Testing the Kerr nature of intermediate-mass and supermassive black hole binaries using spin-induced multipole moment measurements

The gravitational wave measurements of spin-induced multipole moment coefficients of a binary black hole system can be used to distinguish black holes from other compact objects [N. V. Krishnendu et al., PRL 119, 091101 (2017)]. Here, we apply the idea proposed in [N. V. Krishnendu et al., PRL 119, 091101 (2017)] to binary systems composed of intermediate-mass and supermassive black holes and derive the expected bounds on their Kerr nature using future space-based gravitational wave detectors. Using astrophysical models of binary black hole population, we study the measurability of the spin-induced quadrupole and octupole moment coefficients using LISA and DECIGO. The errors on spin-induced quadrupole moment parameter of the binary system are found to be { $\leq 0.1$ for almost $3\%$ of the total supermassive binary black hole population which is detectable by LISA whereas it is $\sim 46\%$ for the intermediate-mass black hole binaries observable by DECIGO at its design sensitivity.} We find that { errors on} {\it both} the quadrupole and octupole moment parameters can be estimated to { be} $\leq 1$ for $\sim 2\%$ and $\sim 50\%$ {of the population} respectively for LISA and DECIGO detectors. { Our findings suggest that a subpopulation of binary black hole events, with the signal to noise ratio thresholds greater than 200 and 100 respectively for LISA and DECIGO detectors, would permit tests of black hole nature to 10\% precision.}Comment: 7 pages, 6 figure

Gap equation in scalar field theory at finite temperature

We investigate the two-loop gap equation for the thermal mass of hot massless $g^2\phi^4$ theory and find that the gap equation itself has a non-zero finite imaginary part. This indicates that it is not possible to find the real thermal mass as a solution of the gap equation beyond $g^2$ order in perturbation theory. We have solved the gap equation and obtain the real and the imaginary part of the thermal mass which are correct up to $g^4$ order in perturbation theory.Comment: 13 pages, Latex with axodraw, Minor corrections, Appendix adde

Nutritional Composition of Bitter Gourd Types (Momordica Charantia L.)

Bitter gourd has important role as a source of carbohydrate, proteins, vitamins, minerals and other nutrients in human diet (Ali et al., 2008) which are necessary for maintaining proper health. To assess the chemical and nutritional composition of the selected bitter gourd types in the fresh and dried form, the following parameters were determined i.e. total carbohydrate, protein, dietary fibre, moisture, β carotene, vitamin C, folic acid, calcium, phosphorus, sodium, potassium, iron, manganese, copper and zinc. The study revealed that highest protein, moisture, vitamin C and folic acid content were found in Light green big (2.06 g, 90.40 per cent, 98.2 mg and 0.10 µg/ ml respectively). Highest carbohydrate and fibre content was found in light green small (8.22 g and 1.21 g). The amount of beta carotene was found to be highest in nei paval sample (140.03 mcg/100g). In the case of mineral analysis, highest calcium, phosphorus and sodium content were found in light green big (25.44 mg/ 100g and 79.64 mg/100 g 20.12 mg / 100 g respectively). The potassium and iron content was found highest in nei paval (174.46 mg/ 100 g 2.14 mg). Highest manganese, copper and zinc content were noticed in light green big (34.57 mg, 40.17 mg and 90.41 mg/ 100g respectively)

Antioxidant Properties of Bitter Gourd (Momordica Charantia L.)

Bitter gourd is regarded as an antioxidant rich vegetable with beneficial properties for the circulatory, respiratory, digestive and nervous systems according to the Indian indigenous system of medicine. Several methods have been used to determine antioxidant activity of plants. The present study, therefore, involved four various established methods to evaluate anti oxidative activity of bitter gourd fruit, namely, total antioxidant capacity, DPPH radical scavenging activity, hydroxyl radical scavenging activity and super oxide anion radical scavenging activity by using different types of solvents like petroleum ether, acetone, ethanol and methanol. The present study revealed that light green big sample had the highest DPPH activity with an IC50 value of 50.88 µg/ ml in methanol solvent. In the case of bitter gourd dried samples, highest DPPH activity with an IC50 value of 50.10 µg/ ml was reported in light green big type. The hydroxyl radical scavenging activity of light green big was found to be highest both in the case of fresh and dried bitter gourd samples with an IC50 values of 50.95 µg/ml and 50.10 µg/ml respectively. Light green small sample showed higher superoxide anion radical scavenging activity with an IC50 value of 50.36 µg/ ml in fresh samples and 49.76 µg/ ml in dried samples, in solvents like petroleum ether and acetone respectively. Antioxidant activity ranged with an IC50 value of 50.09 µg/ml to 61.90 µg/ml in fresh bitter gourd samples and maximum antioxidant capacity was observed in light green big (50.09 µg/ ml) whereas dried samples, the highest antioxidant activity was observed in light green dried (50.07 µg/ ml) in acetone solvent

The Complexity of Graph-Based Reductions for Reachability in Markov Decision Processes

We study the never-worse relation (NWR) for Markov decision processes with an infinite-horizon reachability objective. A state q is never worse than a state p if the maximal probability of reaching the target set of states from p is at most the same value from q, regard- less of the probabilities labelling the transitions. Extremal-probability states, end components, and essential states are all special cases of the equivalence relation induced by the NWR. Using the NWR, states in the same equivalence class can be collapsed. Then, actions leading to sub- optimal states can be removed. We show the natural decision problem associated to computing the NWR is coNP-complete. Finally, we ex- tend a previously known incomplete polynomial-time iterative algorithm to under-approximate the NWR

Cooking practices, air quality, and the acceptability of advanced cookstoves in Haryana, India: an exploratory study to inform large-scale interventions.

BackgroundIn India, approximately 66% of households rely on dung or woody biomass as fuels for cooking. These fuels are burned under inefficient conditions, leading to household air pollution (HAP) and exposure to smoke containing toxic substances. Large-scale intervention efforts need to be informed by careful piloting to address multiple methodological and sociocultural issues. This exploratory study provides preliminary data for such an exercise from Palwal District, Haryana, India.MethodsTraditional cooking practices were assessed through semi-structured interviews in participating households. Philips and Oorja, two brands of commercially available advanced cookstoves with small blowers to improve combustion, were deployed in these households. Concentrations of particulate matter (PM) with a diameter <2.5 μm (PM2.5) and carbon monoxide (CO) related to traditional stove use were measured using real-time and integrated personal, microenvironmental samplers for optimizing protocols to evaluate exposure reduction. Qualitative data on acceptability of advanced stoves and objective measures of stove usage were also collected.ResultsTwenty-eight of the thirty-two participating households had outdoor primary cooking spaces. Twenty households had liquefied petroleum gas (LPG) but preferred traditional stoves as the cost of LPG was higher and because meals cooked on traditional stoves were perceived to taste better. Kitchen area concentrations and kitchen personal concentrations assessed during cooking events were very high, with respective mean PM2.5 concentrations of 468 and 718 µg/m3. Twenty-four hour outdoor concentrations averaged 400 µg/m3. Twenty-four hour personal CO concentrations ranged between 0.82 and 5.27 ppm. The Philips stove was used more often and for more hours than the Oorja.ConclusionsThe high PM and CO concentrations reinforce the need for interventions that reduce HAP exposure in the aforementioned community. Of the two stoves tested, participants expressed satisfaction with the Philips brand as it met the local criteria for usability. Further understanding of how the introduction of an advanced stove influences patterns of household energy use is needed. The preliminary data provided here would be useful for designing feasibility and/or pilot studies aimed at intervention efforts locally and nationally

Quantum chaos in the spectrum of operators used in Shor's algorithm

We provide compelling evidence for the presence of quantum chaos in the unitary part of Shor's factoring algorithm. In particular we analyze the spectrum of this part after proper desymmetrization and show that the fluctuations of the eigenangles as well as the distribution of the eigenvector components follow the CUE ensemble of random matrices, of relevance to quantized chaotic systems that violate time-reversal symmetry. However, as the algorithm tracks the evolution of a single state, it is possible to employ other operators, in particular it is possible that the generic quantum chaos found above becomes of a nongeneric kind such as is found in the quantum cat maps, and in toy models of the quantum bakers map.Comment: Title and paper modified to include interesting additional possibilities. Principal results unaffected. Accepted for publication in Phys. Rev. E as Rapid Com

Interplay of spin-precession and higher harmonics in the parameter estimation of binary black holes

Gravitational-wave (GW) signals from coalescing compact binaries carry enormous information about the source dynamics and are an excellent tool to probe unknown astrophysics and fundamental physics. Though the updated catalog of compact binary signals reports evidence for slowly spinning systems and unequal mass binaries, the data so far cannot provide convincing proof of strongly precessing binaries. Here, we use the GW inference library parallel Bilby to compare the performance of two waveform models for measuring spin-induced orbital precession. One of the waveform models incorporates both spin-precession effects and sub-dominant harmonics. The other model accounts for precession but only includes the leading harmonic. By simulating signals with varying mass ratios and spins, we find that the waveform model with sub-dominant harmonics enables us to infer the presence of precession in most cases accurately. In contrast, the dominant model often fails to extract enough information to measure precession. In particular, it cannot distinguish a face-on highly precessing binary from a slowly precessing binary system irrespective of the binary's mass ratio. As expected, we see a significant improvement in measuring precession for edge-on binaries. Other intrinsic parameters also become better constrained, indicating that precession effects help break the correlations between mass and spin parameters. However, the precession measurements are prior dominated for equal-mass binaries with face-on orientation, even if we employ waveform model including subdominant harmonics. In this case, doubling the signal-to-noise ratio does not help to reduce these prior induced biases. As we expect detections of highly spinning binary signals with misaligned spin orientations in the future, simulation studies like ours are crucial for understanding the prospects and limitations of GW parameter inferences