You will be presented with the full text of a science research paper. Please write an abstract for this paper. Your response should include the abstract and no additional text.

Paper text:
the discoord algorithms proposed in @xcite seek to solve a problem that is described in fig .
[ energy_network ] .
the system of interest is composed of nodes distributed in space , communication network , and physical energy network .
the nodes can generate a certain amount of energy within the node , while it has an initial energy in a certain level , @xmath0 .
the nodes also have some desired levels of energy , @xmath1 .
the nodes are connected through communication layer as well as through physical energy layer . through the communication layer
, they can exchange information about the status of individual node . through the physical layer
, the energy flows from a node to another node , @xmath2 .
the energy flow is called energy distribution .
the main purpose of discoord algorithms is to generate and distribute energies in an attempt to make each node to achieve the desired energy . here ,
as the key constraints , there are the lower and upper levels in the generation of energy ; also all the decision is made only through local interactions between neighboring nodes .
this paper provides case studies taking account of various scenarios ; while analyzing the simulation results , we will discuss the capability of the discoord algorithms .
in discoord algorithms , there are @xmath3 nodes , and each node is able to generate energy within some specified lower and upper boundaries .
the nodes are interconnected for energy exchanges and for communications each other . to make the problem clear , the following symbols are provided .
[ cols= " < , < , < , < " , ]      the combination of the set of nodes and set of edges is called a graph , i.e. , @xmath4 .
thus , the overall topology of the system is defined by the graph @xmath5 .
the discoord algorithms seek to solve the following problem @xcite .
[ prob1 ] given initial and desired energies of each nodes , @xmath0 and @xmath1 , generate energies @xmath6 and exchange energies , @xmath7 , with neighboring nodes such that @xmath8 , by relying upon only local interactions .    in the above problem ,
the energy generation should be done with the constraints of @xmath9    for the energy generation , the node @xmath10 can exchange a certain type of information only with its neighboring nodes .
it is supposed that the information is exchanged through communication layer network ( or cyber - layer network ) @xcite .
the energy exchange means the energy flow between the neighboring nodes ; so the energy exchange is done in physical - layer network .
it is also important to notice that there is a relationship between the desired energies and initial and generated energies .
that is , the sum of the desired energies should be less than the sum of initial energies and the maximum energy that can be generated by the nodes .
it can be constrained as follows : @xmath11    eventually , the discoord algorithms should generate the energies @xmath12 such as @xmath13 which is called the supply - demand balance .
so , given the desired energies of individual nodes , one of the key constraints in the discoord algorithms is to satisfy the supply - demand balance during the generations of @xmath12 .
the purpose of energy generation is to generate @xmath12 only using local neighboring interactions under the constraints of ( [ generation_constraint ] ) and ( [ supply_demand_balance ] ) .
the algorithm is composed of three steps . in the following algorithm ,
the interim parameters @xmath14 and @xmath15 are used .    1
.   initial values +  @xmath16 +  @xmath17 2 .
find the steady state solutions from the following dynamic equations + 
 @xmath19 + where @xmath20 is the cardinality of the set @xmath21 .
let the steady - state solutions of the above equations denote as @xmath22 and @xmath23 .
energy generation of nodes + 
@xmath24    note that in the above @xmath25nd step , for the update of @xmath26 and @xmath27 , the node @xmath10 needs information of @xmath28 and @xmath29 , which are the values of neighboring interim parameters .
so , to compute @xmath6 at the node @xmath10 , it needs to communicate with the neighboring nodes .
since @xmath20 and @xmath30 are fixed and can be exchanged by initial local interactions , it is simply assumed that they are available to neighboring nodes .
the purpose of the energy distribution is to make the level of energy of each node become @xmath1 , i.e. , @xmath31 by the energy flows @xmath7 . this algorithm is also composed of three steps . in the following algorithm , the interim parameters @xmath32 and @xmath33 are used .    1
.   initial values +  @xmath34 + 
@xmath35 + where @xmath6 is computed from the @xmath36-rd step in the energy generation algorithm .
2 .   find the steady state solutions from the following dynamic equations +  @xmath37 + 
@xmath38 + where @xmath39 . let the steady - state solution of the above equation denote @xmath40 .
energy flow from @xmath10-th node to the @xmath41-th node + 
@xmath42    note that in the above @xmath25nd step , for the update of @xmath43 and @xmath44 , the node @xmath10 needs information of @xmath45 from the neighboring nodes .
since @xmath46 are fixed and can be also exchanged by local interactions initially , it is assumed that they are available to neighboring nodes .
the convergence of algorithms has been completely proved in @xcite .
it is assumed that the desired energy of individual node is given as ( [ desired_constraint ] ) .
the energy generation algorithm computes @xmath6 ; and then @xmath6 is used for the computation of @xmath2 at the energy distribution algorithm .
it is also noticeable that the solutions of the energy generation and energy distribution algorithms are computed through communications among neighboring nodes .
so , after obtaining the solutions @xmath6 and @xmath2 , each node generates physical energy and distributes energy to the neighboring nodes simultaneously .
in this case , the sum of the desired energies of all nodes is well given as @xmath47 . for the balanced case , we consider the following scenario : +  six nodes : @xmath48 , and @xmath49 +  seven undirected edges : @xmath50 +  initial energies : @xmath51 , and @xmath52 +  desired energies : @xmath53 , and @xmath54 +  lower boundaries of generation capability : @xmath55 for all @xmath10 +  upper boundaries of generation capability : @xmath56 and @xmath57    clearly , since @xmath58 , @xmath59 , and @xmath60 , the supply - demand balance is satisfied . now using the discoord algorithms given in the previous section ,
we obtain +  the generated energies : @xmath61 , @xmath62 , @xmath63 , @xmath64 , @xmath65 , @xmath66 +  energy flows : @xmath67 , @xmath68 , @xmath69 , @xmath70 , @xmath71 , @xmath72 , @xmath73 + from the above result , we see that the total amount of energy flows is @xmath74 . as shown in fig .
[ case11 ] , the desired energies have been well achieved after energy distribution . fig .
[ case12 ] shows the overall variation in energy level of each node , and overall energy flows in the graph .    :
desired energies(upper figure ) and achieved energies(lower figure ) . ]    : upper figure - initial(blue ) , desired(aqua ) , generated(yellow ) , and initial@xmath75generated(red ) ; lower figure - energy flow diagram . ]      in this case , the sum of the desired energy is less than the minimum energy boundary , i.e. , @xmath76 . in the simulation , the same scenario as the case -@xmath77 is considered except the initial energies +  initial energies : @xmath78 , and @xmath52 + so , we have @xmath79 . from the discoord algorithms ,
we obtain +  the generated energies : @xmath80 , @xmath81 , @xmath82 , @xmath83 , @xmath84 , @xmath85 +  energy flows : @xmath86 , @xmath87 , @xmath88 , @xmath89 , @xmath90 , @xmath91 , @xmath92 + from the above result , we see that the total amount of energy flows is @xmath93 . after the energy distribution
, it is observed that the errors , i.e. , @xmath94 , are @xmath95 .
[ case21 ] shows that the desired energies can not be achieved because there are over energies in the network .
so , as shown in the lower figure of fig .
[ case21 ] , after the energy distribution , each node still has more energy than the desired energy level .
it is interesting to observe that the errors of each node are same as @xmath96 ; so it seems that the discoord algorithms evenly distribute the remaining energies to the network . as shown in fig .
[ case22 ] , clearly there is no energy generation from the discoord algorithms .
thus , we can see that when there are over energy in the network , the algorithms do not generate energy in the whole network .
: desired energies(upper figure ) and achieved energies(lower figure ) . ]    : upper figure - initial(blue ) , desired(aqua ) , generated(yellow ) , and initial@xmath75generated(red ) ; lower figure - energy flow diagram . ]      in this case , the sum of the desired energy is greater than the maximum energy boundary , i.e. , @xmath97 . for the simulation , the same scenario as the case -@xmath77
is considered except the desired energies +  desired energies : @xmath98 , and @xmath54 + so , we have @xmath99 . from the discoord algorithms ,
we obtain +  the generated energies : @xmath100 , @xmath101 , @xmath102 , @xmath103 , @xmath104 , @xmath105 +  energy flow : @xmath106 , @xmath107 , @xmath108 , @xmath109 , @xmath110 , @xmath111 , @xmath112 + from the above result , we see that the total amount of energy flows is @xmath113 . after the energy distribution , it is observed that the errors are @xmath114 .
[ case31 ] shows that the desired energies at each node are not achieved due to the energy deficiency .
[ case32 ] reveals that the energy at each node is generated in maximum .
similarly to the case @xmath25 , the discoord algorithms still attempt to distribute the energies to the network evenly .
so , the errors at each node are same .
the algorithms have attempted to generate the maximum energy ; after generating the maximum energy , the energies have been distributed evenly to the network to make the same errors at all nodes .    :
desired energies(upper figure ) and achieved energies(lower figure ) . ]    : upper figure - initial(blue ) , desired(aqua ) , generated(yellow ) , and initial@xmath75generated(red ) ; lower figure - energy flow diagram . ]      in this case , it is supposed that @xmath115 . then , it does not need to generate energy ; only by distributing the initial energy among the nodes , the desired energy of individual node can be achieved . for the simulation , the same scenario as the case -@xmath77
is considered except the desired energies +  initial energies : @xmath116 , and @xmath52 + so , the sum of initial energies is equal to the sum of the desired energies . from the discoord algorithms ,
we obtain +  the generated energies are all zero .
+  energy flows : @xmath117 , @xmath118 , @xmath119 , @xmath120 , @xmath121 , @xmath122 , @xmath123 + from the above result , we see that the total amount of energy flows is @xmath124 .    :
desired energies(upper figure ) and achieved energies(lower figure ) . ]    : upper figure - initial(blue ) , desired(aqua ) , generated(yellow ) , and initial@xmath75generated(red ) ; lower figure - energy flow diagram . ]    fig .
[ case41 ] shows that the desired energies have been well achieved without generating any energy .
so , as expected , the discoord algorithms only distribute the initial energies to the network to make errors of each node zero .
[ case42 ] also shows that there is no energy generation ; but only there are energy flows .
this paper has presented several cases as applications of discoord algorithms .
as shown in the previous examples , the discoord algorithms can deal with various cases even though the supply - demand balance is not ensured any more .
the main capability of the algorithms is to decide all the generation and distribution through local interactions , i.e. , by distributed coordination .
it is recommended to see ` byeong - yeon kim , `` coordination and control for energy distribution using consensus algorithms in interconnected grid networks '' , ph.d .
dissertation , school of information and mechatronics , gwangju institute of science and technology , 2013 @xcite ' for applications to various engineering problems of the algorithms developed in this paper .
the reader can send email to hyosung@gist.ac.kr to get the matlab source code .
kim , `` coordination and control for energy distribution using consensus algorithms in interconnected grid networks , '' in _
ph.d dissertation _
, school of information and mechatronics , gwangju institute of science and technology , 2013 .
this paper presents case studies of the algorithms called `` energy generation and distribution via distributed coordination '' , which was proposed in @xcite . for a convenience , 
 we call `` energy generation and distribution via distributed coordination '' as `` discoord algorithms '' . 
 after concisely summarizing the `` discoord algorithms '' in compact forms , we will list several scenarios for numerical tests . then , while analyzing the simulation results , we will discuss the capability of the algorithms in handling the various cases .