Detailed Description
Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. When the following description refers to the accompanying drawings, the same numbers in different drawings refer to the same or similar elements, unless otherwise indicated. The implementations described in the following exemplary examples do not represent all implementations consistent with the present specification. Rather, they are merely examples of apparatus and methods consistent with some aspects of the present description as detailed in the accompanying claims.
The terminology used in the description presented herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the description. As used in this specification and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and/or" as used herein refers to and encompasses any or all possible combinations of one or more of the associated listed items.
It should be understood that although the terms first, second, third, etc. may be used in this specification to describe various information, these information should not be limited to these terms. These terms are only used to distinguish one type of information from another. For example, the first information may also be referred to as second information, and similarly, the second information may also be referred to as first information, without departing from the scope of the present description. The term "if" as used herein may be interpreted as "at..once" or "when..once" or "in response to a determination", depending on the context.
The distribution service is widely applied to scenes such as online shopping, dining takeaway, leg running and substituted shopping. As shown in fig. 1A, a schematic diagram of a delivery scenario according to an exemplary embodiment of the present disclosure includes a business party, a delivery capacity, and a user. The server side is provided with a client side which is used for providing the user with the service provided by the server side, and the server side is also used for providing the store side with the client side which is used by the store side and is different from the client side which is used by the user, and the store side can use the service provided by the server side through the client side. Each user can trade with a shop party through a client, each trade order corresponds to a delivery waybill, and a service party can distribute delivery capacity for the delivery waybill, wherein the delivery capacity in the embodiment refers to a party with delivery capacity, and the party with delivery capacity comprises, but is not limited to, delivery personnel, such as commonly known riders, and the delivery capacity can be communicated with the service end through the client used for facing the delivery capacity; in other examples, the delivery capacity may also include unmanned delivery devices, such as unmanned robots, drones, and the like.
In some situations, a user pays attention to the state of a delivery service, for example, the delivery service in the situations such as food and drink takeaway, generally, the user initiates a trade order by using a client, the server generates a corresponding delivery freight list for the trade order, the delivery freight list relates to a delivery starting position and a delivery ending position designated by the user, the server dispatches delivery capacity according to freight list information, and the delivery capacity dispatches the goods required by the user from the delivery starting position to the delivery ending position. In some situations with high requirements on delivery timeliness, such as instant delivery service, users often pay more attention to the delivery state of the waybill after initiating the waybill.
As shown in fig. 1B, which is a schematic diagram of a time axis shown in the present specification according to an exemplary embodiment, in connection with fig. 1B, the delivery status of the delivery manifest refers to at least the following 4 concepts related to time:
(1) The service end estimates the time for delivering the delivery bill to the delivery end position appointed by the user based on a delivery start position and a delivery end position of the delivery bill, a delivery capacity position, the quantity of the delivery bill and other factors. For example, in fig. 1B, the delivery bill is generated at time a, and the estimated promised delivery time of the delivery bill by the server is N, and time N is subtracted from time a, i.e. the promised user duration.
(2) The actual delivery time length is the time length from the user ordering time to the actual delivery reaching the designated delivery end position, and the actual delivery reaching the designated delivery end position indicates that the delivery bill is delivered. In practical application, a delivery bill is faced with a plurality of variable factors in the delivery process of delivery capacity, such as weather, road congestion, prolonged meal delivery time or the influence of other delivery bills, etc., so that the actual delivery time may be different from the duration of the promised user, may be greater than or less than the duration of the promised user, and the situation that the actual delivery time is greater than the duration of the promised user is overtime. For example, in fig. 1B, the actual delivery time is greater than the promised delivery time, and the actual delivery time is M, and the actual delivery time is the actual delivery time, i.e., the actual delivery time, which is the time M minus the time a.
(3) The remaining delivery duration at the current moment, namely the duration between the actual final delivery moment and the current moment in the process of starting to finish delivery of a delivery bill. The current time is any time between time a and time M, for example, in fig. 1B, time O is the current time, the current time is time O, and the remaining delivery time of time O is M minus a.
(4) The remaining promised user duration at the current moment, namely the duration between the promised delivery moment and the current moment in the process of starting to finish delivery by one delivery bill. For example, in fig. 1B, the time O is the current time, the current time is the time O, and the remaining dispensing time length of the time O is N minus a.
In the process of incomplete delivery of the waybill, the actual delivery duration is unknown, so the residual delivery duration at the current moment is also unknown. However, there is a need for accurately estimating the remaining delivery duration at the current time during the incomplete delivery of the waybill in the actual business. For example, some users in the instant delivery scene pay more attention to the delivery state of the delivery bill, when the users consult the client, the client provides the delivery state page with real-time position information of the delivery capacity at the current moment, and the client can estimate and display the residual delivery duration at the current moment based on various practical factors, and optionally can estimate the overtime probability of the bill based on the residual delivery duration at the current moment. The user refers to the client at different times, and the remaining delivery duration and the timeout probability displayed by the client may be different.
On the other hand, the server side can also continuously estimate the remaining delivery duration and the overtime probability at the current moment in a plurality of moments in the delivery process of the delivery bill, so as to determine whether to execute other business processes.
For example, if the remaining delivery duration of the delivery waybill is shorter, the timeout probability is lower, which means that the delivery waybill can be completed in advance within the duration of the promised user, and other delivery waybills can be newly added for the delivery capacity based on the delivery waybill. Or the state of the delivery capacity can be determined in time, the reason of overtime of the delivery capacity is determined to ensure the delivery safety of the delivery capacity, and the like, or the user of the delivery capacity can be reminded, the anxiety of the user is relieved, the user experience is improved, and the like.
Therefore, in the process of delivering the delivery bill, whether the delivery bill overturns or not relates to two important pieces of information of the residual delivery duration and overtime probability at the current moment, and the method has important significance in accurately estimating the residual delivery duration and overtime probability at the current moment.
The method comprises the steps of obtaining the time-out probability of the current time, wherein the time-out probability is estimated by a machine learning model, and the time-out probability is not accurate enough because the time-out probability is estimated by taking the time-out probability as the time-out probability.
The other processing thought is to respectively estimate the residual delivery duration at the current moment and the overtime probability at the current moment by using two machine learning models, but the scheme needs to maintain the two models, and the residual delivery duration at the current moment and the overtime probability at the current moment are correlated, so that the training data of the two models are required to be completely consistent, and if the training data of the two models are inconsistent, the output results of the two models may not be consistent.
According to the analysis, the overtime estimation of the delivery bill relates to a plurality of pieces of information including the actual delivery duration, the residual delivery duration at the current moment and the residual promised user duration at the current moment, so that the overtime estimation is accurately carried out, the maintenance of a model is convenient, and the like, and the overtime estimation is a technical problem to be solved urgently.
Based on this, the embodiment of the present disclosure provides a method for estimating timeout of a delivery waybill, as shown in fig. 2A, fig. 2A is a flowchart of a method for processing information of a delivery waybill according to an exemplary embodiment of the present disclosure, including the following steps:
In step 202, obtaining the waybill information of the delivery waybill in the current time at the current delivery state;
in step 204, the waybill information of the current time is input into a machine learning model, and the average value and the variance of the residual delivery duration of the current time predicted by the machine learning model are obtained;
the machine learning model is obtained by training according to normal distribution based on the residual distribution duration at the current moment.
In step 206, determining a normal distribution of the residual delivery duration at the current time according to the predicted residual delivery duration mean and residual duration variance at the current time;
in step 208, the remaining duration of the promised user at the current time is obtained, and the overtime probability of the distribution waybill at the current time is determined by using the normal distribution.
The training process of the machine learning model can be that a model is represented through modeling, then an evaluation function is constructed to evaluate the model, finally the evaluation function is optimized according to sample data and an optimization method, and the model is adjusted to meet set conditions.
As described above, in the field of machine learning, a very large number of links are involved from modeling to training, such as selection and processing of sample data, design of data features, design of models, design of loss functions or design of optimization methods, and the like, and nuances of any link are factors that cause fine defects in prediction accuracy.
The embodiment designs a machine learning model which is obtained by training according to normal distribution based on the residual distribution duration at the current moment.
If the random variable x obeys a normal distribution with a mathematical expectation μ and variance σ2, it is denoted as N (μ, σ2). That is, the probability density function y is a normal distribution, its expected value μ determines the position of the distribution, and its variance σ determines the magnitude of the distribution. The normal distribution when μ=0, σ=1 is a standard normal distribution.
The expected value μ, i.e. the mean value, is the center of the normal distribution curve, determining the position of the curve peak. The width of the normal distribution curve is determined by the variance σ, which represents the normal distribution variability, and variations in variance cause the curve to become narrower or wider and have an inverse proportional effect on the height of the curve. Thus, the mean and variance are determined, i.e., the corresponding normal distribution curve can be determined.
The probability of a random variable X in a certain interval, such as interval (a, b), i.e. the probability of a < X < b, is the area of the probability density curve under this interval, and the mathematical expression is the integral of the probability density function over interval (a, b). Therefore, the size of the probability is the size of the "area under the probability density function curve".
By way of example, a normal distribution utilization formula may be expressed as:
in this embodiment, it is designed that the remaining distribution duration at the current time is assumed to follow normal distribution, that is, the remaining distribution duration at the current time is taken as a random variable value x of a normal distribution curve, and if the mean value and variance of the remaining distribution duration at the current time can be estimated, the probability of x in different intervals can be calculated according to a normal distribution formula and an integral. Based on the above, the embodiment designs that the output of the machine learning model is two information of the average value of the residual delivery time length at the current moment and the variance of the residual delivery time length at the current moment, so that the normal distribution of the overtime probability of the residual delivery time length can be determined, and then the probability of the residual delivery time length in different intervals is calculated according to a normal distribution formula and integral.
The training data may be obtained by using data of historical delivery orders of a plurality of delivery capacities, for example, in case of authorization approval of a user, the server may obtain data sent by a client used by the delivery capacity, the client may continuously collect the information of the delivery orders according to a set period, and the information of the delivery orders may include geographical location information of the delivery capacity at the time of collection, traffic information of the location, the number of delivery orders received by the delivery capacity, picking status information of delivery articles of each delivery order received by the delivery capacity (for example, whether articles have been picked up, etc.), attribute information of picking up articles of each delivery order received by the delivery capacity (for example, size, weight, type, etc. of the articles), or historical delivery information of the delivery capacity (for example, historical delivery efficiency, time-out number information, time-out proportion information, or delivery speed information of the delivery capacity, etc.).
For example, for data of a historical delivery bill, a time interval may be set to determine a plurality of samples, where the time interval may be flexibly determined according to needs, for example, a custom time of one minute, two minutes, or five minutes, etc. Therefore, a plurality of samples can be obtained from the data of each historical delivery bill, each sample corresponds to a historical moment, and the remaining delivery duration of the historical moment can be used as the label value of the sample.
Another important aspect of the training process is the need to design a suitable evaluation function according to business requirements. In the scene of supervised model training, the sample data is marked with a true value, and an evaluation function is used for measuring the error between the predicted value and the true value of the model. The evaluation function is crucial to the identification accuracy of the model, and it is difficult to design what kind of evaluation function based on the existing sample data and the requirements of the model.
In solving for model parameters, maximum likelihood estimation is often used to solve, i.e., find a set of parameters such that the likelihood (probability) of the data is maximized under the set of parameters. The present embodiment designs that the remaining distribution duration at the current time obeys a normal distribution, and based on the normal distribution, it can be determined that it obtains its maximum likelihood estimation function, as an example:
therefore, the present embodiment designs an evaluation function of a model based on this, as an example:
The pred_y is a mean value of the residual delivery duration of the current time estimated by the model, pred_std is a variance of the residual delivery duration of the current time estimated by the model, namely, two parameters of the mean value and the variance of normal distribution are estimated in the evaluation function at the same time, label is a label value, and a true value of the label is the residual delivery duration of the current time in the sample.
That is, the optimization objective of the evaluation function in the model of the present embodiment is two parameters of normal distribution, namely, the average value of the remaining delivery duration at the present time and the variance of the remaining delivery duration at the present time.
The specific formula of the evaluation function is only schematic, the specific mathematical description of the function can be flexibly configured according to the needs in practical application, whether regularization terms are added or not can be determined according to the needs, and the embodiment is not limited to the specific mathematical description.
Fig. 2B is a schematic diagram showing a normal distribution of the remaining delivery duration at the current time according to an exemplary embodiment of the present disclosure, where in fig. 2B, the average value of the remaining delivery durations at the current time is 10min (minutes), and the variance of the remaining delivery duration at the current time is 2min, which is illustrated as an example, and the remaining user promised duration at the current time of the delivery bill is 16min. In the estimated normal distribution, the true value label appears in different intervals with different probabilities in the normal distribution. When the label is longer than the remaining committed user time, the delivery manifest times out. For example, in fig. 2B, the remaining committed user duration at the current time is 16min, and the time after x=16 indicates the time when the delivery schedule is overtime. Therefore, the shadow area after the dotted line where x=16 is located can be integrated to obtain the overtime probability of the distribution waybill under the current estimated normal distribution, and an exemplary normal distribution integration formula is as follows:
Where P represents the timeout probability of x.
For example, the machine learning model of the present embodiment may be a neural network model, such as the deep learning model DeepFM, and may be flexibly determined according to needs in practical application, which is not limited in this embodiment.
Through the embodiment, a machine learning model can be obtained through training. In practical application, the trained machine learning model can be set in the client or the server. When the machine learning model is used on line, the model can be called for each delivery bill which is not delivered and is delivered in delivery capacity, and the residual delivery duration and the overtime probability at each moment can be predicted.
The method comprises the steps of obtaining the waybill information of the current delivery waybill in the delivery state at the current moment, wherein the waybill information can comprise geographical position information of the delivery capacity, traffic information of the position of the delivery capacity, the number of delivery waybills received by the delivery capacity, picking state information of delivery articles of each delivery waybill received by the delivery capacity, attribute information of delivery articles of each delivery waybill received by the delivery capacity or historical delivery information of the delivery capacity, as in the previous embodiment.
The input of the machine learning model is the waybill information at the current moment, the model predicts the average value and the variance of the residual delivery duration at the current moment based on the waybill information at the current moment, and the normal distribution of the residual delivery duration at the current moment can be determined through the average value and the variance. And determining the overtime probability of the delivery bill at the current moment according to the remaining promised duration at the current moment and the normal distribution. For example, as in the foregoing embodiment, the area size after the remaining promised time at the current time is calculated using the normal distribution integral formula, that is, the integral that the x value is greater than the remaining promised time at the current time is calculated, and the obtained value is the timeout probability at the current time.
In practical application, the scheme of the embodiment can be used for multiple times as required in the distribution process of the distribution menu, for example, the residual distribution duration and the overtime probability at each moment are predicted at multiple different moments.
Therefore, the embodiment designs a machine learning model which is trained by the normal distribution of the residual delivery duration at the current moment, designs the output of the machine learning model as the average value and the variance of the residual delivery duration at the current moment, and can determine the normal distribution curve of the residual delivery duration at the current moment by utilizing the estimated information of the two models based on the average value and the variance of the residual delivery duration at the current moment, and determines the overtime probability of the delivery bill at the current moment by utilizing the normal distribution in combination with the residual promised user duration at the current moment. In the embodiment, by adopting the design that the residual distribution duration at the current moment is subjected to normal distribution, the two pieces of information are associated, and one model simultaneously predicts the two pieces of associated information, so that the training difficulty and the maintenance difficulty of the model are obviously reduced, and the prediction accuracy of the model is also ensured.
And the method also designs to determine the timeout probability by using normal distribution based on two pieces of information output by the model, and can obtain the accurate timeout probability due to the accurate output of the model. In addition, the embodiment utilizes the model to estimate the distribution of the data, so that not only can the estimated value of the true value be obtained, but also the overtime probability can be calculated according to the distribution, and the universality is improved.
According to the method, the predicted value of the residual delivery duration is obtained by predicting the distribution of the shipping bill in the delivery process, the timeout rate of the current shipping bill is also obtained, the scheme is simple and convenient to implement, and the effect is greatly simplified and improved. The normal distribution is obtained through the mean and the variance, so that other various parameters can be calculated according to a distributed mathematical formula, the universality of the scheme of the embodiment is improved, and the maintenance and the iteration are convenient.
By using the information processing method of the delivery bill of the embodiment, after the residual delivery duration of the current moment estimated by the model is obtained and the overtime probability is estimated, the residual waiting duration can be displayed to the user through the client, and whether the overtime early warning process is triggered or not can also be determined according to the overtime probability, for example, if the overtime probability is higher, the reason of the current overtime can be pushed to the user, or rights and interests are issued to the user, so that the user experience is improved. Or the estimated information can be provided to the waybill scheduling system, so that the waybill scheduling can refer to the estimated information to allocate the delivery capacity for the to-be-allocated delivery waybill.
Taking the take-out scenario as an example, the service end can be configured with a waybill scheduling system, and the waybill scheduling system can judge a waybill (namely a back bill) which is responsible for delivery by a rider and the waybill which is to be scheduled and assigned to the rider in the process of the waybill scheduling assignment, for example, when the overtime risk of the current back bill of the rider is higher, and when the overtime risk of the waybill in the delivery stage is also higher, the algorithm for scheduling the assigned waybill can pertinently adjust the scheduling assignment of the waybill, so that the proportion of the whole overtime waybill is reduced. However, when the schedule system judges overtime risks of the waybills, if the overtime risks are estimated inaccurately, the schedule assignment of the whole waybill schedule chain is unstable, so that the efficiency of the schedule system is reduced, and the waybill assignment is inaccurate. By utilizing the scheme of the embodiment, the accurate overtime probability can be estimated, so that the dispatching accuracy of the waybill dispatching system can be improved, and the stable operation of the whole waybill dispatching chain is ensured.
Corresponding to the foregoing embodiments of the information processing method of the delivery manifest, the present specification also provides embodiments of the information processing apparatus of the delivery manifest and a computer device to which the information processing apparatus is applied.
The embodiment of the information processing apparatus for shipping notes of the present specification can be applied to a computer device such as a server or a terminal device. The apparatus embodiments may be implemented by software, or may be implemented by hardware or a combination of hardware and software. Taking software implementation as an example, the device in a logic sense is formed by reading corresponding computer program instructions in the nonvolatile memory into the memory through a processor of the file processing where the device is located. In terms of hardware, as shown in fig. 3, a hardware structure diagram of a computer device where an information processing apparatus for shipping a manifest of the present disclosure is located is shown in fig. 3, and in addition to a processor 310, a memory 330, a network interface 320, and a nonvolatile memory 340, a computer device where an information processing apparatus 331 for shipping a manifest of the present embodiment is located may include other hardware according to an actual function of the computer device, which is not described herein.
As shown in fig. 4, fig. 4 is a block diagram of an information processing apparatus of a distribution menu, which is illustrated in the present specification according to an exemplary embodiment, the apparatus comprising:
the waybill information acquisition module 41 is used for acquiring the waybill information of the distribution waybill in the current distribution state at the current moment;
The model prediction module 42 is configured to input the waybill information at the current time into a machine learning model, and obtain a mean value of the remaining delivery duration and a variance of the remaining delivery duration at the current time predicted by the machine learning model, where the machine learning model is obtained by performing normal distribution training based on the remaining delivery duration at the current time;
a normal distribution determining module 43, configured to determine a normal distribution of the remaining distribution duration at the current time according to the predicted average value and variance of the remaining distribution duration at the current time;
And the timeout determining module 44 is configured to obtain the remaining duration of the promised user at the current time, and determine the timeout probability of the delivery waybill at the current time by using the normal distribution.
In some examples, the machine learning model is trained, and the optimization objective of the evaluation function comprises the difference between the average value of the residual delivery duration and the variance of the residual delivery duration of the current moment estimated by the machine learning model on the delivery bill sample and the residual delivery duration serving as a true value in the delivery bill sample.
In some examples, the determining the timeout probability for the delivery manifest at the current time using the normal distribution includes:
And calculating the area of a horizontal axis interval of the curve of the normal distribution after the residual promise duration of the current moment to obtain the overtime probability.
In some examples, the training data of the machine learning model includes historical delivery waybill data including a committed user duration of the historical delivery waybill, an actual delivery duration, and waybill information of the historical delivery waybill, wherein the historical delivery waybill data includes a plurality of samples determined at set time intervals.
In some examples, the waybill information includes one or more of the following:
Geographical location information of the delivery capacity, traffic information of the position of the delivery capacity, the number of delivery orders received by the delivery capacity, picking state information of delivery articles of each delivery order received by the delivery capacity, attribute information of delivery articles of each delivery order received by the delivery capacity or historical delivery information of the delivery capacity.
In some examples, the method further comprises one or more of the following steps:
displaying the average value of the residual delivery duration at the current moment predicted by the machine learning model and the overtime probability of the delivery waybill to a user;
Determining whether to trigger execution of a preset overtime early warning process according to the overtime probability or not,
And determining other information of the delivery waybill at the current moment according to the normal distribution of the residual delivery duration at the current moment.
The implementation process of the functions and roles of each module in the information processing device of the delivery bill is specifically detailed in the implementation process of the corresponding steps in the information processing method of the delivery bill, and is not described herein again.
Accordingly, embodiments of the present disclosure also provide a computer program product, including a computer program, which when executed by a processor implements the steps of the foregoing embodiments of the information processing method for a shipping manifest.
Accordingly, the embodiments of the present disclosure further provide a computer device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, where the processor implements the steps of the information processing method embodiment of the distribution manifest when the processor executes the program.
Accordingly, the present embodiments also provide a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the information processing method embodiments of a shipping manifest.
For the device embodiments, reference is made to the description of the method embodiments for the relevant points, since they essentially correspond to the method embodiments. The apparatus embodiments described above are merely illustrative, wherein the modules illustrated as separate components may or may not be physically separate, and the components shown as modules may or may not be physical, i.e., may be located in one place, or may be distributed over a plurality of network modules. Some or all of the modules may be selected according to actual needs to achieve the purposes of the present description. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
The method of the present embodiment may be applied to one or more electronic devices, which are devices capable of automatically performing numerical calculation and/or information processing according to instructions set or stored in advance, and the hardware of the electronic devices includes, but is not limited to, microprocessors, application SPECIFIC INTEGRATED Circuits (ASICs), programmable gate arrays (Field-Programmable GATE ARRAY, FPGA), digital processors (DIGITAL SIGNAL processors, DSPs), embedded devices, and the like.
The electronic device may be any electronic product that can interact with a user in a human-computer manner, such as a Personal computer, a tablet computer, a smart phone, a Personal digital assistant (Personal DIGITAL ASSISTANT, PDA), a game console, an interactive internet protocol television (Internet Protocol Television, IPTV), a smart wearable device, etc.
The electronic device may also include a network device and/or a user device. Wherein the network device includes, but is not limited to, a single network server, a server group composed of a plurality of network servers, or a Cloud based Cloud Computing (Cloud Computing) composed of a large number of hosts or network servers.
The network in which the electronic device is located includes, but is not limited to, the internet, a wide area network, a metropolitan area network, a local area network, a virtual private network (Virtual Private Network, VPN), and the like.
The foregoing describes specific embodiments of the present disclosure. Other embodiments are within the scope of the following claims. In some cases, the actions or steps recited in the claims can be performed in a different order than in the embodiments and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.
The above steps of the methods are divided, for clarity of description, and may be combined into one step or split into multiple steps when implemented, so long as they include the same logic relationship, and all the steps are within the scope of protection of the present patent, and adding insignificant modification to the algorithm or the process or introducing insignificant design, but not changing the core design of the algorithm and the process, and all the steps are within the scope of protection of the present application.
Where a description of "a specific example", or "some examples", etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present description. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Other embodiments of the present description will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. This specification is intended to cover any variations, uses, or adaptations of the specification following, in general, the principles of the specification and including such departures from the present disclosure as come within known or customary practice within the art to which the specification pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the specification being indicated by the following claims.
It is to be understood that the present description is not limited to the precise arrangements and instrumentalities shown in the drawings, which have been described above, and that various modifications and changes may be made without departing from the scope thereof. The scope of the present description is limited only by the appended claims.
The foregoing description of the preferred embodiments is provided for the purpose of illustration only, and is not intended to limit the scope of the disclosure, since any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the disclosure are intended to be included within the scope of the disclosure.