Harmonic measures for distributions with finite support on the mapping class group are singular

Kaimanovich and Masur showed that a random walk on the mapping class group for an initial distribution with finite first moment and whose support generates a non-elementary subgroup, converges almost surely to a point in the space PMF of projective measured foliations on the surface. This defines a harmonic measure on PMF. Here, we show that when the initial distribution has finite support, the corresponding harmonic measure is singular with respect to the natural Lebesgue measure on PMF.Comment: 43 pages, 16 figures. Minor improvements overall, specifically Section 12. Added reference

The curves not carried

Suppose t is a train track on a surface S. Let C(t) be the set of isotopy classes of simple closed curves carried by t. Masur and Minsky prove that C(t) is quasi-convex inside the curve complex C(S). We prove that the complement, C(S) - C(t), is quasi-convex

Universal property of the information entropy in atoms, nuclei and atomic clusters

The position- and momentum-space information entropies of the electron distributions of atomic clusters are calculated using a Woods-Saxon single particle potential. The same entropies are also calculated for nuclear distributions according to the Skyrme parametrization of the nuclear mean field. It turns out that a similar functional form S=a+b ln N for the entropy as function of the number of particles N holds approximately for atoms, nuclei and atomic clusters. It is conjectured that this is a universal property of a many-fermion system in a mean field. It is also seen that there is an analogy of our expression for S to Boltzmann's thermodynamic entropy S=k ln W.Comment: 3 pages, REVTEX, one figur

Preferences of eligible women from an Indian medical college hospital for adapting contraceptives

Background: Indian women prefer to avoid unwanted pregnancy, but do not practice contraception adequately. After completing their family size, they are more concerned about terminating their fertility, rather than spacing the births. The main aim and objective of the study is to find out preferences for (a) Regularity if any, of barrier contraceptive usage (b) Use of any contraception at zero gravidity (c) The prevalence of temporary & permanent contraception (d) Prior practice of any temporary contraception before opting for tubectomy (e) Acceptance of male sterilization.Methods: The study was conducted at Obstetrics & Gynaecology department, Chirayu Medical College and Hospital, Bhopal, India. Women in reproductive age group, whether tubectomized or not & postmenopausal women, attending OPD, admitted or those working at the hospital were included. They were given a prestructured, pretested questionnaire. Sociodemographic details, reproductive & contraception details recorded. Analyzed as per the demands of the study objectives.Results: From total 267 study subjects, 81 % were practicing contraception. 103  temporary and  113 had sterilization done. Only 42 % were using barrier contraceptive effectively.46% of the temporary contraceptive users discontinued. There was no significant difference between temporary and permanent method users. 97% did not use any contraception at zero gravidity. 69% of the sterilized population never used any contraception before they underwent sterilization. There was only one vasectomy in 267 study subjects.Conclusions: The contraceptive methods are poorly practiced. The users do not use any temporary contraception effectively & adequately. A negligible percentage of eligible women practice contraception before first pregnancy. Very few women practice temporary methods any time before they get sterilization done. Overall, the concept of spacing is lacking. Women are more inclined towards permanent methods. Male sterilization is very rarely chosen by the couples

Word length statistics for Teichmuller geodesics and singularity of harmonic measure

Given a measure on the Thurston boundary of Teichmuller space, one can pick a geodesic ray joining some basepoint to a randomly chosen point on the boundary. Different choices of measures may yield typical geodesics with different geometric properties. In particular, we consider two families of measures: the ones which belong to the Lebesgue or visual measure class, and harmonic measures for random walks on the mapping class group generated by a distribution with finite first moment in the word metric. We consider the word length of approximating mapping class group elements along a geodesic ray, and prove that this quantity grows superlinearly in time along almost all geodesics with respect to Lebesgue measure, while along almost all geodesics with respect to harmonic measure the growth is linear. As a corollary, the harmonic and Lebesgue measures are mutually singular. We also prove a similar result for the ratio between the word metric and the relative metric (i.e. the induced metric on the curve complex)