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Construction of Jacobi forms using adjoint of the Jacobi–Serre derivative
No full textIn the article, we study the Oberdieck derivative defined on the space of weak Jacobi forms. We prove that the Oberdieck derivative maps a Jacobi form to a Jacobi form. Moreover, we study the adjoint of the Oberdieck derivative of a Jacobi cusp form with respect to the Petersson scalar product defined on the space of Jacobi forms. As a consequence, we also obtain the adjoint of the Jacobi–Serre derivative (defined in an unpublished work of Oberdieck). As an application, we obtain certain relations among the Fourier coefficients of Jacobi forms
Cosmology in R2-gravity: Effects of a higher derivative scalar condensate background
No full textA well known extension of Einstein\u27s General Relativity is the addition of an R2-term, which is free of ghost excitations and in the linearized framework, reduces to the conventional spin-2 graviton and an additional higher derivative scalar. According to Chakraborty and Ghosh (2022), the above scalar sector can sustain a Time Crystal-like minimum energy state, with non-trivial time dependence. Exploiting previous result that the scalar can sustain modes with periodic time dependence in its lowest energy, we consider this condensate as a source and study the Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology in this background. The effect of the R2-term is interpreted as a back reaction. A remarkable consequence of the condensate is that, irrespective of open or close geometry of the Universe, for an appropriate choice of parameter window, the condensate can induce a decelerating phase before the accelerated expansion starts and again, in some cases, it can help to avoid the singularity in the deceleration parameter (that is present in conventional FLRW Cosmology)
Crime, efficiency of labour and trade: a theoretical analysis
No full textWe present a two-sector efficiency wage model of a small open economy in this paper where efficiency of labour not only varies positively with the wage rate and unemployment rate but also varies inversely with the volume of anti-social activity. We analyse how changes in factor endowments affect unemployment rate, size of the anti-social sector, level of output of two sectors, pattern of trade, and level of national income of the country. We also analyse how anti-crime policies, i.e., the punishment policies for anti-socials and unemployment allowances policies affect unemployment rate, output composition, pattern of trade, and the level of national income
Current Status of Stratigraphy of the Proterozoic Cuddapah Basin, Southern India
No full textThe Cuddapah basin in southern India is one of the large Proterozoic basins with rich and strategic mineral resources. As a repository of sedimentary and tectonic records spanning from the Paleoproterozoic to the Neoproterozoic, the intracratonic Cuddapah basin holds vital clues to regional crustal development, paleogeography and tectonic underpinnings of passive margin sedimentation. In this article, a brief overview of the stratigraphy of the basin is presented with emphasis on recent developments in our understanding of the physical stratigraphy controlled by multiple unconformity bound sequences suggesting multiple transgressions of the sea, the emerging geochronological constraints, and broad sedimentary environments of different formation level units. Some issues of stratigraphic classification originating from allochthonus nature of the deformed rock successions of the Nallamalai fold belt have also been examined
Determination of a pair of newforms from the product of their twisted central values
No full textWe show that a pair of newforms (f, g) (f,g) can be uniquely determined by the product of the central-values of their twists. To achieve our goal, we prove an asymptotic formula for the average of the product of the central values of two twisted -functions, L (1/2,f×χ) L (1/2,g×χψ), where (f, g) (f,g) is a pair of newforms. The average is taken over the primitive Dirichlet characters χ and ψ of distinct prime moduli
Domain adaptation framework with ensemble of fuzzy rules-based ELMs for remote-sensing image classification
No full textThe domain adaptation (DA) transfer learning technique can accurately classify land cover in remote-sensing (RS) images, even with a small number of labeled samples. However, traditional architectures and various neural network and deep learning modifications make DA models difficult to learn quickly and computationally demanding. Extreme learning machine (ELM)-based DA models have shown potential for quick learning and improved generalization capabilities. Still, they are also known for their unstable and over-fitting characteristics and the ambiguity of the data sets. To address these difficulties, this article proposes two contributions. First, a modified fuzzy-rule-based ELM model (MFR-ELM) is created within a data-dependent platform to address the imprecision of the RS image land-cover classes and small sample size. Second, an ensemble of fuzzy rule-based ELM networks is proposed in the DA framework to address individual networks’ instability and weak learning properties. The MFR-ELM and other fuzzy rule-based ELM designs are combined in the ensemble architecture for mutual benefit. The suggested model is proven to be superior to competing approaches for categorizing multispectral RS images, as supported by various performance assessment indices
Epidermal Growth Factor Receptor (EGFR) and SMAD4 negatively correlated in the progression of gallbladder cancer in Eastern Indian patients
No full textBackground and introduction: Two and half percent of the Indian population suffer from gallbladder cancer (GBC). The primary factors that lead GBC are associated with mutation of several protooncogenes such as EGFR, ERBB2, Myc, and CCND1 along with dysregulation of several tumor suppressor genes such as SMAD4 and CDKN2A. Bacterial infection caused by S.typhi and H.pylori are also hypothesized to be potential factors driving GBC. Aims: This study aims to investigate the molecular mechanisms driving the progression of gallbladder adenocarcinoma in Eastern Indian patients. We specifically focussed on analyzing the mutational status of the KRAS gene, examining the amplification of the ERBB2/Her2-neu gene, and evaluating the expression patterns of six dysregulated genes (CCND1, MYC, EGFR, ERBB2/Her2-neu, CDKN2A, SMAD4). Additionally, we assessed the expression status of TGF-beta, the association between bacterial infections (S. Typhi and H. pylori) and GBC, and the impact of single nucleotide polymorphisms in ERBB2/Her2-neu and CCND1 genes within this population. Methods: Sixty-seven samples from GBC-diagnosed patients, 26 other unrelated GBC samples for validation cohort, and 68 gallstone tissue samples were collected for this study. Genomic DNA from normal as well as tumor tissues were isolated, exon 2 and exon 3 of KRAS gene were amplified along, DNA sequenced and analyzed. KRAS codon 12 mutation was detected by allele specific PCR (ASPCR) method. Amplification of UreC A (coding for urease subunit α), VacA (coding for Vacuolating cytotoxin A) and CagA genes (coding for cytotoxin-associated gene A) in H.pylori were amplified using PCR. Similarly, FlicC (coding for flagellin gene C) in S.typhi was amplified using PCR. The ERBB2/Her2-neu SNP I655V, and CCND1 SNP A870G were analyzed using PCR followed by RFLP. Expression studies of CCND1, Myc, CDKN2A, ERBB2/Her2-neu, EGFR, and SMAD4 genes were measured in GBC tumor tissues by sybr green quantitative RT PCR. Results: The oncogenes (EGFR and ERBB2/Her2-neu) were statistically significantly overexpressed and the tumor suppressor gene (SMAD4) downregulated in our GBC tumor patient samples. The EGFR and SMAD4 genes were negatively correlated (r = -0.01) in GBC patients and the data is statistically significant and validated through IHC technique. A significant downregulation of TGF-beta had also been observed. Lower frequency (i.e. 11.5%) of KRAS mutation in GBC tumor was observed. Conclusions: EGFR and SMAD4 expression were found to be negatively correlated in GBC tissue samples. ERBB2 overexpression/amplification was observed in 30% of the GBC samples. We also found a low percentage of GBC samples to show KRAS codon 12 mutation in Indian GBC patient population, as had been previously documented in pancreatic cancers
Erratum: Correction: Universal penalized regression (Elastic-net) model with differentially methylated promoters for oral cancer prediction (European journal of medical research (2024) 29 1 DOI: 10.1186/s40001-024-02047-4)
No full textEstimating software reliability using size-biased modelling
No full textSoftware testing is an important step in software development where inputs are administered repeatedly to detect bugs present in the software. In this paper, we have considered the estimation of total number of bugs and software reliability as a size-biased sampling problem by introducing the concept of eventual bug size as a latent variable. We have developed a Bayesian generalised linear mixed model (GLMM) using software testing detection data to estimate software reliability and stopping phase. The model uses size-biased approach where the probability of detecting a bug is an increasing function of eventual size of the bug which is as an index for the potential number of inputs that may eventually pass through the bug. We have tested the sensitivity of the reliability estimates by varying the number of inputs and detection probability via a simulation study and have found that the key parameters could be accurately estimated. Further, we have applied our model to two empirical data sets–one from a commercial software and the other from ISRO launch mission software testing data set. The hierarchical modelling approach provides a unified modelling framework that may find applications in other fields (e.g. hydrocarbon explorations) apart from software management
Evolution of tensile fractures in feldspar porphyroclast and its implication in paleostress estimation
No full textFractures are ubiquitous brittle features of the upper crust. Syntectonic granites are often replete with fractures of various attitudes, cross-cutting each other, which develop under the prevalent states of stress. In this article, we study the origin and mechanism of formation of tensile fractures restricted within rectangular alkali feldspar porphyroclasts found in Closepet granite (Dharwar Craton, India), and venture on the possibility of using them as potential paleostress marker. The study is conducted using finite-element-method (FEM) to assess the distribution of induced stresses within the porphyroclasts considering the geometry and varying mechanical properties of the porphyroclast and the embedding matrix. We infer that fractures in the porphyroclast develop due to amplification and concentration of far-field stresses within it. The direction of maximum principal compressive stress as indicated by the fractured porphyroclasts lies in close proximity to the paleostress direction derived from fault-slip analysis of adjacent bodies such as Chitradurga Schist Belt and Koppal syenite (Dharwar craton). Therefore, we advocate that fractured feldspar porphyroclasts are a reliable indicator of paleostress orientations