Marginal Sums Research Articles

ERPCA-GFCM: An Enhanced DDoS Detection Model on Internet of Things

This research paper introduced an Enhanced Distributed Denial-of-Service (DDoS) Detection model specifically designed for IoT devices. Given the prevalence of DDoS attacks targeting IoT devices, which involve overwhelming a system with malicious traffic to disrupt its normal functioning, the proposed model aimed to enhance the security and resilience of IoT networks. To address this, the proposed model integrated multiple techniques to improve detection and classification accuracy. The first technique, ER-Relief algorithm, is a feature selection method made to address the presence of noise and outliers in the dataset by minimizing a loss function based on the empirical sum of margins. To further enhance the model's performance, Principal Component Analysis (PCA) was utilized for dimensionality reduction. PCA transforms the original high-dimensional feature space into a lower-dimensional space while preserving the most critical information. To achieve better clustering results, the model incorporates the Global Fuzzy C-means algorithm. This algorithm addressed the issue of sensitivity to initial conditions, which lead to suboptimal clustering results. By incorporating fuzzy logic principles, Global Fuzzy C-means assigning data points to multiple clusters with varying degrees of membership, providing a more nuanced representation of the underlying data structure. Lastly, the Random Forest algorithm was employed for training and testing the model. The model was then tested on the CICDDoS2019 dataset, which contains three (3) types of DDoS attacks, namely DNS, UDP, and MSSQL attacks. Based on the evaluation results, the proposed model achieved an impressive accuracy of 97.92%, recall of 97.92%, F1-score of 97.90%, and precision of 97.93%. These metrics highlighted the model's effectiveness, showcasing its ability to accurately detect and classify various types of DDoS attacks with high precision and recall. This research contributes to the advancement of network security by providing a robust and reliable solution for combating DDoS attacks.

Generating series of non-oriented constellations and marginal sums in the Matching-Jack conjecture

Using the description of hypermaps with matchings, Goulden and Jackson have given an expression of the generating series of rooted bipartite maps in terms of the zonal polynomials. We generalize this approach to the case of constellations on non-oriented surfaces that have recently been introduced by Chapuy and Dołęga. A key step in the proof is an encoding of constellations with tuples of matchings.

Novel evolutionary planning technique for flexible-grid transmission in optical networks

This paper proposes a novel joint resource allocation technique for flexible-grid systems by utilizing non-dominant sort genetic algorithm (NSGA-II) in a multi-objective optimization framework. It pioneers the implementation of an evolutionary mechanism to optimize resources as means of mitigation of physical layer impairments. This investigation initially introduces a proposal in which bandwidth reduction, maximization of the minimum signal-to-noise ratio (SNR) margin, and minimization/maximization of the sum of SNR margins are studied under dual-objective Pareto analysis in the link-level scenario. Later, the technique extends existing provisioning strategies for network planning by targeting the reduction of blocking and spectral utilization of optical connections.

On a Family of Log-Gamma-Generated Archimedean Copulas

Modeling dependence structure among various risks, especially the measure of tail dependence and the aggregation of risks, is crucial for risk management. In this article, we present an extension to the traditional one-parameter Archimedean copulas by integrating the log-gamma-generated (LGG) margins. This class of novel multivariate distribution can better capture the tail dependence. The distortion effect on the classic one-parameter Archimedean copulas is well exhibited and the analytical expression of the sum of bivariate margins is proposed. The model provides a flexible way to capture tail risks and aggregate portfolio losses. Sufficient conditions for constructing a legitimate d-dimensional LGG Archimedean copula as well as the simulation framework are also proposed. Furthermore, two applications of this model are presented using concrete insurance datasets.

Investigating the Application of a Transportation Energy Consumption Prediction Model for Urban Planning Scenarios in Machine Learning and Shapley Additive Explanations Method

Accurate forecasts of future energy usage are an important step towards reaching carbon mitigation commitments for city policymakers. Beyond identifying sources of emission intensity for a region, the forecast mechanism must be capable of compensating for gaps in available data and of accounting for the uncertainties behind the dynamics of an urban system. By considering a range of possible scenarios, the prediction model can identify recurring sources of high energy consumption and fine-tune areas of priority with incoming data. This paper considers the impact of predicted shifts in demographic and economic trends for the region on transportation energy consumption. The transportation energy use model is formulated from the Delaware Valley Regional Planning Commission (DVRPC) open-source Household Travel Survey (HTS). Based on these data inputs, a Machine Learning (ML) algorithm is implemented in the form of an Extreme Gradient Boosting (XGBoost) model to estimate energy consumption with a corresponding SHapley Additive exPlanations (SHAP) analysis of feature contribution. From this, a synthetic population is produced using the ML outputs and marginal sums with data from the Census Bureau’s American Community Survey (ACS) to estimate energy consumption for the region. The results indicate that shifting dominant travel modes and income distribution in accordance with the Enduring Urbanism forecast projections led to a decrease in household transportation energy use. Moreover, additional analysis of the model output demonstrates that changes in energy use depend strongly on geographic area and income group.

Estimating the number of usability problems affecting medical devices: modelling the discovery matrix

BackgroundUsability testing of medical devices are mandatory for market access. The testings’ goal is to identify usability problems that could cause harm to the user or limit the device’s effectiveness. In practice, human factor engineers study participants under actual conditions of use and list the problems encountered. This results in a binary discovery matrix in which each row corresponds to a participant, and each column corresponds to a usability problem. One of the main challenges in usability testing is estimating the total number of problems, in order to assess the completeness of the discovery process. Today’s margin-based methods fit the column sums to a binomial model of problem detection. However, the discovery matrix actually observed is truncated because of undiscovered problems, which corresponds to fitting the marginal sums without the zeros. Margin-based methods fail to overcome the bias related to truncation of the matrix. The objective of the present study was to develop and test a matrix-based method for estimating the total number of usability problems.MethodsThe matrix-based model was based on the full discovery matrix (including unobserved columns) and not solely on a summary of the data (e.g. the margins). This model also circumvents a drawback of margin-based methods by simultaneously estimating the model’s parameters and the total number of problems. Furthermore, the matrix-based method takes account of a heterogeneous probability of detection, which reflects a real-life setting. As suggested in the usability literature, we assumed that the probability of detection had a logit-normal distribution.ResultsWe assessed the matrix-based method’s performance in a range of settings reflecting real-life usability testing and with heterogeneous probabilities of problem detection. In our simulations, the matrix-based method improved the estimation of the number of problems (in terms of bias, consistency, and coverage probability) in a wide range of settings. We also applied our method to five real datasets from usability testing.ConclusionsEstimation models (and particularly matrix-based models) are of value in estimating and monitoring the detection process during usability testing. Matrix-based models have a solid mathematical grounding and, with a view to facilitating the decision-making process for both regulators and device manufacturers, should be incorporated into current standards.

On Polyatomic Tomography over Abelian Groups: Some Remarks on Consistency, Tree Packings and Complexity

The paper deals with an inverse problem of reconstructing matrices from their marginal sums. More precisely, we are interested in the existence of rtimes s matrices for which only the following information is available: The entries belong to known subsets of c distinguishable abelian groups, and the row and column sums of all entries from each group are given. This generalizes Ryser’s classical problem of characterizing the set of all 0–1-matrices with given row and column sums and is a basic problem in (polyatomic) discrete tomography. We show that the problem is closely related to packings of trees in bipartite graphs, prove consistency results, give algorithms and determine its complexity. In particular, we find a somewhat unusual complexity behavior: the problem is hard for “small” but easy for “large” matrices.

Factoring a 2 x 2 contingency table.

We show that a two-component proportional representation provides the necessary framework to account for the properties of a 2 × 2 contingency table. This corresponds to the factorization of the table as a product of proportion and diagonal row or column sum matrices. The row and column sum invariant measures for proportional variation are obtained. Geometrically, these correspond to displacements of two point vectors in the standard one-simplex, which are reduced to a center-of-mass coordinate representation, . Then, effect size measures, such as the odds ratio and relative risk, correspond to different perspective functions for the mapping of (δ, μ) to . Furthermore, variations in δ and μ will be associated with different cost-benefit trade-offs for a given application. Therefore, pure mathematics alone does not provide the specification of a general form for the perspective function. This implies that the question of the merits of the odds ratio versus relative risk cannot be resolved in a general way. Expressions are obtained for the marginal sum dependence and the relations between various effect size measures, including the simple matching coefficient, odds ratio, relative risk, Yule’s Q, ϕ, and Goodman and Kruskal’s τc|r. We also show that Gini information gain (IGG) is equivalent to ϕ2 in the classification and regression tree (CART) algorithm. Then, IGG can yield misleading results due to the dependence on marginal sums. Monte Carlo methods facilitate the detailed specification of stochastic effects in the data acquisition process and provide a practical way to estimate the confidence interval for an effect size.

Algorithmic Matching Attacks on Optimally Suppressed Tabular Data

The objective of the cell suppression problem (CSP) is to protect sensitive cell values in tabular data under the presence of linear relations concerning marginal sums. Previous algorithms for solving CSPs ensure that every sensitive cell has enough uncertainty on its values based on the interval width of all possible values. However, we find that every deterministic CSP algorithm is vulnerable to an adversary who possesses the knowledge of that algorithm. We devise a matching attack scheme that narrows down the ranges of sensitive cell values by matching the suppression pattern of an original table with that of each candidate table. Our experiments show that actual ranges of sensitive cell values are significantly narrower than those assumed by the previous CSP algorithms.

Support Vector Machine-Based Transmit Antenna Allocation for Multiuser Communication Systems.

In this paper, a support vector machine (SVM) technique has been applied to an antenna allocation system with multiple antennas in multiuser downlink communications. Here, only the channel magnitude information is available at the transmitter. Thus, a subset of transmit antennas that can reduce multiuser interference is selected based on such partial channel state information to support multiple users. For training, we generate the feature vectors by fully utilizing the characteristics of the interference-limited setup in the multiuser downlink system and determine the corresponding class label by evaluating a key performance indicator, i.e., sum rate in multiuser communications. Using test channels, we evaluate the performance of our antenna allocation system invoking the SVM-based allocation and optimization-based allocation, in terms of sum-rate performance and computational complexity. Rigorous testing allowed for a comparison of a SVM algorithm design between one-vs-one (OVO) and one-vs-all (OVA) strategies and a kernel function: (i) OVA is preferable to OVO since OVA can achieve almost the same sum rate as OVO with significantly reduced computational complexity, (ii) a Gaussian function is a good choice as the kernel function for the SVM, and (iii) the variance (kernel scale) and penalty parameter (box constraint) of an SVM kernel function are determined by 21.56 and 7.67, respectively. Further simulation results revealed that the designed SVM-based approach can remarkably reduce the time complexity compared to a traditional optimization-based approach, at the cost of marginal sum rate degradation. Our proposed framework offers some important insights for intelligently combining machine learning techniques and multiuser wireless communications.

Joint Indirect Standardization When Only Marginal Distributions are Observed in the Index Population

ABSTRACT It is a common interest in medicine to determine whether a hospital meets a benchmark created from an aggregate reference population, after accounting for differences in distributions of multiple covariates. Due to the difficulties of collecting individual-level data, however, it is often the case that only marginal distributions of the covariates are available, making covariate-adjusted comparison challenging. We propose and evaluate a novel approach for conducting indirect standardization when only marginal covariate distributions of the studied hospital are known, but complete information is available for the reference hospitals. We do this with the aid of two existing methods: iterative proportional fit, which estimates the cells of a contingency table when only marginal sums are known, and synthetic control methods, which create a counterfactual control group using a weighted combination of potential control groups. The proper application of these existing methods for indirect standardization would require accounting for the statistical uncertainties induced by a situation where no individual-level data are collected from the studied population. We address this need with a novel method which uses a random Dirichlet parameterization of the synthetic control weights to estimate uncertainty intervals for the standard incidence ratio. We demonstrate our novel methods by estimating hospital-level standardized incidence ratios for comparing the adjusted probability of computed tomography examinations with high radiations doses, relative to a reference standard and we evaluate out methods in a simulation study. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

A Family of Heuristic-Based Inequalities for Maximizing Overall Safety Margins in Aircraft Parking Stands Arrangement Problems

We consider the problem of arranging a set of aircraft in a maintenance hangar operated by an independent aircraft service provider. The overall safety margins of the parking layout need to be maximized within the limited available space, measured by the weighted sum of the individual discrete safety margins of each aircraft. A mixed-integer linear programming model is developed, and the positions of the aircraft are determined by the position-controlling binary variables associated with a set of revised No-Fit Polygons (NFPs). Due to the nonconvex irregular shape of aircraft, the model involves a great number of binary variables associated with the revised NFP. The default branch-and-bound algorithm is inefficient in solving such a model as the infeasibility information of the precedent visited solution cannot be directly utilized by the default method to update the bounds. A heuristic algorithm is developed to provide practical solutions, and the intermediate infeasible solutions identified during searching are utilized to develop valid and approximate inequalities, tightening the optimality gap. The computational results demonstrate that the addition of inequalities improves the computational efficiency in solving a wide range of instances and in tightening the optimality gap while the stopping criterion is met.

Non-Orthogonal Multiple Access for Cooperative Communications: Challenges, Opportunities, and Trends

NOMA is a promising radio access technique for next-generation wireless networks. In this article, we investigate the NOMA-based cooperative relay network. We begin with an introduction of the existing relay-assisted NOMA systems by classifying them into three categories: uplink, downlink, and composite architectures. Then we discuss their principles and key features, and provide a comprehensive comparison from the perspective of spectral efficiency, energy efficiency, and total transmit power. A novel strategy called hybrid power allocation is further discussed for the composite architecture, which can reduce the computational complexity and signaling overhead at the expense of marginal sum rate degradation. Finally, major challenges, opportunities, and future research trends for the design of NOMA-based cooperative relay systems with other techniques are also highlighted to provide insights for researchers in this field.

Pfaffian Equations and Contiguity Relations of the Hypergeometric Function of Type (<i>k</i>+1, <i>k</i>+<i>n</i>+2) and Their Applications

We study the structures of Pfaffian equations and contiguity relations of the hypergeometric function of type $(k+1,k+n+2)$ by using twisted cohomology groups and the intersection form on them. We apply our results to algebraic statistics; numerical evaluation of the normalizing constants of two way contingency tables with fixed marginal sums.

With our powers combined: integrating behavioral and genetic data to estimate mating success and sexual selection

The analysis of sexual selection classically relies on the regression of individual phenotypes against the marginal sums of a males × females matrix of pairwise reproductive success, assessed by genetic parentage analysis. When the matrix is binarized, the marginal sums give the individual mating success. Because such analysis treats male and female mating/reproductive success independently, it ignores that the success of a male × female sexual interaction can be attributable to the phenotype of both individuals. Also, because it is based on genetic data only, it is oblivious to unproductive matings, which may be documented by behavioral observations. To solve these problems, we propose a statistical approach which combines matrices of offspring numbers and behavioral observations. It models reproduction on each mating occasion of a mating season as three stochastic and interdependent pairwise processes, each potentially affected by the phenotype of both individuals and by random individual effect: visit of a female by a male, concomitant gamete emission, and offspring production. Applied to data from a mating experiment on brown trout, the model yielded different results from the classical regression analysis, with only a negative effect of female body size on the probability of visit and gamete release, while the classical approach based on regression found a positive effect of male size on the number of both visits and offspring, and no effect of female size. Because the general structure of the model can be adapted to other partitioning schemes of the reproductive process, it can be used for a variety of biological systems where behavioral and genetic data are available.

Partition structure and the $A$-hypergeometric distribution associated with the rational normal curve

A distribution whose normalization constant is an A-hypergeometric polynomial is called an A-hypergeometric distribution. Such a distribution is in turn a generalization of the generalized hypergeometric distribution on the contingency tables with fixed marginal sums. In this paper, we will see that an A-hypergeometric distribution with a homogeneous matrix of two rows, especially, that associated with the rational normal curve, appears in inferences involving exchangeable partition structures. An exact sampling algorithm is presented for the general (any number of rows) A-hypergeometric distributions. Then, the maximum likelihood estimation of the A-hypergeometric distribution associated with the rational normal curve, which is an algebraic exponential family, is discussed. The information geometry of the Newton polytope is useful for analyzing the full and the curved exponential family. Algebraic methods are provided for evaluating the A-hypergeometric polynomials.

Species‐occupancy distribution removes an excessive parameter from species‐area relationship

AbstractAimAlthough species‐occupancy distributions (SODs) and species‐area relationships (SARs) arise from the two marginal sums of the same presence/absence matrices, the two biodiversity patterns are usually explored independently. Here, we aim to unify the two patterns for isolate‐based data by constraining the SAR to conserve information from the SOD.LocationWidespread.MethodsFocusing on the power‐model SAR, we first developed a constrained form that conserved the total number of occupancies from the SOD. Next, we developed an additive‐constrained SAR that conserves the entire shape of the SOD within the power‐model SAR function, using a single parameter (the slope of the endemics‐area relationship). We then relate this additive‐constrained SAR to multiple‐sites similarity measures, based on a probabilistic view of Sørensen similarity. We extend the constrained and additive‐constrained SAR framework to 23 published SAR functions. We compare the fit of the original and constrained forms of 12 SAR functions using 154 published data sets, covering various spatial scales, taxa and systems.Main conclusionsIn all 23 SAR functions, the constrained form had one parameter less than the original form. In all 154 data sets the model with the highest weight based on the corrected Akaike's information criteria (wAICc) had a constrained form. The constrained form received higher wAICc than the original form in 98.79% of valid pairwise cases, approaching the wAICc expected under identical log‐likelihood. Our work suggests, both theoretically and empirically, that all SAR functions may have one unnecessary parameter, which can be excluded from the function without reduction in goodness‐of‐fit. The more parsimonious constrained forms are also easier to interpret as they reflect the probability of a randomly chosen occupancy to be found in an isolate. The additive‐constrained SARs accounts for two complimentary turn‐over components of occupancies: turnover between species and turnover between sites.

Binary contingency table method for analysing gene mutation in cancer genome

Somatic mutations are considered to initiate several disorders such as cancer and neurological disease. Hence, a number of computational methods have been developed to find loci subject to frequent mutations in cancer cells. Since normal cells turn into cancer cells through the accumulation of gene mutations, the elucidation of interactive relationships among loci has great potential to reveal the cause of cancer progression; however, only a few methods have been proposed for measuring statistical significance of pairs of loci that are co-mutated or exclusively mutated. In this study, we proposed a novel statistical method to find such significantly interactive pairs of loci by employing the framework of binary contingency tables. Using Markov chain Monte Carlo procedure, the statistical significance is evaluated by sampling null matrices whose marginal sums are equal to those of the input matrix. We applied the proposed method to mutation data of colon cancer patients and successfully obtained significant pairs of loci.

Multiple Ordinal Regression by Maximizing the Sum of Margins.

Human preferences are usually measured using ordinal variables. A system whose goal is to estimate the preferences of humans and their underlying decision mechanisms requires to learn the ordering of any given sample set. We consider the solution of this ordinal regression problem using a support vector machine algorithm. Specifically, the goal is to learn a set of classifiers with common direction vectors and different biases correctly separating the ordered classes. Current algorithms are either required to solve a quadratic optimization problem, which is computationally expensive, or based on maximizing the minimum margin (i.e., a fixed-margin strategy) between a set of hyperplanes, which biases the solution to the closest margin. Another drawback of these strategies is that they are limited to order the classes using a single ranking variable (e.g., perceived length). In this paper, we define a multiple ordinal regression algorithm based on maximizing the sum of the margins between every consecutive class with respect to one or more rankings (e.g., perceived length and weight). We provide derivations of an efficient, easy-to-implement iterative solution using a sequential minimal optimization procedure. We demonstrate the accuracy of our solutions in several data sets. In addition, we provide a key application of our algorithms in estimating human subjects' ordinal classification of attribute associations to object categories. We show that these ordinal associations perform better than the binary one typically employed in the literature.

Population Synthesis in Activity-Based Models

Activity-based travel demand modeling requires socioeconomic micro-data of the population under study. Because the acquisition of such data for the entire population is infeasible or highly expensive, techniques such as iterative proportional fitting (IPF) have been applied extensively to estimate such data for the population, synthetically. Despite its many advantages, IPF results in noninteger values instead of integers: fractions of households or individuals are obtained for zones. Although methods have been proposed to produce integers for noninteger tables, seldom has this problem been viewed as tabular rounding. This paper proposes a binary linear programming model for tabular rounding in which the integer-converted table totals and marginal sums perfectly fit the input data obtained from the Census Bureau. Furthermore, the model minimizes distortion to the correlation structure of the household- and individual-level noninteger tables. The model does not bias the joint or marginal distributions of the socioeconomic attributes of population units or the sampling of rare demographic groups (at a significance level of a = .05). The empirical comparison of the proposed method with eight existing methods demonstrates that the proposed model outperforms the tested methods. Sensitivity analysis demonstrates that the integer conversion of small values is as significant as it is for large values. In this study, deterministic methods outperform stochastic methods in accuracy and perfect fit to census data. Finally, a scoring and ranking tool is used to reflect concisely the advantages and disadvantages of these methods.