Abstract: Embodiments of the invention provide methods and systems for improving the reliability of data stored on disk media. Logical redundancy is introduced into the data, and the data within a logical storage unit is divided into sectors that are spatially separated by interleaving them with sectors of other logical storage units. The logical redundancy and spatial separation reduce or minimize the effects of localized damage to the storage disk, such as the damage caused by a scratch or fingerprint. Thus, the data is stored on the disk in a layout that improves the likelihood that the data can be recovered despite the presence of an error that prevents one sector from being read correctly.

Abstract: Provided are systems, methods and techniques that use an embedded error-detection code within a received communication signal to determine when to stop iterative decoding of the communication signal.

Abstract: The present invention relates to a method for analyzing a decoded digital signal stream. The method comprises decoding an encoded digital signal stream to obtain a decoded digital stream and terminating the decoding operation in an N dimension, wherein N is an integer greater than one. The method further comprises calculating one or more syndromes in a dimension not comprising the N dimension of the decoded digital signal stream. At least one invalid syndrome is then detected from the one or more calculated syndromes. In one embodiment, an error is reported in the decoded digital stream based upon detecting at least one invalid syndrome.

Abstract: A signal reception apparatus for a communication system is disclosed in which the signal reception apparatus receives a signal and decodes the received signal using a second decoding scheme approximated from a first decoding scheme. The second decoding scheme is a scheme of applying a correction value to a third decoding scheme approximated from the first decoding scheme, and the correction value is a value for correcting a difference between a first signal obtained by decoding the received signal using the first decoding scheme and a second signal obtained by decoding the received signal using the third decoding scheme.

Abstract: A method of discovering a fault in a circuit is disclosed. The method comprises generating a first result of a selected function by performing the selected function on an operand, wherein the selected function employs a mask. Once the function is performed, an antimask of the mask is created, and the modulo of the antimask is calculated. A modulo function of the first result of the selected function is calculated to obtain a third result. A modulo of the operand is then calculated to obtain a fourth result, and a second function is then performed on the second result and the third result to obtain a fifth result. In response to comparing the fifth result to the fourth result, a signal is propagated to indicate a fault in the circuit.

Abstract: Planar rendering is described. In an implementation, a method includes approximating a shape that corresponds to an overlapping portion of at least one graphical element that is translucent with another graphical element. A color is computed for the approximated shape from respective colors of each of the graphical elements and the translucence of the at least one graphical element. The approximated shape having the computed color is formed into a communication for output to a printer.

Abstract: An information distributing system for distributing data to at least one information processing terminal device from an information center storing data. The information distributing system is structured such that character data, audio data, and both the character data and the audio data are selectively downloaded from the information center to the information processing terminal device on the basis of request information from the information processing terminal device, so that a user has multiple options for information selection and effective information collection becomes possible.

Abstract: Mechanisms are provided for drilling on data elements in arbitrary ad-hoc reports. Data elements in one ad-hoc report can be examined and then drilled on, in order to obtain other related data elements in other ad-hoc reports. Thus, in one exemplary aspect of the disclosure, when a user selects a data element in an ad-hoc report, another ad-hoc report is generated containing data elements that are obtained as a result of taking into account 1) the original query associated with data element in the ad-hoc report; 2) the context of the selection in the ad-hoc report, and 3) the granularity of the resulting query associated with the resulting ad-hoc report.

Abstract: Tools and techniques are provided to visualize and manage data. A hierarchical pie chart is placed in operational correspondence with a hierarchical table. Slices of a pie chart level correspond to nodes of a table level. When a user causes a change in a node/slice, the software automatically performs a matching change in the corresponding slice/node. This occurs for operational changes such as selection, creation, deletion, expanding (zoom in, drill down), contracting, updating data, and changing a label. The path taken through the table to reach the present data breakdown may also be displayed.

Abstract: Techniques to cross-reference information for application programs are described. An apparatus may comprise a first application program to create notes for an operator, a second application program to display a target document, and a context reference module to generate a context reference for the target document indicating a source for the target document, display the context reference, and associate the context reference with a note. Other embodiments are described and claimed.

Abstract: Text is extracted from and information resource such as documents, emails, relational database tables and other digitized information sources. The extracted text is processed using a decomposition function to create. Nodes are a particular data structure that stores elemental units of information. The nodes can convey meaning because they relate a subject term or phrase to an attribute term or phrase. Removed from the node data structure, the node contents are or can become a text fragment which conveys meaning, i.e., a note. The notes generated from each digital resource are associated with the digital resource from which they are captured. The notes are then stored, organized and presented in several ways which facilitate knowledge acquisition and utilization by a user.

Abstract: Layout data relating to layout of a user and a device is obtained. Log data relating to usage of the device, such as a job being performed or to be performed by the device, is obtained. A layout diagram illustrating the layout of the user and the device is generated based on the layout data. Line data to be additionally included in the layout diagram is generated based on the log data.

Abstract: A method (100) is disclosed for generating a page description from a list of items (201 to 204) to be rendered to the page. At least one of the items in the list belongs to a class of key items (201). Such key items may for example be text items. The method (100) traverses (601) the list, and classifies items (202, 203) not designated as key items that would when rendered overlie at least one key item (201). At least one other non-key item is then rendered to image data (104, 105), and the page description is generated (107) from page description commands which describe the key items (201), page description commands describing the classified items (202, 203), and rendered image data of the remaining items (200). Including certain items (201, 202 and 203) in the page description using page description commands ensures that the quality of such items is retained. Also, including the remainder of the items (200) using image data provides for high compression.

Abstract: A method, computer program product, and system for analyzing data using a data warehouse application are provided. The method, computer program product, and system provide for displaying a facet in a user interface of the data warehouse application, the facet classifying a plurality of documents, and displaying a facet attribute of the facet in the user interface of the data warehouse application, the facet attribute corresponding to a characteristic associated with each of the plurality of documents classified by the facet.

Abstract: Some embodiments of the invention provide a user interface of editing video through a multi-stage editing process. The user interface selects a particular stage in the editing process. A particular editing operation is performed on a set of video images during the particular stage. After the selection of the particular stage, the user interface uses a background rendering process to render the result of the particular editing operation on the particular set of video images. The background rendering process is a process that the user interface performs separately from the multi-stage video editing process, so that a user may continue editing the video sequence while the rendering occurs. Some embodiments provide a preview of the rendering process in a preview window. Some of these embodiments update the preview in real time. In some embodiments, the rendering occurs to a temporary location and then stores to a persistent storage.

Abstract: Some embodiments of the invention provide a computer-based application that allows its users to insert their pictures in a variety of different photo album books (called photo books below). Each photo book has several pages that have one or more picture fields for presenting pictures. Different photo books can differ in their size, themes, covers, page designs, page colors, picture-field designs, picture-field layouts, and/or other attributes. In some embodiments, the application also allows the users to modify photo books that they select. For instance, in some embodiments, a user can modify the page design, color, frame design, and/or other thematic aspects of a selected photo books. Also, in some embodiments, the user can add picture and text fields to the photo book. Once the user has completed designing the photo book and inserting pictures in the photo book, the user can order the photo book through an online transaction that is initiated through the application.

Abstract: In a terminal with a display screen that is too small to accept a required input in its entirety, a user is enabled to perform the input without intricate operation. The terminal displays input pages downloaded from a server via a network, and transmits input information entered into the pages by the user. The terminal comprises a page display section, which displays a plurality of input pages using a browser executed on the terminal, an input information storage section, which stores a plurality of input parameters entered into more than one of the input pages, and an input information transmission section, which combines the input parameters and transmits the combination to the server in response to an instruction.

Abstract: Method and apparatus for variable help content and abandonment intervention based on customer behavior in computer applications. A pattern detection and intervention mechanism may be provided that may collect usage and possibly other data for the application for a plurality of users of the application and analyze the usage data to determine usage patterns. The collected data and determined usage patterns may then be used by the pattern detection and intervention mechanism to look for and detect deviations from expected behavior and/or patterns of abnormal behavior. Embodiments may provide one or more methods of intervention to provide context-specific help or otherwise assist users for which deviations from expected behavior and/or abnormal patterns of behavior are detected. The detection that users are having difficulty with the application and proactive intervention when such difficulties are detected may help to prevent the users from abandoning the application.

Abstract: A method, apparatus, and article of manufacture enables users to collaborate on an actual stored drawing document across a network. A single document is stored on a server who establishes a collaboration session with multiple users that collaborate in real time and dynamically view modifications executed by the users. Users maintain simultaneous write access to the document. Asynchronous commands are received from users, that have a delay of a defined time period, include any modifications made in real time by the user transmitting the asynchronous command, and cause the server to transmit any modifications to all of the multiple users in the collaboration session. The server also maintains a history of all modifications to the actual stored drawing document. The history can be used by a user to undo any user's modifications.

Abstract: An apparatus for providing for virtual communication and collaboration comprises a collaborative virtual environment (CVE) application executing within a distributed data processing system, and a shadow module implemented within the CVE application. The CVE application provides a virtual world represented as a grid of an interconnected set of locations each divided into a set of zones and each having an assigned context through a user interface provided to a plurality of users through one or more client systems. The CVE provides each user with a respective avatar representation for navigating and interacting within the locations of the virtual world. The shadow module provides a first user interface element through which a first user can create and leave a shadow object representation for the first user within a zone of a subset of the set of locations when the avatar representation for the user is currently located in that zone.

Abstract: [Object] To provide communication space for the user to have crossing over of discussions with respect to plural phrases while allowing the discussions to be conducted individually in parallel. [Means for Solution] A module for generating phrase object (FO) data which contain identification information of phrase data and position information of a FO on a chat canvas (CC), a module for generating chat data which contain message text data and display position information on CC, a module for transmitting the chat data to a server, and receiving the chat data distributed from the server, a module for transmitting the FO data to the server and receiving the FO data distributed from the server, and a module for displaying the FO or the message text on the CC based on the FO data or the chat data are provided. The display mode of the message text is determined based on the display mode of the FO located close to the display position of the message text.

Abstract: Co-brands, virtual wrappers for web sites that allow clients to expand client inventories across different web sites, are disclosed. Different types of travel inventory can be provided across these web sites. A client can create different URLs, domains, look and feel, product filters, pricing rules, business logic, payment methods, languages, currencies, etc. off a single instance. A client can create a co-brand and, using an administrator application, configure its settings to target specific geographic locations, targets markets or even themes. Additionally, co-brands are used to allow third party vendors to direct traffic to client sites. Co-brand tools are designed to make items such as navigation, images, buttons, domain names, colors, fonts, languages and currencies. Co-brands make it easier for travel companies to have sites based on demographics, destination, and events that can lead to greater adoption and conversion.

Abstract: A mobile electronic communications device and a method for modifying a scheduling database are provided. The scheduling database is modified via the mobile electronic communications device in communication with a proximate electronic device comprising a display device, the mobile electronic communications device is engaging an oral communications session with a second communications device. Time slot data associated with an available time slot is retrieved from the scheduling database, via the mobile electronic communications device. The time slot data is transmitted to the proximate electronic device causing it to display the time slot data at the display device. Input data representative of a command to update the scheduling database is received at the mobile electronic communications device. An entry of the scheduling database is updated, via the mobile electronic device, based on the time slot data associated with the available time slot displayed at the display device.

Abstract: A computer implemented method includes selecting a portion of a data set in a first visualization. A list of visualizations relevant to the context inferred from the selection of the portion of the data set in the first visualization is generated. A second visualization from the list of visualizations is rendered.

Abstract: Techniques are disclosed herein for re-ordering floating objects in an electronic document. An electronic document having floating objects is displayed in a first mode. Each floating object has an x-y location in the document and has a position on a z-order stack. In the first mode the floating objects are displayed in an x-y plane based on the z-order stack. Then, the electronic document is displayed in a second mode in which the electronic document is depicted as x-y plane slices. Each x-y plane slice corresponds to one position on the z-order stack. The x-y plane slices are displayed in particular order to depict the position of the floating objects on the z-order stack. A re-ordering of the x-y plane slices is displayed based on a request. Then, the electronic document is displayed in the first mode again based on the re-ordering of the x-y planes.

Abstract: A method for receiving page-specific user feedback concerning a particular web page of a website includes using a comment icon viewable on the page to solicit one or more page-specific open-ended comments concerning the page from a user. In one embodiment, the method includes using software associated with the comment icon to automatically communicate a request for a comment window to a remote computer system that is separate from a computer system hosting the website in response to the user selecting the comment icon, receive the comment window from the remote computer system, present the comment window to the user, and receive one or more or more page-specific open-ended comments concerning the page from the user provided using the comment window for reporting to a website owner.

Abstract: An image pickup apparatus allows a user to quickly find a changed setting value in a list screen after the user changes the setting value of a desired setting item and returns to the list screen. When a rightward direction button is pressed with the list screen being displayed on a display unit, a setting screen of a drive mode is displayed. When a desired drive mode is selected in the setting screen by using a rightward or leftward direction button, an icon is displayed in a predetermined color for indicating selection. When the setting is activated by a set button, a highlight is displayed on the icon in order to indicate activation. After the highlight is displayed for a predetermined period of time, the screen is changed to the list screen, and the previously set drive mode is highlighted so that the user quickly recognizes the changed drive mode.

Abstract: A method for performing a task, which includes generating a user interface with multiple screens where each screen corresponds to a step in a workflow used for performing the task; generating multiple live thumbnails which include miniaturized sections of the screens; displaying a first screen of the multiple screens and the multiple live thumbnails to a user using the user interface; populating a field on the first screen with input data entered by the user; determining a validity of the input data; updating a first live thumbnail of the multiple live thumbnails corresponding to the first screen based on the input data and the validity; receiving a screen selection from the user; displaying a second screen of the multiple screens corresponding to the screen selection; and updating a second live thumbnail of the multiple live thumbnails corresponding to the second screen based on the screen selection.

Abstract: An apparatus and method for providing a three-dimensional graphic user interface includes a control module which creates a three-dimensional interface space having a predetermined plane and an axis perpendicular to the plane, and a plurality of objects presented in the space, and a user interface module which presents a plurality of object groups including the plurality of objects in the space, and moves an object group including a selected object among the plurality of presented object groups along the axis.

Abstract: A system and method allows a user to specify a presentation by arranging content into a hierarchical arrangement. The presentation is generated in response to the content and the hierarchical arrangement.

Abstract: An apparatus that evaluates a layout of a semiconductor integrated circuit by estimating a result of planarization in manufacturing the circuit includes a unit that divides the layout into partial areas, a unit that calculates, for each partial area, at least one of a wiring density in the partial area, a total perimeter length of wirings in the partial area, and a maximum value of differences of wiring densities in adjacent partial areas adjacent to the partial area from the wiring density in the partial area as partial area data, a unit that sets ranges of the wiring density, the total perimeter length, and the maximum value from which a height variation larger than an upper limit value is expected as critical regions based on an equation corresponding to a type of the layout, and a unit that plots the critical regions and the partial area data on a same map.

Abstract: A computer converts dimensions of design patterns of components of the transistors configuring the semiconductor circuit or component parameters extracted from in-design physical characteristics of the transistors into simulation parameters inputted to the simulator, organize the plurality of transistors included in the semiconductor circuit into a plurality of groups, selects any selection groups from the plurality of groups, sets fixed parameter values as component parameters of the non-selected groups other than the selection groups in the plurality of groups, sets the combinations of the component parameters in the selection groups, acquires circuit characteristics with respect to each combination of the component parameters, selects a group as a next selection group different from the selected groups, and repeatedly executing the setting the fixed parameter values through the selects a group as a next selection group different.

Abstract: A method and system for designing an optimized specification of an integrated circuit (IC) is provided. The IC comprises a plurality of cells, and each of the cells comprises a plurality of transistors. The method includes preparing a linewidth map of at least one device of the plurality of devices, performing a topography-aware analysis of the at least one device based on the linewidth map, and designing the optimized specification of the IC based on the topography-aware analysis. In another embodiment, a method for estimating a leakage power of at least one device in an IC is provided. The method includes determining a defocus and a pitch value, determining a linewidth value based on the defocus and pitch value, and estimating the leakage current and/or leakage power based on the linewidth value.

Abstract: The invention can provide a method of processing a substrate using multi-pitch scatterometry targets (M-PSTs) for de-convolving lithographic process parameters during Single-Patterning (S-P), Double-Patterning (D-P) procedures, and Double-Exposure (D-E) procedures used to control transistor structures. The M-PSTs) can have critical dimension (CD) and sidewall angle (SWA) sensitivity to exposure focus variations, exposure dose variations, and post exposure bake (PEB) temperature variations. In addition, the variation can be de-convolved so that the individual measurement process variable contributor can be identified.

Abstract: A method for implementing virtual metal fill includes obtaining a layout record for a circuit design, and inserting metal fill data into the layout record based on one or more rules, wherein the metal fill data represents a consolidation of actual metal fill. A method for implementing virtual metal fill includes obtaining a layout record for a circuit design, and inserting metal fill data into the layout record, the metal fill data representing a virtual metal fill having a configuration that is different from a configuration of actual metal fill.

Abstract: An interface to a dynamically configurable arithmetic unit can include data alignment modules, where each data alignment module receives input variables being associated with one or more arithmetic expressions. The interface can include multiplexers coupled to the data alignment modules, wherein a data alignment module has outputs coupled to a first multiplexer. The first multiplexer can have a selection line and an output coupled to an input port of the dynamically configurable arithmetic unit. The interface can include a second multiplexer having input instructions and the selection line, where each instruction is associated with one of the arithmetic expressions and has an operation to be performed by the dynamically configurable arithmetic unit. The second multiplexer is configurable to provide selected ones of the input instructions to the dynamically configurable arithmetic unit through an output of the second multiplexer responsive to the selection line.

Abstract: A design structure for a signal-handing apparatus or communication apparatus is provided which includes a common signal node operable to conduct a first signal, a first circuit coupled to the common signal node to utilize the first signal and a signal-handling element coupled to the common signal node. A signal-handling apparatus may include an isolating circuit coupled to a first conductor, a second conductor to conduct an output of the isolating circuit, and a signal-handling circuit coupled to the second conductor. A signal-handling circuit can perform a signal-handling function in response to the output of the isolating circuit. The signal-handling circuit and the first circuit may be isolated from the second conductor and the signal-handling circuit such that a communication signal may be conducted with less capacitance and be subject to less return loss.

Abstract: A minimal leakage power Standard Cell Library is provided. The minimal leakage power Standard Cell Library provides minimal leakage power cells with improved speed characteristics. The minimal leakage power Standard Cell Library includes cells from an existing Standard Cell Library and a set of minimal leakage power cells for a selected set of logic functions. The minimal leakage power Standard Cell Library is formed by identifying a set of logic functions. For each logic function in the identified set, a base case for an unfolded implementation of the logic function is determined. Widths for transistors in a transistor topology used in the unfolded implementation of the logic function are determined based on the non-linear leakage power characteristics for the transistor topology to achieve minimal leakage power. The determined widths are then assigned to the transistors and the minimal leakage cell is added to the library.

Abstract: A Hardware Description Language (HDL) processing method is implemented in a computer and processes a HDL file which is written in HDL having a hierarchical structure including three or more hierarchical levels in a Computer-Aided Design (CAD) which supports hardware design. The HDL processing method analyzes the hierarchical structure of the HDL and obtaining an analysis result, and processes the HDL one at a time for each hierarchical level based on the analysis result or, process the HDL one at a time by a parallel distributed processing for each hierarchical level based on the analysis result.

Abstract: For application to analog, mixed-signal, and custom digital circuits, a system and method to do: global statistical optimization (GSO), global statistical characterization (GSC), global statistical design (GSD), and block-specific design. GSO can perform global yield optimization on hundreds of variables, with no simplifying assumptions. GSC can capture and display mappings from design variables to performance, across the whole design space. GSC can handle hundreds of design variables in a reasonable time frame, e.g., in less than a day, for a reasonable number of simulations, e.g., less than 100,000. GSC can capture design variable interactions and other possible nonlinearities, explicitly capture uncertainties, and intuitively display them. GSD can support the user's exploration of design-to-performance mappings with fast feedback, thoroughly capturing design variable interactions in the whole space, and allow for more efficiently created, more optimal designs.

Abstract: An apparatus, method and program product create multiple copies of a clock signal, or phase, to analyze timing operations within a single timing run of a static timing analysis operation. At least one path comprising logical user defined delay segments and a timing point may be associated with both a common point and no delay. An original clock signal may propagate along the logical path without incurring delay until arriving back at the common point, along with the original signal. All other clocks may be ignored or prevented from propagating long the path. Multiple replicated copies may be accomplished without requiring additional hardware.

Abstract: Design data of a cell group is copied to obtain design data of an antecedent cell group and of a subsequent cell group. Design data of a combinational circuit is copied to generate the combinational circuits in plural corresponding to a given number of cycles n (n=2, 3, 4 . . . , where n=3 in FIG. 4). The design data of the combinational circuits are connected in series between the design data of the antecedent cell group and the design data of the subsequent cell group. As a result, design data of an input constraint circuit representing an input constraint(s) of the circuit can be generated.

Abstract: A delay analysis support apparatus that supports analysis of delay in a target circuit includes an acquiring unit that acquires error information concerning a cell-delay estimation error that is dependent on a characterizing tool; an error calculating unit that calculates, based on the error information and a first probability density distribution concerning the cell delay of each cell and obtained from the cell delay estimated by the characterizing tool, a second probability density distribution that concerns the cell-delay estimation error of each cell; and an linking unit that links the second probability density distribution and a cell library storing therein the first probability density distribution.

Abstract: Methods and apparatuses for retiming of multirate system for clock period minimization with a polynomial time without sub-optimality. In an embodiment, a normalized factor vector for the nodes of multirate graph is introduced, allowing the formulation of the multirate graph retiming constraints to a form similar to a single rate graph. In an aspect, the retiming constraints are formulated to allowed the usage of linear programming methodology instead of integer linear programming, thus significantly reducing the complexity of the solving algorithm. The present methodology also uses multirate constraints, avoiding unfolding to single rate equivalent, thus avoiding graph size increase. In a preferred embodiment, the parameters of the multirate system are normalized to the normalized factor vector, providing efficient algorithm in term of computational time and memory usage, without any sub-optimality.

Abstract: The present invention relates to a system for reducing the delay during technology mapping in FPGA that comprises locating and replicating the critical fan-in nodes in the mapping logic. Parallel computation is performed on the replicated nodes followed by selection of the output. The delay reduction approach in the present invention gives a highly efficient logic implementation when delay is the prime concern and area can be afforded to be expanded. The technique relies on replicating logic and performing parallel computation on delay critical LUT's.

Abstract: A method for detecting reverse engineering of a configuration bitstream for an integrated circuit is described. A user design is obtained. It is determined if the user design is a degenerate design. If the user design is a degenerate design, it is determined if a trip point for bitstream generation has been tripped. If the trip point for the bitstream generation has not been tripped, deterrence information is updated and the bitstream generation is allowed to take place. If the trip point for the bitstream generation has been tripped, at least one reverse engineering countermeasure is initiated.

Abstract: It is an object to provide a semiconductor integrated circuit which can easily be designed and has a low wiring resistance, and a method and apparatus for designing the semiconductor integrated circuit. In a semiconductor integrated circuit apparatus according to the invention, a first wiring layer is provided with a plurality of signal wirings having an equal width which is disposed in parallel with each other at a regular interval, and at least two of the signal wirings which are adjacent to each other are electrically connected to each other.

Abstract: A system, method and computer program product are provided for determining routing of data paths in interconnect circuitry for an integrated circuit. The method includes the steps of defining a plurality of cells to be provided along the wide interface of the circuitry, further devices being associated with at least one of the cells, and defining the circuitry as an array of blocks formed in rows and columns, with each cell abutting one of the columns. The method includes the steps of: providing a predetermined set of tiles, each tile providing a predetermined wiring layout, and for each block, applying predetermined rules to determine one of the tiles to be used to implement that block, where the rules take into account the location of the block in the array and any association between the further devices and the cells.

Abstract: The present invention relates to an automata unit, a tool for designing circuitry and/or checker circuitry, and a method for manufacturing hardware circuitry. The automata unit includes an input unit for receiving assertions using Boolean expressions, an automata generator for translating the assertions into automata, and an automata adaptor. The automata generator uses a dual layer symbolic alphabet for representing the assertions, and the automata adaptor adapts automata algorithms so as to support the symbolic alphabet in the generated automata. The tools for designing circuitry and checker circuitry rely on the automata unit, and further include an assertion unit and either a circuit generator or a checker generator.

Abstract: Described herein are embodiments of methods for extracting various high frequency parameters for a circuit design. In one exemplary embodiment, circuit design information indicating at least a geometric layout of conductors in the circuit design and a desired frequency of operation for the circuit design is received. Conduction modes representing distribution functions for currents in the conductors at the desired frequency of operation are defined. A conduction mode matrix including matrix elements based on the defined conduction modes is generated. Values for one or more matrix elements are computed by decomposing integrands for calculating the matrix elements into simplified terms that are less computationally intensive than the integrands and computing the values of the simplified terms. The values for the one or more matrix elements can be stored (e.g., on one or more computer-readable media).