A Crime concentration is a spatial area to which high levels of crime incidents are attributed. A crime concentration can be the result of homogeneous or heterogeneous crime incidents. Hotspots are the result of various crimes occurring in relative proximity to each other within predefined human geopolitical or social boundaries. Crime concentrations are smaller units or set of crime targets within a hotspot. A single or a conjunction of crime concentrations within a study area can make up a crime hotspot.

Some of the early works in crime analysis aimed to identify hotspots of crime within big regions. These regions could extend as large as states, counties, a group of counties, cities, neighborhoods and police beats. The aim of this approach was to focus on large areas, rather than specific addresses or locations hosting crime events as part of a larger environment. This is important because not all locations are equal generators of crime and not all provide equal opportunity for offenders to conduct criminal activity. Thus, crime concentrations are smaller groups of crime uniformly or randomly distributed within a hotspot's geographical domain; this is because not all hotspots have the same crime composition and patterns. In other words, a hotspot can be composed by multiple layers of crime intensity. Thus, each one has its own variations or rhythms of crime distribution. Therefore, it is each hotspot's composition that dictates what measures need to be employed as crime reduction strategies.

Hotspots are the foundation of crime concentrations because it is from the hotspot's earlier theories and studies that the analysis of crime concentration was derived. Hotspots can be expressed in the form of dots, lines or polygons and even shades of color as in the case of kernel density which estimates the likelihood of a crime event occurring within a given region; this is done through crime mapping which refers to the allocation of individual or multiple crime incidents on a map by utilizing a computer software package such as ArcMap 10.1, a Geographic information system. The different forms of hotspots and consequently crime concentrations are studied and explained by various theories and measured by several spatial and temporal analysis techniques. These techniques generally rely on statistical algorithms for the creation of surface maps. One of predominant theories that explains crime congregations is Crime opportunity theory. It explains that "rather than concentrations of offenders or the absence of social controls, opportunity theories suggest that analysts should look for concentrations of crime targets".Eck, et al, (2005) Repeat victimization%20theory Victimisation victimization theory examines why some areas or targets are repeatedly victimized. Broken windows theory also explains that an area that becomes abandoned or if the guardians and managers cease to be in control of an establishment, then other guardians and managers become less motivated to enforce social controls, consequently allowing criminal activity to increase. Lastly, one of the most influential crime concentration theories is the Crime Place Theory because it focuses on criminal events on specific locations rather than a large view at the high crime density area.

Crime concentrations: critical developments and respective key concepts Kernel density Kernel density is a computer based analysis through the usage of geographic information systems employed for the purpose of measuring crime intensity. It takes the map of the area being studied as the basis for analysis then it proceeds to divide the total area or map into smaller grid cells. The size of those grid cells can be selected by the analyst accordingly to the research questions under study or the indented applications. Each cell grid has a center point. Also, it is necessary for the analyst to select a bandwidth. This bandwidth is essentially a search radius from the center of each map grid. When the analysis is run the bandwidth searches the number of crimes reported within each cell. A greater amount crimes located closer to the cell center indicate higher crime intensity. If cells are found to possess high crime intensity rates then they are assigned high values.

Every cell grid in the map is assigned a value. This results in a continues map, a map of a city under the jurisdiction of a given police department for example. This map portraits the crime incidents data or intensity in the form of shades of colors for each grid throughout the area of study. Every part of the map has cells thus every part of the map has intensity value. Therefore, after conducting the kernel density analysis, it can be determine if grid cells with high crime intensity values are clustered together and thus forming a crime hotspot. The cells that possess higher intensity values within the crime hotspots only show the crime density but cannot be further analyze in order to locate the spatial coverage of crime concentrations. The ability to manipulate cell and bandwidth sizes permits analyst to use kernel density for conducting analysis at a small scope level within a crime hotspot.

Hotspot Matrix The Hotspot Matrix was pioneered by Jerry H. Ratcliffe.Ratcliffe (2004) It is the analysis of hotspots; however, unlike conventional analysis, it is not limited to the examination of hotspots as a mere geographical location. In addition to the implementation of spatial analysis techniques such as kernel density, LISA or STAC; it uses an aoristic analysis for which "The basic premise is that if a time of an event is not known, then the start and end time can be used to estimate a probability matrix for each crime event for each hour of the day". Therefore, the hotspot matrix is the combination of both spatial and temporal characteristics pertaining to hotspots in order to determine crime concentration patterns within a high crime intensity area.

Ratcliffe divided the hotspot matrix as having spatial and temporal attributes. The spatial attributes of a hotspot are: Hotpoint referring to a specific place from which a high volume of crimes are generated. The Clustered is geographical characteristic and representation of hotspots where crimes are concentrated with greater density in various areas in the location being studied. Dispersed crimes are those that are distributed across the study region without formulating major clusters of crimes; it is the closest form of random distribution of crimes in a hotspot. Ratcliffe also introduced the idea of temporal characteristics of crime. Diffused are hotspots where crimes are likely to happen at any time and there is not a specific window of time for crime incidents. Focused describes a phenomenon where crimes are likely to occur within a hotspot through the day, week, month(s) with greater intensity over a set of small windows of time. Acute pertains to hotspots experiencing the vast majority of incidents in a very small time frame; crime incidents outside that time frame are still possible, but nearly nonexistent. These are the six broad categories attributed to the hotspot matrix. These categories can be utilized to identify the areas within administrative boundaries with greater crime intensities. It also facilitates the identification of the type hotspot in the region. After the major crime areas become known, consequently, they can be isolated by the analyst in order to examine them to a closer level.

Crime concentration empirical support Empirical study 1 (Chicago) Crime and Place: Hot Spot Areas and Hot Spot Places of Liquor-Related CrimeBlock

Loyola Community Safety Project was assembled to investigate the potential relationship between taverns and other local licensed businesses whose primary or partial source of income rely the sales of alcoholic beverages in the area of Roger Park & Edgewater communities in the city of Chicago. This initiative was the result the collaboration of many community groups due to the increasing rates of drug and violent crimes in the region. The researchers had access to the equivalent of a geodatabase, which essentially functions as a big folder with the capabilities of storing multiple files such as aerial photographs or any other file capable of depicting geographical information. This geodatabase was compiled from records of police departments and other community groups; it contained data in the form of street addresses of establishments that sell alcohol. This information was stored as software files on a computer; this enabled the analysis, the geocoding and the output of the community maps.

The researchers proceeded to compile a list of all businesses in the area of study holding a liquor sales license. The researchers limited themselves from defining Taverns as the source of the crimes. Instead, they included in their study population every business with a liquor license. This facilitated the inclusion of business that do not fit the category of a Tavern in areas with higher poverty levels, but nevertheless serve the same function.

The researchers initiated geocoding which associates an address in the real world to a map – both the addresses of the several types of liquor selling establishments and the crimes that had occurred in places where liquor beverages are sold. The crimes geocoded varied in nature and ranged from disorderly conduct to felonies. After both the crimes and establishments had been geocoded, the maps were overlaid. This facilitated the identification of liquor places with the greater number of crimes within their location or their vicinity.

Some of the limitations in the study were that a high level of coordinates did not match. This was because the raw data was collected by various agencies and for different purposes. The method of analysis was to calculate the hotspot ellipses through the implementation of Spatial and Temporal Analysis of Crime (STAC). Eck and Weisburb (1995) define the process of how STAC works “STAC hot spot area searches begin with individual pin map data and build areas that reflect the actual scatter of events, regardless of arbitrary or predefined boundaries. STAC finds the densest clusters of events in the map and calculates the standard deviational ellipse that best fits each cluster.” (p. 154). It was determined that the number of liquor stores and liquor related businesses were not randomly dispersed in the area. They were generally located in clusters along major roads. This supports the idea that hotspots may contain different arrangements of crime. After the hotspots were identified by the researchers, they continued to examine the hotspots arrangement and took a look at some specific address level crime concentrations. The study found that high concentrations of taverns or liquor stores do not necessarily produce high levels of crime. It concluded that there were places that were responsible for higher levels of crime than others. Therefore, not all crime concentrations are equally generators of crime. Some crime places have environmental cues that facilitate the occurrence and sustainment of crime victimization.

Empirical study 2 (Boston) Mapping Gangs and Gang Violence in BostonKennedy et al (1997). This study was designed to reduce youth violence and gun markets in Boston. This was a collaboration of Harvard University researchers, Boston Police Department, probation officers and other city employees that had some level of experience when dealing with young offenders or youth vulnerable to violence. The group initiated a multi-agency study under the perception that a high density of gangs were operating in the area of interest or the city of Boston. It was assumed that youth violence was the direct product of gangs involvement almost in every youth violence incident. Some gang members were interviewed and it was learned that many did not classify themselves as gangs or gang members.