Discrete Data Research Articles

Generalized Lipschitz Tracing of Implicit Surfaces

AbstractWe present a versatile and robust framework to render implicit surfaces defined by black‐box functions that only provide function value queries. We assume that the input function is locally Lipschitz continuous; however, we presume no prior knowledge of its Lipschitz constants. Our pre‐processing step generates a discrete acceleration structure, a Lipschitz field, that provides data to infer local and directional Lipschitz upper bounds. These bounds are used to compute safe step sizes along rays during rendering. The Lipschitz field is constructed by generating local polynomial approximations to the input function, then bounding the derivatives of the approximating polynomials. The accuracy of the approximation is controlled by the polynomial degree and the granularity of the spatial resolution used during fitting, which is independent from the resolution of the Lipschitz field. We demonstrate that our process can be implemented in a massively parallel way, enabling straightforward integration into interactive and real‐time modelling workflows. Since the construction only requires function value evaluations, the input surface may be represented either procedurally or as an arbitrarily filtered grid of function samples. We query the original implicit representation upon ray trace, as such, we preserve the geometric and topological details of the input as long as the Lipschitz field supplies conservative estimates. We demonstrate our method on both procedural and discrete implicit surfaces and compare its exact and approximate variants.

Information-Theoretic Modeling of Categorical Spatiotemporal GIS Data.

An information-theoretic data mining method is employed to analyze categorical spatiotemporal Geographic Information System land use data. Reconstructability Analysis (RA) is a maximum-entropy-based data modeling methodology that works exclusively with discrete data such as those in the National Land Cover Database (NLCD). The NLCD is organized into a spatial (raster) grid and data are available in a consistent format for every five years from 2001 to 2021. An NLCD tool reports how much change occurred for each category of land use; for the study area examined, the most dynamic class is Evergreen Forest (EFO), so the presence or absence of EFO in 2021 was chosen as the dependent variable that our data modeling attempts to predict. RA predicts the outcome with approximately 80% accuracy using a sparse set of cells from a spacetime data cube consisting of neighboring lagged-time cells. When the predicting cells are all Shrubs and Grasses, there is a high probability for a 2021 state of EFO, while when the predicting cells are all EFO, there is a high probability that the 2021 state will not be EFO. These findings are interpreted as detecting forest clear-cut cycles that show up in the data and explain why this class is so dynamic. This study introduces a new approach to analyzing GIS categorical data and expands the range of applications that this entropy-based methodology can successfully model.

Discrete versus polymeric structures of coordination compounds of copper(II) with (pyridin-2-yl)methylenenicotinohydrazide and a library of dicarboxylic acids

A series of copper(II) discrete and polymeric coordination compounds, namely [{CuL(H2O)}2(fum)] (1), [{CuL(H2O)}2(mes)] (2), [Cu2L2(glu)]n·2n(H2O) (3·2n(H2O)) and [Cu3L2(adi)2]n (4) were fabricated from (pyridin-2-yl)methylenenicotinohydrazide (HL) and a library of dicarboxylic acids, namely fumaric acid (H2fum), mesaconic acid (H2mes), glutaric acid (H2glu) and adipic acid (H2adi), using evaporative crystallization, grinding and slurry synthesis methods. The obtained coordination compounds have been fully characterized by single crystal X-ray diffraction revealing different types of complexes depending on the linker length, viz. from dinuclear complexes for the shorter linkers (fumaric and mesaconic acids) to 1D and 2D coordination polymers for longer glutaric and adipic acids. Thermal stability and spectroscopic features (FTIR and diffuse reflectance) of complexes were also studied. For the nonpolymeric compounds 1 and 2, the supramolecular assemblies driven by a combination of antiparallel π-stacking and hydrogen bonding interactions have been studied and compared using DFT calculations, MEP surface analysis and a combination of QTAIM and NCIplot computational tools.

Integrating discrete event simulation and data envelopment analysis for system performance and efficiency evaluation

ABSTRACT Healthcare facilities, particularly outpatient clinics, are crucial for local communities’ medical needs. To enhance their performance, these facilities need to optimize their operations. Key system performance metrics, such as patient throughput, waiting times and cycle times, can quantitatively be measured using discrete event simulation (DES). DES replicates facility structures and behaviours, offering a valuable platform for assessing the configuration effects of resources on system performance. However, current DES tools cannot identify the best resource configurations for future performance improvement. To address this issue, this paper develops a DES model for an outpatient clinic and improves its performance through data envelopment analysis (DEA). The case study involves a clinic in Northern Malaysia, where relevant data were observed and collected. The analysed data were then input into the DES model. The model measured the clinic’s current performance and assessed the impact of its resource configurations. 37 different resource configurations were tested, and their relative efficiencies were evaluated using DEA. The analysis revealed room for improvement in resource allocation.

Performance of surface structures in enhancing heat transfer rates of miniaturized pulsating heat pipe

Enhancement of the thermal performance by modifying the evaporator surface of a miniaturized pulsating heat pipe (PHP) is the primary target of the present work. Four PHPs having different evaporator surface types i.e., smooth, dimple cavity array, tunnel cavity, and rectangular cavity array were investigated numerically to compare the gas-liquid interfacial behavior and evaluate the role of bubble nucleation, slug-plug movement, and drop-film condensation on the thermal performance. Detailed modeling of evaporating and condensing interfaces shows that activation of nucleation sites at all defined discrete structures and undisturbed liquid flow path at the evaporator promote heat transfer rate. Through thermo fluidic analysis around different surface structures, evaporation dynamics is analyzed to understand the suitability of a structure type for enhancement of heat transfer. Associated slug-plug motion through the adiabatic zone and processes at the condenser have been also discussed to propose the characteristics of an ideal enhanced PHP. The capacity to transfer heat has been also characterized using thermal resistance for different structured PHPs which may be a guiding factor for the design of heat sinks for thermal applications.

Dynamic analysis and shape sensing of pipes subjected to water hammer by the inverse finite element method

Pipe structures are commonly employed in modern industries. However, the transient pressure induced by water hammer leads to a high risk of structural damage, highlighting the importance of Structural Health Monitoring (SHM). The inverse Finite Element Method (iFEM) offers a way to reverse structural deformations based on a set of discrete strain data. In this paper, the water hammer phenomenon in a Reservoir-Pipe-Valve (RPV) system is investigated. The element iQS4 is adopted to reconstruct dynamic deformations for the pipe using iFEM. The water hammer resulting from an instantaneous closure of the valve can generate significant fluid pressure, leading to severe pipe vibrations. The vibration deformations can be monitored by iFEM. The maximum error of the pipe nodal displacement is below 3 % and the average error is below 2 % in the proposed several sensor location cases, even the mesh of iFEM is coarser than the FE model. Among the sparse sensor location cases, the X path which is suitable for Fiber Bragg Grating (FBG) sensors has the highest accuracy of the displacement reconstruction. The results reveal a promising prospect in the real-time monitoring based on iFEM for pipes.

Impact of reinfection on dynamics of epidemic model with discrete two-state structure

Impact of reinfection on dynamics of epidemic model with discrete two-state structure

An effective drift-diffusion model for pandemic propagation and uncertainty prediction

Predicting pandemic evolution involves complex modeling challenges, typically involving detailed discrete mathematics executed on large volumes of epidemiological data. Making them physics based provides added intuition as well as predictive value. Differential equations have the advantage of offering smooth, well-behaved solutions that try to capture overall predictive trends and averages. In this paper, the canonical susceptible-infected-recovered model is simplified, in the process generating quasi-analytical solutions and fitting functions that agree well with the numerics, as well as infection data across multiple countries. The equations provide an elegant way to visualize the evolution of the pandemic spread, by drawing equivalents with the similar dynamics of a particle, whose location over time represents the growing fraction of the population that is infected. This particle slides down a potential whose shape is set by model epidemiological parameters such as reproduction rate. Potential sources of errors and their growth over time are identified, and the uncertainties are mapped into a diffusive jitter that tends to push the particle away from its minimum. The combined physical understanding and analytical expressions offered by such an intuitive drift-diffusion model sets the foundation for their eventual extension to a multi-patch model while offering practical error bounds and could thus be useful in making policy decisions going forward.

Plant-Driven Assembly of Disease-Suppressive Soil Microbiomes

Plants have coevolved together with the microbes that surround them and this assemblage of host and microbes functions as a discrete ecological unit called a holobiont. This review outlines plant-driven assembly of disease-suppressive microbiomes. Plants are colonized by microbes from seed, soil, and air but selectively shape the microbiome with root exudates, creating microenvironment hot spots where microbes thrive. Using plant immunity for gatekeeping and surveillance, host-plant genetic properties govern microbiome assembly and can confer adaptive advantages to the holobiont. These advantages manifest in disease-suppressive soils, where buildup of specific microbes inhibits the causal agent of disease, that typically develop after an initial disease outbreak. Based on disease-suppressive soils such as take-all decline, we developed a conceptual model of how plants in response to pathogen attack cry for help and recruit plant-protective microbes that confer increased resistance. Thereby, plants create a soilborne legacy that protects subsequent generations and forms disease-suppressive soils.

Three-Layer Artificial Neural Network for Pricing Multi-Asset European Option

This paper studies an artificial neural network (ANN) for multi-asset European options. Firstly, a simple three-layer ANN-3 is established with undetermined weights and bias. Secondly, the time–space discrete PDE of the multi-asset option is given and the corresponding discrete data are fed into the ANN-3. Then, using least squares error as the objective function, the weights and bias of ANN-3 are trained well. Numerical examples are carried out to confirm the stability, accuracy and efficiency. Experiments show the ANN’s relative error is about 0.8%. This method can be extended into multi-layer ANN-q(q>3) and extended into American options.

Triatomine (Hemiptera: Reduviidae) populations and Trypanosoma cruzi genotyping in peridomestic and sylvatic environments in the semiarid region of Sergipe, Northeastern, Brazil

We assessed the diversity of triatomines, the rates of natural infection, and the discrete typing units (DTUs) of Trypanosoma cruzi isolated from them in two municipalities in the state of Sergipe, Brazil. Active searches for triatomines were conducted in the peridomicily and wild enviroments of 10 villages within the two municipalities. Triatomines were taxonomically identified and their feces were extracted using the abdominal compression method. Parasite detection was performed using optical microscopy. For Trypanosoma cruzi genotyping via PCR-FFLB, 151 samples of the subspecies Triatoma brasiliensis macromelasoma and Triatoma brasiliensis were isolated from both municipalities. In total, 505 triatomines were collected, with Triatoma brasiliensis macromelasoma being the most frequent species (58.81 %). Triatoma b. brasiliensis was the only species in both peridomestic and wild environments. Regarding the other species, T. pseudomaculata was found only in the peridomestic environment; and T. b. macromelasoma and Psammolestes tertius were found in the wild environment. Three Discrete Typing Units were identified: TcI (87.51 %) detected in T. b. brasiliensis and T. b. macromelasoma, TcI+TcIII (10.41 %) in T. b. macromelasoma, and TcI+Trypanosoma rangeli (2.08 %) in T. b. macromelasoma. It is concluded that T. b. macromelasoma is the species collected most frequently in the studied region and the one that presents the highest rates of natural infection, highlighting its epidemiological importance for the vectorial transmission of Chagas disease in Sergipe.

Intelligent Method for Mutation of Input Cases with Feedback

Relevance. Fuzzing is one of the effective ways to improve the software reliability and is included in the mandatory list of research carried out at the stage of qualification testing according to national standard GOST R 56939-2016. The use of standard mutators reduces the fuzzing process to brute force, which negatively affects the time of incorrect program behavior detection. In this regard, it is important to rationalize the selection of input data, which takes into account the data corpus specifics, as well as the context describing the software response under test and allowing to determine the mutations at the next iteration of testing. Purpose of the research is to increase the efficiency of fuzzing by intellectualizing the standard mutator using neural networks, which takes into account the syntactic and semantic features of the input corpus and uses program feedback.Methods. The methods of analysis and synthesis, theory of algorithms, discrete and computational mathematics, machine learning were used.Result. The advantages and disadvantages of the standard module for AFL fuzzer’s input corpus mutation are considered. The justification of neural network choice with LSTM-architecture as a mechanism that realizes the intelligent control of input corpora’s’ generation and transformation is given. The proposed mutation method is described, which implies the integration of decision making mechanism on the amount and format of necessary mutations to increase the code coverage into the standard mutator, as well as the subsequent refinement of input data by shell-code to check the operability of the fragment that caused abnormal software’s behavior. The scheme of the mutation module is presented, which includes a component of input corporas conversion for generation of program execution traces and a component aimed at concept confirmation and re-call of abnormal software behavior using the generated shell-code.Novelty. Unlike the known ones, the proposed method uses feedback, fixing the software reaction, when forming the data mutation strategy, which determines the scientific novelty of the obtained results.Significance. The proposed solution allows reducing the program testing time while maintaining the code coverage. The results obtained in the research are universal and, in the future, can be used in white, black and gray box fuzzing methods.

Envy-Free Division of Multilayered Cakes

Dividing a multilayered cake under nonoverlapping constraints captures several scenarios (e.g., allocating multiple facilities over time where each agent can utilize at most one facility simultaneously). We establish the existence of an envy-free multidivision that is nonoverlapping and contiguous within each layer when the number of agents is a prime power, solving partially an open question by Hosseini et al. [Hosseini H, Igarashi A, Searns A (2020) Fair division of time: Multi-layered cake cutting. Proc. 29th Internat. Joint Conf. Artificial Intelligence (IJCAI), 182–188; Hosseini H, Igarashi A, Searns A (2020) Fair division of time: Multi-layered cake cutting. Preprint, submitted April 28, http://arxiv.org/abs/2004.13397 ]. Our approach follows an idea proposed by Jojić et al. [Jojić D, Panina G, Živaljević R (2021) Splitting necklaces, with constraints. SIAM J. Discrete Math. 35(2):1268–1286] for envy-free divisions, relying on a general fixed-point theorem. We further design a fully polynomial-time approximation scheme for the two-layer, three-agent case, with monotone preferences. All results are actually established for divisions among groups of almost the same size. In the one-layer, three-group case, our algorithm is able to deal with any predetermined sizes, still with monotone preferences. For three groups, this provides an algorithmic version of a recent theorem by Segal-Halevi and Suksompong [Segal-Halevi E, Suksompong W (2021) How to cut a cake fairly: A generalization to groups. Amer. Math. Monthly 128(1):79–83]. Funding: This work was partially supported by the Japan Science and Technology Agency [Grant JPMJPR20C], Fusion Oriented REsearch for disruptive Science and Technology [Grant JPMJFR226O], and Exploratory Research for Advanced Technology [Grant JPMJER2301].

Multi-modal fusion deep learning model for excavated soil heterogeneous data with efficient classification

Multimodal fusion, a cutting-edge method aiming to integrate heterogeneous data for prediction tasks, has received limited attention in geotechnical engineering. This study focuses on classifying excavated soils with large quantities rapidly and finely. By using an excavated soil information collecting system at the largest soil transferring platform in China, 3,243 groups of multi-source heterogenous data were created, including soil images, spatial series data of cone index curves, time series data of TDR waveforms, discrete net weight data, and textual descriptions of soil morphology. After data augmentation, a big dataset containing 23,122 sets with labels based on the Unified Soil Classification System, moisture content, and mineral composition was created. Multimodal deep learning models were trained using different fusion strategies: 7 early fusion, 3 intermediate fusion, and 2 late fusion cases. Performance metrics were evaluated, including loss, accuracy, F1 Score, precision, recall, specificity, NPV, FPR, and AUROC. Results showed that intermediate fusions performed best, while late fusions performed the poorest. The two-stage intermediate fusion with five modalities achieved the best results, achieving an accuracy above 0.99 on the test set. This multimodal fusion approach effectively explores the correlation between multi-source heterogeneous data of soils, leading to scientific and engineering value in geotechnics.

Discrete Mathematics in Dynamic Network Analysis: Long-Term Efficacy Evaluation of Fotona Laser Therapy for Overactive Bladder Syndrome Using Clustering-Based Patient Subgroup Identification.

Dynamic network analysis, a state-of-the-art application of discrete mathematics, offers unprecedented insight into complex, time-evolving clinical data. This technical report demonstrates the value of evaluating the long-term efficacy of Fotona laser therapy (Fotona d.o.o., Ljubljana, Slovenia) in overactive bladder (OAB) syndrome. We analyzed data from 101 female patients aged ≥60 years who underwent Fotona laser treatment, including Vaginal Erbium Laser (VEL) and Urethral Erbium Laser (UEL), between 2020 and 2022. OAB symptom scores (OABSS) were collected at baseline (T0) and at six, 12, 18, and 24 months post treatment. Network graphs were constructed, representing patients as nodes, and symptom similarities as edges. Clustering techniques identify patient subgroups, whereas principal component analysis reduces dimensionality. The dynamic evolution of patient clusters was visualized through changes in average degree centrality over time. This approach revealed three distinct patient clusters with unique treatment response patterns. The results showed a progressive reduction in OABSS, with the total score decreasing by 2.82 ± 3.03 at 24 months. Our method provides novel visualization and analysis of complex longitudinal clinical data, offering insights into personalized treatment strategies for OAB. This report presents one of the first applications of discrete mathematics and dynamic network analysis to evaluate the long-term outcomes of Fotona laser therapy for OAB and introduces an innovative perspective for clinical decision-making in urogynecology.

Transdisciplinary approach as a resource for the development of critical thinking in higher mathematical education

Introduction. In a modern digital and globalized society, the higher education system is faced with the task of developing critical thinking skills in graduates that allow them to solve complex problems through the integration of knowledge from various disciplines at a new transdisciplinary level of knowledge. Such integration seems possible based on the use of modeling methodology, methods of computational and discrete mathematics, and mathematical cybernetics, which form the foundation of the language of information technology and processes. The purpose of the study is to identify the role of the transdisciplinary approach in the development of students’ critical thinking through mathematics. Materials and methods. 76 students of the Vyatka State University majoring in 06.03.01 Biology took part in the study, covering 2022–2023. The main methods for measuring critical thinking, presented by the UF/EMI Critical Thinking Disposition Instrument and The Critical Thinking Barriers Scale (CTBS), were supplemented with diagnostic tools from specially designed tasks, taking into account specifics of teaching mathematics to future biotechnologists. Statistical analysis of the obtained results was performed using the Mann-Whitney U test. Results. A number of methodological conditions have been formulated to ensure the development of students' critical thinking in the process of teaching mathematics, which corresponds to the priority goals of modern higher education. The expediency of using contextual mathematical problems containing a real data set, the method of mathematical modeling, the inclusion of modern mathematical theories and their applications in the teaching content, a joint form of work in the classroom and work with scientific articles is substantiated. A quantitative analysis of the results confirmed the significance of the differences (Uemp = 65 < Ucr = 66; р < 0,01), which indicates the effectiveness of the intervention based on the proposed methodological conditions. Conclusion. The practical significance of the study is determined by the possibilities of using its results in improving the critical thinking skills of students in the process of teaching mathematics.

Generalized poisson regression for over-dispersed longitudinal count data

Abstract Longitudinal count data is a common type of discrete data in fields like medicine and social sciences. The Poisson regression model is an important method for analysing count data, and the standard Poisson regression model requires that the mean and variance of discrete count data are equal. However, longitudinal count data are often over-dispersed in practice, i.e., the variance of the data is greater than the mean. Besides, the degree of dispersion between the mean and variance of longitudinal count data varies over time. A generalized Poisson regression model based on joint modeling of the mean and dispersion parameters of over-dispersed longitudinal count data is proposed, which simultaneously describes the trajectories of longitudinal mean and dispersion parameters over time and explains how they are dependent on other covariates. The simulation results and real data analysis illustrate the accuracy and effectiveness of the proposed method.

Bayesian joint modeling of high-dimensional discrete multivariate longitudinal data using generalized linear mixed models

Bayesian joint modeling of high-dimensional discrete multivariate longitudinal data using generalized linear mixed models

Gravity dam displacement monitoring using in situ strain and deep learning

AbstractRecent studies in dam displacement monitoring primarily focus on single‐response monitoring or model updating using advanced techniques. Few studies involve the combination analysis of displacement with other synchronized responses utilizing their monitoring characteristics. In situ strain data provide a strength‐safety perspective for dam displacement monitoring. The challenge lies in that estimating displacement directly using limited discrete strain data may be misleading. This paper analyzes the relationship between displacement and global, and multipoint local strains from the perspective of the differences in load effects of gravity dams, and indicates that introducing appropriate state factors improves the estimation. A displacement estimation model driven by strain data and state factors is developed using stacked convolutional neural network, and the variable relationships within the model are interpretated via accumulated local effects. Incorporating specific strength criteria, a novel displacement monitoring indicator based on the tensile safety of the dam heel is proposed. A case study of a gravity dam showcases the effectiveness of the proposed approach in comparison with the solely strain‐based model and the traditional hydrostatic‐seasonal‐time factors‐based model.

O58 CONTINUOUS MEASUREMENT OF BLOOD PRESSURE DURING NIGHT - INSIGHTS INTO THE GENESIS OF THE NOCTURNAL BLOOD PRESSURE FLUCTUATIONS

Background and Objective: Nighttime blood pressure (BP) is a strongly predictive marker for overall cardiovascular risk. Traditional cuff-based BP measurements methods provide only discrete BP data. Short-term BP fluctuations are not detectable with such methods. Therefore, we applied two independent and continuously measuring methods with the aim to characterize systolic nocturnal blood pressure fluctuations (NBPF) related to sleep apnoea or periodic leg movements (PLM). Methods: BP fluctuations were analysed in patients with suspected sleep disturbances. The Portapres™ device (Penaz method) and a system based on the measurement of the pulse transit time (SOMNOscreen®) were used to measure the BP in addition to a polysomnography performed under the conditions of a clinical sleep laboratory. The calculation of the BP by the SOMNOscreen® was performed using a BP-pulse wave velocity (PWV) transfer function. Results: We saw BP fluctuations which occurred in connection with obstructive apnoeic events as well as in connection with PLM. Both methods recorded the same apnoea related NBPF. The amplitudes of these NBPF accounted for 24.7 mmHg and 22.8 mmHg (Portapres™ and SOMNOscreen®, respectively, 11 patients, number of events: n=695). PLM related PB fluctuations (in 5 of 11 patients, n=317) amounted to 18.4 mmHg (Portapres™ and 16.9 mmHg (SOMNOscreen®). Most of the patients did not show BP dipping when comparing awake with sleep time periods and they had a moderate to severe apnoea/hypopnoea index. Conclusions: The study demonstrates a strong relation between apnoeic events/PLM and NPBF. The NBPF were similarly detected by two different BP measuring methods suggesting that the more indirect method of BP determination using the PWV provides a reliable measurement of NBPF. The results suggest that OSA and PLM related NBPF strongly contribute to non- or reverse dipping of patients with these sleep disorders.