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Erratum: Miocene Stromboid Gastropods (Superfamily Stromboidea Rafinesque, 1815) from the Dwarka Basin, Western India and their Paleobiogeographic Implications (JOURNAL GEOLOGICAL SOCIETY OF INDIA Vol.99, November 2023, pp.1491-1507, https://doi.org/10.1007/s12594-023-2501-z)
No full textThe paragraph Dilatilabrum kathiawarae n. sp. can be differentiated from Dilatilabrum fortisi (Brongniart, 1823) in terms of overall shell shape. D. kathiawarae is obconical whereas D. fostisi is biconical in shape. Also, D. fortisi have wavy subsutural shelf with prominent subsutural nodes which is absent in D. kathiawarae. Dilatilabrum roegli Harzhauser, 2001 has a very sharp break at the transition from the subsutural shelf to the winged flank which is comparatively gentle in D. kathiawarae. Apart from that D. kathiawarae has straight, deep and impressed sutures and a narrow aperture compared to D. roegli. The latter has deeply incised, irregular wavy sutures and broader apertural width. Dilatilabrum sublatissimus (d’ Orbigny, 1852) also resembles to D. kathiawarae in overall shell shape and shape of the winged flank. However, the transition from the subsutural shelf to the flank of the body whorl is marked by a prominent, symmetrically bulging shoulder in D. kathiawarae. The shoulder is not so prominent and well-rounded in case of D. sublatissimus. The most prominent feature for distinguishing D. kathiawarae from other species of the genus is it’s almost flat to slightly depressed spire. The other members of the genus have comparatively elevated spires
Examining the validity of the minimal varying speed of light model through cosmological observations: Relaxing the null curvature constraint
No full textWe revisit a consistency test for the speed of light variability, using the latest cosmological observations. This exercise can serve as a new diagnostics for the standard cosmological model and distinguish between the minimal varying speed of light in the Friedmann-Lemaître-Robertson-Walker universe. We deploy Gaussian processes to reconstruct cosmic distances and ages in the redshift range 01 with a particular reconstruction kernel when a-BAO data are included. Still, we ascribe no statistical significance to this result bearing in mind the degeneracy between the associated priors for combined analysis, and incompleteness of the a-BAO data set at higher z
EXTENDED INVERSE THEOREMS FOR RESTRICTED SUMSET IN INTEGERS
No full textLet h and k be positive integers such that h ≤ k. Let A = {a0, a1, …, ak−1 } be a nonempty finite set of k integers. The h-fold sumset, denoted by hA, is a set of integers that can be expressed as a sum of h elements (not necessarily distinct) of A. The restricted h-fold sumset, denoted by h∧ A, is a set of integers that can be expressed as a sum of h distinct elements of A. The characterization of the underlying set for small deviation from the minimum size of the sumset is called an extended inverse problem. Freiman studied such a problem and proved a theorem for 2A, which is known as Freiman’s 3k − 4 theorem. Very recently, Tang and Xing, and Mohan and Pandey studied some more extended inverse problems for the sumset hA, where h ≥ 2. In this article, we prove some extended inverse theorems for sumsets 2∧ A, 3∧ A and 4∧ A. In particular, we classify the set(s) A for which |2∧ A| = 2k − 2, |2∧ A| = 2k − 1, and |2∧ A| = 2k. Furthermore, we also classify set(s) A when |3∧ A| = 3k − 7, |3∧ A| = 3k − 6, and |4∧ A| = 4k − 14
Generalisation in Natural Language Clustering Through Non-parametric Statistical Approach
No full textRobust statistical methodologies are imperative for effectively analysing data and quantifying specific phenomena, particularly when attempting to comprehend intricate events. The present research endeavours to introduce and assess potent non-parametric statistical approaches that are compatible with heterogeneous data structures. The primary focus lies in their application within the domains of language clustering and natural language processing. A central objective is to refine our understanding of language clustering and its potential implications, including the emergence of linguistic regions known as sprachbunds. To achieve this, the study delves into diverse non-parametric facets of linguistic data processing and exploration. Building upon the foundation established by previous work (Chattopadhyay et al. in International conference on soft computing and its engineering applications, Springer, Cham, 2022), this study extends its scope by proposing a novel framework for structuring language families. This is accomplished through the incorporation of typological and areal characteristics, enriching the accuracy and depth of language classification. The utilisation of non-parametric techniques takes centre stage throughout this process. Notably, multidimensional scaling (MDS) is harnessed to transform resulting data into a Cartesian framework, enabling the deployment of data-depth-based methods for reliable outlier identification. This proves invaluable for effectively categorising a wide array of languages situated on the fringes of existing classifications. Furthermore, it opens avenues for reevaluating established language categorisation schemes in light of newfound insights
Graphon-Explainer: Generating Model-Level Explanations for Graph Neural Networks using Graphons
No full textGraph Neural Networks (GNNs) form the backbone of several state-of-the-art methods for performing machine learning tasks on graphs. As GNNs find application across diverse real-world scenarios, ensuring their interpretability and reliability becomes imperative. In this paper, we propose Graphon-Explainer, a model-level explanation method to elucidate the high-level decision-making process of a GNN. Graphon-Explainer learns a graphon—a symmetric, continuous function viewed as a weighted adjacency matrix of an infinitely large graph—to approximate the distribution of a target class as learned by the GNN. The learned graphon then acts as a generative model, yielding distinct graph motifs deemed significant by the GNN for the target class. Unlike existing model-level explanation methods for GNNs, which are limited to explaining a GNN for individual target classes, Graphon-Explainer can also generate synthetic graphs close to the decision boundary between two target classes by interpolating graphons of both classes, aiding in characterizing the GNN model’s decision boundary. Furthermore, Graphon-Explainer is model-agnostic, does not rely on additional black-box models, and does not require manually specified handcrafted constraints for explanation generation. The effectiveness of our method is validated through thorough theoretical analysis and extensive experimentation on both synthetic and real-world datasets on the task of graph classification. Results demonstrate its capability to effectively learn and generate diverse graph patterns identified by a trained GNN, thus enhancing its interpretability for end-users
Hardy and Hardy–Littlewood–Pólya operators and their commutators on local fields
No full textWe introduce the Hardy and Hardy–Littlewood–Pólya operators on local fields and show that they are bounded on weighted Lebesgue spaces with power weights. Moreover, we compute the precise norms of these operators on these spaces. Further, we prove the boundedness of the commutators generated by these operators and functions with central mean oscillation on Herz spaces, and in particular, on the weighted Lebesgue spaces
How to use randomized response survey data at hand by a specific procedure to judge its efficiency versus a possible rival
No full textIt is well-known that given survey data at hand by a given method, it is possible to examine how this method promises to fare vis- à -vis another one that might have been employed but not actually implemented. We illustrate how this may be extended to cover Randomized Response (RR) Techniques (RRT) by citing a few RR procedures in combination with a few sample selection methods generally in use. Developing the theory, simulated results are presented to demonstrate interesting numerical findings in this context
Improved and formal proposal for device-independent quantum private query
No full textIn this paper, we present a novel quantum private query (QPQ) scheme that is fully device-independent. As far as we know, this is the first QPQ scheme that uses EPR pairs and offers full device independence. Our approach takes into account the self-testing of shared EPR pairs and the self-testing of projective measurement operators in a mistrustful scenario where neither the client nor the server trusts each other. To achieve full device independence, we also exploit self-testing of a specific class of POVM operators used by the client in our scheme. Additionally, we evaluate the performance of our proposal formally and derive an upper limit of the maximum cheating probabilities (when the protocol does not terminate) for both the dishonest client and the dishonest server
Interconnection between density-regulation and stability in competitive ecological network
No full textIn natural ecosystems, species can be characterized by the nonlinear density-dependent self-regulation of their growth profile. Species of many taxa show a substantial density-dependent reduction for low population size. Nevertheless, many show the opposite trend; density regulation is minimal for small populations and increases significantly when the population size is near the carrying capacity. The theta-logistic growth equation can portray the intraspecific density regulation in the growth profile, theta being the density regulation parameter. In this study, we examine the role of these different growth profiles on the stability of a competitive ecological community with the help of a mathematical model of competitive species interactions. This manuscript deals with the random matrix theory to understand the stability of the classical theta-logistic models of competitive interactions. Our results suggest that having more species with strong density dependence, which self-regulate at low densities, leads to more stable communities. With this, stability also depends on the complexity of the ecological network. Species network connectance (link density) shows a consistent trend of increasing stability, whereas community size (species richness) shows a context-dependent effect. We also interpret our results from the aspect of two different life history strategies: r and K-selection. Our results show that the stability of a competitive network increases with the fraction of r-selected species in the community. Our result is robust, irrespective of different network architectures
INVARIANT SUBSPACES OF ANALYTIC PERTURBATIONS
No full textAnałytic perturbations are understood here as shifts of the form Mz+F, where Mz is the uniłaterał shift and F is a finite rank operator on the Hardy space over the open unit disk. Here the term “a shift” refers to the mułtipłication operator Mz on some anałytic reproducing kerneł Hiłbert space. In this paper, first, a naturał cłass of finite rank operators is isołated for which the corresponding perturbations are anałytic, and then a compłete cłassification of invariant subspaces of those anałytic perturbations is presented. Some instructive exampłes and severał distinctive properties (łike cycłicity, essentiał normałity, hyponormałity, etc.) of anałytic perturbations are ałso described