In machine learning, a neural field (also known as implicit neural representation, neural implicit, or coordinate-based neural network), is a mathematical field that is fully or partially parametrized by a neural network. Initially developed to tackle visual computing tasks, such as rendering or reconstruction (e.g., neural radiance fields), neural fields emerged as a promising strategy to deal with a wider range of problems, including surrogate modelling of partial differential equations, such as in physics-informed neural networks. Differently from traditional machine learning algorithms, such as feed-forward neural networks, convolutional neural networks, or transformers, neural fields do not work with discrete data (e.g. sequences, images, tokens), but map continuous inputs (e.g., spatial coordinates, time) to continuous outputs (i.e., scalars, vectors, etc.). This makes neural fields not only discretization independent, but also easily differentiable. Moreover, dealing with continuous data allows for a significant reduction in space complexity, which translates to a much more lightweight network. == Formulation and training == According to the universal approximation theorem, provided adequate learning, sufficient number of hidden units, and the presence of a deterministic relationship between the input and the output, a neural network can approximate any function to any degree of accuracy. Hence, in mathematical terms, given a field y = Φ ( x ) {\textstyle {\boldsymbol {y}}=\Phi ({\boldsymbol {x}})} , with x ∈ R n {\displaystyle {\boldsymbol {x}}\in \mathbb {R} ^{n}} and y ∈ R m {\displaystyle {\boldsymbol {y}}\in \mathbb {R} ^{m}} , a neural field Ψ θ {\displaystyle \Psi _{\theta }} , with parameters θ {\displaystyle {\boldsymbol {\theta }}} , is such that: Ψ θ ( x ) = y ^ ≈ y {\displaystyle \Psi _{\theta }({\boldsymbol {x}})={\hat {\boldsymbol {y}}}\approx {\boldsymbol {y}}} === Training === For supervised tasks, given N {\displaystyle N} examples in the training dataset (i.e., ( x i , y i ) ∈ D t r a i n , i = 1 , … , N {\displaystyle ({\boldsymbol {x_{i}}},{\boldsymbol {y_{i}}})\in {\mathcal {D_{train}}},i=1,\dots ,N} ), the neural field parameters can be learned by minimizing a loss function L {\displaystyle {\mathcal {L}}} (e.g., mean squared error). The parameters θ ~ {\displaystyle {\tilde {\theta }}} that satisfy the optimization problem are found as: θ ~ = argmin θ 1 N ∑ ( x i , y i ) ∈ D t r a i n L ( Ψ θ ( x i ) , y i ) {\displaystyle {\tilde {\boldsymbol {\theta }}}={\underset {\boldsymbol {\theta }}{\text{argmin}}}\;{\frac {1}{N}}\sum _{({\boldsymbol {x_{i}}},{\boldsymbol {y_{i}}})\in {\mathcal {D_{train}}}}{\mathcal {L}}(\Psi _{\theta }({\boldsymbol {x}}_{i}),{\boldsymbol {y}}_{i})} Notably, it is not necessary to know the analytical expression of Φ {\displaystyle \Phi } , for the previously reported training procedure only requires input-output pairs. Indeed, a neural field is able to offer a continuous and differentiable surrogate of the true field, even from purely experimental data. Moreover, neural fields can be used in unsupervised settings, with training objectives that depend on the specific task. For example, physics-informed neural networks may be trained on just the residual. === Spectral bias === As for any artificial neural network, neural fields may be characterized by a spectral bias (i.e., the tendency to preferably learn the low frequency content of a field), possibly leading to a poor representation of the ground truth. In order to overcome this limitation, several strategies have been developed. For example, SIREN uses sinusoidal activations, while the Fourier-features approach embeds the input through sines and cosines. == Conditional neural fields == In many real-world cases, however, learning a single field is not enough. For example, when reconstructing 3D vehicle shapes from Lidar data, it is desirable to have a machine learning model that can work with arbitrary shapes (e.g., a car, a bicycle, a truck, etc.). The solution is to include additional parameters, the latent variables (or latent code) z ∈ R d {\displaystyle {\boldsymbol {z}}\in \mathbb {R} ^{d}} , to vary the field and adapt it to diverse tasks. === Latent code production === When dealing with conditional neural fields, the first design choice is represented by the way in which the latent code is produced. Specifically, two main strategies can be identified: Encoder: the latent code is the output of a second neural network, acting as an encoder. During training, the loss function is the objective used to learn the parameters of both the neural field and the encoder. Auto-decoding: each training example has its own latent code, jointly trained with the neural field parameters. When the model has to process new examples (i.e., not originally present in the training dataset), a small optimization problem is solved, keeping the network parameters fixed and only learning the new latent variables. Since the latter strategy requires additional optimization steps at inference time, it sacrifices speed, but keeps the overall model smaller. Moreover, despite being simpler to implement, an encoder may harm the generalization capabilities of the model. For example, when dealing with a physical scalar field f : R 2 → R {\displaystyle f:\mathbb {R} ^{2}\rightarrow \mathbb {R} } (e.g., the pressure of a 2D fluid), an auto-decoder-based conditional neural field can map a single point to the corresponding value of the field, following a learned latent code z {\displaystyle {\boldsymbol {z}}} . However, if the latent variables were produced by an encoder, it would require access to the entire set of points and corresponding values (e.g. as a regular grid or a mesh graph), leading to a less robust model. === Global and local conditioning === In a neural field with global conditioning, the latent code does not depend on the input and, hence, it offers a global representation (e.g., the overall shape of a vehicle). However, depending on the task, it may be more useful to divide the domain of x {\displaystyle {\boldsymbol {x}}} in several subdomains, and learn different latent codes for each of them (e.g., splitting a large and complex scene in sub-scenes for a more efficient rendering). This is called local conditioning. === Conditioning strategies === There are several strategies to include the conditioning information in the neural field. In the general mathematical framework, conditioning the neural field with the latent variables is equivalent to mapping them to a subset θ ∗ {\displaystyle {\boldsymbol {\theta }}^{}} of the neural field parameters: θ ∗ = Γ ( z ) {\displaystyle {\boldsymbol {\theta }}^{}=\Gamma ({\boldsymbol {z}})} In practice, notable strategies are: Concatenation: the neural field receives, as input, the concatenation of the original input x {\displaystyle {\boldsymbol {x}}} with the latent codes z {\displaystyle {\boldsymbol {z}}} . For feed-forward neural networks, this is equivalent to setting θ ∗ {\displaystyle {\boldsymbol {\theta }}^{}} as the bias of the first layer and Γ ( z ) {\displaystyle \Gamma ({\boldsymbol {z}})} as an affine transformation. Hypernetworks: a hypernetwork is a neural network that outputs the parameters of another neural network. Specifically, it consists of approximating Γ ( z ) {\displaystyle \Gamma ({\boldsymbol {z}})} with a neural network Γ ^ γ ( z ) {\displaystyle {\hat {\Gamma }}_{\gamma }({\boldsymbol {z}})} , where γ {\displaystyle {\boldsymbol {\gamma }}} are the trainable parameters of the hypernetwork. This approach is the most general, as it allows to learn the optimal mapping from latent codes to neural field parameters. However, hypernetworks are associated to larger computational and memory complexity, due to the large number of trainable parameters. Hence, leaner approaches have been developed. For example, in the Feature-wise Linear Modulation (FiLM), the hypernetwork only produces scale and bias coefficients for the neural field layers. === Meta-learning === Instead of relying on the latent code to adapt the neural field to a specific task, it is also possible to exploit gradient-based meta-learning. In this case, the neural field is seen as the specialization of an underlying meta-neural-field, whose parameters are modified to fit the specific task, through a few steps of gradient descent. An extension of this meta-learning framework is the CAVIA algorithm, that splits the trainable parameters in context-specific and shared groups, improving parallelization and interpretability, while reducing meta-overfitting. This strategy is similar to the auto-decoding conditional neural field, but the training procedure is substantially different. == Applications == Thanks to the possibility of efficiently modelling diverse mathematical fields with neural networks, neural fields have been applied to a wide range of problems: 3D scene reconstruction: neural fields can be used to model t
Vote Compass
Vote Compass is an interactive, online voting advice application developed by political scientists and run during election campaigns. It surveys users about their political views and, based on their responses, calculates the individual alignment of each user with the parties or candidates running in a given election contest. It is operated by a social enterprise called Vox Pop Labs in partnership with locale-specific news organizations, including the Wall Street Journal, Vox Media, the Canadian and Australian Broadcasting Corporations, Television New Zealand, France24, RTL Group, and Grupo Globo. Vote Compass also operates under the trademarks Boussole électorale and Wahl-Navi for French- and German-language iterations, respectively. == Background == Vote Compass was developed by Clifton van der Linden, a professor in the Department of Political Science at McMaster University. It is run by van der Linden along with a team of social and statistical scientists from Vox Pop Labs. Although inspired by European Voting Advice Applications, van der Linden explicitly rejects this terminology, arguing that Vote Compass was "never intended to account for every variable that influences voter choice and its results should not be interpreted as voting advice." == Methodology == Using a Likert scale, users indicate their responses to a series of policy propositions designed to discriminate between candidates' policies on prominent issues relevant to the election. Propositions are crafted in collaboration with political scientists local to each jurisdiction in which Vote Compass is run. Based on a candidate or political party's public disclosures (i.e. party manifestos, policy proposals, official websites, speeches, media releases, statements made in the legislature, etc.) they are calibrated on the same propositions and scales as are users. A series of aggregation algorithms calculate the overall distance between the user and the candidates or parties. There have been claims that Vote Compass surveys have the potential to become push polling, if the survey questions posed are poorly designed.
Data analysis
Data analysis is the process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. Data analysis has multiple facets and approaches, encompassing diverse techniques under a variety of names, and is used in different business, science, and social science domains. In today's business world, data analysis plays an important role in making decisions more scientific and helping businesses operate more effectively. It is widely used in fields such as business analytics, healthcare, and artificial intelligence to extract meaningful insights from data. Data mining is a particular data analysis technique that focuses on statistical modeling and knowledge discovery for predictive rather than purely descriptive purposes, while business intelligence covers data analysis that relies heavily on aggregation, focusing mainly on business information. In statistical applications, data analysis can be divided into descriptive statistics, exploratory data analysis (EDA), and confirmatory data analysis (CDA). EDA focuses on discovering new features in the data, while CDA focuses on confirming or falsifying existing hypotheses. Predictive analytics focuses on the application of statistical models for predictive forecasting or classification, while text analytics applies statistical, linguistic, and structural techniques to extract and classify information from textual sources, a variety of unstructured data. All of the above are varieties of data analysis. == Data analysis process == Data analysis is a process for obtaining raw data, and subsequently converting it into information useful for decision-making by users. Statistician John Tukey, defined data analysis in 1961, as:"Procedures for analyzing data, techniques for interpreting the results of such procedures, ways of planning the gathering of data to make its analysis easier, more precise or more accurate, and all the machinery and results of (mathematical) statistics which apply to analyzing data." There are several phases, and they are iterative, in that feedback from later phases may result in additional work in earlier phases. === Data requirements === The data is necessary as inputs to the analysis, which is specified based upon the requirements of those directing the analytics (or customers, who will use the finished product of the analysis). The general type of entity upon which the data will be collected is referred to as an experimental unit (e.g., a person or population of people). Specific variables regarding a population (e.g., age and income) may be specified and obtained. Data may be numerical or categorical (i.e., a text label for numbers). === Data collection === Data may be collected from a variety of sources. A list of data sources are available for study & research. The requirements may be communicated by analysts to custodians of the data; such as, Information Technology personnel within an organization. Data collection or data gathering is the process of gathering and measuring information on targeted variables in an established system, which then enables one to answer relevant questions and evaluate outcomes. The data may also be collected from sensors in the environment, including traffic cameras, satellites, recording devices, etc. It may also be obtained through interviews, downloads from online sources, or reading documentation. === Data processing === Data integration is a precursor to data analysis: Data, when initially obtained, must be processed or organized for analysis. For instance, this may involve placing data into rows and columns in a table format (known as structured data) for further analysis, often through the use of spreadsheet (e.g. Excel) or statistical software. === Data cleaning === Once processed and organized, the data may be incomplete, contain duplicates, or contain errors. The need for data cleaning will arise from problems in the way that the data is entered and stored. Data cleaning is the process of preventing and correcting these errors. Common tasks include record matching, identifying inaccuracy of data, overall quality of existing data, deduplication, and column segmentation. Such data problems can also be identified through a variety of analytical techniques. For example; with financial information, the totals for particular variables may be compared against separately published numbers that are believed to be reliable. Unusual amounts, above or below predetermined thresholds, may also be reviewed. There are several types of data cleaning that are dependent upon the type of data in the set; this could be phone numbers, email addresses, employers, or other values. Quantitative data methods for outlier detection can be used to get rid of data that appears to have a higher likelihood of being input incorrectly. Text data spell checkers can be used to lessen the amount of mistyped words. However, it is harder to tell if the words are contextually (i.e., semantically and idiomatically) correct. === Exploratory data analysis === Once the datasets are cleaned, they can then begin to be analyzed using exploratory data analysis. The process of data exploration may result in additional data cleaning or additional requests for data; thus, the initialization of the iterative phases mentioned above. Descriptive statistics, such as the average, median, and standard deviation, are often used to broadly characterize the data. Data visualization is also used, in which the analyst is able to examine the data in a graphical format in order to obtain additional insights about messages within the data. === Modeling and algorithms === Mathematical formulas or mathematical models (supported by algorithms) may be applied to the data in order to identify relationships among the variables; for example, checking for correlation and by determining whether or not there is the presence of causality. In general terms, models may be developed to evaluate a specific variable based on other variable(s) contained within the dataset, with some residual error depending on the implemented model's accuracy (e.g., Data = Model + Error). Inferential statistics utilizes techniques that measure the relationships between particular variables. For example, regression analysis may be used to model whether a change in advertising (independent variable X), provides an explanation for the variation in sales (dependent variable Y), i.e. is Y a function of X? This can be described as (Y = aX + b + error), where the model is designed such that (a) and (b) minimize the error when the model predicts Y for a given range of values of X. === Data product === A data product is a computer application that takes data inputs and generates outputs, feeding them back into the environment. It may be based on a model or algorithm. For instance, an application that analyzes data about customer purchase history, and uses the results to recommend other purchases the customer might enjoy. === Communication === Once data is analyzed, it may be presented in many formats to the users of the analysis to support their requirements. The users may have feedback, which results in additional analysis. When determining how to communicate the results, the analyst may consider implementing a variety of data visualization techniques to help communicate the message more clearly and efficiently to the audience. Data visualization uses information displays (graphics such as, tables and charts) to help communicate key messages contained in the data. Tables are a valuable tool by enabling the ability of a user to query and focus on specific numbers; while charts (e.g., bar charts or line charts), may help explain the quantitative messages contained in the data. == Quantitative messages == Stephen Few described eight types of quantitative messages that users may attempt to communicate from a set of data, including the associated graphs. Time-series: A single variable is captured over a period of time, such as the unemployment rate over a 10-year period. A line chart may be used to demonstrate the trend. Ranking: Categorical subdivisions are ranked in ascending or descending order, such as a ranking of sales performance (the measure) by salespersons (the category, with each salesperson a categorical subdivision) during a single period. A bar chart may be used to show the comparison across the salespersons. Part-to-whole: Categorical subdivisions are measured as a ratio to the whole (i.e., a percentage out of 100%). A pie chart or bar chart can show the comparison of ratios, such as the market share represented by competitors in a market. Deviation: Categorical subdivisions are compared against a reference, such as a comparison of actual vs. budget expenses for several departments of a business for a given time period. A bar chart can show the comparison of the actual versus the reference amount. Frequency distribution:
Data steward
A data steward is an oversight or data governance role within an organization, and is responsible for ensuring the quality and fitness for purpose of the organization's data assets, including the metadata for those data assets. A data steward may share some responsibilities with a data custodian, such as the awareness, accessibility, release, appropriate use, security and management of data. A data steward would also participate in the development and implementation of data assets. A data steward may seek to improve the quality and fitness for purpose of other data assets their organization depends upon but is not responsible for. Data stewards have a specialist role that utilizes an organization's data governance processes, policies, guidelines and responsibilities for administering an organizations' entire data in compliance with policy and/or regulatory obligations (e.g., GDPR, HIPAA). The overall objective of a data steward is the data quality of the data assets, datasets, data records and data elements. This includes documenting metainformation for the data, such as definitions, related rules/governance, physical manifestation, and related data models (most of these properties being specific to an attribute/concept relationship), identifying owners/custodian's various responsibilities, relations insight pertaining to attribute quality, aiding with project requirement data facilitation and documentation of capture rules. Data stewards begin the stewarding process with the identification of the data assets and elements which they will steward, with the ultimate result being standards, controls and data entry. The steward works closely with business glossary standards analysts (for standards), with data architect/modelers (for standards), with DQ analysts (for controls) and with operations team members (good-quality data going in per business rules) while entering data. Data stewardship roles are common when organizations attempt to exchange data precisely and consistently between computer systems and to reuse data-related resources. Master data management often makes references to the need for data stewardship for its implementation to succeed. Data stewardship must have precise purpose, fit for purpose or fitness. == Data steward responsibilities == A data steward ensures that each assigned data element: Has clear and unambiguous data element definition Does not conflict with other data elements in the metadata registry (removes duplicates, overlap etc.) Has clear enumerated value definitions if it is of type Code Is still being used (remove unused data elements) Is being used consistently in various computer systems Is being used, fit for purpose = Data Fitness Has adequate documentation on appropriate usage and notes Documents the origin and sources of authority on each metadata element Is protected against unauthorised access or change Responsibilities of data stewards vary between different organisations and institutions. For example, at Delft University of Technology, data stewards are perceived as the first contact point for any questions related to research data. They also have subject-specific background allowing them to easily connect with researchers and to contextualise data management problems to take into account disciplinary practices. == Types of data stewards == Depending on the set of data stewardship responsibilities assigned to an individual, there are 4 types (or dimensions of responsibility) of data stewards typically found within an organization: Data object data steward - responsible for managing reference data and attributes of one business data entity Business data steward - responsible for managing critical data, both reference and transactional, created or used by one business function. The data steward may also serve as a liaison between the organization's data users and technical teams, helping to bridge the gap between business needs and technical requirements. They may also play a role in educating others within the organization about best practices for data management, and advocating for data-driven decision-making. Process data steward - responsible for managing data across one business process System data steward - responsible for managing data for at least one IT system == Benefits of data stewardship == Systematic data stewardship can foster: Faster analysis Consistent use of data management resources Easy mapping of data between computer systems and exchange documents Lower costs associated with migration to (for example) service-oriented architecture (SOA) Mitigation of data risk Better control of dangers associated with privacy, legal, errors, etc. Assignment of each data element to a person sometimes seems like an unimportant process. But multiple groups have found that users have greater trust and usage rates in systems where they can contact a person with questions on each data element. == Examples == Delft University of Technology (TU Delft) offers an example of data stewardship implementation at a research institution. In 2017 the Data Stewardship Project was initiated at TU Delft to address research data management needs in a disciplinary manner across the whole campus. Dedicated data stewards with subject-specific background were appointed at every TU Delft faculty to support researchers with data management questions and to act as a linking point with the other institutional support services. The project is coordinated centrally by TU Delft Library, and it has its own website, blog and a YouTube channel. The [1]EPA metadata registry furnishes an example of data stewardship. Note that each data element therein has a "POC" (point of contact). In 2023, ETH Zurich launched the Data Stewardship Network (DSN) to facilitate collaboration among employees engaged in data management, analysis, and code development across research groups. The DSN serves as a platform for networking and knowledge exchange, aiming to professionalize the role of data stewards who support research data management and reproducible workflows. Established by the team for Research Data Management and Digital Curation at the ETH Library, the DSN collaborates with Scientific IT Services to provide expertise in areas such as storage infrastructure and reproducible workflows. == Data stewardship applications == Information stewardship applications are business solutions used by business users acting in the role of information steward (interpreting and enforcing information governance policy, for example). These developing solutions represent, for the most part, an amalgam of a number of disparate, previously IT-centric tools already on the market, but are organized and presented in such a way that information stewards (a business role) can support the work of information policy enforcement as part of their normal, business-centric, day-to-day work in a range of use cases. The initial push for the formation of this new category of packaged software came from operational use cases — that is, use of business data in and between transactional and operational business applications. This is where most of the master data management efforts are undertaken in organizations. However, there is also now a faster-growing interest in the new data lake arena for more analytical use cases.
Data proliferation
Data proliferation refers to the prodigious amount of data, structured and unstructured, that businesses and governments continue to generate at an unprecedented rate and the usability problems that result from attempting to store and manage that data. While originally pertaining to problems associated with paper documentation, data proliferation has become a major problem in primary and secondary data storage on computers. While digital storage has become cheaper, the associated costs, from raw power to maintenance and from metadata to search engines, have not kept up with the proliferation of data. Although the power required to maintain a unit of data has fallen, the cost of facilities which house the digital storage has tended to rise. Data proliferation has been documented as a problem for the U.S. military since August 1971, in particular regarding the excessive documentation submitted during the acquisition of major weapon systems. Efforts to mitigate data proliferation and the problems associated with it are ongoing. == Problems caused == The problem of data proliferation is affecting all areas of commerce as a result of the availability of relatively inexpensive data storage devices. This has made it very easy to dump data into secondary storage immediately after its window of usability has passed. This masks problem that could gravely affect the profitability of businesses and the efficient functioning of health services, police and security forces, local and national governments, and many other types of organizations. Data proliferation is problematic for several reasons: Difficulty when trying to find and retrieve information. At Xerox, on average it takes employees more than one hour per week to find hard-copy documents, costing $2,152 a year to manage and store them. For businesses with more than 10 employees, this increases to almost two hours per week at $5,760 per year. In large networks of primary and secondary data storage, problems finding electronic data are analogous to problems finding hard copy data. Data loss and legal liability when data is disorganized, not properly replicated, or cannot be found promptly. In April 2005, the Ameritrade Holding Corporation told 200,000 current and past customers that a tape containing confidential information had been lost or destroyed in transit. In May of the same year, Time Warner Incorporated reported that 40 tapes containing personal data on 600,000 current and former employees had been lost en route to a storage facility. In March 2005, a Florida judge hearing a $2.7 billion lawsuit against Morgan Stanley issued an "adverse inference order" against the company for "willful and gross abuse of its discovery obligations." The judge cited Morgan Stanley for repeatedly finding misplaced tapes of e-mail messages long after the company had claimed that it had turned over all such tapes to the court. Increased manpower requirements to manage increasingly chaotic data storage resources. Slower networks and application performance due to excess traffic as users search and search again for the material they need. High cost in terms of the energy resources required to operate storage hardware. A 100 terabyte system will cost up to $35,040 a year to run—not counting cooling costs. == Proposed solutions == Applications that better utilize modern technology Reductions in duplicate data (especially as caused by data movement) Improvement of metadata structures Improvement of file and storage transfer structures User education and discipline The implementation of Information Lifecycle Management solutions to eliminate low-value information as early as possible before putting the rest into actively managed long-term storage in which it can be quickly and cheaply accessed.
Pray.com
Pray.com is a Christian social networking service and mobile application designed to facilitate religious communities. Launched in 2016, it was founded by Steve Gatena, Michael Lynn, Ryan Beck and Matthew Potter. The platform offers features for social networking, daily prayers, sermons, biblical content, and podcasts. The COVID-19 pandemic significantly increased Pray.com's user base, with downloads surging by 955%. During this period, the platform collaborated with churches to support virtual ministry services as in-person gatherings were restricted. The Federal Election Commission issued an opinion in 2021 that allows the platform to feature members of the United States Congress. Pray.com serves as a specialized social media platform for religious groups. Congregations can establish their own groups where members and leaders can participate in discussions, livestream services, and manage donations. Additionally, users can join "prayer communities" to post and respond to prayer requests. For those who subscribe to premium services, the platform provides access to biblically-inspired meditations and bedtime stories, and Bible stories for children. Pray.com also produces Radio drama-style productions with notable actors such as Kristen Bell and Blair Underwood narrating biblical stories. == History == === Funding and development === Pray.com has secured significant funding to support its development and growth. In 2017, the platform raised $2 million in seed funding from Science Inc., Greylock Partners, and Spark Capital. This was followed by a Series A funding round in March 2018, in which the company secured an additional $14 million from TPG Growth, Science Inc., and Greylock Partners. Founder Steve Gatena has highlighted difficulties in securing funding, noting some venture capitalists' negative attitudes towards faith-based technology. === Clinical studies === There have been clinical studies on Pray.com. In one study, the app was found to be acceptable and easy to use among racial and ethnic minority groups, with participants reporting improved mental health and well-being. Greater app use was associated with better outcomes, though low and variable usage suggests the need for further research to fully understand its impact. Another study examined Pray.com's impact on mental health by assigning 192 participants to use the app freely, use its meditative prayer function, or not use it at all. Over two months, participants reported overall improvements in mental health and well-being. Although no significant differences were found between groups, greater app usage correlated with better mental health outcomes. This suggests that religiously based mobile apps may help improve mental health and well-being. Another study of pray.com had similar findings. === National Day of Prayer === Pray first hosted a National Day of Prayer event in 2020 when it streamed to nearly one million viewers on Facebook. In 2021, Pray hosted a virtual event for the National Day of Prayer in the United States. The event featured remarks from public figures including United States President Joe Biden and former Vice President Mike Pence. President Biden spoke of his faith and prayed for an end to the COVID-19 pandemic. Biden remarked: "It means the world to me to know that there are people across the country who include Jill and me in their prayers. And I hope you know that you and your families are in our prayers as well. Today I am praying for the end of this great COVID crisis." The event featured musical performances from Gary Valenciano, Brooke Ligertwood from the Christian band Hillsong Worship, Lecrae, Heather Headley and Michael Neale. Other notable speakers included Ronnie Floyd, Ed Young, Mark Driscoll, and Samuel Rodriguez. Pray.com partnered with Sirius XM, DirecTV and Facebook to stream the event across multiple platforms. Pray.com was featured as a pop-up channel on Sirius XM, channel 154, to host the prayer event and celebrate people of all faith. === Partnerships and sponsorships === In 2024, Pray.com partnered with Sting Ray Robb as the primary sponsor for his No. 41 Chevrolet in the 2024 NTT IndyCar Series. The partnership, highlighting Robb's Christian faith, aims to engage younger audiences with faith-based content. The car, featuring Pray.com's branding, was set to debut at the Firestone Grand Prix of St. Petersburg. A partnership with Palantir Technologies for use of its AI systems was also announced in 2024. === Censorship in China === The app was removed from Apple's App Store in China as part of the country's broader efforts to restrict access to religious content. The app was targeted due to China's stringent regulations on religious material, particularly content distributed through digital platforms. The removal aligns with China's ongoing campaign to control online religious expression and maintain state-approved religious activities.
Honey encryption
Honey encryption is a type of data encryption that "produces a ciphertext, which, when decrypted with an incorrect key as guessed by the attacker, presents a plausible-looking yet incorrect plaintext." == Creators == Ari Juels and Thomas Ristenpart of the University of Wisconsin, the developers of the encryption system, presented a paper on honey encryption at the 2014 Eurocrypt cryptography conference. == Method of protection == A brute-force attack involves repeated decryption with random keys; this is equivalent to picking random plaintexts from the space of all possible plaintexts with a uniform distribution. This is effective because even though the attacker is equally likely to see any given plaintext, most plaintexts are extremely unlikely to be legitimate i.e. the distribution of legitimate plaintexts is non-uniform. Honey encryption defeats such attacks by first transforming the plaintext into a space such that the distribution of legitimate plaintexts is uniform. Thus an attacker guessing keys will see legitimate-looking plaintexts frequently and random-looking plaintexts infrequently. This makes it difficult to determine when the correct key has been guessed. In effect, honey encryption "[serves] up fake data in response to every incorrect guess of the password or encryption key." The security of honey encryption relies on the fact that the probability of an attacker judging a plaintext to be legitimate can be calculated (by the encrypting party) at the time of encryption. This makes honey encryption difficult to apply in certain applications e.g. where the space of plaintexts is very large or the distribution of plaintexts is unknown. It also means that honey encryption can be vulnerable to brute-force attacks if this probability is miscalculated. For example, it is vulnerable to known-plaintext attacks: if the attacker has a crib that a plaintext must match to be legitimate, they will be able to brute-force even Honey Encrypted data if the encryption did not take the crib into account. == Example == An encrypted credit card number is susceptible to brute-force attacks because not every string of digits is equally likely. The number of digits can range from 13 to 19, though 16 is the most common. Additionally, it must have a valid IIN and the last digit must match the checksum. An attacker can also take into account the popularity of various services: an IIN from MasterCard is probably more likely than an IIN from Diners Club Carte Blanche. Honey encryption can protect against these attacks by first mapping credit card numbers to a larger space where they match their likelihood of legitimacy. Numbers with invalid IINs and checksums are not mapped at all (i.e. have probability 0 of legitimacy). Numbers from large brands like MasterCard and Visa map to large regions of this space, while less popular brands map to smaller regions, etc. An attacker brute-forcing such an encryption scheme would only see legitimate-looking credit card numbers when they brute-force, and the numbers would appear with the frequency the attacker would expect from the real world. == Application == Juels and Ristenpart aim to use honey encryption to protect data stored on password manager services. Juels stated that "password managers are a tasty target for criminals," and worries that "if criminals get a hold of a large collection of encrypted password vaults they could probably unlock many of them without too much trouble." Hristo Bojinov, CEO and founder of Anfacto, noted that "Honey Encryption could help reduce their vulnerability. But he notes that not every type of data will be easy to protect this way. … Not all authentication or encryption system yield themselves to being honeyed."