Counting Problem Research Articles

Fruit Detection and Counting in Apple Orchards Based on Improved Yolov7 and Multi-Object Tracking Methods.

With the increasing popularity of online fruit sales, accurately predicting fruit yields has become crucial for optimizing logistics and storage strategies. However, existing manual vision-based systems and sensor methods have proven inadequate for solving the complex problem of fruit yield counting, as they struggle with issues such as crop overlap and variable lighting conditions. Recently CNN-based object detection models have emerged as a promising solution in the field of computer vision, but their effectiveness is limited in agricultural scenarios due to challenges such as occlusion and dissimilarity among the same fruits. To address this issue, we propose a novel variant model that combines the self-attentive mechanism of Vision Transform, a non-CNN network architecture, with Yolov7, a state-of-the-art object detection model. Our model utilizes two attention mechanisms, CBAM and CA, and is trained and tested on a dataset of apple images. In order to enable fruit counting across video frames in complex environments, we incorporate two multi-objective tracking methods based on Kalman filtering and motion trajectory prediction, namely SORT, and Cascade-SORT. Our results show that the Yolov7-CA model achieved a 91.3% mAP and 0.85 F1 score, representing a 4% improvement in mAP and 0.02 improvement in F1 score compared to using Yolov7 alone. Furthermore, three multi-object tracking methods demonstrated a significant improvement in MAE for inter-frame counting across all three test videos, with an 0.642 improvement over using yolov7 alone achieved using our multi-object tracking method. These findings suggest that our proposed model has the potential to improve fruit yield assessment methods and could have implications for decision-making in the fruit industry.

Nanopore Filter: A Method for Counting and Extracting Single DNA Molecules Using a Biological Nanopore.

This paper describes a method for the real-time counting and extraction of DNA molecules at the single-molecule level by nanopore technology. As a powerful tool for electrochemical single-molecule detection, nanopore technology eliminates the need for labeling or partitioning sample solutions at the femtoliter level. Here, we attempt to develop a DNA filtering system utilizing an α-hemolysin (αHL) nanopore. This system comprises two droplets, one filling with and one emptying DNA molecules, separated by a planar lipid bilayer containing αHL nanopores. The translocation of DNA through the nanopores is observed by measuring the channel current, and the number of translocated molecules can also be verified by quantitative polymerase chain reaction (qPCR). However, we found that the issue of contamination seems to be an almost insolvable problem in single-molecule counting. To tackle this problem, we tried to optimize the experimental environment, reduce the volume of solution containing the target molecule, and use the PCR clamp method. Although further efforts are still needed to achieve a single-molecule filter with electrical counting, our proposed method shows a linear relationship between the electrical counting and qPCR estimation of the number of DNA molecules.

Pólya’s conjecture for Euclidean balls

The celebrated Pólya’s conjecture (1954) in spectral geometry states that the eigenvalue counting functions of the Dirichlet and Neumann Laplacian on a bounded Euclidean domain can be estimated from above and below, respectively, by the leading term of Weyl’s asymptotics. Pólya’s conjecture is known to be true for domains which tile Euclidean space, and, in addition, for some special domains in higher dimensions. In this paper, we prove Pólya’s conjecture for the disk, making it the first non-tiling planar domain for which the conjecture is verified. We also confirm Pólya’s conjecture for arbitrary planar sectors, and, in the Dirichlet case, for balls of any dimension. Along the way, we develop the known links between the spectral problems in the disk and certain lattice counting problems. A key novel ingredient is the observation, made in recent work of the last named author, that the corresponding eigenvalue and lattice counting functions are related not only asymptotically, but in fact satisfy certain uniform bounds. Our proofs are purely analytic, except for a rigorous computer-assisted argument needed to cover the short interval of values of the spectral parameter in the case of the Neumann problem in the disk.

Distribution and moments of the error term in the lattice point counting problem for three-dimensional Cygan–Korányi balls

We study fluctuations of the error term for the number of integer lattice points lying inside a three-dimensional Cygan–Korányi ball of large radius. We prove that the error term, suitably normalized, has a limiting value distribution which is absolutely continuous, and we provide estimates for the decay rate of the corresponding density on the real line. In addition, we establish the existence of all moments for the normalized error term, and we prove that these are given by the moments of the corresponding density.

Approximate Unitary t-Designs by Short Random Quantum Circuits Using Nearest-Neighbor and Long-Range Gates

We prove that {{,textrm{poly},}}(t) cdot n^{1/D}-depth local random quantum circuits with two qudit nearest-neighbor gates on a D-dimensional lattice with n qudits are approximate t-designs in various measures. These include the “monomial” measure, meaning that the monomials of a random circuit from this family have expectation close to the value that would result from the Haar measure. Previously, the best bound was {{,textrm{poly},}}(t)cdot n due to Brandão–Harrow–Horodecki (Commun Math Phys 346(2):397–434, 2016) for D=1. We also improve the “scrambling” and “decoupling” bounds for spatially local random circuits due to Brown and Fawzi (Scrambling speed of random quantum circuits, 2012). One consequence of our result is that assuming the polynomial hierarchy ({{,mathrm{textsf{PH}},}}) is infinite and that certain counting problems are #{textsf{P}}-hard “on average”, sampling within total variation distance from these circuits is hard for classical computers. Previously, exact sampling from the outputs of even constant-depth quantum circuits was known to be hard for classical computers under these assumptions. However the standard strategy for extending this hardness result to approximate sampling requires the quantum circuits to have a property called “anti-concentration”, meaning roughly that the output has near-maximal entropy. Unitary 2-designs have the desired anti-concentration property. Our result improves the required depth for this level of anti-concentration from linear depth to a sub-linear value, depending on the geometry of the interactions. This is relevant to a recent experiment by the Google Quantum AI group to perform such a sampling task with 53 qubits on a two-dimensional lattice (Arute in Nature 574(7779):505–510, 2019; Boixo et al. in Nate Phys 14(6):595–600, 2018) (and related experiments by USTC), and confirms their conjecture that O(sqrt{n}) depth suffices for anti-concentration. The proof is based on a previous construction of t-designs by Brandão et al. (2016), an analysis of how approximate designs behave under composition, and an extension of the quasi-orthogonality of permutation operators developed by Brandão et al. (2016). Different versions of the approximate design condition correspond to different norms, and part of our contribution is to introduce the norm corresponding to anti-concentration and to establish equivalence between these various norms for low-depth circuits. For random circuits with long-range gates, we use different methods to show that anti-concentration happens at circuit size O(nln ^2 n) corresponding to depth O(ln ^3 n). We also show a lower bound of Omega (n ln n) for the size of such circuit in this case. We also prove that anti-concentration is possible in depth O(ln n ln ln n) (size O(n ln n ln ln n)) using a different model.

The enumerative geometry of cubic hypersurfaces: point and line conditions

The set of smooth cubic hypersurfaces in Pn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb {P}}}^n$$\\end{document} is an open subset of a projective space. A compactification of the latter which allows to count the number of smooth cubic hypersurfaces tangent to a prescribed number of lines and passing through a given number of points is termed a 1–complete variety of cubic hypersurfaces, in analogy with the space of complete quadrics. Imitating the work of Aluffi for plane cubic curves, we construct such a space in arbitrary dimensions by a sequence of five blow-ups. The counting problem is then reduced to the computation of five total Chern classes. In the end, we derive the desired numbers in the case of cubic surfaces.

Counting parity-violating local S-matrices

Four point tree-level local S-matrices form a module over ring of polynomials of Mandelstam invariants s, t and u. The module of local analytic S-matrices can be encoded in terms of a partition function which is enumerated using plethystic techniques. In this paper, we enumerate the plethystic contribution to local four point photon, graviton and gluon multi-particle partition functions that encode parity violating 2 → 2 scattering. We generalise the counting problem solved in [1, 2] to project out parity violating sectors, a subtle task in even dimensions [3]. We explicitly enumerate the parity odd contributions to the multi-letter partition function for gauge fields, gravitons and gluons and evaluate the resulting parity violating partition functions in D = 4, 6. We also perform a large D analysis to show that parity violating local interactions do not contribute to four particle scattering in higher dimensions (D ≥ 8). Our computations and observations for photons, gravitons and gluons agree with the transformation properties of these S-matrices previously conjectured in [1, 2]

Closed-form dynamic stiffness formulation for modal and dynamic response analysis of pile group foundations

A closed-form dynamic stiffness (DS) formulation is proposed for pile group foundations. This model consists of a rigid cap and an arbitrary number of flexible piles. The rigid cap, connecting to all piles, is modeled as a rigid body resting on an elastic foundation. For each pile, a longitudinal soil–pile model and a preloaded Timoshenko beam on viscoelastic Pasternak foundation are adopted to describe the longitudinal and transverse vibration, respectively. The piles can be either friction piles or end-bearing piles, and pile sections surrounded by different soil layers can be easily modeled by the assembly of pile elements with different parameters. The proposed DS formulations essentially use very few degrees of freedom to, nevertheless, describe the broadband dynamic behaviors of complex pile group foundations in a highly accurate manner. The DS formulation is then used for modal and dynamic response analysis. For modal analysis, the Wittrick–Williams algorithm is applied, with the key issue J0 count problems resolved. The proposed method is verified against some existing results. This research provides an exact and highly efficient modal and response analysis tool for pile group foundations, which can be used for the dynamic analysis of pile foundations subjected to earthquake or traffic excitations.

The Relationship of Multiset, Stirling Number, Bell Number, and Catalan Number

Catalan numbers is not as famous as Fibonacci numbers, however this number has own its beauty and arts. Catalan numbers was discovered by Ming Antu in 1730, however, this numbers is credited to Eugene Catalan when he was studying parentheses in 1838. Catalan numbers mostly occurs in counting or enumeration problems. The Catalan numbers can be defined in more than one forms, and the most famous form is Cn = 1/n+1(2nn). In this study we will discuss the multiset construction and the relationship of the results of Multiset with Stirling, Bell, and Catalan numbers.

Novel FDP mechanisms for releasing bipartite graph data on fixed and infinite intervals

As data collection increases, more and more sensitive data is being used to publish query results. This creates a significant risk of privacy disclosure. As a mathematically provable privacy theory, differential privacy (DP) provides a tool to resist background knowledge attacks. Fuzzy differential privacy (FDP) generalizes differential privacy by employing smaller sensitivity and supporting multiple similarity measures. Thus the output error can be reduced under FDP. Existing FDP mechanisms employ sliding window strategy, which perturb the true query value to an interval with this value as the midpoint to maintain similarity of outputs from neighboring datasets. It is still possible for an attacker to infer some sensitive information based on the difference between the left and right endpoints of the output range. To address this issue, this article present two solutions: fixed interval perturbation and infinite interval perturbation. These strategies perturb the true query values of two neighboring datasets to the same interval and provide fuzzy differential privacy protection for the dataset. We apply the proposed method to the privacy-preserving problem of bipartite graph subgraph counting and verify the effectiveness by experiments.

Bayesian improved cross entropy method for network reliability assessment

We identify the zero count problem (or overfitting) of cross-entropy-based methods in the context of network reliability assessment, and propose a consistent Bayesian estimator that mitigates this issue. Thereby, we derive the posterior predictive distribution of importance sampling distribution parameters that replaces the weighted maximum likelihood estimation employed in the standard cross entropy optimization. For rare event estimation, we embed the Bayesian estimator into the improved cross entropy (iCE) method and provide theoretical insights into the adaptive selection of intermediate target distributions in the iCE. The modified version of the iCE, termed the Bayesian iCE (BiCE), is proved to be unbiased. By contrast, even with higher computational cost, the standard iCE method is often significantly biased when solving network reliability problems. Our numerical investigations indicate that a uniform prior in the proposed BiCE method performs suboptimally, and an informative symmetric Dirichlet prior is suggested.

Remarks on the pair correlation statistic of Kronecker sequences and lattice point counting

AbstractIn this short note, we reformulate the task of calculating the pair correlation statistics of a Kronecker sequence as a lattice point counting problem. This can be done analogously to the lattice based approach which was used to (re-)prove the famous three gap property for Kronecker sequences. We show that recently developed lattice point counting techniques can then be applied to derive that a certain class of Kronecker sequences have $$\beta $$ β -pair correlations for all $$0< \beta < 1$$ 0 < β < 1 .

Transportation Object Counting With Graph-Based Adaptive Auxiliary Learning

This paper proposes an adaptive auxiliary task learning-based approach for transport object counting problems such as humans and vehicles. These problems are essential in many real-world tasks such as video surveillance, traffic monitoring, public security, and urban planning, to aid intelligent transportation systems. Unlike existing auxiliary task learning-based methods, we develop an attention-enhanced adaptively shared backbone network to enable both task-shared and task-tailored features that are learned in an end-to-end manner. The network seamlessly combines a standard Convolution Neural Network (CNN) and a Graph Convolution Network (GCN) for feature extraction and feature reasoning among different domains of tasks. Our approach gains enriched contextual information by iteratively and hierarchically fusing features across different task branches of the adaptive CNN backbone. The whole framework pays special attention to objects’ spatial locations and varied density levels, informed by object (or crowd) segmentation and density level segmentation auxiliary tasks. In particular, thanks to the proposed dilated contrastive density loss function, our network benefits from individual and regional context supervision, along with strengthened robustness. Experiments on six challenging multi-domain datasets demonstrate that our method achieves superior performance compared with state-of-the-art auxiliary task learning-based counting methods. Our code is publicly available.

Lattice Points Close to the Heisenberg Spheres

We study a lattice point-counting problem for spheres arising from the Heisenberg groups. In particular, we prove an upper bound on the number of points on and near large dilates of the unit spheres generated by the anisotropic norms $$\Vert (z,t)\Vert _\alpha = ( \left| z\right| ^\alpha + \left| t\right| ^{\alpha /2})^{1/\alpha }$$ for $$\alpha \ge 2$$ . As a first step, we reduce our counting problem to one of bounding an energy integral. The primary new challenges that arise are the presence of vanishing curvature and nonisotropic dilations. In the process, we establish bounds on the Fourier transform of the surface measures arising from these norms. Further, we utilize the techniques developed here to estimate the number of lattice points in the intersection of two such surfaces.

Bipartite 3-regular counting problems with mixed signs

We prove a complexity dichotomy for a class of counting problems expressible as bipartite 3-regular Holant problems. These are also counting CSP problems where every constraint has arity 3 and every variable is read-thrice. For every problem of the form Holant(f|=3), where f is any integer (or equivalently, rational)-valued ternary symmetric constraint function on Boolean variables, we prove that it is either P-time computable or #P-hard, depending on an explicit criterion of f. The constraint function can take both positive and negative values, allowing for cancellations. In addition, we discover a new phenomenon: there is a set F with the property that for every f∈F the problem Holant(f|=3) is planar P-time computable but #P-hard in general, yet its planar tractability is by a combination of a holographic transformation by [111−1] to FKT together with an independent global argument.

Automatic counting of rapeseed inflorescences using deep learning method and UAV RGB imagery.

Flowering is a crucial developing stage for rapeseed (Brassica napus L.) plants. Flowers develop on the main and branch inflorescences of rapeseed plants and then grow into siliques. The seed yield of rapeseed heavily depends on the total flower numbers per area throughout the whole flowering period. The number of rapeseed inflorescences can reflect the richness of rapeseed flowers and provide useful information for yield prediction. To count rapeseed inflorescences automatically, we transferred the counting problem to a detection task. Then, we developed a low-cost approach for counting rapeseed inflorescences using YOLOv5 with the Convolutional Block Attention Module (CBAM) based on unmanned aerial vehicle (UAV) Red-Green-Blue (RGB) imagery. Moreover, we constructed a Rapeseed Inflorescence Benchmark (RIB) to verify the effectiveness of our model. The RIB dataset captured by DJI Phantom 4 Pro V2.0, including 165 plot images and 60,000 manual labels, is to be released. Experimental results showed that indicators R2 for counting and the mean Average Precision (mAP) for location were over 0.96 and 92%, respectively. Compared with Faster R-CNN, YOLOv4, CenterNet, and TasselNetV2+, the proposed method achieved state-of-the-art counting performance on RIB and had advantages in location accuracy. The counting results revealed a quantitative dynamic change in the number of rapeseed inflorescences in the time dimension. Furthermore, a significant positive correlation between the actual crop yield and the automatically obtained rapeseed inflorescence total number on a field plot level was identified. Thus, a set of UAV- assisted methods for better determination of the flower richness was developed, which can greatly support the breeding of high-yield rapeseed varieties.

Detection of Laodelphax striatellus (small brown planthopper) based on improved YOLOv5

Laodelphax striatellus (small brown planthopper, SBPH) is a pest feeding mainly on rice, wheat and corn. Meanwhile, SBPH transmits plant viruses during feeding, which may take more serious damage to the agriculture. The research of SBPH control has great significance. Most of the traditional SBPH detection and counting problems are conducted manually, which is inefficient. In this paper, we proposed the improved YOLOv5s algorithm to implement the recognition and counting the system of SBPH. We improve the YOLOv5s based on the channel attention and spatial attention, adding the Convolutional Block Attention Module (CBAM) to YOLOv5s. In order to fuse the feature information of different scales to improve the model, we add the Adaptively Spatial Feature Fusion (ASFF). Experiments prove that the improved model volume is not much different from YOLOv5s, which is one-seventh of YOLOv5x, but the mAP of the improved model is approximately 4 % better than YOLOv5s and 2 % better than YOLOv5x. Finally, an APP was developed using Android Studio. We developed image recognition, counting module, real-time recognition and counting module, which were migrated to the mobile phone.

Ramie Plant Counting Based on UAV Remote Sensing Technology and Deep Learning

ABSTRACT Plants number is an essential field phenotypic trait that affects the growth status and final quality of crop. In recent years, the integration of remote sensing technology and deep learning technology has provided a solution to the problem of crop plant counting in field. However, most of the previous studies have selected fixed crops (such as rice, wheat) for research, and few studies have reported the limitations in the application of this technology. In addition, as far as we know, there has been no report on the problem of ramie germplasm resources counting. In this study, in combination with DA (Data Augmentation) and three object detection algorithms, ramie germplasm resources were adopted to explore the accuracy of counting plant number under the condition of dense plant growth. The following functions were tested: (1) the influence of DA on the effect of plant counting; (2) the influence of ground sampling distance (GSD) on the effect of plant counting; (3) the influence of object detection algorithms on ramie detection object. The results showed that after the training sample was expanded by DA, the Precision of ramie plant counting model was increased by 6.630%. FCOS (Fully Convolutional One-Stage Object Detection) could perform better in small object and small sample data (Recall = 0.892, Precision = 0.819，RMSE = 0.089). It was necessary to ensure the consistency of GSD between training samples and verification samples for improving the accuracy of ramie plants counting. The ramie plant counting model has sufficient and stable ability to count ramie plants in the field, which can supplement the traditional manual counting method.

Special Issue on : Combinatorics, Cryptography, Computer Science and Computation

The 7th International Conference on Combinatorics, Cryptography, Computer Science and Computation was held on November 16-17th 2022 at Iran. These four interconnected play crucial roles in both theoretical and practical applications. Combinatorics studies combinations, permutations, counting problems, and finite set structures, with applications in biology, computer science, and physics. Cryptography focuses on encrypting and decrypting information for security and integrity, protecting data privacy in electronic transactions. Computer science studies computer design, development, and operation, enabling advanced data analysis tools and efficient automation systems. Computation involves calculating or manipulating information, which is essential for software development and applications in data science, artificial intelligence, and cybersecurity. These fields provide a foundation for understanding information nature, security, and the development of cutting-edge digital technologies.

"Interstellar Wanderers:" Digital Support for Teaching Place Value Within the Activity Approach Framework.

The majority of mistakes students make while using "well-learned" decimal counting, can be attributed to their miscomprehension of the structure and arrangement of the "positional" numeral system. Digital support may merely serve an illustrative and training function, or it may provide the special environment for locating the problem of positional counting as a part of meaningful actions by the students. Following the Activity approach, we aimed to scaffold the students' own learning actions, in such a way as to reveal the origin of the multi-digit number concept. Thus, we used counting in other-base systems as a way for students to reconsider the reasoning behind familiar operations in the most common base-ten system. The purpose of this paper is to present the approach to computer support which we have designed, based on our analysis of the activity content related to the multi-digit number concept, and to discuss some preliminary results of the first training series. The approach to educational environment design developed within the Learning Activity theory defines the ways in which a computer becomes essential. The computer should provide a transparent interface which allows students to perform transformations with objects which will react accordingly. The additional opportunities to perform concept-mediated orientation procedures should also be scaffolded by digital means. For the purposes of our study, the computer-based educational module "Interstellar wanderers" was designed. Four groups of students from 2nd to 5th grade (8-12 years of age, 20 children in total) participated in the experimental computer-based lessons (over 30 hours); classroom observations, videotaped discussions, and logs of students' individual work in the computer simulation were used for analysis. The preliminary results of the experimental teaching showed that the computer support which we developed may scaffold students' progress toward acquisition of the multi-digit number concept through a reflective re-thinking of the well-learned decimal system. Yet further research is needed to get a quantitative analysis of students' performance. The general principles of computer support design based on the Activity approach in education (Galperin, Davydov, & Talyzina) demand a thorough analysis of the origin of the concept being studied, as well as the design of appropriate content and means of students' actions and corresponding contexts and tasks. The digital means which we designed to support students' learning activity, are in demand and bring promising results.