A novel way of constraining the α\alpha-attractor chaotic inflation through Planck data

Defining a scale of $k$-modes of the quantum fluctuations during inflation through the dynamical horizon crossing condition $k = aH$ we go from the physical $t$ variable to $k$ variable and solve the equations of cosmological first-order perturbations self consistently, with the chaotic $\alpha$-attractor type potentials. This enables us to study the behaviour of $n_{s}$, $r$, $n_{t}$ and $N$ in the $k$-space. Comparison of our results in the low-$k$ regime with the Planck data puts constraints on the values of the $\alpha$ parameter through microscopic calculations. Recent studies had already put model-dependent constraints on the values of $\alpha$ through the hyperbolic geometry of a Poincar\'{e} disk: consistent with both the maximal supergravity model $\mathcal{N}=8$ and the minimal supergravity model $\mathcal{N}=1$, the constraints on the values of $\alpha$ are $\frac{1}{3}$, $\frac{2}{3}$, 1, $\frac{4}{3}$, $\frac{5}{3}$, 2, $\frac{7}{3}$. The minimal $\mathcal{N}=1$ supersymmetric cosmological models with $B$-mode targets, derived from these supergravity models, predicted the values of $r$ between $10^{-2}$ and $10^{-3}$. Both in the $E$-model and the $T$-model potentials, we have obtained, in our calculations, the values of $r$ in this range for all the constrained values of $\alpha$ stated above, within $68\%$ CL. Moreover, we have calculated $r$ for some other possible values of $\alpha$ both in low-$\alpha$ limit, using the formula $r=\frac{12\alpha}{N^{2}}$, and in the high-$\alpha$ limit, using the formula $r=\frac{4n}{N}$, for $n=2$ and $4$. With all such values of $\alpha$, our calculated results match with the Planck-2018 data with $68\%$ or near $95\%$ CL.Comment: 41 pages, 29 figures, expanded the abstract, added figures and references, enlarged the discussio

Experimental Studies of Hydroxyl Radical Initiated Tropospheric Oxidation of Unsaturated Hydrocarbons

The tropospheric oxidation of unsaturated hydrocarbons is a central issue in atmospheric chemistry. These hydrocarbons are emitted into the atmosphere from both natural and anthropogenic sources, and their atmospheric oxidation leads to different atmospheric pollutants, including ground level ozone, photochemical smog and secondary organic aerosols. Isoprene and 1,3-butadiene represent a biogenic and an anthropogenic hydrocarbon, respectively, which primarily undergo electrophilic addition of OH radical, followed by chain propagating radical reactions. Their oxidation is the major source for ground level ozone formation in both rural and urban area and understanding their chemistry is essential for regional air quality modeling. Until recently, most of the studies of isoprene chemistry have been non-isomer specific, reflecting the reactivity of combined pathways and therefore were insensitive to specific details of the isomeric pathways. An isomeric selective approach to studying unsaturated hydrocarbon oxidation is described in this dissertation. A synthesized precursor, whose photolysis can provide a route to the formation of energy selected single isomer in the isoprene oxidation pathway, enables the study of important channels that are difficult to unravel in non isomer specific experiments. The major addition channel in OH isoprene oxidation has been studied following the isomeric selective approach and using Laser Photolysis-Laser Induced Fluorescence (LP-LIF) as the primary experimental technique. The study reveals important information about the oxidative chemistry of the δ-peroxy radicals, accounting for about 20 percent of missing carbon balance in isoprene oxidation, and isomeric specific rate constants. A similar approach was applied to study the oxidation of 1,3-butadiene, and the photolytic precursor for the dominant hydroxy alkyl isomer in the OH initiated oxidation of 1,3-butadiene was synthesized. The subsequent experiments and analysis revealed detailed information about the oxidative chemistry accounting for approximately 26 percent of the missing chemistry. Finally, non isomeric selective OH cycling experiments were carried out on the1,3-butadiene system. By analyzing the OH cycling data with the combined information obtained from the isomeric specific studies of the two isomeric channels of 1,3-butadiene oxidation, the relative branching between the two isomeric channels of OH-1,3-butadiene oxidation was determined

Rendezvous on a Known Dynamic Point on a Finite Unoriented Grid

In this paper, we have considered two fully synchronous $\mathcal{OBLOT}$ robots having no agreement on coordinates entering a finite unoriented grid through a door vertex at a corner, one by one. There is a resource that can move around the grid synchronously with the robots until it gets co-located along with at least one robot. Assuming the robots can see and identify the resource, we consider the problem where the robots must meet at the location of this dynamic resource within finite rounds. We name this problem "Rendezvous on a Known Dynamic Point". Here, we have provided an algorithm for the two robots to gather at the location of the dynamic resource. We have also provided a lower bound on time for this problem and showed that with certain assumption on the waiting time of the resource on a single vertex, the algorithm provided is time optimal. We have also shown that it is impossible to solve this problem if the scheduler considered is semi-synchronous

Space and move-optimal Arbitrary Pattern Formation on infinite rectangular grid by Oblivious Robot Swarm

Arbitrary Pattern Formation (APF) is a fundamental coordination problem in swarm robotics. It requires a set of autonomous robots (mobile computing units) to form any arbitrary pattern (given as input) starting from any initial pattern. The APF problem is well-studied in both continuous and discrete settings. This work concerns the discrete version of the problem. A set of robots is placed on the nodes of an infinite rectangular grid graph embedded in a euclidean plane. The movements of the robots are restricted to one of the four neighboring grid nodes from its current position. The robots are autonomous, anonymous, identical, and homogeneous, and operate Look-Compute-Move cycles. Here we have considered the classical $\mathcal{OBLOT}$ robot model, i.e., the robots have no persistent memory and no explicit means of communication. The robots have full unobstructed visibility. This work proposes an algorithm that solves the APF problem in a fully asynchronous scheduler under this setting assuming the initial configuration is asymmetric. The considered performance measures of the algorithm are space and number of moves required for the robots. The algorithm is asymptotically move-optimal. A definition of the space-complexity is presented here. We observe an obvious lower bound $\mathcal{D}$ of the space complexity and show that the proposed algorithm has the space complexity $\mathcal{D}+4$. On comparing with previous related works, we show that this is the first proposed algorithm considering $\mathcal{OBLOT}$ robot model that is asymptotically move-optimal and has the least space complexity which is almost optimal

Asynchronous Gathering of Robots with Finite Memory on a Circle under Limited Visibility

Consider a set of $n$ mobile entities, called robots, located and operating on a continuous circle, i.e., all robots are initially in distinct locations on a circle. The \textit{gathering} problem asks to design a distributed algorithm that allows the robots to assemble at a point on the circle. Robots are anonymous, identical, and homogeneous. Robots operate in a deterministic Look-Compute-Move cycle within the circular path. Robots agree on the clockwise direction. The robot's movement is rigid and they have limited visibility $\pi$, i.e., each robot can only see the points of the circle which is at an angular distance strictly less than $\pi$ from the robot. Di Luna \textit{et al}. [DISC'2020] provided a deterministic gathering algorithm of oblivious and silent robots on a circle in semi-synchronous (\textsc{SSync}) scheduler. Buchin \textit{et al}. [IPDPS(W)'2021] showed that, under full visibility, $\mathcal{OBLOT}$ robot model with \textsc{SSync} scheduler is incomparable to $\mathcal{FSTA}$ robot (robots are silent but have finite persistent memory) model with asynchronous (\textsc{ASync}) scheduler. Under limited visibility, this comparison is still unanswered. So, this work extends the work of Di Luna \textit{et al}. [DISC'2020] under \textsc{ASync} scheduler for $\mathcal{FSTA}$ robot model

Circle Formation by Asynchronous Opaque Fat Robots on an Infinite Grid

This study addresses the problem of "Circle Formation on an Infinite Grid by Fat Robots" ($CF\_FAT\_GRID$). Unlike prior work focused solely on point robots in discrete domain, it introduces fat robots to circle formation on an infinite grid, aligning with practicality as even small robots inherently possess dimensions. The algorithm, named $CIRCLE\_FG$, resolves the $CF\_FAT\_GRID$ problem using a swarm of fat luminous robots. Operating under an asynchronous scheduler, it achieves this with five distinct colors and by leveraging one-axis agreement among the robots

A comparative study of lip print patterns in monozygotic and dizygotic twins

Background: External surface of lips has many elevations and depressions forming a characteristic pattern called lip prints, the study of which is known as cheiloscopy. This is unique for the individuals like in fingerprints.Methods: The present study was conducted in 40 pairs of twins and their families to evaluate the possibility of variation of lip print patterns in twins and their parents to find out any similarity among twins and their families.  The twins were taken as the primary subject and their parents as the secondary subjects.Results: The subjects with congenital lip deformity and any inflammation were excluded from the study. The lip prints were taken on the cello tape and highlighted with the black printer powder of Oddyessy make. the photographs were taken for the permanent record. The prints were studied on Adobe Photoshop 7.0 software and classified under Tsuchihashi classification.Conclusions: Comparison of lip prints showed that they are unique to each individual and among twins revealed that they are similar but not identical and their characteristics resembled either parent. Since the lip print patterns are unique, lip print analysis can be considered as a tool for personal identification