Can Dark Matter be an artifact of extended theories of gravity?

In this article, we propose different background models of extended theories of gravity, which are minimally coupled to the SM fields, to explain the possibility of genesis of dark matter without affecting the SM particle sector. We modify the gravity sector by allowing quantum corrections motivated from (1) local $f(R)$ gravity and (2) non-minimally coupled gravity with SM sector and dilaton field. Next we apply conformal transformation on the metric to transform the action back to the Einstein frame. We also show that an effective theory constructed from these extended theories of gravity and SM sector looks exactly the same. Using the relic constraint observed by Planck 2015, we constrain the scale of the effective field theory ($\Lambda_{UV}$) as well as the dark matter mass ($M$). We consider two cases- (1) light dark matter (LDM) and (2) heavy dark matter (HDM), and deduce upper bounds on thermally averaged cross section of dark matter annihilating to SM particles. Further we show that our model naturally incorporates self interactions of dark matter. Using these self interactions, we derive the constraints on the parameters of the (1) local $f(R)$ gravity and (2) non-minimally coupled gravity from dark matter self interaction. Finally, we propose some different UV complete models from a particle physics point of view, which can give rise to the same effective theory that we have deduced from extended theories of gravity.Comment: 45 pages, 8 figures, Accepted for publication in European Physical Journal

A prospective case control study of the effects of oligohydramnios on fetomaternal outcome in mothers with term pregnancy in a rural medical college

Background: The aim of the current study was to assess the fetomaternal effects of oligohydramnios on term pregnancies in a rural tertiary care setup.Methods: A perspective case control hospital-based trial was conducted at Burdwan Medical College and Hospital for a period of one year. Pregnancies at term (37-42 weeks) were included in the study. 103 patients with sonographically diagnosed oligohydramnios were included in the case group. The control group comprised of 103 mothers at term with normal liquor volume. Demographic data and fetomaternal outcome parameters were assessed and compared.Results: There was increased incidence of fetal and perinatal complications including low birth weight, birth asphyxia and NICU admission. There were more perinatal deaths in the case group compared to the control group. Induction of labour, operative delivery, meconium stained liquor and incidence of preeclampsia were also increased in mothers with low AFI.Conclusions: Oligohydramnios is associated with an increased risk of labour and perinatal complications. Adequate antenatal surveillance and intranatal monitoring coupled with correction of underly-ing factors is the mainstay of management

A (simple) classical algorithm for estimating Betti numbers

We describe a simple algorithm for estimating the $k$-th normalized Betti number of a simplicial complex over $n$ elements using the path integral Monte Carlo method. For a general simplicial complex, the running time of our algorithm is $n^{O\left(\frac{1}{\sqrt{\gamma}}\log\frac{1}{\varepsilon}\right)}$ with $\gamma$ measuring the spectral gap of the combinatorial Laplacian and $\varepsilon \in (0,1)$ the additive precision. In the case of a clique complex, the running time of our algorithm improves to $\left(n/\lambda_{\max}\right)^{O\left(\frac{1}{\sqrt{\gamma}}\log\frac{1}{\varepsilon}\right)}$ with $\lambda_{\max} \geq k$, where $\lambda_{\max}$ is the maximum eigenvalue of the combinatorial Laplacian. Our algorithm provides a classical benchmark for a line of quantum algorithms for estimating Betti numbers. On clique complexes it matches their running time when, for example, $\gamma \in \Omega(1)$ and $k \in \Omega(n)$.Comment: v2: improved gap dependency by using Chebyshev polynomial

Exploring the Gap Between Tolerant and Non-Tolerant Distribution Testing

The framework of distribution testing is currently ubiquitous in the field of property testing. In this model, the input is a probability distribution accessible via independently drawn samples from an oracle. The testing task is to distinguish a distribution that satisfies some property from a distribution that is far in some distance measure from satisfying it. The task of tolerant testing imposes a further restriction, that distributions close to satisfying the property are also accepted. This work focuses on the connection between the sample complexities of non-tolerant testing of distributions and their tolerant testing counterparts. When limiting our scope to label-invariant (symmetric) properties of distributions, we prove that the gap is at most quadratic, ignoring poly-logarithmic factors. Conversely, the property of being the uniform distribution is indeed known to have an almost-quadratic gap. When moving to general, not necessarily label-invariant properties, the situation is more complicated, and we show some partial results. We show that if a property requires the distributions to be non-concentrated, that is, the probability mass of the distribution is sufficiently spread out, then it cannot be non-tolerantly tested with o(?n) many samples, where n denotes the universe size. Clearly, this implies at most a quadratic gap, because a distribution can be learned (and hence tolerantly tested against any property) using ?(n) many samples. Being non-concentrated is a strong requirement on properties, as we also prove a close to linear lower bound against their tolerant tests. Apart from the case where the distribution is non-concentrated, we also show if an input distribution is very concentrated, in the sense that it is mostly supported on a subset of size s of the universe, then it can be learned using only ?(s) many samples. The learning procedure adapts to the input, and works without knowing s in advance

A review on phytochemical and pharmacological, medicinal properties of holy basil (Ocimum sanctum L.)

Ocimum sanctum Linn. commonly referred to as Holy Basil or Tulsi is an Ayurvedic herb of Southeast Asia with extended records of traditional use. The culinary, medicinal, and industrial importance of this plant brought about to explore its chemical and pharmacological residences. right here, we offer a comprehensive assessment of medical findings of O. sanctum chemical materials and their related anticancer, antioxidant, antistress, γ-irradiation protection, antidiabetic and antileishmanicidal sports. more than 60 chemicals have been said from O. sanctum, inclusive of phenolics, flavonoids, phenylpropanoids, terpenoids, fatty acid derivatives, crucial oil, constant oil, and steroids. The pharmacological sports of O. sanctum compounds replicate their medicinal significance and inside the standardization of medicinal merchandise. This compilation could be useful in the improvement of recent active principles and nutraceuticals within the vicinity of drug resistance and rising persistent sickness vectors.Tulsi (Ocimum sanctum) member of the family (Lamiaceae) is the mostgood-sized medicinal flower cited in Ayurvedic creative writing for itsmedicinal and non-secular houses. the foundation, seeds, and leaves are majorly used due toits therapeutically housed.&nbsp