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The Special Issue on Advances in Water Distribution Networks (WDNs) explores four important topics of research in the framework of WDNs, namely simulation and optimization modelling, topology and partitioning, water quality, and service effectiveness. With regard to the first topic, the following aspects are addressed: pressuredriven formulations, algorithms for the optimal location of control valves to minimize leakage, the benefits of water discharge prediction for the remote real time control of valves, and transients generated by pumps operating as turbines. In the context of the second topic, a topological taxonomy of WDNs is presented, and partitioning methods for the creation of district metered areas are compared. In relation to the third topic, the vulnerability to trihalomethane is assessed, and a statistical optimization model to minimize heavy metal releases is presented. Finally, the fourth topic focusses on the estimation of nonrevenue water, including leakage and unauthorized consumption, and on the assessment of service under intermittent supply conditions.
valve  pump  real time control  pressure  water distribution modelling  leakage  nonrevenue water  multiple regression analysis  artificial neural network  water distribution network  water distribution network  graph partitioning  modularity  district metered areas  water distribution network management  complex network theory  topological analysis  mathematical model  valve  pressure  leakage  optimization  water distribution network  snapshot simulation  pressuredriven  energy recovery systems  runaway conditions  unsteady flow  water hammer  water distribution system  water quality  disinfection byproducts  vulnerability  water quality (WQ)  blending  release of heavy metals (HMR)  dual response surface optimization (DRSO)  multiple source waters blending optimization (MSWBO)  intermittent water supply  water service quality  24
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Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group.
strongly regular graph  automorphism group  orbit matrix  binary polyhedral group  icosahedron  dodecahedron  600cell  Electric multiple unit trains  highlevel maintenance planning  time window  0–1 programming model  particle swarm algorithm  fixed point  splitquaternion  quadratic polynomial  splitoctonion  neutrosophic set  neutrosophic rough set  pessimistic (optimistic) multigranulation neutrosophic approximation operators  complete lattice  rough set  matroid  operator  attribute reduction  graded rough sets  rough intuitionistic fuzzy sets  dominance relation  logical conjunction operation  logical disjunction operation  multigranulation  planar point set  convex polygon  disjoint holes  fuzzy logic  pseudoBCI algebra  quasimaximal element  KGunion  quasialternating BCKalgebra  quality function deployment  engineering characteristics  group decision making  2tuple  metro station  emergency routes  graph partitioning  graph clustering  invariant measures  partition comparison  finite automorphism groups  graph automorphisms  Fuzzy sets  ring  normed space  fuzzy normed ring  fuzzy normed ideal  fuzzy implication  quantum Balgebra  qfilter  quotient algebra  basic implication algebra  Detour–Harary index  maximum  unicyclic  bicyclic  cacti  threeway decisions  intuitionistic fuzzy sets  multigranulation rough intuitionistic fuzzy sets  granularity importance degree  complexity  Chebyshev polynomials  gear graph  pyramid graphs  edge detection  Laplacian operation  regularization  parameter selection  performance evaluation  aggregation operator  triangular norm  ?convex set  atombond connectivity index  geometric arithmetic index  line graph  generalized bridge molecular graph  graceful labeling  edge graceful labeling  edge even graceful labeling  polar grid graph  graph  good drawing  crossing number  join product  cyclic permutation  nonlinear  synchronized  linear discrete  chaotic system  algorithm  generalized permanental polynomial  coefficient  copermanental  isoperimetric number  random graph  intersection graph  social network  Abel–Grassmann’s groupoid (AGgroupoid)  Abel–Grassmann’s group (AGgroup)  involution AGgroup  commutative group  filter  graceful labeling  edge even graceful labeling  cylinder grid graph  selective maintenance  multistate system  human reliability  optimization  genetic algorithm  hypernearring  multitransformation  embedding  distance matrix (spectrum)  distance signlees Laplacian matrix (spectrum)  (generalized) distance matrix  spectral radius  transmission regular graph  graph  good drawing  crossing number  join product  cyclic permutation  cyclic associative groupoid (CAgroupoid)  cancellative  variant CAgroupoids  decomposition theorem  construction methods
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