Four-dimensional Set Research Articles

Urban integrated energy system stochastic robust optimization scheduling under multiple uncertainties

The uncertainties of the wind power generation, solar power generation, electricity load, and heat load bring difficulties to the optimal scheduling of the urban integrated energy system (UIES), which influence its secure and reliable operation. To promote the utilization of renewable energy and enhance the scheduling capacity of UIES, a two-stage stochastic robust optimization model with the day-ahead market and the real-time market is developed. The goal is to optimize the UIES’s profit in the day-ahead market and minimize the total system cost in the real-time market, accounting for the most unfavorable situations of uncertainties. To address multiple uncertainties, a four-dimensional ambiguity set considering multiple uncertainties is constructed by using the Dirichlet process mixture model (DPMM) and the variational inference algorithm. Meanwhile, an accelerated column-and-constraint generation algorithm (AC&CG) is presented for iterative solution of the proposed model, with the second stage reformulated via Lagrange dual theory. Besides, a novel acceleration strategy is adopted, which contributes the algorithm to converging faster which can also improve the iteration speed. Finally, simulation examples are used to demonstrate the effectiveness of the proposed model in comparison to stochastic programming and robust optimization. This paper may provide theoretical guidance for relevant research and application.

Fixed points and steady solitons for the two-loop renormalization group flow

Solitons for the two-loop renormalization group flow are studied in the four-dimensional homogeneous setting, providing a classification of algebraic steady four-dimensional solitons.

A Novel Method for Developing Post-quantum Digital Signature Algorithms on Non-commutative Associative Algebras

Introduction: Development of practical post-quantum signature algorithms is a current challenge in the area of cryptography. Recently, several candidates on post-quantum signature schemes, in which the exponentiation operations in a hidden commutative group contained in a non-commutative algebra is used, were proposed. Search for new mechanisms of using a hidden group, while developing signature schemes resistant to quantum attacks, is of significant practical interest. Purpose: Development of a new method for designing post-quantum signature algorithms on finite non-commutative associative algebras. Results: A novel method for developing digital signature algorithms on non-commutative algebras. A new four-dimensional finite non-commutative associative algebra set over the ground field GF(p) have been proposed as algebraic support of the signature algorithms. To provide a higher performance of the algorithm, in the introduced algebra the vector multiplication is defined by a sparse basis vector multiplication table. Study of the algebra structure has shown that it can be represented as a set of commutative subalgebras of three different types, which intersect exactly in the set of scalar vectors. Using the proposed method and introduced algebra, a new post-quantum signature scheme has been designed. The introduced method is characterized in using one of the elements of the signature (e, S) in form of the four-dimensional vector S that is computed as a masked product of two exponentiated elements G and H of a hidden commutative group: S = B-1GnHmC-1, where non-permutable vectors B and C are masking multipliers; the natural numbers n and m are calculated depending on the signed document M and public key. The pair <G, H> composes a minimum generator systems of the hidden group. The signature verification equation has the form R = (Y1SZ1)e(Y2SZ2)e2, where pairwise non-permutable vectors Y1, Z1, Y2, and Z2 are element of the public key and natural number e that is computed depending on the value M and the vector R. Practical relevance: Due to sufficiently small size of public key and signature and high, the developed digital signature scheme represents interest as a practical post-quantum signature algorithm. The introduced method is very attractive to develop a post-quantum digital signature standard.

High Speed Data Exchange Algorithm in Telemedicine with Wavelet based on 4D Medical Image Compression

Existing Medical imaging techniques such as fMRI, positron emission tomography (PET), dynamic 3D ultrasound and dynamic computerized tomography yield large amounts of four-dimensional sets. 4D medical data sets are the series of volumetric images netted in time, large in size and demand a great of assets for storage and transmission. Here, in this paper, we present a method wherein 3D image is taken and Discrete Wavelet Transform(DWT) and Dual-Tree Complex Wavelet Transform(DTCWT) techniques are applied separately on it and the image is split into sub-bands. The encoding and decoding are done using 3D-SPIHT, at different bit per pixels(bpp). The reconstructed image is synthesized using Inverse DWT technique. The quality of the compressed image has been evaluated using some factors such as Mean Square Error(MSE) and Peak-Signal to Noise Ratio (PSNR).

Discontinuous Dynamic Analysis of a Class of 2-DOF Oscillators With Strong Nonlinearity Under a Periodic Excitation

Starting from the car suspension system, the nonlinear characteristics of a class of two-degree-of-freedom oscillators with strong nonlinearity under a periodic excitation are discussed by the switching theory of flow in discontinuous dynamical systems. Based on the discontinuous forces and different motions of the two masses, the phase plane of each mass is composed of stick domain, nonstick domain (or free domain) and separation boundary in absolute and relative coordinates, respectively. The swithching criteria between the stick and nonstick motions and the conditions of grazing motion in two different regions are developed via the G-functions and switching control laws. The mapping dynamics theory is used to give the four-dimensional transformation set and four-dimensional mapping, and the conditions for periodic motions are explored. In addition, the stick motions, two kinds of grazing motions, periodic motions for this system and a comparison of the velocities, accelerations (or forces responses) of the two masses under the two conditions of control force are simulated numerically. The results show that the stability and comfort of the vehicle can be improved by adjusting the control force, which is generated by the control unit of system or exerted by the external excitation. For further investigating the influence of system parameters on dynamical behaviors, the stick and grazing bifurcation scenarios varying with driving frequency or amplitude are also developed, which can provide useful information for parameter selection of vibration systems with clearance and the optimal design of vehicle suspension systems. This paper also has important reference value for practical applications in other industries or machinery with elastic impacts.

Analysis of dynamical behaviors of a 2-DOF friction oscillator with elastic impacts and negative feedbacks

In this paper, the flow switching theory of discontinuous dynamical systems is used as the main tool to study the dynamical behaviors of a two-degree-of-freedom friction oscillator with elastic impacts, where considering that the inequality of static and kinetic friction forces results in the existence of flow barriers at the relative velocity between the mass and conveyor belt tending to zero. The negative feedback is also taken into account, $$\mathrm {i.e.}$$ , when the direction of the relative velocity between the mass and conveyor belt changes, the constant force in the periodic excitation force will also change to adapt to the variation in speed. Due to the discontinuity resulted from the friction and non-smoothness resulted from impact, the motion of the two masses can be divided into the following kinds: non-sliding motion (or free motion), sliding motion, non-sliding–stick motion and sliding–stick motion, and the phase space in system is divided into different domains and boundaries, where the vector field is continuous in each region but discontinuous on the velocity boundary. The corresponding normal vectors and G-functions on the separation boundaries are introduced to acquire the switching conditions for all possible motions such as passable motion, sliding motion, grazing motion and stick motion. The mapping theory provides an effective method for the discussion of periodic motion in discontinuous dynamical systems. The four-dimensional switching sets are defined by the means of the form of direct product of two-dimensional switching sets, and the mapping structures are introduced based on the switching sets to describe periodic motions. Eventually, in order to explain more intuitively the above motions in such a friction–impact system, the velocity, displacement, G-functions time histories and the trajectories in phase plane for the masses are illustrated by simulation numerically.

Multiobjective Direct Policy Search Using Physically Based Operating Rules in Multireservoir Systems

This study explores the ways to introduce physical interpretability into the process of optimizing operating rules for multireservoir systems with multiple objectives. Prior studies applied the concept of direct policy search (DPS), in which the release policy is expressed as a set of parameterized functions (e.g., neural networks) that are optimized by simulating the performance of different parameter value combinations over a testing period. The problem with this approach is that the operators generally avoid adopting such artificial black-box functions for the direct real-time control of their systems, preferring simpler tools with a clear connection to the system physics. This study addresses this mismatch by replacing the black-box functions in DPS with physically based parameterized operating rules, for example by directly using target levels in dams as decision variables. This leads to results that are physically interpretable and may be more acceptable to operators. The methodology proposed in this work is applied to a network of five reservoirs and four power plants in the Nechi catchment in Colombia, with four interests involved: average energy generation, firm energy generation, flood hazard, and flow regime alteration. The release policy is expressed depending on only 12 parameters, which significantly reduces the computational complexity compared to existing approaches of multiobjective DPS. The resulting four-dimensional Pareto-approximate set offers a variety of operational strategies from which operators may choose one that corresponds best to their preferences. For demonstration purposes, one particular optimized policy is selected and its parameter values are analyzed to illustrate how the physically based operating rules can be directly interpreted by the operators.

Analysis of dynamical behaviors of a 2-DOF friction-induced oscillator with one-sided impact on a conveyor belt

In this paper, the flow switchability theory of discontinuous dynamical systems is used to illustrate the dynamical behavior of a 2-DOF (two degrees of freedom) friction-induced oscillator with one-sided impact on a conveyor belt. All the possible motion states such as stick and non-stick motions, impact motion, and stuck motion for such an oscillator are introduced. The phase space in system can be divided into different domains and boundaries according to the discontinuity caused by the friction force jumping and the impact between the mass and the rigid obstacle. The vector field in each domain is continuous and different from that in its adjacent domain. The flow barrier on the separation boundary is considered in this paper. Once the boundary flow leaves the boundary, the boundary flow barrier on the velocity boundary may exist and the leaving flow barriers on the velocity boundary may also exist. The G-functions on different separation boundaries are defined to illustrate the flow switching on the corresponding boundaries. The analytical conditions of the passable, stick, grazing, impact, and stuck motions are developed through G-functions and analysis of vector fields. Since the motions of the two masses interact with each other, the four-dimensional switching sets are given by the form of direct product and the four-dimensional mappings are given to describe periodic motions with different mapping structures. The analytical prediction of different periodic motions is performed through the mapping dynamics. For a better understanding of the motion switching mechanism in such a 2-DOF oscillator , the time histories of displacement, velocity, G-function and the trajectories in phase space for the passable motion, stick motion, impact motion, grazing motion, stuck motion, and periodic motion in system are given by simulation numerically. This investigation has important significance in the optimization design of machinery with friction and impact etc.

Erratum for “Optimizing Crane Selection and Location for Multistage Construction Using a Four-Dimensional Set Cover Approach” by Justin K. W. Yeoh and David K. H. Chua

Erratum for “Optimizing Crane Selection and Location for Multistage Construction Using a Four-Dimensional Set Cover Approach” by Justin K. W. Yeoh and David K. H. Chua

Valid inequalities for separable concave constraints with indicator variables

We study valid inequalities for optimization models that contain both binary indicator variables and separable concave constraints. These models reduce to a mixed-integer linear program (MILP) when the concave constraints are ignored, or to a nonconvex global optimization problem when the binary restrictions are ignored. In algorithms designed to solve these problems to global optimality, cutting planes to strengthen the relaxation are traditionally obtained using valid inequalities for the MILP only. We propose a technique to obtain valid inequalities that are based on both the MILP constraints and the concave constraints. We begin by characterizing the convex hull of a four-dimensional set consisting of a single binary indicator variable, a single concave constraint, and two linear inequalities. Using this analysis, we demonstrate how valid inequalities for the single node flow set and for the lot-sizing polyhedron can be “tilted” to give valid inequalities that also account for separable concave functions of the arc flows. We present computational results demonstrating the utility of the new inequalities for nonlinear transportation problems and for lot-sizing problems with concave costs. To our knowledge, this is one of the first works that simultaneously convexifies both nonconvex functions and binary variables to strengthen the relaxations of practical mixed-integer nonlinear programs.

Development and testing an online near-infrared spectroscopy brain–computer interface tailored to an individual with severe congenital motor impairments

Purpose: For non-verbal individuals, brain–computer interfaces (BCIs) are a potential means of communication. Near-infrared spectroscopy (NIRS) is a brain-monitoring modality that has been considered for BCIs. To date, limited NIRS-BCI testing has involved online classification, particularly with individuals with severe motor impairments.Materials and methods: We tested an online NIRS-BCI developed for a non-verbal individual with severe congenital motor impairments. The binary BCI differentiated categorical verbal fluency task (VFT) performance and rest using prefrontal measurements. The participant attended five sessions, the last two of which were online with classification feedback.Results: An online classification accuracy of 63.33% was achieved using a linear discriminant classifier trained on a four-dimensional feature set. An offline, cross-validation analysis of all data yielded an optimal adjusted classification accuracy of 66.6 ± 9.11%. Inconsistent functional responses, contradictory effects of feedback, participant fatigue and motion artefacts were identified as challenges to online classification specific to this participant.Conclusions: Results suggest potential in using an NIRS-BCI controlled by the VFT in instances of severe congenital impairments. Further testing with users with severe disabilities is necessary.Implications for RehabilitationBrain–computer interfaces (BCIs) can provide a non-motor based means of communication for individuals with severe motor impairments.Near-infrared spectroscopy (NIRS) is a haemodynamic-based brain-imaging modality used in BCIs.To date, NIRS-BCIs have not been thoroughly tested with potential target users.This case study shows that NIRS-BCIs may offer a means of practical communication for individuals with severe congenital impairments and continued exploration is advisable.

Optimizing Crane Selection and Location for Multistage Construction Using a Four-Dimensional Set Cover Approach

AbstractCrane selection and location planning exists as part of a series of critical decisions faced by construction managers. As today’s construction projects grow increasingly complex and complic...

Target identification using bistatic high‐resolution range profiles

A novel target identification scheme that utilises high-resolution range profiles (HRRPs), which are obtained using bistatic (BS) radar (BS-HRRPs) and four-dimensional (4D) parameter sets (PSs), is described. These PSs uniquely determine the BS-HRRPs. In the proposed scheme, a new feature to cope with the scale variances of the BS-HRRPs is devised by using the RELAX algorithm and the resampling process. In addition, a proper classifier to effectively exploit both the BS-HRRPs and 4D PSs is designed to improve the BS identification capability.

Romans-mass-driven flows on the D2-brane

The addition of supersymmetric Chern-Simons terms to ${\cal N}=8$ super-Yang-Mills theory in three-dimensions is expected to make the latter flow into infrared superconformal phases. We address this problem holographically by studying the effect of the Romans mass on the D2-brane near-horizon geometry. Working in a consistent, effective four-dimensional setting provided by $D=4$ ${\cal N}=8$ supergravity with a dyonic $\textrm{ISO(7)}$ gauging, we verify the existence of a rich web of supersymmetric domain walls triggered by the Romans mass that interpolate between the (four-dimensional description of the) D2-brane and various superconformal phases. We also construct domain walls for which both endpoints are superconformal. While most of our results are numerical, we provide analytic results for the $\textrm{SU}(3)\times \textrm{U}(1)$-invariant flow into an ${\cal N}=2$ conformal phase recently discovered.

Distance-Fields-Over-Grids Method for Aircraft Envelope Determination

In this research, the concept of posing the flight envelope as a reachable set is explored further, and it is investigated whether the distance fields over grids (DFOG) method for reachability computations is a viable method for envelope determination. The DFOG method approximates the reachable set of a dynamic system by solving a number of optimal control problems over a grid in the state space. Then, the end points of the resulting optimal trajectories are used to provide an approximation of the reachable set. The DFOG method is improved by using a second-order Runge–Kutta method for the state discretization and developing a new adaptive grid-selection approach. This method is then applied to the computation of a four-dimensional reachable set of a nonlinear high-fidelity F-16 model. The results are compared to the results obtained with the level-set method, demonstrating that the DFOG method provides a less conservative approximation to the reachable set.

The landscape of G-structures in eight-manifold compactifications of M-theory

We consider spaces of “virtual” constrained generalized Killing spinors, i.e. spaces of Majorana spinors which correspond to “off-shell” s-extended supersymmetry in compactifications of eleven-dimensional supergravity based on eight-manifolds M. Such spaces naturally induce two stratifications of M, called the chirality and stabilizer stratification. For the case s = 2, we describe the former using the canonical Whitney stratification of a three-dimensional semi-algebraic set $$ \mathrm{\mathcal{R}} $$ . We also show that the stabilizer stratification coincides with the rank stratification of a cosmooth generalized distribution $$ {\mathcal{D}}_0 $$ and describe it explicitly using the Whitney stratification of a four-dimensional semi-algebraic set $$ \mathfrak{P} $$ . The stabilizer groups along the strata are isomorphic with SU(2), SU(3), G2 or SU(4), where SU(2) corresponds to the open stratum, which is generically non-empty. We also determine the rank stratification of a larger generalized distribution $$ \mathcal{D} $$ which turns out to be integrable in the case of compactifications down to AdS3.

Multi-objective optimization of a nearly zero-energy building based on thermal and visual discomfort minimization using a non-dominated sorting genetic algorithm (NSGA-II)

Multi-objective optimization methods provide a valid support to buildings’ design. They aim at identifying the most promising building variants on the basis of diverse and potentially contrasting needs. However, optimization has been mainly used to optimize the energy performance of buildings, giving secondary importance to thermal comfort and usually neglecting visual comfort and the indoor air quality.The present study addresses the design of a detached net zero-energy house located in Southern Italy to minimize thermal and visual discomfort. The optimization problem admits four objective functions (thermal discomfort during winter and summer and visual discomfort due to glare and an inappropriate quantity of daylight) and uses the non-dominated sorting genetic algorithm, implemented in the GenOpt optimization engine through the Java genetic algorithms package, to instruct the EnergyPlus simulation engine.The simulation outcome is a four-dimensional solution set. The building variants of the Pareto frontier adopt diverse and non-intuitive design alternatives. To derive good design practices, two-dimensional projections of the solution set were also analyzed. Finally, in cases of complex optimization problems with many objective functions, optimization techniques are recommended to effectively explore the large number of available building variants in a relatively short time and, hence, identify viable non-intuitive solutions.

Electroweakino constraints from LHC data

We investigate the sensitivity of existing LHC searches to the charginos and neutralinos of the MSSM when all the other superpartners are decoupled. In this limit, the underlying parameter space reduces to a simple four-dimensional set $\{M_1,\,M_2,\,\mu,\,\tan\beta\}$. We examine the constraints placed on this parameter space by a broad range of LHC searches taking into account the full set of relevant production and decay channels. We find that the exclusions implied by these searches exceed existing limits from LEP only for smaller values of the Bino mass $M_1 \lesssim 150$ GeV. Our results have implications for MSSM dark matter and electroweak baryogenesis.

Horseshoes for the nearly symmetric heavy top

We prove the existence of horseshoes in the nearly symmetric heavy top. This problem was previously addressed but treated inappropriately due to a singularity of the equations of motion. We introduce an (artificial) inclined plane to remove this singularity and use a Melnikov-type approach to show that there exist transverse homoclinic orbits to periodic orbits on four-dimensional level sets. The price we pay for removing the singularity is that the Hamiltonian system becomes a three-degree-of-freedom system with an additional first integral, unlike the two-degree-of-freedom formulation in the classical treatment. We therefore have to analyze three-dimensional stable and unstable manifolds of periodic orbits in a six-dimensional phase space. A new Melnikov-type technique is developed for this situation. Numerical evidence for the existence of transverse homoclinic orbits on a four-dimensional level set is also given.

Discontinuous Galerkin methods for general-relativistic hydrodynamics: Formulation and application to spherically symmetric spacetimes

We have developed the formalism necessary to employ the discontinuous-Galerkin approach in general-relativistic hydrodynamics. The formalism is first presented in a general four-dimensional setting and then specialized to the case of spherical symmetry within a $3+1$ splitting of spacetime. As a direct application, we have constructed a one-dimensional code, EDGES, which has been used to assess the viability of these methods via a series of tests involving highly relativistic flows in strong gravity. Our results show that discontinuous-Galerkin methods are able not only to handle strong relativistic shock waves but, at the same time, to attain very high orders of accuracy and exponential convergence rates in smooth regions of the flow. Given these promising prospects and their affinity with a pseudospectral solution of the Einstein equations, discontinuous-Galerkin methods could represent a new paradigm for the accurate numerical modelling in relativistic astrophysics.