Restrictive Assumptions Research Articles

Numerical Analysis of Time-Fractional Cancer Models with Different Types of Net Killing Rate

This study introduces a novel approach to modeling cancer tumor dynamics within a fractional framework, emphasizing the critical role of the net killing rate in determining tumor growth or decay. We explore a generalized cancer model where the net killing rate is considered across three domains: time-dependent, position-dependent, and concentration-dependent. The primary objective is to derive an analytical solution for time-fractional cancer models using the Residual Power Series Method (RPSM), a technique not previously applied in this conformable context. Traditional methods for solving fractional-order differential models face challenges such as perturbations, complex simplifications, discretization issues, and restrictive assumptions. In contrast, the RPSM overcomes these limitations by offering a robust solution that reduces both complexity and computational effort. The method provides exact analytical solutions through a convergence series and reliable numerical approximations when needed, making it a versatile tool for simulating fractional-order cancer models. Graphical representations of the approximate solutions illustrate the method’s effectiveness and applicability. The findings highlight the RPSM’s potential to advance cancer treatment strategies by providing a more precise understanding of tumor dynamics in a fractional context. This work contributes to both theoretical and practical advancements in cancer research and lays the groundwork for more accurate and efficient modeling of cancer dynamics, ultimately aiding in the development of optimal treatment strategies.

Generalized Coupled Matrix Tensor Factorization Method Based on Normalized Mutual Information for Simultaneous EEG-fMRI Data Analysis.

The complementary properties of both modalities can be exploited through the fusion of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) data. Thus, a joint analysis of both modalities can be used in brain studies to estimate brain activity's shared and unshared components. This study introduces a comprehensive approach for jointly analyzing EEG and fMRI data using the advanced coupled matrix tensor factorization (ACMTF) method. The similarity of the components based on normalized mutual information (NMI) was defined to overcome the restrictive equality assumption of shared components in the common dimension of the ACMTF method. Because the mutual information (MI) measure can identify both linear and nonlinear relationships between the components, the proposed method can be viewed as a generalization of the ACMTF method; thus, it is called the generalized coupled matrix tensor factorization (GCMTF). The proposed GCMTF method was applied to simulated data, in which the components exhibited a nonlinear relationship. The results demonstrate that the average match score increased by 23.46% compared with the ACMTF model, even with different noise levels. Furthermore, applying this method to real data from an auditory oddball paradigm demonstrated that three shared components with frequency responses in the alpha and theta bands were identified. The proposed MI-based method cannot only extract shared components with any nonlinear or linear relationship but can also identify more active brain areas corresponding to an auditory oddball paradigm compared to ACMTF and other similar methods.

Discrete choice in marketing through the lens of rational inattention

Abstract Models derived from random utility theory represent the workhorse methods to learn about consumer preferences from discrete choice data. However, a large body of literature documents various behavioral patterns that cannot be captured by basic random utility models and require different non-unified adjustments to accommodate these patterns. In this article, we discuss strategies how to apply rational inattention theory—which explains a large variety of such departures—to the analysis of discrete choice among multiple alternatives described along multiple attributes. We first review existing applications that make restrictive belief assumptions to obtain choice probabilities in closed multinomial logit form. We then propose a model that allows for general consumer beliefs and demonstrate its empirical identification. Further, we illustrate how this model naturally motivates stylized empirical results that are hard to reconcile from a random utility perspective.

Are European Farms Equally Efficient? What Do Regional FADN Data on Crop Farms Tell Us?

Abstract The study analyzes productive efficiency of crop farming in the EU. We use publicly available data on crop farming from FADN database. Standard efficiency measurement techniques based on frontier analysis indicate that the representative farms provided in the database are fully efficient, even though there is ample evidence in the literature that this is highly unlikely. We find that this is a consequence of overly restrictive assumptions about the compound error in standard SF models. The efficiency benchmark, based on the best model given data with generalized error specification, reveals substantial differences in crop farming efficiency in the EU.

A novel numerical approach for solving generalized fractional Fisher's equation

Abstract This paper aims to construct a novel numerical technique, the General Transform Adomian Decomposition Method (GTADM), for obtaining approximate solutions of fractional generalized Fisher's equation (FGFE). The fractional order is in the sense of Caputo. By applying the General transform(GT) and its inverse, the fractional Fisher equation is simplified within the GT domain, facilitating the treatment of the equation without imposing restrictive assumptions on the variables, then we apply the Adomian Decomposition Method(ADM) to solve the newly obtained equation. Stability analysis is conducted to enhance the theoretical framework. The GTADM requires less computational work and exhibits faster convergence without discretization, linearization, or perturbation, thus preserving the integrity of the FGFE. A comparative analysis with ADM, homotopy perturbation Sumudu transforms method (HPSTM), and q-homotopy analysis transform method (q-HATM) is performed to demonstrate the efficiency and robustness of GTADM. The accuracy and reliability of the GTADM are validated through the computation of absolute and relative errors. Furthermore, 2D and 3D graphical representations, generated using Maple 21 and MATLAB to support this work. The numerical results and graphs clearly demonstrate the efficiency and robustness of the GTADM.

Futures-Based Forecasts of Cotton Prices: Beyond Historical Averages

Abstract This study explores several alternative specifications of futures-based forecasting models to improve existing approaches constrained by restrictive assumptions and limited information sets. In lieu of historical averages, our approaches use rolling regressions and include current market information reflected in the deviation of the current basis from its historical average. To mitigate potential challenges arising from nonstationarity and structural changes in the relationship between farm and futures prices, we employ a 5-year rolling estimation window. We find that a rolling regression approach offers significant improvements (as evidenced by our Modified Diebold–Mariano test) in the accuracy and information content of forecasts of cotton season-average prices (SAPs) mostly at short forecast horizons.

On the generalized N-critical shock model

ABSTRACT According to the N -critical shock model, a system fails if the total number of critical shocks reaches N . The central assumption in this model is that after the arrival of a critical shock, the next shock will be critical with the same probability. This is a restrictive and unrealistic assumption in many natural situations. This paper defines a generalized N -critical shock model that overcomes this limitation. We study the model for two well-known shock arrival processes and derive reliability indices such as reliability function and mean remaining lifetime.

COMPARISON OF SURVIVAL ANALYSIS USING ACCELERATED FAILURE TIME MODEL AND COX MODEL FOR RECIDIVIST CASE

Recidivists, or ex-prisoners who commit crimes after serving a prior sentence, pose a critical challenge to the criminal justice system. This study examines social and economic factors that may reduce the likelihood of recidivists being re-arrested. Using survival analysis, the probability that a recidivist could survive in society without being re-arrested could be estimated. The purpose of this work is to compare the AFT and Cox models to determine which provides a better fit to identify factors affecting the likelihood of re-arrest within one year after release and to statistically assess the impact of these factors. This study utilizes a stratified Cox model to address variables that violate the proportional hazards (PH) assumption. The analysis is limited to four types of AFT models: Weibull, log-normal, log-logistic, and exponential. Results show that the stratified Cox model provides the best fit, based on Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). This demonstrates the Cox model's robustness in analyzing survival data, accurately approximating the distribution of survival times without restrictive assumptions, unlike AFT models. The study reveals that recidivists who received financial aid upon release have a lower risk of re-arrest compared to those who did not, and each additional prior theft arrest increased the risk of re-arrest by 1.09193 times.

Ordered correlation forest

. Empirical studies in various social sciences often involve categorical outcomes with inherent ordering, such as self-evaluations of subjective well-being and self-assessments in health domains. While ordered choice models, such as the ordered logit and ordered probit, are popular tools for analyzing these outcomes, they may impose restrictive parametric and distributional assumptions. This article introduces a novel estimator, the ordered correlation forest, that can naturally handle non linearities in the data and does not assume a specific error term distribution. The proposed estimator modifies a standard random forest splitting criterion to build a collection of forests, each estimating the conditional probability of a single class. Under an “honesty” condition, predictions are consistent and asymptotically normal. The weights induced by each forest are used to obtain standard errors for the predicted probabilities and the covariates’ marginal effects. Evidence from synthetic data shows that the proposed estimator features a superior prediction performance than alternative forest-based estimators and demonstrates its ability to construct valid confidence intervals for the covariates’ marginal effects. Comparisons using various real-world data sets further highlight the advantages of forest-based estimators over parametric models in larger samples while showing that the ordered correlation forest remains competitive in smaller samples.

A Liouville type theorem for ancient Lagrangian mean curvature flows

. We prove a Liouville type result for convex solutions of the Lagrangian mean curvature flow with restricted quadratic growth assumptions at antiquity on the solutions.

CSLens: Towards Better Deploying Charging Stations via Visual Analytics -- A Coupled Networks Perspective.

In recent years, the global adoption of electric vehicles (EVs) has surged, prompting a corresponding rise in the installation of charging stations. This proliferation has underscored the importance of expediting the deployment of charging infrastructure. Both academia and industry have thus devoted to addressing the charging station location problem (CSLP) to streamline this process. However, prevailing algorithms addressing CSLP are hampered by restrictive assumptions and computational overhead, leading to a dearth of comprehensive evaluations in the spatiotemporal dimensions. Consequently, their practical viability is restricted. Moreover, the placement of charging stations exerts a significant impact on both the road network and the power grid, which necessitates the evaluation of the potential post-deployment impacts on these interconnected networks holistically. In this study, we propose CSLens, a visual analytics system designed to inform charging station deployment decisions through the lens of coupled transportation and power networks. CSLens offers multiple visualizations and interactive features, empowering users to delve into the existing charging station layout, explore alternative deployment solutions, and assess the ensuring impact. To validate the efficacy of CSLens, we conducted two case studies and engaged in interviews with domain experts. Through these efforts, we substantiated the usability and practical utility of CSLens in enhancing the decision-making process surrounding charging station deployment. Our findings underscore CSLens's potential to serve as a valuable asset in navigating the complexities of charging infrastructure planning.

Systematics in ETG mass profile modelling: strong lensing & stellar dynamics

Strong gravitational lensing and stellar dynamics are independent and powerful methods to probe the total gravitational potential of galaxies, and thus, their total mass profile. However, inherent degeneracies in the individual models makes it difficult to obtain a full understanding of the distribution of baryons and dark matter (DM), although such degeneracies might be broken by the combination of these two tracers, leading to more reliable measurements of the mass distribution of the lens galaxy. We use mock data from IllustrisTNG50 to compare how dynamical-only, lens-only, and joint modelling can constrain the mass distribution of early-type galaxies (ETGs). The joint model consistently outperforms the other models, achieving a 2% accuracy in recovering the total mass within 2.5R eff. The Einstein radius is robustly recovered for both lens-only and joint models, with the first showing a median fractional error of -5% and the latter a fractional error consistent with zero. The stellar mass-to-light ratio and total mass density slope are well recovered by all models. In particular, the dynamical-only model achieves an accuracy of 1% for the stellar mass-to-light ratio, while the accuracy of the mass density slope is typically of the order of 5% for all models. However, all models struggle to constrain integrated quantities involving DM and the halo parameters. Nevertheless, imposing more restrictive assumptions on the DM halo, such as fixing the scale radius, could alleviate some of the issues. Finally, we verify that the number of kinematical constraints (15, 35, 55 bins) on the kinematical map does not impact the models outcomes.

Reliability Analysis of Load‐Sharing Systems Using a Flexible Model With Piecewise Linear Functions

ABSTRACTA flexible model for analysing load‐sharing data is developed by approximating the cumulative hazard functions of component lifetimes by piecewise linear functions. The proposed model is data‐driven and does not depend on restrictive parametric assumptions on underlying component lifetimes. Maximum likelihood estimation and construction of confidence intervals for model parameters are discussed. Estimates of reliability characteristics such as reliability at a mission time, quantile function, mean time to failure and mean residual time for load‐sharing systems are developed in this setting. As the proposed model is capable of providing a good fit for load‐sharing data, it also results in a better estimation of these important reliability characteristics. The performance of the proposed model is observed to be quite satisfactory through a detailed Monte Carlo simulation study. The analyses of two load‐sharing datasets, one pertaining to the lives of two‐motor load‐sharing systems and another related to basketball games, are provided as illustrative examples. In summary, this article presents a comprehensive discussion on a flexible model that can be used for load‐sharing systems efficiently.

Concentration properties of fractional posterior in 1-bit matrix completion

The problem of estimating a matrix based on a set of observed entries is commonly referred to as the matrix completion problem. In this work, we specifically address the scenario of binary observations, often termed as 1-bit matrix completion. While numerous studies have explored Bayesian and frequentist methods for real-value matrix completion, there has been a lack of theoretical exploration regarding Bayesian approaches in 1-bit matrix completion. We tackle this gap by considering a general, non-uniform sampling scheme and providing theoretical assurances on the efficacy of the fractional posterior. Our contributions include obtaining concentration results for the fractional posterior and demonstrating its effectiveness in recovering the underlying parameter matrix. We accomplish this using two distinct types of prior distributions: low-rank factorization priors and a spectral scaled Student prior, with the latter requiring fewer assumptions. Importantly, our results exhibit an adaptive nature by not mandating prior knowledge of the rank of the parameter matrix. Our findings are comparable to those found in the frequentist literature, yet demand fewer restrictive assumptions.

Digitalization Intensity and Extensive Margins of Exports in Manufacturing Firms from 27 EU Countries - Evidence from Kernel-Regularized Least Squares Regression

The use of digital technologies like artificial intelligence, robotics, or smart devices can be expected to go hand in hand with higher productivity and lower trade costs, and, therefore, to be positively related to export activities. This paper uses firm level data for manufacturing enterprises from the 27 member countries of the European Union to shed further light on this issue by investigating the link between the digitalization intensity of a firm and extensive margins of exports. We use a new machine-learning based regression method, Kernel-Regularized Least Squares (KRLS), which effectively handles non-linear relationships in models and does not impose any restrictive assumptions for the functional form of the relation between margins of exports, digitalization intensity, and any control variables. We find that firms which use more digital technologies do more often export, do more often export to various destinations all over the world, and do export to more different destinations.

Noether’s Problem for p-Groups with Abelian Normal Subgroups and Central p-Powers

This paper addresses Noether’s problem for p-groups G, having an abelian normal subgroup of index p, under the condition Gp={gp:g∈G}≤Z(G)—the center of G. We prove that the fixed field K(G)=K(x(g):g∈G)G is rational over K in such cases, focusing on both the classification and structural analysis of these groups. Our results extend existing work by removing restrictive assumptions and providing a refined understanding of p-groups and their representations.

On The Assembly Line Balancing Problem: A Simplified Perspective With The Precedence Matrix

The assembly line balancing problem (ALBP) has been an attractive research area for decades; however, the industrial application of the research findings remains limited. This can be attributed to the complexity of solution methods, restrictive assumptions, and the numerous variants of the problem in the real-world settings. This article describes using the precedence matrix as the basis for developing simplified, more practical analysis frameworks for the ALBP. We introduce algorithms to construct the precedence matrix from basic assembly problem data and implement it within a spreadsheet model, and to utilize this matrix in assigning the assembly tasks to workstations while ensuring assignment feasibility. The structure and potential uses of the precedence matrix-based framework are presented in detail. Furthermore, we compare selected line balancing priority rules using the proposed framework to demonstrate its effectiveness. The results suggest that the precedence matrix model is a straightforward, efficient tool for line balancing analysis, that can offer substantial support to both industry practitioners and academic researchers.

Stochastic First-Order Methods for Average-Reward Markov Decision Processes

We study average-reward Markov decision processes (AMDPs) and develop novel first-order methods with strong theoretical guarantees for both policy optimization and policy evaluation. Compared with intensive research efforts in finite sample analysis of policy gradient methods for discounted MDPs, existing studies on policy gradient methods for AMDPs mostly focus on regret bounds under restrictive assumptions, and they often lack guarantees on the overall sample complexities. Toward this end, we develop an average-reward stochastic policy mirror descent method for solving AMDPs with and without regularizers and provide convergence guarantees in terms of the long-term average reward. For policy evaluation, existing on-policy methods suffer from suboptimal convergence rates as well as failure in handling insufficiently random policies due to the lack of exploration in the action space. To remedy these issues, we develop a variance-reduced temporal difference (VRTD) method with linear function approximation for randomized policies along with optimal convergence guarantees, and design an exploratory VRTD method that resolves the exploration issue and provides comparable convergence guarantees. By combining the policy evaluation and policy optimization parts, we establish sample complexity results for solving AMDPs under both generative and Markovian noise models. It is worth noting that when linear function approximation is utilized, our algorithm only needs to update in the low-dimensional parameter space, and thus can handle MDPs with large state and action spaces. Funding: T. Li and G. Lan were supported in part by the National Science Foundation [Grant CCF-1909298] and the Office of Navel Research [Grant N00014-20-1-2089].

Handling Distinct Correlated Effects with CCE

AbstractThe common correlated effects (CCE) approach by Pesaran is a popular method for estimating panel data models with interactive effects. Due to its simplicity, i.e., unobserved common factors are approximated with cross‐section averages of the observables, the estimator is highly flexible and lends itself to a wide range of applications. Despite such flexibility, however, the properties of CCE estimators are typically only examined under the restrictive assumption that all the observed variables load on the same set of factors, which ensures joint identification of the factor space. In this article, we take a different perspective, and explore the empirically relevant case where the dependent and explanatory variables are driven by distinct but correlated factors. Hence, we consider the case of Distinct Correlated Effects. Such settings can be argued to be relevant for practice, for instance in studies linking economic growth to climatic variables. In so doing, we consider panel dimensions such that as , which is known to induce an asymptotic bias for the pooled CCE estimator even under the usual common factor assumption. We subsequently develop a robust bootstrap‐based toolbox that enables asymptotically valid inference in both homogeneous and heterogeneous panels, without requiring knowledge about whether factors are distinct or common.

VSS-Hi-C: variance-stabilized signals for chromatin contacts.

The genome-wide chromosome conformation capture assay Hi-C is widely used to study chromatin 3D structures and their functional implications. Read counts from Hi-C indicate the strength of chromatin contact between each pair of genomic loci. These read counts are heteroskedastic: that is, a difference between the interaction frequency of 0 and 100 is much more significant than a difference between the interaction frequency of 1000 and 1100. This property impedes visualization and downstream analysis because it violates the Gaussian variable assumption of many computational tools. Thus heuristic transformations aimed at stabilizing the variance of signals like the shifted-log transformation are typically applied to data before its visualization and inputting to models with Gaussian assumption. However, such heuristic transformations cannot fully stabilize the variance because of their restrictive assumptions about the mean-variance relationship in the data. Here, we present VSS-Hi-C, a data-driven variance stabilization method for Hi-C data. We show that VSS-Hi-C signals have a unit variance improving visualization of Hi-C, for example in heatmap contact maps. VSS-Hi-C signals also improve the performance of subcompartment callers relying on Gaussian observations. VSS-Hi-C is implemented as an R package and can be used for variance stabilization of different genomic and epigenomic data types with two replicates available. https://github.com/nedashokraneh/vssHiC.