Patent Application
20200353311
The present disclosure generally relates to system and method for generating content and style predictions in sports.
How does one predict a player who has only ever played zone will play in man-to-man or predict how a player plays on the right wing, when all that player has done is play on the left? How does one predict how a team will play against the high press when they have not faced the high press before? How will a team react to an unseen situation? These are the types of questions that drive sports analytics. The challenge in answering these questions is having the right kinds and sufficient amounts of data, as well as the correctly trained algorithms for making such predictions.
Embodiments disclosed herein generally relate to a system and method for generating a content and style prediction in sports. In one embodiment, a method of generating a play prediction for a team is disclosed herein. A computing system trajectory data for a plurality of plays from a data store. The computing system generates a predictive model using a variational autoencoder and a neural network by generating one or more input data sets, learning, by the variational autoencoder, to generate a plurality of variants for each play of the plurality of plays, and learning, by the neural network, a team style corresponding to each play of the plurality of plays. Each input data set includes tracking information for a play of the plurality of plays. Each variant includes trajectory information corresponding thereto. The computing system receives trajectory data corresponding to a target play. The predictive model generates a likelihood of a target team executing the target play by determining a number of target variants that correspond to a target team identity of the target team.
In another embodiment, a system for generating a play prediction for a team is disclosed herein. The system includes a processor and a memory. The memory has programming instructions stored thereon, which, when executed by the processor, performs one or more operations. The one or more operations include retrieving trajectory data for a plurality of plays from a data store. The one or more operations further include generating a predictive model using a variational autoencoder and a neural network by generating one or more input data sets, learning, by the variational autoencoder, to generate a plurality of variants for each play of the plurality of plays, and learning, by the neural network, a team style corresponding to each play of the plurality of plays. Each input data set includes tracking information for a play of the plurality of plays. Each variant includes trajectory information corresponding thereto. The one or more operations further include receiving event data corresponding to a target play. The event data includes trajectory data for the target play. The one or more operations further include generating, via the predictive model, a likelihood of a target team executing the target play by determining a number of target variants that correspond to a target team identity of the target team.
In another embodiment, a non-transitory computer readable medium is disclosed herein. The non-transitory computer readable medium includes one or more sequences of instructions that, when executed by the one or more processors, causes one or more operations. The one or more operations include retrieving trajectory data for a plurality of plays from a data store. The one or more operations further include generating a predictive model using a variational autoencoder and a neural network by generating one or more input data sets, learning, by the variational autoencoder, to generate a plurality of variants for each play of the plurality of plays, and learning, by the neural network, a team style corresponding to each play of the plurality of plays. Each input data set includes tracking information for a play of the plurality of plays. Each variant includes trajectory information corresponding thereto. The one or more operations further include receiving trajectory data corresponding to a target play. The one or more operations further include generating, via the predictive model, a likelihood of a target team executing the target play by determining a number of target variants that correspond to a target team identity of the target team.
So that the manner in which the above recited features of the present disclosure can be understood in detail, a more particular description of the disclosure, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrated only typical embodiments of this disclosure and are therefore not to be considered limiting of its scope, for the disclosure may admit to other equally effective embodiments.
To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures. It is contemplated that elements disclosed in one embodiment may be beneficially utilized on other embodiments without specific recitation.
Discrete sports, such as baseball, are well-defined by coarse event-based descriptors, such as, balls, strikes, hits, and outs. Even more specific variants of these events, such as the play “ground-out to the shortstop,” can be discrete, labeled, counted, and analyzed. Furthermore, the natural discrete hierarchy of these labels means that the relationship between plays is easily captured, as well. As a result, the set of all possible events may be finite, well-defined, and (comparatively) small. Therefore, the task of answering questions related to how a team may behave in situations becomes a matter of looking up or retrieving similar examples.
In contrast, continuous sports, such as basketball and soccer, are poorly described by events alone. To describe a play, tracking data is typically used. However, tracking-based description suffers from the curse of dimensionality. In soccer, for example, a fifteen second tracking sequence may consist of nearly 3500 degrees of freedom (e.g., 15 seconds×10 frames per second×2 spatial dimensions×11 players per team×2 teams). With each degree of freedom (E.g., corresponding to a coordinate on the pitch (i.e., field)) being a continuous variable, the potential variability between plays may be massive and any two players may be likely to be far away from one another. Even with tracking data across dozens of leagues and decades of play, there may never be enough data because the set of many contexts and scenarios may be too diverse.
Such problem becomes even more complicated in the world of soccer where two teams from different leagues may rarely, or potentially never, play against one another. This means that in major tournaments, such as the Champions League, there may be many first time match-ups. Therefore, simply looking up similar situations is insufficient to the task.
The one or more techniques disclosed herein address the limitations of conventional systems through the use of generative models and neural networks. The generative models disclosed herein provide the system with the power to create, and therefore understand, complex, continuous, and adversarial sports, such as soccer, basketball, and the like. For example, the generative models disclosed herein allows the system to synthesize many (e.g., infinitely) many variants of any play, which may unlock an improved understanding of how a play may be executed. The neural networks disclosed herein allow the system to identify a team associated with each play and each variant thereof. With the combined generative models and neural networks, the system may be able to disentangle play content with play style. Such disentanglement may allow one to understand the similarity between teams both in types of plays that each team runs and the style and nuance with which each team executes them.
Network 105 may be of any suitable type, including individual connections via the Internet, such as cellular or Wi-Fi networks. In some embodiments, network 105 may connect terminals, services, and mobile devices using direct connections, such as radio frequency identification (RFID), near-field communication (NFC), Bluetooth™, low-energy Bluetooth™ (BLE), Wi-Fi™, ZigBee™, ambient backscatter communication (ABC) protocols, USB, WAN, or LAN. Because the information transmitted may be personal or confidential, security concerns may dictate one or more of these types of connection be encrypted or otherwise secured. In some embodiments, however, the information being transmitted may be less personal, and therefore, the network connections may be selected for convenience over security.
Network 105 may include any type of computer networking arrangement used to exchange data or information. For example, network 105 may be the Internet, a private data network, virtual private network using a public network and/or other suitable connection(s) that enables components in computing environment 100 to send and receive information between the components of computing environment 100.
Tracking system 102 may be positioned in a venue 106. For example, venue 106 may be configured to host a sporting event that includes one or more agents 112. Tracking system 102 may be configured to record the motions of all agents (i.e., players) on the playing surface, as well as one or more other objects of relevance (e.g., ball, referees, etc.). In some embodiments, tracking system 102 may be an optically-based system using, for example, a plurality of fixed cameras. For example, a system of six stationary, calibrated cameras, which project the three-dimensional locations of players and the ball onto a two-dimensional overhead view of the court may be used. In some embodiments, tracking system 102 may be a radio-based system using, for example, radio frequency identification (RFID) tags worn by players or embedded in objects to be tracked. Generally, tracking system 102 may be configured to sample and record, at a high frame rate (e.g., 25 Hz). Tracking system 102 may be configured to store at least player identity and positional information (e.g., (x, y) position) for all agents and objects on the playing surface for each frame in a game file 110.
Game file 110 may be augmented with other event information corresponding to event data, such as, but not limited to, game event information (play, tackle, possession, etc.) and context information (current score, time remaining, etc.).
Tracking system 102 may be configured to communicate with organization computing system 104 via network 105. Organization computing system 104 may be configured to manage and analyze the data captured by tracking system 102. Organization computing system 104 may include at least a web client application server 114, a pre-processing agent 116, a data store 118, and team prediction agent 120. Each of pre-processing agent 116 and team prediction agent 120 may be comprised of one or more software modules. The one or more software modules may be collections of code or instructions stored on a media (e.g., memory of organization computing system 104) that represent a series of machine instructions (e.g., program code) that implements one or more algorithmic steps. Such machine instructions may be the actual computer code the processor of organization computing system 104 interprets to implement the instructions or, alternatively, may be a higher level of coding of the instructions that is interpreted to obtain the actual computer code. The one or more software modules may also include one or more hardware components. One or more aspects of an example algorithm may be performed by the hardware components (e.g., circuitry) itself, rather as a result of the instructions.
Data store 118 may be configured to store one or more game files 124. Each game file 124 may include spatial event data and non-spatial event data. For example, spatial event data may correspond to raw data captured from a particular game or event by tracking system 102. Non-spatial event data may correspond to one or more variables describing the events occurring in a particular match without associated spatial information. For example, non-spatial event data may include play-by-play information for each match. In some embodiments, non-spatial event data may be derived from spatial event data. For example, pre-processing agent 116 may be configured to parse the spatial event data to derive play-by-play information. In some embodiments, non-spatial event data may be derived independently from spatial event data. For example, an administrator or entity associated with organization computing system may analyze each match to generate such non-spatial event data. As such, for purposes of this application, event data may correspond to spatial event data and non-spatial event data.
Pre-processing agent 116 may be configured to process data retrieved from data store 118. For example, pre-processing agent 116 may be configured to generate one or more sets of information that may be used to train one or more or more prediction models associated with team prediction agent 120. Pre-processing agent 116 may scan each of the one or more game files stored in data store 118 to identify one or more metrics corresponding to each player. For example, pre-processing agent 116 may scan each of the one or more game files in data store 118 to identify one or more plays in each game, and identify event and tracking data associated with each play. Tracking data may include the trajectory of each player involved in the play. Event data may include information surrounding the possession, play style, team identities, and the like.
Team prediction agent 120 may be configured to generate a prediction of whether a team is likely to execute a play or a variant of a given play. For example, team prediction agent 120 may be configured to analyze tracking data and event data corresponding to a given play, generate one or more variants of each play, and determine the likelihood of a team executing each variant of the play. In particular, the goal of team prediction agent 120 may be to identify the “style” and content” of a given play. Content of a given play may be referred to as the “what” of the play, independent of the exact specifics of how a team executes the play. In contrast, style may be referred to as the “how” of the play, which captures the various ways a given play can involve.
Team prediction agent 120 may include variational autoencoder 126 and neural network 128. Variational autoencoder 126 may be configured to generate one or more variants of a given play. For example, variational autoencoder 126 is a generative model configured to receive an input play, and then generate an arbitrary amount of variants of this play. Generally, variational autoencoder 126 may be able to generate infinitely many variants of a single play. As such, variational autoencoder 126 may be tasked with generating the one or more plays based on the “content” of the input play. Neural network 128 may be configured to determine a likelihood of a given team executing each input play, and the one or more variants thereof. In some embodiments, neural network 128 may be a feedforward network that produces a likelihood of a given variant being in a style of a given team. As such, neural network 128 may be tasked with identifying the “style” of a given play to determine whether that style fits with a particular team. Accordingly, variational autoencoder 126 and neural network 128 may work in conjunction to generate a prediction as to whether a team is likely to execute a play or some variant thereof.
Interface agent 130 may be configured to generate one or more graphical representations corresponding to the team prediction generated by team prediction agent 120. For example, interface agent 130 may be configured to generate one or more graphical user interfaces (GUIs) that include graphical representations of each prediction generated by team prediction agent 120. Exemplary GUIs are discussed below in conjunction with
Client device 108 may be in communication with organization computing system 104 via network 105. Client device 108 may be operated by a user. For example, client device 108 may be a mobile device, a tablet, a desktop computer, or any computing system having the capabilities described herein. Users may include, but are not limited to, individuals such as, for example, subscribers, clients, prospective clients, or customers of an entity associated with organization computing system 104, such as individuals who have obtained, will obtain, or may obtain a product, service, or consultation from an entity associated with organization computing system 104.
Client device 108 may include at least application 132. Application 132 may be representative of a web browser that allows access to a website or a stand-alone application. Client device 108 may access application 132 to access one or more functionalities of organization computing system 104. Client device 108 may communicate over network 105 to request a webpage, for example, from web client application server 114 of organization computing system 104. For example, client device 108 may be configured to execute application 132 to access content managed by web client application server 114. The content that is displayed to client device 108 may be transmitted from web client application server 114 to client device 108, and subsequently processed by application 132 for display through a graphical user interface (GUI) of client device 108.
Variational autoencoders are a type of deep generative model that are useful in image synthesis, handwriting generation, and speech. The one or more techniques herein may leverage the generative power of variational autoencoder 126 to generate all possible (or a subset thereof) variants of an observed play. For example, variational autoencoder 126 may be configured to generate the motions of all players on both teams and the ball simultaneously. For example, for soccer, variational autoencoder 126 may be configured to generate the trajectories of all twenty-three agents across a thirty second span. Generating the motion together, allows team prediction agent 120 to capture the full adversarial nature of continuous sports and all of its complex interactions.
As illustrate, variational autoencoder structure 200 may include an encoder 202, a variational latent layer 204, and a decoder 206. Encoder 202 may include one or more fully connected encoding layers. For example, encoder 202 may include three fully connected (dense) encoding layers. Encoder 202 may be configured to generate a latent representative space z based on the input provided thereto. Variational latent layer 204 may be configured to compress data passed by encoder 202. For example, variational latent layer 204 may have a dimension of 863 and may be configured to compress the data by 25%. Variational latent layer 204 may be configured to generate a sample, {circumflex over (z)}, of the latent representative space z. Decoder 206 may include one or more fully connected decoding layers. In some embodiments, each of the fully connected layers may use exponential linear unit (i.e., “elu”) activation.
As illustrated, model input may be represented by may represent tracking data for a given game. The set
of players and ball may be observed over the time [t0, tf] to have trajectories
={Xi[t
. For example, the trajectory of the ith player may be defined as Xi[t
The input, , may be provided to encoder 202. The last layer of encoder 202 may be provided to variational latent layer 204. Variational latent layer 204 may be configured to predict the mean, μz, and standard deviation, σz, of the latent variable distribution,
(μz, σz). Variational latent layer 204 may provide the distribution of the latent variable (e.g., {circumflex over (Z)}) to decoder 206. Decoder 206 may take the latent variable z and decode it to generate a set of predicted tracks,
, where tf is some time after tq.
In some embodiments, team prediction agent 120 may minimize the L2 loss (reference numeral “216”) of the generated sample and the input sample, i.e.:
LR=∥−
∥22
Such minimization may aid in checking whether the generated sample is of the same class as the input sample. Additionally, to capture the set of all plays in the family, in some embodiments, team prediction agent 120 may maximize the Evidence Lower Bound (ELBO) using a normal distribution as a prior, i.e., team prediction agent 120 may minimize the Kullback-Leibler (KL) divergence:
DKL((μz, σz)∥
(0.1))
To balance the effects of the two loss functions, in some embodiments, team prediction agent 120 may define the total loss (reference numeral “220”) as L=μDKL+LR. In some embodiments, team prediction agent 120 may train the prediction model using Adam optimizer.
as input (reference numeral 304) and may predict the team identity
of the first team listed in the input data set. In some embodiments, team classifier 302 may include one or more layers (e.g., four) with rectified linear unit (“relu”) activation and an output layer with softmax activations. In some embodiments, the input layer may use a tanh activation. In some embodiments, team prediction agent 120 may train the prediction model using an Adam optimizer to reduce (e.g., minimize) the cross-entropy loss (reference numeral 310) between a predicted team identity,
, and the actual team identity,
.
At step 402, organization computing system 104 may retrieve event data for a plurality of matches. For example, pre-processing agent 116 may retrieve tracking data from data store 118. Tracking data may capture every touch of the ball, with x, y coordinates and time stamps. Tracking data may also capture the x, y coordinates and time stamps associated with the ball.
At step 404, organization computing system 104 may generate one or more input data sets based on the event data. For example, pre-processing agent 116 may be configured to generate a plurality of inputs, each input representing a pre-determined duration of play during a match. For example, pre-processing agent 116 may parse the tracking data to generate one or more sets of trajectories, , where
represents the set of all players in the set. In some embodiments, for each input, pre-processing agent 116 may enrich the data. For example, pre-processing agent 116 may enrich the data with information surrounding one or more of the possession, playing style, and team identities,
. In some embodiments, the team identities may be one-hot encoded. In some embodiments, an input data set may represent a single possession. In some embodiments, an input data set may represent a span of multiple possessions. Still further, in some embodiments, pre-processing agent 116 may align the players on each team to a global template to reduce (e.g., eliminate) permutation noise.
At step 406, organization computing system 104 may learn, based on the one or more input data sets, a plurality of variants for each play. In other words, team prediction agent 120 may generate one or more variants associated with each input data set. For example, team prediction agent 120 may be configured to train variational autoencoder 126 using the one or more input data sets to generate one or more variants of each play. For example, given an input data set , variational autoencoder 126 may generate a plurality of variants. Each variant may be represented by
.
At step 408, organization computing system 104 may reduce any loss between the predicted values and the actual values. For example, as part of the training process, team prediction agent 120 may minimize the L2 loss (i.e., 216) of the generated sample and the input sample, i.e.: LR=∥−
∥22. Such minimization may aid in checking whether the generated sample is of the same class as the input sample. Additionally, to capture the set of all plays in the family, in some embodiments, team prediction agent 120 may maximize the Evidence Lower Bound (ELBO) using a normal distribution as a prior, i.e., team prediction agent 120 may minimize the Kullback-Leibler (KL) divergence, DKL(
(μz, σz) ∥
(0,1)) . To balance the effects of the two loss functions, in some embodiments, team prediction agent 120 may define the total loss (i.e., 220) as L=βDKL+LR. In some embodiments, team prediction agent 120 may train the prediction model using Adam optimizer.
At step 410, organization computing system 104 may learn, based on one or more input data sets, a team identity corresponding to each input data set. In other words, team prediction agent 120 may generate prediction of at least one team identity associated with each input data set. For example, team prediction agent 120 may be configured to train neural network 128 to predict one or more teams associated with each play based on, for example, one or more trajectory based features in the input data sets. For example, given an input data set , neural network 128 may generate a predicted team identity,
.
At step 412, organization computing system 104 may reduce any loss between the predicted values and the actual values. For example, as part of the training process, team prediction agent 120 may train the prediction model using an Adam optimizer to reduce (e.g., minimize) the cross-entropy loss between a predicted team identity, , and the actual team identity,
, associated with each play.
At step 502, organization computing system 104 may receive match data for a given match. For example, pre-processing agent 116 may receive tackle information for a given play in a particular match. In some embodiments, pre-processing agent 116 may receive one or more sets of tracking data. For example, pre-processing agent 116 may receive a set of tracking data corresponding to a given play.
At step 504, organization computing system 104 may extract, from the match data, one or more portions of data corresponding to a given play. In some embodiments, the set of tracking data may correspond to a single possession. In some embodiments, the set of tracking data may span several possessions. In some embodiments, pre-processing agent 116 may enrich the data. For example, pre-processing agent 116 may enrich the data with information surrounding one or more of the possession, playing style, and team identities, .
At step 506, organization computing system 104 may generate one or more variants associated with each play. For example, team prediction agent 120 may generate the one or more variants based on the tracking information associated with each play. Team prediction agent 120 may pass the tracking information through variational autoencoder 126. The output may represent one or more (e.g., a plurality) of variant plays based on the input play. In some embodiments, team prediction agent 120 may limit the number of variants produced by variational autoencoder 126. For example, team prediction agent 120 may limit the number of variants to 1000. Mathematically, variational autoencoder 126 may receive, as input, the set and generate, as output, one or more sets
.
At step 508, organization computing system 104 may predict the likelihood of a team executing each play. For example, team prediction agent 120 may predict at least one team corresponding the each play and variant generated in step 506. Team prediction agent 120 may generate such team prediction by providing neural network 128 with the tracking data corresponding to each play. For example, neural network 128 may receive, as input, the set and one or more sets,
, where
represents a play and each set,
, represents a variant thereof. As output, neural network 128 may generate a team identity,
, for each play. To determine the likelihood of a particular team executing a given play, represented by sets,
, team prediction agent 120 may identify how many variants with which each team is associated.
At step 510, organization computing system 104 may generate one or more graphical representations of the prediction. For example, interface agent 130 may generate one or more graphical representations trajectories of each play corresponding to a given variant and a team corresponding thereto. Exemplary graphical representations may be found below in conjunction with
As illustrated from each set of corresponding graphical elements, variational autoencoder 126 may maintain the content of each play, while changing the style. In the first row, a team begins on the left wing, passes back to the defense, and then advances down the right wing. In the input play (illustrated in graphical element 604a), Paris St. Germain (PSG) executes the play with more width, and the play advances much more quickly as compared to a variant thereof which corresponds to Guingamp (represented by graphical element 604b). Such analysis is consistent with objective viewings of the two teams, as PSG has superior wingers and crosses the ball more often compared to Guingamp.
In the second row, another example from PSG is shown. Variational autoencoder 126 maintains the content of each player. The input play (represented by graphical element 606a) include PSG winning the ball near the middle of the field, passing it back to the wing, back to the defense, and then quickly advancing the ball up the right wing. In the generated variant play (represented by graphical element 606b), Lille starts the ball from the farther left side of the field. Further, it is shown that Lille executes the play with a higher defensive line, attacks more centrally, and the opposite wing stays wider as compared to PSG.
In the last row, a counter-attack from Lyon is illustrated as the input play (represented by graphical element 608a). In the generated variant (represented by graphical element 608b), Dijon executes a similar counter-attack. However, Dijon attacks more centrally and directly than Lyon.
Generally,
Such methodologies allow team prediction agent 120 to support enhanced retrieval methods. For example, typical retrieval methods may be limited by two factors: visible data and a semantically-limit metric. In other words, conventional methods are only capable of finding similar plays that exist. Through the use of variational autoencoder 126, team prediction agent 120 may generate visualizations all stylistic variations of a particular play/content, even if those plays/contents have not yet been witnessed. Further, through the operations discussed herein, similarity may now be defined, not merely based on a purely spatial metric), but based on how similar the contents (e.g., is it generated by a given input) and styles (is it characteristic of a particular team).
By using variational autoencoder 126 and neural network 128, one can see how different teams would execute the same play. However, this does not mean that team prediction agent 120 can generate how every team would play in a given situation (i.e., input play), because not every team can or would execute that play or a variant thereof. For example, most teams may not counter-attack down the right after starting from the left, but Metz and Dijon might.
In some embodiments, for a given content, only a limited number of styles/teams may be generated, because not all teams can do all things. In other words, not all things can happen in a given situation. By using a variational autoencoder 126, team prediction agent 120 can perform an exhaustive search of the set of possible outcomes, rather than a single observed outcome.
As illustrated, for example, all teams in the analysis generate Montpellier. Such analysis may be the result of Montpellier acting similar to general soccer. Additionally, team similarity matrix 702 illustrates that Lille, Monaco, and Nice attempt the same plays as PSG very often, despite doing so in different styles. Team similarity matrix 702 further illustrates that no team tries to do what Etienne and Caen do. In other words, Etienne and Caen have unique content, and the only way to play in those situations is in the style of Etienne and Caen.
To enable user interaction with the system 800, an input device 845 may represent any number of input mechanisms, such as a microphone for speech, a touch-sensitive screen for gesture or graphical input, keyboard, mouse, motion input, speech and so forth. An output device 835 may also be one or more of a number of output mechanisms known to those of skill in the art. In some instances, multimodal systems may enable a user to provide multiple types of input to communicate with system 800. Communications interface 840 may generally govern and manage the user input and system output. There is no restriction on operating on any particular hardware arrangement and therefore the basic features here may easily be substituted for improved hardware or firmware arrangements as they are developed.
Storage device 830 may be a non-volatile memory and may be a hard disk or other types of computer readable media which may store data that are accessible by a computer, such as magnetic cassettes, flash memory cards, solid state memory devices, digital versatile disks, cartridges, random access memories (RAMs) 825, read only memory (ROM) 820, and hybrids thereof.
Storage device 830 may include services 832, 834, and 836 for controlling the processor 810. Other hardware or software modules are contemplated. Storage device 830 may be connected to system bus 805. In one aspect, a hardware module that performs a particular function may include the software component stored in a computer-readable medium in connection with the necessary hardware components, such as processor 810, bus 805, display 835, and so forth, to carry out the function.
Chipset 860 may also interface with one or more communication interfaces 890 that may have different physical interfaces. Such communication interfaces may include interfaces for wired and wireless local area networks, for broadband wireless networks, as well as personal area networks. Some applications of the methods for generating, displaying, and using the GUI disclosed herein may include receiving ordered datasets over the physical interface or be generated by the machine itself by processor 855 analyzing data stored in storage 870 or 875. Further, the machine may receive inputs from a user through user interface components 885 and execute appropriate functions, such as browsing functions by interpreting these inputs using processor 855.
It may be appreciated that example systems 800 and 850 may have more than one processor 810 or be part of a group or cluster of computing devices networked together to provide greater processing capability.
While the foregoing is directed to embodiments described herein, other and further embodiments may be devised without departing from the basic scope thereof. For example, aspects of the present disclosure may be implemented in hardware or software or a combination of hardware and software. One embodiment described herein may be implemented as a program product for use with a computer system. The program(s) of the program product define functions of the embodiments (including the methods described herein) and can be contained on a variety of computer-readable storage media. Illustrative computer-readable storage media include, but are not limited to: (i) non-writable storage media (e.g., read-only memory (ROM) devices within a computer, such as CD-ROM disks readably by a CD-ROM drive, flash memory, ROM chips, or any type of solid-state non-volatile memory) on which information is permanently stored; and (ii) writable storage media (e.g., floppy disks within a diskette drive or hard-disk drive or any type of solid state random-access memory) on which alterable information is stored. Such computer-readable storage media, when carrying computer-readable instructions that direct the functions of the disclosed embodiments, are embodiments of the present disclosure.
It will be appreciated to those skilled in the art that the preceding examples are exemplary and not limiting. It is intended that all permutations, enhancements, equivalents, and improvements thereto are apparent to those skilled in the art upon a reading of the specification and a study of the drawings are included within the true spirit and scope of the present disclosure. It is therefore intended that the following appended claims include all such modifications, permutations, and equivalents as fall within the true spirit and scope of these teachings.
This application claims priority to U.S. Provisional Application Ser. No. 62/844,874, filed May 8, 2019, which is incorporated herein by reference in its entirety.
| Number | Date | Country | |
|---|---|---|---|
| 62844874 | May 2019 | US |
