Continuous Set Research Articles

Parametric dependence between random vectors via copula-based divergence measures

This article proposes copula-based dependence quantification between multiple groups of random variables of possibly different sizes via the family of Φ-divergences. An axiomatic framework for this purpose is provided, after which we focus on the absolutely continuous setting assuming copula densities exist. We consider parametric and semi-parametric frameworks, discuss estimation procedures, and report on asymptotic properties of the proposed estimators. In particular, we first concentrate on a Gaussian copula approach yielding explicit and attractive dependence coefficients for specific choices of Φ, which are more amenable for estimation. Next, general parametric copula families are considered, with special attention to nested Archimedean copulas, being a natural choice for dependence modelling of random vectors. The results are illustrated by means of examples. Simulations and a real-world application on financial data are provided as well.

MSD: Continuous Pharmaceutical Manufacturing Data for the 2024 MSOM Data-Driven Research Challenge

To support the 2024 MSOM Data-Driven Research Challenge, Merck & Co., Inc., Rahway, New Jersey (hereafter “MSD”), provides pharmaceutical manufacturing data from a continuous tablet production setting. The data set contains approximately 300 million data points related to around 75 process parameters monitored over 120 hours. In this paper, we present the data set and share our vision to inspire and facilitate new applications of operations management (OM) methodologies in pharmaceutical manufacturing. We begin with an introduction to pharmaceutical manufacturing for OM researchers and then elaborate on emerging technologies, common industry challenges, and research opportunities. We explain the data set and propose a roadmap for future research directions. Researchers are welcome to examine the proposed research questions or analyze other research questions using the data set. History: This paper has been accepted as part of the 2024 MSOM Data-Driven Research Challenge. Funding: This work was supported by The Dutch Research Council - NWO VIDI Grant. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2024.0860

Measurements of dune erosion processes during the RealDune/REFLEX experiments

Nearshore hydro- and morphodynamic data were collected during a field experiment under calm conditions, moderate conditions, and storm conditions with dune erosion in the collision regime. The experiment was conducted on the Sand Engine near Kijkduin, the Netherlands, from October 18, 2021, to January 7, 2022. Two artificial unvegetated dunes were constructed just above the high water line to measure storm erosion and dune impacts from higher water levels and waves. During the experiment, three storms occurred that resulted in significant erosion of both dunes. The collected hydrodynamic data include pressure sensor and velocimeter data along two cross-shore transects. The collected morphodynamic data include bathymetry and topography surveys, optical backscatter sensor data in the inner surf zone, and a continuous cross-shore line-scanning lidar data set of the dune face. This comprehensive data set can be used to (1) study relevant nearshore hydrodynamic and morphodynamic processes that occur during calm conditions, moderate conditions, and storm conditions with dune erosion in the collision regime, and (2) validate existing dune erosion models.

A new family of distributions using a trigonometric function: Properties and applications in the healthcare sector

Probability distributions play a pivotal and significant role in modeling real-life data in every field. For this activity, a series of probability distributions have been introduced and exercised in applied sectors. This paper also contributes a new method for modeling continuous data sets. The proposed family is called the exponent power sine-G family of distributions. Based on the exponent power sine-G method, a new model, namely, the exponent power sine-Weibull model is studied. Several mathematical properties such as quantile function, identifiability property, and rth moment are derived. For the exponent power sine-G method, the maximum likelihood estimators are obtained. Simulation studies are also presented. Finally, the optimality of the exponent power sine-Weibull model is shown by taking two applications from the healthcare sector. Based on seven evaluating criteria, it is demonstrated that the proposed model is the best competing distribution for analyzing healthcare phenomena.

Exponential convergence to steady-states for trajectories of a damped dynamical system modeling adhesive strings

We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modeling a one-dimensional linearly elastic body interacting with a rigid substrate through an adhesive material. The key feature of of the problem is that the interplay between the nonlinear force and the boundary conditions allows for a continuous set of equilibrium points. We prove an exponential rate of convergence for the solution towards a (uniquely determined) equilibrium point.

Sustainability and risk assessment of data center locations under a fuzzy environment

In the age of digitalization, data centers are critical facilities that help people and businesses in many sectors. Data centers, like other assets requiring high investment, face several risks during their operation. Also, data centers seek sustainable sources to boost their operations when selecting the most appropriate location. Therefore, the location of a data center is chosen based on sustainability and risk assessment. To the best of our knowledge, no study has been conducted for data center risk evaluation with environmental and sustainability assessment. This paper evaluates the eight main criteria and the forty-five sub-criteria for selecting the most appropriate location for the data center when considering the fifty different economies in different business regions. For this particular purpose, the continuous intuitionistic fuzzy sets (CIFS)-based analytical hierarchy process (AHP) is presented to define the weights of each criterion and sub-criterion. Then, the CIFS-based technique for order of preference by similarity to the ideal solution (TOPSIS) is developed to rank the fifty economies integrated with the weights from the CIFS-based AHP. Moreover, eight different scenarios were conducted, and comparison studies were presented. Finally, Denmark, Switzerland, and The Netherlands are the top three selections based on the criteria.

Polytopal templates for semi-continuous vectorial finite elements of arbitrary order on triangulations and tetrahedralizations

The Hilbert spaces H(curl) and H(div) are employed in various variational problems formulated in the context of the de Rham complex in order to guarantee well-posedness. Seeing as the well-posedness follows automatically from the continuous setting to the discrete setting in the presence of commuting interpolants as per Fortin’s criterion, the construction of conforming subspaces becomes a crucial step in the formulation of stable numerical schemes. This work aims to introduce a novel, simple method of directly constructing semi-continuous vectorial base functions on the reference element via template vectors associated with the geometric polytopes of the element and an underlying H1-conforming polynomial subspace. The base functions are then mapped from the reference element to the element in the physical domain via consistent Piola transformations. The method is defined in such a way, that the underlying H1-conforming subspace can be chosen independently, thus allowing for constructions of arbitrary polynomial order. We prove a linearly independent construction of Nédélec elements of the first and second type, Brezzi–Douglas–Marini elements, and Raviart–Thomas elements on triangulations and tetrahedralizations. The application of the method is demonstrated with two examples in the relaxed micromorphic model.

MOLM: Alleviating Congestion through Multi-Objective Simulated Annealing-Based Load Balancing Routing in LEO Satellite Networks

In satellite networks, existing congestion resolution methods do not consider the predictability and stability of paths, leading to frequent path switches and high maintenance costs. In this regard, we propose a novel congestion resolution approach, named MOLM, which introduces a continuous neighbor set during path updates. This set includes nodes capable of establishing sustainable connections with the predecessors and successors of congested nodes. Combined with a multi-objective simulated annealing framework, MOLM iteratively derives an optimal selection from this set to replace congested nodes. Additionally, we employ a Fast Reroute mechanism based on backup paths (FRR-BP) to address node failures. The simulation results indicate that the optimal node endows the new path with optimal path stability and path latency.

Interactive Visual Task Learning for Robots

We present a framework for robots to learn novel visual concepts and tasks via in-situ linguistic interactions with human users. Previous approaches have either used large pre-trained visual models to infer novel objects zero-shot, or added novel concepts along with their attributes and representations to a concept hierarchy. We extend the approaches that focus on learning visual concept hierarchies by enabling them to learn novel concepts and solve unseen robotics tasks with them. To enable a visual concept learner to solve robotics tasks one-shot, we developed two distinct techniques. Firstly, we propose a novel approach, Hi-Viscont(HIerarchical VISual CONcept learner for Task), which augments information of a novel concept to its parent nodes within a concept hierarchy. This information propagation allows all concepts in a hierarchy to update as novel concepts are taught in a continual learning setting. Secondly, we represent a visual task as a scene graph with language annotations, allowing us to create novel permutations of a demonstrated task zero-shot in-situ. We present two sets of results. Firstly, we compare Hi-Viscont with the baseline model (FALCON) on visual question answering(VQA) in three domains. While being comparable to the baseline model on leaf level concepts, Hi-Viscont achieves an improvement of over 9% on non-leaf concepts on average. Secondly, we conduct a human-subjects experiment where users teach our robot visual tasks in-situ. We compare our model’s performance against the baseline FALCON model. Our framework achieves 33% improvements in success rate metric, and 19% improvements in the object level accuracy compared to the baseline model. With both of these results we demonstrate the ability of our model to learn tasks and concepts in a continual learning setting on the robot.

The Inter-batch Diversity of Samples in Experience Replay for Continual Learning

In a Continual Learning setting, models are trained on data with occasional distribution shifts, resulting in forgetting the information learned before each shift. Experience Replay (ER) addresses this challenge by retaining part of the old training samples and replaying them alongside current data, improving the model's understanding of the overall distribution in training batches. The crucial factor in ER performance is the diversity of samples within batches. The impact of sample diversity across a sequence of batches is investigated, introducing a new metric and an associated approach to assess and leverage this diversity. This exploration opens up significant potential for future work, as various strategies can be devised to ensure inter-batch diversity. Achieving optimal results may involve striking a balance between this novel metric and other inherent properties of a batch or sequence.

Interactive Visual Task Learning for Robots

We present a demonstrable framework for robots to learn novel visual concepts and visual tasks via in-situ linguistic interactions with human users. Previous approaches in computer vision have either used large pre-trained visual models to infer novel objects zero-shot, or added novel concepts along with their attributes and representations to a concept hierarchy. We extend the approaches that focus on learning visual concept hierarchies and take this ability one step further to demonstrate novel task solving on robots along with the learned visual concepts. To enable a visual concept learner to solve robotics tasks one-shot, we developed two distinct techniques. Firstly, we propose a novel approach, Hi-Viscont(HIerarchical VISual CONcept learner for Task), which augments information of a novel concept, that is being taught, to its parent nodes within a concept hierarchy. This information propagation allows all concepts in a hierarchy to update as novel concepts are taught in a continual learning setting. Secondly, we represent a visual task as a scene graph with language annotations, allowing us to create novel permutations of a demonstrated task zero-shot in-situ. Combining the two techniques, we present a demonstration on a real robot that learns visual task and concepts in one-shot from in-situ interactions with human users, and generalize to perform a novel visual task of the same type in zero-shot. As shown by the studies in the main conference paper, our system achieves a success rate of 50% on solving the whole task correctly with generalization where the baseline performs at 14% without any ability to generalize to novel tasks and concepts. We will demonstrate our working interactive learning pipeline at AAAI 2024 in person with our robot and other required hardware.

Adaptation in Unstable Environments and Global Gene Losses: Small but Stable Gene Networks by the May-Wigner Theory.

Although gene loss is common in evolution, it remains unclear whether it is an adaptive process. In a survey of seven major mangrove clades that are woody plants in the intertidal zones of daily environmental perturbations, we noticed that they generally evolved reduced gene numbers. We then focused on the largest clade of Rhizophoreae and observed the continual gene set reduction in each of the eight species. A great majority of gene losses are concentrated on environmental interaction processes, presumably to cope with the constant fluctuations in the tidal environments. Genes of the general processes for woody plants are largely retained. In particular, fewer gene losses are found in physiological traits such as viviparous seeds, high salinity, and high tannin content. Given the broad and continual genome reductions, we propose the May-Wigner theory (MWT) of system stability as a possible mechanism. In MWT, the most effective solution for buffering continual perturbations is to reduce the size of the system (or to weaken the total genic interactions). Mangroves are unique as immovable inhabitants of the compound environments in the land-sea interface, where environmental gradients (such as salinity) fluctuate constantly, often drastically. Extending MWT to gene regulatory network (GRN), computer simulations and transcriptome analyses support the stabilizing effects of smaller gene sets in mangroves vis-à-vis inland plants. In summary, we show the adaptive significance of gene losses in mangrove plants, including the specific role of promoting phenotype innovation and a general role in stabilizing GRN in unstable environments as predicted by MWT.

Functional Linear Regression: A Case Study from the Food Industry

A problem of analyzing functions in statistics is a very recent phenomenon that has been extensively investigated. The functionality in observed data, that is, when data are generated through a process naturally described as functional, occurs in many areas of sciences. For example, time series in financial engineering, imagining records in medicine, or spectrometric wavelengths in chemometrics can be considered as a discrete approximation of a continuous set of mathematical objects. In the initial step, observed real-valued data are transposed into functional data by smoothing or interpolation technique. These functional objects can then be directly used in the framework of statistical regressions. The aim of this paper is to show an estimation of the functional linear regression, where the observed covariate is functional, and its corresponding response is scalar. In the empirical study, we utilize spectrometric data with an objective to predict the fat content in a meat sample given the spectrum of absorbances, which are recorded through the infrared analyzer, by using the estimated functional linear regression. The functional regression coefficient is estimated through the basis spline expansion, for which we evaluate a different number of basis splines and propose the best predictor estimator.

Geometric structures in pseudo-random graphs

Abstract In this paper, we provide a general framework for counting geometric structures in pseudo-random graphs. As applications, our theorems recover and improve several results on the finite field analog of questions originally raised in the continuous setting. The results present interactions between discrete geometry, geometric measure theory, and graph theory.

Sharp bounds for a discrete John’s theorem

AbstractTao and Vu showed that every centrally symmetric convex progression $C\subset \mathbb{Z}^d$ is contained in a generalized arithmetic progression of size $d^{O(d^2)} \# C$ . Berg and Henk improved the size bound to $d^{O(d\log d)} \# C$ . We obtain the bound $d^{O(d)} \# C$ , which is sharp up to the implied constant and is of the same form as the bound in the continuous setting given by John’s theorem.

Long term trends in source apportioned particle number concentrations in Rochester NY

During the past two decades, efforts have been made to further reduce particulate air pollution across New York State through various Federal and State policy implementations. Air quality has also been affected by economic drivers like the 2007–2009 recession and changing costs for different approaches to electricity generation. Prior work has focused on particulate matter with aerodynamic diameter ≤2.5 μm. However, there is also interest in the effects of ultrafine particles on health and the environment and analyses of changes in particle number concentrations (PNCs) are also of interest to assess the impacts of changing emissions. Particle number size distributions have been measured since 2005. Prior apportionments have been limited to seasonal analyses over a limited number of years because of software limitations. Thus, it has not been possible to perform trend analyses on the source-specific PNCs. Recent development have now permitted the analysis of larger data sets using Positive Matrix Factorization (PMF) including its diagnostics. Thus, this study separated and analyzed the hourly averaged size distributions from 2005 to 2019 into two data sets; October to March and April to September. Six factors were resolved for both data sets with sources identified as nucleation, traffic 1, traffic 2, fresh secondary inorganic aerosol (SIA), aged SIA, and O3-rich aerosol. The resulting source-specific PNCs were combined to provide continuous data sets and analyzed for trends. The trends were then examined with respect to the implementation of regulations and the timing of economic drivers. Nucleation was strongly reduced by the requirement of ultralow (<15 ppm) sulfur on-road diesel fuel in 2006. Secondary inorganic particles and O3-rich PNCs show strong summer peaks. Aged SIA was constant and then declined substantially in 2015 but rose in 2019. Traffic 1 and 2 have steadily declined bur rose in 2019.

Two-stage problems of optimal location and distribution of the humanitarian logistics system’s structural subdivisions

Purpose. To ensure the rational organization of the evacuation of people from a region affected by an emergency by developing a mathematical and algorithmic toolkit that will allow for the early distribution of transport and material resources, maximizing coverage of the affected areas while minimizing evacuation time. Methodology. System analysis of evacuation processes; mathematical modeling, the theory of continuous problems of optimal partitioning of sets, non-differentiable optimization. Findings. The object of the study is the two-stage evacuation logistic processes that occur when serving the population of areas affected by emergencies of a natural or technogenic nature. The research considers the possibility of optimally distributing human flows within the transportation system, the structural subdivisions of which are first-stage centers (first aid stations that carry out the reception of citizens from areas affected by the disaster) and second-stage centers (specialized units of the emergency aid system that provide further services to the evacuated population). The proposed mathematical model deals with the problem of optimally partitioning a continuous set with the placement of subset centers and additional connections. Methods for its solution have been described. We demonstrate the versatility of these models, as they can be used to describe logistic evacuation processes, organize assembly points, intermediate locations, evacuation reception points, and those providing primary assistance to the affected population. We calculate the appropriate number of essential products and deliver them from existing warehouses through distribution centers to the affected areas. Originality. As preventive measures to increase the level of population safety during an emergency, we consider the optimal placement of rescue facilities and the zoning of the territory to distribute evacuation traffic. We also address the problem of the optimal distribution of human flows in the transport and logistics system. Practical value. The presented models, methods, and algorithms enable the solution of many practical problems related to the development of preventive measures and the planning of rescue operations to ensure the population’s safety in case of emergencies. The theoretical results obtained are translated into specific recommendations that can be utilized when addressing logistical problems related to the organization of primary evacuation of the population from affected areas and their subsequent transportation to safer locations for further assistance.

Simultaneous prediction of 16 quality attributes during protein A chromatography using machine learning based Raman spectroscopy models.

Several key technologies for advancing biopharmaceutical manufacturing depend on the successful implementation of process analytical technologies that can monitor multiple product quality attributes in a continuous in-line setting. Raman spectroscopy is an emerging technology in the biopharma industry that promises to fit this strategic need, yet its application is not widespread due to limited success for predicting a meaningful number of quality attributes. In this study, we addressed this very problem by demonstrating new capabilities for preprocessing Raman spectra using a series of Butterworth filters. The resulting increase in the number of spectral features is paired with a machine learning algorithm and laboratory automation hardware to drive the automated collection and training of a calibration model that allows for the prediction of 16 different product quality attributes in an in-line mode. The demonstrated ability to generate these Raman-based models for in-process product quality monitoring is the breakthrough to increase process understanding by delivering product quality data in a continuous manner. The implementation of this multiattribute in-line technology will create new workflows within process development, characterization, validation, and control.

Risk management in software development in the field of information protection

In the context of increasing digitalization of sea and river transport, the immersion of the entire transport infrastructure in the digital environment, the volume of information flows serving the transport process is increasing, and the requirements for information protection are increasing in conditions of an aggressive external information environment. In the digital environment, a software product must not only serve the document flow of transport chains, but also ensure its confidentiality. Automation of transport facilities (ships, platforms, berths, warehouses) management increases their potential vulnerability from unauthorized access to control systems; the latter must be taken into account in servicing programs, increasing their size (for example, there is a need to fragment coherent information blocks and their alternative routing). This, in turn, increases the risk of errors in the software products themselves and significantly complicates their structure. Risks of failures (including confidentiality violations) during the software operation that implements information exchange can entail significant material and reputational losses for the developer. If the developer is legally and functionally involved in the industry, such losses can and should be considered among the general range of risks in water transport. An important aspect of risk management, which until recently was practically not considered in a quantitative aspect within the framework of mathematical models, is the joint consideration of losses when a risk situation occurs and the developer’s costs associated with reducing the likelihood of such occurrences; the latter may entail a reduction in the total expected losses, formalized as the corresponding mathematical expectation. As a result, risk management can be formulated in terms of mathematical programming problems with different (discrete or continuous) sets of constraints and with different properties of objective functions.

Network Revenue Management With Demand Learning and Fair Resource-Consumption Balancing

In addition to maximizing the total revenue, decision-makers in lots of industries would like to guarantee balanced consumption across different resources. For instance, in the retailing industry, ensuring a balanced consumption of resources from different suppliers enhances fairness and helps maintain a healthy channel relationship; in the cloud computing industry, resource-consumption balance helps increase customer satisfaction and reduce operational costs. Motivated by these practical needs, this paper studies the price-based network revenue management (NRM) problem with both demand learning and fair resource-consumption balancing. We introduce the regularized revenue, that is, the total revenue with a balancing regularization, as our objective to incorporate fair resource-consumption balancing into the revenue maximization goal. We propose a primal-dual-type online policy with the upper-confidence-bound demand learning method to maximize the regularized revenue. We adopt several innovative techniques to make our algorithm a unified and computationally efficient framework for the continuous price set and a wide class of balancing regularizers. Our algorithm achieves a worst-case regret of [Formula: see text], where [Formula: see text] denotes the number of products and [Formula: see text] denotes the number of time periods. Numerical experiments in a few NRM examples demonstrate the effectiveness of our algorithm in simultaneously achieving revenue maximization and fair resource-consumption balancing.