We examine cosmological models with generalized phantom energy (GPE). Generalized phantom energy satisfies the supernegative equation of state, but its evolution with the scale factor is generally independent, i.e. not determined by its equation of state. The requirement of general covariance makes the gravitational constant time-dependent. It is found that a large class of distinct GPE models with different evolution of generalized phantom energy density and gravitational constant, but the same equation of state of GPE have the same evolution of the scale factor of the universe in the distant future. The time dependence of the equation of state parameter determines whether the universe will end in a de Sitter-like phase or diverge in finite time with the accompanying "Big Rip" effect on the bound structures.

We consider the energy of smooth generalized distributions and also of singular foliations on compact Riemannian manifolds for which the set of their singularities consists of a finite number of isolated points and of pairwise disjoint closed submanifolds. We derive a lower bound for the energy of all $q$-dimensional almost regular distributions, for each $q< \dim M,$ and find several examples of foliations which minimize the energy functional over certain sets of smooth generalized distributions.

or any real number α, the general energy of a graph is defined as the sum of the α-th powers of the nonzero singular values of its adjacency matrix. This definition unifies several classical spectral invariants, such as the graph energy and spectral moments. In this paper, we establish bounds on the general energy of graphs. These bounds, in turn, yield new estimates for the ordinary energy and spectral moments, and lead to a more general relationship between these quantities.

The “source” of gravity in the Einstein field equations is the stress-energy tensor. After a discussion of why gravitational mass should be part of a rank two tensor, this chapter derives the stress-energy tensor for a variety of types of matter: point particles, perfect fluids, scalar fields, and electromagnetism. The chapter discusses the relationship of differential and integral conservation laws, and introduces the problem of gravitational energy. It concludes with a discussion of one of the most remarkable results of general relativity, the fact that equations of motion for matter do not need to be introduced separately, but follow from the field equations.

Modifications in the energy momentum dispersion laws due to a noncommutative geometry, have been considered in recent years. We examine the oscillations of extended objects in this perspective and find that there is now a "generation" of energy.

Ecological processes and biodiversity patterns are strongly affected by how animals move through the landscape. However, it remains challenging to predict animal movement and space use. Here we present our new r package enerscape to quantify and predict animal movement in real landscapes based on energy expenditure. enerscape integrates a general locomotory model for terrestrial animals with GIS tools in order to map energy costs of movement in a given environment, resulting in energy landscapes that reflect how energy expenditures may shape habitat use. enerscape only requires topographic data (elevation) and the body mass of the studied animal. To illustrate the potential of enerscape, we analyse the energy landscape for the Marsican bear (Ursus arctos marsicanus) in a protected area in central Italy in order to identify least‐cost paths and high‐connectivity areas with low energy costs of travel. enerscape allowed us to identify travel routes for the bear that minimize energy costs of movement and regions that have high landscape connectivity based on movement efficiency, highlighting potential corridors. It also identifies areas where high energy costs may prevent movement and dispersal, potentially exacerbating human–wildlife conflicts in the park. A major strength of enerscape is that it requires only widely available topographic and body size data. As such, enerscape permits a first cost‐effective way to estimate landscape use and movement corridors even when telemetry data are not readily available, such as for the example with the bear. enerscape is built in a modular way and other movement modes and ecosystem types can be implemented when appropriate locomotory models are available. In summary, enerscape is a new general tool that quantifies, using minimal and widely available data, the energy costs of moving through a landscape. This can clarify how and why animals move in real landscapes and inform practical conservation and restoration decisions.

Quantum systems often contain negative energy densities. In general relativity, negative energies lead to time advancement, rather than the usual time delay. As a result, some Casimir systems appear to violate energy conditions that would protect against exotic phenomena such as closed timelike curves and superluminal travel. However, when one examines a variety of Casimir systems using self-consistent approximations in quantum field theory, one finds that a particular energy condition is still obeyed, which rules out exotic phenomena. I will discuss the methods and results of these calculations in detail and speculate on their potential implications in general relativity.

Coexistence of the human and robot in the same workspace requires the robot to perform robot tasks, such as trajectory tracking, and also interaction tasks, such as keeping a safe distance with the human. According to various human–robot interaction (HRI) scenarios, different interaction tasks usually require different task requirements or specifications, leading to different control strategies. Besides, due to different natures of the robot tasks and interaction tasks, different controllers may be required when the task is switched from one to another. So far, there is no theoretical framework that integrates different robot and interaction task requirements into a unified robot control strategy. In this article, a general HRI control framework is proposed for the scenario of the human and robot coexisting in the same workspace. We propose a general potential energy function that can be used to derive a stable and unified controller for various robot tasks and HRI tasks. By using the proposed method, various tasks can be specified at a user level by simply adjusting certain task parameters. Interactive weights are also defined to specify the interaction behaviors of robots according to different HRI applications. A human-dominant interaction mode is presented to demonstrate the applications of the proposed method. We show how the control framework can be applied to existing robot control systems with the velocity control or torque control mode by developing a joint velocity reference command and an adaptive controller. The stability of the adaptive control system is shown by using Lyapunov-like analysis. The control methods are implemented on two industrial manipulators and experimental results are presented to illustrate the effectiveness of the proposed control framework.

Research in the area of automated test generation has seen remarkable progress in recent years, resulting in several approaches and tools for effective and efficient generation of test cases. In particular, the EvoSuite tool has been at the forefront of this progress embodying various algorithms for automated test generation of Java programs. EvoSuite has been used to generate test cases for a wide variety of programs as well. While there are a number of empirical studies that report results on the effectiveness, in terms of code coverage and other related metrics, of the various test generation strategies and algorithms implemented in EvoSuite, there are no studies, to the best of our knowledge, on the energy consumption associated to the automated test generation. In this paper, we set out to investigate this aspect by measuring the energy consumed by EvoSuite when generating tests. We also measure the energy consumed in the execution of the test cases generated, comparing them with those manually written by developers. The results show that the different test generation algorithms consumed different amounts of energy, in particular on classes with high cyclomatic complexity. Furthermore, we also observe that manual tests tend to consume more energy as compared to automatically generated tests, without necessarily achieving higher code coverage. Our results also give insight into the methods that consume significantly higher levels of energy, indicating potential points of improvement both for EvoSuite as well as the different programs under test.

Abstract Analyzing security issues in systems can depend on many parameters. The purpose of this paper is to develop a modeling that can be applied uniformly to all systems. For this purpose, a system of parameters that is found in every system is examined. The background to the research is the problem of safety. The topic is to examine the relationships between system components that determine the safety without the exact interpretation of safety. For standardization the modeling process is based on the philosophical main topics. Elements of the model can be derived from the abstract categories of human thinking. The study is based on cybernetics with energy modeling. That is, the general energy balance of the systems is tested. Further studies are based on the general system equation under the energy model thus generated. The general shape and special cases of the equation determine the types of system examinations.

We introduce the Generalized Energy Based Model (GEBM) for generative modelling. These models combine two trained components: a base distribution (generally an implicit model), which can learn the support of data with low intrinsic dimension in a high dimensional space; and an energy function, to refine the probability mass on the learned support. Both the energy function and base jointly constitute the final model, unlike GANs, which retain only the base distribution (the "generator"). GEBMs are trained by alternating between learning the energy and the base. We show that both training stages are well-defined: the energy is learned by maximising a generalized likelihood, and the resulting energy-based loss provides informative gradients for learning the base. Samples from the posterior on the latent space of the trained model can be obtained via MCMC, thus finding regions in this space that produce better quality samples. Empirically, the GEBM samples on image-generation tasks are of much better quality than those from the learned generator alone, indicating that all else being equal, the GEBM will outperform a GAN of the same complexity. When using normalizing flows as base measures, GEBMs succeed on density modelling tasks, returning comparable performance to direct maximum likelihood of the same networks.

In this paper, we consider a degenerate viscoelastic Petrovsky-type plate equation K(x)utt + ∆ u− ∫ t 0 g(t− s)∆u(s)ds + f(u) = 0 with boundary feedback. Under the weaker assumption on the relaxation function, the general energy decay is proved by priori estimates and analysis of Lyapunov-like functional. The exponential decay result and polynomial decay result in some literature are special cases of this paper.

Microgrids represent an emerging paradigm of future electric power systems that can utilize both distributed and centralized generations. Two recent trends in microgrids are the integration of local renewable energy sources (such as wind farms) and the use of co-generation (i.e., to supply both electricity and heat). However, these trends also bring unprecedented challenges to the design of intelligent control strategies for microgrids. Traditional generation scheduling paradigms rely on perfect prediction of future electricity supply and demand. They are no longer applicable to microgrids with unpredictable renewable energy supply and with co-generation (that needs to consider both electricity and heat demand). In this paper, we study online algorithms for the microgrid generation scheduling problem with intermittent renewable energy sources and co-generation, with the goal of maximizing the cost-savings with local generation. Based on the insights from the structure of the offline optimal solution, we propose a class of competitive online algorithms, called CHASE (Competitive Heuristic Algorithm for Scheduling Energy-generation), that track the offline optimal in an online fashion. Under typical settings, we show that CHASE achieves the best competitive ratio among all deterministic online algorithms, and the ratio is no larger than a small constant 3.

Artificial Energy General Intelligence (AEGI) is a natural progression of Artificial General Intelligence (AGI) that caters to the energy industry. It is crucial to optimize the entire value chain involved in generating, transporting, and storing energy for the betterment of humanity, the environment, industry, and the scientific community. Most research efforts focus on a specific area of the value chain, leading to a disconnect between multiple disciplines and hindering effective problem-solving. AEGI proposes integrating the learning from each discipline in the energy sector to create an optimal solution that simultaneously addresses multiple objectives. This integration is more complex than solving each discipline's challenges separately, but achieving a sustainable and efficient energy system is necessary.

We consider the mixed $p$-spin mean-field spin glass model with Ising spins and investigate its free energy in the spirit of the TAP approach, named after Thouless, Anderson, and Palmer. More precisely, we define and compute the generalized TAP correction, and establish the corresponding generalized TAP representation for the free energy. In connection with physicists' replica theory, we introduce the notion of generalized TAP states, which are the maximizers of the generalized TAP free energy, and show that their order parameters match the order parameter of the ancestor states in the Parisi ansatz. We compute the critical point equations of the TAP free energy that generalize the classical TAP equations for pure states. Furthermore, we give an exact description of the region where the generalized TAP correction is replica symmetric, in which case it coincides with the classical TAP correction, and show that Plefka's condition is necessary for this to happen. In particular, our result shows that the generalized TAP correction is not always replica symmetric on the points corresponding to the Edwards-Anderson parameter.

In the signal processing, active signal filters are commonly used to filter out the zero-average high-frequency components of a signal. In the power system, the power filters are used to filter and control the harmonics in voltages and current waveforms in the concept of power quality. In this paper, we introduce energy filters to filter and control the undesirable frequency components of power flow waveforms in the concept of energy quality. In contrast to the power filters, a family of general energy filters (GEFs) using energy storage is proposed, which virtually work as low-pass filters of power flow and can smooth, track, and process the power flow, as the power filters do with the current and voltage waveforms. In order to illustrate the GEF, the mainstream electrical energy storage (EES) systems are briefly reviewed and classified, and a general model of the EES is developed accordingly. Then, the series, parallel, and series–parallel GEF in the first and second order are proposed, and the focuses are laid on their topologies and controls. Time-domain demonstrations of the GEF based on different implementations are presented on RTDS. Bode plots of the proposed GEF are also obtained through simulations. Finally, key factors in designing GEF for practical applications are briefly discussed.

O'Hara introduced several functionals as knot energies. One of them is the Möbius energy. We know its Möbius invariance from Doyle-Schramm's cosine formula. It is also known that the Möbius energy was decomposed into three components keeping the Möbius invariance. The first component of decomposition represents the extent of bending of the curves or knots, while the second one indicates the extent of twisting. The third one is an absolute constant. In this paper, we show a similar decomposition for generalized O'Hara energies. On the way to derive it, we obtain an analogue of the cosine formula for the generalized O'Hara energy. Furthermore, using decomposition, the first and second variational formulae are derived.

I present a model in which dark energy interacts with matter. The former is represented by a variable equation of state. It is shown that the phantom crossing takes place at zero redshift, moreover, stable scaling solution of the Friedmann equations is obtained. I show that dark energy is most probably be either generalized phantom energy or the generalized Chaplygin gas.