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ABSTRACT Mechanisms governing the migratory decisions of birds have long fascinated ecologists and sparked considerable debate. Identifying factors responsible for variation in migration distance, also known as differential migration, has been a popular approach to understanding the mechanisms underlying migratory behaviour more generally. However, research progress has been slowed by the continued testing of overlapping, non‐mechanistic, and circular predictions among a small set of historically entrenched hypotheses. We highlight the body size hypothesis and suggest that the predictions commonly tested have impeded progress because body size relationships with migration distance are predictions made by several distinct hypotheses with contrasting mechanisms. The cost of migration itself has not been adequately accounted for in most hypotheses, and we propose two flight efficiency hypotheses with time‐ and energy‐minimizing mechanisms that allow individuals to mitigate the risks inherent to longer migrations. We also advance two conceptual versions of the social dominance hypothesis based on two distinct underlying mechanisms related to distance minimization and food maximization that will help clarify the role of competition in driving migratory decisions. Overall, we describe and refine 12 mechanistic hypotheses proposed to explain differential migration (along with several other special‐case hypotheses), seven of which have underlying mechanisms related to food limitation as past research has identified this to be an important driver of differential migration. We also thoroughly reviewed 145 publications to assess the amount of support for 10 critical assumptions underlying alternative hypotheses for differential migration in birds. Our review reveals that surprisingly few studies explicitly evaluate assumptions within a differential migration context. Generating and testing strong predictions and critical assumptions underlying mechanisms of alternative hypotheses will improve our ability to differentiate among these explanations of differential migration. Additionally, future intraspecific progress will be greatest if investigators continue to focus on mechanisms underlying variation in migration distance within rather than among demographic classes, as previous research has found differing mechanisms to be responsible for differential migration among demographic classes. Interspecifically, a thorough comparative analysis that seeks to explain variation in migration distance among species would broaden both our understanding of the mechanisms regulating current differential migration patterns and those that led to the evolution of migration more generally. Collectively, we provide a framework that, together with advances in animal‐borne tracking and other technology, can be used to advance our understanding of the causes of differential migration distance, and migratory decisions more generally. [ABSTRACT FROM AUTHOR]

Two-dimensional liquid foam systems comprised of an odd number N of bubbles arranged in a staircase configuration are studied as they are packed within a confined straight channel. Energy minimization is employed to characterize the permitted topology and geometry of the system at equilibrium. It is known that in an infinite staircase, bubble films are flat. The configuration for a finite number of bubbles, however, deviates from that of an infinite staircase at the edges. It is known that films near the edges are not flat and structures with a few bubbles (up to N=3) are well characterized. To study what happens as more bubbles are added, and how the behaviour approaches that of an infinite staircase, structures comprised of N=[5,7,...] bubbles are studied here. For these N values, minimum and maximum bubble areas are found that can pack in a staircase configuration within a straight channel. However, for an infinite staircase and also for N=3 , there are maximum areas, but no minima. Staircases with very short films, which make the structure susceptible to break in various ways, are also identified. [ABSTRACT FROM AUTHOR]

This paper focuses on developing a reduction-based algebraic multigrid (AMG) method that is suitable for solving general (non)symmetric linear systems and is naturally robust from pure advection to pure diffusion. Initial motivation comes from a new reduction-based AMG approach, ℓAIR (local approximate ideal restriction), that was developed for solving advection-dominated problems. Though this new solver is very effective in the advection-dominated regime, its performance degrades in cases where diffusion becomes dominant. This is consistent with the fact that in general, reduction-based AMG methods tend to suffer from growth in complexity and/or convergence rates as the problem size is increased, especially for diffusion-dominated problems in two or three dimensions. Motivated by the success of ℓAIR in the advective regime, our aim in this paper is to generalize the AIR framework with the goal of improving the performance of the solver in diffusion-dominated regimes. To do so, we propose a novel way to combine mode constraints as used commonly in energy-minimization AMG methods with the local approximation of ideal operators used in ℓAIR. The resulting constrained ℓAIR algorithm is able to achieve fast scalable convergence on advective and diffusive problems. In addition, it is able to achieve standard low complexity hierarchies in the diffusive regime through aggressive coarsening, something that was previously difficult for reduction-based methods. [ABSTRACT FROM AUTHOR]

Measure-valued structured deformations are introduced to present a unified theory of deformations of continua. The energy associated with a measure-valued structured deformation is defined via relaxation departing either from energies associated with classical deformations or from energies associated with structured deformations. A concise integral representation of the energy functional is provided both in the unconstrained case and under Dirichlet conditions on a part of the boundary. [ABSTRACT FROM AUTHOR]

The paper investigates a problem concerning the equilibrium of a solid body containing a thin rigid inclusion and a crack. It is assumed that the body is hyperelastic, therefore, it is described within the framework of finite strain theory. One of the peculiarities of this problem is a global injectivity constraint, which prevents the body, the crack faces and the inclusion from both mutual and self penetration. First, the paper deals with the differential formulation of the problem. Next, we consider energy minimization, showing that the latter provides the weak formulation of the former. Finally, the existence of the weak solution is demonstrated through the use of the variational technique. This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'. [ABSTRACT FROM AUTHOR]

In recent years, there has been an increased interest in using image processing, computer vision, and machine learning in biological and medical imaging research. One area of this interest is the diagnosis of brain tumors, which is considered a difficult and time‐consuming task traditionally performed manually. In this study, we present a method for tumor detection from magnetic resonance images (MRI) using a well‐known graph‐based algorithm, the Boykov–Kolmogorov algorithm, and the α‐expansion method. This approach involves pre‐processing the MRIs, representing the image positions as nodes, and calculations of the weights between edges as differences in intensity. The problem is formulated as an energy minimization problem and is solved by finding the 0,1 score for the image. Post‐processing is also performed to enhance the overall segmentation. The proposed method is easy to implement and shows high accuracy, precision, and efficiency in the results. We believe that this approach will bring significant benefits to scientists and healthcare researchers in qualitative research and can be applied to various imaging modalities for future research. [ABSTRACT FROM AUTHOR]

We formulate a plausible conjecture for the optimal Ehrhard-type inequality for convex symmetric sets with respect to the Gaussian measure. Namely, letting J_{k-1}(s)=\int ^s_0 t^{k-1} e^{-\frac {t^2}{2}}dt and c_{k-1}=J_{k-1}(+\infty), we conjecture that the function F:[0,1]\rightarrow \mathbb {R}, given by \begin{equation*} F(a)= \sum _{k=1}^n 1_{a\in E_k}\cdot (\beta _k J_{k-1}^{-1}(c_{k-1} a)+\alpha _k) \end{equation*} (with an appropriate choice of a decomposition [0,1]=\cup _{i} E_i and coefficients \alpha _i, \beta _i) satisfies, for all symmetric convex sets K and L, and any \lambda \in [0,1], \begin{equation*} F\left (\gamma (\lambda K+(1-\lambda)L)\right)\geq \lambda F\left (\gamma (K)\right)+(1-\lambda) F\left (\gamma (L)\right). \end{equation*} We explain that this conjecture is "the most optimistic possible", and is equivalent to the fact that for any symmetric convex set K, its Gaussian concavity power p_s(K,\gamma) is greater than or equal to p_s(RB^k_2\times \mathbb {R}^{n-k},\gamma), for some k\in \{1,\dots,n\}. We call the sets RB^k_2\times \mathbb {R}^{n-k} round k-cylinders ; they also appear as the conjectured Gaussian isoperimetric minimizers for symmetric sets, see Heilman [Amer. J. Math. 143 (2021), pp. 53–94]. In this manuscript, we make progress towards this question, and show that for any symmetric convex set K in \mathbb {R}^n, \begin{equation*} p_s(K,\gamma)\geq \sup _{F\in L^2(K,\gamma)\cap Lip(K):\,\int F=1} \left (2T_{\gamma }^F(K)-Var(F)\right)+\frac {1}{n-\mathbb {E}X^2}, \end{equation*} where T_{\gamma }^F(K) is the F-torsional rigidity of K with respect to the Gaussian measure. Moreover, the equality holds if and only if K=RB^k_2\times \mathbb {R}^{n-k} for some R>0 and k=1,\dots,n. As a consequence, we get \begin{equation*} p_s(K,\gamma)\geq Q(\mathbb {E}|X|^2, \mathbb {E}\|X\|_K^4, \mathbb {E}\|X\|^2_K, r(K)), \end{equation*} where Q is a certain rational function of degree 2, the expectation is taken with respect to the restriction of the Gaussian measure onto K, \|\cdot \|_K is the Minkowski functional of K, and r(K) is the in-radius of K. The result follows via a combination of some novel estimates, the L2 method (previously studied by several authors, notably Kolesnikov and Milman [J. Geom. Anal. 27 (2017), pp. 1680–1702; Amer. J. Math. 140 (2018), pp. 1147–1185; Geometric aspects of functional analysis , Springer, Cham, 2017; Mem. Amer. Math. Soc. 277 (2022), v+78 pp.], Kolesnikov and the author [Adv. Math. 384 (2021), 23 pp.], Hosle, Kolesnikov, and the author [J. Geom. Anal. 31 (2021), pp. 5799–5836], Colesanti [Commun. Contemp. Math. 10 (2008), pp. 765–772], Colesanti, the author, and Marsiglietti [J. Funct. Anal. 273 (2017), pp. 1120–1139], Eskenazis and Moschidis [J. Funct. Anal. 280 (2021), 19 pp.]), and the analysis of the Gaussian torsional rigidity. As an auxiliary result on the way to the equality case characterization, we characterize the equality cases in the "convex set version" of the Brascamp-Lieb inequality, and moreover, obtain a quantitative stability version in the case of the standard Gaussian measure; this may be of independent interest. All the equality case characterizations rely on the careful analysis of the smooth case, the stability versions via trace theory, and local approximation arguments. In addition, we provide a non-sharp estimate for a function F whose composition with \gamma (K) is concave in the Minkowski sense for all symmetric convex sets. [ABSTRACT FROM AUTHOR]

Capillary forces generated by capillary adsorption between varied solids have been widely used in micro-objects manipulation. In present study, capillary forces and capillary bridges between an end-adjusted three-finger capillary microgripper with hydrophobic side surface and a plate were investigated. The effects of the separation distance on capillary forces for three configurations of capillary bridges were analyzed experimentally using a customized platform to verify the effectiveness of the established capillary models. The results show that the capillary forces increased sharply in the initial stage, followed by a decrease. The maximum capillary force of 141.1 μN was obtained for the capillary bridge of Structure A with capillary bridge volume of 0.55 μL. The effects of the capillary bridge volume, radial distance between probes and contact angles on the capillary forces were analyzed based on the established simulation model. The results indicate that the variation of capillary force with capillary bridge volume increasing was not monotonic because of the restriction of the probe edge. The capillary force changing was more sensitive to the variation of the contact angle on the plate than the variation of the contact angle on the probe end surface. Additionally, experimental analysis was conducted on variations in capillary forces for two types of the microgripper with variable relative axial distance between probes. The capillary forces increased as the relative axial distance between the probes increased, and then decreased. The maximum capillary force of 159.15 μN was obtained for Type 1 capillary bridge with capillary bridge volume of 0.45 μL. [ABSTRACT FROM AUTHOR]

Object tracking is one of the fundamental processes for many high level applications in the field of machine vision. Many challenges in this field remain unsolved despite the development of several tracking perspectives in recent years. A tracking system can be defined in four steps including object detection, appearance modeling, data association, and trajectory estimation. The idea of combining these processes is attractive, but it raises new challenges. The focus of this paper is on the integration of these processes by relying on the use of local structural information. Quantitative and qualitative comparison of the results of the experiments obtained from the proposed method with some works done shows the improvement of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel energy minimization approach (called R-NCG) that combines a random batch idea with a nonlinear conjugate gradient method to accelerate the dynamics pre-equilibrium simulation of charged polymers in different systems. By using small but random batches, R-NCG can efficiently approximate the collective dynamics numerically while maintaining the numerical behaviours of standard NCG algorithm, and further improving its performance. Our simulation results suggest that the R-NCG can significantly reduce the computational cost of the minimization process for system with N-body interactions, thus reducing the time complexity to O(N). In other words, R-NCG method improves the problem of the dependence of CPU simulation time on the number of charged particles, and achieves acceptable accuracy in most cases. Our work can be helpful for accelerating the pre-equilibrium simulations of systems with N-body interactions, and confer new insights into the optimization of energy minimization algorithms in large electrostatic systems. In this work, we apply the random batch idea to the nonlinear conjugate gradient (NCG) method for improving the dependence of the CPU time on the number of charged particles in the energy minimization of the standard NCG method. Furthermore, we use the local iteration algorithm proposed in previous work to compute the spatial electrostatic potential distribution, which effectively improves the efficiency of the most time-consuming parts of calculating the electrostatic energy and its gradient values. Numerical results show that for different dielectric systems with N-body interactions, the NCG method based on random batch idea is computationally more efficient than the standard NCG method with acceptable accuracy in most cases (time complexity is reduced to O(N)). [ABSTRACT FROM AUTHOR]

The fairing curves and surfaces are used extensively in geometric design, modeling, and industrial manufacturing. However, the majority of conventional fairing approaches, which lack sufficient parameters to improve fairness, are based on energy minimization problems. In this study, we develop a novel progressive-iterative approximation method for the fairing curve and surface generation (fairing-PIA). Fairing-PIA is an iteration method that can generate a series of curves (surfaces) by adjusting the control points of B-spline curves (surfaces). In fairing-PIA, each control point is endowed with an individual weight. Thus, the fairing-PIA has many parameters to optimize the shapes of curves and surfaces. Not only a fairing curve (surface) can be generated globally through fairing-PIA, but also the curve (surface) can be improved locally. Moreover, we prove the convergence of the developed fairing-PIA and show that the conventional energy minimization fairing model is a special case of fairing-PIA. Finally, numerical examples indicate that the proposed method is effective and efficient. [ABSTRACT FROM AUTHOR]

This paper introduces a novel model for image fusion that is based on a fractional-order osmosis approach. The model incorporates a definition of osmosis energy that takes into account nonlocal pixel relationships using fractional derivatives and contrast change. The proposed model was subjected to theoretical and experimental investigation. The semigroup theory was used to demonstrate the existence and uniqueness of the evolution equation solution. Additionally, the model was validated and tested using numerical experiments and compared to local image fusion methods. The findings demonstrate that the proposed model outperforms the competitive local image fusion models. [ABSTRACT FROM AUTHOR]

In the study, based on the analysis of the technological process of drying apricots on a tunnel-type drying machine, the governing parameters and the control parameters at the exit of dehydrator as well as disturbing factors were determined. Fruit and air control parameters at the outlet of the tunnel-type drying chamber were determined as the final value of the state vector components, the solution of the system of non-linear ordinary differential equations with distributed parameters, describing the static mode of the drying process. With respect to assessing the quality of drying process control, the requirements of minimum energy consumption during drying, achieving maximum productivity and maintaining the desired value of the residual moisture content of the product were used. In order to reach a compromise between these requirements, a Pareto-optimal solution of the problem was proposed, for which a linear fold of the first and second criteria was introduced and the dependence of the minimum value of a new criterion on the fold parameter was considered. Based on the analysis of the results, approximately 5 % reduction in energy consumption with a significant increase in the quality of the dried fruits could be achieved. [ABSTRACT FROM AUTHOR]

In wireless sensor networks (WSNs), unmanned aerial vehicles (UAVs) are considered an effective data collection tool. In this paper, we investigate the energy-efficient data collection problem in a UAV-enabled secure WSN without knowing the instantaneous channel state information of the eavesdropper (Eve). Specifically, the UAV collected the information from all the wireless sensors at the scheduled time and forward it to the fusion center while Eve tries to eavesdrop on this confidential information from the UAV. To surmount this intractable and convoluted mixed-integer non-convex problem, we propose an efficient iterative optimization algorithm using the block coordinate descent (BCD) method to minimize the maximum energy consumption of the ground sensor nodes (GSNs) under the constraints of secrecy outage probability (SOP), connection outage probability (COP), minimum secure data, information causality, and UAV trajectory. Numerical results demonstrate the superiority of the algorithm we proposed in energy consumption and secrecy rate compared with other schemes. [ABSTRACT FROM AUTHOR]

We consider a class of models motivated by previous numerical studies of wrinkling in highly stretched, thin rectangular elastomer sheets. The model is characterized by a finite-strain hyperelastic membrane energy perturbed by small bending energy. In the absence of the latter, the membrane energy density is not rank-one convex for general spatial deformations but reduces to a polyconvex function when restricted to planar deformations, i.e., two-dimensional hyperelasticity. In addition, it grows unbounded as the local area ratio approaches zero. The small bending component of the model is the same as that in the classical von Kármán model. The latter penalizes arbitrarily fine-scale wrinkling, resolving both the amplitude and wavelength of wrinkles. Here, we prove the existence of energy minima for a general class of such models. [ABSTRACT FROM AUTHOR]

We introduce a novel relaxed Kačanov scheme for the computation of the discrete minimizer to the p-Laplace problem with 2 ≤ p <∞. The iterative scheme is easy to implement since each iterate results only from the solve of a weighted, linear Poisson problem. It neither requires an additional line search nor involves unknown constants for the step length. The scheme converges globally, and its rate of convergence is independent of the underlying mesh under certain regularity assumptions on the (discrete) solution. [ABSTRACT FROM AUTHOR]

Algebraic multigrid (AMG) is one of the most widely used solution techniques for linear systems of equations arising from discretized partial differential equations. The popularity of AMG stems from its potential to solve linear systems in almost linear time, that is with an O(n) complexity, where n is the problem size. This capability is crucial at the present, where the increasing availability of massive HPC platforms pushes for the solution of very large problems. The key for a rapidly converging AMG method is a good interplay between the smoother and the coarse-grid correction, which in turn requires the use of an effective prolongation. From a theoretical viewpoint, the prolongation must accurately represent near kernel components and, at the same time, be bounded in the energy norm. For challenging problems, however, ensuring both these requirements is not easy and is exactly the goal of this work. We propose a constrained minimization procedure aimed at reducing prolongation energy while preserving the near kernel components in the span of interpolation. The proposed algorithm is based on previous energy minimization approaches utilizing a preconditioned restricted conjugate gradients method, but has new features and a specific focus on parallel performance and implementation. It is shown that the resulting solver, when used for large real-world problems from various application fields, exhibits excellent convergence rates and scalability and outperforms at least some more traditional AMG approaches. [ABSTRACT FROM AUTHOR]

We show that for any even log-concave probability measure \mu on \mathbb {R}^n, any pair of symmetric convex sets K and L, and any \lambda \in [0,1], \begin{equation*} \mu ((1-\lambda) K+\lambda L)^{c_n}\geq (1-\lambda) \mu (K)^{c_n}+\lambda \mu (L)^{c_n}, \end{equation*} where c_n\geq n^{-4-o(1)}. This constitutes progress towards the dimensional Brunn-Minkowski conjecture (see Richard J. Gardner and Artem Zvavitch [Tran. Amer. Math. Soc. 362 (2010), pp. 5333–5353]; Andrea Colesanti, Galyna V. Livshyts, Arnaud Marsiglietti [J. Funct. Anal. 273 (2017), pp. 1120–1139]). Moreover, our bound improves for various special classes of log-concave measures. [ABSTRACT FROM AUTHOR]

With the swift advancement of the geometric modeling industry and computer technology, traditional generalized Ball curves and surfaces are challenging to achieve the geometric modeling of various complex curves and surfaces. Constructing an interpolation curve for the given discrete data points and optimizing its shape have important research value in engineering applications. This article uses an improved golden eagle optimizer to design the shape-adjustable combined generalized cubic Ball interpolation curves with ideal shape. Firstly, the combined generalized cubic Ball interpolation curves are constructed, which have global and local shape parameters. Secondly, an improved golden eagle optimizer is presented by integrating Lévy flight, sine cosine algorithm, and differential evolution into the original golden eagle optimizer; the three mechanisms work together to increase the precision and convergence rate of the original golden eagle optimizer. Finally, in view of the criterion of minimizing curve energy, the shape optimization models of combined generalized cubic Ball interpolation curves that meet the C1 and C2 smooth continuity are instituted. The improved golden eagle optimizer is employed to deal with the shape optimization models, and the combined generalized cubic Ball interpolation curves with minimum energy are attained. The superiority and competitiveness of improved golden eagle optimizer in solving the optimization models are verified through three representative numerical experiments. [ABSTRACT FROM AUTHOR]

The circular cartogram, also known as the Dorling map, is a widely used tool for visualizing statistical data. It represents regions as circles with their areas in proportion to the statistical values and requires circle displacement to avoid overlap and maintain spatial relationships. In this paper, we propose a new approach for circular cartogram production that utilizes the elastic beam displacement algorithm in cartographic generalization. First, the initial circles are generated with their areas in proportion to the statistical values. Second, an elastic beam structure is built as a proximity graph based on the spatial relations between the circles. Third, the circles violating the quality requirements are considered to have a force on the nodes of a beam. Fourth, the elastic beam algorithm is applied to assign forces for each node to determine the new positions of the circles. Steps two through four are repeated until a circular cartogram that meets the defined quality requirements is obtained. The experiments indicate that the proposed approach can successfully generate circular cartograms without overlaps while maintaining topology and relative relationships with higher quality than existing approaches. Project website: [ABSTRACT FROM AUTHOR]

The shape of a pendant drop is studied by employing free energy minimization. This free energy includes the gravitational potential energy and the interfacial surface energy. We employed the Lagrange multipliers method to minimize free energy while maintaining drop volume as constant. The differential equation for the shape of any pendant drop was established as a function of one dimensionless parameter only. This novel dimensionless parameter is defined as the shape factor. Around the origin of the chosen coordinate axis, an analytical solution to the differential equation was found. For a general solution, a numerical approach was followed to estimate drop shape. Furthermore, we calculated the detached volume from the bulk pendant drop. Comparison of the results with the experimental findings shows good agreements. A new Axisymmetric Drop Shape Analysis method is suggested, which can help users estimate any unknown of the problem if one geometrical data of the drop is known. [ABSTRACT FROM AUTHOR]

We present a hybrid approach for generating a character by independently controlling its shape and texture using an input face and a styled face. To effectively produce the shape of a character, we propose an anthropometry-based approach that defines and extracts 37 explicit facial features. The shape of a character's face is generated by extracting these explicit facial features from both faces and matching their corresponding features, which enables the synthesis of the shape with different poses and scales. We control this shape generation process by manipulating the features of the input and styled faces. For the style of the character, we devise a warping field-based style transfer method using the features of the character's face. This method allows an effective application of style while maintaining the character's shape and minimizing artifacts. Our approach yields visually pleasing results from various combinations of input and styled faces. [ABSTRACT FROM AUTHOR]

In a context in which the connectivity level of last-generation vehicles is constantly on the rise, the combined use of Vehicle-To-Everything (V2X) connectivity and autonomous driving can provide remarkable benefits through the synergistic optimization of the route and the speed trajectory. In this framework, this paper focuses on vehicle ecodriving optimization in a connected environment: the virtual test rig of a premium segment passenger car was used for generating the simulation scenarios and to assess the benefits, in terms of energy and time savings, that the introduction of V2X communication, integrated with cloud computing, can have in a real-world scenario. The Reference Scenario is a predefined Real Driving Emissions (RDE) compliant route, while the simulation scenarios were generated by assuming two different penetration levels of V2X technologies. The associated energy minimization problem was formulated and solved by means of a Variable Grid Dynamic Programming (VGDP), that modifying the variable state search grid on the basis of the V2X information allows to drastically reduce the DP computation burden by more than 95%. The simulations show that introducing a smart infrastructure along with optimizing the vehicle speed in a real-world urban route can potentially reduce the required energy by 54% while shortening the travel time by 38%. Finally, a sensitivity analysis was performed on the biobjective optimization cost function to find a set of Pareto optimal solutions, between energy and travel time minimization. [ABSTRACT FROM AUTHOR]

In 1934, Timoshenko derived and published the torsional rigidity of a rectangular bar of isotropic material by using the membrane analogy. The rigidity depends on the bar's shear modulus, width and thickness. In 1950, Lekhnitskii followed Timoshenko's process to derive the torsional rigidity for an orthotropic bar of unidirectional composite laminate, where the rigidity depends on the laminate's width, the thickness and the shear moduli. In 1990, Tsai, Daniel and Yaniv solved the same case, deriving a quasi-exact solution of torsional rigidity. In the same year, Tsai and Daniel verified their result through multiple experiments. All these rigidities become different when the definitions of thickness and width are swapped. However, they remain identical numerically, lacking mathematic proof for nearly a century. In 2022, Tsai et al. resolved Timoshenko's case by considering all the conditions and energy minimization criterion. By a completely different approach, the torsional rigidity was derived in a completely different form from that of Timoshenko but numerically identical. Moreover, the solution satisfies the rule of swapping, which makes perfect sense physically. This work applies Tsai's process to Lekhnitskii's case. A general solution is derived that satisfies the rule of swapping involving the swapping of shear moduli. [ABSTRACT FROM AUTHOR]

The circular cartogram, also known as the famous DorlingMap, is widely used to visualize geographical statistics by representing geographical regions as circles. However, all existing approaches for circular cartograms are only designed for static data. While applying these approaches for time-varying data, the circle locations in each circular cartogram are recomputed separately and will result in low efficiency and low visual stability between sequential circle cartograms. To generate visually stable circular cartograms for time-varying data efficiently, we propose a novel approach by improving the elastic beam algorithm with a hierarchical optimization strategy. First, the time-varying data at different time points are grouped using a hierarchical clustering method based on their similarity, and a hierarchy is then built for their corresponding circular cartograms. Second, we generate intermediate circle locations level by level for clusters of circular cartograms according to the built hierarchy with an improved elastic beam algorithm iteratively. The elastic beam algorithm is improved in its proximity graph construction and force computation by considering that the algorithm will be applied to displace circles in a cluster of circular cartograms. The iterative process stops until we obtain satisfactory circular cartograms for each time point. The evaluation results indicate that the proposed approach can achieve a higher quality (184.85%↑ and 265.69%↑) on visual stability, and a higher efficiency (58.54%↑ and 73.96%↑) with almost the same quality on overlap avoidance and relation maintenance by comparing to the existing approaches. Project website: https://github.com/TrentonWei/DorlingMap. [ABSTRACT FROM AUTHOR]

Scheduling independent tasks on a parallel platform is a widely-studied problem, in particular when the goal is to minimize the total execution time, or makespan (P | | C max problem in Graham's notations). Also, many applications do not consist of sequential tasks, but rather parallel tasks, either rigid, with a fixed degree of parallelism, or moldable, with a variable degree of parallelism (i.e., for which we can decide at the execution on how many processors they are executed). Furthermore, since the energy consumption of data centers is a growing concern, both from an environmental and economical point of view, minimizing the energy consumption of a schedule is a main challenge to be addressed. One can then decide, for each task, on how many processors it is executed, and at which speed the processors are operated, with the goal to minimize the total energy consumption. We further focus on co-schedules, where tasks are partitioned into shelves, and we prove that the problem of minimizing the energy consumption remains NP-complete when static energy is consumed during the whole duration of the application. We are however able to provide an optimal algorithm for the schedule within one shelf, i.e., for a set of tasks that start at the same time. Several approximation results are derived, both with discrete and continuous speed models, and extensive simulations are performed to show the performance of the proposed algorithms. • A model for a theoretical analysis of the energy consumption of a schedule for moldable and rigid tasks. • Most presented scheduling problems are NP-complete. • There exist approximation algorithms for the presented problems (from 1.59 to 3 depending on the problem). • An experimental study of the trade-off between the time complexity of the scheduler and the energy consumed by the schedule. [ABSTRACT FROM AUTHOR]

We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems, where the nonlinear reaction terms need to be neither monotone nor convex. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy reduction approach. More specifically, this procedure aims to generate a sequence of numerical approximations, which results from the iterative solution of related (stabilized) linearized discrete problems, and tends to a critical point of the underlying energy functional in a stable way. Simultaneously, the finite-dimensional approximation spaces are adaptively refined. This is implemented in terms of a new mesh refinement strategy in the context of finite element discretizations, which again relies on the energy structure of the problem under consideration. In particular, in contrast to more traditional approaches, it does not involve any a posteriori error estimators, and is based on local energy reduction indicators instead. In combination, the resulting adaptive algorithm consists of an iterative linearization procedure on a sequence of hierarchically refined discrete spaces, which we prove to converge toward a solution of the continuous problem in an appropriate sense. Numerical experiments demonstrate the robustness and reliability of our approach for a series of examples. [ABSTRACT FROM AUTHOR]

The order reduction method is an important approach to optimize higher-order binary Markov random fields (HoMRFs), which are widely used in information theory, machine learning and image analysis. It transforms an HoMRF into an equivalent and easier reduced first-order binary Markov random field (RMRF) by elaborately setting the coefficients and auxiliary variables of RMRF. However, designing order reduction methods is difficult, and no previous study has investigated this design issue. In this paper, we propose an order reduction design framework to study this problem for the first time. Through study, we find that the design difficulty mainly lies in that the coefficients and variables of RMRF must be set simultaneously. Therefore, the proposed framework decomposes the design difficulty into two processes, and each process mainly considers the coefficients or auxiliary variables of RMRF. Some valuable properties are also proven. Based on our framework, a new family of 14 order reduction methods is provided. Experiments, such as synthetic data and image denoising, demonstrate the superiority of our method. [ABSTRACT FROM AUTHOR]

Objective: The major purpose of the present study was to predict the structure of Radical s-adenosyl-L-methionine Domain 2 (RSAD2), the most targeted protein of the Zika virus using comparative modeling, to validate the models that were generated and molecular dynamics (MD) simulations were performed. Methods: The secondary structure of RSAD2 was estimated using the Garnier-Osguthorpe-Robson, Self-Optimized Prediction method with Alignment, and Position-Specific Iterative-Blast based secondary structure prediction algorithms. The best of them were preferred based on their DOPE score, then three-dimensional structure identification using SWISS-MODEL and the Protein Homology/Analogy Recognition Engine (Phyre2) server. SAVES 6.0 was used to validate the models, and the preferred model was then energetically stabilized. The model with least energy minimization was used for MD simulations using iMODS. Results: The model predicted using SWISS-MODEL was determined as the best among the predicted models. In the Ramachandran plot, there were 238 residues (90.8%) in favored regions, 23 residues (8.8%) in allowed regions, and 1 residue (0.4%) in generously allowed regions. Energy minimization was calculated using Swiss PDB viewer, reporting the SWISS-MODEL with the lowest energy (E = −18439.475 KJ/mol) and it represented a stable structure conformation at three-dimensional level when analyzed by MD simulations. Conclusion: A large amount of sequence and structural data is now available, for tertiary protein structure prediction, hence implying a computational approach in all the aspects becomes an opportunistic strategy. The best three-dimensional structure of RSAD2 was built and was confirmed with energy minimization, secondary structure validation and torsional angles stabilization. This modeled protein is predicted to play a role in the development of drugs against Zika virus infection. [ABSTRACT FROM AUTHOR]

• MSCRs in nonuniform magnetic fields is modeled by energy minimization method. • The energy minimization method shows high computation efficiency and accuracy. • Two control strategies of MSCRs are offered by manipulating a cubic magnet. The emerging magnetic soft continuum robots (MSCRs) – a type of slender and soft rods with embedded hard-magnetic particles – hold great promise in endovascular intervention via remote magnetic actuation. Although numerous advantages of using permanent magnets have been demonstrated for manipulating MSCRs (e.g., simple systems with high actuation force, large operating workspace), the magneto-mechanical behavior of MSCRs in nonuniform magnetic fields, particularly those generated by permanent magnets, remains largely unexplored. In this work, a systematic study of MSCRs in the nonuniform field is presented, which includes theoretical modeling using hard-magnetic elastica theory, numerical analyses by energy minimization method, finite element simulations using ABAQUS user element (UEL), and experimental validation. Without solving governing differential equations, the large deflection of MSCRs is efficiently obtained via the minimization of the total potential energy using sequential quadratic programming (SQP). This efficient modeling method offers insights into the control of MSCRs using nonuniform magnetic fields. Two practical strategies are provided for precisely controlling MSCRs by manipulating a cubic magnet through the adjustment of the actuation distance, rotation angle, and spin angle, laying the foundation for applications of magnetically-assisted endovascular intervention. [Display omitted] [ABSTRACT FROM AUTHOR]

An efficient approach for constructing volumetric parameterization with internal energy-minimizing pair of diagonal surfaces from given boundaries is presented. The expression for the internal energy of one diagonal surface pair is formulated. Then necessary and sufficient conditions for trivariate tensor-product Bézier volume with minimal internal energy of the diagonal surface pair are derived. From the derived conditions, an efficient construction algorithm for single- and multi-block Bézier volumes with minimal diagonal internal energy by the Lagrange multiplier method is presented. The auxiliary linear system only needs to be solved once. As soon the explicit computation masks are obtained, the interior control points of the volume are then directly calculated. Experimental results are given to illustrate the volumetric parameterization effects of the presented approach. [ABSTRACT FROM AUTHOR]

This paper studies cached-aided multicast transmissions in fronthaul fog radio access networks (F-RANs). While index coding and cached-aided non-orthogonal multiple access (NOMA) are techniques commonly used for utilizing cache contents to save transmit energy, there is a lack of general framework to integrate them. This work proposes index-coded NOMA and dynamic coded-NOMA to investigate energy performance of the integration of index coding and NOMA under whole-file and subfile caching, respectively. Besides, dynamic cache space allocation is applied to both caching schemes, which allocates cache sizes to the fog access points (F-APs) according to their large-scale channel conditions. For index-coded NOMA, the general grouping problem is proved to be NP-hard and optimal solutions for some special cases are given. Furthermore, efficient heuristic grouping algorithms are proposed. For dynamic coded-NOMA, we obtain the closed-form minimum transmit energy. The numerical results validate the good performance of our proposed algorithms. Index-coded NOMA and dynamic coded-NOMA have comparable performance and both of them save much energy than the existing schemes. When there are 12 F-APs under small-cache scenarios, index-coded NOMA saves energy by 70.3% compared to traditional NOMA. [ABSTRACT FROM AUTHOR]

The success of convolutional neural networks (CNNs) has made low-latency inference services on Graphic Processing Units (GPUs) a hot research topic. However, GPUs are hardware processors with high power consumption. To have the least energy consumption while meeting latency Service-Level-Objective (SLO), batching strategy and dynamic voltage frequency scaling (DVFS) are two important solutions. However, existing studies do not coordinate them and regard CNN as a black box, which makes inference services less energy-efficient. In this paper, we propose EALI, an energy-aware layer-level adaptive scheduling framework that is comprised of a power prediction model, a layer combination strategy, and an energy-aware layer-level scheduler. The power prediction model uses classic machine learning techniques to predict fine-grained layer-level power consumption. The layer combination strategy combines multiple layers into optimization units to lower scheduling overhead and complexity. The energy-aware layer-level scheduler adaptively coordinates batching strategy and layer-level DVFS according to workloads to minimize the energy consumption while meeting SLO. Our experimental results on NVIDIA Tesla M40 and V100 GPUs show that, compared to the state-of-the-art approaches, EALI decreases energy consumption by up to 36.24% while meeting SLO. [ABSTRACT FROM AUTHOR]

Periodic waves of the modified Korteweg-de Vries (mKdV) equation are identified in the context of a new variational problem with two constraints. The advantage of this variational problem is that its nondegenerate local minimizers are stable in the time evolution of the mKdV equation, whereas the saddle points are unstable. We explore the analytical representation of periodic waves given by Jacobi elliptic functions and compute numerically critical points of the constrained variational problem. A broken pitchfork bifurcation of three smooth solution families is found. Two families represent (stable) minimizers of the constrained variational problem and one family represents (unstable) saddle points. [ABSTRACT FROM AUTHOR]

We propose Graph-Cut RANSAC, GC-RANSAC in short, a new robust geometric model estimation method where the local optimization step is formulated as energy minimization with binary labeling, applying the graph-cut algorithm to select inliers. The minimized energy reflects the assumption that geometric data often form spatially coherent structures – it includes both a unary component representing point-to-model residuals and a binary term promoting spatially coherent inlier-outlier labelling of neighboring points. The proposed local optimization step is conceptually simple, easy to implement, efficient with a globally optimal inlier selection given the model parameters. Graph-Cut RANSAC, equipped with “the bells and whistles” of USAC and MAGSAC++, was tested on a range of problems using a number of publicly available datasets for homography, 6D object pose, fundamental and essential matrix estimation. It is more geometrically accurate than state-of-the-art robust estimators, fails less often and runs faster or with speed similar to less accurate alternatives. The source code is available at https://github.com/danini/graph-cut-ransac. [ABSTRACT FROM AUTHOR]

The hydrogen liquefaction process is highly energy-intensive owing to its cryogenic characteristics, and a large proportion of the total energy is consumed in the subcooling cycle. This study aimed to develop an efficient configuration for the subcooling cycle in the hydrogen liquefaction process. The He-Ne Brayton cycle is one of the most energy-efficient cycles of the various proposed hydrogen liquefaction processes, and it was selected as the base case configuration. To improve its efficiency and economic potential, two different process configurations were proposed: (configuration 1) a dual-pressure cycle that simplified the process configuration, and (configuration 2) a split triple-pressure cycle that decreased the flow rate of the medium- and high-pressure compressors. The ortho–para conversion heat of hydrogen is considered by using heat capacity data of equilibrium hydrogen. Genetic algorithm-based optimization was also conducted to minimize the energy consumption of each configuration, and the optimization results showed that the performance of configuration 1 was worse than that of the base case configuration. In this respect, although less equipment was used, the compression load on each compressor was very intensive, which increased the energy requirements and costs. Configuration 2 provided the best results with a specific energy consumption of 5.69 kWh/kg (3.2% lower than the base case configuration). The total expense of configuration 2 shows the lowest value which is USD 720 million. The process performance improvements were analyzed based on the association between the refrigerant composition and the heat exchange efficiency. The analysis demonstrated that energy efficiency and costs were both improved by dividing the pressure levels and splitting the refrigerant flow rate in configuration 2. [ABSTRACT FROM AUTHOR]

An energy performance comparison between a novel thermosyphon-assisted falling film distillation unit and a conventional tray unit was carried out for three mixtures with different relative volatilities: ethanol-water, acetone-isopropanol, and acetone-water. Experimental data from the pilot-scale plant were used as targets in the simulation runs through the Hysys® software. Thus, the separation performed in the falling film unit was reproduced in a conventional tray column. The thermosyphon-assisted falling film unit required less energy, with reductions of 24% for acetone-isopropanol, 30% for ethanol-water, and 55% for the acetone-water mixture. The energy-use ratio also showed that for each kW consumed in the falling film unit, the conventional unit would consume 1.33 kW for acetone-isopropanol, 1.44 kW for ethanol-water, and 2.21 kW for acetone-water, based in the same separation. Therefore, this novel distillation apparatus is more advantageous as an energy-saving viable option for separating mixtures with different relative volatilities. [ABSTRACT FROM AUTHOR]

Periodic waves in the modified Korteweg–de Vries (mKdV) equation are revisited in the setting of the fractional Laplacian. Two families of solutions in the local case are given by the sign-definite dnoidal and sign-indefinite cnoidal solutions. Both solutions can be characterized in the general fractional case as global minimizers of the quadratic part of the energy functional subject to the fixed L 4 norm: the sign-definite (sign-indefinite) solutions are obtained in the subspace of even (odd) functions. Morse index is computed for both solutions and the spectral stability criterion is derived. We show numerically that the family of sign-definite solutions has a generic fold bifurcation for the fractional Laplacian of lower regularity and the family of sign-indefinite solutions has a generic symmetry-breaking bifurcation both in the fractional and local cases. [ABSTRACT FROM AUTHOR]

Conventional finite element methods are known to be tedious in adaptive refinements due to their conformal regularity requirements. Further, the enrichment functions for adaptive refinements are often not readily available in general applications. This work introduces a novel neural network-enriched Partition of Unity (NN-PU) approach for solving boundary value problems via artificial neural networks with a potential energy-based loss function minimization. The flexibility and adaptivity of the NN function space are utilized to capture complex solution patterns that the conventional Galerkin methods fail to capture. The NN enrichment is constructed by combining pre-trained feature-encoded NN blocks with an additional untrained NN block. The pre-trained NN blocks learn specific local features during the offline stage, enabling efficient enrichment of the approximation space during the online stage through the Ritz-type energy minimization. The NN enrichment is introduced under the Partition of Unity (PU) framework, ensuring convergence of the proposed method. The proposed NN-PU approximation and feature-encoded transfer learning form an adaptive approximation framework, termed the neural-refinement (n-refinement), for solving boundary value problems. Demonstrated by solving various elasticity problems, the proposed method offers accurate solutions while notably reducing the computational cost compared to the conventional adaptive refinement in the mesh-based methods. [ABSTRACT FROM AUTHOR]

An energy functional describes the equilibrium state of a system. In this work, we present a novel technique, Functional Optimization using Neural Networks (FONN), for minimizing the system's energy. FONN utilizes neural networks to process information at discrete grid points, considering their interactions with neighboring grid points, to update the state of the system. The training process involves formulating a loss function based on the system's energy, and with the help of multiple fine-tuning steps, the method employs a progressive energy reduction technique that decreases the energy in multiple steps. FONN's effectiveness is demonstrated across various problems, including the minimization of the heat and Lyapunov energy. Moreover, the paper explores the minimization of the elastic bending energy with an area constraint. [ABSTRACT FROM AUTHOR]

An energy functional describes the equilibrium state of a system. In this work, we present a novel technique, Functional Optimization using Neural Networks (FONN), for minimizing the system's energy. FONN utilizes neural networks to process information at discrete grid points, considering their interactions with neighboring grid points, to update the state of the system. The training process involves formulating a loss function based on the system's energy, and with the help of multiple fine-tuning steps, the method employs a progressive energy reduction technique that decreases the energy in multiple steps. FONN's effectiveness is demonstrated across various problems, including the minimization of the heat and Lyapunov energy. Moreover, the paper explores the minimization of the elastic bending energy with an area constraint. [ABSTRACT FROM AUTHOR]

The paper presents a morphodynamic model which can be coupled with any wave model capable of producing time/spectral averaged wave quantities. This model based on a wave energy minimization principle highlights the morphodynamic phenomenology, such as the sandbar creation. Such a model can be used in solving engineering optimization problems. It is also developed to illustrate the idea that beach sand transport can be thought as a non-local phenomenon. We used wave calculations from SWAN and XBeach in our model, and we compared the morphodynamic results to LIP and SANDS hydro-morphodynamic benchmark as well as open-sea simulations. Using supplementary mathematical development, we improved the minimization method using the Hadamard derivative. • A morphodynamic model by minimization that can be coupled with any wave model. • Fast, robust and low complexity model involving only two hyperparameters. • Encouraging results on known morphodynamic benchmarks and open-sea configurations. • An encouraging lead for lateral displacement. • Reproduces certain natural coastal mechanisms (sandbars, erosion, ...). [ABSTRACT FROM AUTHOR]

Energy is the most valuable resource in WSN. As the power storage capability of the tiny WSN is very limited, efficient mechanisms for energy minimization should be implemented to increase the overall lifetime of the network. Efficient clusterization of the area, cluster head selection leads toward the energy minimization of the whole network. Previously very few research works had been reported where the use of serve points had been considered. In this research work, the WSN has been configured depending upon many important parameters like (1) the frequency of serve points in a particular area and (2) WSN node deployment strategy in the target area. The main goal of this paper is to construct an efficient wireless sensor network. The efficiency of the network directly depends on the minimization technique of the consumed energy. So by minimizing the consumed energy an efficient wireless sensor network has been established. In this research, the specific region (target area) has been clustered using a modified K-mean algorithm to fix the position of the sink node. Deployment of WSN nodes in the target area has been done using least distance connect first (LDCF) deployment strategy. The cluster head has been selected for each cluster for each duty cycle. After configuring the WSN by using a modified k-mean algorithm and (LDCF) deployment strategy, a modified metaheuristic hybrid algorithm (GA-SAMP-MWPSO) has been used to get the optimized energy consumption for the network. Ultimately the consumed energy and the total day-life of the network have been calculated. The result has been compared with the existing literature, and it has been noted that the proposed technique yields 15.5544456 day-life of the network where the existing literature's approach gives 6.333777 day-life of the network. The proposed algorithm delivers a better outcome. [ABSTRACT FROM AUTHOR]

Wireless sensor networks (WSNs) refer to a group of battery-operated tiny sensor nodes having vast application areas in daily use. These are spatially dispersed and dedicated wireless sensor nodes for observing and recording the different parameter and physical conditions of the surroundings. There is a recent advancement in the field of network connectivity and computations in WSNs. The key functions of WSNs are a data extraction and to transmit the extracted data to the server placed at an isolated location. Various types of WSNs like underground underwater, terrestrial, and multimedia networks get applications domains such as in industrial automation, traffic monitoring and control medical device monitoring, and many other areas. Despite the thriving market, there are several challenges like energy efficiency, limited storage and computation, low bandwidth, high error rates, scalability, and survivability in harsh environment; hence, network lifespan expanding is a critical demanding issues. So many researchers have earlier focused towards finding the optimal path in between member node and sink node, so that energy depletion can be reduced to improve the network lifespan. There are different challenges in WSNs but one of the most challenging issues is how to minimize the energy consumption; numerous bio-inspired techniques have been proposed previously to obtain an optimal path between the member node and the sink node. In this manuscript, we are presenting a comprehensive survey on optimization technique-based routing and clustering. The study of this comprehensive survey offers in-depth summary of the past researches in the area of WSNs. [ABSTRACT FROM AUTHOR]

Ball surfaces play a crucial role in modeling 3D objects with varying thickness. In this paper, energy functionals for surface design are extended to Ball surfaces and the variational problem of finding the energy-minimizing Ball surface within the constraints imposed by the controls is investigated. Besides, owing to the excellent properties of Bernstein bases, we propose a computationally inexpensive algorithm for the construction of energy-minimizing Ball Bézier surfaces. Finally, an efficient design tool is provided for the construction of Cr continuous energy-minimizing blend surface from two disjoint Ball surfaces. The feasibility of the method is verified by several examples. By adjusting the weighted coefficients, different energy functionals are defined and thus Ball surfaces with different shapes and thickness can be obtained, achieving the deformable modeling of Ball surfaces. [ABSTRACT FROM AUTHOR]

This paper proposes a new model for image shadow removal. The model reformulates a recent osmosis model with nonlocal differential operators. This allows to benefit from distant pixels similarities and thus improves restoration results. Some properties of this model are established and discussed, making it suitable for our application. Experimental results show that the nonlocal model obtained very good qualitative and quantitative results compared with state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

In this paper, the binary tomographic reconstruction problem for very limited projection data availability is considered. Being this inverse problem highly ill-posed, we propose a new reconstruction model that uses a shape centroid-based regularization term, i.e., we assume that the center of gravity of the object of interest is known, at least approximately, in advance. Motivation for this regularization is found in the close connection between the projection data and the object centroid, as we will show. Experimental evaluation underpins that reasonable results can be obtained from practically minimal amount of projection data, gathered from just one projection direction. [ABSTRACT FROM AUTHOR]

Assessment of local magnetization in objects exhibiting hysteresis is crucial to the accurate design and performance estimation for a wide range of electromagnetic devices. In the past, different efforts have been carried out to incorporate hysteresis models in field computation approaches. While those models varied in methodologies, they shared a common goal of offering an accurate and computationally efficient field computation tool. Recently, it was demonstrated that a two-dimensional (2-D) vector hysteresis operator may be realized using a tri-node Hopfield neural network (HNN). The purpose of this article is to offer a novel 2-D field computation approach in media exhibiting hysteresis that uses the aforementioned hysteresis operator. The approach is based on incorporating domain-to-domain interactions in the overall network energy formulation while using typical HNN energy minimization algorithms. Details of the proposed model, numerical simulations, and comparisons with finite-element calculations are given in the article. [ABSTRACT FROM AUTHOR]

[Display omitted] Droplet wetting on a solid substrate is affected by the surface heterogeneity. Introducing patterned wettability on the solid substrate is expected to engender anisotropic wetting morphologies, thereby manipulating droplet wetting behaviors. However, when the droplet size is comparable with that of the surface heterogeneity, the wetting morphologies cannot be depicted by the quintessential Cassie's theory but should be possible to be predicted from the perspective of thermodynamics via surface energy minimization. Here, we investigate the equilibrium droplet shapes on chemically patterned substrates by using an analytical model, phase-field simulations, and experiments. The former two methods are sharp and diffuse interface treatments, respectively, which both are based on minimizing the free energy of the system. The experimental results are obtained by depositing droplets on chemically patterned glass substrates. Various anisotropic wetting shapes are found from the three methods. Excellent agreement is observed between different methods, showing the possibility to quantify the anisotropic wetting droplet morphologies on patterned substrates by present methods. We also address a series of non-rotationally symmetric droplet shapes, which is the first resport about these special wetting morphologies. Furthermore, we reveal the anisotropic wetting shapes in a quasi-equilibrium evaporation process. [ABSTRACT FROM AUTHOR]