1. A metal organic framework comprising a linking moiety connecting at least two metals, the linking moiety having the structure:
wherein, FG refer to functional linking groups selected from the group consisting of CO2H, CS2H, NO2, SO3H, Si(OH)3, Ge(OH)3, Sn(OH)3, Si(SH)4, Ge(SH)4, Sn(SH)4, PO3H, AsO3H, AsO4H, P(SH)3, As(SH)3, CH(RSH)2, C(RSH)3, CH(RNH2)2, C(RNH2)3, CH(ROH)2, C(ROH)3, CH(RCN)2, C(RCN)3, CH(SH)2, C(SH)3, CH(NH2)2, C(NH2)3, CH(OH)2, C(OH)3, CH(CN)2, and C(CN)3, that undergo condensation with a metal to link the at least two metals, wherein R is an alkyl group having from 1 to 5 carbon atoms, or an aryl group comprising 1 to 2 phenyl rings and wherein the functional linking group forms a coordination complex with the metals; and
wherein R1 and R4 are linked together to form a macrocycle andor wherein R2 and R3 are linked together to form a macrocycle, wherein the macrocycle linking R1 and R4 andor the macrocycle linking R2 and R3 each comprises seven or more ring atoms.
2. The metal organic framework of claim 1, wherein the macrocycle is selected from the group consisting of a crown ether; and a cyclic macromolecule comprising C, O, N, or S.
3. The metal organic framework of claim 1, wherein the macrocycle is selected from the group consisting of:
wherein the arrows denote R1 and R4 or R2 and R3 of the linking moiety.
4. The metal organic framework of claim 1, wherein the linking moiety comprising the macrocycle or a functional group moiety with stereospecific and stereoelectronic control comprises a structure selected from the group consisting of structures I, XI-XV and XXVI-XXX or any combination thereof:
5. The metal organic framework of claim 1, wherein the metal organic framework comprises a macrocycle selected from the group consisting of pseudorotaxane, rotaxane, catenane, chelates and cryptand.
6. The metal organic framework of claim 5, wherein the catenane framework comprises linking moieties having a structure selected from the group consisting of structures XXXI-XXXIII:
7. The framework of claim 1, wherein the functional linking group comprises a carboxylic acid functional group.
8. The framework of claim 1, wherein the metal is a transition metal.
9. The framework of claim 1, wherein the metal is selected from the group consisting of Li+, Na+, Rb+, Mg2+, Ca2+, Sr2+, Ba2+, Sc3+, Ti4+, Zr4+, Ta3+, Cr3+, Mo3+, W3+, Mn3+, Fe3+, Fe2+, Ru3+, Ru2+, Os3+, Os2+, Co3+, Co2+, Ni2+, Ni+, Pd2+, Pd+, Pt2+, Pt+, Cu2+, Cu+, Au+, Zn2+, Al3+, Ga3+, In3+, Si4+, Si2+, Ge4+, Ge2+, Sn4+, Sn2+, Bi5+, Bi3+, and combinations thereof.
10. A microelectronic switch comprising a metal organic framework of claim 1.
11. The microelectronic switch of claim 10, wherein at least two monodentate or multidentate cores are linked to one another by a structure selected from the group consisting of structures I, XI-XV, and XXVI-XXXIII and any combination thereof.
12. A sensor comprising a framework of claim 1.
13. A gas separation device comprising a framework of claim 1.
14. A small molecule separationpurification device comprising a framework of claim 1.
15. A guest recognition device comprising a framework of claim 1.
16. A chiral molecule separation medium comprising a framework of claim 1.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A method of assisting the division of a geographic region into a predetermined number of contiguous, non-overlapping districts that completely cover the region, each district having the same population to within a predetermined tolerance, making maximum use of preexisting geopolitical boundaries, comprising automatically generating at least one super district cover comprising a set of contiguous, non-overlapping super districts that completely cover the region, each super district defined entirely by preexisting geopolitical boundaries and containing an integer multiple of the required district population to within the predetermined tolerance.
2. The method of claim 1 further comprising selecting one or more super district covers having the greatest number of super districts.
3. The method of claim 1 wherein the region is a state.
4. The method of claim 1 wherein the preexisting geopolitical boundaries comprise geographically mutually exclusive boundaries selected from the group consisting of county, borough, parish, and municipal boundaries.
5. The method of claim 1 wherein automatically generating at least one super district cover comprises:
determining the required district population;
determining the population tolerance;
determining the contiguousness of preexisting geopolitical sub-regions and the population contained within each preexisting geopolitical sub-region;
determining a maximum allowable number NMAX of preexisting geopolitical sub-regions for each super district in a working library of super districts; and
automatically generating at least one super district cover based on the determined information.
6. The method of claim 5 wherein determining the required district population comprises dividing the total population of the region by a required number of districts.
7. The method of claim 6 wherein the required number of districts corresponds to a number of political offices.
8. The method of claim 5 wherein automatically generating at least one super district cover based on the determined information comprises:
building a library of super districts by combining one or more contiguous, preexisting geopolitical sub-regions to generate each super district, the super district containing an integer multiple of the required district population to within the predetermined tolerance and such that no super district can be created from some but not all of the preexisting geopolitical sub-regions; and
selecting super districts from the library to create at least one super district cover for the region.
9. The method of claim 8 wherein selecting super districts from the library to create at least one super district cover for the region comprises iteratively performing the steps of:
for each size N of preexisting geopolitical sub-regions per super district:
choosing a candidate super district randomly from among the not-yet-chosen super districts of size N;
tentatively adding the candidate super district to the super district cover;
determining whether the remaining region comprises a collection of super districts of any size;
if so, adding the candidate super district to the cover and removing from the library of not-yet-chosen super districts of size N, all super districts having a preexisting geopolitical sub-region in common with the candidate super district, and if not, excluding the candidate super district from the cover and deleting it from the library;
repeating for all super districts of size N; and
incrementing N and repeating until the library is exhausted.
10. The method of claim 9 further comprising, for each candidate super district, if the remaining region comprises a collection of super districts, determining whether the sum of the multiples of the required district population for each super district equals the predetermined number of contiguous, non-overlapping districts to be created.
11. The method of claim 9 wherein at least the step of selecting super districts from the library to create at least one super district cover for the region are performed by one or more software programs.
12. The method of claim 11 wherein the one or more software programs are further operative to perform the step of generating a map of the region for each cover, the map depicting the super district boundaries and indicating the integer multiple of the required district population contained in each super district.
13. The method of claim 12 wherein indicating the integer multiple of the required district population contained in each super district comprises printing the multiple within the super district.
14. The method of claim 12 wherein indicating the integer multiple of the required district population contained in each super district comprises outputting the map with each super district containing a different multiple depicted in a different color.
15. The method of claim 1 wherein automatically generating at least one super district cover comprises:
determining the required district population;
determining the population tolerance;
determining the contiguousness of preexisting geopolitical sub-regions and the population contained within each preexisting geopolitical sub-region; and
iteratively performing the steps of:
combining one or more contiguous, preexisting geopolitical sub-regions not in a super district, to generate a candidate super district, the candidate super district containing an integer multiple of the required district population to within the predetermined tolerance;
determining whether the remaining region can be covered by at least one set of super districts; and
if so, making the candidate super district a super district and adding the super district to the super district cover.
16. The method of claim 1, further comprising:
selecting a super district cover; and
dividing all super districts containing an integer multiple of the required district population greater than one as required to create districts containing the required district population, to within the predetermined tolerance.
17. A computer readable medium including one or more computer programs operative to cause a computer to assist in the division of a region into a predetermined number of contiguous, non-overlapping districts that completely cover the region, each district having the same population to within a predetermined tolerance, making maximum use of preexisting geopolitical boundaries, the computer programs causing the computer to automatically generate at least one super district cover comprising a set of contiguous, non-overlapping super districts that completely cover the region, each super district defined entirely by preexisting geopolitical boundaries and containing an integer multiple of the required district population to within the predetermined tolerance.
18. The computer readable medium of claim 17 wherein the computer programs further cause the computer to:
determine the required district population;
determine the population tolerance;
determine the contiguities of preexisting geopolitical sub-regions and the population contained within each preexisting geopolitical sub-region;
determine a maximum allowable number N of preexisting contiguous geopolitical sub-regions for each super district; and
automatically generate at least one super district cover based on the determined information.
19. The computer readable medium of claim 18 wherein the computer programs automatically generate at least one super district cover based on the determined information by:
building a library of super districts by combining one or more contiguous, preexisting geopolitical sub-regions to generate each super district, the super district containing an integer multiple of the required district population to within the predetermined tolerance and such that no super district can be created from some but not all of the preexisting geopolitical sub-regions; and
selecting super districts from the library to create at least one super district cover for the region.
20. The computer readable medium 19 wherein selecting super districts from the library to create at least one super district cover for the region comprises iteratively performing the steps of:
for each size N of preexisting geopolitical sub-regions per super district:
choosing a candidate super district randomly from among the not-yet-chosen super districts of size N;
tentatively adding the candidate super district to the super district cover;
determining whether the remaining region comprises a collection of super districts of any size;
if so, adding the candidate super district to the cover and removing from the not-yet-chosen super districts of size N, all super districts having a preexisting geopolitical sub-region in common with the candidate super district, and if not, excluding the candidate super district from the cover;
repeating for all super districts of size N; and
incrementing N and repeating until the library is exhausted.