Let $\mathcal C$ be a category, and define $\mathcal D$ to be the category whose objects are maps in $\mathcal C$, and where a map $f\to g$ is a factorization $pfq=g$. Composition of $(p_1,q_1):f\to g$ and $(p_2,q_2):g\to h$ being $h=(p_2p_1)f(q_1q_2)$ and the obvious identity $f\to f$.

Abstract:This paper proposes a method for quantitative evaluation of perception deviations due to generalization in choropleth maps. The method proposed is based on comparison of class values assigned to different aggregation units chosen for representing the same dataset. It is illustrated by the results of application of the method to population density maps of Lithuania. Three spatial aggregation levels were chosen for comparison: the 1  1 km statistical grid, elderships (NUTS3), and municipalities (NUTS2). Differences in density class values between the reference grid map and the other two maps were calculated. It is demonstrated that a perceptual fallacy on the municipality level population map of Lithuania leads to a misinterpretation of data that makes such maps frankly useless. The eldership level map is, moreover, also largely misleading, especially in sparsely populated areas. The method proposed is easy to use and transferable to any other field where spatially aggregated data are mapped. It can be used for visual analysis of the degree to which a generalized choropleth map is liable to mislead the user in particular areas.Keywords: choropleth maps; perception; fallacy; aggregation; mapping


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Floods occur naturally and can happen almost anywhere. They may not even be near a body of water, although river and coastal flooding are two of the most common types. Heavy rains, poor drainage, and even nearby construction projects can put you at risk for flood damage.

Flood maps show how likely it is for an area to flood. Any place with a 1% chance or higher chance of experiencing a flood each year is considered to have a high risk. Those areas have at least a one-in-four chance of flooding during a 30-year mortgage.

Flood maps help mortgage lenders determine insurance requirements and help communities develop strategies for reducing their risk. The mapping process helps you and your community understand your flood risk and make more informed decisions about how to reduce or manage your risk.

Updates to flood maps are a collaboration between your community and FEMA. Every community that participates in the National Flood Insurance Program has a floodplain administrator who works with FEMA during the mapping process.

Once the data analysis is done, preliminary flood maps will be available for review. Before your community decides to adopt the maps, you have 90 days to submit technical data to support an appeal to the map.

There are already multiple places in a story where authors can record information like this such as the attribution field for media and the credits section at the end of the story. If you are already aware of these, please share some details about why or how these do not meet your need.

I will try further to explain the same example: Let's say I am the faculty member teaching 'food studies' class every semester. Since last three years, let's say I have taught this class for 6 times with about 20 students in each class. I ask Story Maps as a final project from each student, which then I stitch it into a larger collection of Story Maps - now it has grown to 120 stories with various web maps, images, videos, and such assets, and is published publicly. Students from the first two years have graduated i.e. they do not have access to their Story Maps as they are not currently enrolled (SSO determination). So let's walk through a few hypothetical scenarios:

3. A graduated student's story has been incorporated, cited, or embedded by various researchers. This student comes back after 3 years and wants his assets/data moved to his personal account. If the data is copied thats great but if the student does not want to share this data. Now how do one find out where all this has been cited? What links will be broken?

While flood maps have provided some answers, surveys are laborious and expensive, so they rarely have all the data needed. Surveyors fix a few point elevations and estimate the rest. Updates are infrequent. Structural elements are generally ignored.

Gong and his research team sent an ambitious proposal to Trenton, where it received an enthusiastic welcome and enough funding to get underway. The team has since mapped elevation data on more than ten thousand miles of roadway and all the homes along these roadways.

Lidar, an acronym for laser imaging, detection and ranging, creates three-dimensional maps by bombarding its surroundings with lasers and noting how long it takes the lasers to bounce back from different locations.

Back in the lab, software integrates information from the van with satellite images, open-source street maps, and other data to create precisely georeferenced 3D data of both the natural landscape and the built objects on it.

Even thinking just about advanced flood warning, potential uses for the system are numerous. Gong said he hopes NJ Transit will approve early warning systems for all its low-lying tracks and facilities, including the Meadowlands train yard where much of its rolling stock flooded during Sandy. Alert systems also could warn flood-prone towns or individual properties within those towns.

To estimate the location and size of myocardial infarction (MI), an isointegral mapping technique was adopted from among various body surface electrocardiographic mapping techniques. QRS isointegral and departure maps were made in 35 patients with MI. These patients were separated into 3 groups, based on the location of MI: anterior, inferior, and anterior plus inferior. The severity and location of MI were estimated by thallium-201 myocardial perfusion imaging and the degree of scintigraphic defect was represented by a defect score. The extent of MI was expected to be reflected on the QRS isointegral maps as a distribution of negative QRS complex time-integral values. However, the extent and the location of MI were hardly detectable by the original maps. A departure mapping technique was then devised to observe the distribution of departure index on the body surface. Particular attention was given to the area where the departure index was less than -2, and this area was expected to reflect the location and size of specific abnormality of isointegral map due to MI. There were strong correlations between departure area and defect score in the anterior and inferior MI cases (r = 0.88 and r = 0.79, respectively). However, patients with anterior MI plus inferior MI showed no such correlation. Q-wave mapping was compared with QRS isointegral mapping, and QRS isointegral mapping was found to be more accurate in the estimation of the location and size of MI than Q wave mapping. Thus, QRS isointegral mapping, especially departure mapping, is more useful and convenient for detecting the location and size of MI than methods such as isopotential and Q wave mapping.

The problem of synchronization of coupled Hamiltonian systems presents interesting features due to the mixed nature (regular and chaotic) of the phase space. We study these features by examining the synchronization of unidirectionally coupled area-preserving maps coupled by the Pecora-Caroll method. The master stability function approach is used to study the stability of the synchronous state and to identify the percentage of synchronizing initial conditions. The transient to synchronization shows intermittency with an associated power law. The mixed nature of the phase space of the studied map has notable effects on the synchronization times as is seen in the case of the standard map. Using finite-time Lyapunov exponent analysis, we show that the synchronization of the maps occurs in the neighborhood of invariant curves in the phase space. The phase differences of the coevolving trajectories show intermittency effects, due to the existence of stable periodic orbits contributing locally stable directions in the synchronizing neighborhoods. Furthermore, the value of the nonlinearity parameter, as well as the location of the initial conditions play an important role in the distribution of synchronization times. We examine drive response combinations which are chaotic-chaotic, chaotic-regular, regular-chaotic, and regular-regular. A range of scaling behavior is seen for these cases, including situations where the distributions show a power-law tail, indicating long synchronization times for at least some of the synchronizing trajectories. The introduction of coherent structures in the system changes the situation drastically. The distribution of synchronization times crosses over to exponential behavior, indicating shorter synchronization times, and the number of initial conditions which synchronize increases significantly, indicating an enhancement in the basin of synchronization. We discuss the implications of our results. ff782bc1db

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