PYTHAGOREAN FUZZY MULTI SET AND ITS APPLICATIONS IN FISH FEED FOR INDIAN MAJOR CARP

Pythagorean fuzzy set is an extension of Intutionistic fuzzy set, which is more capable of expressing and handling the uncertainty under uncertain environments, so that it was broadly applied in various fields. In this paper, we explored the concept of Pythagorean fuzzy multi set (PFMS). We describe some basic set operations of Pythagorean fuzzy multi set and also, we proposed sine exponential distance function. Finally, through an illustrative example it is shown how the proposed distance works in decision-making problem.

Scaling of gene transcriptional gradients with brain size across mouse development

The structure of the adult brain is the result of complex physical mechanisms acting through development. These physical processes, acting in threedimensional space, mean that the brain’s spatial embedding plays a key role in its organization, including the gradient-like patterning of gene expression that encodes the molecular underpinning of functional specialization. However, we do not yet understand how the dramatic changes in brain shape and size that occur in early development influence the brain’s transcriptional architecture. Here we investigate the spatial embedding of transcriptional patterns of over 1800 genes across seven time points through mousebrain development using data from the Allen Developing Mouse Brain Atlas. We find that transcriptional similarity decreases exponentially with separation distance across all developmental time points, with a correlation length scale that follows a powerlaw scaling relationship with a linear dimension of brain size. This scaling suggests that the mouse brain achieves a characteristic balance between local molecular similarity (homogeneous gene expression within a specialized brain area) and longer-range diversity (between functionally specialized brain areas) throughout its development. Extrapolating this mouse developmental scaling relationship to the human cortex yields a prediction consistent with the value measured from microarray data. We introduce a simple model of brain growth as spatially autocorrelated gene-expression gradients that expand through development, which captures key features of the mouse developmental data. Complementing the well-known exponential distance rule for structural connectivity, our findings characterize an analogous exponential distance rule for transcriptional gradients that scales across mouse brain development, providing new understanding of spatial constraints on the brain’s molecular patterning.

Clustering Longitudinal Life-Course Sequences using Mixtures of Exponential-Distance Models

Sequence analysis is an increasingly popular approach for the analysis of life courses represented by an ordered collection of activities experienced by subjects over a given time period. Several criteria exist for measuring pairwise dissimilarities among sequences. Typically, dissimilarity matrices are employed as input to heuristic clustering algorithms, with the aim of identifying the most relevant patterns in the data.Here, we propose a model-based clustering approach for categorical sequence data. The technique is applied to a survey data set containing information on the career trajectories of a cohort of Northern Irish youths tracked between the ages of 16 and 22.Specifically, we develop a family of methods for clustering sequences directly, based on mixtures of exponential-distance models, which we call MEDseq. The use of the Hamming distance or weighted variants thereof as the distance metrics permits closed-form expressions for the normalising constant, thereby facilitating the development of an ECM algorithm for model fitting. Additionally, MEDseq models allow the probability of component membership to depend on fixed covariates. Sampling weights, which are often associated with life-course data arising from surveys, are also accommodated. Simultaneously including weights and covariates in the clustering process yields new insights on the Northern Irish data.

Influence Area of Transit-Oriented Development for Individual Delhi Metro Stations Considering Multimodal Accessibility

Understanding the influence areas for transit stations in Indian cities is a prerequisite for adopting transit-oriented development (TOD). This study provides insights into the last mile patterns for selected Delhi Metro Rail (DMR) stations, specifically, Karkardooma, Dwarka Mor, Lajpat Nagar, and Vaishali, and the extent of the influence area based on different access modes. The variation in the extent of the influence areas based on various modes and the locational characteristics of stations have been considered in this study. The last mile distances reported in the conducted survey involved the problems of rounding and heaping, and they were subjected to multiple imputation to remove the bias. The spatial extent of the influence areas for various modes was estimated based on the compound power exponential distance decay function. Further, the threshold walking distances were calculated using the receiver operating characteristic (ROC) curves. The variations were noted in the last mile distances among stations. The walking distances (mean and 85th percentile) among stations did not vary considerably; however, large variations were noted when comparing other modes. These differences in accessibility must be taken into account when considering multimodal accessibility and multimode-based TOD. The study can provide useful inputs for planning and implementing TOD in New Delhi.

The Arithmetic Tutte polynomial of two matrices associated to Trees

Arithmetic matroids arising from a list A of integral vectors in Zn are of recent interest and the arithmetic Tutte polynomial MA(x, y) of A is a fundamental invariant with deep connections to several areas. In this work, we consider two lists of vectors coming from the rows of matrices associated to a tree T. Let T = (V, E) be a tree with |V| = n and let LT be the q-analogue of its Laplacian L in the variable q. Assign q = r for r ∈ ℤ with r/= 0, ±1 and treat the n rows of LT after this assignment as a list containing elements of ℤn. We give a formula for the arithmetic Tutte polynomial MLT (x, y) of this list and show that it depends only on n, r and is independent of the structure of T. An analogous result holds for another polynomial matrix associated to T: EDT, the n × n exponential distance matrix of T. More generally, we give formulae for the multivariate arithmetic Tutte polynomials associated to the list of row vectors of these two matriceswhich shows that even the multivariate arithmetic Tutte polynomial is independent of the tree T. As a corollary, we get the Ehrhart polynomials of the following zonotopes: - ZEDT obtained from the rows of EDT and - ZLT obtained from the rows of LT. Further, we explicitly find the maximum volume ellipsoid contained in the zonotopes ZEDT, ZLT and show that the volume of these ellipsoids are again tree independent for fixed n, q. A similar result holds for the minimum volume ellipsoid containing these zonotopes.