Counting Problem Research Articles

First-Year Undergraduate Students’ Ways of Thinking in Combinatorics

The fundamental counting principle and counting problems, jointly called combinatorics in this study, commence in the last year of secondary school and proceeds in undergraduate studies and beyond. The South African secondary school situation reflect the same worldwide scenario where counting principles is regarded as difficult and poorly performed in the final national examinations. The purpose of this study was to explore undergraduate students’ mental constructions in solving counting problems against the backdrop of Grade 12 fundamental counting principles. The Action-Process-Object-Schema theory was used to describe undergraduate students’ thinking ways in combinatorics. A single case of a first-year class of 182 students was considered in this study, whereby they all wrote a task on combinatorics and a seven were further interviewed. The findings revealed that students were skilled at solving problems involving the counting principles, which was mainly step-by-step application of the formulae. This conception is at action level according to APOS theory, but the goal of teaching is to guide students to attain the object mental conception. Object conception allows for solving of diverse real-world counting problems and promotes mathematical thinking skills.

Asymptotic speedup via effect handlers

Abstract We study a fundamental efficiency benefit afforded by delimited control, showing that for certain higher-order functions, a language with advanced control features offers an asymptotic improvement in runtime over a language without them. Specifically, we consider the generic count problem in the context of a pure functional base language ${\lambda_{\textrm{b}}}$ and an extension ${\lambda_{\textrm{h}}}$ with general effect handlers. We prove that ${\lambda_{\textrm{h}}}$ admits an asymptotically more efficient implementation of generic count than any implementation in ${\lambda_{\textrm{b}}}$ . We also show that this gap remains even when ${\lambda_{\textrm{b}}}$ is extended to a language ${{{{{{\lambda_{\textrm{a}}}}}}}}$ with affine effect handlers, which is strong enough to encode exceptions, local state, coroutines and single-shot continuations. This locates the efficiency difference in the gap between ‘single-shot’ and ‘multi-shot’ versions of delimited control. To our knowledge, these results are the first of their kind for control operators.

Orientable vertex imprimitive complete maps

<abstract><p>In the work by Li (<italic>J. Combin. Theory Ser. B</italic>, <bold>99</bold> (2009), 447–454.), the author characterized the classification of vertex transitive embeddings of complete graphs, and proposed how to enumerate such maps. In this paper, we study the counting problem of orientable vertex imprimitive complete maps, which is the automorphism group of this map acts imprimitively on its vertex set. Moreover, we obtain the number of non-isomorphic embeddings when the vertex-stabilizer subgroups of the automorphism groups of maps are isomorphic to $ \text{Z}_{p-1} $ with odd prime $ p $.</p></abstract>

A Deep Learning and Image Processing Pipeline for Object Characterization in Firm Operations

Given the abundance of images related to operations that are being captured and stored, it behooves firms to innovate systems using image processing to improve operational performance that refers to any activity that can save labor cost. In this paper, we use deep learning techniques, combined with classic image/signal processing methods, to propose a pipeline to solve certain types of object counting and layer characterization problems in firm operations. Using data obtained by us through a collaborative effort with real manufacturers, we demonstrate that the proposed pipeline method is able to achieve higher than 93% accuracy in layer and log counting. Theoretically, our study conceives, constructs, and evaluates proof of concept of a novel pipeline method in characterizing and quantifying the number of defined items with images, which overcomes the limitations of methods based only on deep learning or signal processing. Practically, our proposed method can help firms significantly reduce labor costs and/or improve quality and inventory control by recording the number of products in real time, more accurately and with minimal up-front technological investment. The codes and data are made publicly available online through the INFORMS Journal on Computing GitHub site. History: Accepted by Ram Ramesh, Area Editor for Data Science and Machine Learning. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0260 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0260 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Scalable Approximate Butterfly and Bi-triangle Counting for Large Bipartite Networks

A bipartite graph is a graph that consists of two disjoint sets of vertices and only edges between vertices from different vertex sets. In this paper, we study the counting problems of two common types of em motifs in bipartite graphs: (i) butterflies (2x2 bicliques) and (ii) bi-triangles (length-6 cycles). Unlike most of the existing algorithms that aim to obtain exact counts, our goal is to obtain precise enough estimations of these counts in bipartite graphs, as such estimations are already sufficient and of great usefulness in various applications. While there exist approximate algorithms for butterfly counting, these algorithms are mainly based on the techniques designed for general graphs, and hence, they are less effective on bipartite graphs. Not to mention that there is still a lack of study on approximate bi-triangle counting. Motivated by this, we first propose a novel butterfly counting algorithm, called one-sided weighted sampling, which is tailored for bipartite graphs. The basic idea of this algorithm is to estimate the total butterfly count with the number of butterflies containing two randomly sampled vertices from the same side of the two vertex sets. We prove that our estimation is unbiased, and our technique can be further extended (non-trivially) for bi-triangle count estimation. Theoretical analyses under a power-law random bipartite graph model and extensive experiments on multiple large real datasets demonstrate that our proposed approximate counting algorithms can reach high accuracy, yet achieve up to three orders (resp. four orders) of magnitude speed-up over the state-of-the-art exact butterfly (resp. bi-triangle) counting algorithms. Additionally, we present an approximate clustering coefficient estimation framework for bipartite graphs, which shows a similar speed-up over the exact solutions with less than 1% relative error.

Poissonian Pair Correlation for $\alpha n^{\theta }$ mod 1

Abstract We show that sequences of the form $\alpha n^{\theta } \pmod {1}$ with $\alpha> 0$ and $0 < \theta < \tfrac {43}{117} = \tfrac {1}{3} + 0.0341 \ldots $ have Poissonian pair correlation. This improves upon the previous result by Lutsko, Sourmelidis, and Technau, where this was established for $\alpha> 0$ and $0 < \theta < \tfrac {14}{41} = \tfrac {1}{3} + 0.0081 \ldots $. We reduce the problem of establishing Poissonian pair correlation to a counting problem using a form of amplification and the Bombieri–Iwaniec double large sieve. The counting problem is then resolved non-optimally by appealing to the bounds of Robert–Sargos and (Fouvry–Iwaniec–)Cao–Zhai. The exponent $\theta = \tfrac {2}{5}$ is the limit of our approach.

Literature Review: pola makan dan kualitas diet pada remaja dan dewasa dengan HIV/AIDS

Background: Human Immunodeficiency Virus (HIV) infection remains an unresolved health problem in Brazil. Diet plays an important role in the immune system of HIV/AIDS patients because adequate amounts of macronutrients and micronutrients are important. Food quality has also been used as a proxy for predicting the risk of death and chronic diseases. Measuring diet quality is an indicator that can describe a person's dietary practices in accordance with the dietary recommendations set out to be able to live healthily.Objective: This study aimed to analyze the dietary patterns and diet quality of adolescents and adults with HIV/AIDS.Methods: This study was a systematic literature review. The protocol used in the systematic literature review of this study used the PRISMA method. The SLR protocol and evaluation were performed using the PRISMA method to select research articles that had been found. The PRISMA method collects articles from PubMed, Google Scholar, Research Gate, SINTA, Garuda, and Scopus databases. The search terms used were Indonesian and English. The search terms used in Indonesian were "Diet and HIV/AIDS" OR "Diet Quality and HIV/AIDS". The search terms in English were "dietary habit and HIV/AIDS" OR "diet quality and HIV/AIDS". The articles collected were published between 2014 and 2022.Results: According to the findings of a systematic literature review, consumption patterns that do not meet the needs of HIV infection will lead to chronic malnutrition and AIDS, resulting in a drastic decrease in resistance to other infections. Diet plays an important role in the immune system of HIV/AIDS patients, because adequate intake of macro-and micronutrients is essential for normal functioning. Diet quality is influenced by the diversity of food ingredients and food security, which remains low. Diet quality in HIV/AIDS patients affects their body weight, mental health status, physical health status, CD4 count, and other health problems.Conclusion: Dietary habits do not meet intake requirements due to HIV infection, which causes chronic malnutrition and, at the AIDS stage, results in a drastic decrease in resistance to other infections. Diet quality in HIV/AIDS patients affects their body weight, mental health status, physical health status, CD4 count, and other health problems.

Bounded Degree Nonnegative Counting CSP

Constraint satisfaction problems (CSP) encompass an enormous variety of computational problems. In particular, all partition functions from statistical physics, such as spin systems, are special cases of counting CSP (#CSP). We prove a complete complexity classification for every counting problem in #CSP with nonnegative valued constraint functions that is valid when every variable occurs a bounded number of times in all constraints. We show that, depending on the set of constraint functions \(\mathcal {F} \) , every problem in the complexity class # \(\text{CSP}(\mathcal {F}) \) defined by \(\mathcal {F} \) is either polynomial-time computable for all instances without the bounded occurrence restriction, or is #P-hard even when restricted to bounded degree input instances. The constant bound in the degree depends on \(\mathcal {F} \) . The dichotomy criterion on \(\mathcal {F} \) is decidable. As a second contribution, we prove a slightly modified but more streamlined decision procedure (from [14]) to test for the tractability of # \(\text{CSP}(\mathcal {F}) \) . This procedure on an input \(\mathcal {F} \) tells us which case holds in the dichotomy for # \(\text{CSP}(\mathcal {F}) \) . This more streamlined decision procedure enables us to fully classify a family of directed weighted graph homomorphism problems. This family contains both P-time tractable problems and #P-hard problems. To our best knowledge, this is the first family of such problems explicitly classified that are not acyclic , thereby the Lovász-goodness criterion of Dyer-Goldberg-Paterson [24] cannot be applied.

Grouped People Counting Using mm-Wave FMCW MIMO Radar

The problem of radar-based counting of multiple individuals moving as a single group is addressed using a mm-wave multiple-input-multiple-output (MIMO) frequency-modulated continuous wave (FMCW) radar. This problem is challenging because the different individuals are closer to each other than the range/azimuth resolution, and their bulk Doppler signatures are difficult to distinguish, as they tend to move together. A processing pipeline is proposed, based on the combination of a multiple target tracking algorithm with a classifier to track each group and count the number of people within. Specific salient features are defined for the classifier and extracted from range-azimuth maps and cadence velocity diagrams (CVD). The proposed pipeline has been experimentally validated in several outdoor scenarios with grouped people. The results show that the combination of tracking algorithm and classifier in the proposed pipeline outperforms alternative methods from the literature as well as a commercial toolbox for people counting.

TFA-CNN: an efficient method for dealing with crowding and noise problems in crowd counting

TFA-CNN: an efficient method for dealing with crowding and noise problems in crowd counting

The computational complexity of Holant problems on 3-regular graphs

Holant problem is a framework to study counting problems, which is expressive enough to contain Counting Graph Homomorphisms (#GH) and Counting Constraint Satisfaction Problems (#CSP) as special cases. In the present paper, we classify the computational complexity of Holant problems on 3-regular graphs, where the signature is complex valued and not necessarily symmetric. In details, we prove that Holant problem on 3-regular graphs is #P-hard except for the signature is not genuinely entangled, A-transformable, P-transformable or vanishing, in which cases the problem is tractable.

Inapproximability of counting independent sets in linear hypergraphs

It is shown in this note that approximating the number of independent sets in a k-uniform linear hypergraph with maximum degree at most Δ is NP-hard if Δ≥5⋅2k−1+1. This confirms that for the relevant sampling and approximate counting problems, the regimes on the maximum degree where the state-of-the-art algorithms work are tight, up to some small factors. These algorithms include: the approximate sampler and randomised approximation scheme by Hermon et al. (2019) [5], the perfect sampler by Qiu et al. (2022) [6], and the deterministic approximation scheme by Feng et al. (2023) [7].

Frobenian multiplicative functions and rational points in fibrations

We consider the problem of counting the number of varieties in a family over \mathbb{Q} with a rational point. We obtain lower bounds for this counting problem for some families over \mathbb{P}^1 , even if the Hasse principle fails. We also obtain sharp results for some multinorm equations and for specialisations of certain Brauer group elements on higher-dimensional projective spaces, where we answer some cases of a question of Serre. Our techniques come from arithmetic geometry and additive combinatorics.

The polynomials X2+(Y2+1)2$X^2+(Y^2+1)^2$ and X2+(Y3+Z3)2$X^{2} + (Y^3+Z^3)^2$ also capture their primes

AbstractWe show that there are infinitely many primes of the form and . This extends the work of Friedlander and Iwaniec showing that there are infinitely many primes of the form . More precisely, Friedlander and Iwaniec obtained an asymptotic formula for the number of primes of this form. For the sequences and , we establish Type II information that is too narrow for an aysmptotic formula, but we can use Harman's sieve method to produce a lower bound of the correct order of magnitude for primes of form and . Estimating the Type II sums is reduced to a counting problem that is solved by using the Weil bound, where the arithmetic input is quite different from the work of Friedlander and Iwaniec for . We also show that there are infinitely many primes where is represented by an incomplete norm form of degree with variables. For this, we require a Deligne‐type bound for correlations of hyper‐Kloosterman sums.

Motional foreground attention-based video crowd counting

In this paper, we tackle the problem of video crowd counting. Compared with single image crowd counting, video provides gradual spatial and temporal variation information that would help to strengthen the robustness of crowd counting. Therefore, it is critical to make full use of neighboring frames both in feature extraction and final prediction for current frame’s estimation. Based on the above observations, we propose a motional foreground attention-based video crowd counting method. Specifically, we first leverage an foreground estimation module based on ConvNeXt to extract the motional features from bidirectional frame differences and output a foreground estimation map. Then the motional features combined with the static features of current frame are sent into feature fusion network, where foreground estimation map is transformed as attention weights for crowd number estimation. Three new indoor video datasets are manually annotated. The proposed method achieves state-of-the-art performance on all indoor and outdoor video datasets.

A distributed streaming framework for edge–cloud triangle counting in graph streams

The triangle counting problem in graph streams has been extensively studied in social network analysis, recommendation systems, user portraits and other fields. However, cloud computing based streaming algorithms cause high bandwidth occupation and long transmission latency due to limited bandwidth of the cloud. Recently, edge computing is promising to overcome the issue of transmitting large-scale data for cloud computing. However, directly applying edge computing in streaming triangle counting will reduce the accuracy of the triangle count estimation, due to the limitation of local computing at the edge network. We term the cooperations between edge computing and cloud computing for streaming triangle counting as edge–cloud triangle counting in graph streams. In this paper, we first propose a streaming framework for edge–cloud triangle counting in graph streams. Then, we propose a streaming triangle counting algorithm called Trie-based Edge Compression (TbEC) by using the binary trie at the edge network that enables lossless compression and efficient transmission to the cloud. In addition, to extend our algorithms for triangle counting in multigraphs, we present a dual deduplication strategy collaboratively using the trie-based data structure and a Bloom Filter. Our experiments with real-world datasets show that TbEC is (a) Accurate: yielding up to 3.35×more accurate smaller estimation error than the state-of-the-art distributed streaming algorithm, (b) Fast: yielding up to 10.59×faster than the state-of-the-art distributed streaming algorithm, (c) Scalable: scaling linearly with the number of edges in the input graph stream.

Comprehensive review on vehicle Detection, classification and counting on highways

Vehicle detection, counting and finally classification has been an important aspect of traffic analysis specially on highways in many developed and developing nations. This has vitalized the monitoring of freeways and reduced the reliance on human traffic monitors specially in developed nations. However, much research carried out in this regard since 1995 have been slow to progress until around 2000. Since then, much more encouraging outcomes have been achieved. This has been mainly due to the advances on vision-based computing and the miniaturizing of hardware since the early 2000. Initial vision-based systems used basic computer vision approaches such as background subtraction and edge detection to detect and count vehicles. Early progress of classification had little success until around 2010. Since 2010, many computer vision approaches using Neural Networks have been gradually increasing the efficiency and the realtime operation of such systems. Since then, many deep learning based neural network approaches have produced remarkable outcomes specially in classification. We have also reported highly accurate and efficient deep learning based YOLOv5 system that has recorded an astounding success. We have used models YOLOv5l, YOLOv5m, YOLOv5n and YOLOv5s in our research to ascertain the best model for the task.However, low light conditions associated with overcast, and dusk have significantly reduced the accuracy in many deep learning-based systems. There are other techniques based on approaches such as headlight detection have appeared to increase the accuracy of counting however, classification at night without adequate lighting still pauses a formidable challenge. The work presented here analyses the vehicle counting problem using computer vision providing many different viewpoints in a view to provide the reader with accurate problem definition.

Synthetic Data Generation for Morphological Analyses of Histopathology Images with Deep Learning Models

In this study, we introduce a new synthetic data generation procedure for augmentation of histopathology image data. This is an extension to our previous research in which we proved the possibility to apply deep learning models for morphological analysis of tumor cells, trained on synthetic data only. The medical problem considered is related to the Ki-67 protein proliferation index calculation. We focused on the problem of cell counting in cell conglomerates, which are considered as structures composed of overlapping tumor cells. The lack of large and standardized data sets is a critical problem in medical image classification. Classical augmentation procedures are not sufficient. Therefore, in this research, we expanded our previous augmentation approach for histopathology images and we proved the possibility to apply it for a cell-counting problem.

Tools for Ground-Truth-Free Passive Client Density Mapping in MAC-Randomized Outdoor WiFi Networks.

In the past few years, data privacy legislation has hampered the ability of WiFi network operators to count and map client activity for commercial and security purposes. Indeed, since client device MAC devices are now randomized at each transmission, aggregating client activity using management frames such as Probe Requests, as has been common practice in the past, becomes problematic. Recently, researchers have demonstrated that, statistically, client counts are roughly proportional to raw Probe Request counts, thus somewhat alleviating the client counting problem, even if, in most cases, ground truth measurements from alternate sensors such as cameras are necessary to establish this proportionality. Nevertheless, localizing randomized MAC clients at a network site is currently an unsolved problem. In this work, we propose a set of nine tools for extending the proportionality between client counts and Probe Requests to the mapping of client densities in real-world outdoor WiFi networks without the need for ground truth measurements. The purpose of the proposed toolkit is to transform raw, randomized MAC Probe Request counts into a density map calibrated to an estimated number of clients at each position.

Shared Trading Strategy of Multiple Microgrids Considering Joint Carbon and Green Certificate Mechanism

With a background of carbon peak and neutrality, the economic and environmental requirements are increasing for microgrids. In view of the problem of energy wastage and conflicts of interest among multiple microgrid integrated energy systems, it is important to study the operation optimization of microgrid clusters while considering the sharing and trading of both carbon emissions and green certificates. In this study, a Stackelberg game mechanism is applied, in which the microgrid operator is the leader and its subscribers are the followers, forming a master–slave interaction model. Following this, breaking the trading barriers of energy and various policy markets, the joint carbon and green certificate trading mechanism is proposed. Moreover, a mutually beneficial shared trading model of multi-microgrids considering coupled energy and carbon and green certificate trading is proposed to avoid the problem of double counting of environmental attributes. In addition, a cooperative sharing center is assumed to propose a flexible multi-resource sharing price mechanism. It guides each microgrid operator to conduct internal multi-resource sharing trading, so as to reduce the daily operating costs of energy supplying entities in the cooperative system of multiple microgrids, effectively reduce carbon emissions, and improve the balance of network group mutual aid. According to the simulation results of an illustrative example, the proposed trading strategy can effectively unlock the potential of resource sharing and mutual aid within multi-microgrids and improve the economy and carbon reduction effects of the overall system.