On the number of pancake stacks requiring four flips to be sorted

Using existing classification results for the 7- and 8-cycles in the pancake graph, we determine the number of permutations that require 4 pancake flips (prefix reversals) to be sorted. A similar characterization of the 8-cycles in the burnt pancake graph, due to the authors, is used to derive a formula for the number of signed permutations requiring 4 (burnt) pancake flips to be sorted. We furthermore provide an analogous characterization of the 9-cycles in the burnt pancake graph. Finally we present numerical evidence that polynomial formulae exist giving the number of signed permutations that require $k$ flips to be sorted, with $5\leq k\leq9$.Comment: We have finalized for the paper for publication in DMTCS, updated a reference to its published version, moved the abstract to its proper location, and added a thank you to the referees. The paper has 27 pages, 6 figures, and 2 table

Cycles in the burnt pancake graphs

The pancake graph $P_n$ is the Cayley graph of the symmetric group $S_n$ on $n$ elements generated by prefix reversals. $P_n$ has been shown to have properties that makes it a useful network scheme for parallel processors. For example, it is $(n-1)$-regular, vertex-transitive, and one can embed cycles in it of length $\ell$ with $6\leq\ell\leq n!$. The burnt pancake graph $BP_n$, which is the Cayley graph of the group of signed permutations $B_n$ using prefix reversals as generators, has similar properties. Indeed, $BP_n$ is $n$-regular and vertex-transitive. In this paper, we show that $BP_n$ has every cycle of length $\ell$ with $8\leq\ell\leq 2^n n!$. The proof given is a constructive one that utilizes the recursive structure of $BP_n$. We also present a complete characterization of all the $8$-cycles in $BP_n$ for $n \geq 2$, which are the smallest cycles embeddable in $BP_n$, by presenting their canonical forms as products of the prefix reversal generators.Comment: Added a reference, clarified some definitions, fixed some typos. 42 pages, 9 figures, 20 pages of appendice

A data-driven framework for modelling community energy demand

Data driven models that integrate advanced analytics involving statistical and machine learning algorithms are widely applied for simulating and predicting energy demand at the community level. These models are used to inform various energy efficiency measures, infrastructure development, planning and investment decision. The paper presents an innovative framework for simulating and projecting climate change impacts on the future dynamics of community energy demand. The modelling framework selectively couples some of the most advanced analytical approaches and its potential are demonstrated using a case study community “Auroville” located in India

Production Potential of Different Pasture Grasses under Off-Season Rainfall in Arid Conditions of Bikaner, India

Livestock rearing is the important source of livelihood in arid region of Rajasthan where the crop production is unstable due to low and erratic rainfall. The rangelands and pastures are important land use system and provide main support to the livestock in the arid region of Rajasthan. Grazing of livestock is a common practice in arid zone as about 50 % of total area of western Rajasthan is available for grazing mainly for cows, sheep and goat, however, the availability of green fodder is restricted to monsoon and post monsoon months only and during rest of the period livestock graze on dry grasses and crop residues available in cultivated, fallow and wastelands and other grazing lands. The perennial grasses like Lasiurus sindicus, Cenchrus ciliaris, C. setigerus, Panicum turgidum, P. antidotale etc. with some annuals are dominated in the rangelands and pastures in the arid zone of Rajasthan. Generally these grasses are grown during rainy season but also regenerated during off-season condition when sufficient moisture is available through rainfall or irrigation and provide fodder during the lean period. Productivity of these pasture grasses were assessed during rainy season but information of the production potential during off-season is not available in literature. Therefore, present study was conducted during March to May 2015 at Arid Region Campus of CSWRI, Bikaner to assess the production potential and regeneration of different grasses during off-season under arid condition

Physico-chemical attributes and organoleptic assessment of guava (Psidium guajava L.) cultivars grown in eastern Uttar Pradesh

A study was conducted to evaluate the different guava cultivars for their physico-chemical composition and organoleptic assessment during the year 2012-2013. Results of study indicated that Gorakh Bilas Pasand cultivar proved to be superior on the basis of physical characters (Length-7.64 cm, Breadth-7.79 cm , Weight-240.60 g, Number of seeds per fruit-251 etc.) followed by Lucknow-49. However, Lucknow-49 was found noteworthy in respect of chemical composition (TSS-13.00 oBrix, Acidity-0.50%, pH-5.86, Vitamin C-300.36 mg/100g etc). In organoleptic assessment, it was found that ‘liked very much’ rating was provided by consumer to Lucknow-49. On the basis of overall findings, it was concluded that ‘Lucknow-49’ was superior in most of characters studied and might be one of the promising cultivars for quality fruits under eastern Uttar Pradesh conditions

Climate change, extreme heat, and South Asian megacities: Impact of heat stress on inhabitants and their productivity

Of the 33 global megacities, 10 were situated in South Asia. Extreme heat waves have become an annual phenomenon due to climate change in South Asian megacities, causing severe health issues and even deaths. In this study, we evaluated 29 years (1990–2019) of historical data on heat stress in ten selected megacities (existing and prospective)—New Delhi, Dhaka, Mumbai, Kolkata, Ahmedabad, Chennai, Bengaluru, Hyderabad, Chittagong, and Pune—in India and Bangladesh. We used heat index (HI) and environmental stress index (ESI) analyses to evaluate stress and vulnerability. Our results showed New Delhi, Mumbai, Kolkata, Ahmedabad, and Chennai in India; Dhaka and Chittagong in Bangladesh were already experiencing an elevated number of hours of “danger” levels of heat stress, which may lead to heat cramps, exhaustion, stroke, and even death. Furthermore, the frequency of “danger” levels of heat stress and vulnerable levels of ESI has increased significantly since 2011 in the selected megacities, which elevated the heat-related vulnerability among the millions of inhabitants in terms of work hours lost for light, moderate, and heavy work due to heat stress. The vulnerable population in the studied megacities might have to reduce annual work hours by 0.25–860.6 h (light work), 43–1595.9 h (moderate work), and 291–2402 h (heavy work) due to extreme heat in 1990–2019. We also discussed the implication of the work-hour loss on productivity, income, gross domestic product, and sustainable development goal progress because of heat stress and its causes and suggested recommendations to reduce its impact

An unconditionally stable nonstandard finite difference method to solve a mathematical model describing Visceral Leishmaniasis

In this paper, a mathematical model of Visceral Leishmaniasis is considered. The model incorporates three populations, the human, the reservoir and the vector host populations. A detailed analysis of the model is presented. This analysis reveals that the model undergoes a backward bifurcation when the associated reproduction threshold is less than unity. For the case where the death rate due to VL is negligible, the disease-free equilibrium of the model is shown to be globally-asymptotically stable if the reproduction number is less than unity. Noticing that the governing model is a system of highly nonlinear differential equations, its analytical solution is hard to obtain. To this end, a special class of numerical methods, known as the nonstandard finite difference (NSFD) method is introduced. Then a rigorous theoretical analysis of the proposed numerical method is carried out. We showed that this method is unconditionally stable. The results obtained by NSFD are compared with other well-known standard numerical methods such as forward Euler method and the fourth-order Runge–Kutta method. Furthermore, the NSFD preserves the positivity of the solutions and is more efficient than the standard numerical methods

Applying dissipative dynamical systems to pseudorandom number generation: Equidistribution property and statistical independence of bits at distances up to logarithm of mesh size

The behavior of a family of dissipative dynamical systems representing transformations of two-dimensional torus is studied on a discrete lattice and compared with that of conservative hyperbolic automorphisms of the torus. Applying dissipative dynamical systems to generation of pseudorandom numbers is shown to be advantageous and equidistribution of probabilities for the sequences of bits can be achieved. A new algorithm for generating uniform pseudorandom numbers is proposed. The theory of the generator, which includes proofs of periodic properties and of statistical independence of bits at distances up to logarithm of mesh size, is presented. Extensive statistical testing using available test packages demonstrates excellent results, while the speed of the generator is comparable to other modern generators.Comment: 6 pages, 3 figures, 3 table

Symptom Domain Groups of the Patient-Reported Outcomes Measurement Information System Tools Independently Predict Hospitalizations and Re-hospitalizations in Cirrhosis

Background Patient-Reported Outcomes Measurement Information System (PROMIS) tools can identify health-related quality of life (HRQOL) domains that could differentially affect disease progression. Cirrhotics are highly prone to hospitalizations and re-hospitalizations, but the current clinical prognostic models may be insufficient, and thus studying the contribution of individual HRQOL domains could improve prognostication. Aim Analyze the impact of individual HRQOL PROMIS domains in predicting time to all non-elective hospitalizations and re-hospitalizations in cirrhosis. Methods Outpatient cirrhotics were administered PROMIS computerized tools. The first non-elective hospitalization and subsequent re-hospitalizations after enrollment were recorded. Individual PROMIS domains significantly contributing toward these outcomes were generated using principal component analysis. Factor analysis revealed three major PROMIS domain groups: daily function (fatigue, physical function, social roles/activities and sleep issues), mood (anxiety, anger, and depression), and pain (pain behavior/impact) accounted for 77% of the variability. Cox proportional hazards regression modeling was used for these groups to evaluate time to first hospitalization and re-hospitalization. Results A total of 286 patients [57 years, MELD 13, 67% men, 40% hepatic encephalopathy (HE)] were enrolled. Patients were followed at 6-month (mth) intervals for a median of 38 mths (IQR 22–47), during which 31% were hospitalized [median IQR mths 12.5 (3–27)] and 12% were re-hospitalized [10.5 mths (3–28)]. Time to first hospitalization was predicted by HE, HR 1.5 (CI 1.01–2.5, p = 0.04) and daily function PROMIS group HR 1.4 (CI 1.1–1.8, p = 0.01), independently. In contrast, the pain PROMIS group were predictive of the time to re-hospitalization HR 1.6 (CI 1.1–2.3, p = 0.03) as was HE, HR 2.1 (CI 1.1–4.3, p = 0.03). Conclusions Daily function and pain HRQOL domain groups using PROMIS tools independently predict hospitalizations and re-hospitalizations in cirrhotic patients