Infinite Solution Space Research Articles

Inherent color symmetry in quantum Yang-Mills theory

We present the basic non-perturbative structure of the space of classical dynamical solutions and corresponding one particle quantum states in SU(3) Yang-Mills theory. It has been demonstrated that the Weyl group of su(3) algebra plays an important role in constructing non-perturbative solutions and leads to profound changes in the structure of the classical and quantum Yang-Mills theory. We show that the Weyl group as a non-trivial color subgroup of SU(3) admits singlet irreducible representations on a space of classical dynamical solutions which lead to strict concepts of one particle quantum states for gluons and quarks. The Yang-Mills theory is a non-linear theory and, in general, it is not possible to construct a Hilbert space of classical solutions and quantum states as a linear vector space, so, usually, a perturbative approach is applied. We propose a non-perturbative approach based on Weyl symmetric solutions to full non-linear equations of motion and construct a full space of dynamical solutions representing an infinite but countable solution space classified by a finite set of integer numbers. It has been proved that the Weyl singlet structure of classical solutions provides the existence of a stable non-degenerate vacuum which serves as a main precondition of the color confinement phenomenon. Some physical implications in quantum chromodynamics are considered.

Optimal outpatient capacity allocation under the capacity-addition policy

Outpatient departments are under great pressure to meet increasing demand with limited medical resources. Facing a high-demand environment, the capacity-addition policy (CAP) has been widely applied, where outpatients allocate additional capacity in a demand-driven approach. Under the CAP, outpatient managers estimate an effective demand. Additional capacity is determined depends on the relationship between the estimate and regular capacity. Moreover, regular capacity is also a decision variable, which leads to great difficulties when conducting capacity allocation. The joint decisions on the optimal regular capacity, its allocation scheme of different phases and proper rule for estimating the effective demand become important concerns for outpatient managers, under uncertainties in demand and patient no-show. This paper addresses the problem towards maximizing the expected profit composed of expected revenue minus the costs of idleness and overwork. Several properties are proposed to address the difficulty in the infinite solution space. Properties help transform the joint decisions into orderly single decisions and prove the unimodality of the objective. Algorithms are designed accordingly. Experiments indicate that it is better to pre-offset the effect of no-show rather than consider its reduction in the determination of additional capacity. Outpatient managers need to enlarge the estimate of effective demand, and 1.1 to 1.2 times of the total expected demand is suggested, where outpatients can balance the expected overload with the expected profit. The optimal regular capacity is stable to the variety of no-show probability.

Minimizing Energy Consumption in Wireless Rechargeable UAV Networks

With the development of airborne equipment and integrated avionics technology, the unmanned aerial vehicle (UAV) network replaces human beings in many works. However, the limited energy capacity of UAVs has great restrictions on long-time missions. To prolong the lifetime of the UAV network, we introduce the wireless static chargers (WSCs) into the UAV network, and a nondisruptive wireless rechargeable UAV network (WRUN) model is proposed, in which UAVs can be wirelessly charged without returning back to the charging platform and WSCs are scheduled to turn on and release energy only in the charging time periods. The goal of this article is to minimize the energy waste of WSCs under the premise that UAVs will not run out of energy. To calculate the efficient charging time periods of WSCs, we first discretize flight paths of UAVs so that the nondisruptive charging time schedule problem (nCTSP) that has an infinite solution space both in the spatial and time dimensions can be formalized as an optimization problem. Then, we propose the baseline algorithm exhaust candidate solutions (ECSs) to calculate the charging time periods and propose an improved algorithm using the idea of pruning (PECS) to reduce the computational complexity of ECS. Finally, experiments are conducted and PECS achieves better performance in terms of saving energy consumption and maximizing energy utilization.

Predicting Post-Concussion Symptom Recovery in Adolescents Using a Novel Artificial Intelligence.

This pilot study explores the possibility of predicting post-concussion symptom recovery at one week post-injury using only objective diffusion tensor imaging (DTI) data inputs to a novel artificial intelligence (AI) system composed of Genetic Fuzzy Trees (GFT). Forty-three adolescents age 11 to 16 years with either mild traumatic brain injury or traumatic orthopedic injury were enrolled on presentation to the emergency department. Participants received a DTI scan three days post-injury, and their symptoms were assessed by the Post-Concussion Symptom Scale (PCSS) at 6 h and one week post-injury. The GFT system was trained using one-week total PCSS scores, 48 volumetric magnetic resonance imaging inputs, and 192 DTI inputs per participant over 225 training runs. Each training run contained a randomly selected 80% of the total sample followed by a 20% validation run. Over a different randomly selected sample distribution, GFT was also compared with six common classification methods. The cascading GFT structure controlled an effectively infinite solution space that classified participants as recovered or not recovered significantly better than chance. It demonstrated 100% and 62% classification accuracy in training and validation, respectively, better than any of the six comparison methods. Recovery sensitivity and specificity were 59% and 65% in the GFT validation set, respectively. These results provide initial evidence for the effectiveness of a GFT system to make clinical predictions of trauma symptom recovery using objective brain measures. Although clinical and research applications will necessitate additional optimization of the system, these results highlight the future promise of AI in acute care.

Deployment of Unmanned Aerial Vehicles for Anisotropic Monitoring Tasks

This paper considers the fundamental problem of deployment of Unmanned Aerial <u>V</u> eh <u>I</u> cles for ani <u>S</u> otropic mon <u>I</u> toring <u>T</u> asks (VISIT), that is, given a set of objects with determined coordinates and directions in 2D area, deploy a fixed number of UAVs by adjusting their coordinates and orientations such that the overall monitoring utility for all objects is maximized. We develop a theoretical framework to address VISIT problem. First, we establish monitoring model whose quality of monitoring (QoM is anisotropic with monitoring angle and varying with various monitoring distance. To the best of our knowledge, we are the first considering the anisotropy of monitoring angle. Then, we propose a framework consisting of area discretization and Monitoring Dominating Set (MDS) extraction to reduce the infinite solution space of VISIT to a limited one with performance bound. Finally, we model the reformulated problem as maximizing a monotone submodular function subject to a matroid constraint, and present a greedy algorithm with <inline-formula><tex-math notation="LaTeX">$1-1/e-\epsilon$</tex-math></inline-formula> approximation ratio. We conduct both simulations and field experiments to evaluate our framework, and the results show that our algorithm outperforms comparison algorithms by at least 41.3 percent.

On dispersion of solute in steady flow through a channel with absorption boundary: an application to sewage dispersion

The paper describes the longitudinal dispersion of passive tracer materials released into an incompressible viscous fluid, flowing through a channel with walls having first-order reaction. Its model is based on a steady advection–diffusion equation with Dirichlet’s and mixed boundary conditions, and whose solution represents the concentration of the tracers in different downstream stations. For imposing the boundary conditions properly, artanh transformation is used to convert the infinite solution space to a finite one. A finite difference implicit scheme is used to solve the advection–diffusion equation in the computational region, and an inverse transformation is employed for the solution in the physical region. It is shown how the mixing of the tracer molecule influenced by the shear flow and due to the action of the absorption parameter at both the walls of the channel. For convection-dominated flow, uniform mesh is failed to capture the layer phenomena along the different downstream stations and a piecewise uniform mesh; namely, Shishkin mesh is used. The results are compared with existing experimental and numerical data available in the literature, and we have achieved an excellent agreement with them. The study plays a significant role to understand the basic mechanisms of sewage dispersion.

Placement of Unmanned Aerial Vehicles for Directional Coverage in 3D Space

This paper considers the fundamental problem of P lacement of unmanned A erial vehicles achievi N g 3D D irectional cover A ge (PANDA), that is, given a set of objects with determined positions and orientations in a 3D space, deploy a fixed number of UAVs by adjusting their positions and orientations such that the overall directional coverage utility for all objects is maximized. First, we establish the 3D directional coverage model for both cameras and objects. Then, we propose a Dominating Coverage Set (DCS) extraction method to reduce the infinite solution space of PANDA to a limited one without performance loss. Finally, we model the reformulated problem as maximizing a monotone submodular function subject to a matroid constraint and present a greedy algorithm with $1-1/e$ approximation ratio to address this problem. We conduct simulations and field experiments to evaluate the proposed algorithm, and the results show that our algorithm outperforms comparison ones by at least 75.4%.

Energy efficient positioning of mobile base stations to improve wireless sensor network lifetime

Base station placement problem has concerned the attention of lot of researchers as it has a major impact on the lifetime of wireless sensor network. This paper suggests using multiple mobile base stations and proposes a near optimal solution for maximising the lifetime of wireless sensor network. The base station placement problem relies on the idea of discretising the search space and is formulated as an optimisation problem. The optimum positions for base stations are obtained as the solution to an integer linear programming (ILP) formulation. The contribution of our paper is twofold. First we have offered a novel technique to transform the infinite solution space to a finite space with promising performance. Second we have formulated an ILP formulation to determine best locations for positioning the base station. We expand our contribution further to a distributed protocol which will provide a completely distributed and localised solution to the placement problem.

Study on Spatial Nonlinear Vibration Characteristics of Cables with a Particular Constraint

In order to study the nonlinear vibration problems of cable with a particular constraint, the mathematical model for the object of study should be established firstly with the elastic mechanics method. In order to obtain the mathematical model of differential form, the Galerkin method is used to make the mathematical model discrete and modal truncation, so the infinite dimensional solution space of the mathematical model can be transformed into the finite dimensional one. Main factors influencing the vibration of the cable system are analyzed, and the simulation analysis about the effects of various parameters on frequency is carried out. The analysis results show that the internal resonance modes may exist, and provide a theoretical basis for improving the safety and reliability of laying cables in actual conditions.

A low-complexity data-dependent beamformer

The classical problem of choosing apodization functions for a beamformer involves a trade-off between main lobe width and side lobe level, i.e., a trade-off between resolution and contrast. To avoid this trade-off, the application of adaptive beamforming, such as minimum variance beamforming, to medical ultrasound imaging has been suggested. This has been an active topic of research in medical ultrasound imaging in the recent years, and several authors have demonstrated significant improvements in image resolution. However, the improvement comes at a considerable cost. Where the complexity of a conventional beamformer is linear with the number of elements [O(M)], the complexity of a minimum variance beamformer is as high as O(M³). In this paper, we have applied a method based on an idea by Vignon and Burcher which is data-adaptive, but selects the apodization function between several predefined windows, giving linear complexity. In the proposed method, we select an apodization function for each depth along a scan line based on the optimality criterion of the minimum variance beamformer. However, unlike the minimum variance beamformer, which has an infinite solution space, we limit the number of possible outcomes to a set of predefined windows. The complexity of the method is then only P times that of the conventional method, where P is the number of predefined windows. The suggested method gives significant improvement in image resolution at a low cost. The method is robust, can handle coherent targets, and is easy to implement. It may also be used as a classifier because the selected window gives information about the object being imaged. We have applied the method to simulated data of wire targets and a cyst phantom, and to experimental RF data from a heart phantom using P = 4 and P = 12. The results show significant improvement in image resolution compared with delay-and-sum.

Combining of Direct Search and Signal-to-Noise Ratio for economic dispatch optimization

This paper integrated the ideas of Direct Search and Signal-to-Noise Ratio (SNR) to develop a Novel Direct Search (NDS) method for solving the non-convex economic dispatch problems. NDS consists of three stages: Direct Search (DS), Global SNR (GSNR) and Marginal Compensation (MC) stages. DS provides a basic solution. GSNR searches the point with optimization strategy. MC fulfills the power balance requirement. With NDS, the infinite solution space becomes finite. Furthermore, a same optimum solution can be repeatedly reached. Effectiveness of NDS is demonstrated with three examples and the solutions were compared with previously published results. Test results show that the proposed method is simple, robust, and more effective than many other previously developed algorithms.

Demarcation of potential seismic sources on integration of genetic algorithm and BP algorithm

In this paper potential seismic sources in coastal region of South China are identified by integration of genetic algorithm (GA) and back propagation (BP algorithm). GA is used for finding the best parameter combination rapidly in an infinite solution space for artificial neural networks (ANN). The results show that the distribution of potential seismic sources with different upper magnitude demarcated by this classifier is mostly satisfied the intrinsic relationship between seismic environment and earthquake occurrence, with less effect from subjective judgment of human being.

Hybridising Tabu Search with Optimisation Techniques for Irregular Stock Cutting

Sequential meta-heuristic implementations for the irregular stock-cutting problem have highlighted a number of common problems. The literature suggests a consensus that it is more efficient to allow configurations with overlapping pieces in the solution space and to penalise these in the evaluation function. However, depending on the severity of the penalty this relaxation results in a tendency to converge toward infeasible solutions or to seek out feasible solutions at the expense of overall quality. A further problem is encountered in defining a neighbourhood search strategy that can deal with the infinite solution space inherent in the irregular stock-cutting problem. The implementation in this paper adopts a hybrid tabu search approach that incorporates two very different optimisation routines that utilise alternative neighbourhoods to address the described problems.