A kernel-enriched order-dependent nonparametric spatio-temporal process

Spatio-temporal processes are necessary modeling tools for various environmental, biological, and geographical problems. The underlying model is commonly considered to be parametric and to be a Gaussian process. Additionally, the covariance function is expected to be stationary and separable. This structure need not always be realistic. Moreover, attempts have been made to construct nonparametric processes of neither stationary nor separable covariance functions. Nevertheless, as we elucidate, some desirable and necessary spatio-temporal properties are not guaranteed by the existing approaches, thus, calling for further innovative ideas. In this article, using kernel convolution of order-based dependent Dirichlet process, we construct a novel spatio-temporal model. We show that this satisfies desirable properties and includes the stationary, separable, parametric processes as special cases. Our resultant posterior distribution is variable dimensional, which we attack using Transdimensional Transformation based Markov Chain Monte Carlo, which can update all the variables and change dimensions using deterministic transformations of a random variable drawn from some arbitrary density defined on relevant support. We demonstrate our model’s performance on simulated and real data sets. In all situations, the findings are highly encouraging

Faster counting and sampling algorithms using colorful decision oracle

In this work, we consider $d$-{\sc Hyperedge Estimation} and $d$-{\sc Hyperedge Sample} problem in a hypergraph $\mathcal{H}(U(\mathcal{H}),\mathcal{F}(\mathcal{H}))$ in the query complexity framework, where $U(\mathcal{H})$ denotes the set of vertices and $\mathcal{F}(\mathcal{H})$ denotes the set of hyperedges. The oracle access to the hypergraph is called {\sc Colorful Independence Oracle} ({\sc CID}), which takes $d$ (non-empty) pairwise disjoint subsets of vertices $A_1,\ldots,A_d \subseteq U(\mathcal{H})$ as input, and answers whether there exists a hyperedge in $\mathcal{H}$ having (exactly) one vertex in each $A_i, i \in \{1,2,\ldots,d\}$. The problem of $d$-{\sc Hyperedge Estimation} and $d$-{\sc Hyperedge Sample} with {\sc CID} oracle access is important in its own right as a combinatorial problem. Also, Dell {\it{et al.}}~[SODA '20] established that {\em decision} vs {\em counting} complexities of a number of combinatorial optimization problems can be abstracted out as $d$-{\sc Hyperedge Estimation} problems with a {\sc CID} oracle access. The main technical contribution of the paper is an algorithm that estimates $m= \lvert {\mathcal{F}(\mathcal{H})}\rvert$ with $\widehat{m}$ such that { $$\frac{1}{C_{d}\log^{d-1} n} \;\leq\; \frac{\widehat{m}}{m} \;\leq\; C_{d} \log ^{d-1} n .$$ by using at most $C_{d}\log ^{d+2} n$ many {\sc CID} queries, where $n$ denotes the number of vertices in the hypergraph $\mathcal{H}$ and $C_{d}$ is a constant that depends only on $d$}. Our result coupled with the framework of Dell {\it{et al.}}~[SODA '21] implies improved bounds for a number of fundamental problems

Biography and Homoeopathy in Bengal: Colonial lives of a European heterodoxy

AbstractDespite being recognized as a significant literary mode in understanding the advent of the modern self, biographies as agenrehave received relatively little attention from South Asian historians. Likewise, histories of science and healing in British India have largely ignored the colonial trajectories of those sectarian, dissenting, supposedly pseudo-sciences and medical heterodoxies that have flourished in Europe since the late eighteenth century. This article addresses these gaps in the historiography to identify biographies as a principal mode through which an incipient, ‘heterodox’ Western science like homoeopathy could consolidate and sustain itself in Bengal. In recovering the cultural history of a category that the state archives render largely invisible, this article argues that biographies are more than a mere repository of individual lives, and in fact are a veritable site of power. In bringing histories of print and publishing, histories of medicine, and histories of life writing practices together, it pursues two broad themes: first, it analyses the sociocultural strategies and networks by which scientific doctrines and concepts are translated across cultural borders. It explores the relation between medical commerce, print capital, and therapeutic knowledge to illustrate that acculturation of medical science necessarily drew upon and reinforced local constellations of class, kinship, and religion. Second, it simultaneously reflects upon the expanding genre of homoeopathic biographies published since the mid-nineteenth century: on their features, relevance, and functions, examining in particular the contemporary status of biography vis-à-vis ‘history’ in writing objective pasts.This is the accepted manuscript. The final version is available from CUP at http://dx.doi.org/10.1017/S0026749X1400057

Assessing the long-term fluctuations in dry-wet spells over Indian region using Markov model in GEE cloud platform

The long-term fluctuations in dry-wet spells were assessed at standard meteorological week (SMW) over India using Climate Hazards Group InfraRed Precipitation with Station (CHIRPS) rainfall data. The weekly sum of rainfall was embedded in Markov Chain Probability Model in Google Earth Engine (GEE) platform to compute initial and conditional probabilities of dry-wet spells during 2009-2020. An effective monsoon window (23rd SMW–39th SMW) was identified where initial probabilities (IPs) of dry (Pd) and wet (Pw) spells intersect at 50% probability level. Significant spatiotemporal variation of IPs was observed with initiation and withdrawal of monsoon over India. The analysis of co-efficient of variation (CV) showed low CV (60%) in Pw in semi-arid and arid regions whereas northern, central and eastern regions observed high CV (>60%) in Pd and low CV (<40%) in Pw. The drought prone and moisture sufficient zones were indentified based on the analysis of long-term frequency distribution of dry-wet spells and trend. Inter-comparison of IPs between CHIRPs with IMD (Indian Meteorological Department) and NOAA CPC (National Oceanic and Atmospheric Administration/Climate Prediction Centre) showed encouraging results. The study provides baseline reference for climate-resilient agricultural crop planning with respect to food security

Simple theoretical analysis of the effective electron mass in semiconductor nanowires

In this paper we study the effective electron mass (EEM) in Nano wires (NWs) of nonlinear optical materials on the basis of newly formulated electron dispersion relation by considering all types of anisotropies of the energy band constants within the framework of k . p formalism. The results for NWs of III-V, ternary and quaternary semiconductors form special cases of our generalized analysis. We have also investigated the EEM in NWs of Bi, IV-VI, stressed Kane type materials, Ge, GaSb and Bi2Te3 by formulating the appropriate 1D dispersion law in each case by considering the influence of energy band constants in the respective cases. It has been found that the 1D EEM in nonlinear optical materials depend on the size quantum numbers and Fermi energy due to the anisotropic spin orbit splitting constant and the crystal field splitting respectively. The 1D EEM is Bi, IV-VI, stressed Kane type semiconductors and Ge also depends on both the Fermi energy and the size quantum numbers which are the characteristic features of such NWs. The EEM increases with increase in concentration and decreasing film thickness and for ternary and quaternary compounds the EEM increases with increase in alloy composition. Under certain special conditions all the results for all the materials get simplified into the well known parabolic energy bands and thus confirming the compatibility test

Fine needle aspiration cytology of ovarian tumors with histological correlation

Background: Till today, there has been some hesitation to accept the role of fine needle aspiration cytology (FNAC) in pelvic mass. We have tried to study the role of ultrasonography (USG) and computed tomography (CT) guided FNAC as diagnostic and supportive investigation for ovarian tumors. Aim: To evaluate the current status of image-directed percutaneous aspiration of ovarian neoplasm for the purpose of early detection of malignancy. Materials and Methods: Seventy-four fine needle aspirations of ovarian neoplasms were performed between January 2007 and December 2008 by transabdominal approach under USG and CT guidance and correlated with histopathological findings and tumor markers. Results: A total of 47 (63.5%) cases were assessed as malignant and 21 (28.3%) as benign and 6 (8.1%) as inconclusive. The neoplastic lesions were categorized as per World Health Organization (WHO) classification. Conclusion: With the availability of modern techniques, USG and CT guided FNAC can be an optimum modality for the diagnosis of primary and metastatic ovarian neoplasms and evaluation of recurrent malignant tumors, which has great impact on patient management consequently