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Fractional Approximation of Broad Learning System
No full textApproximation ability is of much importance for neural networks. The broad learning system (BLS) (Chen and Liu, 2018), widely used in the industry with good performance, has been proved to be a universal approximator from the aspect of density. This kind of approximation property is very important, which proves the existence of the desired network but does not provide a means of construction that is commonly implemented through complexity aspect. Thus, such an approach lacks the advantage of determining constructively the network architecture and its weights. To the best of our knowledge, for a BLS, there is a few theory providing a constructive approach to obtain the network structure along with weights ensuring the approximation properties. By virtue of the long-term memory and nonlocality properties, fractional calculus has observed many distinctive applications. The purpose of this article is to study the BLS approximation ability constructively, which is valid for fractional case as well. Specifically, first we introduce two simplified BLSs by means of extending functions. For each of the simplified BLSs, an upper bound of error is derived through the modulus of continuity of Caputo fractional derivatives. As a result, two types of fractional convergent behaviors of BLS, that is: 1) pointwise and 2) uniform convergence, have been rigorously proved as well. Finally, some numerical experiments are conducted to demonstrate the approximation capabilities of BLSs
Granular knowledge and rational approximation in general rough sets–I
No full textRough sets are used in numerous knowledge representation contexts and are then empowered with varied ontologies. These may be intrinsically associated with ideas of rationality under certain conditions. In recent papers, specific granular generalisations of graded and variable precision rough sets are investigated by the present author from the perspective of rationality of approximations (and the associated semantics of rationality in approximate reasoning). The studies are extended to ideal-based approximations (sometimes referred to as subsethood-based approximations). It is additionally shown that co-granular or point-wise approximations defined by σ-ideals/filters (for an arbitrary relation σ) fit easily into the entire scheme. Concepts of the rationality of objects (vague or crisp) and their types are introduced and are shown to be applicable to most general rough sets by the present author. Surprising results on these are proved on these by her in this part of the research paper. The present paper is the first of a three part study on the topic
Heat causes large earnings losses for informal-sector workers in India
No full textHeat reduces labor productivity and output in formal manufacturing but little is known about its impacts on the earnings and welfare of workers in the informal sector that comprise 82% of the labor force in low-income and lower-middle-income countries. This study reports the results from daily surveys of nearly 400 workers in two slums in Delhi for a month in the summer of 2019. Every degree Celsius increase in wet bulb temperature was associated with a fall in gross earnings of 13 ( ± 3.5 ) percentage points, a fall in earnings net of work-related expenditure of 19 ( ± 4.5 ) percentage points, an increase in the self-reported probability of sickness of the worker or a family member of 6 ( ± 0.5 ) percentage points, and a decrease in the probability that a worker went to work of 2 ( ± 0.5 ) percentage points. Net earnings were 40% lower during the two heatwaves that occurred during the study period. Over 320 million informal-sector workers in low-income and lower-middle-income countries are currently exposed to temperatures similar to those observed in this study
Image Registration for Zooming Using Similarity Matching
No full textImage registration techniques are used for mapping two images of the same scene or image objects to one another. There are several image registration techniques available in the literature for registering rigid body as well as non-rigid body transformations. A very important image transformation is zooming in or out which also called scaling. Very few research articles address this particular problem except a number of feature-based approaches. This paper proposes a method to register two images of the same image object where one is a zoomed-in version of the other. In the proposed intensity-based method, we consider a circular neighborhood around an image pixel of the zoomed-in image, and search for the pixel in the reference image whose circular neighborhood is most similar to that of the neighborhood in the zoomed-in image with respect to various similarity measures. We perform this procedure for all pixels in the zoomed-in image. On images where the features are small in number, our proposed method works better than the state-of-the-art feature-based methods. We provide several numerical examples as well as a mathematical justification in this paper which support our statement that this method performs reasonably well in many situations
Impact of Fear and Group Defense on the Dynamics of a Predator-Prey System
No full textTo reduce the chance of predation, many prey species adopt group defense mechanisms. While it is commonly believed that such defense mechanisms lead to positive feedback on prey density, a closer observation reveals that it may impact the growth rate of species. This is because individuals invest more time and effort in defense rather than reproductive activities. In this study, we delve into a predator-prey system where predator-induced fear influences the birth rate of prey, and the prey species exhibit group defense mechanism. We adopt a nonmonotonic functional response to govern the predator-prey interaction, which effectively captures the group defense mechanism. We present a detailed mathematical analysis, encompassing the determination of feasible equilibria and their stability conditions. Through the analytical approach, we demonstrate the occurrence of Hopf and Bogdanov-Takens (BT) bifurcations. We observe two distinct types of bistabilities in the system: one between interior and predator-free equilibria, and another between limit cycle and predator-free equilibrium. Our findings reveal that the parameters associated with group defense and predator-induced fear play significant roles in the survival and extinction of populations
Inequalities for Maximal Operators Associated with a Family of General Sets
No full textLet E={Er(x):r\u3e0,x∈X} be a family of open subsets of a topological space X equipped with a nonnegative Borel measure μ satisfying some basic properties. We establish sharp quantitative weighted norm inequalities for the Hardy–Littlewood maximal operator ME associated with E in terms of mixed Ap–A∞ constants. The main ingredient to prove this result is a sharp form of a weak reverse Hölder inequality for the A∞,E weights. As an application of this inequality, we also provide a quantitative version of the open property for Ap,E weights. Next, we prove a covering lemma in this setting and using this lemma establish the endpoint Fefferman–Stein weighted inequality for the maximal operator ME. Moreover, vector-valued extensions for maximal inequalities are also obtained in this context
Intergenerational consequences of spousal violence: effect on nutritional status of children
No full textIn this paper, we empirically estimate the causal impact of spousal violence experienced by mothers on the nutritional status of her children aged below five years. Using detailed dataset from the fourth round of the National Family Health Survey, we find evidence that violence experienced by mothers at the hands of their husbands significantly increases the likelihood of their children being malnourished. When we focus on identifying the pathways through which spousal violence affect child health outcomes, we find that while spousal violence primarily affects child health via deterioration in maternal health, neglect of children in terms of inadequate provision of essential child-care also seem to matter. The results from the heterogeneity analysis finally suggest that the detrimental effect of such violence is significantly less pronounced for children born to mothers who are currently working and are thus empowered
Intermediate qutrit-assisted Toffoli gate decomposition with quantum error correction
No full textIntroducing a few intermediate qutrits for efficient decomposition of 3-qubit unitary gates has been proposed recently to obtain an exponential reduction in the depth of the decomposed circuit. An intermediate qutrit implies that a qubit is operated as a qutrit in a particular execution cycle. This method, primarily for the NISQ era, treats a qubit as a qutrit only for the duration when it requires access to the state | 2 〉 during the computation. In this article, we study the challenges of extending this decomposition to the error-corrected regime. We first we show that if a qubit has to be in state | 2 〉 at any point of time, then it must be encoded using a qutrit quantum error correcting code (QECC), thus resulting in a circuit with both qubits and qutrits. Qutrits being noisier than qubits, the former are expected to require higher levels of concatenation to achieve a particular accuracy than that for qubit-only decomposition. We derive analytically a relation between the levels of concatenation required for qubit-only and that for qubit–qutrit decomposition to achieve the same level of accuracy. Finally, we estimate (i) the degree of concatenation for both qubit–qutrit and qubit-only decompositions as a function of the probability of error and (ii) the criterion for which qubit–qutrit decomposition leads to a lower gate count than that for qubit-only decomposition
Intraspecific variability of rice root knot nematodes across diverse agroecosystems for sustainable management
No full textIn the rice agroecosystems of Southeast Asia, rice root knot nematode (Meloidogyne graminicola) significantly impairs yield, representing a major species within the ‘graminis-group’ known for its morphological similarities with other root knot nematodes (RKNs). This study delves into the variations in reproductive potential, morphology, morphometrics, and genetic diversity among thirty RKN populations in rice across three distinct agroecological zones in Jharkhand, India. Despite notable differences in reproductive potential among the populations, morphological and morphometric correlations to reproductive potential were inconclusive. However, male and juvenile morphometrics were crucial for identifying intraspecific variability. Genetic analysis utilizing five molecular markers (ITS, 18 S rRNA, D2-D3 of 28 S, COX-I, and COX-II) affirmed the populations as M. graminicola, with ITS marker revealing significant intraspecific variability. Phylogenetic analysis underscored the close relationship between M. oryzae and M. graminicola, distinct from other mitotic RKN species. Low genetic distance and nucleotide diversity, coupled with high haplotype diversity, negative Tajima’s D, and Fu’s Fs of haplotype network analysis, suggested that all M. graminicola populations are expanding. These findings highlight the urgent need for comprehensive management strategies against M. graminicola, providing valuable insights for growers, extension officials, and plant breeders to develop targeted management approaches and resistance breeding programs