Polythematic Structured Subject Heading System (abbreviated as PSH from the Czech Polytematický Strukturovaný Heslář) is a bilingual Czech–English controlled vocabulary of subject headings developed and maintained by the National Technical Library (the former State Technical Library) in Prague. It was designed for describing and searching information resources according to their subject. PSH contains more than 13,900 terms, which cover the main fields of human knowledge. Because of its release in SKOS, PSH can be used not only for describing documents in a library, but also for indexing web pages. Everyone can use PSH for free. PSH is a part of the Linked Open Data cloud diagram (LOD cloud diagram). The image of the LOD cloud diagram shows datasets that have been published in Linked Data format, by contributors to the Linked Open Data community project and other individuals and organisations. == History and development == The PSH preparation project started in 1993, supported by several grants from the Czech Ministry of Culture and Czech Ministry of Education, Youth and Sport. Since 1995, PSH has been used for indexing the State Technical Library's documents. Starting 1997, PSH has been distributed to other libraries and companies, originally as a commercial, paid product; since 2009 for free. In 2000, the State Technical Library received a grant from the Ministry of Culture to translate PSH into English. The next milestone in its development was its releasing in the SKOS format, in 2009. The vast majority of new subject headings is suggested and approved by the indexing experts from the National Technical Library. However, the users and public can also make suggestions, using an online form, which are then assessed by the experts. The main decisions about the development and the future of PSH are done by the Committee for Coordination of Polythematic Structured Subject Heading System. The Committee consists of specialists from the National Technical Library and cooperating institutions, and representatives from the libraries and companies which use PSH. The Committee meets once a year in the National Technical Library; in the meantime, the members communicate using an electronic mailing list. == Browsing PSH == PSH Browser was released in June 2009. It serves for browsing the PSH system and its distribution in SKOS format. This tool navigates users through PSH from general to specific terms. Users can also use the Search field. PSH manager tool was released in 2012. It serves as an indexing tool especially to catalogers. Catalogers can easy orient in its clear structure. All the terms in PSH manager contain link to the catalogue of NTK. There can be also viewed the record in MARC21 format. == Autoindexing == In 2012 was released beta version of autoindexing application. It is accessible on Autoindexing. Users enter chosen text into indexing field and activate indexing. In few seconds the terms describing content are displayed. == PSH structure == PSH is a tree structure with 44 thematic sections. Subject headings are included in a hierarchy of six (or seven) levels according to their semantic content and specificity. There are hierarchical, associative ("see also") and equivalence ("see") relations in PSH. Hierarchical relations are represented by broader and narrower terms (e.g. physical diagnostic methods is broader term to electrocardiography, and on the other hand, electrocardiography is narrower term to physical diagnostic methods). Equivalence relations link subject headings with their nonpreferred versions (e.g. electrocardiography and ECG). Moreover, associative relations are used to link related subject headings from different parts of PSH, regardless their affiliation to a section, (e.g. electrocardiography: see also cardiology). Every subject heading belongs to just one section, which has its own two-character abbreviation, assigned to every subject heading of the section. This enables users to recognize affiliation of subject headings from lower levels to the thematic sections. The 44 thematic sections have following root nodes: == PSH formats == The main format for storage, maintenance and sharing PSH is the MARC 21 Format for Authority Data, which is implemented in library automated systems. PSH is also available in SKOS, using RDF/XML syntax, which is a version suitable for web distribution. Single headings can be accessed on the PSH website through URI links. Alternatively, the whole vocabulary can be downloaded in one file. It is possible to display tags from PSH (metadata snippets – Dublin Core and CommonTag), which can be embedded in an HTML document to provide its semantic description in a machine-readable way. == New subject headings == New subject headings are primarily obtained through the log analysis in the National Technical Library's on-line catalogue of documents, which are the terms used by end-users when searching various documents. Google Analytics service is now used for gaining search queries used by users. Within the data analysis, users queries are divided into seven categories that contain the title of the document, person, subject, action, institution, geographical terms and others. Then the candidates for new preferred terms and non-preferred terms are identified in the subject category. Users can suggest preferred or non-preferred terms through the web form or via e-mail psh(@)techlib.cz. == PSH and Creative Commons == PSH/SKOS has been available under the Creative Commons License CC BY 3.0 CZ (Attribution-ShareAlike 3.0 Czech Republic)since 2011. Users are free to copy, distribute, display and perform the work and make derivative works, but they must give the original author credit and if they alter, transform, or build upon this work, they have to distribute the resulting work only under a licence identical to this one. Users can download all data in one zip file, which is continuously updated.
Valantic
Valantic GmbH (stylised as valantic) is an IT service and consulting company headquartered in Munich, Germany. == History == Valantic GmbH was founded in 2012 under the name Dabero Service Group. Until it was renamed Valantic GmbH in 2017, the company merged with IT service providers and consulting firms. These included, among others, Realtime AG, a company for SAP systems. The companies involved in these mergers were also renamed in 2017 and have since used the Valantic brand name. Realtime AG, for example, became Valantic ERP Services AG. During the COVID-19 pandemic and the resulting economic pressures, demand increased for IT service providers, particularly those offering customised software, IT consulting, SAP services, customer experience, cybersecurity, IoT, and digital work environments. In the following years, Valantic expanded by integrating additional companies. In 2021, Valantic expanded into other European countries through the integration of the Dutch company ISM eCompany and the Portuguese consulting firm Abaco. In 2022, the consulting firm C-Clear/Atom Ideas from Belgium joined Valantic. In February 2019, DPE Deutsche Private Equity Management III GmbH (DPE) took over the majority shareholding in Valantic. The founder, Holger von Daniels, and the further management retained a 25% stake. By 2025, DPE had invested €500 million in Valantic. In the following years, Valantic expanded its international locations. In 2023, Valantic incorporated the Danish company Inspari into the group, thereby entering the Scandinavian market. Inspari is a company for Microsoft technologies such as Azure and Power Platform. In the same year, Valantic joined forces with the Aiopsgroup, an international provider of online shopping applications for private and business customers of large companies. The company is based in Bulgaria with additional locations across Eastern Europe and other places. Additionally, the SAP applications division was expanded through the merger with the Spanish company Saptools. As a result, the companies became one of the largest European end-to-end consulting and implementation house for SAP services. By the end of 2023, Valantic had locations in 18 countries. In November 2024, Valantic announced its merger with the Danish digital consultancy Venzo. Through the integration of the company, founded in 2007 and oriented towards Microsoft technologies and digital transformation projects in the areas of automation, artificial intelligence, security, infrastructure and change management, Valantic further expanded its presence in Denmark and the Nordic countries. In July 2025, Valantic announced its merger with Utiligence GmbH, a Mannheim-based consulting firm for SAP technologies. Utiligence works primarily for the energy industry and supports companies in the integration of SAP S/4HANA and the digitalisation of business processes. == Company structure == Valantic is a partnership-based organisation, with partners acting as decision-makers in matters relating to corporate strategy, employee development and acquisitions. Valantic pursues a holacratic approach, promoting an open and self-organised way of working instead of hierarchical structures. By merging with other companies, Valantic is expanding its range of services and tapping into international markets and market shares. The new companies use Valantic's core systems and support processes, but usually retain their original structure. In the 2024 financial year, the company generated revenue of €544 million and employed 3,874 on average. Valantic has over 40 locations internationally. == Services == Valantic GmbH is a consulting firm, software provider and implementation partner. The company offers services in the areas of digital strategy and analytics (business intelligence and data science), customer experience management, SAP services, smart industries (Industry 4.0, supply chain management, and production planning and control processes), and financial services automation. The automation of financial services is aimed at financial service providers and banks. Valantic has been offering services in the field of generative artificial intelligence (GenAI) since 2023. Part of these services involves enabling companies to use GenAI securely and in compliance with regulations in order to make internal work processes more efficient. Its customers include large corporations, several medium-sized companies and DAX-listed companies. == Research == Since 2018, Valantic has published an annual study on the development of the SAP landscape in German-speaking countries. The study examines topics such as the migration to SAP S/4HANA, cloud strategies, technological trends and the use of artificial intelligence in business processes. The 2025 survey of 201 SAP professionals from the DACH region showed, for example, an increase in ongoing and completed S/4HANA migration projects, as well as a further shift towards private-cloud systems. The use of artificial intelligence continued to grow, as did the use of the SAP Business Technology Platform and the Business Data Cloud. In 2025, Valantic, together with the Handelsblatt Research Institute, published the trend study Digital 2030 – The Rise of Applied AI. The study was based on a survey of around 700 executives from companies in Germany, Austria, and Switzerland on the economic effects of current digitalisation trends. According to the study, most respondents consider artificial intelligence, cybersecurity, and cloud computing to hold the greatest strategic importance for business success by 2030. Around 70% of the participating companies stated that they are already achieving measurable business benefits through the use of AI applications, for example in quality control, document management, logistics, or customer service.
Audio inpainting
Audio inpainting (also known as audio interpolation) is an audio restoration task which deals with the reconstruction of missing or corrupted portions of a digital audio signal. Inpainting techniques are employed when parts of the audio have been lost due to various factors such as transmission errors, data corruption or errors during recording. The goal of audio inpainting is to fill in the gaps (i.e., the missing portions) in the audio signal seamlessly, making the reconstructed portions indistinguishable from the original content and avoiding the introduction of audible distortions or alterations. Many techniques have been proposed to solve the audio inpainting problem and this is usually achieved by analyzing the temporal and spectral information surrounding each missing portion of the considered audio signal. Classic methods employ statistical models or digital signal processing algorithms to predict and synthesize the missing or damaged sections. Recent solutions, instead, take advantage of deep learning models, thanks to the growing trend of exploiting data-driven methods in the context of audio restoration. Depending on the extent of the lost information, the inpainting task can be divided in three categories. Short inpainting refers to the reconstruction of few milliseconds (approximately less than 10) of missing signal, that occurs in the case of short distortions such as clicks or clipping. In this case, the goal of the reconstruction is to recover the lost information exactly. In long inpainting instead, with gaps in the order of hundreds of milliseconds or even seconds, this goal becomes unrealistic, since restoration techniques cannot rely on local information. Therefore, besides providing a coherent reconstruction, the algorithms need to generate new information that has to be semantically compatible with the surrounding context (i.e., the audio signal surrounding the gaps). The case of medium duration gaps lays between short and long inpainting. It refers to the reconstruction of tens of millisecond of missing data, a scale where the non-stationary characteristic of audio already becomes important. == Definition == Consider a digital audio signal x {\displaystyle \mathbf {x} } . A corrupted version of x {\displaystyle \mathbf {x} } , which is the audio signal presenting missing gaps to be reconstructed, can be defined as x ~ = m ∘ x {\displaystyle \mathbf {\tilde {x}} =\mathbf {m} \circ \mathbf {x} } , where m {\displaystyle \mathbf {m} } is a binary mask encoding the reliable or missing samples of x {\displaystyle \mathbf {x} } , and ∘ {\displaystyle \circ } represents the element-wise product. Audio inpainting aims at finding x ^ {\displaystyle \mathbf {\hat {x}} } (i.e., the reconstruction), which is an estimation of x {\displaystyle \mathbf {x} } . This is an ill-posed inverse problem, which is characterized by a non-unique set of solutions. For this reason, similarly to the formulation used for the inpainting problem in other domains, the reconstructed audio signal can be found through an optimization problem that is formally expressed as x ^ ∗ = argmin X ^ L ( m ∘ x ^ , x ~ ) + R ( x ^ ) {\displaystyle \mathbf {\hat {x}} ^{}={\underset {\hat {\mathbf {X} }}{\text{argmin}}}~L(\mathbf {m} \circ \mathbf {\hat {x}} ,\mathbf {\tilde {x}} )+R(\mathbf {\hat {x}} )} . In particular, x ^ ∗ {\displaystyle \mathbf {\hat {x}} ^{}} is the optimal reconstructed audio signal and L {\displaystyle L} is a distance measure term that computes the reconstruction accuracy between the corrupted audio signal and the estimated one. For example, this term can be expressed with a mean squared error or similar metrics. Since L {\displaystyle L} is computed only on the reliable frames, there are many solutions that can minimize L ( m ∘ x ^ , x ~ ) {\displaystyle L(\mathbf {m} \circ \mathbf {\hat {x}} ,\mathbf {\tilde {x}} )} . It is thus necessary to add a constraint to the minimization, in order to restrict the results only to the valid solutions. This is expressed through the regularization term R {\displaystyle R} that is computed on the reconstructed audio signal x ^ {\displaystyle \mathbf {\hat {x}} } . This term encodes some kind of a-priori information on the audio data. For example, R {\displaystyle R} can express assumptions on the stationarity of the signal, on the sparsity of its representation or can be learned from data. == Techniques == There exist various techniques to perform audio inpainting. These can vary significantly, influenced by factors such as the specific application requirements, the length of the gaps and the available data. In the literature, these techniques are broadly divided in model-based techniques (sometimes also referred as signal processing techniques) and data-driven techniques. === Model-based techniques === Model-based techniques involve the exploitation of mathematical models or assumptions about the underlying structure of the audio signal. These models can be based on prior knowledge of the audio content or statistical properties observed in the data. By leveraging these models, missing or corrupted portions of the audio signal can be inferred or estimated. An example of a model-based techniques are autoregressive models. These methods interpolate or extrapolate the missing samples based on the neighboring values, by using mathematical functions to approximate the missing data. In particular, in autoregressive models the missing samples are completed through linear prediction. The autoregressive coefficients necessary for this prediction are learned from the surrounding audio data, specifically from the data adjacent to each gap. Some more recent techniques approach audio inpainting by representing audio signals as sparse linear combinations of a limited number of basis functions (as for example in the Short Time Fourier Transform). In this context, the aim is to find the sparse representation of the missing section of the signal that most accurately matches the surrounding, unaffected signal. The aforementioned methods exhibit optimal performance when applied to filling in relatively short gaps, lasting only a few tens of milliseconds, and thus they can be included in the context of short inpainting. However, these signal-processing techniques tend to struggle when dealing with longer gaps. The reason behind this limitation lies in the violation of the stationarity condition, as the signal often undergoes significant changes after the gap, making it substantially different from the signal preceding the gap. As a way to overcome these limitations, some approaches add strong assumptions also about the fundamental structure of the gap itself, exploiting sinusoidal modeling or similarity graphs to perform inpainting of longer missing portions of audio signals. === Data-driven techniques === Data-driven techniques rely on the analysis and exploitation of the available audio data. These techniques often employ deep learning algorithms that learn patterns and relationships directly from the provided data. They involve training models on large datasets of audio examples, allowing them to capture the statistical regularities present in the audio signals. Once trained, these models can be used to generate missing portions of the audio signal based on the learned representations, without being restricted by stationarity assumptions. Data-driven techniques also offer the advantage of adaptability and flexibility, as they can learn from diverse audio datasets and potentially handle complex inpainting scenarios. As of today, such techniques constitute the state-of-the-art of audio inpainting, being able to reconstruct gaps of hundreds of milliseconds or even seconds. These performances are made possible by the use of generative models that have the capability to generate novel content to fill in the missing portions. For example, generative adversarial networks, which are the state-of-the-art of generative models in many areas, rely on two competing neural networks trained simultaneously in a two-player minmax game: the generator produces new data from samples of a random variable, the discriminator attempts to distinguish between generated and real data. During the training, the generator's objective is to fool the discriminator, while the discriminator attempts to learn to better classify real and fake data. In GAN-based inpainting methods the generator acts as a context encoder and produces a plausible completion for the gap only given the available information surrounding it. The discriminator is used to train the generator and tests the consistency of the produced inpainted audio. Recently, also diffusion models have established themselves as the state-of-the-art of generative models in many fields, often beating even GAN-based solutions. For this reason they have also been used to solve the audio inpainting problem, obtaining valid results. These models generate new data instances by inverting the
Cross-validation (statistics)
Cross-validation, sometimes called rotation estimation or out-of-sample testing, is any of various similar model validation techniques for assessing how the results of a statistical analysis will generalize to an independent data set. Cross-validation includes resampling and sample splitting methods that use different portions of the data to test and train a model on different iterations. It is often used in settings where the goal is prediction, and one wants to estimate how accurately a predictive model will perform in practice. It can also be used to assess the quality of a fitted model and the stability of its parameters. In a prediction problem, a model is usually given a dataset of known data on which training is run (training dataset), and a dataset of unknown data (or first seen data) against which the model is tested (called the validation dataset or testing set). The goal of cross-validation is to test the model's ability to predict new data that was not used in estimating it, in order to flag problems like overfitting or selection bias and to give an insight on how the model will generalize to an independent dataset (i.e., an unknown dataset, for instance from a real problem). One round of cross-validation involves partitioning a sample of data into complementary subsets, performing the analysis on one subset (called the training set), and validating the analysis on the other subset (called the validation set or testing set). To reduce variability, in most methods multiple rounds of cross-validation are performed using different partitions, and the validation results are combined (e.g. averaged) over the rounds to give an estimate of the model's predictive performance. In summary, cross-validation combines (averages) measures of fitness in prediction to derive a more accurate estimate of model prediction performance. == Motivation == Assume a model with one or more unknown parameters, and a data set to which the model can be fit (the training data set). The fitting process optimizes the model parameters to make the model fit the training data as well as possible. If an independent sample of validation data is taken from the same population as the training data, it will generally turn out that the model does not fit the validation data as well as it fits the training data. The size of this difference is likely to be large especially when the size of the training data set is small, or when the number of parameters in the model is large. Cross-validation is a way to estimate the size of this effect. === Example: linear regression === In linear regression, there exist real response values y 1 , … , y n {\textstyle y_{1},\ldots ,y_{n}} , and n p-dimensional vector covariates x1, ..., xn. The components of the vector xi are denoted xi1, ..., xip. If least squares is used to fit a function in the form of a hyperplane ŷ = a + βTx to the data (xi, yi) 1 ≤ i ≤ n, then the fit can be assessed using the mean squared error (MSE). The MSE for given estimated parameter values a and β on the training set (xi, yi) 1 ≤ i ≤ n is defined as: MSE = 1 n ∑ i = 1 n ( y i − y ^ i ) 2 = 1 n ∑ i = 1 n ( y i − a − β T x i ) 2 = 1 n ∑ i = 1 n ( y i − a − β 1 x i 1 − ⋯ − β p x i p ) 2 {\displaystyle {\begin{aligned}{\text{MSE}}&={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-{\hat {y}}_{i})^{2}={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-a-{\boldsymbol {\beta }}^{T}\mathbf {x} _{i})^{2}\\&={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-a-\beta _{1}x_{i1}-\dots -\beta _{p}x_{ip})^{2}\end{aligned}}} If the model is correctly specified, it can be shown under mild assumptions that the expected value of the MSE for the training set is (n − p − 1)/(n + p + 1) < 1 times the expected value of the MSE for the validation set (the expected value is taken over the distribution of training sets). Thus, a fitted model and computed MSE on the training set will result in an optimistically biased assessment of how well the model will fit an independent data set. This biased estimate is called the in-sample estimate of the fit, whereas the cross-validation estimate is an out-of-sample estimate. Since in linear regression it is possible to directly compute the factor (n − p − 1)/(n + p + 1) by which the training MSE underestimates the validation MSE under the assumption that the model specification is valid, cross-validation can be used for checking whether the model has been overfitted, in which case the MSE in the validation set will substantially exceed its anticipated value. (Cross-validation in the context of linear regression is also useful in that it can be used to select an optimally regularized cost function.) === General case === In most other regression procedures (e.g. logistic regression), there is no simple formula to compute the expected out-of-sample fit. Cross-validation is, thus, a generally applicable way to predict the performance of a model on unavailable data using numerical computation in place of theoretical analysis. == Types == Two types of cross-validation can be distinguished: exhaustive and non-exhaustive cross-validation. === Exhaustive cross-validation === Exhaustive cross-validation methods are cross-validation methods which learn and test on all possible ways to divide the original sample into a training and a validation set. ==== Leave-p-out cross-validation ==== Leave-p-out cross-validation (LpO CV) involves using p observations as the validation set and the remaining observations as the training set. This is repeated on all ways to cut the original sample on a validation set of p observations and a training set. LpO cross-validation require training and validating the model C p n {\displaystyle C_{p}^{n}} times, where n is the number of observations in the original sample, and where C p n {\displaystyle C_{p}^{n}} is the binomial coefficient. For p > 1 and for even moderately large n, LpO CV can become computationally infeasible. For example, with n = 100 and p = 30, C 30 100 ≈ 3 × 10 25 . {\displaystyle C_{30}^{100}\approx 3\times 10^{25}.} A variant of LpO cross-validation with p=2 known as leave-pair-out cross-validation has been recommended as a nearly unbiased method for estimating the area under ROC curve of binary classifiers. ==== Leave-one-out cross-validation ==== Leave-one-out cross-validation (LOOCV) is a particular case of leave-p-out cross-validation with p = 1. The process looks similar to jackknife; however, with cross-validation one computes a statistic on the left-out sample(s), while with jackknifing one computes a statistic from the kept samples only. LOO cross-validation requires less computation time than LpO cross-validation because there are only C 1 n = n {\displaystyle C_{1}^{n}=n} passes rather than C p n {\displaystyle C_{p}^{n}} . However, n {\displaystyle n} passes may still require quite a large computation time, in which case other approaches such as k-fold cross validation may be more appropriate. Pseudo-code algorithm: Input: x, {vector of length N with x-values of incoming points} y, {vector of length N with y-values of the expected result} interpolate( x_in, y_in, x_out ), { returns the estimation for point x_out after the model is trained with x_in-y_in pairs} Output: err, {estimate for the prediction error} Steps: err ← 0 for i ← 1, ..., N do // define the cross-validation subsets x_in ← (x[1], ..., x[i − 1], x[i + 1], ..., x[N]) y_in ← (y[1], ..., y[i − 1], y[i + 1], ..., y[N]) x_out ← x[i] y_out ← interpolate(x_in, y_in, x_out) err ← err + (y[i] − y_out)^2 end for err ← err/N === Non-exhaustive cross-validation === Non-exhaustive cross validation methods do not compute all ways of splitting the original sample. These methods are approximations of leave-p-out cross-validation. ==== k-fold cross-validation ==== In k-fold cross-validation, the original sample is randomly partitioned into k equal sized subsamples, often referred to as "folds". Of the k subsamples, a single subsample is retained as the validation data for testing the model, and the remaining k − 1 subsamples are used as training data. The cross-validation process is then repeated k times, with each of the k subsamples used exactly once as the validation data. The k results can then be averaged to produce a single estimation. The advantage of this method over repeated random sub-sampling (see below) is that all observations are used for both training and validation, and each observation is used for validation exactly once. 10-fold cross-validation is commonly used, but in general k remains an unfixed parameter. For example, setting k = 2 results in 2-fold cross-validation. In 2-fold cross-validation, the dataset is randomly shuffled into two sets d0 and d1, so that both sets are equal size (this is usually implemented by shuffling the data array and then splitting it in two). We then train on d0 and validate on d1, followed by training on d1 and validating on d0. When k = n (the number of observations), k-fold cross-validation is equivalent to leave-one-out cr
Pattern theory
Pattern theory, formulated by Ulf Grenander, is a mathematical formalism to describe knowledge of the world as patterns. It differs from other approaches to artificial intelligence in that it does not begin by prescribing algorithms and machinery to recognize and classify patterns; rather, it prescribes a vocabulary to articulate and recast the pattern concepts in precise language. Broad in its mathematical coverage, Pattern Theory spans algebra and statistics, as well as local topological and global entropic properties. In addition to the new algebraic vocabulary, its statistical approach is novel in its aim to: Identify the hidden variables of a data set using real world data rather than artificial stimuli, which was previously commonplace. Formulate prior distributions for hidden variables and models for the observed variables that form the vertices of a Gibbs-like graph. Study the randomness and variability of these graphs. Create the basic classes of stochastic models applied by listing the deformations of the patterns. Synthesize (sample) from the models, not just analyze signals with them. The Brown University Pattern Theory Group was formed in 1972 by Ulf Grenander. Many mathematicians are currently working in this group, noteworthy among them being the Fields Medalist David Mumford. Mumford regards Grenander as his "guru" in Pattern Theory.
GoodRx
GoodRx Holdings, Inc. is an American healthcare company that operates a telemedicine platform and free-to-use website and mobile app that track prescription drug prices in the United States and provide drug coupons for discounts on medications. GoodRx compares prescription drug prices at more than 75,000 pharmacies in the United States. The platform allows users to consult a doctor online and obtain a prescription for certain types of medications. == History == === Financial performance === GoodRx was founded in Santa Monica, California in 2011. GoodRx experienced substantial growth in net income in 2017 ($9 million), 2018 ($44 million), and 2019 ($66 million), but recorded a loss of $293.6 million in 2020 due to IPO-related expenses. In September 2020, GoodRx went public on the Nasdaq under the ticker symbol GDRX. The company priced its initial public offering at $33 per share, above the expected range of $24 to $28, raising more than $1.1 billion at an initial valuation of approximately $12.7 billion. In the first half of 2020, the company reported revenues of $257 million and net income of $55 million. GoodRx generated $745.4 million in revenue for the full year 2021, a 35.36% increase over 2020. During the first half of 2021, the company’s share price declined by 10.7%. The decline was attributed to increased competition in online pharmacy services and slower user growth. GoodRx reported full-year revenue of $766.6 million, with adjusted EBITDA reaching $213.5 million, exceeding guidance in the fourth quarter. GoodRx reported that 41% of prescriptions filled using its coupons were newly adherent, meaning they would not have been filled without the service. GoodRx reported a full-year 2023 revenue of $750.3 million, a decrease of 2.1% from 2022. However, its fourth-quarter revenue increased by 7% year-over-year. GoodRx achieved an Adjusted EBITDA of $217.4 million for the year and an Adjusted EBITDA Margin of 28.6%. In 2024, GoodRx achieved 6% revenue growth with $792.3 million for the full year and turned a net loss into a positive net income of $16.4 million. The company also demonstrated strong operational efficiency, with a 32.8% increase in full-year Adjusted EBITDA. In Q2 2025, GoodRx reported revenue of $203.1 million, a 1.2% increase from the previous year, and a net income of $12.8 million, a significant 92% jump, which resulted in a 6.3% net income margin. However, prescription transaction revenue declined by 3% due to a decrease in monthly active consumers, but this was offset by strong 32% growth in its Pharma Manufacturer Solutions business. GoodRx also saw a 7% decrease in subscription revenue. === Mergers and acquisitions === In 2019, GoodRx acquired HeyDoctor, a telemedicine company, to integrate virtual healthcare services into the platform. In 2021, a health video content producer, HealthiNation was acquired by GoodRx, which helped provide consumers with health information and offered pharmaceutical manufacturers new ways to reach relevant audiences. In April 2022, GoodRx acquired VitaCare Prescription Services from TherapeuticsMD to strengthen its pharma manufacturer solutions business. === Partnerships === In 2017, the company announced partnerships with major pharmaceutical companies to negotiate lower prescription drug costs. GoodRx has deep relationships with major pharmacy chains, including Walgreens, Walmart, CVS Caremark, and Publix, to allow customers to use GoodRx discounts and Gold benefits. GoodRx began its partnership with CVS Caremark in July 2023 to automatically apply coupons to insured CVS customers purchasing generic prescriptions at certain locations. In April 2024, GoodRx added Publix into its network, allowing GoodRx Gold members to use their cards at Publix Pharmacies. GoodRx partners with Pharmacy Benefit Management like Caremark, Express Scripts, and MedImpact to apply their savings directly to eligible insurance plans and members. GoodRx partners with companies like Affirm, Benefitfocus, and DoorDash to integrate their services that offer members discounts and financial flexibility for prescriptions. GoodRx also partners with organizations like the American Academy of Family Physicians Foundation to support broader access to care. In October 2022, GoodRx launched Provider Mode, which allows healthcare providers to use the app to compare costs of drugs for patients based on different payment methods and drug alternatives. In 2025, GoodRx partnered with Novo Nordisk to offer discounted cash-pay access to semaglutide products like Ozempic and Wegovy through its platform and participating pharmacies. == Products and services == GoodRx started its telemedicine service GoodRx Care in September 2019. It lets people talk to a licensed provider online for common issues and get prescriptions even if they don't have insurance. They also run condition-specific subscription plans that bundle online doctor visits, FDA-approved meds, and home delivery into one monthly payment. On the weight management side, GoodRx offers prescriptions for GLP-1 drugs like semaglutide through their telemedicine platform. This got a boost when the oral version of Wegovy became widely available in the US in early 2026. GoodRx works with drug makers like Novo Nordisk to make some medications (including semaglutide options) more affordable for people paying cash. The telemedicine part took off after GoodRx bought HeyDoctor in 2019 and brought their virtual care tools into the main platform. == Key people == The Santa Monica-based startup was founded in September 2011 by Trevor Bezdek and former Facebook executives Doug Hirsch and Scott Marlette. Marlette was one of the first 20 employees at Facebook and built Facebook's photo application. In 2005, Hirsch was the Vice President of Product at Facebook, working closely with Mark Zuckerberg. Bezdek and Hirsch served as co-chief executive officers until April 2023, when they stepped down from those roles and technology executive Scott Wagner was appointed interim chief executive officer. Bezdek became chair of the board, while Hirsch took on the role of chief mission officer. In December 2024, GoodRx announced that healthcare executive Wendy Barnes would become president and chief executive officer effective January 1, 2025. As of 2025, Barnes serves as the company’s CEO, while Trevor Bezdek and Scott Wagner serve as co-chairs of the board, and Doug Hirsch remains involved as a co-founder and senior executive. == Controversy == On February 25, 2020, Consumer Reports published an article stating that GoodRx shared user data—specifically, pseudonymized advertising ID numbers that companies use to track the behavior of web users across websites, the names of the drugs that users browsed, and the pharmacies where users sought to fill prescriptions—with Google, Facebook, and around twenty other Internet-based companies. A few days later, GoodRx released a statement saying that it had made changes to prevent user search data on medical conditions and pharmaceuticals from being shared with Facebook. In March 2020, GoodRx stopped sending data about user prescriptions to Facebook. On February 1, 2023, the Federal Trade Commission fined GoodRx US$1.5 million for violations of the Breach Notification Rule and the Federal Trade Commission Act for allegedly failing to obtain specific, informed, and unambiguous consent from users before disclosing health-related information to Facebook and Google. In November 2024, independent pharmacies filed at least three class action lawsuits against GoodRx and major pharmacy benefit managers. The cases, brought by independent pharmacies in California, Michigan, Pennsylvania, and Rhode Island, allege that GoodRx and the PBMs collaborated to suppress reimbursements for generic prescription drugs. They allege that agreements using GoodRx’s software suppressed reimbursements for generic drugs and violated the Sherman Antitrust Act. The suits claim the practices amount to price fixing which harms small pharmacies while benefiting PBMs and their affiliates. GoodRx settled both the 2023 FTC action and the 2025 class action lawsuit without admitting wrongdoing.
Empowerment (artificial intelligence)
Empowerment in the field of artificial intelligence formalises and quantifies (via information theory) the potential an agent perceives that it has to influence its environment. An agent which follows an empowerment maximising policy, acts to maximise future options (typically up to some limited horizon). Empowerment can be used as a (pseudo) utility function that depends only on information gathered from the local environment to guide action, rather than seeking an externally imposed goal, thus is a form of intrinsic motivation. The empowerment formalism depends on a probabilistic model commonly used in artificial intelligence. An autonomous agent operates in the world by taking in sensory information and acting to change its state, or that of the environment, in a cycle of perceiving and acting known as the perception-action loop. Agent state and actions are modelled by random variables ( S : s ∈ S , A : a ∈ A {\displaystyle S:s\in {\mathcal {S}},A:a\in {\mathcal {A}}} ) and time ( t {\displaystyle t} ). The choice of action depends on the current state, and the future state depends on the choice of action, thus the perception-action loop unrolled in time forms a causal bayesian network. == Definition == Empowerment ( E {\displaystyle {\mathfrak {E}}} ) is defined as the channel capacity ( C {\displaystyle C} ) of the actuation channel of the agent, and is formalised as the maximal possible information flow between the actions of the agent and the effect of those actions some time later. Empowerment can be thought of as the future potential of the agent to affect its environment, as measured by its sensors. E := C ( A t ⟶ S t + 1 ) ≡ max p ( a t ) I ( A t ; S t + 1 ) {\displaystyle {\mathfrak {E}}:=C(A_{t}\longrightarrow S_{t+1})\equiv \max _{p(a_{t})}I(A_{t};S_{t+1})} In a discrete time model, Empowerment can be computed for a given number of cycles into the future, which is referred to in the literature as 'n-step' empowerment. E ( A t n ⟶ S t + n ) = max p ( a t , . . . , a t + n − 1 ) I ( A t , . . . , A t + n − 1 ; S t + n ) {\displaystyle {\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n})=\max _{p(a_{t},...,a_{t+n-1})}I(A_{t},...,A_{t+n-1};S_{t+n})} The unit of empowerment depends on the logarithm base. Base 2 is commonly used in which case the unit is bits. === Contextual Empowerment === In general the choice of action (action distribution) that maximises empowerment varies from state to state. Knowing the empowerment of an agent in a specific state is useful, for example to construct an empowerment maximising policy. State-specific empowerment can be found using the more general formalism for 'contextual empowerment'. C {\displaystyle C} is a random variable describing the context (e.g. state). E ( A t n ⟶ S t + n ∣ C ) = ∑ c ∈ C p ( c ) E ( A t n ⟶ S t + n ∣ C = c ) {\displaystyle {\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n}{\mid }C)=\sum _{c{\in }C}p(c){\mathfrak {E}}(A_{t}^{n}\longrightarrow S_{t+n}{\mid }C=c)} == Application == Empowerment maximisation can be used as a pseudo-utility function to enable agents to exhibit intelligent behaviour without requiring the definition of external goals, for example balancing a pole in a cart-pole balancing scenario where no indication of the task is provided to the agent. Empowerment has been applied in studies of collective behaviour and in continuous domains. As is the case with Bayesian methods in general, computation of empowerment becomes computationally expensive as the number of actions and time horizon extends, but approaches to improve efficiency have led to usage in real-time control. Empowerment has been used for intrinsically motivated reinforcement learning agents playing video games, and in the control of underwater vehicles.