FreshBooks is accounting software operated by 2ndSite Inc. primarily for small and medium-sized businesses. It is a web-based software as a service (SaaS) model, that can be accessed through a desktop or mobile device. The company was founded in 2003 and is based in Toronto, Canada. == History == FreshBooks was founded in 2004 by Mike McDerment, Levi Cooperman, and Joe Sawada in Toronto, Ontario. McDerment incorporated a second company, BillSpring in January 2015 to work on new product development. It was rolled back into FreshBooks as an updated interface in 2016. Initially FreshBooks functioned like an electronic invoicing program targeting IT professionals. After the release of the new interface, the initial release of FreshBooks was referred to as "FreshBooks Classic." FreshBooks Classic was discontinued in 2022 after migrating users to the new platform. FreshBooks Classic's front-end application was built in PHP, and the backend services were built in Python while the new FreshBooks uses the same backend services with a JavaScript single-page application. == Product == FreshBooks is a subscription-based accounting software platform that provides features such as invoicing, accounts payable, expense and time tracking, retainers, fixed asset depreciation, purchase orders, payroll integrations, mileage tracking, double-entry accounting, and standard business reporting. Financial data is stored in the cloud on a unified ledger, enabling access from desktop and mobile devices. The platform includes a free API for integration with external applications and supports multiple tax rates and currencies. It also offers project management and payroll functionalities. Pricing is based on a recurring monthly fee. FreshBooks supports country-specific tax calculations, including GST and HST in Canada, sales taxes in the United States, and MTD compliance in the UK. == Operations == FreshBooks has its headquarters in Toronto, Canada with operations in North America, Europe and Australia. Founder Mike McDerment was the chief executive officer of the company from 2003 until 2021, when he stepped down and was replaced by Don Epperson, but stayed as the executive chair. Don Epperson had previously joined FreshBooks as executive director in 2019. == Funding == FreshBooks was initially self-funded. In 2014, the company raised a Series A venture investment of $30 million led by the venture capital firm Oak Investment Partners, with participation by Georgian Partners and Atlas Venture. In 2017, FreshBooks announced that it raised another $43 million in funding from Accomplice, Georgian Partners and Oak Investment Partners. On August 10, 2021, FreshBooks announced that it had secured $80.75 million in Series E funding and $50 million in debt financing. FreshBooks also reached a valuation of more than $1 billion.
Keith Youngin George II
Keith "Youngin" George II is a former mixtape DJ, music executive, manager, producer, and technology app director. He has collaborated with Maino, T-Pain, Nas and Soulja Boy, among others. He was instrumental in the launch of social media app and website, Kandiid in 2021 and served as Fliiks App Director of Regional Development. == Career == Keith Anthony George II was born in Upper Heyford, Oxfordshire, England. His father was in the Air Force which exposed him to different cultures and music. He graduated from Allen High School and attended San Antonio College. George's music career began in 2006 as a mixtape DJ working as DJ Youngin Beatz. He performed at various shows and worked with a variety of artists, managers, and music executives. In 2007, George released the mixtape, Untapped market Vol. 1 (Da Underdogz), which featured tracks from artists including Kanye West, Lil Wayne, 50 Cent, Yung Berg, and Nelly. In 2008, he began working with Def Jam executive Sarah Alminawi who was managing Maino at the time. George played a key role in the marketing and promotional success of Maino's single, Hi Hater, which peaked at #8 on Billboard's US Bubbling Under Hot 100 chart. In 2021, George was an advisor and infrastructure head at Kandiid, a social media app which won a W3 Award in 2022. In 2023, he became involved with Fliiks App as Director of Regional Development which earned a Telly Award, two Muse Awards, and a W3 Award in 2025. In 2025, George was a composer and producer on two singles on Sekou Andrews's album, Koumami; The Chosen One: ACT 1 (featuring Lion Babe) and Love Don't Care (featuring Jordin Sparks and Omari Hardwick). In 2025, he was awarded an Atlanta City Proclamation for Philanthropy and Community Leadership for his partnership with Women's International Grail, a nonprofit organization that assists women, single mothers, and low-income families. He also collaborates with local youth programs, creative networks, and minority-owned startups, providing access to mentorship and industry knowledge. == Awards ==
Imieliński–Lipski algebra
In database theory, Imieliński–Lipski algebra is an extension of relational algebra onto tables with different types of null values. It is used to operate on relations with incomplete information. Imieliński–Lipski algebras are defined to satisfy precise conditions for semantically meaningful extension of the usual relational operators, such as projection, selection, union, and join, from operators on relations to operators on relations with various kinds of "null values". These conditions require that the system be safe in the sense that no incorrect conclusion is derivable by using a specified subset F of the relational operators; and that it be complete in the sense that all valid conclusions expressible by relational expressions using operators in F are in fact derivable in this system. For example, it is well known that the three-valued logic approach to deal with null values, supported treatment of nulls values by SQL is not complete, see Ullman book. To show this, let T be: Take SQL query Q SQL query Q will return empty set (no results) under 3-valued semantics currently adopted by all variants of SQL. This is the case because in SQL, NULL is never equal to any constant – in this case, neither to “Spring” nor “Fall” nor “Winter” (if there is Winter semester in this school). NULL='Spring' will evaluate to MAYBE and so will NULL='Fall'. The disjunction MAYBE OR MAYBE evaluates to MAYBE (not TRUE). Thus Igor will not be part of the answer (and of course neither will Rohit). But Igor should be returned as the answer. Indeed, regardless what semester Igor took the Networks class (no matter what was the unknown value of NULL), the selection condition will be true. This “Igor” will be missed by SQL and the SQL answer would be incomplete according to completeness requirements specified in Tomasz Imieliński, Witold Lipski, 'Incomplete Information in Relational Databases'. It is also argued there that 3-valued logic (TRUE, FALSE, MAYBE) can never provide guarantee of complete answer for tables with incomplete information. Three algebras which satisfy conditions of safety and completeness are defined as Imielinski–Lipski algebras: the Codd-Tables algebra, the V-tables algebra and the Conditional tables (C-tables) algebra. == Codd-tables algebra == Codd-tables algebra is based on the usual Codd's single NULL values. The table T above is an example of Codd-table. Codd-table algebra supports projection and positive selections only. It is also demonstrated in [IL84 that it is not possible to correctly extend more relational operators over Codd-Tables. For example, such basic operation as join is not extendable over Codd-tables. It is not possible to define selections with Boolean conditions involving negation and preserve completeness. For example, queries like the above query Q cannot be supported. In order to be able to extend more relational operators, more expressive form of null value representation is needed in tables which are called V-table. == V-tables algebra == V-tables algebra is based on many different ("marked") null values or variables allowed to appear in a table. V-tables allow to show that a value may be unknown but the same for different tuples. For example, in the table below Gaurav and Igor order the same (but unknown) beer in two unknown bars (which may, or may not be different – but remain unknown). Gaurav and Jane frequent the same unknown bar (Y1). Thus, instead one NULL value, we use indexed variables, or Skolem constants . V-tables algebra is shown to correctly support projection, positive selection (with no negation occurring in the selection condition), union, and renaming of attributes, which allows for processing arbitrary conjunctive queries. A very desirable property enjoyed by the V-table algebra is that all relational operators on tables are performed in exactly the same way as in the case of the usual relations. === Conditional tables (c-tables) algebra === Example of conditional table (c-table) is shown below. It has additional column “con” which is a Boolean condition involving variables, null values – same as in V-tables. over the following table c-table Conditional tables algebra, mainly of theoretical interest, supports projection, selection, union, join, and renaming. Under closed-world assumption, it can also handle the operator of difference, thus it can support all relational operators. == History == Imieliński–Lipski algebras were introduced by Tomasz Imieliński and Witold Lipski Jr. in Incomplete Information in Relational Databases.
Esdat
ESdat is a data management, analysis and reporting software for environmental and groundwater data, developed by EarthScience Information Systems (EScIS). It is used to manage many types of environmental data including laboratory chemistry (analytical results, QA data, lab sample planning, and electronic Chain of Custody), field chemistry (water, gas, and soil), hydrogeological data (groundwater, borehole and well construction, lithological, geotechnical and stratigraphic, and LNAPL), meteorological data (rain, wind, and temperature), emission data (dust deposition, HiVol, air quality, and noise) and logger data. Data can be compared against environmental standards or site-specific trigger levels to generate exceedence tables, time series graphs, maps, statistics, and other outputs. ESdat integrates with Power BI and ArcGIS and data can also be exported in a range of other database formats, including USEPA Regions 2,4 & 5, and NYS DEC. ESdat is used by environmental consultants, government, mining and industry for validation, interrogation, and reporting of data derived from complex environmental programs, such as contaminated sites, groundwater investigations, and regulatory compliance for landfills or mining operations.
Human Race Machine
The Human Race Machine (HRM) is a computerized console composed of four different programs. The Human Race Machine program allows participants to see themselves with the facial characteristics of six different races: Asian, White, African, Middle Eastern, and Indian, mapped onto their own face. The Age Machine allows viewers see an aged version of his or her face. A version of this methodology has been used for over twenty years by the FBI and the National Center for Missing and Exploited Children to help locate kidnap victims and missing children. The Couples Machine combines photographs of two people in different percentages to show the appearance of their child. The Anomaly Machine lets viewers see themselves with facial anomalies. The HRM was created by artist Nancy Burson and David Kramlich; it uses morphing technology. It was shown on Oprah on 2006-02-16.
Reconstruction from projections
The problem of reconstructing a multidimensional signal from its projection is uniquely multidimensional, having no 1-D counterpart. It has applications that range from computer-aided tomography to geophysical signal processing. It is a problem which can be explored from several points of view—as a deconvolution problem, a modeling problem, an estimation problem, or an interpolation problem. == Motivation and applications == Many fields in science and engineering use reconstruction from projections, especially in imaging. It is widely applied geophysical tomography, medical imaging and industrial radiography. For example, in a CT scanner, the 3D structure of the patient’s body being scanned is measured with beams going through the tissue and hitting a detector, giving a flat projection of the body from that angle. Multiple projections are put together to get an image of the position and shape of structures inside in 3D. == Problem statement and basics == A projection is a linear mapping of an M {\displaystyle M} dimensional signal into an N {\displaystyle N} dimensional one, where N ≤ M {\displaystyle N\leq M} . And the objective of reconstruction is to restore the M {\displaystyle M} dimensional signal based on the N {\displaystyle N} dimensional signal. The following case is a 2-D signal projected into 1D signal. The signal in the original coordinate is denoted as d ( u , v ) {\displaystyle d(u,v)} . Now consider a collimated beam of radiation coming from the opposite orientation of v ^ {\displaystyle {\hat {v}}} , producing a projection along u ^ {\displaystyle {\hat {u}}} . v ^ {\displaystyle {\hat {v}}} and u ^ {\displaystyle {\hat {u}}} are normal to each other, and the angle between u {\displaystyle u} and u ^ {\displaystyle {\hat {u}}} is theta. The signal obtained along u ^ {\displaystyle {\hat {u}}} axis is defined to be p θ ( u ^ ) {\displaystyle p_{\theta }({\hat {u}})} . The relationship between the original coordinate and the rotated coordinate is given by [ u ^ v ^ ] = [ cos θ sin θ − sin θ cos θ ] [ u v ] {\displaystyle {\begin{bmatrix}{\hat {u}}\\{\hat {v}}\end{bmatrix}}={\begin{bmatrix}\cos \theta &\sin \theta \\-\sin \theta &\cos \theta \end{bmatrix}}{\begin{bmatrix}u\\v\end{bmatrix}}} or inversely, [ u v ] = [ cos θ − sin θ sin θ cos θ ] [ u ^ v ^ ] {\displaystyle {\begin{bmatrix}u\\v\end{bmatrix}}={\begin{bmatrix}\cos \theta &-\sin \theta \\\sin \theta &\cos \theta \end{bmatrix}}{\begin{bmatrix}{\hat {u}}\\{\hat {v}}\end{bmatrix}}} Then we have p θ ( u ^ ) = ∫ − ∞ ∞ d ( u , v ) d v ^ = ∫ − ∞ ∞ d ( u ^ cos ( θ ) − v ^ sin ( θ ) , u ^ sin ( θ ) + v ^ cos ( θ ) ) d v ^ {\displaystyle p_{\theta }({\hat {u}})=\int _{-\infty }^{\infty }d(u,v)\,\mathrm {d} {\hat {v}}=\int _{-\infty }^{\infty }d({\hat {u}}\cos(\theta )-{\hat {v}}\sin(\theta ),{\hat {u}}\sin(\theta )+{\hat {v}}\cos(\theta ))\,\mathrm {d} {\hat {v}}} By varying theta, a large number of projections can be obtained. Given the projection-slice theorem, D ( Ω , θ ) {\displaystyle D(\Omega ,\theta )} ,the slice of the Fourier transform of d ( u , v ) {\displaystyle d(u,v)} at angle theta, is equivalent to P θ ( Ω ) {\displaystyle P_{\theta }(\Omega )} , the Fourier Transform of the projection p θ ( u ^ ) {\displaystyle p_{\theta }({\hat {u}})} . Therefore, the unknown d ( u , v ) {\displaystyle d(u,v)} can be obtained from its Fourier transform by means of the Fourier transform inversion integral d ( u , v ) = 1 4 π 2 ∫ − ∞ ∞ ∫ − ∞ ∞ D ( Ω 1 , Ω 2 ) e j Ω 1 u e j Ω 2 v d Ω 1 , Ω 2 {\displaystyle \mathrm {d} (u,v)={\frac {1}{4\pi ^{2}}}\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }D(\Omega _{1},\Omega _{2})e^{j\Omega _{1}u}e^{j\Omega _{2}v}\,\mathrm {d} \Omega _{1},\Omega _{2}} = 1 4 π 2 ∫ 0 ∞ ∫ − π π D ( Ω , θ ) e j Ω u cos ( θ ) e j Ω v s i n θ | Ω | d Ω d θ {\displaystyle ={\frac {1}{4\pi ^{2}}}\int _{0}^{\infty }\int _{-\pi }^{\pi }D(\Omega ,\theta )e^{j\Omega u\cos(\theta )}e^{j\Omega vsin\theta }{\begin{vmatrix}\Omega \end{vmatrix}}\,\mathrm {d} \Omega \mathrm {d} \theta } = 1 4 π 2 ∫ − π π ∫ 0 ∞ P θ ( Ω ) e j Ω ( u cos θ + v sin θ ) | Ω | d Ω d θ {\displaystyle ={\frac {1}{4\pi ^{2}}}\int _{-\pi }^{\pi }\int _{0}^{\infty }P_{\theta }(\Omega )e^{j}\Omega (u\cos \theta +v\sin \theta ){\begin{vmatrix}\Omega \end{vmatrix}}\,\mathrm {d} \Omega \mathrm {d} \theta } = 1 4 π 2 ∫ 0 π ( ∫ − ∞ ∞ P θ ( Ω ) | Ω | {\displaystyle ={\frac {1}{4\pi ^{2}}}\int _{0}^{\pi }(\int _{-\infty }^{\infty }P_{\theta }(\Omega ){\begin{vmatrix}\Omega \end{vmatrix}}} e j Ω u ^ d Ω ) d θ {\displaystyle e^{j\Omega {\hat {u}}}\mathrm {d} \Omega )\mathrm {d} \theta } By taking the inverse Fourier Transform and assuming g ( u ^ ) = F − 1 ( | Ω | 2 ) {\displaystyle g({\hat {u}})={\mathcal {F}}^{-1}({{\begin{vmatrix}\Omega \end{vmatrix}}^{2}})} , we get d ( u , v ) = ∑ i △ θ i [ p θ ( u ^ ) ∗ g θ i ( u ^ ) ] {\displaystyle d(u,v)=\sum _{i}\vartriangle \theta _{i}[p_{\theta }({\hat {u}})g_{\theta i}({\hat {u}})]} == Approaches == In practice, there are a wide variety of methods that are utilized, most of which are reconstruct 3-D information (volume) from 2-D signals (image). Typically used methods are CT, MRI, PET and SPECT. And the filtered back projection based on the principles introduced above are commonly applied. === Computed Tomography (CT) === In CT, a volume is formed by stacking the axial slices. The software cuts the volume in a different plane (usually orthogonal). Commonly, slice data is generated using an X-ray source that rotates around the object. X-ray sensors are positioned on the opposite side of the circle from the X-ray source. === Magnetic resonance imaging (MRI) === In MRI, energy from an oscillating magnetic field is temporarily applied to the patient at the appropriate resonance frequency. The protons (hydrogen atoms) emit a radio frequency signal which is measured by a receiving coil. The radio signal can be made to encode position information by varying the main magnetic field using gradient coils. === Positron emission tomography (PET) === The system detects pairs of gamma rays emitted indirectly by a positron-emitting radionuclide (tracer), which is introduced into the body on a biologically active molecule. Three-dimensional images of tracer concentration within the body are then constructed by computer analysis. In modern PET-CT scanners, three dimensional imaging is often accomplished with the aid of a CT X-ray scan performed on the patient during the same session, in the same machine. === Single-photon emission computed tomography (SPECT) === SPECT imaging is performed by using a gamma camera to acquire multiple 2-D images (projections) from multiple angles. Multiple projections are used to yield a 3-D data set. This data set may then be manipulated to show thin slices along any chosen axis of the body. SPECT is similar to PET in its use of radioactive tracer material and detection of gamma rays, while the tracers used in SPECT emit gamma radiation that is measured more directly.
WomanStats Project
The WomanStats Project is a donor-funded research and database project housed at Brigham Young University that "seeks to collect detailed statistical data on the status of women around the world, and to connect that data with data on the security of states." The WomanStats Database aims to provide a comprehensive compilation of information on the status of women in the world. Coders comb the extant literature and conduct expert interviews to find qualitative and quantitative information on over 300 indicators of women's status in 174 countries with populations of at least 200,000. Access to the online database is free. == History and structure == WomanStats began as an outgrowth of a paper Dr. Valerie M. Hudson (of the Brigham Young University Political Science department) and one of her graduate students, Andrea den Boer, published in International Security on the association between national security and the abnormal sex ratio in Asia. After the success and influence of their first article, (later added as one of their top twenty national security articles of that journal of all time), Hudson and den Boer did further research on the connection between the status of women and national security, but found that there was no single database that covered the range of topics that they needed for their research. Consequently, they began compiling information on variables regarding the status of women around the world. The database was officially formed in 2001 and grew exponentially as it later added more variables. The Project went live on the Internet in July 2007. The principal investigators are: Valerie M. Hudson (International Relations), Bonnie Ballif-Spanvill (Psychology, emeritus), and Chad F. Emmett (Geography) all from Brigham Young University, Mary Caprioli from the University of Minnesota, Duluth (International Relations), Rose McDermott from Brown University (International Relations), Andrea Den Boer from the University of Kent at Canterbury in the United Kingdom (International Relations) and S. Matthew Stearmer from the Ohio State University (Sociology; doctoral student). Approximately a dozen undergraduate and graduate students at Brigham Young University and Texas A&M University work at any one time as coders for the project. The coders take the raw quantitative and qualitative data collected in government reports, news articles, research papers, etc. and sort the applicable information on women into categories. They may also implement scales developed by the principal investigators, or that they (the students) themselves have developed. == Database == As of February 2011, the database has 307 variables, covers 174 nations with populations over 200,000, uses 18,015 sources and contains over 111,000 individual data points. All data is referenced to original sources. Not every variable has information for each country; similarly, not all countries have information for each variable: overall, about 70% of country-variable combinations have information. These database coding gaps exist where information is not available or is incomplete, or variables are not collected and reported by governments or international organizations. At times, information from different sources may be contradictory, and the WomanStats Database records this discrepant information for triangulation purposes. == Users and role of the database == The database is meant to help fill a hole in the extant data on the situation of women around the world. WomanStats data and research has been vetted and/or used by the United Nations, the United States Department of Defense, the Central Intelligence Agency, and the World Bank. Their data and research were also used by the United States Senate Committee on Foreign Relations in crafting the International Violence Against Women’s Act. The Inter-Agency Network on Women and Gender Equality (IANWGE) of the United Nations has stated that the WomanStats project "filled a major gap in the availability of data on women" (2007). Victor Asal and Mitchell Brown, researchers not affiliated with WomanStats, stated in an article published in Politics and Policy that "one of the most significant challenges of cross-national empirical studies of the prevalence of interpersonal violence is the paucity of available data, particularly reliable data," and that "WomanStats has allowed for an important first glimpse at analyzing the factors related to interpersonal violence." They conclude by stating that "Our findings suggest that, in the same way that larger disciplinary resources have invested in interstate and intrastate war, disciplinary resources need to be expended in creating a data set exploring interpersonal violence. Until the rights and the lives of women and children are taken as seriously as the survival of states by more proactively collaborating on projects like WomanStats, we will continue to only have a small lens through which to understand problems like this." Princeton University professor Evan S. Liberman wrote, "Although data on political regimes and group conflict have been in far greater demand by political scientists than data on gender politics and policies, two gender-related databases provide...examples of innovative HIRDs. Both the Womanstats database project (Hudson et al. 2009) and the Research Network on Gender Politics and the State (RNGS) project (McBride et al. 2008) are well-integrated presentations of quantitative and qualitative data characterizing the quality of gender relations around the world and, in particular, analytic descriptions of the treatment of women."." == Research == The research component of WomanStats focuses on exploring the relationship between the situation of women and the behavior and security of states. Current research initiatives include: Exploring the relationship between violent instability and inequity and family law. Examining the effect of polygyny and marriage market dislocations on the rise of suicide terrorism. Documenting discrepancies between laws on the books and cultural practices on the ground concerning gender issues. Investigating how well the situation of women predicts the peacefulness of nations-states, compared to their variables such as democracy, wealth, and civilization. The Project has published articles in International Security, International Studies Quarterly, Peace and Conflict, Journal of Peace Research, Political Psychology, Cumberland Law Review, and World Political Review, and has a forthcoming book from Columbia University Press.