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Computational cognitive modeling is an important tool for understanding the processes supporting human and animal decision-making. Choice data in decision-making tasks are inherently noisy, and separating noise from signal can improve the quality of computational modeling. Common approaches to model decision noise often assume constant levels of noise or exploration throughout learning (e.g., the ϵ-softmax policy). However, this assumption is not guaranteed to hold – for example, a subject might disengage and lapse into an inattentive phase for a series of trials in the middle of otherwise low-noise performance. Here, we introduce a new, computationally inexpensive method to dynamically estimate the levels of noise fluctuations in choice behavior, under a model assumption that the agent can transition between two discrete latent states (e.g., fully engaged and random). Using simulations, we show that modeling noise levels dynamically instead of statically can substantially improve model fit and parameter estimation, especially in the presence of long periods of noisy behavior, such as prolonged lapses of attention. We further demonstrate the empirical benefits of dynamic noise estimation at the individual and group levels by validating it on four published datasets featuring diverse populations, tasks, and models. Based on the theoretical and empirical evaluation of the method reported in the current work, we expect that dynamic noise estimation will improve modeling in many decision-making paradigms over the static noise estimation method currently used in the modeling literature, while keeping additional model complexity and assumptions minimal.

Correction to: Transport in Porous Media (2024) 151:55–84https://doi.org/10.1007/s11242-023-02033-0. There are three numbers in Table 2 of the original paper that were incorrect. Specfically, the value of the density of hydrogen (H2) for the DB model and the values of density and viscosity of H2 for the TOUGH2 model listed in Table 2 of the original paper were incorrect. (Table presented.) Properties of the H2-water upconing system for comparison against the DB model. Property DB model Used for TOUGH2 Gas cap thickness, total reservoir thickness, and radial extent (outer radius) of the reservoir Infinite, infinite, infinite 50 m, 100 m (with open boundary at bottom), 100 m (open boundary condition) Porosity (ϕ) 0.10 0.10 Permeability (kH) 1.0 × 10−12 m2 1.0 × 10−12 m2 Permeability (kV) 1.0 × 10−12 m2 1.0 × 10−12 m2 Relative permeability (krel) Not applicable Linear with Slr = 0.99 Distance from well to H2-water interface (d) 10 m 10 m Extraction rate of rate of H2 (Qm) − 5.5 kg s−1 − 5.5 kg s−1 Density of water 996 kg m−3 996 kg m−3 Density of H2 7.32 kg m−3 7.87 kg m−3 Viscosity of water 6.54 × 10−4 Pa s 5.11 × 10−4 Pa s Viscosity of H2 9.31 × 10−6 Pa s 9.53 × 10−6 Pa s A corrected Table 2 is shown below. The erroneous values in Table 2 were not used in any of the modeling and simulation. Accurate values for density and viscosity in the modeling and simulation come from CoolProp for the DB model and from EOS7CH for the TOUGH2 simulations.

Pulmonary hypertension is a cardiovascular disorder manifested by elevated mean arterial blood pressure (>20 mmHg) together with vessel wall stiffening and thickening due to alterations in collagen, elastin, and smooth muscle cells. Hypoxia-induced (type 3) pulmonary hypertension can be studied in animals exposed to a low oxygen environment for prolonged time periods leading to biomechanical alterations in vessel wall structure. This study introduces a novel approach to formulating a reduced order nonlinear elastic structural wall model for a large pulmonary artery. The model relating blood pressure and area is calibrated using ex vivo measurements of vessel diameter and wall thickness changes, under controlled pressure conditions, in left pulmonary arteries isolated from control and hypertensive mice. A two-layer, hyperelastic, and anisotropic model incorporating residual stresses is formulated using the Holzapfel-Gasser-Ogden model. Complex relations predicting vessel area and wall thickness with increasing blood pressure are derived and calibrated using the data. Sensitivity analysis, parameter estimation, subset selection, and physical plausibility arguments are used to systematically reduce the 16-parameter model to one in which a much smaller subset of identifiable parameters is estimated via solution of an inverse problem. Our final reduced one layer model includes a single set of three elastic moduli. Estimated ranges of these parameters demonstrate that nonlinear stiffening is dominated by elastin in the control animals and by collagen in the hypertensive animals. The pressure-area relation developed in this novel manner has potential impact on one-dimensional fluids network models of vessel wall remodeling in the presence of cardiovascular disease.

In this article, we evaluate the challenges and best practices associated with the Markov bases approach to sampling from conditional distributions. We provide insights and clarifications after 25 years of the publication of the Fundamental theorem for Markov bases by Diaconis and Sturmfels. In addition to a literature review, we prove three new results on the complexity of Markov bases in hierarchical models, relaxations of the fibers in log-linear models, and limitations of partial sets of moves in providing an irreducible Markov chain. Supplementary materials for this article are available online.

In turbulent flows, energy production is associated with highly organized structures, known as coherent structures. Since these structures are three dimensional, their detection remains challenging in the most common situation in experiments, when single-point temporal measurements are considered. While previous research on coherent structure detection from time series employs a thresholding approach, either in spectral or temporal domain, the thresholds are ad hoc and vary significantly from one study to another. To circumvent this issue, we introduce the level-crossing method and show how specific features of a turbulent time series associated with coherent structures can be objectively identified, without assigning a priori any arbitrary threshold. By using two wall-bounded turbulence time-series datasets (at a Reynolds number of 104), we successfully extract through level-crossing analysis the impacts of coherent structures on turbulent dynamics and therefore open an alternative avenue in experimental turbulence research. By utilizing this framework further, we discover a metric, characterized by a statistical asymmetry between the peaks and troughs of a turbulent signal, to quantify inner-outer interaction in wall turbulence. Most importantly, through phase-randomized surrogate data modeling, we demonstrate that the level-crossing statistics are quite sensitive to the nonlinear dependencies in a turbulent signal. Physically, this finding implies that the large-scale coherent structures modulate the near-wall turbulent dynamics through a nonlinear interaction associated with low-speed streaks, a mechanism not identifiable from spectral analysis alone. Moreover, a connection is established between extreme value statistics and level-crossing analysis, thereby allowing additional possibilities to study extreme events in other dynamical systems.

In the early 1990s, Billera and Sturmfels introduced the monotone path polytope (MPP), an important case of the general theory of fiber polytopes, which has led to remarkable combinatorics. Given a pair (P, φ) of a polytope P and a linear functional φ , the MPP is obtained from averaging the fibers of the projection φ(P) . They also showed that MPPs of (regular) simplices and hyper-cubes are combinatorial cubes and permutahedra respectively. As a natural follow-up we investigate the monotone paths of cross-polytopes for a generic linear functional φ . We show the face lattice of the MPP of the cross-polytope is isomorphic to the lattice of intervals in the sign poset from oriented matroid theory. We also describe its f-vector, some geometric realizations, an irredundant inequality description, the 1-skeleton and we compute its diameter. In contrast to the case of simplices and hyper-cubes, monotone paths on cross-polytopes are not always coherent.

Abstract: This work presents a multi-resolution physics-informed recurrent neural network (MR PI-RNN), for simultaneous prediction of musculoskeletal (MSK) motion and parameter identification of the MSK systems. The MSK application was selected as the model problem due to its challenging nature in mapping the high-frequency surface electromyography (sEMG) signals to the low-frequency body joint motion controlled by the MSK and muscle contraction dynamics. The proposed method utilizes the fast wavelet transform to decompose the mixed frequency input sEMG and output joint motion signals into nested multi-resolution signals. The prediction model is subsequently trained on coarser-scale input–output signals using a gated recurrent unit (GRU), and then the trained parameters are transferred to the next level of training with finer-scale signals. These training processes are repeated recursively under a transfer-learning fashion until the full-scale training (i.e., with unfiltered signals) is achieved, while satisfying the underlying dynamic equilibrium. Numerical examples on recorded subject data demonstrate the effectiveness of the proposed framework in generating a physics-informed forward-dynamics surrogate, which yields higher accuracy in motion predictions of elbow flexion–extension of an MSK system compared to the case with single-scale training. The framework is also capable of identifying muscle parameters that are physiologically consistent with the subject’s kinematics data.

Abstract: This work presents an approach for automating the discretization and approximation procedures in constructing digital representations of composites from micro-CT images featuring intricate microstructures. The proposed method is guided by the Support Vector Machine (SVM) classification, offering an effective approach for discretizing microstructural images. An SVM soft margin training process is introduced as a classification of heterogeneous material points, and image segmentation is accomplished by identifying support vectors through a local regularized optimization problem. In addition, an Interface-Modified Reproducing Kernel Particle Method (IM-RKPM) is proposed for appropriate approximations of weak discontinuities across material interfaces. The proposed method modifies the smooth kernel functions with a regularized Heaviside function concerning the material interfaces to alleviate Gibb's oscillations. This IM-RKPM is formulated without introducing duplicated degrees of freedom associated with the interface nodes commonly needed in the conventional treatments of weak discontinuities in the meshfree methods. Moreover, IM-RKPM can be implemented with various domain integration techniques, such as Stabilized Conforming Nodal Integration (SCNI). The extension of the proposed method to 3-dimension is straightforward, and the effectiveness of the proposed method is validated through the image-based modeling of polymer-ceramic composite microstructures.

Abstract: Understanding cascading processes on complex network topologies is paramount for modelling how diseases, information, fake news and other media spread. In this article, we extend the multi-type branching process method developed in Keating et al., (2022), which relies on networks having homogenous node properties, to a more general class of clustered networks. Using a model of socially inspired complex contagion we obtain results, not just for the average behaviour of the cascades but for full distributions of the cascade properties. We introduce a new method for the inversion of probability generating functions to recover their underlying probability distributions; this derivation naturally extends to higher dimensions. This inversion technique is used along with the multi-type branching process to obtain univariate and bivariate distributions of cascade properties. Finally, using clique-cover methods, we apply the methodology to synthetic and real-world networks and compare the theoretical distribution of cascade sizes with the results of extensive numerical simulations.

A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the ``small cut-cell"" problem without mesh modifications, cell merging, or state redistribution. Spatial discretizations are based on a weighted least-squares technique that has been extended to fourth-order operators and boundary conditions, including an approximate projection to enforce the divergence-free constraint. Solutions are advanced in time using a fourth-order additive implicit-explicit Runge-Kutta method, with the viscous and source terms treated implicitly and explicitly, respectively. Formal accuracy of the method is demonstrated with several grid convergence studies, and results are shown for an application with a complex bio-inspired material. The developed method achieves fourth-order accuracy and is stable despite the pervasive small cells arising from complex geometries.

In this paper, we explore affine semigroup versions of the convex geometry theorems of Helly, Tverberg, and Carathéodory. Additionally, we develop a new theory of colored affine semigroups, where the semigroup generators each receive a color and the elements of the semigroup take into account the colors used (the classical theory of affine semigroups coincides with the case in which all generators have the same color). We prove an analog of Tverberg’s theorem and colorful Helly’s theorem for semigroups, as well as a version of colorful Carathéodory’s theorem for cones. We also demonstrate that colored numerical semigroups are particularly rich by introducing a colored version of the Frobenius number.

We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems with high-contrast and spatially varying coefficients, large discontinuities in the source term, and complex interface geometries. We include a generalized truncation error analysis based on cell-centered Taylor series expansions, which then define stencils in terms of local discrete solution data and geometric information. In the process, we develop a simple method based on Green's theorem for computing exact geometric moments directly from an implicit function definition of the embedded interface. This approach produces stencils with a simple bilinear representation, where spatially-varying coefficients and jump conditions can be easily included and finite volume conservation can be enforced.

Motivated by the analysis of the performance of the simplex method, we study the behavior of families of pivot rules of linear programs. We introduce normalized-weight pivot rules which are fundamental for the following reasons: First, they are memory-less, in the sense that the pivots are governed by local information encoded by an arborescence. Second, many of the most used pivot rules belong to that class, and we show this subclass is critical for understanding the complexity of all pivot rules. Finally, normalized-weight pivot rules can be parametrized in a natural continuous manner. The latter leads to the existence of two polytopes, the pivot rule polytopes and the neighbotopes, that capture the behavior of normalized-weight pivot rules on polytopes and linear programs. We explain their face structure in terms of multi-arborescences and compute upper bounds on the number of coherent arborescences, that is, vertices of our polytopes. We introduce a normalized-weight pivot rule, called the max-slope pivot rule, which generalizes the shadow-vertex pivot rule. The corresponding pivot rule polytopes and neighbotopes refine the monotone path polytopes of Billera and Sturmfels. Our constructions are important beyond optimization and provide new perspectives on classical geometric combinatorics. Special cases of our polytopes yield permutahedra, associahedra, and multiplihedra. For the greatest-improvement pivot rules we draw connections to sweep polytopes and polymatroids.

This article presents a fast and approximate multifrontal solver for large sparse linear systems. In a recent work by Liu et al., we showed the efficiency of a multifrontal solver leveraging the butterfly algorithm and its hierarchical matrix extension, HODBF (hierarchical off-diagonal butterfly) compression to compress large frontal matrices. The resulting multifrontal solver can attain quasi-linear computation and memory complexity when applied to sparse linear systems arising from spatial discretization of high-frequency wave equations. To further reduce the overall number of operations and especially the factorization memory usage to scale to larger problem sizes, in this article we develop a composite multifrontal solver that employs the HODBF format for large-sized fronts, a reduced-memory version of the nonhierarchical block low-rank format for medium-sized fronts, and a lossy compression format for small-sized fronts. This allows us to solve sparse linear systems of dimension up to 2.7 × larger than before and leads to a memory consumption that is reduced by 70% while ensuring the same execution time. The code is made publicly available in GitHub.

Abstract: We study constructible invariants of the moduli space $$\hspace{0.83328pt}\overline{\hspace{-0.83328pt}\mathcal {M}\hspace{-0.83328pt}}\hspace{0.83328pt}(\varvec{x})$$ M ¯ ( x ) of stable maps from genus zero curves to $$\mathbb {P}^1$$ P 1 , relative to 0 and $$\infty $$ ∞ , with ramification profiles specified by $${\varvec{x}\in \mathbb {Z}^n}$$ x ∈ Z n . These spaces are central to the enumerative geometry of $$\mathbb {P}^1$$ P 1 , and provide a large family of birational models of the Deligne–Mumford–Knudsen moduli space $$\hspace{0.83328pt}\overline{\hspace{-0.83328pt}\mathcal {M}\hspace{-0.83328pt}}\hspace{0.83328pt}_{0,n}$$ M ¯ 0 , n . For the sequence of vectors $$\varvec{x}$$ x corresponding to maps which are maximally ramified over 0 and unramified over $$\infty $$ ∞ , we prove that a generating function for the topological Euler characteristics of these spaces satisfies a differential equation which allows for its recursive calculation. We also show that the class $${[\hspace{0.83328pt}\overline{\hspace{-0.83328pt}\mathcal {M}\hspace{-0.83328pt}}\hspace{0.83328pt}(\varvec{x})] \in K_0(\textsf{Var}/\mathbb {C})}$$ [ M ¯ ( x ) ] ∈ K 0 ( Var / C ) of the moduli space in the Grothendieck ring of varieties is constant as $$\varvec{x}$$ x varies within a fixed chamber in the resonance decomposition of $$\mathbb {Z}^n$$ Z n . We conclude by suggesting several further directions in the study of these spaces, giving conjectures on (1) the asymptotic behavior of the Euler characteristic and (2) a potential chamber structure for the Chern numbers.

In this study, a marine fog event that occurred from 0000 to 1800 UTC 7 September 2018 near Canada’s Grand Banks is used to investigate the sensitivity of simulated fog properties to six model parameters found primarily in the microphysics scheme. To do so, we ran a large suite of regional simulations that spanned the life cycle of the fog event using the Regional Atmospheric Modeling System (RAMS). We randomly selected parameter combinations for the simulation suite and used Gaussian process regression to emulate the response of a variety of simulated fog properties to the parameters. We find that the microphysics shape parameter, which controls the relative width of the droplet size distribution, and the aerosol number concentration have the greatest impact on fog in terms of spatial extent, duration, and surface visibility. In general, parameters that reduce mean fall speed of droplets and/or suppress drizzle formation lead to reduced visibility in fog but also delayed onset, shorter lifetimes, and reduced spatial extent. The importance of the distribution width suggests a need for better characterization of this property for fog droplet distributions and better treatment of this property in microphysics schemes.

In many real life situations one has m types of random events happening in chronological order within a time interval and one wishes to predict various milestones about these events or their subsets. An example is birdwatching. Suppose we can observe up to m different types of birds during a season. At any moment a bird of type i is observed with some probability. There are many natural questions a birdwatcher may have: how many observations should one expect to perform before recording all types of birds? Is there a time interval where the researcher is most likely to observe all species? Or, what is the likelihood that several species of birds will be observed at overlapping time intervals? Our paper answers these questions using a new model based on random interval graphs. This model is a natural follow up to the famous coupon collector’s problem.

Cannabis use is growing among older adults to manage medical concerns including poor sleep. In this study, we characterized how patients seen at a geriatrics clinic use cannabis to address sleep disturbance. Specifically, we conducted an anonymous survey of 568 adults, including 83 who reported cannabis use within the past 3 years, to inquire about such use. We compared cannabis use characteristics between those using it for sleep disturbance versus all other conditions. We considered a p-value

Problem definition: The Centers for Medicare & Medicaid Services launched the Primary Care First (PCF) initiative in January 2021. The initiative builds upon prior innovative payment models and aims at incentivizing a redesign of primary care delivery, including new modes of delivery, such as remote care. To achieve this goal, the initiative blends capitation and fee-for-service (FFS) payments and includes performance-based adjustments linked to service quality and health outcomes. We analyze a model motivated by this new payment system, and its impact on the different stakeholders, and derive insights on how to design it to reach the best possible outcome. Methodology/results: We propose an analytical model that captures patient heterogeneity in terms of health complexity, provider choice of care-delivery mode (referral to a specialist, in-person visit, or remote care), and quality of service (health outcomes and wait time). We analyze the provider decision on the mode of care delivery under both FFS and PCF and study whether PCF can be designed to yield a socially optimal outcome. We characterize analytically when patients, payer, and providers are better off under PCF and show that, in many cases, PCF can be designed to yield a socially optimal outcome. We numerically calibrate our model for 14 states in the United States. We observe that the average health status in a state is a source of heterogeneity that crucially drives the performance of PCF. We find that the model motivated by the current PCF implementation results in too much adoption of referral care and too little adoption of remote care. In addition, states with poor average health status may use more in-person care than socially optimal under a baseline (low) level of capitation. Moreover, relying on high levels of capitation leads to low adoption of in-person care. Managerial implications: Our results have health policy implications by shedding light on how PCF might impact patients, payer, and providers. Under the current performance-based adjustments, low levels of capitation should be preferred. PCF has the potential to be designed to achieve socially optimal outcomes. However, the fee per visit may need to be tailored to the local population’s health status. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.1207 .

This article proposes an adaptive robust formation control scheme for the connected and autonomous vehicle (CAV) swarm system by utilizing swarm property, diffeomorphism transformation, and constraint following. The control design is processed by starting from a 2-D dynamics model with (possibly fast) time varying but bounded uncertainty. The uncertainty bounds are unknown. For compact formation, the CAV system is treated as an artificial swarm system, for which the ideal swarm performance is taken as a desired constraint. By this, formation control is converted into a problem of constraint following and then a performance measure β is defined as the control object to evaluate the constraint following error. For collision avoidance, a diffeomorphism transformation on space measure between two vehicles is creatively performed, by which the space measure is positive restricted. For uncertainty handling, an adaptive robust control scheme is proposed to render the β -measure to be uniformly bounded and uniformly ultimately bounded, that is, drive the controlled (CAV) swarm system to follow the desired constraint approximatively. As a result, the system can achieve the ideal swarm performance; thereout, compact formation is realized, regardless of the uncertainty. The main contribution of this article is exploring a 2-D formation control scheme for (CAV) swarm system under the consideration of collision avoidance and time-varying uncertainty.

Abstract: Model reduction methods usually focus on the error performance analysis; however, in presence of uncertainties, it is important to analyze the robustness properties of the error in model reduction as well. This problem is particularly relevant for engineered biological systems that need to function in a largely unknown and uncertain environment. We give robustness guarantees for structured model reduction of linear and nonlinear dynamical systems under parametric uncertainties. We consider a model reduction problem where the states in the reduced model are a strict subset of the states of the full model, and the dynamics for all of the other states are collapsed to zero (similar to quasi‐steady‐state approximation). We show two approaches to compute a robustness guarantee metric for any such model reduction—a direct linear analysis method for linear dynamics and a sensitivity analysis based approach that also works for nonlinear dynamics. Using the robustness guarantees with an error metric and an input‐output mapping metric, we propose an automated model reduction method to determine the best possible reduced model for a given detailed system model. We apply our method for the (1) design space exploration of a gene expression system that leads to a new mathematical model that accounts for the limited resources in the system and (2) model reduction of a population control circuit in bacterial cells.

We develop and solve a constrained optimization model to identify an integrable optics rapid-cycling synchrotron lattice design that performs well in several capacities. Our model encodes the design criteria into 78 linear and nonlinear constraints, as well as a single nonsmooth objective, where the objective and some constraints are defined from the output of Synergia, an accelerator simulator. We detail the difficulties of optimizing within the 32-dimensional, simulation-constrained decision space and establish that the space is nonempty. We use a derivative-free manifold sampling algorithm to account for structured nondifferentiability in the objective function. Our numerical results quantify the dependence of approximate solutions on constraint parameters and the effect of the form of objective function.

We consider unconstrained stochastic optimization problems with no available gradient information. Such problems arise in settings from derivative-free simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients using finite differences of stochastic function evaluations within a common random number framework. We develop modified versions of a norm test and an inner product quasi-Newton test to control the sample sizes used in the stochastic approximations and provide global convergence results to the neighborhood of a locally optimal solution. We present numerical experiments on simulation optimization problems to illustrate the performance of the proposed algorithm. When compared with classical zeroth-order stochastic gradient methods, we observe that our strategies of adapting the sample sizes significantly improve performance in terms of the number of stochastic function evaluations required.

Since Galileo's time, the pendulum has evolved into one of the most exciting physical objects in mathematical modeling due to its vast range of applications for studying various oscillatory dynamics, including bifurcations and chaos, under various interests. This well-deserved focus aids in comprehending various oscillatory physical phenomena that can be reduced to the equations of the pendulum. The present article focuses on the rotational dynamics of the two-dimensional forced-damped pendulum under the influence of the ac and dc torque. Interestingly, we are able to detect a range of the pendulum's length for which the angular velocity exhibits a few intermittent extreme rotational events that deviate significantly from a certain well-defined threshold. The statistics of the return intervals between these extreme rotational events are supported by our data to be spread exponentially at a specific pendulum's length beyond which the external dc and ac torque are no longer sufficient for a full rotation around the pivot. The numerical results show a sudden increase in the size of the chaotic attractor due to interior crisis, which is the source of instability that is responsible for triggering large amplitude events in our system. We also notice the occurrence of phase slips with the appearance of extreme rotational events when the phase difference between the instantaneous phase of the system and the externally applied ac torque is observed.

Growth mindset (belief in the malleability of intelligence) is a unique predictor of young learners' increased motivation and learning, and may have broader implications for cognitive functioning. Its role in learning in older adulthood is unclear. As part of a larger longitudinal study, we examined growth mindset and cognitive functioning in older adults engaged in a 3-month multi-skill learning intervention that included growth mindset discussions. Before, during, and after the intervention, participants reported on their growth mindset beliefs and completed a cognitive battery. Study 1 indicated that intervention participants, but not control participants, increased their growth mindset during the intervention. Study 2 replicated these results and found that older adults with higher preexisting growth mindsets showed larger cognitive gains at posttest compared to those with lower preexisting growth mindsets. Our findings highlight the potential role of growth mindset in supporting positive learning cycles for cognitive gains in older adulthood.

AbstractIn the last decade, the interactions among histone modifications and DNA methylation and their effect on the DNA structure, i.e., chromatin state, have been identified as key mediators for the maintenance of cell identity, defined as epigenetic cell memory. In this paper, we determine how the positive feedback loops generated by the auto- and cross-catalysis among repressive modifications affect the temporal duration of the cell identity. To this end, we conduct a stochastic analysis of a recently published chromatin modification circuit considering two limiting behaviors: fast erasure rate of repressive histone modifications or fast erasure rate of DNA methylation. In order to perform this mathematical analysis, we first show that the deterministic model of the system is a singular singularly perturbed (SSP) system and use a model reduction approach for SSP systems to obtain a reduced one-dimensional model. We thus analytically evaluate the reduced system’s stationary probability distribution and the mean switching time between active and repressed chromatin states. We then add a computational study of the original reaction model to validate and extend the analytical findings. Our results show that the absence of DNA methylation reduces the bias of the system’s stationary probability distribution toward the repressed chromatin state and the temporal duration of this state’s memory. In the absence of repressive histone modifications, we also observe that the time needed to reactivate a repressed gene with an activating input is less stochastic, suggesting that repressive histone modifications specifically contribute to the highly variable latency of state reactivation.

Aviation is one of the most global industries, and if we can model and predict a country’s air transportation flow and indicators ahead of time, we may be able to use it as a key decision-making tool for the management and operation process. This study proposes a new modeling, and prediction method that employs both fractional calculus and Multi Deep Assessment Methodology (MDAM) techniques. For the application, air passengers carried, air freight, available seat kilometers, number of flights, destination points, international travelers, international destination points, and international flight data between 2011 and 2019 for eight countries with the busiest airports were chosen. As a result, the highest modeling error was discovered to be Germany’s air transport freight factor expressed as a percentage of 1,59E-02. The percentage of predictions with errors less than 10% was 90.278. We also compared the performance of two different MDAM methodologies. The novel MDAM wd methodology proposed in this paper has a higher accuracy in aviation factors prediction and modeling.