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This essay explores the material imperatives of nineteenth-century statistical ambition, at a time when the nature of paper itself underwent rapid change. It expands the concept of paper technologies to include knowledge about the materials themselves, as well as the infrastructures, techniques, and agreements that made it possible for the right kind of paper to be made available for particular purposes. Taking the production of the forms for the Prussian census as a case in point, it argues that the enumeration effort of Prussian census statisticians went far beyond designing a form, collecting information, noting and compiling figures, or creating tables. Paper knowledge to define and control the material substance of the forms mattered as much as political impetus and statistical methods in getting the census right. [ABSTRACT FROM AUTHOR]

The h-index has become more popular nowadays and is used for some scientific performance criteria worldwide. This indexing method does not correctly measure any performance or career specifications because of the parameters used to form the measurement basis. The h-index is located based on citation(C) and paper(N) parameters that involve no logical criterion on the counting process, and so measurement on this basis can only give quantity results not any quality information. Therefore, we need a new indexing instrument to find out also the scientific quality unique to an individual author even if that takes into account the effect of multiple coauthorships. Ipso facto, we create a new bibliometric indicator or academic performance indicator called the u-index. [ABSTRACT FROM AUTHOR]

Some states in the U.S. have traditionally received less federal research funding than other states. The National Science Foundation (NSF) created a program in 1979, called the Experimental Program to Stimulate Competitive Research (EPSCoR) to enhance the research competitiveness in such states. While the geographic disparity in federal research funding is well known, the overall impact of federal funding on the research performance of EPSCoR and non-EPSCoR has not been previously studied. In the current study, we compared the combined research productivity of Ph.D. granting institutions in EPSCoR versus the non-EPSCoR states to better understand the scientific impact of federal investments in sponsored research across all states. The research outputs we measured included journal articles, books, conference papers, patents, and citation count in academic literature. Unsurprisingly, results indicated that the non-EPSCoR states received significantly more federal research funding than their EPSCoR counterparts, which correlated with a higher number of faculty members in the non-EPSCoR versus EPSCoR states. Also, in the overall research productivity expressed on a per capita, the non-EPSCoR states fared better than EPSCoR states. However, when the research output was measured based on per $1M investment of federal research funding, EPSCoR states performed significantly better than the non-EPSCoR states in many research productivity indicators, with the notable exception of patents. Together, this study found preliminary evidence that EPSCoR states achieved a high degree of research productivity despite receiving significantly fewer federal research dollars. The limitations and next steps of this study are also discussed. [ABSTRACT FROM AUTHOR]

We demonstrate a rapid, 2-step, and ultrasensitive assay approach for quantification of target protein molecules from a single droplet test sample. The assay is comprised of antibody-conjugated gold nanoparticles (AuNPs) that are "activated" when they are mixed with the test sample and bind their targets. The resulting liquid is passed through a microfluidic channel with a photonic crystal (PC) biosensor that is functionalized with secondary antibodies to the target biomarker, so that only activated AuNPs are captured. Utilizing recently demonstrated hybrid optical coupling between the plasmon resonance of the AuNP and the resonance of the PC, each captured AuNP efficiently quenches the resonant reflection of the PC, thus enabling the captured AuNPs to be digitally counted with high signal-to-noise. To achieve a 2-step assay process that is performed on a single droplet test sample without washing steps or active pump elements, controlled single-pass flow rate is obtained with an absorbing paper pad waste reservoir embedded in a microfluidic cartridge. We use the activate capture and digital counting (AC + DC) approach to demonstrate HIV-1 capsid antigen p24 detection from a 40 μL spiked-in human serum sample at a one thousand-fold dynamic range (1–103 pg mL−1) with only a 35-minute process that is compatible with point-of-care (POC) analysis. The AC + DC approach allows for ultrasensitive and ultrafast biomolecule detection, with potential applications in infectious disease diagnostics and early stage disease monitoring. [ABSTRACT FROM AUTHOR]

Topographic maps comprise a rich data source for the processing and analysis of geographic information. However, the management of paper topographic maps is still dominated by an inefficient manual method, and there is no counting equipment for topographic maps that is suitable for narrow map warehouse passages. The existing algorithms relating to paper counting require paper hardness and cannot directly obtain the internal information of topographic maps. To address the above problems, using a map inventory machine transformed from a paddle-type paper counting machine to perform a preliminary count and obtain the video data of the counting progress, an automatic counting algorithm for topographic maps for map management is proposed in this study. First, the periodic feature changes of all the targets and each individual target in the videos are analyzed. Second, a deformable parts model accelerated by fast feature pyramids and by reducing the region of interest is used for the object detection of mechanical wheels. The grayscale variance function is selected to quantify the quality change in the images. Finally, a fusion window counting model is constructed with the adaptive window and fixed window methods. The experimental results show that the average counting accuracy of the model is about 95%, which can verify the initial counting results of the machine and provide high-quality keyframes for the subsequent sheet designation recognition.

Crowd counting from a single image is a challenging task due to perspective distortion and large-scale variation in crowd scenes. Many Researches only focus on local features to create density maps which is not effective in handing the challenges. This paper proposes a novel network named global-to-local adaptive spatial encoder network, which focuses on global features to generate a total structure density map of the population distribution, and then utilizes local features to reconstruct the total structure density map in detail to generate high-quality density map. To capture global features, local information and correlate them, we design a contextual module using different kernels with convolution and transposed convolution. To create a density map from global structure to local detail, two branches are designed, the global distribution branch and the local detail branch. The former aims to capture the population distribution region of interest in terms of global structure, and the latter aims to focus on the local details of each unit. Furthermore, to overcome the problem of pixel-wise loss of MSE, this paper proposes an efficient loss function that focuses on perceiving the possible crowd distribution over the whole image. We also apply a new upsampling mechanism that learns to create high-quality density maps on its own is advisable. The proposed network can capture the characteristics of pedestrian distribution and predict accurate results. It is evaluated on four crowd counting datasets (ShanghaiTech, NWPU, UCF_QNRF, UCF_CC_50), it obtains MAE of 67.1 and MSE, and achieves 108.8 in ShanghaiTech and gets MAE of 139.2 and the best MSE of 217.7 in UCF_CC_50 dataset and so on, and our method shows state-of-the-art on all the datasets. [ABSTRACT FROM AUTHOR]

Topographic maps comprise a rich data source for the processing and analysis of geographic information. However, the management of paper topographic maps is still dominated by an inefficient manual method, and there is no counting equipment for topographic maps that is suitable for narrow map warehouse passages. The existing algorithms relating to paper counting require paper hardness and cannot directly obtain the internal information of topographic maps. To address the above problems, using a map inventory machine transformed from a paddle-type paper counting machine to perform a preliminary count and obtain the video data of the counting progress, an automatic counting algorithm for topographic maps for map management is proposed in this study. First, the periodic feature changes of all the targets and each individual target in the videos are analyzed. Second, a deformable parts model accelerated by fast feature pyramids and by reducing the region of interest is used for the object detection of mechanical wheels. The grayscale variance function is selected to quantify the quality change in the images. Finally, a fusion window counting model is constructed with the adaptive window and fixed window methods. The experimental results show that the average counting accuracy of the model is about 95%, which can verify the initial counting results of the machine and provide high-quality keyframes for the subsequent sheet designation recognition. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this study is to investigate the relationship of the post-publication peer review (PPPR) polarity of a paper to that paper's citation count. Design/methodology/approach: Papers with PPPRs from Publons.com as the experimental groups were manually matched 1:2 with the related papers without PPPR as the control group, by the same journal, the same issue (volume), the same access status (gold open access or not) and the same document type. None of the papers in the experimental group or control group received any comments or recommendations from ResearchGate, PubPeer or F1000. The polarity of the PPPRs was coded by using content analysis. A negative binomial regression analysis was conducted to examine the data by controlling the characteristics of papers. Findings: The four experimental groups and their corresponding control groups were generated as follows: papers with neutral PPPRs, papers with both negative and positive PPPRs, papers with negative PPPRs and papers with positive PPPRs as well as four corresponding control groups (papers without PPPRs). The results are as follows: while holding the other variables (such as page count, number of authors, etc.) constant in the model, papers that received neutral PPPRs, those that received negative PPPRs and those that received both negative and positive PPPRs had no significant differences in citation count when compared to their corresponding control pairs (papers without PPPRs). Papers that received positive PPPRs had significantly greater citation count than their corresponding control pairs (papers without PPPRs) while holding the other variables (such as page count, number of authors, etc.) constant in the model. Originality/value: Based on a broader range of PPPR sentiments, by controlling many of the confounding factors (including the characteristics of the papers and the effects of the other PPPR platforms), this study analyzed the relationship of various polarities of PPPRs to citation count. [ABSTRACT FROM AUTHOR]

Fast and accurate counting and positioning of flowers is the foundation of automated flower cultivation production. However, it remains a challenge to complete the counting and positioning of high-density flowers against a complex background. Therefore, this paper proposes a lightweight flower counting and positioning model, Light-FC-YOLO, based on YOLOv8s. By integrating lightweight convolution, the model is more portable and deployable. At the same time, a new efficient detection head, Efficient head, and the integration of the LSKA large kernel attention mechanism are proposed to enhance the model's feature detail extraction capability and change the weight ratio of the shallow edge and key point information in the network. Finally, the SIoU loss function with target angle deviation calculation is introduced to improve the model's detection accuracy and target positioning ability. Experimental results show that Light-FC-YOLO, with a model size reduction of 27.2% and a parameter reduction of 39.0%, has a Mean Average Precision (mAP) and recall that are 0.8% and 1.4% higher than YOLOv8s, respectively. In the counting comparison experiment, the coefficient of determination (R2) and Root Mean Squared Error (RMSE) of Light-FC-YOLO reached 0.9577 and 8.69, respectively, both superior to lightweight models such as YOLOv8s. The lightweight flower detection method proposed in this paper can efficiently complete flower positioning and counting tasks, providing technical support and reference solutions for automated flower production management. [ABSTRACT FROM AUTHOR]

Bipartite graphs widely exist in real-world scenarios and model binary relations like host-website, author-paper, and user-product. In bipartite graphs, a butterfly (i.e., $2\times 2$ 2 × 2 bi-clique) is the smallest non-trivial cohesive structure and plays an important role in applications such as anomaly detection. Considerable efforts focus on counting butterflies in static bipartite graphs. However, they suffer from high time and space complexity when the bipartite graph of interest is given as a stream of edges. Although there are methods for approximately counting butterflies from bipartite graph streams, they suffer from either low accuracy or high time complexity. Therefore, it is still a challenge to accurately estimate butterfly counts from bipartite graph streams in a short time. To address this issue, we develop novel algorithms by exploiting the bipartite nature, which subtly integrates sampling and sketching techniques. We provide accurate estimators for butterfly counts and derive simple yet exact formulas for bounding their errors. We also conduct extensive experiments on a variety of real-world large bipartite graphs. Experimental results demonstrate that our algorithms are up to 20.0 times more accurate and up to 286.3 times faster than state-of-the-art methods under the same memory usage. [ABSTRACT FROM AUTHOR]

Shrimp fry counting is an important task for biomass estimation in aquaculture. Accurate counting of the number of shrimp fry in tanks can not only assess the production of mature shrimp but also assess the density of shrimp fry in the tanks, which is very helpful for the subsequent growth status, transportation management, and yield assessment. However, traditional manual counting methods are often inefficient and prone to counting errors; a more efficient and accurate method for shrimp fry counting is urgently needed. In this paper, we first collected and labeled the images of shrimp fry in breeding tanks according to the constructed experimental environment and generated corresponding density maps using the Gaussian kernel function. Then, we proposed a multi-scale attention fusion-based shrimp fry counting network called the SFCNet. Experiments showed that our proposed SFCNet model reached the optimal performance in terms of shrimp fry counting compared to CNN-based baseline counting models, with MAEs and RMSEs of 3.96 and 4.682, respectively. This approach was able to effectively calculate the number of shrimp fry and provided a better solution for accurately calculating the number of shrimp fry. [ABSTRACT FROM AUTHOR]

While inequalities in science are common, most efforts to understand them treat scientists as isolated individuals, ignoring the network effects of collaboration. Here, we develop models that untangle the network effects of productivity defined as paper counts, and prominence referring to high-impact publications, of individual scientists from their collaboration networks. We find that gendered differences in the productivity and prominence of mid-career researchers can be largely explained by differences in their coauthorship networks. Hence, collaboration networks act as a form of social capital, and we find evidence of their transferability from senior to junior collaborators, with benefits that decay as researchers age. Collaboration network effects can also explain a large proportion of the productivity and prominence advantages held by researchers at prestigious institutions. These results highlight a substantial role of social networks in driving inequalities in science, and suggest that collaboration networks represent an important form of unequally distributed social capital that shapes who makes what scientific discoveries. While inequalities in science are common, most efforts to understand them treat scientists as isolated individuals, ignoring the network effects of collaboration. Here, the authors develop models that untangle the network effects of productivity and prominence of individual scientists from their collaboration networks. [ABSTRACT FROM AUTHOR]

The Euclidean length of a citation list is "depth relevant": the metric increases when citations are transferred from less to more cited papers. We introduce "breadth relevance," which favors consistent achievers over one‐hit wonders. The exponent of the CES aggregator then is less than unity rather than greater than unity, as for depth relevance. Using two datasets on citations of economists for the top 50 US and global universities, simply counting citations maximizes the correlation between the citation metrics of researchers and the peer‐reviewed rank of their department. However, citation depth may explain the allocation of researchers across lower‐ranked departments. [ABSTRACT FROM AUTHOR]

This paper critically examines the possibilities of using the British Museum's collection database as a research tool to examine acquisition history. It publishes initial findings from the author's research into the history of the collection through a quantitative analysis of collection data. Rather than focusing on individual collectors, collections or areas of the collection, it takes a high-level comprehensive view of the current body of material, across time, departments and material. The paper asks three questions of the database: when did objects enter the museum's collection, from whom and how? Through a numerical analysis, acquisition patterns are revealed which both challenge and augment our understanding of the history of the collection. [ABSTRACT FROM AUTHOR]

In recent years, real-time vehicle congestion detection has become a hot research topic in the field of transportation due to the frequent occurrence of highway traffic jams. Vehicle congestion detection generally adopts a vehicle counting algorithm based on object detection, but it is not effective in scenarios with large changes in vehicle scale, dense vehicles, background clutter, and severe occlusion. A vehicle object counting network based on a feature pyramid split attention mechanism is proposed for accurate vehicle counting and the generation of high-quality vehicle density maps in highly congested scenarios. The network extracts rich contextual features by using blocks at different scales, and then obtains a multi-scale feature mapping in the channel direction using kernel convolution of different sizes, and uses the channel attention module at different scales separately to allow the network to focus on features at different scales to obtain an attention vector in the channel direction to reduce mis-estimation of background information. Experiments on the vehicle datasets TRANCOS, CARPK, and HS-Vehicle show that the proposed method outperforms most existing counting methods based on detection or density estimation. The relative improvement in MAE metrics is 90.5% for the CARPK dataset compared to Fast R-CNN and 73.0% for the HS-Vehicle dataset compared to CSRNet. In addition, the method is also extended to count other objects, such as pedestrians in the ShanghaiTech dataset, and the proposed method effectively reduces the misrecognition rate and achieves higher counting performance compared to the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

3D modelling represents a fundamental survey technique to represent archaeological evidence. It is particularly important to draw and analyse engravings because it is more descriptive and, somehow, objective than traditional drawings, which result interpretative and not replicable, becoming a debatable and often controversial matter. A technique able to verify the overlaying of signs is essential to establish the relative sequence, thus the chronology of engravings. However, there are several techniques and they provide different results. The paper tries to empirically compare SfM and PS methods to understand how they work on surface representation and which are their specificities in a difficult context such as the Pianaùra engravings. The aim of the paper is to verify the accuracy of the techniques. Three paths are pursued: the first analyses pure quantitative data, such as counting the number of points or faces built and so on; the second aims to verify quantitatively distortions by geometric measurements analysis; the third is a visual quality test, which focuses on users' perception of 3D models. It can be concluded that the distinct fields of application and the diverse purposes of the research enhance the different specificities of the two techniques. [ABSTRACT FROM AUTHOR]

Let Fq be the finite field of order q where q = pk, k is a positive integer and p is an odd prime. Let F*q represent the nonzero elements of Fq. For f(x1,···,xn) ∊ Fq[x1,···,xn], we used N(f(x1,···,xn) = 0) to denote the number of Fq-rational points of the affine hypersurface f(x1,···,xn) = 0. In 2020, Zhao et al. obtained the explicit formulae for N(x41 + x42 = c), N(x41 + x42+ x43 = c) and N(41+ x42+ x43+ x44 = c) over Fq, with c ∊ F*q. In this paper, by using Jacobi sums and an analog of the Hasse-Davenport theorem, we arrived at explicit formulae for N(a1x41 + a2x42 = c) and N(b1x41 + b2x42 + b3x43 = c) with ai, bj ∊ F*q(1 ≤ i ≤ 2, 1 ≤ j ≤ 3) and c ∊ Fq. Furthermore, by using the reduction formula for Jacobi sums, the number of rational points of the quartic diagonal hypersurface a1x41 + a2x42 +···+ anx4n = c of n ≥ 4 variables with ai ∊ F*q (1 ≤ i ≤ n), c ∊ Fq and p = 1(mod 4), can also be deduced. These extended and improved earlier results. [ABSTRACT FROM AUTHOR]

Traffic analysis is one of the crucial tasks of intelligent transport system that utilizes deep learning for range of purposes. Many tasks, such as vehicle recognition, vehicle counting, traffic violation monitoring, vehicle speed monitoring, vehicle density and so on, can be accomplished by using cameras installed in strategic locations along roads. In this paper powerful deep learning techniques such as (Yolov5, Mask RCNN, SSD) and state-of-the-art object tracking algorithm known as DeepSORT was used to perform real time vehicle detection and counting in a video. A new highway vehicle detection dataset with overall of 32,265, instances of four vehicle classes named: bus, car, motorbike, truck was created in this paper and utilized for training vehicle detection and counting system. Result shows that average counting accuracy by using Yolov5 combined DeepSORT reaches to 95% while reaches to 91% by using Mask R-CNN combined DeepSORT and 84% by using SSD combined DeepSORT in hard environment. From the experimental work, counting accuracy by using Yolov5 outperforms other two deep learning techniques. [ABSTRACT FROM AUTHOR]

Event sequences are common types of data. Several episode mining algorithms have been developed to find episodes (subsequences of events) that appear frequently in an event sequence, with the aim of discovering useful knowledge for decision-making and predictions. However, most of these algorithms can only process simple event sequences (where, at most, one event occurs at each timestamp). In contrast, in many real-life applications, multiple events may occur at the same timestamp, resulting in complex event sequences. Moreover, numerous episode mining algorithms overestimate the frequency of episodes by counting the same events multiple times. As a solution, some algorithms have been designed to count only non-overlapping occurrences. Yet, it can be argued that this definition is too strict and discards many important events. To address these limitations, this paper presents an algorithm named EMDO (Episode Mining under Distinct Occurrences (EMDO) to find frequent episodes in a complex sequence by counting distinct occurrences. The proposed concept of distinct occurrences ensures that each event is not counted more than once but allows distinct occurrences to overlap. A second algorithm, called EMDO-P, is also presented in this paper to derive strong episode rules in event sequences from episodes found by EMDO. To the best of our knowledge, this is the first study on mining frequent episodes using a frequency definition based on distinct occurrences. The experimental results confirm that the proposed algorithms are efficient. [ABSTRACT FROM AUTHOR]

In this paper, the asmptotics is considered for the distribution tail of a randomly stopped sum Sν = X1 + ··· + Xν of independent identically distributed consistently varying random variables with zero mean, where ν is a counting random variable independent of {X1,X2, . . .}. The conditions are provided for the relation P(Sν > x) ∼ Eν P(X1 > x) to hold, as x →∞, involving the finiteness of E|X1|. The result improves that of Olvera-Cravioto [14], where the finiteness of a moment E|X1|r for some r > 1 was assumed. [ABSTRACT FROM AUTHOR]

A new multi gain SC inverter topology with fewer switching components and lower voltage stress is presented in this paper. It comprises eight switches and two capacitors, which raise the output voltage by three times the supply voltage. The capacitors voltages are automatically balanced to ensure proper operation. The circuit constructional, operation, and parameter optimisation techniques are discussed in details. A simple logic-based multicarrier Level Shift Pulse Width Modulation (LS-PWM) is employed to control the switching operation that reduces the complexity of the control circuit. Furthermore, a comparative analysis with other recent topologies has been presented to demonstrate the virtues of this approach. Finally, the proposed topology (PT) verification, feasibility, and effectiveness have been demonstrated both in simulation and experimentation. [ABSTRACT FROM AUTHOR]

Estimating the population in a given scene is a process known as crowd counting. The field has recently garnered significant attention, and many innovative methods have emerged. However, intense scale variations and background interference make crowd counting in realistic scenes always challenging. To address these in this paper, a multi-level attention network with multi-scale feature fusion named MLANet is proposed. The network consists of three sections: a multi-level base feature extraction front-end network, a centralized dilated multi-scale feature fusion mid-end network with a global attention module, and a back-end network for the generation of density maps. By incorporating a flexible attention module and multi-scale features, the method can accurately capture crowd information at different scales and achieve accurate counting results. We evaluated the method on four public datasets (UCF_CC_50, ShanghaiTech, WorldExpo'10, and Beijing BRT), and the experimental results demonstrate a significant reduction in counting error when compared with existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we study counting perfect matchings in linear chain graphs, focusing on identically colored and alternatingly colored odd faces, using recurrence relations. Our primary objective is to derive explicit formulas for the numbers of perfect matchings in linear chain graphs with identically colored odd faces. Furthermore, we establish a relationship between the numbers of perfect matchings in linear chain graphs with identically colored odd faces and strip snake chain graphs. This relationship provides us with an alternative way of validating the numbers of perfect matchings in linear chain graphs with the same colored odd faces. [ABSTRACT FROM AUTHOR]

In this study, it was investigated whether early tweets counts could differentially benefit female and male (first, last) authors in terms of the later citation counts received. The data for this study comprised 47,961 articles in the research area of Life Sciences & Biomedicine from 2014–2016, retrieved from Web of Science's Medline. For each article, the number of received citations per year was downloaded from WOS, while the number of received tweets per year was obtained from PlumX. Using the hurdle regression model, I compared the number of received citations by female and male (first, last) authored papers and then I investigated whether early tweet counts could predict the later citation counts received by female and male (first, last) authored papers. In the regression models, I controlled for several important factors that were investigated in previous research in relation to citation counts, gender or Altmetrics. These included journal impact (SNIP), number of authors, open access, research funding, topic of an article, international collaboration, lay summary, F1000 Score and mega journal. The findings showed that the percentage of papers with male authors in first or last authorship positions was higher than that for female authors. However, female first and last-authored papers had a small but significant citation advantage of 4.7% and 5.5% compared to male-authored papers. The findings also showed that irrespective of whether the factors were included in regression models or not, early tweet counts had a weak positive and significant association with the later citations counts (3.3%) and the probability of a paper being cited (21.1%). Regarding gender, the findings showed that when all variables were controlled, female (first, last) authored papers had a small citation advantage of 3.7% and 4.2% in comparison to the male authored papers for the same number of tweets. [ABSTRACT FROM AUTHOR]

Crowd counting aims to estimate the number, density, and distribution of crowds in an image. The current mainstream approach, based on CNN, has been highly successful. However, CNN is not without its flaws. Its limited receptive field hampers the modeling of global contextual information, and it struggles to effectively handle scale variation and background complexity. In this paper, we propose a Multi-scale Hybrid Attention Network called MHANet to solve crowd counting challenges more effectively. To address the issue of scale variation, we have developed a Multi-scale Aware Module (MAM) that incorporates multiple sets of dilated convolutions with varying dilation rates. The MAM significantly improves the network's ability to extract information at multiple scales. To tackle the problem of background complexity, we have introduced a Hybrid Attention Module (HAM) that combines spatial attention and channel attention. The HAM effectively directs attention to the crowd region while suppressing background interference, resulting in more accurate counting. MHANet has been extensively experimented on four benchmark datasets and compared against state-of-the-art algorithms. It consistently achieves superior performance in terms of the MAE evaluation metric. MHANet outperforms the current state-of-the-art methods by margins of 1.9%, 5.4%, 0.4%, and 0.8% on the ShanghaiTech Part_A, ShanghaiTech Part_B, UCF-QNRF, and UCF_CC_50 datasets, respectively. Furthermore, a series of ablation experiments targeting MAM and HAM were conducted in this paper, and the experimental results fully demonstrate that MAM and HAM can effectively address the challenges of scale variation and background complexity, ultimately enhancing the accuracy and robustness of the network. [ABSTRACT FROM AUTHOR]

The Zhang–Zhang polynomial of a benzenoid system is a well-known counting polynomial that was introduced in 1996. It was designed to enumerate Clar covers, which are spanning subgraphs with only hexagons and edges as connected components. In 2018, the generalized Zhang–Zhang polynomial of two variables was defined such that it also takes into account 10-cycles of a benzenoid system. The aim of this paper is to introduce and study a new variation of the Zhang–Zhang polynomial for phenylenes, which are important molecular graphs composed of 6-membered and 4-membered rings. In our case, Clar covers can contain 4-cycles, 6-cycles, 8-cycles, and edges. Since this new polynomial has three variables, we call it the multivariable Zhang–Zhang (MZZ) polynomial. In the main part of the paper, some recursive formulas for calculating the MZZ polynomial from subgraphs of a given phenylene are developed and an algorithm for phenylene chains is deduced. Interestingly, computing the MZZ polynomial of a phenylene chain requires some techniques that are different to those used to calculate the (generalized) Zhang–Zhang polynomial of benzenoid chains. Finally, we prove a result that enables us to find the MZZ polynomial of a phenylene with branched hexagons. [ABSTRACT FROM AUTHOR]

This paper considers a deterministic susceptible-infected-susceptible (SIS) networked bivirus epidemic model (termed the bivirus model for short), in which two competing viruses spread through a set of populations (nodes) connected by two graphs, which may be different if the two viruses have different transmission pathways. The networked dynamics can give rise to complex equilibria patterns, and most current results identify conditions on the model parameters for convergence to the healthy equilibrium (where both viruses are extinct) or a boundary equilibrium (where one virus is endemic and the other is extinct). However, there are only limited results on coexistence equilibria (where both viruses are endemic). This paper establishes a set of "counting" results which provide lower bounds on the number of coexistence equilibria and, perhaps more importantly, establish properties on the local stability/instability properties of these equilibria. In order to do this, we employ the Poincaré--Hopf theorem but with significant modifications to overcome several challenges arising from the bivirus system model, such as the fact that the system dynamics do not evolve on a manifold in the typical sense required to apply Poincaré--Hopf theory. Subsequently, Morse inequalities are used to tighten the counting results, under the reasonable assumption that the bivirus system is a Morse--Smale dynamical system. Numerical examples are provided which demonstrate the presence of multiple attractor equilibria and multiple coexistence equilibria. [ABSTRACT FROM AUTHOR]

Colony-Forming Unit (CFU) counting is a complex problem without a universal solution in biomedical and food safety domains. A multitude of sophisticated heuristics and segmentation-driven approaches have been proposed by researchers. However, U-Net remains the most frequently cited and used deep learning method in these domains. The latter approach provides a segmentation output map and requires an additional counting procedure to calculate unique segmented regions and detect microbial colonies. However, due to pixel-based targets, it tends to generate irrelevant artifacts or errant pixels, leading to inaccurate and mixed post-processing results. In response to these challenges, this paper proposes a novel hybrid counting approach, incorporating a multi-loss U-Net reformulation and a post-processing Petri dish localization algorithm. Firstly, a unique innovation lies in the multi-loss U-Net reformulation. An additional loss term is introduced in the bottleneck U-Net layer, focusing on the delivery of an auxiliary signal that indicates where to look for distinct CFUs. Secondly, the novel localization algorithm automatically incorporates an agar plate and its bezel into the CFU counting techniques. Finally, the proposition is further enhanced by the integration of a fully automated solution, which comprises a specially designed uniform Petri dish illumination system and a counting web application. The latter application directly receives images from the camera, processes them, and sends the segmentation results to the user. This feature provides an opportunity to correct the CFU counts, offering a feedback loop that contributes to the continued development of the deep learning model. Through extensive experimentation, the authors of this paper have found that all probed multi-loss U-Net architectures incorporated into the proposed hybrid approach consistently outperformed their single-loss counterparts, as well as other comparable models such as self-normalized density maps and YOLOv6, by at least 1% to 3% in mean absolute and symmetric mean absolute percentage errors. Further significant improvements were also reported through the means of the novel localization algorithm. This reaffirms the effectiveness of the proposed hybrid solution in addressing contemporary challenges of precise in vitro CFU counting. [ABSTRACT FROM AUTHOR]

The article describes an activity program for elementary education which teaches third graders about iterating or counting fractions using whole-number counting concepts.

We define slopes in the flat torus as the set of equivalence classes of the solutions of linear equations in ℝ². The definition is equivalent to that of closed geodesics in the flat torus passing through the equivalence class of the point (0, 0). In this paper we derive formulas for counting the number of points in the intersection of multiple slopes in the flat torus. [ABSTRACT FROM AUTHOR]

In this paper, we solve a classical counting problem for non-degenerate forms of symplectic and hermitian type defined on a vector space: given a subspace π , we find the number of non-singular subspaces that are trivially intersecting with π and span a non-singular subspace with π. Lower bounds for the quantity of such pairs where π is non-singular were first studied in "Glasby, Niemeyer, Praeger (Finite Fields Appl., 2022)", which was later improved in "Glasby, Ihringer, Mattheus (Des. Codes Cryptogr., 2023)" and generalised in "Glasby, Niemeyer, Praeger (Linear Algebra Appl., 2022)". In this paper, we derive explicit formulae, which allow us to give the exact proportion and improve the known lower bounds. [ABSTRACT FROM AUTHOR]

Prevailing crowd counting approaches primarily rely on density map regression methods. Despite wonderful progress, significant scale variations and complex background interference within the same image remain challenges. To address these issues, in this paper we propose a novel DETR-based crowd counting framework called Crowd Counting DETR (CC-DETR), which aims to extend the state-of-the-art DETR object detection framework to the crowd counting task. In CC-DETR, a DETR-like encoder–decoder structure (Hybrid Context DETR, i.e., HCDETR) is proposed to tackle complex visual information by fusing features from hybrid semantic levels through a transformer. In addition, we design a Coordinate Dilated Convolution Module (CDCM) to effectively employ position-sensitive context information in different scales. Extensive experiments on three challenging crowd counting datasets (ShanghaiTech, UCF-QNRF, and NWPU) demonstrate that our model is effective and competitive when compared against SOTA crowd counting models. [ABSTRACT FROM AUTHOR]

The identification of seedling numbers is directly related to the acquisition of seedling information, such as survival rate and emergence rate. It indirectly affects detection efficiency and yield evaluation. Manual counting methods are time-consuming and laborious, and the accuracy is not high in complex backgrounds or high-density environments. It is challenging to achieve improved results using traditional target detection methods and improved methods. Therefore, this paper adopted the density estimation method and improved the population density counting network to obtain the rapeseed seedling counting network named BCNet. BCNet uses spatial attention and channel attention modules and enhances feature information and concatenation to improve the expressiveness of the entire feature map. In addition, BCNet uses a 1 × 1 convolutional layer for additional feature extraction and introduces the torch.abs function at the network output port. In this study, distribution experiments and seedling prediction were conducted. The results indicate that BCNet exhibits the smallest counting error compared to the CSRNet and the Bayesian algorithm. The MAE and MSE reach 3.40 and 4.99, respectively, with the highest counting accuracy. The distribution experiment and seedling prediction showed that, compared with the other density maps, the density response points corresponding to the characteristics of the seedling region were more prominent. The predicted number of the BCNet algorithm was closer to the actual number, verifying the feasibility of the improved method. This could provide a reference for the identification and counting of rapeseed seedlings. [ABSTRACT FROM AUTHOR]

Let S = {z C : P(z) = zn+azn-1+b = 0}, where a, b C be nonzero constants satisfying b an = (-1)n(n - 1)n-1 nn . The uniqueness of meromorphic functions sharing S counting multiplicity(resp. with weight 2) has been studied by Yi ([18]) (resp. Lahiri, Banerjee ([12])). In this paper, we consider the uniqueness of meromorphic functions sharing S ignoring multiplicity. We first obtain the analog of Yi's Theorem 2 ([18]). Next, we show that S is a unique range set for the class of meromorphic functions ignoring multiplicity of higher multiplicities of either zeros or poles, which different from S. Mallick - D. Sarkar's ([13]). We discuss some applications of the main result. Our results are inspired by a work of Yi ([18]) and Khoai ([11]). [ABSTRACT FROM AUTHOR]

In rice cultivation and breeding, obtaining accurate information on the quantity and spatial distribution of rice plants is crucial. However, traditional field sampling methods can only provide rough estimates of the plant count and fail to capture precise plant locations. To address these problems, this paper proposes P2PNet-EFF for the counting and localization of rice plants. Firstly, through the introduction of the enhanced feature fusion (EFF), the model improves its ability to integrate deep semantic information while preserving shallow spatial details. This allows the model to holistically analyze the morphology of plants rather than focusing solely on their central points, substantially reducing errors caused by leaf overlap. Secondly, by integrating efficient multi-scale attention (EMA) into the backbone, the model enhances its feature extraction capabilities and suppresses interference from similar backgrounds. Finally, to evaluate the effectiveness of the P2PNet-EFF method, we introduce the URCAL dataset for rice counting and localization, gathered using UAV. This dataset consists of 365 high-resolution images and 173,352 point annotations. Experimental results on the URCAL demonstrate that the proposed method achieves a 34.87% reduction in MAE and a 28.19% reduction in RMSE compared to the original P2PNet while increasing R 2 by 3.03%. Furthermore, we conducted extensive experiments on three frequently used plant counting datasets. The results demonstrate the excellent performance of the proposed method. [ABSTRACT FROM AUTHOR]

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