The Size of the Formal Solution Space

2009 ◽  
pp. 329-355
Author(s):  
Werner M. Seiler
Keyword(s):  
Formal Solution ◽  
Solution Space

scholarly journals Syllabification of the Divine Comedy

2021 ◽  
Vol 14 (3) ◽  
pp. 1-26
Author(s):  
Andrea Asperti ◽  
Stefano Dal Bianco
Keyword(s):  
Text Processing ◽  
Solution Space ◽  
Generative Models ◽  
Divine Comedy ◽  
Point Of View ◽  
Computer Assisted ◽  
Wide Range ◽  
The Divine Comedy ◽  
Left And Right ◽  
Assisted Analysis

We provide a syllabification algorithm for the Divine Comedy using techniques from probabilistic and constraint programming. We particularly focus on the synalephe , addressed in terms of the "propensity" of a word to take part in a synalephe with adjacent words. We jointly provide an online vocabulary containing, for each word, information about its syllabification, the location of the tonic accent, and the aforementioned synalephe propensity, on the left and right sides. The algorithm is intrinsically nondeterministic, producing different possible syllabifications for each verse, with different likelihoods; metric constraints relative to accents on the 10th, 4th, and 6th syllables are used to further reduce the solution space. The most likely syllabification is hence returned as output. We believe that this work could be a major milestone for a lot of different investigations. From the point of view of digital humanities it opens new perspectives on computer-assisted analysis of digital sources, comprising automated detection of anomalous and problematic cases, metric clustering of verses and their categorization, or more foundational investigations addressing, e.g., the phonetic roles of consonants and vowels. From the point of view of text processing and deep learning, information about syllabification and the location of accents opens a wide range of exciting perspectives, from the possibility of automatic learning syllabification of words and verses to the improvement of generative models, aware of metric issues, and more respectful of the expected musicality.

scholarly journals A hybrid metaheuristic for solving asymmetric distance-constrained vehicle routing problem

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ha-Bang Ban ◽  
Phuong Khanh Nguyen
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Natural Extension ◽  
Solution Space ◽  
Neighborhood Search ◽  
Np Hard ◽  
Routing Problem ◽  
Hybrid Metaheuristic ◽  
Asymmetric Distance ◽  
Constrained Vehicle Routing

AbstractThe Asymmetric Distance-Constrained Vehicle Routing Problem (ADVRP) is NP-hard as it is a natural extension of the NP-hard Vehicle Routing Problem. In ADVRP problem, each customer is visited exactly once by a vehicle; every tour starts and ends at a depot; and the traveled distance by each vehicle is not allowed to exceed a predetermined limit. We propose a hybrid metaheuristic algorithm combining the Randomized Variable Neighborhood Search (RVNS) and the Tabu Search (TS) to solve the problem. The combination of multiple neighborhoods and tabu mechanism is used for their capacity to escape local optima while exploring the solution space. Furthermore, the intensification and diversification phases are also included to deliver optimized and diversified solutions. Extensive numerical experiments and comparisons with all the state-of-the-art algorithms show that the proposed method is highly competitive in terms of solution quality and computation time, providing new best solutions for a number of instances.

scholarly journals Forest Height Estimation Based on P-Band Pol-InSAR Modeling and Multi-Baseline Inversion

2020 ◽  
Vol 12 (8) ◽  
pp. 1319
Author(s):  
Xiaofan Sun ◽  
Bingnan Wang ◽  
Maosheng Xiang ◽  
Liangjiang Zhou ◽  
Shuai Jiang
Keyword(s):  
Standard Deviation ◽  
Vertical Structure ◽  
Incidence Angle ◽  
Three Dimensional ◽  
Solution Space ◽  
Model Complexity ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
Model Inversion ◽  
Forest Height

The Gaussian vertical backscatter (GVB) model has a pivotal role in describing the forest vertical structure more accurately, which is reflected by P-band polarimetric interferometric synthetic aperture radar (Pol-InSAR) with strong penetrability. The model uses a three-dimensional parameter space (forest height, Gaussian mean representing the strongest backscattered power elevation, and the corresponding standard deviation) to interpret the forest vertical structure. This paper establishes a two-dimensional GVB model by simplifying the three-dimensional one. Specifically, the two-dimensional GVB model includes the following three cases: the Gaussian mean is located at the bottom of the canopy, the Gaussian mean is located at the top of the canopy, as well as a constant volume profile. In the first two cases, only the forest height and the Gaussian standard deviation are variable. The above approximation operation generates a two-dimensional volume only coherence solution space on the complex plane. Based on the established two-dimensional GVB model, the three-baseline inversion is achieved without the null ground-to-volume ratio assumption. The proposed method improves the performance by 18.62% compared to the three-baseline Random Volume over Ground (RVoG) model inversion. In particular, in the area where the radar incidence angle is less than 0.6 rad, the proposed method improves the inversion accuracy by 34.71%. It suggests that the two-dimensional GVB model reduces the GVB model complexity while maintaining a strong description ability.

scholarly journals Efficient Operative Cost Reduction in Distribution Grids Considering the Optimal Placement and Sizing of D-STATCOMs Using a Discrete-Continuous VSA

2021 ◽  
Vol 11 (5) ◽  
pp. 2175
Author(s):  
Oscar Danilo Montoya ◽  
Walter Gil-González ◽  
Jesus C. Hernández
Keyword(s):  
Objective Function ◽  
Reactive Power ◽  
Programming Model ◽  
Search Algorithm ◽  
Solution Space ◽  
Distribution Networks ◽  
Optimal Placement ◽  
Mixed Integer ◽  
Solution Vector ◽  
The Impact

The problem of reactive power compensation in electric distribution networks is addressed in this research paper from the point of view of the combinatorial optimization using a new discrete-continuous version of the vortex search algorithm (DCVSA). To explore and exploit the solution space, a discrete-continuous codification of the solution vector is proposed, where the discrete part determines the nodes where the distribution static compensator (D-STATCOM) will be installed, and the continuous part of the codification determines the optimal sizes of the D-STATCOMs. The main advantage of such codification is that the mixed-integer nonlinear programming model (MINLP) that represents the problem of optimal placement and sizing of the D-STATCOMs in distribution networks only requires a classical power flow method to evaluate the objective function, which implies that it can be implemented in any programming language. The objective function is the total costs of the grid power losses and the annualized investment costs in D-STATCOMs. In addition, to include the impact of the daily load variations, the active and reactive power demand curves are included in the optimization model. Numerical results in two radial test feeders with 33 and 69 buses demonstrate that the proposed DCVSA can solve the MINLP model with best results when compared with the MINLP solvers available in the GAMS software. All the simulations are implemented in MATLAB software using its programming environment.

Applications of Erdélyi-Kober fractional integral for solving time-fractional Tricomi-Keldysh type equation

2020 ◽  
Vol 23 (5) ◽  
pp. 1381-1400 ◽  
Author(s):  
Kangqun Zhang
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Integral Operator ◽  
Nonlinear Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Formal Solution ◽  
Type Equation ◽  
Multiplier Theorem ◽  
Problem Of Time

Abstract In this paper we consider Cauchy problem of time-fractional Tricomi-Keldysh type equation. Based on the theory of a Erdélyi-Kober fractional integral operator, the formal solution of the inhomogeneous differential equation involving hyper-Bessel operator is presented with Mittag-Leffler function, then nonlinear equations are considered by applying Gronwall-type inequalities. At last, we establish the existence and uniqueness of L p -solution of time-fractional Tricomi-Keldysh type equation by use of Mikhlin multiplier theorem.

Molecular replacement and high-throughput structure determination

2002 ◽  
Vol 217 (12) ◽  
Author(s):  
J. Navaza ◽  
P. M. Alzari
Keyword(s):  
High Throughput ◽  
Structure Determination ◽  
Solution Space ◽  
Molecular Replacement ◽  
Fast Rotation ◽  
The Way

AbstractWe describe the philosophy of the MR method as implemented in the AMoRe package. Fast rotation and translation functions are first used to obtain a meaningful sampling of solution space, whose elements are subsequently assessed by using more robust criteria. The introduction of fast and accurate algorithms for screening a large number of possible solutions opened the way to automation, thus bringing MR methods to the realm of high-throughput structure determination. Selected examples are discussed to illustrate specific aspects of the method.

scholarly journals Optimization on Vehicle Routing Problem Based on Immune Clonal Selection Algorithm

2012 ◽  
Vol 6-7 ◽  
pp. 256-260
Author(s):  
Hai Hua Li ◽  
Zong Yan Xu ◽  
Fei Fei Zhou
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Clonal Selection ◽  
Solution Space ◽  
Genetic Mutation ◽  
Initial Population ◽  
Local Optimum ◽  
Clonal Selection Algorithm ◽  
Routing Problem ◽  
Optimum Solution

Vehicle routing problem is a typical NP-hard problem and is difficult to get an optimum solution. Aiming at the shortages of the existing methods, this paper proposed an algorithm based on immune clonal selection to solve vehicle routing problem. In the algorithm, expressed antibody with matrix, generated the initial population of antibodies randomly, and employed the operations such as clonal selection, genetic mutation iteratively to search optimum solution in solution space. The experimental results show that the algorithm presented here can converge to the global optimum solution rapidly, overcoming such disadvantages of the genetic algorithm as slower convergent velocity and the convergence to a local optimum solution.

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