941 resultados para Multi-objective linear programming
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The Iowa Transportation Improvement Program (Program) is published to inform Iowans of planned investments in our state’s transportation system. The Iowa Transportation Commission (Commission) and Iowa Department of Transportation (Iowa DOT) are committed to programming those investments in a fiscally responsible manner. A major component of the 2010-2014 Program is the full integration of funding allocated to the Iowa DOT from the American Recovery and Reinvestment Act of 2009 (Recovery Act). To date, the Recovery Act has provided over $400 million of additional federal funding for transportation in Iowa, including funding that is allocated to local governments and entities. Recovery Act funding will result in a record year for transportation construction in Iowa and the creation and retention of jobs. Opportunities for additionalRecovery Act transportation funding remain and will be pursued as they becomeavailable. While Recovery Act funding will make a one-time significant impact in addressing Iowa’s backlog of needs, it is important to note that there remains a large shortfall in sustained annual transportation investment to meet Iowa’s current and future critical transportation needs. In recognition of this shortfall, Governor Culver introduced and the legislature passed an I-JOBS proposal. I-JOBS will result in an additional $50 million of state funding to reduce structurally deficient and functionally obsolete bridges on the primary road system and approximately $10 million in funding for other modes of transportation including $3 million of new funding to support the expansion of passenger rail service in Iowa. I-JOBS, and the continuing gradual increase in funding due to TIME-21, will complement and extend the benefits of Recovery Act funding and set the stage for addressing the shortfall in annual funding in the next few years. Iowa’s transportation system is multi-modal; therefore, the Program encompasses investments in aviation, transit, railroads, trails, and highways. A major component of the Program is the highway section. The FY2010-2014 highway section is financially balanced and was developed to achieve several objectives. The Commission’s primary highway investment objective is stewardship (i.e. safety, maintenance and preservation) of Iowa’s existing highway system. The highway section includes an annual average of $104 million for preserving the interstate system; an annual average of $78 million for non-interstate pavement preservation; an annual average of $36 million for non-interstate bridges; and an annual average of $14 million for safety projects. Another objective is to maintain the scheduled completion of interstate and non-interstate capacity and economic development projects that were identified in the previous Program and this Program does so. The final Commission objective is to further address capacity and economic development needs and the Commission has done so by adding several such projects to the Program. Construction improvements are partially funded through the current federal transportation act, Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (SAFETEA-LU). The act will expire September 30, 2009. With the expiration of SAFETEA-LU, there is significant uncertainty in the forecast of federal revenues in the out-years of this Program. The Commission and Iowa DOT will monitor federal actions closely and make adjustments to the Program as necessary. The Iowa DOT and Commission appreciate the public’s involvement in the state’s transportation planning process. Comments received personally, by letter, or through participation in the Commission’s regular meetings or public input meetings held around the state each year are invaluable in providing guidance for the future of Iowa’s transportation system. It should be noted that this document is a planning guide. It does not represent a binding commitment or obligation of the Commission or Iowa DOT, and is subject to change. You are invited to visit the Iowa DOT’s Web site at iowadot.gov for additional and regular updates about the department’s programs and activities.
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OBJECTIVE: When we examined a previously published prospective multi-center clinical trial in which complete denture-wearers were followed over a period of 2 years, we found that about 30% of the variability in the clinical wear data of denture teeth was due to unknown characteristics of the subjects. In the second part of the study, we try to identify which patient- and therapy-related factors may explain some of this variability. METHODS: The clinical wear data of denture teeth at different recall times (6, 12, 18, 24 months) in 89 subjects (at baseline) were correlated with the following parameters, which may all have an influence on the wear of denture teeth: age, gender, bruxism as reported by the subjects, number of prostheses used so far, time since last extraction, smoking, fit of dentures as judged by the subject and the clinician, average denture wearing time and wearing of denture during the night. To evaluate the influence of the different patient- and therapy-related variables, both a univariate analysis (one extra factor to the model) and a multivariate analysis were carried out using linear mixed models with the variable Log mean as the outcome. RESULTS: None of the patient- and therapy-related parameters showed a statistically significant effect on the wear of denture teeth. There was, however, a trend for women to show less wear compared to men and a trend of decreasing wear with increasing age. SIGNIFICANCE: Further research is required to identify the factors which are responsible for the high variability observed between the subjects regarding clinical wear data.
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Background and objective: Optimal care of diabetic patients (DPs) decreases the risk of complications. Close blood glucose monitoring can improve patient outcomes and shorten hospital stay. The objective of this pilot study was to evaluate the treatment of hospitalized DPs according to the current standards, including their diabetic treatment and drugs to prevent diabetes related complications [=guardian drugs: angiotensin converting enzyme inhibitors (ACEI) or Angiotensin II Receptor Blockers (ARB), antiplatelet drugs, statins]. Guidelines of the American Diabetes Association (ADA) [1] were used as reference as they were the most recent and exhaustive for hospital care. Design: Observational pilot study: analysis of the medical records of all DPs seen by the clinical pharmacists during medical rounds in different hospital units. An assessment was made by assigning points for fulfilling the different criteria according to ADA and then by dividing the total by the maximum achievable points (scale 0-1; 1 = all criteria fulfilled). Setting: Different Internal Medicine and Geriatric Units of the (multi-site) Ho^pital du Valais. Main outcome measures: - Completeness of diabetes-related information: type of diabetes, medical history, weight, albuminuria status, renal function, blood pressure, (recent) lipid profile. - Management of blood glucose: Hb1Ac, glycemic control, plan for treating hyper-/hypoglycaemia. - Presence of guardian drugs if indicated. Results: Medical records of 42 patients in 10 different units were analysed (18 women, 24 men, mean age 75.4 ± 11 years). 41 had type 2 diabetes. - Completeness of diabetes-related information: 0.8 ± 0.1. Information often missing: insulin-dependence (43%) and lipid profile (86%). - Management of blood glucose: 0.5 ± 0.2. 15 patients had suboptimal glycemic balance (target glycaemia 7.2-11.2 mmol/ l, with values[11.2 or\3.8 mmol/l, or Hb1Ac[7%), 10 patients had a deregulated balance (more than 10 values[11.2 mmol/l or \3.8 mmol/l and even values[15 mmol/l). - Presence of guardian drugs if indicated: ACEI/ARB: 19 of 23 patients (82.6%), statin: 16 of 40 patients (40%), antiplatelet drug: 16 of 39 patients (41%). Conclusions: Blood glucose control was insufficient in many DPs and prescription of statins and antiplatelet drugs was often missing. If confirmed by a larger study, these two points need to be optimised. As it is not always possible and appropriate to make those changes during hospital stay, a further project should assess and optimise diabetes care across both inpatient and outpatient settings.
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The Iowa Transportation Improvement Program (Program) is published to inform Iowans of planned investments in our state’s transportation system. The Iowa Transportation Commission (Commission) and Iowa Department of Transportation (Iowa DOT) are committed to programming those investments in a fiscally responsible manner. This document serves as the Iowa DOT's annual report as required by Iowa Code section 7A.9. This document reflects Iowa’s multimodal transportation system by the inclusion of investments in aviation, transit, railroads, trails, and highways. A major component of this program is the highway section that documents programmed investments on the primary highway system for the next five years. A large part of funding available for highway programming comes from the federal government. Accurately estimating future funding levels of this federal funding is dependent on having a current enacted multi-year federal transportation authorization. The most recent authorization, Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (SAFETEA-LU), expired September 30, 2009, and to date it has been extended five times because a new authorization has not yet been enacted. The current extension expires December 31, 2010. While Iowa law does not require the adoption of a Program when federal transportation funding is being reauthorized, the Commission believes it is important to adopt a Program in order to continue on-going planning and project development efforts and to be well positioned when a new authorization is adopted. However, it is important to recognize that, absent a federal authorization bill, there is significant uncertainty in the forecast of federal revenues. The Commission and the Iowa DOT will continue to monitor federal revenues and will adjust future investments as needed to maintain a fiscally responsible Program. In developing the highway section of the program, the Commission’s primary investment objective remains stewardship (i.e. safety, maintenance and preservation) of Iowa’s existing highway system. In fact, over $1.2 billion is programmed in FY2011 through FY2015 for preservation of Iowa’s existing highway system and for enhanced highway safety features. The highway section also includes significant investments for interstate modernization on I-29 inSioux City, on I-29/80/480 in Council Bluffs, and on I-74 in Bettendorf/ Davenport. Another highway programming objective reflected in this Program is maintaining the scheduled completion of capacity and economic development projects that were identified in the previous Program. Finally, with the limited remaining funds the Commission has furthered the investment in capacity and economic development by adding a few projects to the Program. The Iowa DOT and Commission appreciate the public’s involvement in the state’s transportation planning process. Comments received personally, by letter or through participation in the Commission’s regular meetings or public input meetings held around the state each year, are invaluable in providing guidance for the future of Iowa’s transportation system.
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The Iowa Transportation Improvement Program (Program) is published to inform Iowans of planned investments in our state’s transportation system. The Iowa Transportation Commission (Commission) and Iowa Department of Transportation (Iowa DOT) are committed to programming those investments in a fiscally responsible manner. This document reflects Iowa’s multimodal transportation system by the inclusion of investments in aviation, transit, railroads, trails, and highways. A major component of this program is the highway section that documents programmed investments on the primary highway system for the next five years. A large part of funding available for highway programming comes from the federal government. Accurately estimating future federal funding levels is dependent on having a current enacted multi-year federal transportation authorization. The most recent authorization, Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (SAFETEA-LU), expired September 30, 2009, and to date it has been extended seven times because a new authorization has not yet been enacted. The current extension will expire September 30, 2011. This leads to significant uncertainty in federal funding; however, it is becoming evident that, in Federal Fiscal Year 2012 and beyond, federal funding revenue will likely be reduced by 25 percent from current levels in order to match revenue that flows into the Highway Trust Fund. This Program reflects this anticipated reduction in federal funding. While Iowa law does not require the adoption of a Program when federal transportation funding is being reauthorized, the Commission believes it is important to adopt a Program in order to continue on-going planning and project development efforts so that Iowa will be well positioned when a new authorization is adopted. However, it is important to recognize that, absent a federal authorization bill, there is significant uncertainty in the forecast of federal revenues. The Commission and the Iowa DOT will continue to monitor federal revenues and will adjust future investments as needed to maintain a fiscally responsible Program. For 2012-2016, approximately $2.3 billion is forecast to be available for highway right of way and construction. In developing the highway section of the Program, the Commission’s primary investment objective remains stewardship (i.e. safety, maintenance and preservation) of Iowa’s existing highway system. Over $1.3 billion is programmed in FY2012 through FY2016 for preservation of Iowa’s existing highway system and for enhanced highway safety features. The highway section also includes significant interstate investments on I-29 in Sioux City, I-29/80/480 in Council Bluffs, and I-74 in Bettendorf/Davenport. The FY2016 programming for construction on I-74 in Bettendorf/Davenport is the first of several years of significant investments that will be monitored for available funding. Approximately $200 million of the investments on these three major urban interstate projects address preservation needs. In total, approximately $1.5 billion is programmed for highway preservation activities for 2012- 2016. Another highway programming objective is maintaining the scheduled completion of capacity and economic development projects. Projects that were previously scheduled to be completed within the previous Program continue on their current schedule. However, due to the reduction of projected federal revenues, the Commission has delayed by one year the initiation of construction of all multi-year non-Interstate capacity and economic development projects that cannot be completed within this Program. These projects are U.S. 20 in Woodbury County, U.S. 30 in Benton County, U.S. 61 in Louisa County, and Iowa 100 in Linn County. The Iowa DOT and Commission appreciate the public’s involvement in the state’s transportation planning process. Comments received personally, by letter or through participation in the Commission’s regular meetings or public input meetings held around the state each year, are invaluable in providing guidance for the future of Iowa’s transportation system. It should be noted that this document is a planning guide. It does not represent a binding commitment or obligation of the Commission or Iowa DOT, and is subject to change.
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BACKGROUND: The goal of this paper is to investigate the respective influence of work characteristics, the effort-reward ratio, and overcommitment on the poor mental health of out-of-hospital care providers. METHODS: 333 out-of-hospital care providers answered a questionnaire that included queries on mental health (GHQ-12), demographics, health-related information and work characteristics, questions from the Effort-Reward Imbalance Questionnaire, and items about overcommitment. A two-level multiple regression was performed between mental health (the dependent variable) and the effort-reward ratio, the overcommitment score, weekly number of interventions, percentage of non-prehospital transport of patients out of total missions, gender, and age. Participants were first-level units, and ambulance services were second-level units. We also shadowed ambulance personnel for a total of 416 hr. RESULTS: With cutoff points of 2/3 and 3/4 positive answers on the GHQ-12, the percentages of potential cases with poor mental health were 20% and 15%, respectively. The effort-reward ratio was associated with poor mental health (P < 0.001), irrespective of age or gender. Overcommitment was associated with poor mental health; this association was stronger in women (β = 0.054) than in men (β = 0.020). The percentage of prehospital missions out of total missions was only associated with poor mental health at the individual level. CONCLUSIONS: Emergency medical services should pay attention to the way employees perceive their efforts and the rewarding aspects of their work: an imbalance of those aspects is associated with poor mental health. Low perceived esteem appeared particularly associated with poor mental health. This suggests that supervisors of emergency medical services should enhance the value of their employees' work. Employees with overcommitment should also receive appropriate consideration. Preventive measures should target individual perceptions of effort and reward in order to improve mental health in prehospital care providers.
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The objective of this study was to investigate whether it is possible to pool together diffusion spectrum imaging data from four different scanners, located at three different sites. Two of the scanners had identical configuration whereas two did not. To measure the variability, we extracted three scalar maps (ADC, FA and GFA) from the DSI and utilized a region and a tract-based analysis. Additionally, a phantom study was performed to rule out some potential factors arising from the scanner performance in case some systematic bias occurred in the subject study. This work was split into three experiments: intra-scanner reproducibility, reproducibility with twin-scanner settings and reproducibility with other configurations. Overall for the intra-scanner and twin-scanner experiments, the region-based analysis coefficient of variation (CV) was in a range of 1%-4.2% and below 3% for almost every bundle for the tract-based analysis. The uncinate fasciculus showed the worst reproducibility, especially for FA and GFA values (CV 3.7-6%). For the GFA and FA maps, an ICC value of 0.7 and above is observed in almost all the regions/tracts. Looking at the last experiment, it was found that there is a very high similarity of the outcomes from the two scanners with identical setting. However, this was not the case for the two other imagers. Given the fact that the overall variation in our study is low for the imagers with identical settings, our findings support the feasibility of cross-site pooling of DSI data from identical scanners.
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BACKGROUND: The association between smoking and total energy expenditure (TEE) is still controversial. We examined this association in a multi-country study where TEE was measured in a subset of participants by the doubly labeled water (DLW) method, the gold standard for this measurement. METHODS: This study includes 236 participants from five different African origin populations who underwent DLW measurements and had complete data on the main covariates of interest. Self-reported smoking status was categorized as either light (<7 cig/day) or high (≥7 cig/day). Lean body mass was assessed by deuterium dilution and physical activity (PA) by accelerometry. RESULTS: The prevalence of smoking was 55% in men and 16% in women with a median of 6.5 cigarettes/day. There was a trend toward lower BMI in smokers than non-smokers (not statistically significant). TEE was strongly correlated with fat-free mass (men: 0.70; women: 0.79) and with body weight (0.59 in both sexes). Using linear regression and adjusting for body weight, study site, age, PA, alcohol intake and occupation, TEE was larger in high smokers than in never smokers among men (difference of 298 kcal/day, p = 0.045) but not among women (162 kcal/day, p = 0.170). The association became slightly weaker in men (254 kcal/day, p = 0.058) and disappeared in women (-76 kcal/day, p = 0.380) when adjusting for fat-free mass instead of body weight. CONCLUSION: There was an association between smoking and TEE among men. However, the lack of an association among women, which may be partly related to the small number of smoking women, also suggests a role of unaccounted confounding factors.
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When dealing with multi-angular image sequences, problems of reflectance changes due either to illumination and acquisition geometry, or to interactions with the atmosphere, naturally arise. These phenomena interplay with the scene and lead to a modification of the measured radiance: for example, according to the angle of acquisition, tall objects may be seen from top or from the side and different light scatterings may affect the surfaces. This results in shifts in the acquired radiance, that make the problem of multi-angular classification harder and might lead to catastrophic results, since surfaces with the same reflectance return significantly different signals. In this paper, rather than performing atmospheric or bi-directional reflection distribution function (BRDF) correction, a non-linear manifold learning approach is used to align data structures. This method maximizes the similarity between the different acquisitions by deforming their manifold, thus enhancing the transferability of classification models among the images of the sequence.
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OBJECTIVES: in a retrospective study, attempts have been made to identify individual organ-dysfunction risk profiles influencing the outcome after surgery for ruptured abdominal aortic aneurysms. METHODS: out of 235 patients undergoing graft replacement for abdominal aortic aneurysms, 57 (53 men, four women, mean age 72 years [s.d. 8.8]) were treated for ruptured aneurysms in a 3-year period. Forty-eight preoperative, 13 intraoperative and 34 postoperative variables were evaluated statistically. A simple multi-organ dysfunction (MOD) score was adopted. RESULTS: the perioperative mortality was 32%. Three patients died intraoperatively, four within 48 h and 11 died later. A significant influence for pre-existing risk factors was identified only for cardiovascular diseases. Multiple linear-regression analysis indicated that a haemoglobin <90 g/l, systolic blood pressure <80 mmHg and ECG signs of ischaemia at admission were highly significant risk factors. The cause of death for patients, who died more than 48 h postoperatively, was mainly MOD. All patients with a MOD score >/=4 died (n=7). These patients required 27% of the intensive-care unit (ICU) days of all patients and 72% of the ICU days of the non-survivors. CONCLUSION: patients with ruptured aortic aneurysms from treatment should not be excluded. However, a physiological scoring system after 48 h appears justifiable in order to decide on the appropriateness of continual ICU support.
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The Iowa Department of Transportation (IDOT) has been requiring Critical Path Method (CPM) schedules on some larger or more schedule sensitive projects. The Office of Construction's expectations for enhanced project control and improved communication of project objectives have not been fully met by the use of CPM. Recognizing that the current procedures might not be adequate for all projects, IDOT sponsored a research project to explore the state-of-the-art in transportation scheduling and identify opportunities for improvement. The first phase of this project identified a technique known as the Linear Scheduling Method (LSM) as an alternative to CPM on certain highway construction projects. LSM graphically displays the construction process with respect to the location and the time in which each activity occurs. The current phase of this project was implemented to allow the research team the opportunity to evaluate LSM on all small groups of diverse projects. Unlike the first phase of the project, the research team was closely involved in the project from early in the planning phase throughout the completion of the projects. The research strongly suggests that the linear scheduling technique has great potential as a project management tool for both contractors and IDOT personnel. However, before this technique can become a viable weapon in the project management arsenal, a software application needs to be developed. This application should bring to linear scheduling a degree of functionality as rich and as comprehensive as that found in microcomputer based CPM software on the market today. The research team recommends that the IDOT extend this research effort to include the development of a linear scheduling application.
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Introduction: The field of Connectomic research is growing rapidly, resulting from methodological advances in structural neuroimaging on many spatial scales. Especially progress in Diffusion MRI data acquisition and processing made available macroscopic structural connectivity maps in vivo through Connectome Mapping Pipelines (Hagmann et al, 2008) into so-called Connectomes (Hagmann 2005, Sporns et al, 2005). They exhibit both spatial and topological information that constrain functional imaging studies and are relevant in their interpretation. The need for a special-purpose software tool for both clinical researchers and neuroscientists to support investigations of such connectome data has grown. Methods: We developed the ConnectomeViewer, a powerful, extensible software tool for visualization and analysis in connectomic research. It uses the novel defined container-like Connectome File Format, specifying networks (GraphML), surfaces (Gifti), volumes (Nifti), track data (TrackVis) and metadata. Usage of Python as programming language allows it to by cross-platform and have access to a multitude of scientific libraries. Results: Using a flexible plugin architecture, it is possible to enhance functionality for specific purposes easily. Following features are already implemented: * Ready usage of libraries, e.g. for complex network analysis (NetworkX) and data plotting (Matplotlib). More brain connectivity measures will be implemented in a future release (Rubinov et al, 2009). * 3D View of networks with node positioning based on corresponding ROI surface patch. Other layouts possible. * Picking functionality to select nodes, select edges, get more node information (ConnectomeWiki), toggle surface representations * Interactive thresholding and modality selection of edge properties using filters * Arbitrary metadata can be stored for networks, thereby allowing e.g. group-based analysis or meta-analysis. * Python Shell for scripting. Application data is exposed and can be modified or used for further post-processing. * Visualization pipelines using filters and modules can be composed with Mayavi (Ramachandran et al, 2008). * Interface to TrackVis to visualize track data. Selected nodes are converted to ROIs for fiber filtering The Connectome Mapping Pipeline (Hagmann et al, 2008) processed 20 healthy subjects into an average Connectome dataset. The Figures show the ConnectomeViewer user interface using this dataset. Connections are shown that occur in all 20 subjects. The dataset is freely available from the homepage (connectomeviewer.org). Conclusions: The ConnectomeViewer is a cross-platform, open-source software tool that provides extensive visualization and analysis capabilities for connectomic research. It has a modular architecture, integrates relevant datatypes and is completely scriptable. Visit www.connectomics.org to get involved as user or developer.
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The choice network revenue management (RM) model incorporates customer purchase behavioras customers purchasing products with certain probabilities that are a function of the offeredassortment of products, and is the appropriate model for airline and hotel network revenuemanagement, dynamic sales of bundles, and dynamic assortment optimization. The underlyingstochastic dynamic program is intractable and even its certainty-equivalence approximation, inthe form of a linear program called Choice Deterministic Linear Program (CDLP) is difficultto solve in most cases. The separation problem for CDLP is NP-complete for MNL with justtwo segments when their consideration sets overlap; the affine approximation of the dynamicprogram is NP-complete for even a single-segment MNL. This is in contrast to the independentclass(perfect-segmentation) case where even the piecewise-linear approximation has been shownto be tractable. In this paper we investigate the piecewise-linear approximation for network RMunder a general discrete-choice model of demand. We show that the gap between the CDLP andthe piecewise-linear bounds is within a factor of at most 2. We then show that the piecewiselinearapproximation is polynomially-time solvable for a fixed consideration set size, bringing itinto the realm of tractability for small consideration sets; small consideration sets are a reasonablemodeling tradeoff in many practical applications. Our solution relies on showing that forany discrete-choice model the separation problem for the linear program of the piecewise-linearapproximation can be solved exactly by a Lagrangian relaxation. We give modeling extensionsand show by numerical experiments the improvements from using piecewise-linear approximationfunctions.
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There are many known examples of multiple semi-independent associations at individual loci; such associations might arise either because of true allelic heterogeneity or because of imperfect tagging of an unobserved causal variant. This phenomenon is of great importance in monogenic traits but has not yet been systematically investigated and quantified in complex-trait genome-wide association studies (GWASs). Here, we describe a multi-SNP association method that estimates the effect of loci harboring multiple association signals by using GWAS summary statistics. Applying the method to a large anthropometric GWAS meta-analysis (from the Genetic Investigation of Anthropometric Traits consortium study), we show that for height, body mass index (BMI), and waist-to-hip ratio (WHR), 3%, 2%, and 1%, respectively, of additional phenotypic variance can be explained on top of the previously reported 10% (height), 1.5% (BMI), and 1% (WHR). The method also permitted a substantial increase (by up to 50%) in the number of loci that replicate in a discovery-validation design. Specifically, we identified 74 loci at which the multi-SNP, a linear combination of SNPs, explains significantly more variance than does the best individual SNP. A detailed analysis of multi-SNPs shows that most of the additional variability explained is derived from SNPs that are not in linkage disequilibrium with the lead SNP, suggesting a major contribution of allelic heterogeneity to the missing heritability.
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Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.