Patent Publication Number: US-11640639-B2

Title: Systems and methods for allocating fractional shares of a public offering

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of priority to U.S. Provisional Application No. 63/183,948, filed May 4, 2021, the contents and disclosure of which are incorporated herein by reference in their entirety. 
    
    
     BACKGROUND 
     The field of the disclosure relates generally to allocation of assets in an offering, and more specifically, to systems and methods for allocating fractional shares of the offering to individual participants. 
     Business entities undertake offerings of assets, such as initial public offerings (IPOs) and secondary offerings, to raise capital. Traditionally such offerings were targeted almost exclusively to large institutions (e.g., banks, insurance companies, hedge funds, and mutual funds) which have the resources to purchase blocks of shares. More recently, business entities engaged in IPOs and secondary offerings have found it worthwhile to include individual investors who engage in certain investing behaviors, such as holding assets acquired in an IPO over a long period of time, so as to reduce volatility in the price of the assets. Systems and methods for identifying such individual investors and integrating them as a group into the offering alongside the traditional investing institutions are disclosed, for example, in U.S. patent application Ser. No. 16/253,657 entitled SYSTEM AND METHOD FOR QUANTIFIABLE CATEGORIZATION OF CANDIDATES FOR ASSET ALLOCATION, filed on Jan. 22, 2019 and assigned to the applicant of the instant application, which is incorporated by reference herein in its entirety. 
     Given share price levels in many current offerings, some such individual investors operate with resources that correspond to the price of just a few shares. Because such investors are conventionally limited to purchasing whole shares, the potential participation of each investor is limited to just a few discrete levels (e.g., the purchase of one, two, three, or four shares). These discrete levels impose constraints upon any attempt to optimize the allocation of shares among such investors based on predicted investor behavior. For a simplified example, if investor A is strongly associated with a preferred behavior for a current offering, has more than sufficient resources to purchase three shares, but has insufficient resources to purchase four shares, it may be that the best predicted outcome for the business entity offering the assets would occur if investor A received 3.6 shares, rather than being limited to three shares. These effects aggregated across a large number of individual investors can become significant to the after-market performance of the offered shares. However, known processes for initial public offerings (IPOs) and secondary offerings cannot accommodate issuance of fractional shares. Although fractional shares trading is proposed for internal trades in the after-market within a small number of online broker-dealers, capital-raising asset offerings require a unit share to be the smallest individually acquirable asset, to enable the shares to subsequently trade within any exchange. Incorporating the potential for fractional shares into an initial allocation of assets presents a complex problem in view of the traditional unit share offering infrastructure. 
     Moreover, any rigorous evaluation of the utility of distributing shares of an asset offering in a particular distribution among hundreds, thousands, or even millions of interested individual investors must depend heavily on large data sets and factors specific to each particular offering, and poses problems of computational tractability. 
     It is therefore desirable for a computing device to be capable of allocating fractional shares in an asset offering in an integrated process that provides measurable utility to the offering entity, and is also computationally tractable. 
     BRIEF DESCRIPTION 
     In one aspect, a share allocation (SA) computing device is provided. The SA computing device includes at least one processor in communication with a database. The at least one processor is configured to execute a computational model including a plurality of model layers arranged in a sequence. The plurality of model layers includes a fractional node layer configured to assign each candidate investor of a plurality of candidate investors to a corresponding node. Each node is associated with a weight, and the nodes define an interconnected neural network. The fractional node layer is also configured to apply a machine learning algorithm configured to adjust the weights of the nodes in response to respective fitness values input to the nodes, and convert the adjusted weight for each node into a corresponding fraction. The fractional node layer is further configured to allocate, to each candidate investor, a respective fractional share of an offering, the fractional share corresponding to the fraction associated with the corresponding node. 
     In another aspect, a computer-implemented method is provided. The computer-implemented method is implemented by a share allocation (SA) computing device including at least one processor in communication with a database. The method includes executing, by the at least one processor, a computational model including a plurality of model layers arranged in a sequence. The plurality of model layers includes a fractional node layer. The method also includes assigning, by the fractional node layer, each candidate investor of a plurality of candidate investors to a corresponding node. Each node is associated with a weight, and the nodes define an interconnected neural network. The method further includes applying, by the fractional node layer, a machine learning algorithm configured to adjust the weights of the nodes in response to respective fitness values input to the nodes, and converting, by the fractional node layer, the adjusted weight for each node into a corresponding fraction. Additionally, the method includes allocating, to each candidate investor, a respective fractional share of an offering, the fractional share corresponding to the fraction associated with the corresponding node. 
     In yet another aspect, at least one non-transitory computer-readable storage media having computer-executable instructions embodied thereon is provided. When executed by a share allocation (SA) computing device having at least one processor in communication with a database, the computer-executable instructions cause the at least one processor to execute a computational model including a plurality of model layers arranged in a sequence, the plurality of model layers including a fractional node layer. The computer-executable instructions also cause the at least one processor to assign, by the fractional node layer, each candidate investor of a plurality of candidate investors to a corresponding node. Each node is associated with a weight, and the nodes define an interconnected neural network. The computer-executable instructions further cause the at least one processor to apply, by the fractional node layer, a machine learning algorithm configured to adjust the weights of the nodes in response to respective fitness values input to the nodes, and convert, by the fractional node layer, the adjusted weight for each node into a corresponding fraction. Additionally, the computer-executable instructions cause the at least one processor to allocate, by the fractional node layer to each candidate investor, a respective fractional share of an offering, the fractional share corresponding to the fraction associated with the corresponding node. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a schematic diagram of an example computer-implemented public asset offering illustrating an example share allocation computing device in communication with investor computing devices, broker-dealer computing devices, and an issuer computing device. 
         FIG.  2    is a schematic data flow diagram illustrating an example of a computational model executed by the share allocation computing device shown in  FIG.  1   . 
         FIG.  3    is a schematic block diagram illustrating an example isolated node layer that may be implemented as one of the plurality of computational layers shown in  FIG.  2   . 
         FIG.  4    is a schematic block diagram illustrating an example fractional node layer that may be implemented as one of the plurality of computational layers shown in  FIG.  2   . 
         FIG.  5    is an example configuration of a client system that may be used to implement the investor computing devices, broker-dealer computing devices, and/or issuer computing device shown in  FIG.  1    in accordance with embodiments of the present disclosure. 
         FIG.  6    is an example configuration of a server system that may be used to implement the share allocation computing device shown in  FIG.  1    in accordance with embodiments of the present disclosure. 
         FIG.  7 A  is a portion of a flow diagram illustrating an example process that may be implemented by the share allocation computing device shown in  FIG.  1   . 
         FIG.  7 B  is a second portion of the flow diagram of  FIG.  7 A . 
         FIG.  7 C  is a third portion of the flow diagram of  FIGS.  7 A and  7 B . 
     
    
    
     DETAILED DESCRIPTION 
     The following detailed description illustrates embodiments of the disclosure by way of example and not by way of limitation. The description enables one skilled in the art to make and use the disclosure, and describes several embodiments, adaptations, variations, alternatives, and uses of the disclosure, including what is presently believed to be the best mode of carrying out the disclosure. The disclosure is described as applied to an example embodiment, namely, systems and methods for allocating assets in a public offering, such as but not limited to an initial public offering (IPO) of shares in a company. The system described herein includes at least one share allocation (SA) computing device that allocates assets in a public offering. The SA computing device may be in communication with at least one broker-dealer computing device, a large number of investor computing devices, and at least one issuer computing device. In particular, while institutional investors, which represent aggregations of individuals (e.g., pension funds, publicly owned institutions) and are typically in a position to purchase relatively large blocks of shares, may participate in the offering by receiving communications directly from an issuer of the shares in a conventional fashion, the SA computing device is in communication with individual investors (e.g., individual human beings or small businesses), who typically are not in a position to purchase large blocks of shares and are not, by themselves, involved directly with the issuer of the shares. The SA computing device aggregates offers to buy from candidate individual investors, determines which candidate investors have desirable characteristics (e.g., an inclination to hold shares purchased in the offering for a long period of time, which reduces a volatility of the share price after the offering is completed) to the business entity offering the shares, and submits an aggregate offer to buy on behalf of the individual investors on a scale competitive with the institutional investors. 
     The SA computing device includes at least one processor in communication with a memory. The SA computing device is further in communication with at least one database for storing information, such as historical investor data for a plurality of candidate individual investors. In the example embodiment, the SA computing device utilizes the historical investor data, along with data associated with the particular offering under consideration, to predict which candidate individual investors will provide the most value to the business entity making the offering. The SA computing device applies a multi-level model to allocate shares of the offering among individual investors. In particular, given that the available resources of each candidate individual investor may enable the purchase of only a small number (e.g., three, five, or seven) of shares, the ability to optimize the allocation of solely whole values of shares to these individuals would be severely constrained. In other words, there is little flexibility to optimize when selecting from among solely a few discrete allocation values for each worthy candidate investor. The SA computing device removes this constraint from the optimization problem by optimizing to fractions of a share for each individual investor. 
     Moreover, an optimization process that relies solely on exhibited attributes or notional attributes of the candidate investors and the offering under consideration is unlikely to approach the best achievable result in actual practice. Rather, it is the case that hidden or latent knowledge within the input data set, to the extent it can be uncovered in a computationally practical fashion, leads to a better prediction of which candidate investors, and which corresponding share amounts allocated per investor, will provide the highest achievable benefit to the business entity offering the shares. However, exposing and utilizing this hidden or latent knowledge is a quite complex computational processing challenge, particularly when requests to participate are received from a large number of individual investors. The SA computing device solves this computational challenge by applying a sequence of model layers. More specifically, each layer provides an increasingly beneficial (in terms of performance desired by the business entity and the issuer) output for the allocation of shares to the candidate investors, and one or more layers (after the first) operate primarily on the output of the previous upstream layer, which reduces computational complexity by reducing a need to operate on full model state information passed from layer to layer. In addition, a downstream layer provides relative optimization at a scale of fractions of a share allocated to worthy candidate investors, which improves results relative to conventional processes which can only allocate assets in multiples of whole shares. The system disclosed herein thus enables the solution of a computationally complex problem by applying different types of models in a layered approach, maintaining the processing load for each layer at a tractable level even when exceedingly large data sets must be processed. 
     The historical investor data may include data fields relating to past investment activity of the plurality of individual investors conducted through channels external to the SA computing device (e.g., through their associated broker-dealers). For example, such “external” historical investor data may include one or more of: average number of days holding an asset at peak value, average number of days holding an asset of a particular asset classification, percentage of the aftermarket accumulation of a particular asset, number of transactions per year, and/or average size of transaction per buying power at the time of the transaction. Historical investor data may also include data relating to previous investment activity with respect to public offerings previously offered through the SA computing device, referred to as “internal” historical investor data. For example, such internal historical investor data may include one or more of: the fraction of assets actually purchased relative to the amount of assets the investor indicated a willingness to purchase at the candidate stage, the number of days the previous offering was held divided by a threshold number of days, a percentage of social share by the investor, and/or size of the order with respect to buying power. The threshold number of days is selected as a threshold time period for holding the assets that is associated with stability of the asset price after the offering. The percentage of social share by the investor is a percentage of offerings previously offered to the investor through the SA computing device for which the investor has electronically shared information regarding the offering (e.g., by sharing that the investor has made an investment via a social media platform). 
     In some embodiments, historical investor data may include indications of a specific classification of industry to which the asset offering was related (e.g., defense, energy, or technology). Thus, the layered model may accurately predict, for an asset offering of a particular classification, the behavior of the investor with respect to the particular asset offering (e.g., how long the investor will hold assets acquired in the offering). Consequently, the output of the model may be trusted by issuers in a new asset offering to indicate the desirability in allocating assets to particular individual investors in the environment and to the aggregate of individual investors in the environment based on the industry to which the new asset offering is related. 
     In the example embodiment, the SA computing device is further configured to transmit notices of an asset offering to the plurality of individual investors in the environment. The notices of the asset offering may be transmitted to each of the plurality of investors in the environment, or to a subset of the plurality of investors (e.g., investors identified as viable candidates with respect to the particular offering in a pre-processing step). In the example embodiment, the SA computing device is further configured to receive responses from these candidate investors indicating a degree of investor willingness to take part in the offering. The responses may include, for example, a statement of an amount the candidate investor is willing to invest in the offering. Because the SA computing device is in communication with the broker-dealer associated with each investor, the SA computing device can determine whether each candidate investor is capable of investing the amount stated by the investor and decline to consider offers where the candidate investor is not capable of investing the stated amount (e.g., when the investor lacks adequate funds). Moreover, certain data associated with a timing of a candidate investor&#39;s response may be used as input data with respect to one or more layers of the model. For example, an offering may be open over a ten-day window, and the relative timing of each offer to participate from a candidate investor is used as an input to one or more layers of the model. 
     In the example embodiment, the SA computing device is further configured to determine a total amount of assets available to allocate to individual investors indicating a willingness to invest in the public offering. The SA computing device may generate and transmit an offer to the issuer including a number of responses received from individual candidate investors indicating a willingness to take part in the offering, an aggregate amount of funds stated by the candidate investors indicating a willingness to take part in the offering, and an indicator of an aggregate expected performance (e.g., an indication of how long the candidate investors can be expected to hold the assets, on a per-investor and/or statistical distribution basis) for the candidate individual investors indicating a willingness to take part in the offering. In response, the SA computing device may receive from the issuer an amount of available assets that are available for allocation to the plurality of individual investors. The issuer, in determining the amount of assets to offer via the SA computing device, may utilize the asset distribution computed by the model for each of the plurality of candidate individual investors willing to take part in the offering. For example, the issuer may be offering shares of a technology corporation in an IPO. If the model for the individual investors willing to take part in the IPO indicates that the individual investors are likely to purchase and hold technology stock over a long period of time, the issuer may decide a greater amount should be allocated via the SA computing device because the investors are likely to engage in investing behavior favorable to the technology corporation (e.g., by holding the acquired technology corporation stock over a long period of time). 
     In the example embodiment, the SA computing device is further configured to allocate the available assets to the candidate individual investors based on the allocation determined by the model. The SA computing device may normalize the model allocation such that the sum of the normalized shares allocated to the candidate investors equals the total amount of assets to be allocated to candidate individual investors. The SA computing device may allocate the available assets so that each of the candidate individual investors taking part in the offering receives an allocation correlating to the allocation produced by the model for the individual investor. 
     The technical problems addressed by the disclosure include at least one of: (i) inability of computer-implemented asset offering systems to sell fractional shares of an asset offering; (ii) inability of algorithms to effectively optimize a distribution of assets among a large number of recipients due to the constraint that only a few discrete levels of whole shares may be allocated to some recipients; and (iii) intractability of the computational problem of predicting and evaluating the comparative utility, to an issuer of the assets, of different distribution amounts across a large number of recipients. 
     The technical effects achieved by the systems and methods described herein include at least one of: (i) executing a computational model including a plurality of model layers arranged in a sequence; (ii) assigning, by a fractional node layer, each candidate investor of a plurality of candidate investors to a corresponding node, wherein each node is associated with a weight, and wherein the nodes define an interconnected neural network; (iii) applying, by the fractional node layer, a machine learning algorithm configured to adjust the weights of the nodes in response to respective fitness values input to the nodes; (iv) converting, by the fractional node layer, the adjusted weight for each node into a corresponding fraction; (v) allocating, to each candidate investor, a respective fractional share of an offering, the fractional share corresponding to the fraction associated with the corresponding node; (vi) outputting a second allocation of shares of the offering among the plurality of candidate investors, the second allocation of shares including, for each of the plurality of candidate investors, a respective number of whole shares from a first allocation of shares, adjusted by the respective fractional share; (vii) constraining the weight for each node such that a purchase price of the shares in the second allocation to the corresponding candidate investor does not exceed a stated amount the candidate investor is willing to spend on the offering; (viii) implementing, by the fractional node layer, the machine learning algorithm including a heuristic algorithm; (ix) applying the heuristic algorithm to groups of nodes, including adjusting upward the weight of at least one relatively most fit node in each group; (x) iteratively, re-grouping the nodes and applying the heuristic algorithm to the re-grouped nodes; (xi) assigning, by a first upstream layer of the plurality of model layers, each candidate investor of a second plurality of candidate investors to a corresponding node of the first upstream layer, wherein each node of the first upstream layer is associated with a set of weights; (xii) inputting to each node of the first upstream layer a vector of data associated with the corresponding candidate investor; (xiii) generating an investor score for each candidate investor by applying the set of weights to the respective vector of data, wherein the investor score for the candidate investor corresponds to the fitness value for the candidate investor; (xiv) retrieving example input vectors drawn from historical investor data and actual outcome data associated with the example input vectors, and tuning the set of weights by applying a second machine learning algorithm to the example input vectors and the actual outcome data; and (xv) implementing the second machine learning algorithm including a backpropagation algorithm. 
     The resulting technical benefits achieved by the systems and methods of the disclosure include at least one of: (i) enabling computer-implemented asset offering systems to sell fractional shares of an asset offering; (ii) a computational model capable of effectively optimizing a distribution of assets among a large number of recipients by removing the constraint that only a few discrete levels of whole shares may be allocated to some recipients; and (iii) a computational model that enables predicting and evaluating the comparative utility, to an issuer of the assets, of different distribution amounts across a large number of recipients in a computationally practicable fashion. 
     In one embodiment, a computer program is provided, and the program is embodied on a computer readable medium. In an example embodiment, the system is executed on a single computer system, without requiring a connection to a server computer. In a further example embodiment, the system is being run in a Windows® environment (Windows is a registered trademark of Microsoft Corporation, Redmond, Wash.). In yet another embodiment, the system is run on a mainframe environment and a UNIX® server environment (UNIX is a registered trademark of X/Open Company Limited located in Reading, Berkshire, United Kingdom). In a further embodiment, the system is run on an iOS® environment (iOS is a registered trademark of Cisco Systems, Inc. located in San Jose, Calif.). In yet a further embodiment, the system is run on a Mac OS® environment (Mac OS is a registered trademark of Apple Inc. located in Cupertino, Calif.). The application is flexible and designed to run in various different environments without compromising any major functionality. In some embodiments, the system includes multiple components distributed among a plurality of computing devices. One or more components are in the form of computer-executable instructions embodied in a computer-readable medium. The systems and processes are not limited to the specific embodiments described herein. In addition, components of each system and each process can be practiced independently and separately from other components and processes described herein. Each component and process can also be used in combination with other assembly packages and processes. 
     In one embodiment, a computer program is provided, and the program is embodied on a computer readable medium and utilizes a Structured Query Language (SQL) with a client user interface front-end for administration and a web interface for standard user input and reports. In another embodiment, the system is web enabled and is run on a business-entity intranet. In yet another embodiment, the system is fully accessed by individuals having an authorized access outside the firewall of the business-entity through the Internet. In a further embodiment, the system is being run in a Windows® environment (Windows is a registered trademark of Microsoft Corporation, Redmond, Wash.). The application is flexible and designed to run in various different environments without compromising any major functionality. 
     As used herein, an element or step recited in the singular and preceded with the word “a” or “an” should be understood as not excluding plural elements or steps, unless such exclusion is explicitly recited. Furthermore, references to “example embodiment” or “one embodiment” of the present disclosure are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features. 
     As used herein, the term “database” may refer to either a body of data, a relational database management system (RDBMS), or to both. A database may include any collection of data including hierarchical databases, relational databases, flat file databases, object-relational databases, object oriented databases, and any other structured collection of records or data that is stored in a computer system. The above examples are for example only, and thus are not intended to limit in any way the definition and/or meaning of the term database. Examples of RDBMS&#39;s include, but are not limited to including, Oracle® Database, MySQL, IBM® DB2, Microsoft® SQL Server, Sybase®, and PostgreSQL. However, any database may be used that enables the systems and methods described herein. (Oracle is a registered trademark of Oracle Corporation, Redwood Shores, Calif.; IBM is a registered trademark of International Business Machines Corporation, Armonk, N.Y.; Microsoft is a registered trademark of Microsoft Corporation, Redmond, Wash.; and Sybase is a registered trademark of Sybase, Dublin, Calif.). 
     The term processor, as used herein, may refer to central processing units, microprocessors, microcontrollers, reduced instruction set circuits (RISC), application specific integrated circuits (ASIC), logic circuits, and any other circuit or processor capable of executing the functions described herein. 
     As used herein, the terms “software” and “firmware” are interchangeable, and include any computer program stored in memory for execution by a processor, including RAM memory, ROM memory, EPROM memory, EEPROM memory, and non-volatile RAM (NVRAM) memory. The above memory types are for example only, and are thus not limiting as to the types of memory usable for storage of a computer program. 
       FIG.  1    is a schematic diagram illustrating an example environment  100 . Environment  100  includes at least one investor computing device  102 , at least one broker-dealer computing device  104 , an issuer computing device  106 , and a share allocation (SA) computing device  108 . 
     Each investor computing device  102  is associated with an investor in environment  100 . Each investor may be an individual who desires to purchase assets through public offerings. For example, the investor may wish to purchase stock in a corporation having an initial public offering. Each investor may have associated historical investor data corresponding to the investor&#39;s historical involvement in IPOs and other public offerings. Each investor computing device  102  is in direct communication with SA computing device  108 . As shown in  FIG.  1   , in the example embodiment, environment  100  may include a plurality of investor computing devices  102  each associated with a respective individual investor. For example, each individual investor registers with a service provided by SA computing device  108 . In response to the registration, SA computing device  108  transmits notifications of upcoming public asset offerings to investor computing device  102 , and may indicate an offering time window during which requests from investor computing device  102  to purchase assets will be accepted. For example, but not by way of limitation, SA computing device  108  transmits notifications to investor computing device  102  via a client application installed on investor computing device  102 , or via a web page accessible to investor computing device  102  in response to investor computing device  102  transmitting log-in credentials to the web server. 
     In response, investor computing device  102  may transmit a request to SA computing device  108  including request data indicating the investor is willing to invest in an upcoming offering. The request data may indicate an amount of money the investor wishes to invest in the upcoming offering, and may be time-stamped. The time stamp may include, for example, at least one of a date/time of submission of the request, and a cardinality of the request relative to requests for the current offering received from other investor computing devices  102  (e.g., the request data indicates that the request was the first, second, third, etc. request received by SA computing device  108  for the current offer). Some embodiments include offers transmitted to hundreds, thousands, tens of thousands, or millions of investor computing devices  102 . 
     Each broker-dealer computing device  104  is associated with a corresponding broker-dealer in environment  100 . The broker-dealer is an individual or organization that engages in the business of trading securities (e.g., stock) on behalf of the broker-dealer&#39;s customers (e.g., individual investors). Broker-dealer computing device  104  may store or generate historical investor data corresponding to investment activity of individual investors through the broker-dealer corresponding to broker-dealer computing device  104 . Broker-dealer computing device  104  is in direct communication with SA computing device  108  and with investor computing devices  102  of each customer/individual investor of the broker-dealer. Broker-dealer computing device  104  transmits historical investor data accumulated by broker-dealer computing device  104  to SA computing device  108 . As shown in  FIG.  1   , environment  100  may include a plurality of broker-dealer computing devices  104  each associated with a corresponding broker-dealer. 
     Issuer computing device  106  is associated with an issuer of a public offering such as an IPO. The issuer sells, for example, shares of stock in a corporation in exchange for funds. The issuer may select investors in the public offering based on, for example, a perceived financial capability and expected future investing behavior. As such, the issuer may be in communication with any number of institutional investors  110  and may allocate any suitable portion of the offering to institutional investors  110  outside the channels provided by SA computing device  108 . Additionally or alternatively, the issuer may consider allocating a portion of the offering to individual investors via SA computing device  108 . The issuer may consider the individual investors in environment  100  in aggregate, such that the issuer&#39;s decision on how much of the offering to allocate may be based on the aggregate perceived financial capability and expected future investing behavior of all the individual investors in environment  100 . Issuer computing device  106  is in direct communication with SA computing device  108  to receive data regarding the expected behavior of the individual investors. While one issuer computing device  106  is shown in  FIG.  1   , environment  100  may include a plurality of issuer computing devices  106  each associated with a corresponding issuer. 
     SA computing device  108  is further in communication with at least one database (which may be implemented by a storage device  625  shown in  FIG.  6   ) for storing information, such as historical investor data. In the example embodiment, the historical investor data is stored in at least one data structure having a plurality of data fields and a plurality of records, each record including a plurality of data values corresponding to the plurality of data fields. The historical investor data may include data fields relating to past investment activity of the plurality of individual investors executed through channels external to SA computing device  108 . In the example embodiment, the external historical investor data may be received from one or more of the broker-dealer computing devices  104  in communication with SA computing device  108 . For example, the external historical investor data fields may include one or more of average number of days holding an asset at peak value, average number of days holding an asset of a particular asset classification, percentage of the aftermarket accumulation of a particular asset, number of transactions per year, and/or average size of transaction per buying power at the time of the transaction. 
     Historical investor data may also include data relating to previous investment activity with respect to public offerings through SA computing device  108 , referred to as “internal” historical investor data. In some embodiments, SA computing device  108  is configured to capture data from previous investment activity of the plurality of individual investors conducted through SA computing device  108 , and store the captured data as at least a portion of the historical investor data in the database. For example, the internal historical investor data fields may include one or more of: the fraction of assets actually purchased relative to the amount of assets the investor indicated a willingness to purchase at the candidate stage, the number of days the previous offering was held divided by the threshold number of days, percentage of social share by the investor, and/or size of the order with respect to buying power. As discussed above, the percentage of social share by the investor is a percentage of offerings previously offered to the investor through the SA computing device for which the investor has electronically shared information regarding the offering (e.g., by sharing that the investor has made an investment via a social media platform). In some embodiments, such sharing over electronic social media platforms by candidate individual investors is a behavior that the issuer and/or corporation offering the asset wish to encourage in order to build positive momentum for the offering. 
       FIG.  2    is a schematic data flow diagram illustrating an example of a computational model  200  executed by SA computing device  108 . In order to allocate shares of an asset offering proffered by issuer computing device  106 , SA computing device  108  feeds an input data signal  201 , representative of, for example, request data associated with requests submitted by investor computing devices  102  to participate in a current asset offering and/or the historical investor data, as inputs to model  200 . As noted above, SA computing device  108  may transmit notifications of offers to hundreds, thousands, tens of thousands, or millions of investor computing devices  102 , and may receive requests to participate in the offering from a commensurate number of investor computing devices  102 . Accordingly, the sheer quantity of data included in input data signal  201  creates a problem of computational tractability and scalability for any algorithmic attempt to identify, according to a suitable basis of utility, an optimal allocation of shares of the offering among those investor computing devices  102 . 
     To solve this problem of computational tractability and scalability, model  200  includes a plurality of model layers  202  arranged in a sequence, i.e., with a model layer output  204  of each respective upstream model layer  202  being transmitted as an input to a downstream model layer  202 . The layer output  204  of each model layer  202  includes data representative of an allocation of shares of the offering among investor computing devices  102  that submitted requests to participate in the offering. Moreover, the layer output  204  of each upstream model layer  202  is passed as an input signal to a next downstream model layer  202 . Each downstream model layer  202  successively refines the layer share allocation received from the previous upstream layer  202  to better meet the objectives of the issuer and the business entity represented by the issuer, while operating within the request parameters provided by each investor computing device  102 . Notably, in the example embodiment, each upstream model layer  202  executes with no knowledge or inhibitions about downstream model layers  202 . In other words, each model layer  202  operates as if the domain of model  200  ends after completion of that model layer  202 , allowing one or more layers  202  to execute in a substantially stateless fashion. 
     For example, in the illustrated embodiment, a first model layer  202 , designated model layer  250 , operates on input data signal  201  and generates a first layer model output  204 , including a share allocation. The first layer share model output  204  is provided as an input signal to a second model layer  202 , designated model layer  252 . In some embodiments, input data signal  201  is also provided to second model layer  252 , as illustrated in  FIG.  2   . In some such embodiments, input data signal  201  is filtered, as illustrated as filter  210 , before reaching one or more downstream model layers  202 , to remove portions of input data signal  201  associated with candidate investors who did not pass a minimum requirements filter embodied in model layer  250 , as discussed below. However, in other embodiments, input data signal  201  is not provided to one or more downstream model layers  202 . Model layer  252  operates on the input first layer share allocation, and optionally on input data signal  201 , and generates a second layer model output  204  including a refined share allocation. Similarly, the second layer model output  204  is provided as an input signal to a third model layer  202 , designated model layer  254 . In some embodiments, input data signal  201  is also provided to model layer  254 , as discussed above. However, in other embodiments, input data signal  201  is not provided to model layer  254 . Model layer  254  operates on the input second layer share allocation, and optionally on input data signal  201 , and generates a third layer model output  204  including a further refined share allocation. In the illustrated embodiment, the share allocation included in third layer model output  204  is stored by SA computing device  108  as a purchase offer share allocation  206 , used to generate details of the aggregate offer to purchase assets submitted to issuer computing device  106  and to allocate actual shares received from issuer computing device  106  among the candidate investors. 
     Although three model layers  202  are shown in the illustrated embodiment, it should be understood that in other embodiments, any suitable number of model layers  202  may be implemented. 
     Input data signal  201  may include data drawn from the historical investor data for a plurality of investors, such as, for each investor, one or more of average number of days holding an asset obtained in a previous offering at peak value, average number of days holding an asset obtained in a previous offering of a particular asset classification (e.g., defense, energy, or technology), percentage of the aftermarket accumulation of a particular asset obtained in a previous offering, number of transactions per year in previous asset offerings, and/or average size of transaction in a previous offering per buying power at the time of the transaction. As noted above, in some embodiments this information may be obtained from investment transactions executed external to SA computing device  108 , such as via broker-dealer computing devices  104 . Data included in input data signal  201  and drawn from the historical investor data may additionally or alternatively include one or more of the fraction of assets actually purchased relative to the amount of assets the investor indicated a willingness to purchase at the candidate stage of a previous offering, percentage of social share by the investor of a previous offering, and/or size of the order in a previous offering with respect to buying power of the investor at the time of the previous offering. As noted above, in some embodiments this information may be generated internally within SA computing device  108  based on past activity of the candidate IBP with SA computing device  108 . 
     Additionally or alternatively, input data signal  201  may include data drawn from the request data received from the plurality of investors for the current offer, such as, for each investor, the amount of money the investor wishes to invest in the current offering, a date/time of submission of the request to invest in the current offering, and a cardinality of the request relative to requests for the current offering received from other investors. 
     In some embodiments, model layer  250  is implemented as a qualification model layer. More specifically, model layer  250  applies a rules-based filter to respective portions of input data signal  201  associated with each candidate investor to determine whether the respective candidate investor meets an initial qualifying threshold for receiving shares in the current offering. The filter may apply rules against one or more exhibited or notional data attributes of the candidate investors, such as current financial resources of the candidate investor available for investment (as observed, for example, by the broker-dealer computing device  104  associated with the candidate investor and/or by previous interactions with SA computing device  108 ), the stated amount the candidate investor is willing to invest in the current offering, any undesirable historical performance by the candidate investor (e.g., relatively quick sale of acquired shares into the aftermarket, as observed, for example, by the associated broker-dealer computing device  104 ) in a similar previous offering, etc. Exhibited or notional data attributes refer to quantities expressly present in input data signal  201 , or easily derivable therefrom. If the portions of input data signal  201  corresponding to a particular candidate investor do not pass the initial qualifying threshold filter, that particular candidate investor is removed from consideration for receiving shares in the asset offering. The layer output  204  of model layer  250  includes a share allocation for only those candidate investors that successfully pass the initial qualifying threshold filter. 
     Notably, model layer  250  operates on (e.g., accesses) the full input data signal  201 , which includes comprehensive historical investor data and request data for hundreds, thousands, tens of thousands, or millions of candidate investors who submitted requests to buy shares via associated investor computing devices  102 . Accordingly, in order to maintain a computational tractability of model layer  250 , in some embodiments no optimization per se is performed for the candidate investors in model layer  250 . Instead, every candidate investor that successfully passes the initial qualifying threshold filter, based on exhibited or notional data attributes, is assigned the same small, predetermined base number of shares in the share allocation of layer output  204 . More computationally rigorous optimization of share allocation is preserved for downstream model layers  202 , which typically operate on a reduced portion of input data signal  201  due to the removal of candidate investors by the filter in upstream model layer  250 . 
     Alternatively, model layer  250  selectively passes a subset of the candidate investors who responded with requests to participate in the current offering to one or more downstream model layers  202  in any suitable fashion that enables model  200  to function as described herein. 
     In certain embodiments, model layer  250  also calculates a number of shares that will be provided in layer output  204  as available for further allocation by the next downstream model layer  202 . The number of shares available for further allocation may be determined based on notice from issuer computing device  106  of an actual number of shares to be sold via distribution through SA computing device  108 , less the base allocation already made in model layer  250  to candidate investors that passed the initial qualifying threshold filter. Alternatively, in cases where final notice from issuer computing device  106  of the actual number of shares available has not yet been received, the number of shares available for further allocation may be an estimated number based on, for example, the number of candidate investors that passed the initial qualifying threshold filter, an aggregation of the stated amounts each candidate investor that passed the filter is willing to invest in the current offering, and/or other suitable factors. After the estimated number of shares is allocated by downstream model layers  202 , adjustments to the allocation (e.g., on a pro rata basis) may be made when the actual number of shares available for allocation by SA computing device  108  is determined. 
       FIG.  3    is a schematic block diagram illustrating an example implementation of one of model layers  202  as an isolated node layer  300 . In the example embodiment, isolated node layer  300  is implemented as an intermediate model layer  252 , downstream from the first model layer  250  implemented as the qualification model layer. Alternatively, isolated node layer  300  is implemented at any suitable upstream or downstream model layer  202 . 
     In the example embodiment, each candidate investor included in the layer output from the immediately upstream layer  202  is represented as a node  302 . Nodes  302  may be viewed as neurons that define a simple neural network implemented by isolated node layer  300 . Output  204  from the upstream model layer  202  is used identify candidate investors eligible for allocations by the current node layer  300 , and filter  210  for node layer  300  extracts the vector  301  of input data signal  201  corresponding to the respective candidate investor for input to the associated node  302 . Each node  302  is associated with a set of weights  304  (e.g., and/or biases) that are applied to corresponding values within the vector  301  (e.g., and/or portion) of input data signal  201  associated with the respective candidate investor. In the example embodiment, the same set of weights  304  is applied by each node  302 . Alternatively, the set of weights applied by at least one node  302  differs from that applied by others of nodes  302 . 
     For example, vector  301  for each respective candidate investor may be a vector of values including one or more of: absolute size of the stated amount the candidate investor is willing to invest in the current offering; relative size of the stated amount the candidate investor is willing to invest in the current offering, as compared to the aggregate total of the stated amounts of all candidate investors; relative size of the stated amount the candidate investor is willing to invest in the current offering, as compared to current purchasing power of the candidate investor (as observed, for example, by the associated broker-dealer computing device  104 ); time elapsed between an opening of the current offering window to individual investors and the time the request to participate was received from the corresponding computing device  102 ; cardinality of receipt of the request to participate from the corresponding computing device  102  (i.e., was the request received first, second, third, etc. in time among all requests received for the current offering); number of investment transactions by the candidate investor over one or more time frames (e.g., previous 24 months, previous 12 months, previous 6 months, previous 3 months, as observed, for example, by the associated broker-dealer computing device  104  and/or SA computing device  108 ); number of investment transactions in a same category (e.g., transportation, pharmaceutical, energy) by the candidate investor over one or more time frames); amount of time a previous offering was held by the candidate investor, in absolute time or as compared to a threshold time; percentage of social share of previous participations by the candidate investor; and/or any other suitable values. 
     Likewise, the set of weights  304  associated with nodes  302  may be a set of values, with each weight value in the set applied to a respective value in vector  301  for the candidate investor. Values of weights  304  are selected such that application of weights  304  to the vector  301  for each candidate investor results in an investor score proportionate to a fitness of the candidate investor, measured in terms of utility to issuer computing device  106  (and thus ultimately in terms of utility to the business entity offering the assets). In other words, the investor score represents a predicted likelihood that the candidate investor will exhibit a behavior preferred by issuer computing device  106  with respect to the current offering (e.g., that the candidate investor would hold shares obtained in the current offering for at least a threshold period of time), with a higher investor score corresponding to a higher likelihood of the preferred behavior and a lower investor score corresponding to a lower likelihood of the preferred behavior. 
     In some embodiments, the set of weights  304  is established or “tuned” via application of a machine learning algorithm. Machine learning refers broadly to various algorithms that may be used to train isolated node layer  300  to identify and recognize patterns in existing data in order to facilitate making predictions for subsequent new input data. Using machine learning, the set of weights  304  may be automatically tuned based upon example input vectors  301  drawn from historical investor data and historical request data for previously completed offerings of shares, and corresponding actual outcome data for those previously completed offerings. For example, the actual outcome data indicates actual investor behavior (e.g., actual time until sale of the acquired assets in the aftermarket) associated with each example input vector  301 . Weights  304  are tuned based upon the example input vectors and the actual outcome data drawn from previously completed offerings in order to yield valid and reliable investor score outputs for novel input vectors  301  for a current offering. For example, isolated node layer  300  includes an optimization module  312  programmed to apply a loss function to the output of nodes  302  generated in response to the example input vectors. It should be understood that terms such as “optimization” and “optimize” in this context need not refer to a deterministic single best or “optimal” solution for the set of weights  304 , but rather to a solution for the set of weights  304  that tends to reduce the loss function relative to the allocation of shares received in model layer output  204  from the upstream model layer  250 . 
     In some embodiments, the loss function is defined as a discrepancy between the predicted time that a respective investor would hold an asset, as represented by the investor score based on example vector  301  and a current state of the set of weights  304 , and the actual time that the respective investor held the asset, as indicated in the actual outcome data. A suitable backpropagation algorithm, represented schematically by dashed line  306 , is then applied to adjust the set of weights  304  to minimize the loss function. In this fashion, isolated node layer  300  is trained to produce investor scores that reliably predict a degree to which the candidate investor will exhibit a post-offering behavior preferred by issuer computing device  106 . Alternatively, the set of weights  304  are selected in any suitable fashion. 
     In some embodiments, vector  301  also includes an indicator for whether the broker-dealer computing device  104  associated with the respective investor supports allocation of fractional shares, and the value in the set of weights  304  corresponding to that indicator is constrained to bias in favor of allocating shares to such investors. For example, the marginal allocation of additional whole shares to such investors in model layer  252  enables leveraging the added utility of fractional share allocation among such investors in a downstream layer  254 , as described below, to achieve a better final output allocation. Alternatively, an ability of the associated broker-dealer computing device  104  to support allocation of fractional shares is not considered in model layer  252 . 
     Notably, isolated node layer  300  is “isolated” in the sense that there is no signal path connecting node  302  for a particular candidate investor to portions  301  of input data signal  201  associated with other candidate investors. Rather, each node  302  operates to apply the set of weights  304  solely to the vector  301  associated with the same candidate investor, thereby reducing a computational load that would be required to train and execute model layer  252  if each node  302  operated on vectors  301  for multiple candidate investors. Thus, in certain embodiments, the architecture of isolated node layer  300  enables hidden complexity or relationships within the data representing any particular candidate investor to be discovered and exploited (e.g., through application of machine learning algorithms to set the weights/biases for nodes  302  as described above), while avoiding the exponentially higher computational burden of an interconnected node layer at this stage of model  200 . For example, the reduced computational burden enables isolated node layer  300  to be re-trained periodically on a relatively frequent basis (e.g., every 12 hours) to incorporate newly available external historical investor data and request data obtained from one or more broker-dealer computing devices  104 , and/or re-trained each time a preferred asset holding period elapses after the completion of an asset offering handled SA computing device  108  to incorporate the most recent internal historical investor data and actual investor post-offering behavior. 
     In the example embodiment, isolated node layer  300  also includes a layer allocation module  308  that outputs a data signal  310  representative of an allocation of shares among investor computing devices  102  associated with each node  302 . More specifically, after application of the set of weights  304  to vector  301  of input data signal  201  for each respective candidate investor node  302  to arrive at investor scores, layer allocation module  308  allocates, among the respective investors represented by nodes  302 , in blocks of whole shares and based on the relative investor scores, the number of shares identified as available for further allocation in layer output  204  received from the upstream model layer  202 . For example, the available shares are allocated in proportion to the respective investor&#39;s investor score, as constrained by the stated amount the investor is willing to spend. Alternatively, the available shares are allocated based on the investor score in any suitable fashion that enables isolated node layer  300  to function as described herein. 
     In some embodiments, the shares allocated by layer allocation module  308  to each node  302  are added to the predetermined base number of shares allocated by upstream model layer  250  to arrive at the allocation represented by data signal  310 . In other embodiments, the predetermined base number of shares is first subsumed back into the total number of available shares by layer allocation module  308 , and the shares allocated by layer allocation module  308  represent the complete allocation to each candidate investor in data signal  310 . In the example embodiment, however, whole shares allocated to a particular investor by isolated node layer  300  may be subject to fractional reallocation to another investor in a downstream model layer  202 , as will be described below. 
     In the example embodiment, optimization module  312  is further programmed to evaluate a data quality of the allocation of shares represented by data signal  310 . For example, optimization module  312  checks for outlier share allocations, in which an allocation to one or more candidate investors exceeds a predetermined threshold statistical deviation relative to the overall distribution of shares. In some circumstances, optimization module  312  may cure the outlier allocation locally (i.e., within optimization module  312 ), e.g. by re-allocating shares among the candidate investors to cure the deviation. In other circumstances, optimization module  312  may respond to the outlier allocation by triggering a re-training of the machine learning model to refine the set of weights  304 , and then instructing isolated node layer  300  to re-apply the refined set of weights  304  to vector  301  of input data signal  201  for each respective candidate investor node  302  to arrive at updated investor scores. After optimization module  312  causes any applicable corrections, optimization module  312  outputs model layer output  204  of isolated node layer  300 , designated isolated-node model layer output  314 , which includes data representative of the allocation of shares (in blocks of whole shares) to each candidate investor represented by a node  302 . Alternatively, optimization module  312  is not programmed to evaluate the data quality of the allocation of shares represented by data signal  310 . For example, isolated node layer  300  passes the allocation of shares represented by data signal  310  directly to model layer output  314 . 
     In some embodiments, model layer output  314  further includes the investor scores for each candidate investor. 
     In some embodiments, layer allocation module  308  is programmed to allocate all of the shares that were identified as available for further allocation in layer output  204  received from the upstream model layer  202 . In other embodiments, layer allocation module  308  reserves a portion of the available shares for initial allocation in a downstream model layer  202 . In embodiments in which a portion of the available shares is reserved, isolated node layer  300  includes the number of reserved shares in layer model output  314 . 
       FIG.  4    is a schematic block diagram illustrating an example implementation of one of model layers  202  as a fractional node layer  400 . In the example embodiment, fractional node layer  400  is implemented as final model layer  254 , directly downstream from intermediate model layer  252  implemented as isolated node layer  300 , and indirectly downstream from the first model layer  250  implemented as the qualification model layer. Alternatively, fractional node layer  400  is implemented at any suitable upstream or downstream model layer  202 . 
     Fractional node layer  400  identifies, from the received model layer output  204  from the immediately upstream layer  202 , a subset of candidate investors that are associated with a respective broker-dealer computing device  104  that supports trading of fractional shares, and assigns each candidate investor in the subset to a node  402  in fractional node layer  400 . In the example embodiment, candidate investors included in model layer output  314  from isolated node layer  300  are identified, and then the broker-dealer computing device  104  associated with each of the initially identified candidate investors is reviewed to determine whether the associated broker-dealer supports trading of fractional shares. If the associated broker-dealer does not support the allocation of fractional shares to its investor clients, then the potential candidate investors who participate through that broker-dealer computing device  104  are filtered out from participation in fractional node layer  400 , leaving only the subset of candidate investors for assignment to nodes  402 . 
     As noted above, in some embodiments, an inability of a respective broker-dealer computing device  104  to support fractional shares is implemented as a bias factor in isolated node layer  300  that tends to reduce an allocation of whole shares to candidate investors associated with that broker-dealer. In some embodiments, this preemptive upstream allocation reduction (e.g., a one-share reduction) provides advantages such as (i) ensuring that candidate investors who “lose” a fraction of a share in fractional node layer  400  (as described further below) are treated no worse than candidate investors who did not compete at all for fractional shares, and/or (ii) enabling the additional optimization provided by fractional node layer  400  to operate on a greater portion of the overall allocation. 
     Nodes  402  may be viewed as neurons that define a fully connected neural network implemented by fractional node layer  400 . Each node  402  receives, as an input, a fitness value  401  associated with the corresponding candidate investor. In addition, each node  402  is associated with a weight  404  (e.g., and/or bias) that directly represents an addition of a fractional share to, or potentially in some embodiments the subtraction of a fractional share from, the whole share allocation received from the upstream model layer  202  for the corresponding candidate investor. In the example embodiment, the weights  404  are initially set to zero, i.e., nodes  402  begin the adjustment process in fractional node layer  400  on an equal footing. Weights  404  are then adjusted by applying a suitable machine learning algorithm on the neural network, and the final weights  404  correspond directly to fractions of a share added to (or, potentially, subtracted from) the allocation of shares to the candidate investor associated with the respective node  402 . 
     In some embodiments, an absolute value of each weight  404  is constrained to lie between zero and one (inclusive). In embodiments in which a portion of the available shares is reserved for allocation in fractional node layer  400 , the weight  404  for each node  402  is constrained to be a real value between zero and positive one, and nodes  402  compete against each other to accumulate the largest weight (which corresponds to the largest fractional share allocation). For example, the number of reserved shares is selected in the upstream model layer  252  based on the number of candidate investors associated with broker-dealer computing devices  104  that support fractional shares trading (i.e., the number of candidate investors that will be competing for fractional shares). Alternatively, in embodiments in which all available shares are provisionally allocated in the upstream model layer  252 , the weight  404  for each node  402  is constrained to be a real value between negative one and positive one (inclusive), and nodes  402  compete against each other in a zero-sum competition to accumulate the largest weight (which corresponds to the largest fractional share allocation) and/or avoid losing shares via a negative final weight  404 . 
     For example, fractional node layer  400  includes an optimization module  408  programmed to award fractional shares to (i.e., to increase weights  404  of) nodes  402  associated with the candidate investors in the subset that demonstrate a relatively higher relative fitness value  401 . Again, it should be understood that terms such as “optimization” and “optimize” in this context need not refer to a deterministic single best or “optimal” solution for weights  404 , but rather to a solution for weights  404  that tends to reduce a loss function relative to the allocation of shares received in model layer output  204  from the upstream model layer  252 . 
     In some embodiments, the fitness value  401  is received in, or otherwise derived from, the model layer output  204  of upstream layer  252 . As discussed above, the fitness value  401  may correspond, for example, to the predicted time that each share allocated to the candidate investor will be held before the share is traded in the aftermarket. For example, the fitness value  401  input to each node  402  may be derived from, or calculated in a similar fashion to, the investor score associated with the same candidate investor in isolated node layer  300 , based on vector  301  for the candidate investor and the set of weights  304  from isolated node layer  300 . A suitable algorithm, represented schematically by dashed line  406 , is then applied to adjust weights  404  to reward nodes  402  with relatively higher fitness values  401 , under the constraint that a purchase price of the resulting total allocation (including weight  404 ) of shares to the candidate investor associated with a respective node  402  cannot exceed the amount stated in the request data by the candidate investor as willing to spend. 
     In some such embodiments, optimization module  408  utilizes a heuristic algorithm, such as a “greedy” algorithm, in which nodes  402  are assigned to groups and the nodes  402  within each group compete against each other, with the weight  404  of one or more of the most relatively fit nodes in the group being adjusted upward, subject to the price constraint noted above. In zero-sum implementations, the increase in weight  404  for the one or more relatively most fit nodes may be accompanied by a decrease in weight  404  for one or more relatively least fit nodes in the group. The greedy algorithm may be iterated a number of times with random or algorithmically defined re-groupings of nodes  402 . In some embodiments, the iterations may be stopped dynamically in response to weights  404  for a suitable number of nodes  402  converging at a stable value across iterations, as defined by a suitable stability threshold. Additionally or alternatively, the number of iterations may be capped at a suitable predefined value. 
     In alternative embodiments, optimization module  408  utilizes any suitable algorithm that enables fractional node layer  400  to function as described herein. 
     Accordingly, in certain embodiments, the architecture of fractional node layer  400  causes nodes  402  associated with candidate investors that exhibit a relatively better predicted post-offering behavior preferred by issuer computing device  106  (as predicted by deep, hidden connections among characteristics of the corresponding candidate investors, e.g. as discovered by the neural network in isolated node layer  300 ) to advantageously attract larger allocations of fractional shares, relative to other nodes  402 . 
     In the example embodiment, fractional node layer  400  also includes a normalization module  412  configured to translate weights  404  into fractional share allocations. In some embodiments, after the machine-learning algorithm implemented by optimization module  408  arrives at a final value for weights  404  for each node  402 , optimization module  408  transmits an output  410  that includes the final weight  404  (i.e., a real value between zero and one or, alternatively, a real value between negative one and positive one) for each node  402 . In some embodiments, normalization module  412  converts weights  404  to corresponding fractional values using a selected base denominator (for example, quarters, eighths, or sixteenths), rounding the real values as necessary to generate simple fractions having the selected base denominator. Normalization module  412  is also configured to adjust fractions for one or more nodes  402  as necessary to ensure that the purchase price constraint remains satisfied. 
     In the example embodiment, fractional node layer  400  also includes a final allocation module  414  that receives the normalized fractional share allocations from normalization module  412  and computes the model layer output  204  of normalization module  412 , designated fractional-node model layer output  416 , which includes data representative of the allocation of shares to all candidate investors that passed the minimum requirements filter embodied in model layer  250 . More specifically, for candidate investors represented by nodes  402 , final allocation module  414  adds (or, potentially, subtracts) the fractional share allocation for the respective node  402 , received from normalization module  412 , to the whole share allocation received for the respective candidate investor in the model layer output  204  from the upstream model layer  202  (in the example embodiment, isolated-node model layer output  314 ), to arrive at a final allocation that includes fractional shares for most or all candidate investors represented by nodes  402 . (It should be understood that in some circumstances, at least one node  402  may receive a final weight  404  of zero during execution of optimization module  408 , in which case the corresponding candidate investor would end with a whole share allocation despite competing for fractional shares.) In addition, for candidate investors represented in the model layer output  204  from the upstream model layer  202  (in the example embodiment, isolated-node model layer output  314 ) but not represented by nodes  402  (e.g., candidate investors associated with broker-dealer computing devices  104  that do not support trading of fractional shares), final allocation module  414  passes through the whole share allocation received for the respective candidate investor in the model layer output  204  from the upstream model layer  252 . Accordingly, in the example embodiment, fractional-node model layer output  416  includes share allocations for all candidate investors that passed the minimum requirements filter embodied in model layer  250 , with fractional share allocations for a subset of candidate investors represented by nodes  402  and whole share allocations for the other candidate investors. 
     Alternatively, final allocation module  414  arrives at share allocation values for candidate investors in any suitable fashion. 
     In some embodiments, final allocation module  414  also identifies a number of unallocated fractions of shares after the final share allocation is generated. Final allocation module  414  assigns the unallocated shares to one or more buckets that enables after-market trades by candidate investors who received a fractional portion of a share. More specifically, when an investor computing device  102  sends a signal requesting an after-market trade of a fraction of a share, a complementary fraction of a share is drawn from the bucket to enable a trade of a whole share. In some such embodiments, final allocation module  414  allocates to each broker-dealer computing device  104  a respective bucket of fractional shares proportional to the fractional shares allocated to candidate investors associated with that broker-dealer computing device  104 , and the broker-dealer computing device  104  provides the complementary fraction of a share directly when one of its candidate investors performs an after-market trade of a fractional share. Additionally or alternatively, SA computing device  108  retains a bucket of fractional shares, and sells complementary fractions of a share from the bucket to broker-dealer computing devices  104  as needed to enable the respective broker-dealer computing device  104  to complete fractional share trades initiated by respective investor computing devices  102 . 
     As noted above, in cases where final notice from issuer computing device  106  of the actual number of shares available has not yet been received when model  200  is executed, adjustments to the allocation in fractional-node model layer output  416  may be made when the actual number of shares available for allocation by SA computing device  108  is determined. In some such cases, the adjustment includes a pro rata adjustment, and may include fractional share adjustments for candidate investors represented by nodes  402  as appropriate. Additionally or alternatively, the adjustment includes a subtraction of whole shares from candidate investors not represented by nodes  402 , as appropriate. 
     Certain contrasts between isolated node model layer  300  and fractional node layer  400  may be noted. In some embodiments, as explained above, isolated node model layer  300  applies one or more machine learning algorithms periodically to historical investor and request data and corresponding actual outcome data to tune a set of node weights  304 , and then applies that tuned set of weights  304  to input vectors  301  for all minimally qualified candidate investors to arrive at a model layer share allocation to candidate investors for a current offering. In contrast, fractional node layer  400  executes a machine learning algorithm specifically in response to each current offering, and the resultant node weights  404  themselves represent further share allocations, in positive (or, potentially in some embodiments, negative) fractions of a share. 
     In addition, while nodes  302  of isolated node model layer are “isolated” as discussed previously, nodes  402  of fractional node layer  400  are interconnected. While applying the machine learning algorithm to nodes  402  that are interconnected may cause a relative increase in the processing load imposed on SA computing device  108 , this computational load is mitigated by the fact that the node weights  404  themselves represent the model layer allocation, eliminating computational steps that would otherwise be required to convert input vectors and generically trained node weights to allocation values. Moreover, the computational load is further mitigated in embodiments in which optimization module  408  utilizes a “greedy” or other heuristic algorithm, as such algorithms are characterized by fewer computational steps and, thus, a relatively lower processing load as compared to dynamic programming algorithms that search for a single “best” or “optimal” solution. The computational load imposed by the interconnected nodes  402  is further mitigated in at least some embodiments because the optimizations already performed in upstream model layers  202 , which are designed to be relatively less computationally burdensome, do not need to be repeated in the interconnected node architecture. The computational load imposed by the interconnected nodes  402  is still further mitigated in at least some applications because the number of nodes  402  is smaller than the number of nodes  302  (i.e., the subset of candidate investors associated with broker-dealer computing devices  104  that support fractional shares trading is smaller than the number of candidate investors that pass the minimum requirements filter embodied in model layer  250 ). 
     For any or all of the above reasons, a sequence of model layers  202  as described herein, including fractional node layer  400  in a downstream model layer  254 , provides advantages in solving the complex computational processing challenges inherent in discovering and utilizing the hidden or latent knowledge within the input data set formed by the characteristics and historical share transactions of hundreds, thousands, tens of thousands, or even millions of candidate investors to enable improved allocations at the level of fractions of a share. 
       FIG.  5    is an example configuration of a client system  500  that may be used to implement investor computing devices  102 , issuer computing device  106 , and/or broker-dealer computing device  104  in accordance with embodiments of the present disclosure. In the example embodiment, client system  500  is operable by a user  501 , such as a candidate investor, a broker-dealer, or an issuer. Client system  500  includes a processor  505  for executing instructions stored in a memory area  510 . Processor  505  may, for example, include one or more processing units (e.g., in a multi-core configuration). Memory area  510  may, for example, be any device allowing information, such as executable instructions, to be stored and retrieved. Memory area  510  may further include one or more computer readable media. Processor  505  executes computer-executable instructions for implementing aspects of the disclosure. In some embodiments, the processor  505  is transformed into a special purpose microprocessor by executing computer-executable instructions or by otherwise being programmed. 
     In the example embodiment, processor  505  is also operatively coupled to a storage device  535 , which may be, for example, any computer-operated hardware unit suitable for storing and/or retrieving data. Storage device  535  may be used, for example by client system  500  implemented as broker-dealer computing device  104 , to store historical investor data associated with investors who participate in offerings and after-market trading via the respective broker-dealer computing device  104 . Storage device  535  may also be used, for example by client system  500  implemented as issuer computing device  106 , to store data defining a current offering. 
     In some embodiments, storage device  535  is integrated in client system  500 . For example, client system  500  may include one or more hard disk drives as storage device  535 . In other embodiments, storage device  535  is external to client system  500  and may be accessed by a plurality of client systems  500 . For example, storage device  535  may include multiple storage units such as hard disks or solid state disks in a redundant array of inexpensive disks (RAID) configuration. Storage device  535  may include a storage area network (SAN) and/or a network attached storage (NAS) system. 
     In some embodiments, processor  505  is operatively coupled to storage device  535  via a storage interface  530 . Storage interface  530  may include, for example, a component capable of providing processor  505  with access to storage device  535 . In an exemplary embodiment, storage interface  530  further includes one or more of an Advanced Technology Attachment (ATA) adapter, a Serial ATA (SATA) adapter, a Small Computer System Interface (SCSI) adapter, a RAID controller, a SAN adapter, a network adapter, and/or any similarly capable component providing processor  505  with access to storage device  535 . 
     In the example embodiment, client system  500  further includes at least one media output component  515  for presenting information to user  501 . Media output component  515  may, for example, be any component capable of converting and conveying electronic information to user  501 . For example, media output component  515  may be a display component configured to display offer data and/or historical investor data in the form of reports, dashboards, communications, and the like In some embodiments, media output component  515  includes an output adapter (not shown), such as a video adapter and/or an audio adapter, which is operatively coupled to processor  505  and operatively connectable to an output device (also not shown), such as a display device (e.g., a cathode ray tube (CRT), liquid crystal display (LCD), light emitting diode (LED) display, or “electronic ink” display) or an audio output device (e.g., a speaker or headphones). 
     In some embodiments, media output component  515  is configured to include and present a graphical user interface (not shown), such as a web browser and/or at least one client application, to user  501 . The graphical user interface may include, for example, an interface for viewing and/or responding to offers or other information presented through SA computing device  108 . In some embodiments, client system  500  includes an input device  520  for receiving input from user  501 . For example, for client system  500  implemented as investor computing device  102 , user  501  may use input device  520  to, without limitation, select and view offers from SA computing device  108 , submit a share and/or purchase request to SA computing device  108 , access log-in credential information, and/or submit payment information. For another example, for client system  500  implemented as broker-dealer computing device  104 , user  501  may use input device  520  to, without limitation, access log-in credential information, view permissions from investor computing devices  102  to communicate information to SA computing device  108 , and/or select historical investor data for transmission to SA computing device  108 . For another example, for client system  500  implemented as issuer computing device  106 , user  501  may use input device  520  to, without limitation, access log-in credential information, view and select offer data for transmission to SA computing device  108 , and/or view and select an aggregate share purchase request for a current offer submitted by SA computing device  108  on behalf of a plurality of candidate investors. 
     Input device  520  may include, for example, a keyboard, a pointing device, a mouse, a stylus, a touch sensitive panel, a touch pad, a touch screen, a gyroscope, an accelerometer, a position detector, an audio input device, a fingerprint reader/scanner, a palm print reader/scanner, a iris reader/scanner, a retina reader/scanner, a profile scanner, or the like. A single component such as a touch screen may function as both an output device of media output component  515  and input device  520 . Client system  500  may also include a communication interface  525 , which is communicatively connectable to a remote device such as SA computing device  108  (shown in  FIG.  1   ) or another client system  500 . Communication interface  525  may include, for example, a wired or wireless network adapter or a wireless data transceiver for use with a mobile phone network (e.g., Global System for Mobile communications (GSM), 3G, 4G or Bluetooth) or other mobile data network (e.g., Worldwide Interoperability for Microwave Access (WIMAX)). 
     Stored in memory area  510  are, for example, computer readable instructions for providing a user interface to user  501  via media output component  515  and, optionally, receiving and processing input from input device  520 . A user interface may include, among other possibilities, a web browser, and at least one client application. Web browsers enable users, such as user  501 , to display and interact with media and other information typically embedded on a web page or a website from SA computing device  108 . A client application allows user  501  to interact with a server application from SA computing device  108 . For example, instructions may be stored by a cloud service, and the output of the execution of the instructions sent to the media output component  515 . 
       FIG.  6    illustrates an example configuration of a server system  600  that may be used to implement SA computing device  108 . In the example embodiment, server system  600  includes one or more server computing devices  601  in electronic communication with at least one storage device  625 . In the exemplary embodiment, each server computing device  601  includes a processor  605  for executing instructions stored in a memory area  610 . In some embodiments, processor  605  includes one or more processing units (e.g., in a multi-core configuration) for executing instructions. The instructions may be executed within various different operating systems on the server system  600 , such as UNIX®, LINUX® (LINUX is a registered trademark of Linus Torvalds), Microsoft Windows®, etc. More specifically, the instructions may cause various data manipulations on data stored in storage device  625  (e.g., create, read, update, and delete procedures). It should also be appreciated that upon initiation of a computer-based method, various instructions may be executed during initialization. Some operations may be required in order to perform one or more processes described herein, while other operations may be more general and/or specific to a particular programming language (e.g., C, C#, C++, JSDA, or other suitable programming languages, etc.). 
     In the example embodiment, processor  605  is operatively coupled to a communication interface  615  such that server system  600  is capable of communicating with remote devices such as investor computing devices  102 , issuer computing device  106 , and/or broker-dealer computing devices  104 . For example, communication interface  615  may receive requests from remote devices via the Internet. 
     In the example embodiment, processor  605  is also operatively coupled to a storage device  625 , which may be, for example, any computer-operated hardware unit suitable for storing and/or retrieving data. Storage device  625  is used, for example, to store historical investor data, offer data received from issuer computing device  106 , and request data received from investor computing devices  102 . In some embodiments, storage device  625  is integrated into the one or more server computing devices  601 . For example, at least one server computing device  601  may include one or more hard disk drives as storage device  625 . In other embodiments, storage device  625  is external to server system  600  and may be accessed by a plurality of server systems  600 . For example, storage device  625  may include multiple storage units such as hard disks or solid state disks in a redundant array of inexpensive disks (RAID) configuration. Storage device  625  may include a storage area network (SAN) and/or a network attached storage (NAS) system. 
     In some embodiments, processor  605  is operatively coupled to storage device  625  via a storage interface  620 . Storage interface  620  may include, for example, a component capable of providing processor  605  with access to storage device  625 . In an exemplary embodiment, storage interface  620  further includes one or more of an Advanced Technology Attachment (ATA) adapter, a Serial ATA (SATA) adapter, a Small Computer System Interface (SCSI) adapter, a RAID controller, a SAN adapter, a network adapter, and/or any similarly capable component providing processor  605  with access to storage device  625 . 
     Memory area  610  may include, but is not limited to, random-access memory (RAM) such as dynamic RAM (DRAM) or static RAM (SRAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), non-volatile RAM (NVRAM), and magneto-resistive random-access memory (MRAM). The above memory types are for example only, and are thus not limiting as to the types of memory usable for storage of a computer program. Stored in memory area  610  are, for example, computer readable instructions for implementing the functionality described above with respect to SA computing device  108  and computational model  200 . 
       FIGS.  7 A,  7 B, and  7 C  are a flow diagram illustrating steps that may be included in an example process  700  implemented by SA computing device  108 . 
     In some embodiments, process  700  includes executing  702  computational model  200  including plurality of model layers  202  arranged in a sequence. 
     In certain embodiments, process  700  includes assigning  704 , by fractional node layer  400 , each candidate investor of a plurality of candidate investors to a corresponding node  402 , wherein each node  402  is associated with a weight  404 , and wherein the nodes  402  define an interconnected neural network. 
     In some embodiments, process  700  includes applying  706 , by fractional node layer  400 , a machine learning algorithm configured to adjust weights  404  of nodes  402  in response to respective fitness values  401  input to the nodes. 
     In certain embodiments, process  700  includes converting  708 , by fractional node layer  400 , the adjusted weight  404  for each node  402  into a corresponding fraction. 
     In some embodiments, process  700  includes allocating  710 , to each candidate investor, a respective fractional share of an offering, the fractional share corresponding to the fraction associated with the corresponding node  402 . 
     In certain embodiments, process  700  includes outputting  712  a second allocation of shares of the offering among the plurality of candidate investors, the second allocation of shares including, for each of the plurality of candidate investors, a respective number of whole shares from a first allocation of shares, adjusted by the respective fractional share. 
     In some embodiments, process  700  includes constraining  714  the weight  404  for each node  402  such that a purchase price of the shares in the second allocation to the corresponding candidate investor does not exceed a stated amount the candidate investor is willing to spend on the offering. 
     In certain embodiments, process  700  includes implementing  716 , by fractional node layer  400 , the machine learning algorithm including a heuristic algorithm. 
     In some embodiments, process  700  includes applying  718  the heuristic algorithm to groups of nodes, including adjusting upward the weight of at least one relatively most fit node in each group. 
     In certain embodiments, process  700  includes an iterative step  720  of re-grouping the nodes and applying the heuristic algorithm to the re-grouped nodes. 
     In some embodiments, process  700  includes assigning  722 , by a first upstream layer (e.g., model layer  252  implemented as isolated node layer  300 ) of the plurality of model layers  202 , each candidate investor of a second plurality of candidate investors to a corresponding node  302  of the first upstream layer, wherein each node of the first upstream layer is associated with a set of weights  304 . 
     In certain embodiments, process  700  includes inputting  724  to each node  302  of the first upstream layer a vector  301  of data associated with the corresponding candidate investor. 
     In some embodiments, process  700  includes generating  726  an investor score for each candidate investor by applying the set of weights  304  to the respective vector  301  of data, wherein the investor score for the candidate investor corresponds to the fitness value  401  for the candidate investor. 
     In certain embodiments, process  700  includes retrieving  728  example input vectors drawn from historical investor data and actual outcome data associated with the example input vectors, and tuning  730  the set of weights by applying a second machine learning algorithm to the example input vectors and the actual outcome data. 
     In some embodiments, process  700  includes implementing  732  the second machine learning algorithm including a backpropagation algorithm. 
     Additionally or alternatively, process  700  includes other steps consistent with the functionality of SA computing device  108  and computational model  200  as described herein. 
     It should be understood that the ordering of steps as shown in  FIGS.  7 A- 7 C  is non-limiting to embodiments of process  700 . 
     While the disclosure has been described in terms of various specific embodiments, those skilled in the art will recognize that the disclosure can be practiced with modification within the spirit and scope of the claims. 
     As used herein, the term “non-transitory computer-readable media” is intended to be representative of any tangible computer-based device implemented in any method or technology for short-term and long-term storage of information, such as, computer-readable instructions, data structures, program modules and sub-modules, or other data in any device. Therefore, the methods described herein may be encoded as executable instructions embodied in a tangible, non-transitory, computer readable medium, including, without limitation, a storage device and/or a memory device. Such instructions, when executed by a processor, cause the processor to perform at least a portion of the methods described herein. Moreover, as used herein, the term “non-transitory computer-readable media” includes all tangible, computer-readable media, including, without limitation, non-transitory computer storage devices, including, without limitation, volatile and nonvolatile media, and removable and non-removable media such as a firmware, physical and virtual storage, CD-ROMs, DVDs, and any other digital source such as a network or the Internet, as well as yet to be developed digital means, with the sole exception being a transitory, propagating signal. 
     As will be appreciated based on the foregoing specification, the above-described embodiments of the disclosure may be implemented using computer programming or engineering techniques including computer software, firmware, hardware or any combination or subset thereof, wherein the technical effect is a flexible system for various aspects of investor scoring. Any such resulting program, having computer-readable code means, may be embodied or provided within one or more computer-readable media, thereby making a computer program product, i.e., an article of manufacture, according to the discussed embodiments of the disclosure. The article of manufacture containing the computer code may be made and/or used by executing the code directly from one medium, by copying the code from one medium to another medium, or by transmitting the code over a network. 
     This written description uses examples to disclose the embodiments, including the best mode, and also to enable any person skilled in the art to practice the embodiments, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the disclosure is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial locational differences from the literal language of the claims.