Integrated Water Resources Management requires the analysis of information from multiple sources. Data must be visualized for different audiences.

CB&I is the world's leading designer and builder of industrial storage facilities, tanks and terminals. We use Mathematica to perform the engineering calculations to design our products. The functions that run these calculations may have hundreds of inputs that require proper units, ranges, and data types. We need to help users quickly enter and validate these inputs and fix problems such as accidentally modified or deleted code while keeping the flexibility that Wolfram Notebooks allow. Our solution is a package called NotebookInterface. The package combines the benefits of standard Input cells that can be modified by the user and a dynamic user interface that validates inputs, highlights changes, and repairs invalid or out-of-date cells. We will show how we use the package in a large corporate environment and how you can use it to create user interfaces for your own software.

The Wolfram Compiler converts Wolfram Language code into native machine instructions that run directly on the machine hardware. It offers a powerful way to speed up programs and provides many opportunities for innovative programming features such as building connections to external libraries and accessing new technologies. It is also used for an increasing amount of new development. This talk will describe the Wolfram Compiler and its latest advances and directions.

In this talk I will show the state of the Video object in the Wolfram Language as well as all the computational power developed around it in order to create, process or analyze videos. https://wolfr.am/video

The Victorian Curriculum and Assessment Authority Systems Engineering Study involves the design, iteration and production of integrated systems. Integral to the study design is the identification and quantification of systems goals, the generation of system designs, trial and error, justification, modelling and the implementation of a response. The study considers the interactions of systems with people, society and ecosystems and seeks to optimise system efficiency and performance through agile processes. Learners design, conduct, analyse, critique and display meaningful research. The study design rewards risk taking with rubric-assessed processes of intention development, making and evaluation of response, and iteration processes. The study encourages multimedia narratives that recognise those moments when intentions met reality. Wolfram System Modeler and Mathematica through the Computational Essay approach allow rich, thick descriptions of achievement as learners engage in responses to curated stimulus in an Extreme Citizen Science frame. This workshop works through the development of a Polarimeter from scratch using an Arduino microcontroller, the ModelPlug library in Wolfram System Modeler and the computational functionality of Wolfram Mathematica. The Computational Essay gives a narrative of data wrangling, uncertainty and calibration. The Polarimeter was contrived to determine the sugar content of soft drinks, in support of an investigation into athlete nutrition.

The Wolfram Compiler is one of the largest applications built from the Wolfram Language. This talk will review the software engineering practices used to build the Wolfram Compiler, ensure it runs correctly and improve its efficiency. It will also discuss its internal organization, showing how this is an innovative way to understand compiler-related computer science. It will discuss how the compiler is a powerful way to learn about compilers and also to develop new compiler techniques.

Come chat with the chemists who develop chemistry in the Wolfram Language.

The Wolfram Data Structure library offers performant implementation of many traditional data structures. It is implemented with the Wolfram Compiler. This talk will review the current data structures and show how they can be used to improve your code. It will also show how data structures can be used inside compiled code to gain particularly optimal performance.

Wolfram|Alpha on mobile devices has changed this year. In this presentation, we will talk about everything that is new with Wolfram|Alpha for iOS and everything that is to come soon to Wolfram|Alpha for Android. We'll be going over the new look and the new features, including math OCR and the personal and professional assistants.

This talk will cover the structure and innovative uses of food data within the Wolfram Language. We will demonstrate how to retrieve data for popular fast foods and how to analyze and manipulate a large dataset of alcoholic beverages. We will introduce new food safety data available in the Wolfram Language, including maximum refrigerator and freezer storage times for more than 200 foods, and demonstrate the synergy of Wolfram|Alpha food data and biology data to analyze foodborne-illness pathogens and their food sources. Next, we will invite the audience to play "Should I Eat That?," in which audience members have fun testing their food safety knowledge against Wolfram|Alpha data. We'll wrap up with a sneak peek at exciting future developments for food in the Wolfram Language.

In '20 I focused on Olympiad geometry and in '21 I covered four problems about circle inversion, asymptotics, number theory and combinatorics just like the IMO exam syllabus. Both talks were welcomed by virtual event attendees and YouTube viewers. This year I am going to use the same instruction style as in '21 and demonstrate problem-solving skills in these four domains. In the past years there have been a large amount of Wolfram Function Repository submissions, which opens several new paths for solving challenging problems with even fewer lines of code and in clearer ways of thinking. I have selected couple of problems and examples from the following published resources: L.A. Graham's Ingenious Mathematical Problems and Methods, R. Honsberger's From Erdös to Kiev: Problems of Olympia Caliber (or related CRUX volumes), M. H. Weissman's An Illustrated Theory of Numbers and lastly Stanley's Enumerative Combinatorics. The Wolfram Language's built-in functions and Wolfram Function Repository resources have a unique charm to make the exploration of the solutions very expressive. It is critical to see the connection between the "Aha!" moment and solid examples generated by the Wolfram Language, even with silly brute-force methods at first. It is my wish all my audience will enjoy the talk and start their own journeys of solving challenging problems with the Wolfram Language.

This talk gives an update on our efforts to bring the full power of Wolfram Language graphics to the Wolfram Cloud.

We present updates to the automated geometric functionality of the Wolfram Language introduced in Version 12, including new functionality for automated geometric reasoning and for creating GeometricScene objects.

Wolfram technology provides access to a diverse range of computable knowledge about biology. In this talk, topics such as taxonomic classifications, dinosaurs and genomics are explored as examples of the breadth of information available in the Wolfram Language. The latest taxonomic data collections deliver biological classification of groups of organisms and the ability to analyze them by physiological, geographic and ecological characteristics. Furthermore, new standardized dinosaur datasets are introduced to compute information such as discovery locations, geological periods and formations, behaviors, and diets, providing answers to the most popular dinosaur queries. Finally, updates to genomics data include access to gene homology information, as well as tying gene properties like chromosome position to the latest reference genome assemblies, while maintaining data for previously supported human assemblies. Genome assembly statistics, such as release date and percentage of gaps, are also included.

After a general introduction to the Wolfram Cloud, we'll talk about what's new in the world of cloud notebooks and beyond. We'll also give a brief update at the ongoing "containerization" of the cloud architecture, which will be particularly interesting for Wolfram Enterprise Private Cloud (EPC).

Drop in and chat with our Visualization team. Ask questions, get help, or just say hello!

An introduction and review of the latest step-by-step programs for Wolfram|Alpha including a discussion of developing step-by-step functions from both algorithmic and rule-based approaches will be shown. Topics to be discussed will include new steps for elementary number theory, grade-school algorithms for addition and multiplication, trigonometric simplifications and expansions, statistics, vector analysis, difference equations, and recurrence relations.

Wolfram Web Engine is a new solution for serving your Wolfram Language–based web applications. It is lean and mean and you can configure it any way you want. It supports modern Wolfram Language web deployments like APIFunction and FormFunction, and is also backwards compatible with JSP-based technology. You can run it directly on your own server, or deploy it in a Docker container. When you want to give the power of the Wolfram Language to the world, this is your gateway.

An informal gathering for all who are interested in sharing insights and experiences, asking and answering questions and connecting with others for an in-depth discussion.

The objective of this workshop is getting you started with the main concepts of working with Relational Databases through the Entity framework in the Wolfram Language.

Much of the trouble in software engineering stems from our inability to determine precisely the function of a program. Programmers routinely write programs whose precise function they do not know, and can only speculate about, and most modern software development processes involve composing existing software components on the basis of documentation that is typically vague, incomplete and outdated. In this talk we discuss the design and implementation of a tool that derives the function of a C-like program by mapping it onto a mathematical equation formulated in the syntax of Mathematica (© Wolfram Research). Such an equation involves the program’s inputs and outputs; by solving this equation in the output as a function of the input, we obtain the function of the program. Also, whether the function can or cannot be solved, it can still be used to prove or disprove the correctness of the program with respect to specifications. The unique novelty of our approach is that we can capture the semantics of iterative constructs in full, provided we codify the requisite programming knowledge and domain knowledge.

Using Wolfram Language, many aspects of astronomical observations can be automated. Using Wolfram Language and .NET/Link to interface to the industry standard ASCOM interface, a monochrome CCD camera and a motorized filter wheel were controlled to automate the tedious process of capturing an image sequence through four color filters plus calibration frames. All the alignment, stacking and calibration plus the initial image processing were done in the same notebook using Python routines called from Wolfram Language code.

In this presentation, the key features for System Modeler 13.1, as well as the upcoming release, will be presented. This includes new free model libraries, task-oriented documentation and integrated machine learning workflows.

Drop in and chat with our experts. Ask questions, get help, or just say hello!

This talk will showcase the recently added functionality to design model predictive controllers. The formulation of the problem as a multiparametric optimization problem, along with workflows and related functionality, will be presented.

Leonardo da Vinci's manuscripts present a puzzle for scholars who aim to recreate the pages' original formats, sequence, and chronology. While the most practical way to capture just two inner structural features—watermarks and chain lines—is via transmitted light, these traces of manufacture can be difficult to decipher when writing and other surface marks found on the recto and verso of the sheet obscure them. Using diffuse specular (normal) light and transmitted light images of Leonardo's Codex Leicester (Bill Gates Collection) and the Codex Arundel (British Library) as case studies, we will describe a computational approach, whereby surface marks and writing are minimized in order to facilitate the accurate matching of watermarks and chain/wire lines. Using enhanced images of the inner structural features of da Vinci's papers, it is then possible to suggest moldmates (papers made from the same papermaking mold) in both Codices. The existence of moldmates in one or both manuscripts provides meaningful evidence of origin, sequence, and date.

Based on teaching the Field Theory of Games to upper-class students, there were interesting lessons learned. For example, it is possible in a short time to educate them to use the Wolfram Language sufficiently to apply the field theory of games to problems of interest to them. It is possible to teach them the elements of traditional game theory and the key elements of the field theory of games in that same time. However, there were ideas that appeared more difficult to communicate: changing the mindset that decision processes have a fixed stable behavior as opposed to a dynamic behavior. This talk explores these issues and focuses on an idea that is important and was not communicated in the course: games can be cohesive and thus illustrate concepts of control and effectiveness.

In this presentation, you will see how data provides new avenues and connections to physical modeling with the new support for neural networks in system modeling. Applications and examples will be explored.

The effective porosity of a medium defines the volume of pore space conducive to through-flow (otherwise known as the "mobile zone"). In the field of groundwater hydrology, the concept of effective porosity is well known, but there exists no such work in the literature that details the dependence of effective porosity on the Reynolds number. Knowing the details of the relationship between the Reynolds number and effective porosity affords researchers the ability to manipulate the effective porosity of a medium. Additional benefit comes from the ability to more accurately estimate rates of mass transfer between cavities and mobile zones, which directly impacts the calculated timescales, costs and therefore the anticipated feasibility of groundwater remediation projects. To determine the effective porosity of a porous medium, we study the medium at pore scale and assume an idealized pore geometry that separates the pore space into two regions: the "immobile" and mobile zones. The hydrodynamic boundary between these zones is known as the "separatrix." To observe movement of the separatrix in the idealized pore space, we use Mathematica's numerical differential equation solver, NDSolve, to solve the Navier–Stokes equations and associated boundary conditions. The suite of tools built into the Wolfram Language allows for straightforward postprocessing of the resolved flow field, which we demonstrate through use of the DynamicModule and StreamPlot functions to describe the position of the separatrix, and therefore the effective porosity of the medium, under various flow conditions.

This talk will demonstrate how to install and use paclets from the new Wolfram Language Paclet Repository. Paclets are the ideal way to package and distribute significant pieces of Wolfram Language functionality. The Wolfram Language Paclet Repository is a growing collection of useful add-ons contributed by users and developers like you. This presentation will focus on the basics of paclets and how to use ones from the Wolfram Language Paclet Repository; later talks will dive into how to develop your own paclets for submission. Come learn how to use and contribute to this exciting new repository!

The Wolfram Language Paclet Repository is here! This talk shows how to use the paclet definition notebook to help develop a paclet and prepare it for publication or distribution.

The recently implemented fractional order integro-differentiation operator, FractionalD, is a particular case of more general integral transforms. The majority of classical integral transforms are representable as compositions of only two transforms: the modified direct and inverse Laplace transforms with power multipliers. Using MellinTransform, one can construct two main classes of integral transforms: convolution type (FourierSinTransform, FourierExpTransform, HankelTransform, Stieltjes transform, G-transform, etc.) and transforms with respect to indices (Kontorovich–Lebedev transform, Mehler–Fock transform, Wimp transform, etc.). For these transforms, we give definitions, inversions, compositional structure, representations through more general transforms (like the G- and Wimp transforms) and more. These transforms can be directly applied to rational and other functions representable through MeijerG functions.

Come chat with the educators who develop Wolfram|Alpha Notebook Edition.

Drop in and chat with our experts. Ask questions, get help, or just say hello!

The cell tray widget interface allows developers to produce high-quality cell-level user interface tools that are managed by the front end. Widgets are organized into "trays" placed near the cell bracket.

Drop in and chat with John about our cloud development. Ask questions, get help, or just say hello!

Differential equations are solved to the task of graphing the change in concentration of the prostate-specific antigen in prostate cancer patients. Note: Most equations are original to the writings of Ernest Rutherford.

Implemented in top-level Wolfram Language code, the new notebook toolbar used existing features of the desktop front end to produce an interface with unique structure and function. In this talk I will review the front end technologies that were used and detail the construction of the toolbar, especially how attached cells provided a viable way of efficiently eliding controls into an overflow menu. This talk will be of particular interest to those wanting to build attached cell-based interfaces in the Wolfram Language.

Multiomics (genomics, proteomics, lipisomics, etc.) data is typically ill-conditioned with many (coupled) variables and relatively few data records. As a result, such data sets are very difficult to analyze with conventional statistical and machine learning techniques. ParetoGP assumes we can develop simple algebraic models using just a few of the inputs via an evolutionary search rewarding model simplicity and accuracy. From the thousands of candidate models, we can garner insights on key variables, variable associations and combinations as well as generate concise explainable and human-interpretable models. In this presentation, we demonstrate the insight and modeling process using DataModeler applied to cancer therapeutics and bone regeneration data sets.

The Cambodia Ministry of Education, Youth and Sport, with support from Wolfram Research, invited students in grades 4–12 to participate in Cambodia Wolfram Student Stars! In addition to Wolfram computational thinking activities, we supported student STEM projects with System Modeler and Mathematica using Arduino and Raspberry Pi. As CWSS STEM project director, I will describe the implementation of the program in Cambodia to support STEM projects, and share student STEM projects.

This talk will present some new features and updates of Mathematica's 2D and 3D Graphics language, including DropShadowing, Blur, improved support of AbsoluteOptions, 3D Camera dolly and look-around interaction, and other improvements. This talk will also show users how to customize 2D/3D rendering with SurfaceAppearance.

Cellular Automata rules are represented by integers where we encode the output of the function without knowing the details on how it might be implemented. The CellularAutomaton function in Mathematica only requires these integers, along with the values of r and k, to evolve rules for a given input. The BooleanFunction function in Mathematica provides a polynomial of the function given its representing integer which we can use to get the functions when k = 2. Unfortunately, there is no Mathematica function that does the same for other values of k. We present a uniform way to generate these functions using certain kinds of polynomials. Every function in a rule space can be generated by changing the coefficients of its corresponding polynomial. We find that when the value of k is prime, the polynomial is relatively simple and straightforward. When the value of k is composite, we need a composition of polynomials, each based on a prime factor of k. A possible use of these polynomials is the creation of Probabilistic Cellular Automata by defining one or more of the coefficients as random variables. For every step, for every cell, the random coefficients will take on different values and hence generate different rules. This may allow for a better analysis of these stochastic processes.

Drop in and chat with our experts from the Geometry team. Ask questions, get help, or just say hello!

Origami attracts the minds of people all over the world. Some are interested in its geometric aspects, and others in artistic or recreational elements, so-called traditional origami. Although both origami categories rely on a single notion of paper folding, their methodologies differ due to the pursuits' objectives. We focus on traditional origami, but approach it with mathematical formalism rather than artistic values. In particular, we realize origami in a virtual space, using Mathematica's leading-edge symbolic, numeric, and graphics computation capabilities. The origami creators' interest lies more in artistic creativity than general folding rules. In contrast, origami geometers' underlying motivation is finding a few basic fold rules. Although we have such a set of rules in 2D origami geometry, we are more liberal in defining basic fold rules in traditional origami. The fold rules may be many, even open (infinite). Nevertheless, we can give some basic fold rules essential in traditional origami. We first address squash and outside-reverse folds among classical folds; these classical folds intricately combine several simple folds. One squash fold, for example, requires three simultaneous simple folds, i.e. mountain or valley folds, subjected to nontrivial constraints. We understand the 2D origami geometry to the extent that we do the 2D Euclidean geometry in terms of the constructible points in the two geometries. Namely, the set of the points constructible by Huzita–Justin's fold rules is the strict superset of intersecting points of the circles and the lines made by a straightedge and a compass, the construction tools of Euclidean geometry. We extend Huzita–Justin's rules by introducing a cut along a crease. The operations of cutting and later gluing simplify a squash fold significantly. We can apply the cut operation to other classical folds and streamline their modeling and subsequent realization in a virtual origami space. We then present the construction of a flying crane. It not only serves as a mathematical and computational description of this famous origami but also shows the effectiveness and expandability of our modeling for origami virtualization.

We present a method for automatically generating new geometry theorems, suitable for solution using "angle chasing". Specifically, we consider geometry theorems whose premises and conclusion comprise a set of bisector conditions. Each premise and the conclusion can be represented as the rows of a "bisector matrix": one whose rows contain 1,1,–2 as their only nonzero entries. The existence of a theorem corresponds to rank deficiency in this matrix. We initially consider rank-deficient matrices which have an underlying graph whose vertices correspond to matrix rows and whose edges correspond to matrix columns. We give each edge of the graph (considered in a specific direction) a head-weight equal to the matrix entry in the row corresponding to the vertex adjacent to its head and column corresponding to the edge. Similarly, we give the edge a tail-weight. With this definition, a bisector matrix with an underlying graph is rank deficient if and only if the graph is bicubic and for any cycle the product of head-weights equals the product of tail-weights. We present a Mathematica program which uses this characterization to identify all possible such matrices for 14 or fewer rows. We present methods of transforming the rank-deficient matrices into forms which incorporate line angles in addition to bisectors, and which have columns of more than two non-zero entries, while retaining the rank deficiency. We present code which takes such transformed matrices as input and outputs geometry theorems in the form of GeometricScene.

Working with arrays is fundamental to efficient use of Wolfram Language and appears in almost any computation. The basic representation for an array is a nested list, but there are other representations such as PackedArray, SparseArray and structured arrays that are more effective for some applications. This presentation will show how to use the various representations of arrays combined with compilation to make your computations more efficient.

This talk will give an overview of the various optimization functions that can be used to solve a wide variety of convex, nonconvex and multidomain problems. The Wolfram optimization functionality will be demonstrated using a diverse set of examples. Visiting this talk will enable you to solve optimization-type problems efficiently.

Uncertainty is a major component of subjective logic beliefs. We discuss the cloud of uncertainty across Markov networks, insights from computational irreducibility, and negative quantum quasiprobabilities and beliefs.

In this meet-up, we will discuss the virtual labs, including ideas for new labs.

This talk will discuss the global optimization functionality in Wolfram Language. It builds upon the convex and convertible to convex optimization functionality developed previously and extends to functionality for solving nonlinear, nonconvex problems with real-valued and mixed-integer variables. Available methods and library solvers will be discussed and illustrated by examples.

In this presentation we discuss the completion of computational templates with parameters that are extracted from text specifications using a question answering system (QAS) [Wk1]. We outline the general method and then demonstrate it with several types of computational workflows: classification, latent semantic analysis (LSA), quantile regression (QR), random data generation (RDG) and recommendations. We show how to leverage the engine by bringing your own templates (BYOT). The demonstrated functionalities use the packages in the project ""NLP Template Engine"" [AAr1], which is based on FindTextualAnswer [WRI1, JL1]. We concentrate on data science (DS) and machine learning (ML) computations, but the described method and overall algorithm are applicable to computation workflows from other fields.

Dataset has become a widely used tool to process and manipulate data in the Wolfram Language, but its scope has been limited to the data stored in kernel's memory. In this talk, I will discuss the general strategy to extend the scope of Dataset's query language to query other types of data sources and illustrate general ideas with examples of using Dataset's query language to query a relational database (SQLite).

In this talk, we will cover the usage of the NDSolve family of functions and the finite element method. The aim is to enable attendees to set up partial differential equation models from various fields of engineering. The focus will be on recent development such as axisymmetric regions and hyperelastic solid mechanics.

Since 2016, Airy Optics Inc. has leveraged interactive Mathematica features for the real-time analysis of cutting-edge imaging systems, such as design of optics for augmented and virtual reality. Losses of image quality that are based in polarization are often poorly understood, and can be the result of the delicate interaction of many elements within an optical system. Airy Optics' premier software Polaris-M was written in Mathematica as the first dedicated tool for analyzing these effects using real-world data and scientifically proven modeling. This presentation will examine functions and displays written for Polaris-M and for broader demonstrations that leverage the power of Mathematica's interactive features to present complex concepts and data in a simple and easy-to-understand manner. One such function expands the built-in Grid function to better format and display multifaceted datasets, both improving readability and ease of data interaction. Another uses a custom-built framework to allow easy styling control of composed plots of many surfaces. A third example uses dynamic interactivity to condense a variety of analysis functions for high-dimensional measured polarization data into one flexible display. Airy Optics also uses simple, interactive Manipulate examples to teach optical engineering students basic polarization concepts, including helping them visualize polarization states in terms of ellipticity and the degree of polarization. All of these tools have helped us provide faster analysis to our customers in visually engaging ways, contributing substantially to the development of the next generation of AR/VR headsets as well as many other exciting applications.

The recent addition of PatternReaction and ApplyReaction to the Wolfram Language now allows the user to programmatically manipulate the atoms and bonds in Molecule objects in a chemically meaningful way. This talk will show how these functions can be used with token-event graphs to model chemical reaction networks. Examples with the Diels–Alder reaction, Cope rearrangement, Wagner–Meerwein rearrangement and terpene biosynthesis will be demonstrated. As these networks represent multiway systems, they can also be studied from that perspective with branchial and causal graphs.

In this talk I will present NetExternalObject, a new symbol in Wolfram Language 13.2. It exposes new functionality to interface with external deep learning frameworks and run neural networks in their native format without having to manually install any external software.

Drop in and chat with our experts. Ask questions, get help, or just say hello!

I will give an overview of upcoming features related to calculus and algebra in the Wolfram Language. These features include dramatic performance improvements in polynomial algebra functions and in linear algebra for matrices of polynomials, new NFractionalD and NCaputoD functions for numerical computation of fractional derivatives, algorithmic advances for symbolic and asymptotic solutions of differential equations, large-scale table lookup for Laplace transforms, support for computing power series representations of functions using Asymptotic, and new built-in structured matrices for efficient computations in numerical linear algebra. I will also discuss current projects related to documentation, engineering education and online courses in this area.

The upcoming release of Mathematica includes significant performance improvements in polynomial algebra functions and in linear algebra for matrices of univariate polynomials. The release also includes functionality extensions in polynomial algebra over Z_p The improvements and extensions are based on the FLINT library. In my talk, I will discuss the improvements and show some examples and performance comparison results.

This is an introduction to a unified model of Cellular Automata in which a rule is represented not by a single function but by a vector of functions we call genes. These functions can be ordered so that they maintain the same order regardless of the rule space where they are realized. This order allows the vectors to be normalized and positions all rules in a unit hypercube. There are operations on the rules that are simple to implement in the normalized space, such as Modulo-Additive Equivalent rules, known as complement in the binary k-value case. We also introduce the concept of symmetry index based on the number of symmetric genes that make up the rule. We also show the concept of canonical rule which is the rule number for the minimum value of r where the rule can be realized. There are many other functions that are introduced, such as genetic trees, equation trees, evolution trees and canonical trees, among others. There are also functions to perform reflection, reversibility, monotonicity and symmetry tests. Also, measures such as Langton's Lambda, Delta parameter and symmetry index are implemented.

Fractional calculus develops the theory of differentiation and integration of any real or complex order. It extends the basic operations of classical calculus to fractional orders and studies the methods of solving differential equations involving these fractional-order derivatives and integrals. Nowadays fractional calculus is gaining more and more interest as it is able to generalize the well-known integrodifferential equations to ones containing fractional order derivatives or integrals of the target function—these more general equations are able to precisely describe different real-world phenomena. This talk will give a brief introduction to fractional calculus, an overview of the FractionalD and CaputoD functions standing for the two main definitions of fractional order derivatives, their numerical analogues NFractionalD/NCaputoD functions, learning resources for this subject and some real-world applications of this theory.

Drop in and chat with our experts. Ask questions, get help, or just say hello!

Martin and Quinn (2002) apply Item Response Theory (IRT) to Supreme Court votes in order to infer the "location" of justices on a simple left/right spectrum. We modify their model, adopting a non-conjugate prior for the case parameters and allowing justices' locations to vary with each change in the court's composition (instead of with each term).

During this talk I will give an overview of recent developments, new features and improvements in Wolfram Language related to symbolic solutions of ordinary differential equations. I will begin by speaking about the recently introduced DSolve option IncludeSingularSolutions, which allows one to get the singular solutions of a nonlinear ODE together with the general solution. Next, the significant improvements in the method of undetermined coefficients will be discussed, which allows one to find fast and simple solutions for inhomogeneous linear ODEs with constant coefficients. Finally, in the last part of the talk I will speak about a new type of ODE: fractional differential equations. Fractional differential equations are differential equations involving fractional order derivatives. These are generalizations of the ordinary differential equations that have attracted much attention and have been widely used in engineering, physics, chemistry, biology and other fields. I will demonstrate how to solve some linear fractional ODEs in Wolfram Language using DSolve and AsymptoticDSolveValue. I will end by discussing the updated tutorial on symbolic differential equation solving using DSolve.

From small to big companies, operations work on top of traditional relational databases (RDBMS) and SQL is a lingua franca in business. To keep track of complex activities with vast amounts of transactions, lots of data is produced with ERPs, CRMs, BI, financial systems, RH, sales and internally built custom enterprise systems too. We can explore this information better to find patterns and insights for companies. The Wolfram Language can be used to import, process and combine all this info and relate it to real-world curated data. This data science hype brings P&D to many companies that can add value to the business and avoid risks.

SearchOnMath is a search engine specializing in formulas and text from several domains with math content. The web version indexes domains like Wolfram MathWorld, Stack Exchange (Math, Physics, and MathOverflow), Wikipedia, and others. The scientific version indexes preprints from arXiv, allowing users to submit queries and filter results by year, author, and/or area of knowledge. The SearchOnMath core is mainly composed of two parts: (i) Lexical analysis, which makes representation independent of notation. For example, variables can be denoted by Roman letters (x, y, z, x₀, x₁, …), Greek letters (α, β, …), and so on. (ii) Degree of similarity analysis, using a powerful engine to compare the structure of the target formula with that of all other formulas in the database. Formulas that are more similar in structure tend to appear first on the results page. This presentation shows a detailed view of SearchOnMath, including the ability to search arXiv preprints. It also shows how to integrate the SearchOnMath API into Wolfram Mathematica, including access to all features available on the SearchOnMath website. This integration enables countless possibilities, such as instantly searching from inside a Mathematica notebook all the main websites of mathematical content as well as all of arXiv.

In recent versions, we have added functionality to make Wolfram Language more directly applicable to the calculus classroom. I will focus, in particular, on the new functions ImplicitD, IntegrateChangeVariables and DSolveChangeVariables. Other related enhancements will be covered as time permits.

The dual-phase low-Cr ferritic stainless steels are characterized by severe poor shape, especially at the outer diameter (20–30%) of the hot pickling line (HPL) output coil or inner diameter of the hot strip mill (HSM) output black coil. The objective of this work is to study the parameters affecting the waviness level and affected length. We will be using the various statistical capabilities of Wolfram Language, including ANOVA, multiple linear regression and logistic regression, to study the parameters affecting the shape of the coil during the entire rolling operation (including the chemistry of the grade). Overall, we will explore the ways in which Wolfram Language can be used to solve industrial challenges.

See how to create courseware using the question and assessment framework. This talk shows how each piece of the system works, from custom, automated assessment functions to full quizzes.

One of many wonderful components waiting to be discovered in Wolfram Language is powerful graphics. I will share some of my techniques developed to harness this power for documentation illustrations and marketing images. Learn style, lighting and camera tips to solve mysteries you may have encountered while creating your visualizations. Leave encouraged to explore the broad range of graphic functions.

This talk will present four Unity 3D Math Games/Simulations with companion Wolfram Notebooks, the development of which is ongoing. The potential for melds such as these to evolve into active learning resources for science education will be explored.

This work details the assignment of a digital, fluid mechanics laboratory to a class of undergraduate engineering students at Duke University. In this laboratory, students are asked to numerically simulate flow through a sudden expansion. The primary learning objective of this laboratory is for students to understand the physical limitations associated with this experiment. Physical measurements disrupt the flow through such a geometry, imparting needless—and simultaneously unmeasurable—sources of error into the measurement process. The digital nature of this laboratory allows students to take these measurements without disturbing the flow, altogether avoiding this issue. The second learning objective of this laboratory is for students to gain experience utilizing the Wolfram Language—a severely underutilized tool in engineering curricula. Among the many advantages to utilizing Mathematica for this laboratory exercise is the fact that students can observe and understand the mechanics of the numerical flow solver they are tasked with using, which is often not the case; commercial flow solvers operate more like "black-box" technologies and low-level programming languages require advanced knowledge to code such simulations. In this work, we also document the experience of the students as they complete the laboratory assignment. The novelty of this work is attributed to the fact that no such exercise has been previously detailed in the literature. And while this work describes a fluid mechanics laboratory, the digital nature of this exercise can easily be implemented in any course to supplement student learning when physical experimentation is challenged by nuances like the observer effect.