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Rats and pigeons have shown striking differences in their behavior in the suboptimal choice procedure: while pigeons show a strong and consistent preference for the discriminative alternative, most studies performed with rats have found optimal preferences, and in the cases in which suboptimal preferences have been reported, those results have not been replicated. Currently, there is no consensus about the reasons for these discrepant results between species, but different explanations have been proposed either with an empirical base or exclusively in theoretical terms. In the latter category it has been proposed that the discrepancy might have arisen because of differences in the relationship between the natural foraging response of each species, and the response required in the laboratory. For analyzing this possibility, we conducted two experiments carried out within a maze that was specifically designed to allow rats to display behaviors related to their natural foraging. In experiment 1, we explored rats' preferences when facing a discriminative alternative with probability of reinforcement (p) = 0.5, and a non-discriminative alternative with p =.75. In experiment 2, we evaluated preferences when the discriminative alternative had p =.20 and the non-discriminative had p =.50, rats were evaluated in a closed economy, with longer terminal links, and were allowed to escape from the outcome found. In both studies, rats showed a strong preference for the non-discriminative alternative and showed very high levels of discrimination between the positive and the negative outcomes of the discriminative alternative. [ABSTRACT FROM AUTHOR]

According to a recent proposal, natural concepts are represented in an optimally designed similarity space, adhering to principles a skilled engineer would use for creatures with our perceptual and cognitive capacities. One key principle is that natural concepts should be easily learnable. While evidence exists for parts of this optimal design proposal, there has been no direct evidence linking naturalness to learning until now. This article presents results from a computational study on perceptual color space, demonstrating that naturalness indeed facilitates learning. [ABSTRACT FROM AUTHOR]

This is a commentary for a special issue on predictive processing and rational constructivist models of development. Mainly I use the opportunity to ask a bunch of questions about what these theoretical frameworks show us (and what they do not) and mostly where the open questions still are. To get meta for a moment, I thought these questions were the best way to maximize the value of my commentary: They have the highest probability of leading to the most uncertainty reduction for our field in the long term. Please read in that spirit. [ABSTRACT FROM AUTHOR]

Abstract.Adaptive designs for clinical trials address the ethical requirement of allocating fewer patients to the inferior treatment as the trial progresses. We present here a generic strategy partly motivated by play-the-winner heuristic for reducing the variability of such designs. It is shown through simulations from a real clinical setting that employing this strategy improves the safety and the performance of some standard response adaptive designs. A closely related alternate strategy amenable to a theoretical analysis is also proposed with the same objective of lower variability. [ABSTRACT FROM AUTHOR]

The moving sofa problem, introduced by Leo Moser in 1966, seeks to determine the maximal area of a 2D shape that can navigate an L-shaped corridor of unit width. Joseph Gerver's 1992 solution, providing a lower bound of approximately 2.2195, is the best known, though its global optimality remains unproven. This paper leverages neural networks' approximation power and recent advances in invexity optimization to explore global optimality. We propose two approaches supporting Gerver's conjecture that his sofa is the unique global maximum. The first approach uses continuous function learning, discarding assumptions about the monotonicity, symmetry, and differentiability of sofa movements. The sofa area is computed as a differentiable function using our "waterfall" algorithm, with the loss function incorporating both differential terms and initial conditions based on physics-informed machine learning. Extensive training with diverse network initialization consistently converges to Gerver's solution. The second approach applies discrete optimization to the Kallus–Romik upper bound, improving it from 2.37 to 2.3337 for five rotation angles. As the number of angles increases, our model asymptotically converges to Gerver's area from above, indicating that no larger sofa exists. [ABSTRACT FROM AUTHOR]

Through suitable changes of variables for a typical problem in hyper-elasticity, either in the reference or deformed configurations, one can setup and analyze versions of the same problem in terms of inner or outer maps or variations. Though such kind of transformations are part of the classical background in the Calculus of Variations, we explore under what sets of hypotheses such versions can be shown to have minimizers and be equivalent to the standard form of the problem. Such sets of hypotheses lead naturally to some distinct poly-convex energy densities for hyper-elasticity. Likewise we explore optimality in either of the two forms through a special way to generate one-parameter families of feasible deformations, feasibility including injectivity and non-interpenetration of matter. [ABSTRACT FROM AUTHOR]

Extant crocodilian jaws are subject to functional demands induced by feeding and hydrodynamics. However, the morphological and ecological diversity of extinct crocodile-line archosaurs is far greater than that of living crocodilians, featuring repeated convergence towards disparate ecologies including armoured herbivores, terrestrial macropredators and fully marine forms. Crocodile-line archosaurs, therefore, present a fascinating case study for morphological and functional divergence and convergence within a clade across a wide range of ecological scenarios. Here, we build performance landscapes of two-dimensional theoretical jaw shapes to investigate the influence of strength, speed and hydrodynamics in the morphological evolution of crocodile-line archosaur jaws, and test whether ecologically convergent lineages evolved similarly optimal jaw function. Most of the 243 sampled jaw morphologies occupy optimized regions of theoretical morphospace for either rotational efficiency, resistance to Von Mises stress, hydrodynamic efficiency or a trade-off between multiple functions, though some seemingly viable shapes remain unrealized. Jaw speed is optimized only in a narrow region of morphospace whereas many shapes possess optimal jaw strength, which may act as a minimum boundary rather than a strong driver for most taxa. This study highlights the usefulness of theoretical morphology in assessing functional optimality, and for investigating form–function relationships in diverse clades. [ABSTRACT FROM AUTHOR]

In this paper, we study the asymptotic behavior of transmission system for coupled Kirchhoff plates, where one equation is conserved and the other has dissipative property, and the dissipation mechanism is given by fractional damping (- Δ) 2 θ v t with θ ∈ [ 1 2 , 1 ] . By using the semigroup method and the multiplier technique, we obtain the exact polynomial decay rates, and find that the polynomial decay rate of the system is determined by the inertia/elasticity ratios and the fractional damping order. Specifically, when the inertia/elasticity ratios are not equal and θ ∈ [ 1 2 , 3 4 ] , the polynomial decay rate of the system is t - 1 / (10 - 4 θ) . When the inertia/elasticity ratios are not equal and θ ∈ [ 3 4 , 1 ] , the polynomial decay rate of the system is t - 1 / (4 + 4 θ) . When the inertia/elasticity ratios are equal, the polynomial decay rate of the system is t - 1 / (4 + 4 θ) . Furthermore it has been proven that the obtained decay rates are all optimal. The obtained results extend the results of Oquendo and Suárez (Z Angew Math Phys 70(3):88, 2019) for the case of fractional damping exponent 2 θ from [0, 1] to [1, 2]. [ABSTRACT FROM AUTHOR]

We give a detailed proof of a well-known theorem in quantum computing. The theorem characterizes the number of two-qubit gates that is necessary for implementing three-qubit quantum gates with two controls. For example, the theorem implies that five 2-qubit gates are necessary for implementing the Toffoli gate. No detailed proof was available earlier. [ABSTRACT FROM AUTHOR]

In this study, we derive a simple transportation scheme by post-optimizing the costs of a modified problem. The strategy attempts to make the original (mainly feasible) option more practicable by adjusting the building components' costs. Next, we employ the previously mentioned cell or area cost operators to gradually restore the modified costs to their initial levels, while simultaneously implementing the necessary adjustments to the "optimal" solution. This work presents a multi-goal, multi-item substantial transportation problem with interval-valued fuzzy variables, such as transportation costs, supplies, and demands, as parameters to maintain the transportation cost. This research addresses two circumstances where task ambiguity may occur: the interval solids transportation problem and the fuzzy substantial transportation issue. In the first scenario, we express data problems as intervals instead of exact values using an interval-valued fermatean neutrosophic number; in the second case, the information is not entirely obvious. We address both models when uncertainty solely affects the constraint set. For the interval scenario, we define an additional problem to solve. Our existing efficient systems have dependable transportation, so they are also capable of handling this new problem. In the fuzzy case, a parametric technique generates a fuzzy solution to the preceding problem. Since transportation costs have a direct impact on market prices, lowering them is the primary goal. Using parametric analysis, we provide optimal parameterization solutions for complementary situations. We provide a recommended algorithm for determining the stability set. In conclusion, we offer a sensitivity analysis and a numerical example of the transportation problem involving both balanced and imbalanced loads. [ABSTRACT FROM AUTHOR]

To reduce total test time and increase the efficiency of statistical analysis of a life-testing experiment adaptive progressive Type-II censoring scheme has been proposed. This paper addresses the statistical inference of the unknown parameters, reliability, and hazard rate functions of logistic exponential distribution under adaptive progressive Type-II censored samples. Maximum likelihood estimates (MLEs) and maximum product spacing estimates (MPSEs) for the model parameters, reliability, and hazard rate functions can not be obtained explicitly, hence these are derived numerically using the Newton–Raphson method. Bayes estimates for the unknown parameters and reliability and hazard rate functions are computed under squared error loss function (SELF) and linear exponential loss function (LLF). It has been observed that the Bayes estimates are not in explicit forms, hence an approximation method such as Markov Chain Monte Carlo (MCMC) method is employed. Further, asymptotic confidence intervals (ACIs) and highest posterior density (HPD) credible intervals for the unknown parameters, reliability, and hazard rate functions are constructed. Besides, point and interval Bayesian predictions have been derived for future samples. A Monte Carlo simulation study has been carried out to compare the performance of the proposed estimates. Furthermore, three different optimality criteria have been considered to obtain the optimal censoring plan. Two real-life data sets, one from electronic industry and other one from COVID-19 data set containing the daily death rate from France are re-analyzed to demonstrate the proposed methodology. [ABSTRACT FROM AUTHOR]

In the context of an energy crisis, efficient energy management has become an unavoidable issue for sustainability, regardless of the domain under consideration. Smart grids are no exception; they aim to motivate energy optimization according to billing strategies and users’ comfort. In this paper, two optimization problems (OP) are proposed involving billing strategies and users’ flexibility. A single-centralized OP aims to minimize the total energy provided by a company, while a distributed OP targets minimizing individual user costs independently, involving users’ flexibilities, different billing strategies, and a variable number of users, with random appliances assigned during simulations. The resolution was carried out using the Non-dominated Sorting Algorithm II and Multi-Criteria Analysis, with a Game-based algorithm also utilized. Additionally, simulations were performed under three billing mechanisms. The findings show that costs decrease exponentially with user participation. Similarly, both individual user costs and total costs at the energy provider level were minimized as users’ flexibilities increased. The Peak-to-Average-Ratio is minimized and exhibits a bimodal behavior when observed as a random variable. Regarding the interplay of billing mechanisms, simulation results demonstrate that the smart billing mechanism proposed by the authors outperforms other billing models proposed in the literature for both consumers and utility companies. [ABSTRACT FROM AUTHOR]

This article analyzes the theoretical and methodological provisions of seminal works concerning the efficiency of research, development and development management, and production for hi-tech products in the context of uncertainty in order to make reliable managerial decisions. Competitive advantages can be achieved and the market share of Russian-made competitive products can be increased by combining the improvement of their technological specifications when using cutting-edge materials and components with economic, process, and production capabilities of manufacturing. The probabilistic assessment of reliable managerial decisions is based on information theories. [ABSTRACT FROM AUTHOR]

Providing sufficient, high-quality food without compromising efforts in climate change and environmental pollution control is a long-term imperative for humanity. Livestock product trade may help bridge the gap in micro-nutrient supply; however, its potential environmental impacts remain underexplored. Using data from 200 countries and 77 different livestock commodities from 1961 to 2019, this study uncovers the impact of livestock trade on micro-nutrient productivity per livestock unit and per feed nitrogen input. Our results indicate that livestock trade has improved productivity for all seven studied micro-nutrients over the past 59 years, except for vitamin A. This improvement has led to a substantial reduction in the number of livestock units and feed nitrogen requirements needed to deliver the same amount of micro-nutrients, thereby reducing related greenhouse gas emissions and nitrogen losses globally. Generally, livestock trade has become more optimal and functional in terms of livestock productivity and feed use efficiency, particularly in the most recent decade, although there were slight differences between various micro-nutrients. We recommend continuing and potentially increasing international livestock trade, given the higher efficiency gap between exporting and importing countries; however, this should be structured more appropriately. [ABSTRACT FROM AUTHOR]

A code has locality r if a symbol in any coordinate of a codeword in the code can be recovered by accessing the value of at most r other coordinates. Such codes are called locally recoverable codes (LRCs for short). Since LRCs can recover a failed node by accessing the minimum number of the surviving nodes, these codes are used in distributed storage systems such as Microsoft Azure. In this paper, constacyclic LRCs are obtained from their parity-check polynomials. Constacyclic codes with locality r ≤ 2 and dimension 2 are obtained and a sufficient and necessary condition for these codes to have locality 1 is given. Then, the construction is generalized. Distance optimal constacyclic LRCs with distance 2 are obtained. Also, constacyclic codes with locality 1 are constructed. They may be so useful in practice thanks to their minimum locality. Constacyclic codes whose locality is equal to their dimension are given. Furthermore, constacyclic LRCs are obtained from cyclotomic cosets. [ABSTRACT FROM AUTHOR]

When dealing with the discretization of differential equations on non‐rectangular domains, a careful treatment of the boundary is mandatory and may result in implementation difficulties and in coefficient matrices without a prescribed structure. Here we examine the numerical solution of a two‐dimensional constant coefficient distributed‐order space‐fractional diffusion equation with a nonlinear term on a convex domain. To avoid the aforementioned inconvenience, we resort to the volume‐penalization method, which consists of embedding the domain into a rectangle and in adding a reaction penalization term to the original equation that dominates in the region outside the original domain and annihilates the solution correspondingly. Thanks to the volume‐penalization, methods designed for problems in rectangular domains are available for those in convex domains and by applying an implicit finite difference scheme we obtain coefficient matrices with a 2‐level Toeplitz structure plus a diagonal matrix which arises from the penalty term. As a consequence of the latter, we can describe the asymptotic eigenvalue distribution as the matrix size diverges as well as estimate the intrinsic asymptotic ill‐conditioning of the involved matrices. On these bases, we discuss the performances of the conjugate gradient with circulant and τ$$ \tau $$‐preconditioners and of the generalized minimal residual with split circulant and τ$$ \tau $$‐preconditioners and conduct related numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of generalized convexity for an $ E $-differentiable multiobjective variational problem, and to solve this problem, an associated multiobjective $ E $-variational problem is formulated with the help of an $ E $-operator. The necessary and sufficient optimality conditions are derived under the assumption of $ E $-convexity. The so-called Wolfe and Mond-Weir $ E $-dual problems are defined for the considered $ E $-differentiable multiobjective variational programming problem, and several Wolfe and Mond-Weir $ E $-duality theorems are derived under the $ E $-convexity assumption. Furthermore, to emphasize the significance of the results of this study, we considered a cake-eating problem, and the solution obtained by constructing its associated $ E $-differentiable problem and the sufficiency theorem. Throughout the paper, non-trivial illustrations are presented to support the findings. [ABSTRACT FROM AUTHOR]

The JPEG algorithm is a defacto standard for image compression. We investigate whether adaptive mesh refinement can be used to optimize the compression ratio and propose a new adaptive image compression algorithm. We prove that it produces a quasi-optimal subdivision grid for a given error norm with high probability. This subdivision can be stored with very little overhead and thus leads to an efficient compression algorithm. We demonstrate experimentally, that the new algorithm can achieve better compression ratios than standard JPEG compression with no visible loss of quality on many images. The mathematical core of this work shows that Binev's optimal tree approximation algorithm is applicable to image compression with high probability, when we assume small additive Gaussian noise on the pixels of the image. [ABSTRACT FROM AUTHOR]

One of the main challenges in cancer treatment is the selection of treatment resistant clones which leads to the emergence of resistance to previously efficacious therapies. Identifying vulnerabilities in the form of cellular tradeoffs constraining the phenotypic possibility space could allow to avoid the emergence of resistance by simultaneously targeting cellular processes that are involved in different alternative phenotypic strategies linked by trade-offs. The Pareto optimality theory has been proposed as a framework allowing to identify such trade-offs in biological data from its prediction that it would lead to the presence of specific geometrical patterns (polytopes) in, e.g., gene expression space, with vertices representing specialized phenotypes. We tested this approach in diffuse large B-cell lymphoma (DLCBL) transcriptomic data. As predicted, there was highly statistically significant evidence for the data forming a tetrahedron in gene expression space, defining four specialized phenotypes (archetypes). These archetypes were significantly enriched in certain biological functions, and contained genes that formed a pattern of shared and unique elements among archetypes, as expected if trade-offs between essential functions underlie the observed structure. The results can be interpreted as reflecting trade-offs between aerobic energy production and protein synthesis, and between immunotolerant and immune escape strategies. Targeting genes on both sides of these trade-offs simultaneously represent potential promising avenues for therapeutic applications. [ABSTRACT FROM AUTHOR]

In this article, we consider the inference of a dependent competing risk model when the data are collected from a simple step-stress stage life testing experiment. We assume that there are two causes of failure and they are dependent causes. The dependency structure is explained through Marshall–Olkin bivariate Weibull distribution. The distribution under two stress levels is connected through Khamis Higgins model. We obtain the maximum likelihood estimates and the Bayes estimates of the model parameters. We also provide the asymptotic confidence intervals, symmetric credible intervals and the highest posterior density credible intervals of the model parameters. An optimality study has been done under different optimality criteria. An extensive simulation study and a data analysis have been performed for illustrative purpose. [ABSTRACT FROM AUTHOR]

This article considers how CUmulative SUM (CUSUM) and Exponentially Weighted Moving Average (EWMA) multi-charts were used to monitor the variance (variability). Multi-chart schemes are a combination of several single charts that detect changes in a process quickly. We give a theoretical equation to arrive at the optimality of the CUSUM multi-chart for the variance. Simulation studies and asymptotic analyses show that the CUSUM multi-chart has better performance than the EWMA multi-chart in detecting variance shifts in an $$i.i.d.$$ i. i. d. normal observations. The variance change problem has diverse and attractive application areas; we give a real example in the field of agriculture that monitors the price variability of maize to demonstrate the practicality of the schemes. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new classes of higher order generalized strong invex functions under non-differentiable settings. The optimality results are derived for higher order strict global minimizers of non-differentiable multiobjective programming problems using these functions. Numerical examples and illustrations are provided in support of new classes of functions and the optimality conditions. We also study the mixed dual problem and establish weak, strong and converse duality results. Furthermore, as an application, we present a non-differentiable case of vector variational-like inequality problem and establish the equivalence between its solutions and higher order strict global minimizers of the non-differentiable multiobjective programming problem. [ABSTRACT FROM AUTHOR]

In this paper, my aim is to develop a phenomenological understanding of discrimination from the perspective of the discriminator. Since early existential phenomenology, the phenomenon of discrimination has received a great deal of attention. While much of this work has focused on the experience of the discriminatee, recent scholarship has begun to reflect on the intentional structures on the side of the discriminator. In a contribution to this trend, I argue that our sense of what is (ab)normal plays a constitutively significant role in the reiteration and reinforcement of harmful discriminatory practices. More specifically, I argue that Husserl's distinction between two forms of normality, namely, concordance-normality [Einstimmigkeit] and optimal-normality [Optimalität], is an important tool for illuminating otherwise overlooked aspects of the discriminator's experience. I achieve this by demonstrating how these two notions of normality play distinct constitutive roles when comparing deliberate acts of discrimination committed with malintent, compared with more habitual and prereflective expectations which are already discriminatory in nucleo. I argue that at the heart of discriminatory practices there is a naïve, normalizing attempt to stabilize concordance at the expense of critical self-reflection, normative revisions, and enriched horizons of expectation. In doing so, this paper provides a novel and important contribution to philosophical discussions surrounding discrimination. [ABSTRACT FROM AUTHOR]

Purpose: A progressive hybrid censoring scheme (PHCS) becomes impractical for ensuring dependable outcomes when there is a low likelihood of encountering a small number of failures prior to the predetermined terminal time T. The generalized progressive hybrid censoring scheme (GPHCS) efficiently addresses to overcome the limitation of the PHCS. Design/methodology/approach: In this article, estimation of model parameter, survival and hazard rate of the Unit-Lindley distribution (ULD), when sample comes from the GPHCS, have been taken into account. The maximum likelihood estimator has been derived using Newton–Raphson iterative procedures. Approximate confidence intervals of the model parameter and their arbitrary functions are established by the Fisher information matrix. Bayesian estimation procedures have been derived using Metropolis–Hastings algorithm under squared error loss function. Convergence of Markov chain Monte Carlo (MCMC) samples has been examined. Various optimality criteria have been considered. An extensive Monte Carlo simulation analysis has been shown to compare and validating of the proposed estimation techniques. Findings: The Bayesian MCMC approach to estimate the model parameters and reliability characteristics of the generalized progressive hybrid censored data of ULD is recommended. The authors anticipate that health data analysts and reliability professionals will get benefit from the findings and approaches presented in this study. Originality/value: The ULD has a broad range of practical utility, making it a problem to estimate the model parameters as well as reliability characteristics and the significance of the GPHCS also encourage the authors to consider the present estimation problem because it has not previously been discussed in the literature. [ABSTRACT FROM AUTHOR]

Abstract The exchange of carbon dioxide and water vapor between terrestrial ecosystems and the atmosphere is regulated by stomata (small pores in the leaves of plants). Unsurprisingly, environmental factors controlling the opening and closure of stomata has been sought as early as 1800. One approach, popularized in the early 1970s, is a stomatal optimization framework. This framework is based on the hypothesis that plants optimize carbon gain subject to water loss or water availability constraints. This constraint optimization problem was solved in various forms assuming instantaneous adjustments of stomatal aperture to maximize a reward function with no future foresight or legacy effects. Holtzman et al. (2024, https://doi.org/10.1029/2023av001113) offers a novel approach that can diagnose the effective timescale over which the reward function maximization must be time‐integrated. The developed method thus optimizes an integrated carbon gain function but adjusted by a discount factor subject to water availability in the root zone. The discount factor considers how the plant values carbon gain to save water and its timescale can be inferred from observations because the model is analytically tractable. The results suggest that the most important climate factor that determines this discount timescale is multi‐annual mean of the longest dry period during the growing season. The findings highlight how local climate traits influence the spatial variation in ecosystem‐level water use strategies. This sets the stage for expanding such a framework to cases where multiple constraints act in concert while operating at distinct time scales.

This article presents a proactive approach to resolving the conflict between safety and optimality for continuous-time (CT) safety-critical systems with unknown dynamics. The presented method guarantees safety and performance specifications by combining two controllers: a safe controller and an optimal controller. On the one hand, the safe controller is designed using only input and state data measurements and without requiring the state derivative data, which are typically required in data-driven control of CT systems. State derivative measurement is costly, and its approximation introduces noise to the system. On the other hand, the optimal controller is learned using a low-complexity one-shot optimization problem, which again does not rely on prior knowledge of the system dynamics and state derivative data. Compared to existing optimal control learning methods for CT systems, which are typically iterative, a one-shot optimization is considerably more sample-efficient and computationally efficient. The share of optimal and safe controllers in the overall control policy is obtained by solving a computationally efficient optimization problem involving a scalar variable in a data-driven manner. It is shown that the contribution of the safe controller dominates that of the optimal controller when the system's state is close to the safety boundaries, and this domination drops as the system trajectories move away from the safety boundaries. In this case, the optimal controller contributes more to the overall controller. The feasibility and stability of the proposed controller are shown. Finally, the simulation results show the efficacy of the proposed approach.

This article investigates the dichotomy between higher statistical power and higher allocation to better treatment in an ethical-optimal response-adaptive design. Although many response-adaptive designs in the literature promise higher allocation to the superior treatment, this is not always guaranteed due to the variability of the designs. A new criterion for evaluating response-adaptive designs, motivated by the value-at-risk measure, is proposed to address this problem. We also provide an illustration of applying this criterion in a real clinical trial.

The moving sofa problem, introduced by Leo Moser in 1966, seeks to determine the maximal area of a 2D shape that can navigate an L-shaped corridor of unit width. Joseph Gerver’s 1992 solution, providing a lower bound of approximately 2.2195, is the best known, though its global optimality remains unproven. This paper leverages neural networks’ approximation power and recent advances in invexity optimization to explore global optimality. We propose two approaches supporting Gerver’s conjecture that his sofa is the unique global maximum. The first approach uses continuous function learning, discarding assumptions about the monotonicity, symmetry, and differentiability of sofa movements. The sofa area is computed as a differentiable function using our “waterfall” algorithm, with the loss function incorporating both differential terms and initial conditions based on physics-informed machine learning. Extensive training with diverse network initialization consistently converges to Gerver’s solution. The second approach applies discrete optimization to the Kallus–Romik upper bound, improving it from 2.37 to 2.3337 for five rotation angles. As the number of angles increases, our model asymptotically converges to Gerver’s area from above, indicating that no larger sofa exists.

Photosynthesis is co-limited by multiple factors depending on the plant and its environment. These include biochemical rate limitations, internal and external water potentials, temperature, irradiance and carbon dioxide (CO 2 ⁠). Amphistomatous leaves have stomata on both abaxial and adaxial leaf surfaces. This feature is considered an adaptation to alleviate CO 2 diffusion limitations in productive environments as the diffusion path length from stomate to chloroplast is effectively halved in amphistomatous leaves. Plants may also reduce CO 2 limitations through other aspects of optimal stomatal anatomy: stomatal density, distribution, patterning and size. Some studies have demonstrated that stomata are overdispersed compared to a random distribution on a single leaf surface; however, despite their prevalence in nature and near ubiquity among crop species, much less is known about stomatal anatomy in amphistomatous leaves, especially the coordination between leaf surfaces. Here, we use novel spatial statistics based on simulations and photosynthesis modelling to test hypotheses about how amphistomatous plants may optimize CO 2 diffusion in the model angiosperm Arabidopsis thaliana grown in different light environments. We find that (i) stomata are overdispersed, but not ideally dispersed, on both leaf surfaces across all light treatments; (ii) the patterning of stomata on abaxial and adaxial leaf surfaces is independent and (iii) the theoretical improvements to photosynthesis from abaxial–adaxial stomatal coordination are miniscule (⁠ ≪ 1 %) across the range of feasible parameter space. However, we also find that (iv) stomatal size is correlated with the mesophyll volume that it supplies with CO 2 ⁠ , suggesting that plants may optimize CO 2 diffusion limitations through alternative pathways other than ideal, uniform stomatal spacing. We discuss the developmental, physical and evolutionary constraints that may prohibit plants from reaching this theoretical adaptive peak of uniform stomatal spacing and inter-surface stomatal coordination. These findings contribute to our understanding of variation in the anatomy of amphistomatous leaves. [ABSTRACT FROM AUTHOR]

In the multidimensional setting, we consider the nonparametric regression estimation with errors-in-variables. Both ordinary smooth noise and super smooth one are assumed for errors in the covariates. An anisotropic kernel estimator is provided based on a deconvolution technique. We study the pointwise estimation and obtain the optimal rates of convergence under the anisotropic Hölder condition. [ABSTRACT FROM AUTHOR]

We consider the problem of optimal partisan gerrymandering: a legislator in charge of redrawing the boundaries of equal-sized congressional districts wants to ensure the best electoral outcome for his own party. The so-called gerrymanderer faces two issues: the number of districts is finite and there is uncertainty at the level of each district. Solutions to this problem consists in cracking favorable voters in as many districts as possible to get tight majorities, and in packing unfavorable voters in the remaining districts. The optimal payoff of the gerrymanderer tends to increase as the uncertainty decreases and the number of districts is large. With an infinite number of districts, this problem boils down to concavifying a function, similarly to the optimal Bayesian persuasion problem. We introduce a measure of fairness and show that optimal gerrymandering is accordingly closer to uniform districting (full cracking), which is most unfair, than to community districting (full packing), which is very fair. [ABSTRACT FROM AUTHOR]

Cross-Over Designs or Repeated Measurements Designs are experimental designs in which treatments (e.g., medicines, fertilizers, diets) are applied to experimental units (usually humans) in different time periods. A common problem is to find the distribution of n experimental units in order to find the optimal experimental design for the well-known criteria of optimality (A, D, E optimality, etc.). If there is only one parameter of interest, the criterion is the minimization of the variance of the parameter estimator. In this case, a Repeated Measurements Design with one parameter of interest (the direct effect of the treatment) is examined and the distribution of n which minimizes the variance of that parameter is found. The objective of the research is the estimation of the variance of the Ordinal Least-Squares estimators of the Repeated Measurements Design model for two treatments and five periods. Heydayat and Afsarinejad introduced the basic model which is used. The optimal Repeated Measurements Designs are derived for n experimental units. Optimality criterion is the minimization of the variance of the estimated direct effects. [ABSTRACT FROM AUTHOR]

The task of managing unstable systems is a critically important management problem, as an unstable object can pose significant danger to humans and the environment when it fails. In this paper, a neural network was trained to determine the optimal control for an unstable system, based on a comparative analysis of two control methods: the implicit Euler method and the linearization method. This neural network identifies the optimal control based on the position of a point on the phase plane. [ABSTRACT FROM AUTHOR]

This paper studies the learnability of natural concepts in the context of the conceptual spaces framework. Previous work proposed that natural concepts are represented by the cells of optimally partitioned similarity spaces, where optimality was defined in terms of a number of constraints. Among these is the constraint that optimally partitioned similarity spaces result in easily learnable concepts. While there is evidence that systems of concepts generally regarded as natural satisfy a number of the proposed optimality constraints, the connection between naturalness and learnability has been less well studied. To fill this gap, we conduct a computational study employing two standard models of concept learning. Applying these models to the learning of color concepts, we examine whether natural color concepts are more readily learned than nonnatural ones. Our findings warrant a positive answer to this question for both models employed, thus lending empirical support to the notion that learnability is a distinctive characteristic of natural concepts. [ABSTRACT FROM AUTHOR]

This paper presents the introduction of d-ρ-(η, θ)- univex functions, which are built upon the concepts of d-ρ- (η, θ)-invex functions and univex functions. By utilizing these concepts, the paper derives various optimality results for feasible solutions to be considered as efficient or weak efficient solutions. Additionally, the paper establishes several duality theorems for Mond-Weir and Wolf duality. [ABSTRACT FROM AUTHOR]

Quantifying water use efficiency, and the impact of stomata on CO2 uptake are pivotal in physiology and efforts to improve crop yields. Although tempting, relying on regression slopes from assimilation-stomatal conductance plots to estimate water use efficiency or stomatal control over assimilation is erroneous. Through numerical simulations, I substantiate this assertion. I propose the term 'instantaneous transpiration efficiency' for the assimilation-to-transpiration ratio to avoid confusion with 'intrinsic water use efficiency' which refers to the assimilation-to-stomatal conductance ratio, and recommend to compute both metrics for each gas exchange data point. [ABSTRACT FROM AUTHOR]

Abstract Stomatal optimization theory is a commonly used framework for modeling how plants regulate transpiration in response to the environment. Most stomatal optimization models assume that plants instantaneously optimize a reward function such as carbon gain. However, plants are expected to optimize over longer timescales given the rapid environmental variability they encounter. There are currently no observational constraints on these timescales. Here, a new stomatal model is developed and is used to analyze the timescales over which stomatal closure is optimized. The proposed model assumes plants maximize carbon gain subject to the constraint that they cannot draw down soil moisture below a critical value. The reward is integrated over time, after being weighted by a discount factor that represents the timescale (τ) that a plant considers when optimizing stomatal conductance to save water. The model is simple enough to be analytically solvable, which allows the value of τ to be inferred from observations of stomatal behavior under known environmental conditions. The model is fitted to eddy covariance data in a range of ecosystems, finding the value of τ that best predicts the dynamics of evapotranspiration at each site. Across 82 sites, the climate metrics with the strongest correlation to τ are measures of the average number of dry days between rainfall events. Values of τ are similar in magnitude to the longest such dry period encountered in an average year. The results here shed light on which climate characteristics shape spatial variations in ecosystem‐level water use strategy.

An energy-efficient switched reluctance electric drive is considered in relation to electric rolling stock. It fully meets such requirements as good adjustment properties, high energy efficiency and operational reliability. The scientific and technical value of the results of the work lies in the development of an algorithm for controlling a traction switched reluctance motor that reduces the operating current while providing the necessary power. The calculations are made by means of specialized programs interacting with each other FEMM and MATLAB. The materials of this study are of practical value for improving the operational and technical and economic indicators of electric rolling stock.

In this study, we derive a simple transportation scheme by post-optimizing the costs of a modified problem. The strategy attempts to make the original (mainly feasible) option more practicable by adjusting the building components’ costs. Next, we employ the previously mentioned cell or area cost operators to gradually restore the modified costs to their initial levels, while simultaneously implementing the necessary adjustments to the “optimal” solution. This work presents a multi-goal, multi-item substantial transportation problem with interval-valued fuzzy variables, such as transportation costs, supplies, and demands, as parameters to maintain the transportation cost. This research addresses two circumstances where task ambiguity may occur: the interval solids transportation problem and the fuzzy substantial transportation issue. In the first scenario, we express data problems as intervals instead of exact values using an interval-valued fermatean neutrosophic number; in the second case, the information is not entirely obvious. We address both models when uncertainty solely affects the constraint set. For the interval scenario, we define an additional problem to solve. Our existing efficient systems have dependable transportation, so they are also capable of handling this new problem. In the fuzzy case, a parametric technique generates a fuzzy solution to the preceding problem. Since transportation costs have a direct impact on market prices, lowering them is the primary goal. Using parametric analysis, we provide optimal parameterization solutions for complementary situations. We provide a recommended algorithm for determining the stability set. In conclusion, we offer a sensitivity analysis and a numerical example of the transportation problem involving both balanced and imbalanced loads.

Living beings are composite thermodynamic systems in non-equilibrium conditions. Within this context, there are a number of thermodynamic potential differences (forces) between them and the surroundings, as well as internally. These forces lead to flows, which, ultimately, are essential to life itself, but, at the same time, are associated with entropy generation, i.e., a loss of useful work. The maintenance of homeostatic conditions, the tenet of physiology, demands the regulation of these flows by control of variables. However, due to the very nature of these systems, the regulation of flows and control of variables become entangled in closed loops. Here, we show how to combine entropy generation with respect to a process, and control of parameters (in such a process) in order to create a criterium of optimal ways to regulate changes in flows, the coefficient of flow-entropy (CJσ). We demonstrate the restricted possibility to obtain an increase in flow along with a decrease in entropy generation, and the more general situation of increases in flow along with increases in entropy generation of the process. In this scenario, the CJσ aims to identify the best way to combine the gain in flow and the associated loss of useful work. As an example, we analyze the impact of vaccination effort in the spreading of a contagious disease in a population, showing that the higher the vaccination effort the higher the control over the spreading and the lower the loss of useful work by the society.