Count Distribution Research Articles

Assessment of the hematological profiles among COVID-19 patients during the first and second waves in Ethiopia: A multicenter retrospective cohort study

Background: The coronavirus disease 2019 is highly infectious and patients with coronavirus diseases demonstrated a series of clinical symptoms caused by severe acute respiratory syndrome coronavirus-2. Without a break of the wave’s hematological profile of the patients is still ambiguous and differs from wave to wave. Objective: This study aimed to assess the hematological profile among coronavirus disease 2019 patients during the first and the second waves in Ethiopia. Methods: A multi-centered facility-based retrospective cohort study design was conducted at six coronavirus disease 2019 treatment centers. A total of 538 study participants were enrolled in the selected coronavirus disease 2019 treatment centers during the first and second waves of the pandemic. The demographic characteristics, underlying diseases, symptoms, and hematological parameters of patients were recorded. Data were entered into Epi-Data Manager 4.6 and analyzed using STATA 14.2. An independent sample t-test was used to assess the mean differences in hematological parameters across waves. Associations between categorical variables across waves were also determined using Chi-square and Fisher exact tests. Results: Among the total study participants, 240 (44.6%) and 298 (55.4%) patients were taken from wave-1 and wave-2, respectively. The average age of the study participants was 56.44 ± 16.25 years. The most frequent comorbidities in this study were hypertension, diabetes mellitus, ischemic heart disease, and asthma. The most presenting symptoms of COVID-19 infection across the two waves were presented. In the first wave, dry cough 166 (69.2%), fatigue 153 (63.75%), shortness of breath 148 (61.67%), and fever accounted 116 (48.33%), while during the second wave, dry cough 242 (81.2%), fatigue 244 (81.88%) shortness of breath 204 (68.47%) and fever account 180 (60.40%). White blood cells (WBC), neutrophils, and lymphocytes had shown increment during the first wave. Platelet count and platelet distribution width ( p < 0.001) had significant mean differences across the two waves, while the other had no significant mean difference. Conclusion: In the present study, dry cough, fatigue, shortness of breath, and fever were found to be the most presenting symptoms of COVID-19 infection across the two waves. Only the platelet count and platelet distribution width had significant mean differences across the two waves, while the other had no significant mean difference across waves.

Utilising Machine Learning for the Automated Characterisation of In Situ Electron Microscopy Experiments with Catalytic Systems

The data analysis workflow for in situ electron microscopy experiments can require a lot of human-intensive and repetitive effort. The generation of Python-based scripts that incorporate simple machine learning algorithms are quite well established in biological sciences but not often utilised in the study of catalytic systems. Such scripted analysis is not only more efficient, but readily reproducible and allows a wide range of quantitative results to be reported, including but not limited to average and total particle size, particle counting and particle size distributions. In this work we utilise these tools to examine the effect of cycling reducing and oxidising atmospheres on CuO nanoparticles.

Platelet indices and plasma gelsolin in patients presenting with acute stroke

Abstract Background: Cerebrovascular diseases are the most common and devastating disorders. Early diagnosis using biochemical tests plays a significant role. Methods: This hospital-based analytical cross-sectional study conducted over 18 months using a pre-designed structured questionnaire. Patients (n = 82) presenting with aute stroke belonged to age group of 30-85 years were included in the study. Patients with an old stroke, transient ischaemic attacks and those on antiplatelet and statin therapy were excluded. We studied the correlation between serum platelet indices and plasma gelsolin (GSN) levels in patients presenting with acute stroke. Results: Among the study participants 59.8% were males; 31.7% were 56–65 years of age. Ischaemic stroke was evident in 78.5% of the study participants; the others had haemorrhagic stroke. There was a weak negative correlation between platelets and GSN levels, which was not statistically significant. There was no correlation between platelet count and platelet distribution width (DW) and severity of the stroke, and a weak correlation was observed between mean platelet volume (MPV) and severity of stroke (r = 0.142, P = 0.21). Conclusions: MPV and pGSN can be used as an indicator to determine the severity and prognosis of the patient.

Trans-ancestry analysis in over 799,000 individuals yields new insights into the genetic etiology of colorectal cancer.

Recent studies have demonstrated the relevance of circulating factors in the occurrence and development of colorectal cancer (CRC); however, the causal relationship remains unclear. Summary-level data for CRC were obtained from the UK Biobank (5,657 cases and 372,016 controls), FinnGen cohort (3,022 cases and 215,770 controls), and BioBank Japan Project (BBJ, 7,062 cases and 195,745 controls). Thirty-two peripheral markers with consistent definitions were collected from the three biobanks. Mendelian randomization (MR) was used to evaluate the causal effect of circulating factors on CRC. The effects from the three consortiums were combined using trans-ancestry meta-analysis methods. Our analysis provided compelling evidence for the causal association of higher genetically predicted eosinophil cell count (EOS, odds ratio [OR], 0.8639; 95% confidence interval [CI] 0.7922-0.9421) and red cell distribution width (RDW, OR, 0.9981; 95% CI, 0.9972-0.9989) levels with a decreased risk of CRC. Additionally, we found suggestive evidence indicating that higher levels of total cholesterol (TC, OR, 1.0022; 95% CI, 1.0002-1.0042) may increase the risk of CRC. Conversely, higher levels of platelet count (PLT, OR, 0.9984; 95% CI, 0.9972-0.9996), total protein (TP, OR, 0.9445; 95% CI, 0.9037-0.9872), and C-reactive protein (CRP, OR, 0.9991; 95% CI, 0.9983-0.9999) may confer a protective effect against CRC. Moreover, we identified six ancestry-specific causal factors, indicating the necessity of considering patients' ancestry backgrounds before formulating prevention strategies. MR findings support the independent causal roles of circulating factors in CRC, which might provide a deeper insight into early detection of CRC and supply potential preventative strategies.

The Effectiveness of Human Formation of Maradjao Magbalantay College Seminary as Perceived by the Seminarians

The seminary formation is composed of four aspects: human, spiritual, intellectual and pastoral. Seminarian is educated and prepared for the priesthood through preparation and practice, field education, spiritual instruction, retreats, seminars, and community life. This study thus aimed to determine the Effectiveness of Human Formation of Maradjao Magbalantay College Seminary as perceived by the Seminarians. This study utilized the research method descriptive-survey with 32 participants and a total Maradjao Magbalantay College Seminary population. The main tool used in gathering the requisite data was a questionnaire made by the researcher. The data collected were treated using frequency count and percentage distribution descriptive statistical tools, mean and standard deviation, and variance analysis (ANOVA). In general, there was no significant difference in the effectiveness of the Seminary Formation to the Seminarians of Maradjao Magbalantay College Seminary when grouped according to the profile variable, age. On the other hand, the stage in seminary under the variable Formation of Conscience shown that there was significant difference as to the effectiveness of the Human Formation. With the collected results, the researcher recommended that the formators should be more observant to the seminarians in the community life. Same as to the seminarians, they should be more faithful and devoted to their vocation.

Challenges and Adaptation Practices of Farmers on Climate Change

Climate change presents the agricultural industry with unforeseen difficulties, impacting livelihoods, food security, crop productivity, and sustainability. This descriptive study aims to illuminate the prevalent challenges in production and cropping patterns experienced by farmers due to climate change, along with their primary adaptation practices to mitigate adverse effects. It employs statistical tools such as ranking, mean, standard deviation, frequency count, and percentage distribution for data analysis. The respondents primarily consisted of high school graduate women with extensive farming experience and land ownership. Results indicate that climate change has exacerbated challenges in crop production, with low yields, pest and disease outbreaks, and flood damage being the most prominent issues. Farmers encounter numerous challenges in deciding on cropping patterns, mainly due to limited knowledge about viable techniques such as crop mapping, intercropping, pest and nutrient management, and water scarcity in non-irrigated fields. The results also show that farmers have adopted several strategies, including reducing the use of pesticides and petroleum-based fertilizers, conserving water during dry seasons, and improving drainage and soil mulching to prevent weed growth. Interestingly, indigenous methods have also been continuously utilized to mitigate the effects of climate change. This emphasizes the importance of innovative farming methods and ongoing farmer education initiatives for capacity building. Additionally, the results found no statistically significant association between challenges and adaptation practices.

Bernoulli Poisson Moment Exponential Distribution: Mathematical Properties, Regression Model, and Applications

We introduce a new flexible count distribution by combining Bernoulli and Poisson moment exponential (PMEx) distributions. The new model named the Bernoulli PMEx distribution. Some mathematical properties are studied, including the hazard rate function, moments, moment generating function, probability generating function, and dispersion index. A count regression model is also proposed based on this distribution. The maximum likelihood estimation method is used to estimate the model parameters. In the end, three datasets from different fields are utilized for application purposes. The findings show that the new model efficiently analyzed these datasets as compared to Poisson, discrete Pareto, discrete Rayleigh, discrete Burr‐Hatke, and discrete inverted Topp–Leone distributions.

XOR count and block circulant MDS matrices over finite commutative rings

<p>Block circulant MDS matrices are used in the design of linear diffusion layers for lightweight cryptographic applications. Most of the work on construction of block circulant MDS matrices focused either on finite fields or $ GL(m, \mathbb{F}_2) $. The main objective of this paper is to extend the above study of block circulant MDS matrices to finite commutative rings. Additionally, we examine the behavior of the XOR count distribution under different reducible polynomials of equal degree over $ \mathbb{F}_2 $. We show that the determinant of a block circulant matrix over a ring can be expressed in a simple form. We construct $ 4 \times 4 $ and $ 8 \times 8 $ block circulant matrices over a ring. Furthermore, for non-negative integer $ l $, we identify the conditions under which a ring $ \mathfrak{R}_l = \frac{\mathbb{F}_2[x]}{\langle (f(x))^{2^l} \rangle} $, contains a finite field of order $ 2^m $, where $ f(x) $ is an irreducible polynomial of degree $ m $. To facilitate efficient implementation, we analyze XOR distributions within specific rings, such as $ R_1 = \frac{\mathbb{F}_2[x]}{\langle (1+x^2+x^6) \rangle} $ and $ R_2 = \frac{\mathbb{F}_2[x]}{\langle (1+x^4+x^6) \rangle} $. Our calculations reveal distinct XOR distributions when utilizing two reducible polynomials of equal degree, with XOR count distributions 776 and 764, respectively. However, when using irreducible polynomials of the same degree, the XOR count distributions remain the same. This difference is advantageous for applications in lightweight cryptography.</p>

Estimation of Population Size Based on One-Inflated, Zero-Truncated Count Distribution with Covariate Information

In order to estimate the unknown size of the population that is difficult or hidden to enumerate, the capture-recapture method is widely used for this purpose. We propose the one-inflated, zero-truncated geometric (OIZTG) model to deal with three important characteristics of some capture–recapture data: zero-truncation, one-inflation, and observed heterogeneity. The OIZTG model is generated by two distinct processes, one from a zero-truncated geometric (ZTG) process, and the other one-count producing process. To explain heterogeneity at an individual level, the OIZTG model provides a simple way to link the covariate information. The new estimator was proposed based on the OIZTG distributions through the modified Horvitz-Thomson approach, and the parameters of the OIZTG distributions are estimated by using a maximum likelihood estimator (MLE). With regard to making inferences about the unknown size of the population, confidence interval estimations are proposed where variance estimate of population size estimator is achieved by using conditional expectation technique. All of these are assessed through simulation studies. The real data sets are provided for understanding the methodologies.

Measuring Innovativeness: A ranking of the ordinal utility from consumption is more robust than either of ‘outcomes of commercialization’ or patent counts

This study provides formal theoretical evidence that patent counts are not robust measures of the innovativeness of economic agents. Study inferences are rationalized by two complementary insights, the first quantitative, the second qualitative. Whereas, feasibly the assumption that the distribution of patent counts is quasiconcave surmounts the quantitative rationale, the qualitative rationale – Net Present Values (NPVs) of patents dominate patent counts as measures of the innovativeness of agents – is binding. The robustness of the qualitative rationale is evident in the finding that it rules out the feasibility, to wit, all other tools for the appropriation of innovations, such as secrecy, lead time, learning curve, etc. are robust proxies for the innovativeness of agents. The realization that a higher NPV can be the outcome of high demand that is induced by consumers’ budget constraints, equivalently can be the ‘outcome of commercialization’, vis-a-vis the ‘technological dominance’ of new products results in the insight that the NPV rule also is, itself not a robust measure of the innovativeness of agents. In aggregate, ‘a ranking of the ordinal utility’ that rational consumers derive from products, a ranking that, feasibly is violated by their budget constraints, is shown to be a more robust measure of the innovativeness of agents than a ranking of innovations’ NPVs. Since technological complexity has, as objective the satisficing of consumers’ utility, a ranking of utility also is a more robust measure of the innovativeness of agents than a ranking of technological complexity.

Deriving a zero-truncated modelling methodology to analyse capture–recapture data from self-reported social networks

Capture–recapture (CRC) is widely used to estimate the size (N) of hidden human populations (e.g., the homeless) from the overlap of sample units between two or more repeated samples or lists (a.k.a., capture occasions). There is growing interest in deriving CRC data from social-network data. The current paper hence explored if self-reported social networks (lists of social ties) submitted by participants from the target population could function as distinct capture occasions. We particularly considered the application of zero-truncated count distribution modelling to this type of data. A case study and follow-up simulation study focused on two methodological issues: (1) that a participant cannot be named in their own self-reported social network and hence cannot be named as many times as non-participants; and (2) positive dependence between being a participant and being named by (a social tie of) other participants. Regarding the latter, a further motivation of the simulation study was to consider the impact of using respondent-driven sampling to select participants, because all non-seed RDS participants are recruited as a social tie of another participant. Exponential random graph modelling was used to generate the simulation study’s target populations. Early comparison was also made to estimates of N from Successive Sampling.

4D nucleome equation predicts gene expression controlled by long-range enhancer-promoter interaction.

Recent experimental evidence strongly supports that three-dimensional (3D) long-range enhancer-promoter (E-P) interactions have important influences on gene-expression dynamics, but it is unclear how the interaction information is translated into gene expression over time (4D). To address this question, we developed a general theoretical framework (named as a 4D nucleome equation), which integrates E-P interactions on chromatin and biochemical reactions of gene transcription. With this equation, we first present the distribution of mRNA counts as a function of the E-P genomic distance and then reveal a power-law scaling of the expression level in this distance. Interestingly, we find that long-range E-P interactions can induce bimodal and trimodal mRNA distributions. The 4D nucleome equation also allows for model selection and parameter inference. When this equation is applied to the mouse embryonic stem cell smRNA-FISH data and the E-P genomic-distance data, the predicted E-P contact probability and mRNA distribution are in good agreement with experimental results. Further statistical inference indicates that the E-P interactions prefer to modulate the mRNA level by controlling promoter activation and transcription initiation rates. Our model and results provide quantitative insights into both spatiotemporal gene-expression determinants (i.e., long-range E-P interactions) and cellular fates during development.

Multivariate zero-inflated Bell–Touchard distribution for multivariate counts: An application to COVID-related data

Multivariate zero-inflated Bell–Touchard distribution for multivariate counts: An application to COVID-related data

#313 : The Correlation Between Ultrasound Morphological Parameters and Phenotypes of Polycystic Ovary Syndrome in Indonesian Women

Background and Aims: Polycystic ovary syndrome (PCOS) is a complex endocrine disorder that affects women of reproductive age. Ultrasound morphological parameters of ovarian morphology, ovarian volume, follicle number, endometrial plate thickness, and doppler analysis are necessary for the diagnosis of PCOS. The aim of this study is to evaluate the correlation between ultrasound morphological parameters and classic and nonclassic phenotypes of PCOS in Indonesian Women. Method: A single-center, observational analytic study from May 2022 until October 2022 was performed upon 50 women with PCOS at Halim Fertility Center (HFC), Indonesia. Fifty PCOS women were classified into two groups: 20 PCOS women with classic phenotype and 30 PCOS women with non-classic phenotype. Data on patient’s age, body mass index (BMI), LH level, FSH level, LH: FSH ratio, Testosterone, Free testosterone index, SHBG, HOMA-IR, Ultrasound parameters (antral follicle count, follicle size, ovarian volume, stromal volume, Stromal/total area (S/A) ratio, Pulsatility index (PI), Peak systolic velocity (PS) and follicle distribution) were assessed and compared between the two groups. Results: The antral follicle count was higher in classic phenotype of PCOS than in nonclassic phenotype and there was a significant difference between the groups (p<0.05). The stromal volume and PI were higher in non-classic phenotype PCOS than in classic phenotype and there was significantly difference between the groups (p<0.05). Most of the follicle distribution in the classic phenotype of PCOS was central and the follicle distribution in the non-classic phenotype was peripheral and there was significantly difference between the groups (p<0.05). The number of antral follicles, stromal volume, PI, and follicle distribution were positively correlated with the PCOS phenotypes (r=0.734; r=0.594; r=0.577; r=0.196), respectively. Conclusion: Classic phenotype of PCOS in Indonesian women has high antral follicle count and central follicle distribution and nonclassic phenotype has high stromal volume, PI and peripheral follicle distribution.

A query-response causal analysis of reaction events in biochemical reaction networks

The stochastic kinetics of biochemical reaction networks is described by a chemical master equation (CME) and the underlying laws of mass action. Assuming network-free simulations of the rule-based models of biochemical reaction networks (BRNs), this paper departs from the usual analysis of network dynamics as the time-dependent distributions of chemical species counts, and instead considers statistically evaluating the sequences of reaction events generated from the stochastic simulations. The reaction event-time series can be used for reaction clustering, identifying rare events, and recognizing the periods of increased or steady-state activity. However, the main aim of this paper is to device an effective method for identifying causally and anti-causally related sub-sequences of reaction events using their empirical probabilities. This allows discovering some of the causal dynamics of BRNs as well as uncovering their short-term deterministic behaviors. In particular, it is proposed that the reaction sub-sequences that are conditionally nearly certain or nearly uncertain can be considered as being causally related. Moreover, since the time-ordering of reaction events is locally irrelevant, the reaction sub-sequences can be transformed into the reaction sets or multi-sets. The distance metrics can be then used to define the equivalences among the reaction events. The proposed method for identifying the causally related reaction sub-sequences has been implemented as a computationally efficient query-response mechanism. The method was evaluated for five models of genetic networks in seven defined numerical experiments. The models were simulated in BioNetGen using the open-source network-free simulator NFsim. This simulator had to be modified first to allow recording the traces of reaction events, and it is available in the Github repository, ploskot/nfsim_1.20. The generated event time-series were analyzed with Python and Matlab scripts. The whole process of data generation, analysis and visualization has been nearly fully automated using shell scripts. This demonstrates the opportunities for substantially increasing the research productivity by creating automated data generation and processing pipelines.

Ectoparasitosis induced severe anemia: a rare cause of severe iron deficiency anemia

Abstract Introduction/Objective Ectoparasites generally infest human’s head and body. It is primarily asymptomatic, however, it can cause iron deficiency anemia on rare occasions, even in developed countries. Bird mites can feed on the blood of people who live near infested pigeons or other infested animals. Methods/Case Report We present a 53 years old homeless male who lives in the New York City’s streets. He was brought to the emergency department by EMS due to ataxia and not being able to stand. Upon arrival, he was covered with countless small ectoparasites later identified as bird mites according to an exterminator. Decontamination and stabilization of patient was begun. No active bleeding or sign of trauma was identified. Complete blood count (CBC) was performed and hemoglobin (Hb) of 2.2 g/dL with Hematocrit of 9.2 % was confirmed after repeat on a second sample. Mean corpuscular volume (MCV), red blood cell (RBC) count, reticulocyte percent and red cell distribution width (RDW) was 73.3 fl, 1.26 M/uL, 3.3 % and 19.9 % respectively. Iron study was not performed initially. White blood cell and Platelets count were normal. Hemoglobin electrophoresis was negative for hemoglobinopathies. After initial transfusion of 2 packs of RBC, the Hb was 3.4 g/dL. He started to have seizures and was intubated. He was transferred to ICU. Ferritin level was checked after transfusion and was still markedly decreased (10.9 ng/mL). He received 6 packs of RBC in total (within 10 hours) and Hb reached 8.7 g/dL, and 48 hours after intubation he was extubated. The patient discharged himself against medical advice the next day. Results (if a Case Study enter NA) NA Conclusion With increasing homelessness, physicians should be aware that ectoparasitosis: 1) is a rare cause of iron deficiency anemia, and 2) because of the gradual onset of the anemia, rapid correction with a massive transfusion is neither warranted nor advised.

Morse theory for discrete magnetic operators and nodal count distribution for graphs

Given a discrete Schrödinger operator h on a finite connected graph G of n vertices, the nodal count \phi(h,k) denotes the number of edges on which the k -th eigenvector changes sign. A signing h' of h is any real symmetric matrix constructed by changing the sign of some off-diagonal entries of h , and its nodal count is defined according to the signing. The set of signings of h lie in a naturally defined torus \mathbb{T}_{h} of “magnetic perturbations” of h . G. Berkolaiko [Anal. PDE 6 (2013), 1213–1233] discovered that every signing h' of h is a critical point of every eigenvalue \lambda_{k}\colon \mathbb{T}_{h} \to \mathbb{R} , with Morse index equal to the nodal surplus. We add further Morse theoretic information to this result. We show if h_{\alpha}\in \mathbb{T}_{h} is a critical point of \lambda_{k} and the eigenvector vanishes at a single vertex v of degree d , then the critical point lies in a non-degenerate critical submanifold of dimension d+n-4 , closely related to the configuration space of a planar linkage. We compute its Morse index in terms of spectral data. The average nodal surplus distribution is the distribution of values of \phi(h',k)-(k-1) , averaged over all signings h' of h . If all critical points correspond to simple eigenvalues with nowhere-vanishing eigenvectors, then the average nodal surplus distribution is binomial. In general, we conjecture that the nodal surplus distribution converges to a Gaussian in a CLT fashion as the first Betti number of G goes to infinity.

The distribution of strongylid egg and lungworm (Dictyocaulus eckerti) larval counts in adult female farmed red deer (Cervus elaphus), and the implications for parasite control

Whilst healthy adult farmed red deer show little clinical indication of parasite infection, they may still be maintaining infection levels on the farm through low-level shedding of nematode eggs and lungworm larvae. This work was undertaken to establish the long-term distribution of parasite counts, to determine whether the higher counts seen in previous trials are repeatable across the same animals. All adult female red deer on a New Zealand North Island property were faecal sampled (n = 209), weighed, and body condition scored (BCS) on five sampling occasions from March – August 2021. Faecal samples were processed by modified Baermanns to recover, identify, and enumerate lungworm 1st stage larvae (FLC), and nematode faecal egg counts (FEC) were determined by mini-FLOTAC. Between animal variation for FEC was significant (p < 0.001); whilst many counts were low to zero, a few individuals were consistently shedding higher egg counts. Younger animals tended to have higher egg counts (p = 0.003), but there was no association between FEC and BCS (p = 0.22), and FEC and liveweight (p = 0.58). Modelling of the data indicated that 50% of the egg output resulted from 21% of the animals. Additionally, there was no significant association between the higher egg counts and the gastrointestinal nematode classification; ‘long tails’ (likely Oesophagostomum sp.) p = 0.76, and the Ostertagiinae complex p = 0.75. Lungworm counts tended to be very low (0 – 26 lpg); consistent with previous trials and literature in farmed adult deer. However, between animal differences were statistically significant (p < 0.001) indicating some animals were passing more larvae than others, and poorer conditioned animals (BCS 2.5) were significantly associated with higher larval count (p = 0.03). There was no relationship between larval count and age (p = 0.62) and larval count and liveweight (p = 0.22). Modelling indicates that 50% of pasture larval contamination was contributed by 15% of the animals. There was no correlation between nematode egg count and lungworm larvae count (p = 0.22). Adult deer may play an important role as a source of infection for young deer, therefore, an improved understanding of the distribution of infection is needed to improve parasite control.

ZERO-INFLATED POISSON TRANSMUTED WEIGHTED EXPONENTIAL DISTRIBUTION: PROPERTIES AND APPLICATIONS

Count observations with high frequencies of zero counts abound in diverse fields. In actuary science, for example, insurance claims are often underreported, leading to a higher frequency of zero counts. This invariably reduces the mean and leads to over-dispersion. Different techniques to model such occurrences exist. This study uses the cubic rank transmutation map to compound the weighted exponential distribution and obtain a new count distribution in the mixed Poisson paradigm. The zero-inflated form of the proposition is obtained along with some mathematical properties. Simulated skewness, kurtosis, and dispersion index for the new distributions reveal they are suitable for model dispersed observation with positive skewness. Five datasets with high frequencies of zero counts are used to assess the performance of the new distribution along with some popular count distributions by using the maximum likelihood for parameter estimation. Results show that the natural form of the new proposition performs creditably better than its zero-inflated forms, even when there is a higher proportion of zero counts. The classical negative binomial distribution is also observed to outperform its zero-inflated form in most cases. In contrast, the zero-inflated Poisson distribution better fits the datasets than the classical Poisson distribution.

Using a Bayesian approach to reconstruct graph statistics after edge sampling

Often, due to prohibitively large size or to limits to data collecting APIs, it is not possible to work with a complete network dataset and sampling is required. A type of sampling which is consistent with Twitter API restrictions is uniform edge sampling. In this paper, we propose a methodology for the recovery of two fundamental network properties from an edge-sampled network: the degree distribution and the triangle count (we estimate the totals for the network and the counts associated with each edge). We use a Bayesian approach and show a range of methods for constructing a prior which does not require assumptions about the original network. Our approach is tested on two synthetic and three real datasets with diverse sizes, degree distributions, degree-degree correlations and triangle count distributions.