Classifications

• • G—PHYSICS
  • G08—SIGNALLING
  • G08G—TRAFFIC CONTROL SYSTEMS
  • G08G1/00—Traffic control systems for road vehicles
  • G08G1/09—Arrangements for giving variable traffic instructions
  • G08G1/0962—Arrangements for giving variable traffic instructions having an indicator mounted inside the vehicle, e.g. giving voice messages
  • G08G1/09626—Arrangements for giving variable traffic instructions having an indicator mounted inside the vehicle, e.g. giving voice messages where the origin of the information is within the own vehicle, e.g. a local storage device, digital map
• • G—PHYSICS
  • G08—SIGNALLING
  • G08G—TRAFFIC CONTROL SYSTEMS
  • G08G1/00—Traffic control systems for road vehicles
  • G08G1/16—Anti-collision systems
  • G08G1/166—Anti-collision systems for active traffic, e.g. moving vehicles, pedestrians, bikes
• • G—PHYSICS
  • G08—SIGNALLING
  • G08G—TRAFFIC CONTROL SYSTEMS
  • G08G5/00—Traffic control systems for aircraft
  • G08G5/20—Arrangements for acquiring, generating, sharing or displaying traffic information
  • G08G5/21—Arrangements for acquiring, generating, sharing or displaying traffic information located onboard the aircraft
• • G—PHYSICS
  • G08—SIGNALLING
  • G08G—TRAFFIC CONTROL SYSTEMS
  • G08G5/00—Traffic control systems for aircraft
  • G08G5/20—Arrangements for acquiring, generating, sharing or displaying traffic information
  • G08G5/23—Details of user output interfaces, e.g. information presented
• • G—PHYSICS
  • G08—SIGNALLING
  • G08G—TRAFFIC CONTROL SYSTEMS
  • G08G5/00—Traffic control systems for aircraft
  • G08G5/20—Arrangements for acquiring, generating, sharing or displaying traffic information
  • G08G5/25—Transmission of traffic-related information between aircraft
• • G—PHYSICS
  • G08—SIGNALLING
  • G08G—TRAFFIC CONTROL SYSTEMS
  • G08G5/00—Traffic control systems for aircraft
  • G08G5/50—Navigation or guidance aids
  • G08G5/51—Navigation or guidance aids for control when on the ground, e.g. taxiing or rolling
• • G—PHYSICS
  • G08—SIGNALLING
  • G08G—TRAFFIC CONTROL SYSTEMS
  • G08G5/00—Traffic control systems for aircraft
  • G08G5/50—Navigation or guidance aids
  • G08G5/55—Navigation or guidance aids for a single aircraft
• • G—PHYSICS
  • G08—SIGNALLING
  • G08G—TRAFFIC CONTROL SYSTEMS
  • G08G5/00—Traffic control systems for aircraft
  • G08G5/70—Arrangements for monitoring traffic-related situations or conditions
  • G08G5/72—Arrangements for monitoring traffic-related situations or conditions for monitoring traffic
  • G08G5/723—Arrangements for monitoring traffic-related situations or conditions for monitoring traffic from the aircraft
• • G—PHYSICS
  • G08—SIGNALLING
  • G08G—TRAFFIC CONTROL SYSTEMS
  • G08G5/00—Traffic control systems for aircraft
  • G08G5/80—Anti-collision systems

Definitions

• Embodiments of the present disclosure generally relate to techniques for improved operation of vehicles, and specifically to systems and methods for determining intersection threat indices.
• vehicles may encounter various risks and operational hazards, such as the risk of colliding with other vehicles. In many cases, such collisions between vehicles may be more likely to occur at specific locations, such as intersections. In some examples, an intersection associated with an elevated collision risk when compared to other intersections may be identified using signage or an identifier displayed via a map.
• an airport map providing navigational runway and taxiway layouts for pilots may include callouts that identify hotspots at various locations. A hotspot may be a designated location where collisions between vehicles have historically occurred.
• a method is provided.
• the method is executable by at least one computing device embodied in hardware, software, firmware, and/or any combination thereof as described herein.
• the example method includes identifying geometry data representing a set of pathways in an environment.
• the example method further includes generating an initial threat index value for a first intersection based at least in part on a quantity of pathways in a subset of the set of pathways defining the first intersection, wherein the initial threat index value for the first intersection indicates a vehicular collision risk level associated with the first intersection.
• the example method further includes generating an intermediate threat index value for the first intersection based at least in part on the initial threat index value for the first intersection and at least one other initial threat index value for at least one other intersection determined to be adjacent to the first intersection.
• the example method further includes generating a final threat index value based at least in part on the intermediate threat index value and dynamically received data associated with the environment.
• the example method further includes providing information indicative of the final threat index value for the first intersection to a user interface.
• At least one characteristic of a representation for the first intersection, displayed via the user interface is visually distinguished based at least in part on the final threat index value.
• the at least one characteristic comprises at least one of: (i) a color of the representation, (ii) a size of the representation, or (iii) a font of the representation.
• the method further includes detecting a first type of trigger event that triggers the generation of the initial threat index value and the intermediate threat index value; and detecting a second type of trigger event that triggers the generation of the final threat index value.
• an apparatus in accordance with a second aspect of the disclosure, includes at least one processor and at least one memory storing instructions that, when executed by the at least one processor, cause the apparatus to perform any one of the methods described herein.
• a second example apparatus includes means for performing each step of any one of the methods described herein.
• An intersection may include a plurality of entry/exit points.
• An entry/exit point may be a location or region at an edge of an intersection where a vehicle may enter or exit the intersection.
• a plurality of line segments may be generated for each intersection within an environment. Each line segment may represent a pathway through an intersection. Accordingly, the entry/exit points of an intersection may be connected by line segments. For example, if an intersection has three entry/exit points, a first entry/exit point may be connected to a second entry/exit point by a first line segment and to a third entry/exit point by a second line segment.
• the second entry/exit point may be connected to the first entry/exit point by the first line segment and to the third entry/exit point by a third line segment.
• the intersection may have a total of three line segments.
• each line segment may represent two potential transitions through an intersection.
• a line segment connecting a first point and a second point may represent a first path of travel (e.g., a first transition) from the first point to the second point and a second path of travel (e.g., a second transition) from the second point to the first point.
• the term "environment" refers to a geographical location or a region of space associated with a particular use.
• An environment may include at least one vehicle (e.g., at least one type of vehicle) and at least one pathway for vehicular travel.
• an environment may include at least one airport.
• the techniques described herein may also apply to other types of environments.
• the techniques described herein may be applied to environments associated with automotive transportation, rail transportation, maritime transportation, or automated transportation systems utilized in manufacturing or order fulfillment environments.
• a threat index value may be represented by a number (e.g., an integer or a decimal value), or any other type of character, indicator, or representation configured to convey a degree to which a collision risk is present.
• a threat index value may be indicated by an integer, where increasing integer values represent increasing collision risks.
• a threat index value may be indicated by a color of a symbol (e.g., a color of a polygon), shape, or character.
• a threat index value may be updated or revised through multiple iterations. For example, a first threat index value may be generated at a first time, a second threat index value may be generated at a second time by updating the first threat index value, and a third threat index value may be generated at a third time by updating the second threat index value.
• the generation of a threat index value may include generating an initial threat index value (e.g., TIi), generating an intermediate threat index value (e.g., TI 2 ), and generating the final threat index value (e.g., TI 3 ).
• the phrase "threat index value" may refer to any of an initial threat index value, an intermediate threat index value, and/or a final threat index value.
• the term "initial threat index value" refers to a value indicating a collision risk level.
• the initial threat index value may indicate a likelihood that a collision will occur between two or more vehicles.
• an initial threat index value may be generated for an intersection.
• the initial threat index value may represent a likelihood of two or more vehicles colliding in or around the intersection.
• an initial threat index value may represent an initial assessment or evaluation of a vehicular collision risk. The initial assessment may then be refined or updated to arrive at an intermediate threat index value.
• the term "intermediate threat index value" refers to a value indicating a collision risk level.
• the intermediate threat index value may indicate a likelihood that a collision will occur between two or more vehicles.
• an intermediate threat index value may be generated for an intersection.
• the intermediate threat index value may represent a likelihood of two or more vehicles colliding in or around the intersection.
• the intermediate threat index value may represent an intermediate assessment or evaluation of a vehicular collision risk (e.g., an assessment performed after the generation of the initial threat index value and before the generation of the final threat index value).
• an intermediate threat index value for a first intersection may be based on an initial threat index value for the first intersection and at least one environmental or contextual condition. For example, an intermediate threat index value for the first intersection may be based on whether the first intersection is adjacent to or within a threshold distance of at least one other second intersection. In some examples, two intersections may be adjacent if intersection polygons for each intersection are in contact. In some examples, an intermediate threat index value for the first intersection may be generated by adjusting an initial threat index value for the first intersection based on the at least one environmental or contextual condition.
• an intermediate threat index value for the first intersection may be one initial threat index value higher (e.g., one odd integer value higher) than the same initial threat index value. Accordingly, if an initial threat index value for a first intersection is three and an initial threat index value for a second intersection adjacent to the first intersection is also three, an intermediate threat index value for the first intersection may be five. Additionally, or alternatively, an intermediate threat index value for the second intersection may be five. Although, in some examples, the second intersection may have a different intermediate threat index value if the second intersection is adjacent to at least one other intersection.
• an intermediate threat index value for the first intersection may be one integer value higher than a maximum value of the first initial threat index value and the second initial threat index value. Accordingly, if the first initial threat index value is three and the second initial threat index value is five, an intermediate threat index value for the first intersection may be six (e.g., MAX (3,5) + 1). Additionally, or alternatively, an intermediate threat index value for the second intersection may be six. Although, in some examples, the second intersection may have a different intermediate threat index value if the second intersection is adjacent to at least one other intersection.
• the term "final threat index value" refers to a value indicating a collision risk level.
• the final threat index value may indicate a likelihood that a collision will occur between two or more vehicles.
• a final threat index value may be generated for an intersection.
• the final threat index value may represent a likelihood of two or more vehicles colliding in or around the intersection.
• the final threat index value may represent a final assessment or evaluation of a vehicular collision risk (e.g., an assessment performed after the generation of the intermediate threat index value).
• a final threat index value for an intersection may be based on an intermediate threat index value for the intersection and at least one real-time condition.
• the at least one real-time condition may be indicated by received data (e.g., dynamically received data).
• the final threat index value may be based on notice to airmen (NOTAM) data or traffic information services (TIS) data, among other examples.
• NOTAM notice to airmen
• TIS traffic information services
• a computing entity e.g., installed at a first vehicle
• the computing system may generate a final threat index value.
• the final threat index value may be generated by adding at least one integer value to the intermediate threat index value.
• the intermediate threat index value may be increased by a value of one or a value of two to arrive at the final threat index value.
• a final threat index value may be generated dynamically.
• the generation of a final threat index value may be triggered by the receipt of data (e.g., dynamically received data). Accordingly, the generation of a final threat index may not be performed periodically and may instead be performed at times when relevant data is received.
• a computing entity may be configured to operate utilizing intermediate threat index values if final threat index values have not been generated.
• a user interface such as a display of an FMS, may by default display intermediate threat index values or representations of intermediate threat index values and then display at least one final threat index value when the generation of the at least one final threat index value is triggered.
• dynamically received data refers to data received by a computing system (e.g., a computing entity of a computing system).
• dynamically received data may be received and/or transmitted based on the occurrence of an event.
• NOTAM data may be an example of dynamically received data and may be transmitted and/or received based on the occurrence of an unplanned event.
• a runway closure e.g., an unplanned runway closure due to an emergency landing
• NOTAM data may be communicated to at least one vehicle via NOTAM data.
• the communication of the NOTAM data may be described as "dynamically received” given that the communication of the NOTAM data was not transmitted based on a preconfigured transmission schedule, but instead transmitted based on the occurrence of an expected event.
• the receipt of data e.g., dynamically received data
• may constitute a trigger event e.g., a dynamically occurring trigger event.
• the trigger event may trigger the generation of a threat index value (e.g., a final threat index value).
• receiving NOTAM data may trigger the generation of a final threat index value that is adjusted based on the NOTAM data.
• the term "information indicative of the final threat index value" refers to information that communicates or otherwise indicates the final threat index value.
• the information indicative of the final threat index value may be a message (e.g., an alert message) that includes the final threat index value.
• the information indicative of the final threat index value may be an auditory alert that communicates the final threat index value.
• the auditory alert may include a voice message that states the final threat index value. Additionally, or alternatively, the auditory alert may include at least one alert tone corresponding to at least one final threat index value.
• the information indicative of the final threat index value may include at least one characteristic, which may be adjusted or configured to indicate a final threat index value.
• a user interface may display at least one intersection identifier representative of at least one intersection in an environment.
• at least one characteristic of the at least one intersection identifier may be set or adjusted to communicate a final threat index value. For example, a color, a size, a font (e.g., bold, underline, italics, and/or the like), a position, or any other characteristic of an intersection identifier may be utilized to indicate a final threat index value.
• the term "characteristic of an identifier" refers to an attribute, property, quality, of an identifier, which may be utilized to communicate information.
• a characteristic of an identifier may be utilized to communicate information indicative of a final threat index value. For example, an intersection may be identified using a polygon that surrounds the intersection, and a color of the polygon may indicate a final threat index value. In such examples, each color in a color pallet or color spectrum may correspond to a specific final threat index value.
• a characteristic of a text-based identifier may be utilized to communicate a final threat index value. For example, a color of a text label for an intersection may indicate a final threat index value for the intersection.
• the term "user interface" refers to a display or interactive system that enables an individual to receive communications.
• a user interface may be configured to display information indicative of at least one threat index value, such as information indicative of a final threat index value.
• the user interface may display at least one message including at least one threat index value.
• the user interface may display other information indicative of the at least one threat index value.
• the user interface may display polygons representative of intersections, where a color of each polygon indicates a threat index value for the intersection.
• a user interface may be a subcomponent of a computing system, which may itself be a subcomponent of a vehicle.
• a user interface may be a subcomponent of an FMS of an aircraft.
• the term "auditory alert” refers to an audio signal or audio message that provides information to at least one individual.
• the information may include a warning of at least one risk or hazard, such as a vehicular collision risk.
• an auditory alert may indicate a threat index value or may indicate that a threat index value satisfies a threat index value threshold.
• an auditory alert may be provided or broadcast to at least one individual (e.g., via a computing system) if a final threat index value satisfies (e.g., is greater than) a final threat index value threshold.
• an individual operating a vehicle may reduce the speed of the vehicle or perform at least one other action that reduces a likelihood of a collision occurring.
• an auditory alert may include a message, such as an audio message of a recorded voice stating a threat index value or a generalized warning to perform at least one action to reduce collision risk.
• the term "trigger event” refers to an event or action that causes at least one other event or action.
• the receipt of data or a message including data may constitute a trigger event.
• a timer or clock reaching a specified value may constitute a trigger event.
• a weather event or the occurrence of a collision may be an example of a trigger event.
• trigger events may be classified according to type.
• a trigger event may be a preconfigured trigger event or a dynamically occurring trigger event.
• a preconfigured trigger event may occur periodically, at a preconfigured or set interval.
• a startup or boot process for a computing system may be an example of a preconfigured trigger event.
• FIG. 1 illustrates a system for determining and communicating threat index values in accordance with at least some embodiments of the present disclosure.
• the system 100 includes at least one aerial vehicle onboard system 102, for example, which embodies at least one system of an aerial vehicle 150, or any other type of vehicle, operating within a particular environment.
• the at least one aerial vehicle onboard system 102 is optionally communicable with at least one other computing device and/or system, such as at least one other connected vehicle system 104, flight management system 106, and environmental data system 108.
• the at least one aerial vehicle onboard system 102 is communicable with at least one of the other computing devices and/or systems over at least one communications network, such as the communications network 110.
• FIG. 5B is an operational example 500-b of an intersection configuration in accordance with some embodiments discussed herein.
• the operational example 500-b includes two adjacent intersections 410 having different quantities of branches (e.g., different quantities of line segments, different quantities of pathways), and accordingly, different initial threat index values.
• the techniques described herein provide an example process for generating intermediate threat index values for adjacent intersections that have different initial threat index values.
• intersection 410-f has an initial threat index value of three and the intersection 410-g has an initial threat index value of five. Accordingly, the intersection 410-f and the intersection 410-g each have intermediate threat index values of six (e.g., MAX (3,5) +1).
• FIG. 6 is an operational example 600 of a display configuration for emphasizing intersections based on threat index values in accordance with some embodiments discussed herein.
• the operational example 600 may include polygons 610, which may be displayed via a user interface.
• a color coding scheme e.g., a color ramp
• a fill pattern scheme may be utilized to represent varying threat index values.
• the polygon 610-a may be representative of a first intersection with a first final threat index value.
• the polygon 610-a may be displayed using a color 605-a, which may correspond to the first final threat index value.
• the polygon 610-b may be representative of a second intersection with a second final threat index value (e.g., higher than the first final threat index value).
• the polygon 610-b may be displayed using a color 605-b, which may correspond to the second final threat index value.
• the polygon 610-c may be representative of a third intersection with a third final threat index value (e.g., higher than the second final threat index value).
• the polygon 610-c may be displaying using a color 605-c, which may correspond to the third final threat index value.
• FIG. 7 is an operational example of a system 700 for generating and communicating threat index values in accordance with some embodiments discussed herein.
• the system 700 may include at least one component of at least one computing entity 200.
• a computing entity 200 as described with reference to FIG. 2 may include the database 705, the processor 710-a, the processor 710-b, the algorithm 720, and the user interface 725.
• the components of the system 700 may be included in at least one computing entity 200.
• a first computing entity may include the database 705 and a second computing entity may include the processor 710-a, the processor 710-b, the algorithm 720, and the user interface 725.
• system 700 may be a functional block diagram of system 700 (e.g., an aircraft system) configured to fetch (e.g., request and receive) geometry data (e.g., an airport layout) from the database 705 (e.g., an AMDB).
• system 700 may be configured to fetch at least one pre-computed (e.g., by the database 705 or at least one computing entity 200 associated with the database 705) intermediate threat index value for at least one intersection.
• the processor 710-a may be configured to generate at least one final threat index value by increasing or decreasing the intermediate threat index values based on real-time conditions, received data, or both.
• the processor 710-a may adjust at least one intermediate threat index value based on at least one NOTAM, at least one TIS message, or both.
• the at least one final threat index value may be communicated to the processing system 715 (e.g., to the processor 710-b).
• the processing system 715 may be an FMS of an aircraft that hosts an algorithm 720 to emphasize intersections.
• the algorithm 720 may identify at least one appropriate time to graphically emphasize intersections (e.g., using graduated symbols, using color coded polygons, using aural alerts) based on threat index values. For example, an intersection polygon may be visually emphasized on a user interface 725 when a vehicle is within a threshold distance of the intersection.
• the algorithm may trigger an aural alert to a pilot (e.g., at the at least one appropriate time).
• FIG. 8 is an operational example of a system 800 for generating and communicating threat index values in accordance with some embodiments discussed herein.
• the components of the system 800 may be embodied by at least one computing entity 200, as described with reference to FIG. 2 .
• the FMS 805, the database 705, the alerting system 810, the inertial navigation system (INS) 815, the pitot static system 820, and the global position system (GPS) 825 may be embodied by at least one computing entity 200.
• the components of the system 800 may be embodied by a single computing entity 200, while in other examples, the components of the system 800 may be embodied by multiple computing entities 200 in communication with one another.
• the FMS 805 may be an example of the processor 710-a, as described with reference to FIG. 7 .
• the FMS 805 may receive position and ground speed information for an aircraft from the INS 815, air data computer (e.g., the pitot static system 820), and GPS 825.
• the FMS 805 may compute a current position for an aircraft and may receive at least one intermediate threat index value from the database 705 (e.g., the AMDB).
• the FMS 805 may generate at least one final threat index value based on the at least one intermediate threat index value received from the database 705.
• the FMS 805 may then provide information indicative of the at least one final threat index value to the alerting system 810.
• the alerting system 810 may utilize an algorithm to determine at least one time for providing the information (e.g., via an alert or other information representative of at least one final threat index value) to a user (e.g., a pilot) via a user interface.
• the alerting system 810 may be an example of the processing system 715, as described with reference to FIG. 7 .
• a user interface may be an example of a primary flight display (PFD) and may display an airport moving map (AMM). In such examples, intersections may be emphasized graphically using graduated symbols based on final threat index values.
• an aural alert may be provided (e.g., via the alerting system 810), which may assist a pilot in taking appropriate actions based on final threat index values.
• FIG. 9 illustrates a process for generating intersection threat index values in accordance with at least some embodiments of the present disclosure.
• FIG. 9 depicts operations of an example process 900.
• the process 900 is embodied by computer program code stored on a non-transitory computer-readable storage medium of a computer program product configured for execution to perform the process as depicted and described. Additionally, or alternatively, in some embodiments, the process 900 is performed by at least one specifically configured computing device, such as at least one computing entity 200 alone or in communication with at least one other component, device, system, and/or the like.
• the computing entity 200 is specially configured by computer-coded instructions (e.g., computer program instructions) stored thereon, for example in the memory 204 and/or another component depicted and/or described herein and/or otherwise accessible to the computing entity 200, for performing the operations as depicted and described.
• the computing entity 200 is in communication with at least one external apparatus, system, device, and/or the like, to perform at least one of the operations as depicted and described.
• the computing entity 200 in some embodiments, is in communication with an end-user computing device, client device, and/or the like.
• the process 900 is described as performed by and from the perspective of the computing entity 200.
• the process 900 begins at operation 905.
• the computing entity 200 includes means such as the sensors 210, navigation circuitry 212, flight operations circuitry 214, virtual management circuitry 215, communications circuitry 208, input/output circuitry 206, and/or processor 202, or a combination thereof, to identify geometry data representing a set of pathways in an environment.
• the geometry data comprises a polygon representative of the first intersection, the polygon comprising a set of lines representative of the subset of the set of pathways.
• the computing entity 200 includes means such as the sensors 210, navigation circuitry 212, flight operations circuitry 214, virtual management circuitry 215, communications circuitry 208, input/output circuitry 206, and/or processor 202, or a combination thereof, to generate an initial threat index value for a first intersection based at least in part on a quantity of pathways in a subset of the set of pathways defining the first intersection.
• the initial threat index value for the first intersection indicates a vehicular collision risk level associated with the first intersection.
• a first type of trigger event that triggers the generation of the initial threat index value is detected.
• the first type of trigger event may include a preconfigured trigger event.
• the computing entity 200 includes means such as the sensors 210, navigation circuitry 212, flight operations circuitry 214, virtual management circuitry 215, communications circuitry 208, input/output circuitry 206, and/or processor 202, or a combination thereof, to generate an intermediate threat index value for the first intersection based at least in part on the initial threat index value for the first intersection and at least one other initial threat index value for at least one other intersection determined to be adjacent to the first intersection.
• the intermediate threat index value is based at least in part on a determination of whether the initial threat index value for the first intersection and the at least one other initial threat index value for the at least one other intersection are different.
• the intermediate threat index value is generated by adding a first value to the initial threat index value in a circumstance where the initial threat index value is equal to the at least one other initial threat index value. In some embodiments, the intermediate threat index value is generated by adding a second value to a higher of: (i) the initial threat index value or (ii) the at least one other initial threat index value in a circumstance where the initial threat index value is different from the at least one other initial threat index value. In some embodiments, a first type of trigger event that triggers the generation of the intermediate threat index value is detected. The first type of trigger event may include a preconfigured trigger event.
• the computing entity 200 includes means such as the sensors 210, navigation circuitry 212, flight operations circuitry 214, virtual management circuitry 215, communications circuitry 208, input/output circuitry 206, and/or processor 202, or a combination thereof, to generate a final threat index value based at least in part on the intermediate threat index value and dynamically received data associated with the environment.
• the dynamically received data comprises at least one of: (i) notice to airmen (NOTAM) data or (ii) traffic information services (TIS) data.
• the dynamically received data is associated with at least one vehicle operating within the environment.
• a second type of trigger event that triggers the generation of the final threat index value is detected.
• the second type of trigger event may include a dynamically occurring trigger event.
• the computing entity 200 includes means such as the sensors 210, navigation circuitry 212, flight operations circuitry 214, virtual management circuitry 215, communications circuitry 208, input/output circuitry 206, and/or processor 202, or a combination thereof, to provide information indicative of the final threat index value for the first intersection to a user interface.
• at least one characteristic of a representation for the first intersection, displayed via the user interface is visually distinguished based at least in part on the final threat index value.
• the at least one characteristic comprises at least one of: (i) a color of the representation, (ii) a size of the representation, or (iii) a font of the representation.
• at least one auditory alert may be provided based at least in part on the final threat index value.
• the at least one auditory alert may be provided in response to the final threat index value satisfying a threshold threat index value.
• some of the operations above may be modified or further amplified. Furthermore, in some embodiments, additional optional operations may be included. Modifications, amplifications, or additions to the operations above may be performed in any order and in any combination.

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