Endpoint Conditions Research Articles

The Clinical Characteristics and Prognosis Factors of Mild-Moderate Patients With COVID-19 in a Mobile Cabin Hospital: A Retrospective, Single-Center Study.

Background: Novel mobile cabin hospitals have been built to provide more makeshift beds for patients with COVID-19 in Wuhan. However, the characteristics of these patients needed be further described.Methods: This was a retrospective, single-center study. A total of 869 patients with confirmed COVID-19 were admitted to Wuchang Mobile Cabin Hospital in Wuhan, between February 6th, 2020 and February 20th, 2020. The final date of follow-up was March 6th, 2020. Clinical characteristics and outcome data were collected and analyzed.Results: Of 869 patients, the median age was 51 years (IQR, 40–58 years), and 377 patients (377/869; 43.4%) were men. A total of 616 patients (616/869; 70.9%) were discharged, 95 patients (95/869; 10.9%) were transferred to the designated hospital due to worsening condition (endpoint), and 158 patients (158/869; 18.2%) were still in the hospital. The incidence of the main symptoms, including fever, cough, fatigue, muscle aches, and anorexia, decreased with time. However, there were no differences in outcome among the patients with different onset times. Generally, both patients aged 45 years or older and patients with comorbidities were more likely to reach the endpoint (transfer to designated high-level hospitals due to condition worsen). In the other model, patients with the lung CT feature (e.g., ground-glass opacity, reticular/linear, air bronchogram, or consolidation shadow) were more likely to reach the endpoint.Conclusion: Older age, comorbidity, special chest CT features (e.g., ground-glass opacity, reticular/linear, air bronchogram, or consolidation shadow) are associated with poor prognosis for mild-moderate patients. The initial symptoms of mild-moderate patients may become insidious, which deserves our attention.

Browder’s Convergence Theorem for Multivalued Mappings in Banach Spaces without the Endpoint Condition

We prove Browder’s convergence theorem for multivalued mappings in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm by using the notion of diametrically regular mappings. Our results are significant improvement on results of Jung (2007) and Panyanak and Suantai (2020).

Optimal balance for rotating shallow water in primitive variables

ABSTRACT Optimal balance is a near-optimal computational algorithm for nonlinear mode decomposition of geophysical flows into balanced and unbalanced components. It was first proposed as “optimal potential vorticity balance” by Viúdez and Dritschel [J. Fluid Mech., 2004, 521, 343] in the specific setting of semi-Lagrangian potential vorticity-based numerical codes. Later, it was recognised as an instance of the more general principle of adiabatic invariance of fast degrees of motion under slow perturbations. From this point of view, the system is slowly deformed from a linearised configuration to the full nonlinear dynamics. In the former, linear analysis yields an exact separation of balanced and unbalanced flow. In the latter, a given base-point coordinate, e.g. the height or potential vorticity field, can be matched. This formulation leads to a boundary value problem in time. In this paper, we show that this more general viewpoint leads to practical implementations of optimal balance on top of a primitive variables (here, velocity-height variables) numerical code. We identify preferred choices for several design parameters. The most critical choices concern the linear projector onto the slow modes at the linear-end boundary and the choice of base-point coordinate at the nonlinear end. We find that, even though the evolutionary model is formulated in primitive variables, potential vorticity based end-point conditions are advantageous. In particular, the only universally robust linear projector is the oblique projector onto the Rossby modes along the gravity-wave modes, which can be interpreted as the distinct non-orthogonal projector onto the Rossby modes that preserves the linear potential vorticity. Hence, the projector can be formulated as an elliptic partial differential equation which holds promise for using the method to produce an accurate nonlinear mode decomposition for more general models without the need to resort to asymptotic analysis.

Impact of heated triangular ribs on hydrodynamic forces in a rectangular domain with heated elliptic cylinder: Finite element analysis

Abstract The heat transfer in flowing liquid stream towards confined geometries having natural or man-made obstacles offers complex mathematical constraints at the heated body-liquid stream interface. Therefore, to appraise the heat transfer in liquid stream with installed obstacles particularly in terms of hydrodynamic forces remains a topic of great interest for the researchers. Owing such interest, the present article contains the extended evaluation of hydrodynamic forces in a flowing liquid stream with heat transfer individualities. To be more, the Newtonian liquid stream is initiated with the parabolic velocity profile at an inlet of partially heated rectangular channel. The heated elliptic shaped cylinder is placed fixed in between channel as an obstacle. The heated triangular ribs are installed case-wise namely (i) channel without ribs (ii) heated triangular rib at lower wall (iii) heated triangular rib at upper wall (iv) heated triangular rib at both upper and lower walls. The presence of heated triangular ribs as an obstacles modifies the endpoint conditions and hence the developed flow narrating differential system cannot be solved exactly. Therefore, the most trustful numerical method named finite element method with LBB-stable finite element pair is utilized to report acceptable solution in terms of streamlines and isotherms contour plots. The hydrodynamic forces are evaluated for each case by adopting line integration around outer surface of heated elliptic obstacle. It is noticed that when the heated triangular rib is installed on both upper and lower channel walls, the drag coefficient is found considerably high.

Diametrically Regular Mappings and Browder’s Theorem Without the Endpoint Condition

In this paper, we introduce the class of diametrically regular mappings and prove that it includes the class of multi-valued mappings having endpoints. We also prove the existence of endpoints and the convergence of an iterative process for mappings of this class. Our approach provides a new idea of proving Browder’s theorem without the endpoint condition.

A direct method for solving calculus of variations problems using the whale optimization algorithm

A numerical algorithm for solving problems of calculus of variations is proposed and analyzed in the present paper. The method is based on direct minimizing the functional in its discrete form with finite dimension. To solve the resulting optimization problem , the recently proposed whale optimization algorithms is used and adopted. The method proposed in this work is capable of solving constrained and unconstrained problems with fixed or free endpoint conditions. Numerical examples are given to check the validity and accuracy of the proposed method in practice. The results show the superior accuracy and efficiency of the proposed technique as compared to other numerical methods.

Curvature-Bounded Lengthening and Shortening for Restricted Vehicle Path Planning

In this paper, the traditional shortest path planning problem for vehicle is advanced to length-targeted path planning problem, i.e., to plan path with its length being as close to a specified value as possible. Lengthening and shortening of given initial paths are used to solve this problem. Based on an operation set consisting of three basic path homotopies, we build a comprehensive and systematic framework to plan paths with target length, which is a generalization of the existing related studies. Thereby, the expected paths can be independently searched through such deformation processes within topological classes. The proposed framework can produce the largest length coverage in different scenarios and under different conditions, and it can also generate expected paths with arbitrary topological classification in terms of the curvature constraint and the obstacle constraint. Examples show that our lengthening and shortening method can effectively solve the length-targeted path planning problem in environment without or with obstacles. Note to Practitioners —This paper presents a curvature-bounded lengthening and shortening approach for path planning of vehicles. The curvature and obstacle constraints in the path planning problem are handled using the topological technique. In addition, a rigorous classification system is presented to systematically categorize the potential paths. Within a path class, any path can be deformed to other paths while keeping the curvature bounded. Then, the path deformation process is conducted via a series of basic homotopy operations to approach the target length. The length coverage range of this process is reduced when some endpoint conditions are meet or the vehicle is trapped into a closed region.

Closed-form solution of optimal control problem of a fractional order system

A formulation and an analytical solution technique of fractional optimal control problem (FOCP) is presented in this paper. The performance index (PI) considered is a conformable fractional integral (CFI) function and is a function of both the state and the control variables. Dynamic behaviour of the system is described by conformable fractional differential equation (FDE). The necessary conditions of optimality and the general transversality condition in terms of Hamiltonian are obtained using variational approach. Both the fixed and free final end point conditions have been considered. An analytical solution technique is presented for solving the conformable FOCPs. To validate the formulation and solution scheme numerical examples are presented.

Evaluation of chemical speciation and environmental risk levels of heavy metals during varied acid corrosion conditions for raw and solidified/stabilized MSWI fly ash

In this work, the leaching pattern, chemical speciation, and environmental risks of various heavy metals (Pb, Zn, Cu, Cd, Cr, and Ni) were investigated synchronously under different acid corrosion conditions through end-point pH leaching experiments. The heavy metals were present in raw, stabilized (phosphoric acid; chelating agent), and solidified (Portland cement) municipal solid waste incineration (MSWI) fly ash. The results showed that the stabilization and solidification pre-treatment could effectively decrease the leaching of most heavy metals. However, phosphoric acid stabilization and Portland cement solidification increased the solubility of Ni and Pb/Cu/Cd under low end-point pH conditions, while that of Cr and Pb increased under high end-point pH conditions. Overall, the leaching pattern of heavy metals was not affected by the addition of binders/additives. The results from speciation analysis showed that the bioavailable fractions (exchangeable and carbonate-bound) were leached out from initial raw or solidified/stabilized fly ash after distilled water leaching. However, with the decrease in end-point pH levels, the bioavailable fractions increased again due to the increase in acid corrosion on metal-bearing mineral matrixes. The risk assessment results indicated that, after exposing the raw or solidified/stabilized fly ash to highly acidic conditions, not only the high-content Pb/Zn/Cu, but also some low-content Cd posed potential risks to the environment. During the leaching process, under extremely acidic conditions, the increased environmental risks posed by Pb/Zn/Cu/Cd in residual fly ash solids were greatly ascribed to the increase in bioavailable fractions, which might result in the re-leaching of some heavy metals to the environment.

Toward Optimizing LNAPL Remediation

AbstractOptimizing the remediation of light nonaqueous phase liquids (LNAPLs) to achieve an acceptable endpoint status for a site is not trivial. Recently, Sookhak Lari, Johnston, et al. (2018, https://doi.org/10.1016/j.jhazmat.2017.11.006), Sookhak Lari, Rayner, and Davis (2018, https://doi.org/10.1016/j.jenvman.2018.07.041) conducted three‐dimensional multiphase, multicomponent simulations to address LNAPL remediation endpoints for a single recovery well. However, optimized LNAPL remediation for multiple wells is not addressed in the literature. In the first part of this paper, we establish a matrix of 10 simulation scenarios to show the sensitivity of the remedial endpoint (i.e., what is feasibly achieved) to several parameters including viscosity and partitioning attributes of the LNAPL, heterogeneity of the formation, and the location and number of the recovery wells. While this addresses the variability of LNAPL removal from the subsurface and is valuable in its own right, it does not address the optimal removal of LNAPL. We address this in the second part of the paper by linking a genetic algorithm to TMVOC‐MP to allow, for example, the assessment of the optimal number and location of LNAPL recovery wells in a field‐scale problem. Using supercomputing facilities and within 49 genetic algorithm generations, each including 150 members, highly optimized answers to different objective functions were obtained. For the first time, such a multiphase, multicomponent optimization tool promises the possibility of optimizing LNAPL remediation at field scale to achieve practicable endpoint conditions, within computational affordability.

Generalized implicit viscosity approximation method for multivalued mappings in CAT(0) spaces

Abstract We prove strong convergence of the sequence generated by implicit viscosity approximation method involving a multivalued nonexpansive mapping in framework of CAT(0) space. Under certain appropriate conditions on parameters, we show that such a sequence converges strongly to a fixed point of the mapping which solves a variational inequality. We also present some convergence results for the implicit viscosity approximation method in complete ℝ-trees without the endpoint condition.

An Efficient Algorithm for Optimal Trajectory Generation for Heterogeneous Multi-Agent Systems in Non-Convex Environments

Generating optimal trajectories for a large numbers of vehicles in real-time becomes extremely challenging when including realistic dynamic models and time-varying obstacle constraints. We present a novel method to efficiently produce time-optimal collision-free trajectories in complex non-convex maze-like environments while enforcing nonlinear constraints on velocity, acceleration, jerk, and snap. The approach combines two complementary numerical techniques for optimal control: level set reachability analysis and pseudospectral orthogonal collocation. Applied in a multi-agent prioritized planning framework, the methodology allows for heterogeneous sizes, dynamics, endpoint conditions, and individualized optimization objectives, while achieving linear scaling in computation time relative to the number of vehicles. Simulation examples are shown with up to 26 static obstacles and 32 quadcopters in a tightly constrained space with average computation times of 1–3.5 s per vehicle, depending on scenario complexity.

Variational principle and time-space finite element method for dynamic thermoelasticity based on mixed convolved action

Abstract A new variational formulation is proposed for time-domain analysis of initial/boundary value problems of dynamic thermoelasticity. By using the concept of mixed convolved action, the difficulties with dissipative phenomena and proper representations of the temporal end point conditions can be overcome to create a true stationary variational principle. After an elementary illustrative development for a lumped parameter thermoelastic model, the convolved action functional for linear thermoelastic continuum is written directly in terms of mixed variables, which include displacements and the impulses of stress, temperature and heat flux. Unlike previous variational approaches, based for example upon a generalization of Hamilton's principle , the present mixed convolved action formulation allows direct application of finite element methodology in both space and time. Here, simple linear shape functions are employed for the temporal representations. Meanwhile, standard three-noded triangular elements are used in the present two-dimensional numerical implementation. Several computational examples are considered to test this original approach and to investigate interesting aspects of coupled dynamic thermoelastic response.

A comparative study of nanofluids flow yields by an inclined cylindrical surface in a double stratified medium

In this paper, we have considered both Newtonian and non-Newtonian nanofluids stagnation point flow towards an inclined cylindrical surface. The flow field is manifested with physical effects, namely thermal radiation, mixed convection, chemical reaction, temperature and concentration stratification, heat generation/absorption, magnetic field. The reduced system of ODEs is obtained by transforming flow narrating PDEs with the aid of appropriate transformation. A computational algorithm is executed to trace out the solution of an initial value problem. To be more specific, the effects of involved pertinent flow parameters are discussed for both \( \lambda\) = 0 (Newtonian fluid) and \( \lambda\) = 0.5 (non-Newtonian fluid). The non-Newtonian fluid reflects considerable variations towards flow parameters as compared to Newtonian fluid. Further, the compatibility of endpoint conditions is validated by providing stream lines pattern towards the velocities ratio parameter. In addition, the influence of Brownian motion and thermophoresis parameters are reported on mass and heat transfer rates by way of both straight line and parabolic curve fitting schemes. It is concluded that the heat transfer rate normal to the cylindrical surface is a decreasing function of both thermophoresis and Brownian motion parameters while the mass transfer rate admits inciting trends towards the Brownian motion parameter.

Bounded curvature path planning with expected length for Dubins vehicle entering target manifold

Bounded curvature path planning with specified length is a significant technique for single-vehicle assignments and multi-vehicle coordination, especially in the real-time applications. Any existed path can be reached from the curvature-bounded deformation of some other paths. Based on that, this paper proposes a structured homotopy-based (SH-based) planner as an improvement of the conventional path elongation strategy. Not alike path elongation which is driven by initial path, the proposed planner is driven by endpoint condition. It searches expected path within the synthesis of several path homotopies, therefore it has stronger flexibility and adaptability for different endpoint condition than simple elongation. Special homotopy structures which ensure the monotonicity of path length with respect to the homotopy parameter are employed for implementation of fast solution searching. In addition, the proposed method is extended from the point target case to the manifold target case, and the target point transference strategy is adopted to make a trade-off between the path length deviation and the target position value. Static and dynamic cases are respectively simulated for an example of Dubins vehicle, which validate the performance of the proposed method.

Addition of 2-(ethylamino)acetonitrile group to nitroxoline results in significantly improved anti-tumor activity in vitro and in vivo.

Lysosomal cysteine peptidase cathepsin B, involved in multiple processes associated with tumor progression, is validated as a target for anti-cancer therapy. Nitroxoline, a known antimicrobial agent, is a potent and selective inhibitor of cathepsin B, hence reducing tumor progression in vitro and in vivo. In order to further improve its anti-cancer properties we developed a number of derivatives using structure-based chemical synthesis. Of these, the 7-aminomethylated derivative (compound 17) exhibited significantly improved kinetic properties over nitroxoline, inhibiting cathepsin B endopeptidase activity selectively. In the present study, we have evaluated its anti-cancer properties. It was more effective than nitroxoline in reducing tumor cell invasion and migration, as determined in vitro on two-dimensional cell models and tumor spheroids, under either endpoint or real time conditions. Moreover, it exhibited improved action over nitroxoline in impairing tumor growth in vivo in LPB mouse fibrosarcoma tumors in C57Bl/6 mice. Taken together, the addition of a 2-(ethylamino)acetonitrile group to nitroxoline at position 7 significantly improves its pharmacological characteristics and its potential for use as an anti-cancer drug.

OIL BEHAVIOUR AND THE RESPONSE TO A SUNKEN OIL SPILL OF SLURRY IN QUINTERO BAY, CHILE

ABSTRACT Slurry oils are one of the few groups of oils that have a density greater than full salinity seawater. Slurry spills at sea are rare, but when they do occur, the response can be difficult, with low final recovery rates. Oil spill response planning and recovery techniques have been refined over many years and the research and development of most methods has been underpinned by the principle that oil floats on water. This recent case study provides an example of the behavior of a slurry spill and the subsequent response operations. A leak of an API gravity 4° slurry occurred from a submarine pipeline in Quintero Bay, Chile, on 14th May 2016. The oil sank to the adjacent sea bed and covered an area of approximately 10,000 m2 in water depths of 18–22 m. The initial response involved over 20 dry-suit divers with surface air to recover the oil with vacuum hoses. These were then supplemented by four diver-operated vacuum dredges. Fortunately weak bottom currents did not redistribute the oil; nevertheless “sea bed booms” were deployed around the perimeter to prevent migration. These “booms” were initially a screen mesh that was later supplemented by sturdier metal frame screens deployed around the zone of the sunken oil in a zigzag configuration. Baseline benthic sediment samples were collected from the adjacent unaffected area and subsequently from the treatment area after completion of operations. A benthic SCUBA SCAT survey using a track-line positioning system was conducted to systematically document the distribution of the oil and post-treatment systematic ROV survey ensured that the end-point oiling conditions had been achieved.

Backward-stochastic-differential-equation approach to modeling of gene expression.

In this article, we introduce a backward method to model stochastic gene expression and protein-level dynamics. The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation (BSDE). Unlike many other SDE techniques proposed in the literature, the BSDE method is backward in time; that is, instead of initial conditions it requires the specification of end-point ("final") conditions, in addition to the model parametrization. To validate our approach we employ Gillespie's stochastic simulation algorithm (SSA) to generate (forward) benchmark data, according to predefined gene network models. Numerical simulations show that the BSDE method is able to correctly infer the protein-level distributions that preceded a known final condition, obtained originally from the forward SSA. This makes the BSDE method a powerful systems biology tool for time-reversed simulations, allowing, for example, the assessment of the biological conditions (e.g., protein concentrations) that preceded an experimentally measured event of interest (e.g., mitosis, apoptosis, etc.).

An iteration scheme for a family of multivalued mappings in CAT(0) spaces with an application to image recovery

In this paper, we introduce a new iterative scheme for a finite family of multivalued nonexpansive mappings in CAT(0) spaces and utilize the same to prove \(\Delta \)-convergence as well as strong convergence theorems with and without end point conditions. As an application, we prove a result on image recovery problem in CAT(0) space setting. Our results generalize and extend the existing relevant previous results

High-accuracy optimal finite-thrust trajectories for Moon escape

The optimization problem of fuel-optimal trajectories from a low circular Moon orbit to a target hyperbolic excess velocity vector using finite-thrust propulsion is solved. The ability to obtain the most accurate satisfaction of necessary optimality conditions in a high-accuracy dynamic model is the main motivation of the current study. The solutions allow attaining anytime-return Earth-interface conditions from a low lunar orbit. Gravitational effects of the Sun, Earth, and Moon are included throughout the entire trajectory. Severe constraints on the fuel budget combined with high-accuracy demands on the endpoint conditions necessitate a high-fidelity solution to the trajectory optimization problem and JPL DE405 ephemeris model is used to determine the perturbing bodies' positions. The optimization problem is solved using an indirect method. The optimality of the solution is verified by an application of Pontryagin's maximum principle. More accurate and fuel-efficient trajectories are found for the same mission objectives and constraints published in other research, emphasizing the advantages of this technique. It is also shown that the thrust structure consists of three finite burns. In contrast to previous research, no singular arc is required in the optimal solutions, and all the controls appear bang-bang.