IP Library › Granted Patent US 12,229,641
Granted Patent B2
US 12,229,641 · App. 17/193,229 · Granted Feb 18, 2025

Methods of training a gamma mixture hurdle model for estimating corresponding food flows between regions

Inventors: Megan Konar (Champaign, IL); Xiaowen Lin (Sunnyvale, CA)
Assignee: The Board of Trustees of The University of Illinois
G06N20/00G06F3/048G06N5/027G06N7/01G06Q10/06315
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Quick Facts
Patent No.
US 12,229,641
App. No.
17/193,229
Granted
Feb 18, 2025
Kind
B2
Abstract

Embodiments described herein relate to training, by a computing system, a gamma mixture hurdle model. The model may characterize a functional relationship between: output data specifying food flows between zones, and input variables representing food production and food consumption in the zones. The training involves: (i) using binary logistic regression to estimate whether corresponding food flows exist between zone pairs, and (ii) for pairs in which corresponding food flows exist, using a gamma mixture model to estimate amounts of the corresponding food flows. Based on the gamma mixture hurdle model, the computing system can estimate, where each zone includes a respective set of regions: (i) whether corresponding food sub-flows exist between region pairs, and (ii) for pairs in which the corresponding food sub-flows are estimated to exist, potentials of the corresponding food sub-flows. The computing system can also determine, using a linear programming framework, values for the corresponding food sub-flows.

Claims (64)

1. A method comprising:

training, by a computing system, a gamma mixture hurdle model characterizing a functional relationship between: output data specifying food flows between zones, and input variables representing food production and food consumption in the zones, wherein the training involves: (i) using binary logistic regression to estimate whether corresponding food flows exist between pairs of the zones, and (ii) for pairs of the zones in which the corresponding food flows are estimated to exist, using a gamma mixture model to estimate amounts of the corresponding food flows, and wherein each zone includes a respective set of regions;

based on parameters of the gamma mixture hurdle model, estimating, by the computing system: (i) whether corresponding food sub-flows exist between pairs of the regions, and (ii) for pairs of the regions in which the corresponding food sub-flows are estimated to exist, potentials of the corresponding food sub-flows;

determining, by the computing system and using a linear programming framework, values for the corresponding food sub-flows, wherein the linear programming framework uses data specifying food flows as mass balance constraints on totals of the corresponding food sub-flows that are within each of the zones, the potentials as inequality constraints on the corresponding food sub-flows that are within each of the zones, and region-to-region distance data for the regions as a minimization constraint on the corresponding food sub-flows;

generating, based on the values for the corresponding food sub-flows, a map of simulated food flows between geographic regions;

providing, for display on a graphical user interface, the map of simulated food flows between the geographic regions, wherein the corresponding food sub-flows are illustrated as lines connecting the geographic regions on the map; and

receiving a limitation, via the graphical user interface, of the values for the corresponding food sub-flows to determine vulnerabilities in a food system, wherein limiting the corresponding food sub-flows comprises a change in the lines connecting the geographic regions on the map.

2. The method of claim 1 , wherein the zones are non-overlapping geographic zones, and wherein the regions are non-overlapping geographic regions.

3. The method of claim 2 , wherein the regions are counties and wherein a respective set of regions within each zone include a plurality of counties.

4. The method of claim 1 , wherein the output data specifies food flows for a particular type of food, and wherein the input variables represent food production and food consumption for the particular type of food.

5. The method of claim 1 , wherein the output data specifying food flows between zones is based on food-related freight movement between the zones or food-related energy sources and transport corridors.

6. The method of claim 1 , wherein the gamma mixture model is based on a linear combination of gamma function regressions representing the corresponding food flows.

7. The method of claim 1 , wherein the region-to-region distance data is a great circle distance between region centroids, and wherein the great circle distance is estimated by:

determining a central angle of each region centroid; and

multiplying Earth's radius and the central angle of each region centroid.

8. The method of claim 1 , wherein using binary logistic regression to estimate whether corresponding food flows exist between pairs of the zones comprises:

sampling a probability from a prior generalized exponential distribution that a food flow exists between a particular pair of the zones;

selecting a random value between 0 and 1;

determining that the probability is greater than the random value; and

based on the probability being greater than the random value, determining that the food flow exists between the particular pair of the zones.

9. The method of claim 1 , wherein using the gamma mixture model to estimate amounts of the corresponding food flows includes modeling the food flows using Poisson processes.

10. The method of claim 1 , wherein estimating the potentials of the corresponding food sub-flows comprises estimating potentials of the corresponding food sub-flows for a region that is both an origin region and a destination region.

11. The method of claim 1 , wherein estimating the potentials of the corresponding food sub-flows comprises:

determining a flow potential for a zone based on the potentials of the corresponding food sub-flows for regions within the zone;

determining that the flow potential for the zone is lower than a reported flow for the zone; and

re-estimating the potentials of the corresponding food sub-flows for regions within the zone using the gamma mixture model and food importing information from international ports.

12. The method of claim 11 , wherein estimating the potentials of the corresponding food sub-flows further comprises:

after re-estimating the potentials of the corresponding food sub-flows for regions within the zone, determining that the flow potential for the zone is still lower than the reported flow for the zone; and

scaling the flow potential for the zone to be commensurate with the reported flow for the zone.

13. The method of claim 1 , wherein using the gamma mixture model to estimate amounts of the corresponding food flows comprises an indication of whether a transit hub contributes to the corresponding food flows.

14. An article of manufacture including a non-transitory computer-readable medium, having stored thereon program instructions that, upon execution by a computing system, cause the computing system to perform operations comprising:

training a gamma mixture hurdle model characterizing a functional relationship between: output data specifying food flows between zones, and input variables representing food production and food consumption in the zones, wherein the training involves: (i) using binary logistic regression to estimate whether corresponding food flows exist between pairs of the zones, and (ii) for pairs of the zones in which the corresponding food flows are estimated to exist, using a gamma mixture model to estimate amounts of the corresponding food flows, and wherein each zone includes a respective set of regions;

based on parameters of the gamma mixture hurdle model, estimating: (i) whether corresponding food sub-flows exist between pairs of the regions, and (ii) for pairs of the regions in which the corresponding food sub-flows are estimated to exist, potentials of the corresponding food sub-flows;

determining, using a linear programming framework, values for the corresponding food sub-flows, wherein the linear programming framework uses data specifying food flows as mass balance constraints on totals of the corresponding food sub-flows that are within each of the zones, the potentials as inequality constraints on the corresponding food sub-flows that are within each of the zones, and region-to-region distance data for the regions as a minimization constraint on the corresponding food sub-flows;

generating, based on the values for the corresponding food sub-flows, a map of simulated food flows between geographic regions;

providing, for display on a graphical user interface, the map of simulated food flows between the geographic regions, wherein the corresponding food sub-flows are illustrated as lines connecting the geographic regions on the map; and

receiving a limitation, via the graphical user interface, of the values for the corresponding food sub-flows to determine vulnerabilities in a food system, wherein limiting the corresponding food sub-flows comprises a change in the lines connecting the geographic regions on the map.

15. The article of manufacture of claim 14 , wherein the gamma mixture model is based on a linear combination of gamma function regressions representing the corresponding food flows.

16. The article of manufacture of claim 14 , wherein estimating the potentials of the corresponding food sub-flows comprises:

determining a flow potential for a zone based on the potentials of the corresponding food sub-flows for regions within the zone;

determining that the flow potential for the zone is lower than a reported flow for the zone; and

re-estimating the potentials of the corresponding food sub-flows for regions within the zone using the gamma mixture model and food importing information from international ports.

17. The article of manufacture of claim 16 , wherein estimating the potentials of the corresponding food sub-flows further comprises:

after re-estimating the potentials of the corresponding food sub-flows for regions within the zone, determining that the flow potential for the zone is still lower than the reported flow for the zone; and

scaling the flow potential for the zone to be commensurate with the reported flow for the zone.

18. A computing system comprising:

one or more processors;

memory; and

program instructions, stored in the memory, that upon execution by the one or more processors cause the computing system to perform operations comprising:

training a gamma mixture hurdle model characterizing a functional relationship between: output data specifying food flows between zones, and input variables representing food production and food consumption in the zones, wherein the training involves: (i) using binary logistic regression to estimate whether corresponding food flows exist between pairs of the zones, and (ii) for pairs of the zones in which the corresponding food flows are estimated to exist, using a gamma mixture model to estimate amounts of the corresponding food flows, and wherein each zone includes a respective set of regions;

based on parameters of the gamma mixture hurdle model, estimating: (i) whether corresponding food sub-flows exist between pairs of the regions, and (ii) for pairs of the regions in which the corresponding food sub-flows are estimated to exist, potentials of the corresponding food sub-flows;

determining, using a linear programming framework, values for the corresponding food sub-flows, wherein the linear programming framework uses data specifying food flows as mass balance constraints on totals of the corresponding food sub-flows that are within each of the zones, the potentials as inequality constraints on the corresponding food sub-flows that are within each of the zones, and region-to-region distance data for the regions as a minimization constraint on the corresponding food sub-flows;

generating, based on the values for the corresponding food sub-flows, a map of simulated food flows between geographic regions;

providing, for display on a graphical user interface, the map of simulated food flows between the geographic regions, wherein the corresponding food sub-flows are illustrated as lines connecting the geographic regions on the map; and

receiving a limitation, via the graphical user interface, of the values for the corresponding food sub-flows to determine vulnerabilities in a food system, wherein limiting the corresponding food sub-flows comprises a change in the lines connecting the geographic regions on the map.

19. The computing system of claim 18 , wherein using binary logistic regression to estimate whether corresponding food flows exist between pairs of the zones comprises:

sampling a probability that a food flow exists from a prior generalized exponential distribution;

selecting a random value between 0 and 1;

determining whether the probability is greater than the random value; and

determining food flows exist between pairs of the zones.

20. The computing system of claim 18 , wherein estimating the potentials of the corresponding food sub-flows comprises:

determining a flow potential for a zone based on the potentials of the corresponding food sub-flows for regions within the zone;

determining that the flow potential for the zone is lower than a reported flow for the zone; and

re-estimating the potentials of the corresponding food sub-flows for regions within the zone using the gamma mixture model and food importing information from international ports.

Assignments (2)
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded Apr 19, 2024
From: KONAR, MEGAN; LIN, XIAOWEN
To: THE BOARD OF TRUSTEES OF THE UNIVERSITY OF ILLINOIS
Reel/Frame 067163/0139 →
CONFIRMATORY LICENSE Recorded Dec 6, 2023
From: THE BOARD OF TRUSTEES OF THE UNIVERSITY OF ILLINOIS
To: NATIONAL SCIENCE FOUNDATION
Reel/Frame 065788/0984 →
Continuity (2)
Provisional Application 62986215 · Mar 6, 2020
Related Publication 20210279641A1 · Sep 9, 2021
References Cited (181)
US 20190188616A1 · Urban · 2019 [cited by examiner]
US 20200342465A1 · Ruddell et al. · 2020 [cited by applicant]
US 20210065031A1 · Parikh · 2021 [cited by examiner]
Konar et al. (Konar) Scaling properties of food flow networks, Jul. 10, 2018, PLOS|one https://doi.org/10.1371/journal.pone.0199498 (Year: 2018). [cited by examiner]
Zhou et al. (Zhou) “A linear threshold-hurdle model for product adoption prediction incorporating social network effects” Information Sciences vol. 307, Jun. 20, 2015, pp. 95-109, https://doi.org/10.1016/j.ins.2015.02.0… [cited by examiner]
Cassa, “Spatial outbreak detection analysis tool : a system to create sets of semi-synthetic geo-spatial clusters” 2004, URI http://hdl.handle.net/1721.1/33124, Department Massachusetts Institute of Technology. Departme… [cited by examiner]
Lancichinetti et cl. (Lancichinett) “Finding Statistically Significant Communities in Networks”, Published: Apr. 29, 2011, https://doi.org/10.1371/journal.pone.0018961 (Year: 2011). [cited by examiner]
Ghosn et al. (Ghosn) “Performance Indicators for Structural Systems and Infrastructure Networks” Jun. 2, 2016, Publication: Journal of Structural Engineering, vol. 142, Issue 9, https://doi.org/10.1061/(ASCE)ST.1943-541… [cited by examiner]
Lin et al. “A Network Analysis of Food Flows within the United States of America” Publication Date:Apr. 28, 2014 https://doi.org/10.1021/es500471d (Year: 2014). [cited by examiner]
P.J. Boland, Statistical and Probabilistic Methods in Actuarial Science (New York: Chapman and Hall) (https://doi.org/10.1201/9781584886969), 2007. [cited by applicant]
Oak Ridge National Laboratory, County-to-county Distance Matrix (http://cta.ornl.gov/transnet/SkimTree.htm), 2011. [cited by applicant]
S. Venkatramanan et al., Towards robust models of food flows and their role in invasive species spread, 2017 IEEE Int. Conf. on Big Data (BIGDATA), (https://doi.org/10.1109/BigData.2017.8257955), 2017. [cited by applicant]
N. Balakrishnan, et al., The exponential distribution: Theory, methods and applications, SIAM Review, 40 (1), 167-168, 1998. [cited by applicant]
M.T. Thai, et al., Handbook of optimization in complex networks, 544 pp., Springer, 2012. [cited by applicant]
J. Tinbergen, An Analysis of World Trade Flows, in: Shaping the world economy, Twentieth Century Fund, 1962. [cited by applicant]
S. Han, et al., US trade overview, 2013, Department of Commerce, International Trade Administration, Oct. 2014. [cited by applicant]
J.A. Hanley, et al., The meaning and use of the area under a receiver operating characteristic (roc) curve1, Radiology, 143 (1), 29-36, Apr. 1982. [cited by applicant]
M.C. Hansen, et al., Quantification of global gross forest cover loss, PNAS, 107 (19), 8650-8655, doi: 10.1073/pnas.0912668107, Mar. 17, 2010. [cited by applicant]
T. Hertel, et al., The poverty implications of climate-induced crop yield changes by 2030, Global Environmental Change, 20 (4), 577-585, Jul. 5, 2010. [cited by applicant]
A.Y. Hoekstra, et al., The water footprint of humanity, Proceedings of the national academy of sciences, 109 (9), 3232-3237, Feb. 28, 2012. [cited by applicant]
P.W. Holland, et al., Robust regression using iteratively reweighted least-squares, Communications in Statistics-theory and Methods, 6 (9), 813-827, 1977. [cited by applicant]
E. Holt-Gimenez, et al. We already grow enough food for 10 billion people and still can't end hunger, 2012. [cited by applicant]
E.M. Hoover, Interstate redistribution of population, 1850-1940, J. Econ. Hist., 1, 199-205, 1941. [cited by applicant]
M. Jackson, Social and economic networks, Princeton University Press, 2008. [cited by applicant]
M.O. Jackson, et al., The existence of pairwise stable networks, 2001. [cited by applicant]
M.O. Jackson, et al., Social capital and social quilts: Network patterns of favor exchange, American Economic Review, 102 (5), 1857-97, Aug. 2012. [cited by applicant]
H. Jeong, et al., Measuring preferential attachment in evolving networks, EPL (Europhysics Letters), 61 (4), 567, Feb. 15, 2003. [cited by applicant]
V. Kalapala, et al., Scale invariance in road networks, Phys. Rev. E, 73 (2), 2006. [cited by applicant]
P. Kaluza, et al., The complex network of global cargo ship movements, Journal of the Royal Society Interface, 7, 1093-1103, doi: 10.1098/rsif.2009.0495, Jan. 19, 2010. [cited by applicant]
T. Kastner, et al., Global changes in diets and the consequences for land requirements for food, Proc. Nat. Acad. Sci., 109 (18), 6868-6872, doi:10.1073/pnas. 1117054109, May 1, 2012. [cited by applicant]
R. Kohavi, et al., A study of cross-validation and bootstrap for accuracy estimation and model selection, in ljcai, vol. 14, pp. 1137-1145, Montreal, Canada, 1995. [cited by applicant]
M. Konar, et al., Virtual water trade and development in Africa, Hydrol. Earth Syst. Sci., 17, 3969-3982, doi:10.5194/ness-17-3969-2013, Jun. 6, 2013. [cited by applicant]
M. Konar, et al., Water for food: The global virtual water trade network, Water Resources Research, 47 (W05520), doi:10.1029/2010WR010307, 2011. [cited by applicant]
M. Konar, et al., Temporal dynamics of blue and green virtual water trade networks, Water Resources Research, 48 (W07509), doi:10.1029/2012WR011959, Jul. 12, 2012. [cited by applicant]
M. Konar, et al., Water resources sustainability in a globalizing world: who uses the water?, Hydrological Processes, 30 (18), 3330-3336, Apr. 19, 2016. [cited by applicant]
M. Konar, et al., The water footprint of staple crop trade under climate and policy scenarios, Environmental Research Letters, 11 (3), 035,006, Feb. 26, 2016. [cited by applicant]
F. Kyriakopoulos, et al., Network and eigenvalue analysis of financial transaction networks, The European Physical Journal B, 71, 523-531, Jul. 21, 2009. [cited by applicant]
V. Leroy, et al., Cold start link prediction, in Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining, pp. 393-402, ACM, 2010. [cited by applicant]
S.A. Levin, The problem of pattern and scale in ecology: the robert h. macarthur award lecture, Ecology, 73 (6), 1943-1967, Dec. 1992. [cited by applicant]
J. Liu, et al., Framing sustainability in a telecoupled world, Ecology and Society, 18 (2), Jun. 2013. [cited by applicant]
L. Lu, et al., Link prediction in complex networks: A survey, Physica A: statistical mechanics and its applications, 390 (6), 1150-1170, 2011. [cited by applicant]
G.K. MacDonald, et al., Embodied phosphorus and the global connections of united states agriculture, Environmental Research Letters, 7 (4), 044,024, Nov. 5, 2012. [cited by applicant]
L. Marston, et al., Drought impacts to water footprints and virtual water transfers of the central valley of california, Water Resources Research, 53 (7), 5756-5773, Jul. 18, 2017. [cited by applicant]
L. Marston, et al., Virtual groundwater transfers from overexploited aquifers in the united states, Proceedings of the National Academy of Sciences, 112 (28), 8561-8566, Jul. 14, 2015. [cited by applicant]
D. Mas, et al., Networks and syndication strategies: Does a venture capitalist need to be in the center?, ERMES-CNRS Universite Pantheon Assas Paris II, Working Paper No. 07-14, 2007. [cited by applicant]
A. Masucci, et al., Random planar graphs and the london street network, UCL Working Paper Series, 146, Aug. 18, 2009. [cited by applicant]
R. May, et al., Ecology for bankers, Nature, 451 (21), 893-895, Feb. 2008. [cited by applicant]
P.P. Micklin, Desiccation of the aral sea: a water management disaster in the soviet union, Science, 241 (4870), 1170-1176, Sep. 2, 1988. [cited by applicant]
R. Milo, et al., Superfamilies of evolved and designed networks, Science, 303 (5663), 1538-1542, doi: 10.1126/science.1089167, Mar. 5, 2004. [cited by applicant]
M.D. Morris, et al., Factorial sampling plans for preliminary computational experiments, Technometrics, 33 (2), 161-174, May 1991. [cited by applicant]
A.E. Motter, et al., Cascade-based attacks on complex networks, Physical Review E, 66, 065, 102, doi: 10.1103/PhysRevE.66.065102, Dec. 20, 2002. [cited by applicant]
M. Newman, Scientific collaboration networks: 1. Network construction and fundamental results, Physical Review E, 64, 016,131, Jun. 28, 2001. [cited by applicant]
M. Newman, Assortative mixing in networks, Phys. Rev. Lett., 89, 208,701, Nov. 11, 2002. [cited by applicant]
J.I.L. Miguens, et al., “Weighted and Directed Network on Traveling Patterns,” P. Lio et al. (Eds.): BIOWIRE 2007, LNCS 5151, pp. 145-154, 2008. [cited by applicant]
C. Gini, Concentration and dependency ratios (in italian), english translation in, Rivista di Politica Economica, 87, 769-789, 1909, (including machine translation of section 1 (abstract/introduction). [cited by applicant]
S. Wasserman, et al., “Social network analysis: Methods and applications,” 1st ed., Cambridge University Press, 1994. [cited by applicant]
F. Ramsey, et al., “The statistical sleuth: a course in methods of data analysis,” Cengage Learning, 2012. [cited by applicant]
M. Convertino, et al., Untangling drivers of species distributions:global sensitivity and uncertainty analyses of MaxEnt, Environ. Modelling & Software, 51 296-309, 2014. [cited by applicant]
D.R. Cox, The regression analysis of binary sequences, J. R. Stat. Soc., B 20 215-42, 1958. [cited by applicant]
A.D. Cuellar, et al., Wasted food, wasted energy: the embedded energy in food waste in the United States, Environ. Sci. Technol., 44 6464-9, Jul. 2, 2010. [cited by applicant]
R.I. Cukier, et al., A. study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients. I theory, J. Chem. Phys., 59 3873-8, Jan. 18, 1973. [cited by applicant]
C. Dalin, et al., Environmental impacts of food trade via resource use and greenhouse gas emissions, Environ. Res. Lett., 11 035012, Mar. 4, 2016. [cited by applicant]
Q. Dang, et al., Agricultural virtual water flows within the United States, Water Resour. Res., 51 973-86, Feb. 19, 2015. [cited by applicant]
T. Deryugina, et al., Impacts of crop insurance on water withdrawals for irrigation, Adv. Water Res., 110 437-44, Mar. 18, 2017. [cited by applicant]
A.C. Disdier, et al., The puzzling persistence of the distance effect on bilateral trade, Rev. Econ. Stat., 90 37-48, Feb. 2008. [cited by applicant]
Fao, Staple foods: what do people eat? (http://fao.org/docrep/u8480e/U8480E07.htm#Staple%20foods%20What%20do%20people%20eat), 2013. [cited by applicant]
J.C. Gower, A general coefficient of similarity and some of its properties, Biometrics, 27 857-71, Dec. 1971. [cited by applicant]
T. Homma, et al., Importance measures in global sensitivity analysis of nonlinear models, Reliab. Eng. Syst. Saf., 52 1-17, Jan. 5, 1996. [cited by applicant]
A.M. Isserman, et al., 1.5 million missing Nos. overcoming employment suppression in county business patterns data, Int. Reg. Sci. Rev. (https://doi.org/10.1177/0160017606290359), Jul. 2006. [cited by applicant]
M. Klein, A primal method for minimal cost flows with applications to the assignment and transportation problems, Manage. Sci., 14 205-20, Nov. 1967. [cited by applicant]
X. Lin, et al., A network analysis of food flows within the United States of America, Environ. Sci. Technol., 48 5439-47, 2014. [cited by applicant]
N. Ludtke, et al., Information-theoretic sensitivity analysis: a general method for credit assignment in complex networks, J. R. Soc. Interface, 5 223-35, Jun. 26, 2007. [cited by applicant]
G.K. Macdonald, et al., Rethinking agricultural trade relationships in an era of globalization, BioScience, 65 275-89, Mar. 2015. [cited by applicant]
M. Mohri et al., Foundations of Machine Learning (Cambridge, MA: MIT Press), 2012. [cited by applicant]
A. Saltelli, et al., Global Sensitivity Analysis: The Primer (Chichester: Wiley), 2008. [cited by applicant]
D. Seekell, et al., Resilience in the global food system, Environ. Res. Lett., Feb. 9, 2017. [cited by applicant]
J.L. Servadio, et al., Optimal information networks: application for data-driven integrated health in populations, Sci. Adv., Feb. 2, 2018. [cited by applicant]
US Census Bureau 2015b, 2012 Commodity Flow Survey Public Use Microdata (https://census.gov/econ/cfs/pums.html). [cited by applicant]
N. Vora et al., Food-energy-water nexus: quantifying embodied energy and ghg emissions from irrigation through virtual water transfers in food trade, ACS Sustain. Chem. Eng., 5 2119-28, Jan. 16, 2017. [cited by applicant]
S. Walker, et al., Estimation of the probability of an event as a function of several independent variables, Biometrika, 54 167-78, 1967. [cited by applicant]
G. Wang, et al., A comparative assessment of ensemble learning for credit scoring, Expert Syst. Appl., 38 223-30, 2011. [cited by applicant]
Xiaowen Lin, Understanding and Modeling Food Flow Networks Across Spatial Scales, Dissertation submitted in Graduate College of the University of Illinois at Urbana-Champaign, 2019, pp. 118. [cited by applicant]
Xiaowen LIN, et al., Food flows between counties in the United States, Environmental Research Letters, Jul. 26, 2019, 18 pgs., IOP Publishing. [cited by applicant]
R.K. Ahuja, et al., Network Flows: Theory, Algorithms, and Applications (London: Pearson), 1993. [cited by applicant]
M. Ercsey-Ravasz, et al., Complexity of the international agro-food trade network and its impact on food safety, PLoS One, 7 e37,810, 2012. [cited by applicant]
M. Konar, et al., Scaling properties of food flow networks, PLoS One, 13 e0199498, 2018. [cited by applicant]
S. Liang, et al., Socioeconomic drivers of greenhouse gas emissions in the united states, Environ. Sci. Technol., 50 7535-45, 2016. [cited by applicant]
X-Z Liang, et al., Determining climate effects on US total agricultural productivity, Proc. Natl Acad. Sci., 114 E2285- 92, 2017. [cited by applicant]
G.R. Llorden, Gamma Mixture Model Estimation withEM Algorithm MathWorks File Exchange (https://www.mathworks.com/matlabcentral/fileexchange/53028-gamma-mixture-model-estimation-with-em-algorithm), 2017. [cited by applicant]
D.B. Lobell, et al., Climate trends and global crop production since 1980, Science, 333 616-20, 2011. [cited by applicant]
S.P. Long, et al., Meeting the global food demand of the future by engineering crop photosynthesis and yield potential, Cell, 161 56-66, 2015. [cited by applicant]
L. Marston, et al., High-resolution water footprints of production of the United States, Water Resour. Res., 54 2288-316, 2018. [cited by applicant]
M. Nesheim, et al., A Framework for Assessing Effects of the Food System (Washington, DC:National Academies Press), 2015. [cited by applicant]
M. Porkka et al., From food insufficiency towards trade dependency: a historical analysis of global food availability, PLoS One, 714, 2013. [cited by applicant]
R.R. Rushforth et al., Aspatially detailed and economically complete blue water footprint of the United States, Hydrol. Earth Syst. Sci. (https://doi.org/10.5194/hess-22-3007-2018), 2018. [cited by applicant]
A. Saltelli, et al., A quantitative modelindependent method for global sensitivity analysis of model output, Technometrics, 41 39-56, 1999. [cited by applicant]
T.M. Smith, et al., Subnational mobility and consumption-based environmental accounting of US corn in animal protein and ethanol supply chains, Proc. Natl Acad. Soc., 11 E7891-9, 2017. [cited by applicant]
US Bureau of Economic Analysis, Input-Output Accounts Data (https://bea.gov/industry/io_annual.htm), 2014. [cited by applicant]
US Census Bureau 2015a, 2012 Economic Census (http://census.gov/data.html). [cited by applicant]
US Census Bureau, US Census Bureau USA Trade Database (https://usatrade.census.gov/index.php), 2018. [cited by applicant]
US Department of Agriculture, National Agricultural Statistics Service Quick Stats (http://quickstats.nass.usda.gov), 2014. [cited by applicant]
USDA, United States Department of Agriculture Economic, Research Service (http://ers.usda.gov/data-products.aspx), 2013. [cited by applicant]
C.L. Weber, et al., Food-miles and the relative climate impacts of food choices in the United States, Environ. Sci. Technol., 42 3508-13, 2008. [cited by applicant]
M. Xu, et al., Interconnectedness and resilience of the US economy, Adv. Complex Syst., 14 649-72, 2011. [cited by applicant]
M.M. Aldaya, et al., The water footprint assessment manual: Setting the global standard, Routledge, 2012. [cited by applicant]
E. Artin, The gamma function, Courier Dover Publications, 2015. [cited by applicant]
M.O. Jackson, Social and economic networks, Princeton university press, 2010. [cited by applicant]
Oak Ridge National Laboratory, Freight Analysis Framework, version 4 (http://faf.ornl.gov/fafweb/), 2015. [cited by applicant]
US Bureau of Economic Analysis, Local Area Personal Income and Employment (https://bea.gov/iTable/itable.cfm?reqid=70&step=1&isuri=1&acrdn=7#reqid=70&step=1&isuri=1), 2017. [cited by applicant]
CFS (2013), Commodity Flow Survey, http://www.census.gov/econ/cfs/. [cited by applicant]
Feed America (2018b), Hunger a harsh reality for 14 million children nationwide. [cited by applicant]
SCTG (2017), 2012 commodity flow survey standard classification of transported goods (sctg). [cited by applicant]
M. Newman, Coauthorship networks and patterns of scientific collaborations, Proc. Nat. Acad. Sci., 101, 5200-5205, Apr. 6, 2004. [cited by applicant]
M. Newman, et al., The structure and dynamics of networks, 1st ed., Princeton University Press, 2006. [cited by applicant]
M.E. Newman, Clustering and preferential attachment in growing networks, Physical review E, 64 (2), 025, 102, Jul. 26, 2001. [cited by applicant]
P.A. Nolin, Food-sharing networks in lamalera, indonesia, Human Nature, 21 (3), 243-268, Aug. 27, 2010. [cited by applicant]
C. O'Bannon, et al., Globalization of agricultural pollution due to international trade, Hydrol. Earth Syst. Sci. Discuss., 10, 11,221-11,239, doi:10.5194/hessd-10-11221-2013, Aug. 27, 2013. [cited by applicant]
D.M. Pennock, et al., Winners don't take all: Characterizing the competition for links on the web, Proc. Nat. Acad. Sci., 99 (8), 5207-5211, Apr. 16, 2002. [cited by applicant]
G. Peters, et al., Growth in emission transfers via international trade from 1990 to 2008, Proc. Nat. Acad. Sci., 108 (21), 8903-8908, doi: 10.1073/pnas.1006388108, May 24, 2011. [cited by applicant]
M.J. Puma, et al., Assessing the evolving fragility of the global food system, Environmental Research Letters, 10 (2), 024,007, Feb. 4, 2015. [cited by applicant]
Python (2018), python, http://geocoder.readthedocs.io. [cited by applicant]
J.J. Reimer, et al., Trade costs and the gains from trade in crop agriculture, American Journal of Agricultural Economics, 92 (4), 1024-1039, Jun. 10, 2010. [cited by applicant]
S.M. Rinaldi, et al., Identifying, understanding, and analyzing critical infrastructure interdependencies, IEEE Control Systems, 21 (6), 11-25, Dec. 2001. [cited by applicant]
R.R. Rushforth, et al., The vulnerability and resilience of a city's water footprint: The case of flagstaff, arizona, USA, Water Resources Research, 52 (4), 2698-2714, Apr. 8, 2016. [cited by applicant]
R.R. Rushforth, et al., A Spatially Detailed and Economically Complete Blue Water Footprint of the United States, Hydrology and Earth System Sciences, doi:10.5194/hess-2017-650, 2018. [cited by applicant]
G.D. Ruxton, The unequal variance t-test is an underused alternative to student's t-test and the mann-whitney u test, Behavioral Ecology, 17 (4), 688-690, May 17, 2006. [cited by applicant]
K. Ryu, An extension of marshall and olkin's bivariate exponential distribution, Journal of the American Statistical Association, 88 (424), 1458-1465, Dec. 1993. [cited by applicant]
F. Salako, et al., Soil water depletion under various leguminous cover crops in the derived savanna of west africa, Agriculture, Ecosystems & Environment, 100 (2-3), 173-180, 2003. [cited by applicant]
U.S. Sayles, et al., Social ecological network analysis of scale mismatches in estuary watershed restoration, Proceedings of the National Academy of Sciences, 114 (10), E1776-E1785, Feb. 21, 2017. [cited by applicant]
M. Schipanski, et al., The influence of agricultural trade and livestock production on the global phosphorus cycle, Ecosystems, 15 (2), 256-268, doi:10.1007/s10021-011-9507-x, Mar. 2012. [cited by applicant]
D. Seekell, et al., Virtual water transfers unlikely to redress inequality in global water use, Environ. Res. Lett., 6 (024017), Jun. 7, 2011. [cited by applicant]
M. Serrano, et al., Topology of the world trade web, Phys. Rev. E, 68 (1), 015, 101, Jul. 11, 2003. [cited by applicant]
K.C. Seto, et al., Urban land teleconnections and sustainability, Proceedings of the National Academy of Sciences, 109 (20), 7687-7692, May 15, 2012. [cited by applicant]
Q. Shen, et al., Virtual water scarcity risk to the global trade system, Environmental Science & Technology, 52 (2), 673-683, doi:10.1021/acs.est.7b04309, 2018. [cited by applicant]
S.T. Shutters, et al., Agricultural trade networks and patterns of economic development, PLoS One, 7 (7), 39,756, doi:10.1371/journal.pone.0039756, Jul. 2012. [cited by applicant]
I.M. Sobol, Global sensitivity indices for nonlinear mathematical models and their monte carlo estimates, Mathematics and computers in simulation, 55 (1-3), 271-280, 2001. [cited by applicant]
R. Tibshirani, Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society: Series B (Methodological), 58 (1), 267-288, 1996. [cited by applicant]
D. Tilman, Global environmental impacts of agricultural expansion: The need for sustainable and efficient practices, PNAS, 96 (11), 5995-6000, doi: 10.1073/pnas.96.11.5995, May 1999. [cited by applicant]
P. Vitousek, et al., Human domination of Earth's ecosystems, Science, 277 (5325), 494-499, Jul. 25, 1997. [cited by applicant]
D. Watts, Small worlds: the dynamics of networks between order and randomness, 1st ed., Princeton University Press, 1999. [cited by applicant]
D.J. Watts, et al., Collective dynamics of small-world networks, Nature, 393 (6684), 440-442, Jun. 4, 1998. [cited by applicant]
G.B. West, et al., A general model for the origin of allometric scaling laws in biology, Science, 276 (5309), 122-126, Apr. 4, 1997. [cited by applicant]
F. Wu, et al., Global maize trade and food security: Implications from a social network model, Risk Analysis, 33 (12), doi:10.1111/risa.12064, May 2013. [cited by applicant]
M. Xu, et al., Developing a science of infrastructure ecology for sustainable urban systems, Jul. 9, 2012. [cited by applicant]
M. Konar, A national strategy for a resilient food supply chain, 2019. [cited by applicant]
R. Wang, et al., Freshwater vulnerability beyond local water stress:heterogeneous effects of water-electricity nexus across the continental United States, Environ. Sci. Technol., 51 9899-910, 2017. [cited by applicant]
S. Agarwal, et al., A generalized gamma distribution and its application in reliabilty, Communications in Statistics-Theory and Methods, 25 (1), 201-210, 1996. [cited by applicant]
J.A. Baggio, et al., Multiplex social ecological network analysis reveals how social changes affect community robustness more than resource depletion, Proceedings of the National Academy of Sciences, 113 (48), 13,708-13… [cited by applicant]
A.L. Barabasi, Linked: The new science of networks, Perseus Publishing, 2002. [cited by applicant]
A.L. Barabasi, et al., Emergence of scaling in random networks, Science, 286, 509-512, Oct. 15, 1999. [cited by applicant]
M. Barigozzi, et al., Multinetwork of international trade: A commodity-specic analysis, Physical Review E, 81, 046, 104, 2010. [cited by applicant]
A. Barrat, et al., The architecture of complex weighted networks, Proceedings of the National Academy of Sciences, 101 (11), 3747-3752, 2004. [cited by applicant]
M. Barthelemy, Betweenness centrality in large complex networks, The European Physical Journal B, 38 (2), 163-168, May 14, 2004. [cited by applicant]
J. Berkoff, China: the south-north water transfer project is it justified?, Water policy, 5 (1), 1-28, Jan. 31, 2003. [cited by applicant]
M. Bettencourt, et al., Growth, innovation, scaling, and the pace of life in cities, Proceedings of the national academy of sciences, 104 (17), 7301-7306, Apr. 24, 2007. [cited by applicant]
K. Bhattacharya, et al., The international trade network, Econophysics of markets and business networks, pp. 139-147, 2007. [cited by applicant]
G. Bloschl, et al., Scale issues in hydrological modelling: a review, Hydrological processes, 9 (3-4), 251-290, 1995. [cited by applicant]
R.W. Bohannon, Standing balance, lower extremity muscle strength, and walking performance of patients referred for physical therapy, Perceptual and motor skills, 80 (2), 379-385, 1995. [cited by applicant]
L. Bouwman, et al., Exploring global changes in nitrogen and phosphorus cycles in agriculture induced by livestock production over the 19002050 period, PNAS, 110 (52), 20,882-20,887, doi:10.1073/pnas.1012878108, Dec. 24… [cited by applicant]
M. Burger, et al., On the specification of the gravity model of trade: zeros, excess zeros and zero-inflated estimation, Spatial Economic Analysis, 4 (2), 167-190, 2009. [cited by applicant]
R. Burgess, et al., Can openness mitigate the effects of weather shocks? Evidence from India's famine era, American Economic Review: Papers and Proceedings, pp. 449-453, May 2010. [cited by applicant]
J. Burton, et al., Community-based health education programs designed to improve clinical measures are unlikely to reduce short-term costs or utilization without additional features targeting these outcomes, Population … [cited by applicant]
C.M. Chini, et al., Direct and indirect urban water footprints of the united states, Water Resources Research, 53 (1), 316-327, Jan. 13, 2017. [cited by applicant]
CIA (2017), Central intelligence agency. [cited by applicant]
COMTRADE (2016), U.n. comtrade database. [cited by applicant]
L. Costa, et al., Characterization of complex networks: a survey of measurements, Advances in Physics, 56 (1), 167-242, 2007. [cited by applicant]
C. Dalin, et al., Evolution of the global virtual water trade network, Proc. Nat. Acad. Sci., 109 (16), 5989-5994, doi:10.1073/pnas.1203176109, Apr. 17, 2012. [cited by applicant]
C. Damgaard, et al., Describing inequality in plant size or fecundity, Ecology, 81, 1139-1142, Apr. 2000. [cited by applicant]
P. D'Odorico, et al., Feeding humanity through global food trade, Earth's Future, 2 (9), 458-469, Sep. 10, 2014. [cited by applicant]
P. Erdos, et al., On the evolution of random graphs, Publ. Math. Inst. Hung. Acad. Sci, 5 (1), 17-60, 1960. [cited by applicant]
G. Fagiolo, Clustering in complex directed networks, Phys. Rev. E, 76, 026, 107, 2007. [cited by applicant]
G. Fagiolo, et al., On the topological properties of the world trade web: A weighted network analysis, Physica A, 387, 3868-3873, Jan. 15, 2008. [cited by applicant]
J.J. Faraway, Extending the linear model with R: generalized linear, mixed effects and nonparametric regression models, Chapman and Hall/CRC, 2006. [cited by applicant]
Feed America (2018a), Understanding hunger and food insecurity. [cited by applicant]
J.A. Foley, et al., Global Consequences of Land Use, Science, 309, Jul. 22, 2005. [cited by applicant]
W.A. Foundation, Hunger statistics, 2018. [cited by applicant]
D. Fricke, et al., On assortative and disassortative mixing scale-free networks: The case of interbank credit network, Kiel Working Paper No. 1830, Feb. 2013. [cited by applicant]
D. Garlaschelli, et al., Structure and evolution of the world trade network, Physica A, 355, 491-499, May 4, 2005. [cited by applicant]
H.C.J. Godfray, et al., Food security: The challenge of feeding 9 billion people, Science, 327 (5967), 812-818, doi:10.1126/science.1185383, Feb. 12, 2010. [cited by applicant]
R. Guimera, et al., The real communication network behind the formal chart: Community structure in organizations, Journal of Economic Behavior and Organization, 61, 653-667, Jul. 7, 2006. [cited by applicant]
R.D. Gupta, et al., Theory & methods: Generalized exponential distributions, Australian & New Zealand Journal of Statistics, 41 (2), 173-188, 1999. [cited by applicant]