Pairwise Balanced Designs From Cyclic PBIB Designs

A pairwise balanced designs was constructed using cyclic partially balanced incomplete block designs with either (λ1 – λ2) = 1 or (λ2 – λ1) = 1. This method of construction of Pairwise balanced designs is further generalized to construct it using cyclic partially balanced incomplete block design when |(λ1 – λ2)| = p. The methods of construction of pairwise balanced designs was supported with examples. A table consisting parameters of Cyclic PBIB designs and its corresponding constructed pairwise balanced design is also included

Do dinosaurs still walk the earth

While most branches of the dinosaur family tree were wiped out during a mass-extinction event 65.5 million years ago, some of their direct descendants still live on. What do we know about these creatures, their mysterious survival, and their relationship to the dinosaurs of yore

Analysis of Elephant Movement in Sub-Saharan Africa: Ecological, Climatic, and Conservation Perspectives

The interaction between elephants and their environment has profound implications for both ecology and conservation strategies. This study presents an analytical approach to decipher the intricate patterns of elephant movement in Sub-Saharan Africa, concentrating on key ecological drivers such as seasonal variations and rainfall patterns. Despite the complexities surrounding these influential factors, our analysis provides a holistic view of elephant migratory behavior in the context of the dynamic African landscape. Our comprehensive approach enables us to predict the potential impact of these ecological determinants on elephant migration, a critical step in establishing informed conservation strategies. This projection is particularly crucial given the impacts of global climate change on seasonal and rainfall patterns, which could substantially influence elephant movements in the future. The findings of our work aim to not only advance the understanding of movement ecology but also foster a sustainable coexistence of humans and elephants in Sub-Saharan Africa. By predicting potential elephant routes, our work can inform strategies to minimize human-elephant conflict, effectively manage land use, and enhance anti-poaching efforts. This research underscores the importance of integrating movement ecology and climatic variables for effective wildlife management and conservation planning.Comment: 11 pages, 17 figures, Accepted in ACM SIGCAS SIGCHI Conference on Computing and Sustainable Societies (COMPASS 2023

Lower bound of the expressibility of ansatzes for Variational Quantum Algorithms

The expressibility of an ansatz used in a variational quantum algorithm is defined as the uniformity with which it can explore the space of unitary matrices. The expressibility of a particular ansatz has a well-defined upper bound. In this work, we show that the expressibiliity also has a well-defined lower bound in the hypothesis space. We provide an analytical expression for the lower bound of the covering number, which is directly related to expressibility. We also perform numerical simulations to to support our claim. To numerically calculate the bond length of a diatomic molecule, we take hydrogen ($H_2$) as a prototype system and calculate the error in the energy for the equilibrium energy point for different ansatzes. We study the variation of energy error with circuit depths and show that in each ansatz template, a plateau exists for a range of circuit depths, which we call the set of acceptable points, and the corresponding expressibility is known as the best expressive region. We report that the width of this best expressive region in the hypothesis space is inversely proportional to the average error. Our analysis reveals that alongside trainability, the lower bound of expressibility also plays a crucial role in selecting variational quantum ansatzes