A computer-based method and system accomplish automatic optimization of a preferred merchandising figure of merit like revenue, profit, etc. by concurrent optimization of prices and in-store promotion schedules for groups of interrelated products in a supermarket or in a chain of supermarkets. The basis of the system is a statistical model that combines effects of prices, promotion schedules and other factors that could influence demands, and produces a flexible nonparametric predictive demand function that can be optimized simultaneously in prices and promotion schedules. The system generates demand predictions for groups of interrelated products by applying data mining procedures to historical database that contains sales data along with various sales conditions, adjusting statistical predictive demand models, and then optimizing them in prices and promotion schedules. The user can interact with the system by selecting and customizing optimization and prediction scenarios provided by the system, and by requesting customized reports with results of particular optimization and prediction schemes.

1. Field of the Invention
This invention relates to systems and methods that use point-of-sale data for optimization of prices and promotion schedules for groups of interrelated products with the purpose of maximization of a preferred merchandising figure of merit like revenue, profit, etc.
2. Background and State of the Art
Businesses commonly and supermarket chains in particular, use various promotional and pricing schemes to improve revenues, profits and sales volumes. For instance, a supermarket manager may adjust prices to encourage sales of particular products. Also, he may specially present or advertise the products to increase consumer awareness and demand. Because of the variety of promotion discounts often applied at any one time, the complexity of the market, and difficulties in understanding of customer response, it is usually very difficult to accurately forecast effectiveness of various promotional tools and price adjustments, and to evaluate the influence of each selected tool on the overall sales revenues. It may still be even more difficult to plan various marketing campaigns and pricing adjustments beforehand to achieve the overall business optimality. Since predicting and assessing the consequences of various pricing and promotion strategies in a reliable manner is beyond the capabilities of the unaided human mind, there have been developed a number of approaches and computerized systems for dealing with the arising problems.
Commercially available inventory management systems such as the Maxagrid system include a yield management system which produces a pricing forecast used to determine prices for sales based on factors such as past trends and performance data which are updated periodically in order to maintain an accurate pricing model. The user making promotion and pricing decisions is faced with the following problems: connecting various promotion tools and prices with resulting sales in the past (for which construction of statistical models is necessary), isolating additional factors (many of which may be outside of decision-maker's control) that could influence sales volumes, developing statistical tools for predicting future demands, optimizing model parameters that will render optimal sales, performing necessary adjustments in promotions and prices.
The range and severity of the accompanying problems could be glimpsed from the following incomplete list:                1. Historical data available is usually insufficient, incomplete and often may appear contradictory. Relying on older data improves observations to parameters ratio but raises the questions of data relevancy for the current situation. Missing and outlying observations do not make life easier.        2. Isolating useful observable relevant factors, beyond promotions and prices, is a difficult task in itself.        3. While prices make a single most important factor, promotion effects are much less pronounced, interdependent, sometimes contradictory and confusing.        4. Especially complex are promotion effects for products with substitution demand and complementary demand. For example, offering one product at a discount might cannabalize sales from another product, and ultimately fail to yield greater revenue or greater profit. It is even more difficult to evaluate effects of promotions that pair more than one product.        5. Clearance sales of selected products, so often employed by department managers, may effect demand for substitute products in unpredictable ways.        6. The estimated optimal values of prices may be incompatible with overall management goals and therefore unacceptable.
The system and method in the present invention have been constructed with explicit purpose of solving these and many other problems arising in the process of optimizing joint pricing and promotion influences on the overall figure of merit, such as revenue, gross margin, etc. Detailed description of our invention is given in the following sections, while in the remainder of this section we list most relevant existing inventions, and pinpoint their major differences from our invention.
U.S. Pat. No. 5,596,493 (Tone, et al., 1997): It is an early work describing a complete statistical demand model suitable for prediction of sale amounts based on historical database. Log-normal linear regression model of demand is used. Besides demand prediction, regression model is used for purposes of determining safe stock, restocking, etc. Suggested possible relevant regressors include days of week, weather, prices and various categories of advertisements. The problem of selection of relevant regressors is addressed, as well as probabilistic measures of model uncertainty due to numerous sourced of error. The method for ordering for restocking is proposed that comprises the steps of entering POS data, finding sale amount data of individual goods for a predetermined time period obtained on the basis of the POS data, calculating basic statistical values of daily sale amounts of the individual goods based on the sale amount data of the individual goods, classifying the basic statistical data into one of plural class types, estimating the sale amount in accordance with the class types and calculating the amount of a restocking order based on the estimated sale amount and an amount on stock. The system for classifying sale amount characteristics comprises means for entering POS data, means for finding sale amount data of individual goods for a predetermined time period obtained on the basis of the POS data, means for calculating basic statistical values of daily sale amounts of the individual goods based on the sale amount data of the individual goods, and means for classifying the basic statistical data into one of preset plural class types.
Like most later patent applications, the model in our invention uses some of ideas of the present invention while making considerable additions and refinements, and developing sophisticated statistical tools for comparative assessment of influences of various factors on demand levels. For instance, our system is capable of direct estimation of promotion effects of various clips run on in-store monitors, and of estimating comparative efficiency of those clips. Also, it integrates influences of pricing and promotion into a single system and uses it for optimization of both prices and promotion schedules simultaneously.
U.S. Pat. No. 5,712,985 (Lee, et al., 1998) is a continuation in part of U.S. Pat. No. 5,459,656. The invention provides a system and method for analyzing business demand which incorporates tracking of past business demand for a plurality of products or tasks, time intervals during the day, and providing improved projection of business demand for such items. The system uses the concept of a business influence to aggregate, store, access, and manipulate demand data for the purpose of forecasting future demand levels for one or more business items. A business influence is any type of quantifiable factor that produces a variation in demand for some type of business item. The business influences model is composed of three distinct entities: a base profile, at least one influence profile, and a forecast profile. The base profile, influence profiles, and forecast profiles are data storage structures that persistently maintain their associated profile information in selected files in a database. The profiles are time-demand curves where demand is represented as either quantity or percentage units. An influence profile reflects the changes in demand for a business item due to a particular identifiable condition, such as the weather, or a sale, or the like. Influence profiles are selected and combined with the base profile to create a forecast profile. The base profile and influence profiles are demand curves representing a particular level of demand for a business item in each of the number of time intervals. Seasonality influence profiles may also be created to represent the influence of long-term seasonal influences. The forecast profile is a projection of anticipated demand for a business item based on its base profile and any selected influence profiles or seasonality profiles, for a selected period. The selected period may be any useful time period, such as a business quarter, month, week, day, hour, minute, and so forth. In order to project demand then, a base profile for a selected business item is combined with any number of influence profiles to create a forecast profile. The user selects a business item to be produced or scheduled during some time interval. The selection of a business item, and subsequent forecasting may be repeated for multiple business items. The user selects a base profile for the business item and any number of influence profiles. In a preferred embodiment the business item is associated with a base profile, and selected influence profiles, so that selection of the business item results in automatic selection of the profiles. In a preferred embodiment, each business day is associated with at least one base profile and influence profile that captures the variations in demand patterns which effect each demand for a business item associated with the base profile. In the preferred embodiment, the base profile stores a historical exponentially smoothed average of actual demand for the item in each of a variable number of time intervals. In alternative embodiments, the base profile stores a moving average of actual, a forward trend average, or other types of historical averages.
From the given description of the invention, it is not quite clear how it differs from a standard statistical approach of setting-up a regression model, estimating model parameters, and updating the whole process as new data arrive. The regression model need not be linear: it may be a locally weighted regression, or a generalized additive model, or whatever. Such an approach adopted in our own patent application would use well-developed tools for weighting, updating, estimating statistical properties of the available data, etc. It could work automatically, i.e. without user's intervention, or provide an opportunity for interaction.
U.S. Pat. No. 5,987,425 (Hartman, et al. 1999) describes a variable margin pricing system that generates retail prices based on price sensitivity and cost, and allows dealers more flexibility and control over the retail pricing of the products. After receiving electronic information identifying a plurality of products and electronic product cost information, the customer price sensitivity, and logical relationships between gross profit margins and the customer price sensitivity, are determined for the products. The system electronically assigns varying margins to the products based on the logical relationships between margins and the customer price sensitivities. Retail prices for each of the products are then electronically generated, as determined by the cost information and the assigned margins for each of the corresponding products. In short, the system ranks products by their dollar costs and assigns smaller gross profit margins to products with higher costs because of higher price sensitivity of consumers to such products. This assignment is based on ready-made formulas that can be modified from expert knowledge. This invention can be seen as computerization of earlier manual optimization of variable price margins based on expert assessments and comparisons with competitors' prices. The described invention differs considerably from our invention in which pricing and promotion are optimized in the framework of a constructed statistical model and estimated using historical database and data mining tools.
U.S. Pat. No. 6,029,139 (Cunningham, et al. 2000) describes a system and method of evaluating and optimizing promotional plans for products, segments of products or categories of products. The promotion optimization system determines both the costs and the benefits of a proposed promotion plan for the sale of products. Using both costs and benefits, it proposes a promotional plan that will better meet the user's goals. This may involve new promotion plans or existing promotions scheduled at different times. Another option may be the coordination of promotions between two related segments of products, i.e. groups of products that may be promoted together. Each product has an associated sales history and manufacturer. Neural networks are used for processing the corresponding data structures. Sales objectives and constraints are applied to neural networks generating promotional plans for product segments.
Since the cited patent application does not go into description of statistical techniques for processing historical data, it does not easily render itself to comparisons. Still, it is clear that it does not contain modern data-dependent means for assessing efficiency or inefficiency of promotional plans that may depend on huge number of parameters, and in particular it does not provide means for estimating efficiency of in-store monitors carrying promotion clips which is suggested in our own patent application. Its estimation structure appears fixed in that it does not provide means of integration of large numbers of various factors like different forms of promotion schedules, pricing plans, time-dependent structures, etc. into a common estimation system capable of sorting out partial influences of various factors on cumulative product demand. Furthermore, it is well known that neural networks are not useful for isolating influences of multiple factors operating simultaneously in different directions. At the same time, it can be seen from the description of our own work that isolating influences of different factors is extremely important for effective optimization of promotion and pricing effects simultaneously.
U.S. Pat. No. 6,076,071 (Freeny, Jr., 2000) describes an automated product pricing system including a physical store system, a virtual store system, and a control system. The physical and virtual store systems transmit sales data indicative of the number of sales of respective products. The control system receives the sales data from the physical store system and the virtual store system, and generates price change data including a changed price of an identified product based on the sales data received from at least one of the physical and virtual store systems. The price change data is then transmitted by the control system to at least one of the physical and virtual store systems to thereby change the price of the identified product. Thus, the system communicates advertising price change codes indicative of different advertised prices, i.e. it is capable of price optimization. On the other hand, although it handles advertising, it does not have means for assessing efficacy of different methods of advertising, neither means for sharing out a cumulative demand increase to various sources of advertising. By implication, it cannot estimate sources of demand variability and cannot simultaneously optimize pricing and advertising.
U.S. Pat. No. 6,078,893 (Ouimet, et al., 2000). In this invention, the user selects a demand model and a market model. The market model describes how some of the parameters of the demand model behave according to external market information. The market model is derived by studying prior sets of sales histories and determining an empirical relationship between the sales histories and the parameters of the demand model. The user first selects a consumer demand model to be tuned to the sales data. Consumer demand models are known in the art, and in a preferred embodiment, the user will be provided with a database of predefined demand models from which to choose. The user will also be given the option of defining a new demand model that can be tailored to meet the user's specific needs. Next, the user selects a market model, which describes how some parameters of the demand model are expected to behave according to external market information. He will be given a number of options for selecting a market model. In addition, the user can also be provided with a database of predefined market models, each corresponding to a particular demand model, from which to choose. In a similar fashion, the user is given a number of other options for making important decisions.
This model is very complex and contains a lot of elements that have to be fixed by the user to enable the system to work. Consider, for instance, selection of a market model that functions as a penalty function for the demand function. Such a selection is by no means a simple matter for an average user. Moreover, its parameters are to be estimated before it could be used in the system for modifying the demand function. Erroneous selection or estimation of a market model will result in an erroneous combined model, thereby ruining the initial demand function instead of correcting it. By contrast, in our own invention this problem is solved by restricting potential prices to an priori selected neighborhood of the current price in the pricing space. Such an approach does not require from the user to make decisions that he may be unwilling or unable to make.
U.S. Pat. No. 6,094,641 (Ouimet, et al., 2000). In this invention, the original demand model is modified to include a mechanism to convert actual prices into perceived prices, thus causing the demand model to predict higher demand for certain prices. The user specifies the function that converts from real prices to perceived prices. This modified demand function is then fitted to a sales history to yield the parameters appropriate to its particular form. Also, the demand model can be modified to account for promotional effects. The user defines a visibility model, which gives the relative increase in demand for an item caused by a promotion, and the cost of the promotion. The demand model is modified to include the effect of increased demand based on the visibility, and a profit model is modified to account for the added cost due to the added visibility. The profit model is then optimized with respect to both prices and promotions. Advertising is used in a general sense including newspaper ads, etc. Psychological effects include price thresholds, etc. Model selection refers, apparently, to a choice of the form of demand function. Although it ostensibly provides additional features to the user, it is hard to see how the user could make a meaningful choice between different forms of demand function. Even more problematic for the user may be the need for defining a visibility model that should give the relative increase in demand for an item caused by a promotion. Visibility model is suggested to be given by a table providing the relative increase in demand for an item at a given price vis-à-vis promotion. It is not clear from the text how this 'relative increase' is to be estimated. Model estimation called "tuning process" in the patent, includes also optimization and uses simulated annealing without any reasoning for its appropriateness.
U.S. Pat. No. 6,553,352 (Delurgio et al., 2000) describes a method for enabling a user to determine optimum prices of products on sale. The interface includes a scenario/results processor that enables the user to prescribe an optimization scenario, and that presents the optimum prices to the user. The optimum prices are determined to maximize a merchandising figure of merit such as revenue, profit, or sales volume. The optimum prices are determined by execution of the optimization scenario, where the optimum prices are determined based upon estimated product demand and calculated activity based costs. The patent contains extended arguments for optimizing product groups rather than individual products. Promotion optimization is dealt with in the co-pending patent application 20030110072. Detailed descriptions concern mainly interfaces, other parts are very short and do not present sufficient detail for implementing the methods as stated. In particular, the patent does not contain description of method for estimating target functions for optimization, nor methods of optimization, nor methods for estimating errors that contaminate the results.
US Patent Application 20020099678 A1 (Albright et al., 2002) describes a system and method for predicting and analyzing the consequences of a pricing or promotional action in a retail setting, and also for monitoring the actual result of marketing actions and communicating real-time or near-real-time information regarding the results. According to one aspect of the invention, a management tool links sales data and modeling algorithms to predict the results of pricing or promotion actions, thereby allowing a user to propose an action and view the predicted results. According to another aspect of the invention, the management tool monitors an implemented action and assesses the effect of the action on performance metrics. According to another aspect of the invention, users can select elements for a template for a web page displaying select company information, such as news, a scorecard showing pricing/promotion action results, the company's and/or its competitors' stock prices, current market capitalization and corporate PSP sales. Graphical user interfaces allow a user to easily interact with the underlying modeling applications to set a specified goal, to query the consequences of proposed actions to compare results from more than one potential action using selected performance metrics.
Despite these attractive features, the modeling system as described in patent application 20020099678 contains no clear method of integrating pricing and promotion influences into cumulative influence onto product's demand. In particular, it does not contain a means of simultaneous balancing of pricing influences that apparently are very strong with promotion influences that may be unreliable and sometimes negligible and statistically insignificant. Neither, does it contain means for assessing significance of promotion influences and deciding whether they warrant considerable changes of promotion scheduling in particular ways and directions. Next, although the system contains means for manipulating 'if-then' scenarios and queried proposed actions, it does not allow for optimization of prices and promotions by searching for optimal courses of action in the pricing-promotion space. Thus, on a number of important points, the system falls short of achieving the targets set up for the system described in our invention.
US Patent Application 20020123930 A1 (Boyd et al., 2002) provides a promotion pricing system for producing and evaluating promotion pricing strategies. In particular, a user may evaluate historical data to determine a promotional strategy to accomplish various business goals, such as increasing total sales volumes or increasing sales in certain desired market segments. The promotion pricing system can either propose a promotional strategy or evaluate the expected effect of a promotional policy provided by the user. The promotion pricing system works by defining market by specifying the various products in the market, as well as the suppliers and consumers. The promotion pricing system then looks to historical market data to create a market model which may be used to determine various information, such as profit or sales maximizing sales conditions.
The model is very general in that it is capable of using multiple sources of external information like data on market share of various products, data from competitors' transactions, etc. As always, however, generality comes at a price: much more of varied historical data are needed for reliable estimation of model's parameters and for testing for statistical effects. Also, optimization modules may face difficulties when trying to find solutions in high dimensional spaces. In contrast, the model in our invention can work with a bare minimum of historical data, i.e., with scanner data available in any computerized business environment. In addition, our system is capable of direct estimation of promotion effects of various clip series run on in-store monitors, and of estimating their efficiency or lack thereof while creating and monitoring promotion schedules.
US Patent Application 20030110072 (Delurgio et al., 2003). This patent application is related to co-pending application U.S. Pat. No. 6,553,352 and describes a method for enabling a user to determine optimum prices of products on sale. The interface includes a scenario/results processor that enables the user to prescribe an optimization scenario, and that presents the optimum prices to the user. The optimum prices are determined to maximize a merchandising figure of merit such as revenue, profit, or sales volume. The optimum prices are determined by execution of the optimization scenario, where the optimum prices are determined based upon estimated product demand and calculated activity based costs. Detailed descriptions concern mainly interfaces, other parts are very short and do not present sufficient detail for implementing the methods as stated. In particular, although promotion optimization is mentioned, neither method for estimating target functions for optimization, nor methods of optimization are given.
Our own previous invention described in US Patent Application no. 20030220830 A1: Method And System for Maximizing Sales Profits by Automatic Display Promotion Optimization, filed Apr. 4, 2002. The system in this patent application evaluates among other things, influences of various in-store promotion displays in a supermarket by using locally-weighted straight-line smoothers applied to historical data on demands in a database. A real time iterative optimization algorithm is used for calculation of optimal clip schedules. These functions are also present in our new invention in which they make part of the "promotion part" of the model. At the same time, the new model, or better say its "promotion part" is much more sophisticated and has a number of new features: it is not locally linear, is suitable for dealing with groups of interconnected products rather than with individual products, is provided with a learning algorithm for evaluating comparative efficiency of different promotion schedules, and some others.

System and method for profit maximization in retail industry


A method of encrypting data using a first key and multiple encryption keys at least in part based on the first key. The method includes encoding the data into a redundant representation by distributing the information content of the data among a number of groups, each group being associated with a respective encryption key of the multiple encryption keys, each encryption key being associated with at least one group, the redundant representation allowing recovery of the data in the absence of the groups associated with the at least one of the multiple encryption keys, and encrypting each group by the respective associated encryption key.

In present-day society, information is predominantly stored in a digital manner. Digital data can be reproduced, transmitted and stored in a simple manner and thus provides great ease of use. However, this ease of use also entails a potential privacy and security risk in the form of access by unauthorized parties. In order to cope with privacy and security issues, valuable information is often encrypted.
Encryption effectively forms a barrier that blocks unauthorized persons from accessing the information while allowing authorized persons to access the information. When encrypting information, data is generally encrypted by means of an encryption key resulting in encrypted data. In order to provide security, the encrypted data should not provide an outsider with information regarding the original data. In order to recover the data from the encrypted data, it needs to be decrypted by means of a decryption key corresponding to the encryption key.
Most encryption schemes use keys to encrypt and decrypt information. Data is encrypted by means of an encryption key and the encrypted data is decrypted by means of a decryption key. Two different types of encryption can be distinguished: symmetric encryption, wherein both the encryption and decryption key are the same, and asymmetric encryption, wherein the encryption and decryption keys differ. Although the encryption and decryption keys in asymmetric cryptography are different, they form a pair of keys, hereinafter referred to as "key pair", and use of other keys in combination with either the encryption or the decryption key will result in loss of data.
A relatively new trend is the use of biometric data as a source of key information in cryptography. Biometric data is derived from preferably unique physical features of an individual that are preferably stable over time. Examples of biometric modalities that are often used for access control are modalities such as fingerprints, palm prints, iris images, and facial characteristics. Biometric data is often used to provide individual access control.
Apart from the fact that the physical features of an individual may change, biometrics derived from such physical characteristics are acquired through measurement and/or detection. As a result, biometrics are often noisy. This noise may result from e.g. acquisition noise, the use of different sensors, different environmental conditions, and/or minor changes in the physical features of the individual. In order to reduce noise and derive more robust and more discerning data, there is a trend to derive feature vectors from the biometric measurement(s). However, feature vectors still exhibit a considerable variation and are thus inappropriate for use as key information. There has therefore been much research in order to derive robust keys from noisy data in biometrics.
"Fuzzy identity-based encryption" by A. Sahai and B. Waters published in Proceedings of EUROCRYPT, 2005 discloses a different approach that uses noisy data as a key in an Identity Based Cryptosystem. This particular scheme has the disadvantage that the noisy encryption key used to encrypt the data is also required for decrypting the encrypted data.

Method and apparatus for encrypting/decrypting data


A method for analyzing unconventional rock samples using nuclear magnetic resonance (NMR), tracking fluid change in the rock sample over a time period, calculating transverse relaxation time (T2) generating fluid distribution profiles by the computer processor and based on a NMR imaging, where the fluid distribution profiles representing a movement of the fluid, and obtaining, quantification of fracture volume by the computer processor and based on the NMR imaging.

Fluid flow is one of the most important properties in describing a reservoir and determining its production. It is important in producing unconventional tight reservoirs, including shale reservoirs, which generally have extremely low matrix permeability. In these reservoirs, the presence of fractures significantly enhances the flow capability. Fluid movement is much faster through the fractures than through the pore networks for tight formation rocks. In fracture-free, nanoporous samples, such as shales, it would take months for the fluid to flow from one side of a rock sample to the other without applying an external pressure gradient across the sample. If fluid is able to break through the sample in a short amount of time (e.g., 1-2 days), then such fast flow may be attributed to fractures that exist along the sample.
Nuclear magnetic resonance (NMR) spectroscopy and imaging has long been used to measure the rock and fluid property of conventional and unconventional rocks such as porosity, water and hydrocarbon saturation, and pore size distribution. Further, NMR may track the temporal and spatial changes of fluids into the rock samples.

Nuclear magnetic resonance method quantifying fractures in unconventional source rocks


A pixel electrode is located in a pixel area defined by the intersections of the two adjacent gate lines and the two adjacent data lines, and has two linear openings extending in the transverse direction, which divide the pixel electrodes into three rectangular portions arranged in the longitudinal direction. The portions are connected in turn, and each portion of the pixel electrode has an X-shaped projection formed by the X-shaped member thereunder, and portions of the gate insulating film and the passivation film on the member. Since the gate insulating film and the passivation film are also located on the gate lines and the data lines, and the layered structure on the wires acts as peripheral projections of the pixel electrode. Each area enclosed by the projections, the openings and the peripheral projections is in a shape of equilateral trapezoid. The areas may be defined as the areas where the pixel electrode is in direct contact with the substrate. That is, each area has a planar shape of triangle, of which corner at the center of X-shape is chamfered. This structure causes a splay arrangement or a bend arrangement of the liquid crystal molecules in each domain, which is defined as a portion of the liquid crystal layer over each divided area, to be reinforced to improve the response time.

(a) Field of the Invention
The present invention relates to a liquid crystal display (LCD) panel, and, in particular, to a thin film transistor (TFT) array panel for an LCD.
(b) Description of the Related Art
Generally, an LCD includes an upper panel having a common electrode and a plurality of color filters, a lower panel having pluralities of TFTs and pixel electrodes, and a liquid crystal layer between the two panels. The pixel electrodes and the common electrode are applied with different electric potentials to generate electric fields which change the alignment of liquid crystal molecules to control the light transmittance, thereby displaying images.
However, an LCD has a serious disadvantage of its narrow viewing angle. To overcome this disadvantage, various techniques for widening the viewing angle are suggested. Among them, there is a technique that the liquid crystal molecules are aligned perpendicular to the upper and the lower panels and pluralities of openings and/or projections are provided in the pixel electrodes and a common electrode facing the pixel electrodes.
In a conventional technique directed to the openings, the openings are provided in both the pixel electrodes and the common electrode to generate fringe field. The tilt directions of the liquid crystal molecules are adjusted by using the fringe field. A conventional technique related to the projections adjusts the tilt directions of the liquid crystal molecules by using electric fields which are distorted by the projections. In a European Patent EP 0 884 626 A2, various features of the projections are suggested.
Although the viewing angle of the LCD is improved as suggested by the above conventional techniques, the response time of the liquid crystal molecules is not still improved so that it is difficult to display dynamic images due to afterimages.