Circular convolution, also known as cyclic convolution, is a special case of periodic convolution, which is the convolution of two periodic functions that have the same period. Periodic convolution arises, for example, in the context of the discrete-time Fourier transform (DTFT). In particular, the DTFT of the product of two discrete sequences is the periodic convolution of the DTFTs of the individual sequences. And each DTFT is a periodic summation of a continuous Fourier transform function (see Discrete-time Fourier transform § Relation to Fourier Transform). Although DTFTs are usually continuous functions of frequency, the concepts of periodic and circular convolution are also directly applicable to discrete sequences of data. In that context, circular convolution plays an important role in maximizing the efficiency of a certain kind of common filtering operation. == Definitions == The periodic convolution of two T-periodic functions, h T ( t ) {\displaystyle h_{_{T}}(t)} and x T ( t ) {\displaystyle x_{_{T}}(t)} can be defined as: ∫ t o t o + T h T ( τ ) ⋅ x T ( t − τ ) d τ , {\displaystyle \int _{t_{o}}^{t_{o}+T}h_{_{T}}(\tau )\cdot x_{_{T}}(t-\tau )\,d\tau ,} where t o {\displaystyle t_{o}} is an arbitrary parameter. An alternative definition, in terms of the notation of normal linear or aperiodic convolution, follows from expressing h T ( t ) {\displaystyle h_{_{T}}(t)} and x T ( t ) {\displaystyle x_{_{T}}(t)} as periodic summations of aperiodic components h {\displaystyle h} and x {\displaystyle x} , i.e.: h T ( t ) ≜ ∑ k = − ∞ ∞ h ( t − k T ) = ∑ k = − ∞ ∞ h ( t + k T ) . {\displaystyle h_{_{T}}(t)\ \triangleq \ \sum _{k=-\infty }^{\infty }h(t-kT)=\sum _{k=-\infty }^{\infty }h(t+kT).} Then: Both forms can be called periodic convolution. The term circular convolution arises from the important special case of constraining the non-zero portions of both h {\displaystyle h} and x {\displaystyle x} to the interval [ 0 , T ] . {\displaystyle [0,T].} Then the periodic summation becomes a periodic extension, which can also be expressed as a circular function: x T ( t ) = x ( t m o d T ) , t ∈ R {\displaystyle x_{_{T}}(t)=x(t_{\mathrm {mod} \ T}),\quad t\in \mathbb {R} \,} (any real number) And the limits of integration reduce to the length of function h {\displaystyle h} : ( h ∗ x T ) ( t ) = ∫ 0 T h ( τ ) ⋅ x ( ( t − τ ) m o d T ) d τ . {\displaystyle (hx_{_{T}})(t)=\int _{0}^{T}h(\tau )\cdot x((t-\tau )_{\mathrm {mod} \ T})\ d\tau .} == Discrete sequences == Similarly, for discrete sequences, and a parameter N, we can write a circular convolution of aperiodic functions h {\displaystyle h} and x {\displaystyle x} as: ( h ∗ x N ) [ n ] ≜ ∑ m = − ∞ ∞ h [ m ] ⋅ x N [ n − m ] ⏟ ∑ k = − ∞ ∞ x [ n − m − k N ] {\displaystyle (hx_{_{N}})[n]\ \triangleq \ \sum _{m=-\infty }^{\infty }h[m]\cdot \underbrace {x_{_{N}}[n-m]} _{\sum _{k=-\infty }^{\infty }x[n-m-kN]}} This function is N-periodic. It has at most N unique values. For the special case that the non-zero extent of both x and h are ≤ N, it is reducible to matrix multiplication where the kernel of the integral transform is a circulant matrix. == Example == A case of great practical interest is illustrated in the figure. The duration of the x sequence is N (or less), and the duration of the h sequence is significantly less. Then many of the values of the circular convolution are identical to values of x∗h, which is actually the desired result when the h sequence is a finite impulse response (FIR) filter. Furthermore, the circular convolution is very efficient to compute, using a fast Fourier transform (FFT) algorithm and the circular convolution theorem. There are also methods for dealing with an x sequence that is longer than a practical value for N. The sequence is divided into segments (blocks) and processed piecewise. Then the filtered segments are carefully pieced back together. Edge effects are eliminated by overlapping either the input blocks or the output blocks. To help explain and compare the methods, we discuss them both in the context of an h sequence of length 201 and an FFT size of N = 1024. === Overlapping input blocks === This method uses a block size equal to the FFT size (1024). We describe it first in terms of normal or linear convolution. When a normal convolution is performed on each block, there are start-up and decay transients at the block edges, due to the filter latency (200-samples). Only 824 of the convolution outputs are unaffected by edge effects. The others are discarded, or simply not computed. That would cause gaps in the output if the input blocks are contiguous. The gaps are avoided by overlapping the input blocks by 200 samples. In a sense, 200 elements from each input block are "saved" and carried over to the next block. This method is referred to as overlap-save, although the method we describe next requires a similar "save" with the output samples. When an FFT is used to compute the 824 unaffected DFT samples, we don't have the option of not computing the affected samples, but the leading and trailing edge-effects are overlapped and added because of circular convolution. Consequently, the 1024-point inverse FFT (IFFT) output contains only 200 samples of edge effects (which are discarded) and the 824 unaffected samples (which are kept). To illustrate this, the fourth frame of the figure at right depicts a block that has been periodically (or "circularly") extended, and the fifth frame depicts the individual components of a linear convolution performed on the entire sequence. The edge effects are where the contributions from the extended blocks overlap the contributions from the original block. The last frame is the composite output, and the section colored green represents the unaffected portion. === Overlapping output blocks === This method is known as overlap-add. In our example, it uses contiguous input blocks of size 824 and pads each one with 200 zero-valued samples. Then it overlaps and adds the 1024-element output blocks. Nothing is discarded, but 200 values of each output block must be "saved" for the addition with the next block. Both methods advance only 824 samples per 1024-point IFFT, but overlap-save avoids the initial zero-padding and final addition.
Vulnerability Discovery Model
A Vulnerability Discovery Model (VDM) uses discovery event data with software reliability models for predicting the same. A thorough presentation of VDM techniques is available in. Numerous model implementations are available in the MCMCBayes open source repository. Several VDM examples include: Alhazmi-Malaiya: Time based model (Alhazmi-Malaiya Logistic (AML) model) Alhazmi-Malaiya: Effort based model Rescorla: Quadratic Model and Exponential Model Anderson: Thermodynamic Model Kim: Weibull Model Linear Model Hump-Shaped Model Independent and Dependent Model Vulnerability Discovery Modeling using Bayesian model averaging Multivariate Vulnerability Discovery Models
Word error rate
Word error rate (WER) is a common metric of the performance of a speech recognition or machine translation system. The WER metric typically ranges from 0 to 1, where 0 indicates that the compared pieces of text are exactly identical, and 1 (or larger) indicates that they are completely different with no similarity. This way, a WER of 0.8 means that there is an 80% error rate for compared sentences. The general difficulty of measuring performance lies in the fact that the recognized word sequence can have a different length from the reference word sequence (supposedly the correct one). The WER is derived from the Levenshtein distance, working at the word level instead of the phoneme level. The WER is a valuable tool for comparing different systems as well as for evaluating improvements within one system. This kind of measurement, however, provides no details on the nature of translation errors and further work is therefore required to identify the main source(s) of error and to focus any research effort. This problem is solved by first aligning the recognized word sequence with the reference (spoken) word sequence using dynamic string alignment. Examination of this issue is seen through a theory called the power law that states the correlation between perplexity and word error rate. Word error rate can then be computed as: W E R = S + D + I N = S + D + I S + D + C {\displaystyle {\mathit {WER}}={\frac {S+D+I}{N}}={\frac {S+D+I}{S+D+C}}} where S is the number of substitutions, D is the number of deletions, I is the number of insertions, C is the number of correct words, N is the number of words in the reference (N=S+D+C) The intuition behind 'deletion' and 'insertion' is how to get from the reference to the hypothesis. So if we have the reference "This is wikipedia" and hypothesis "This _ wikipedia", we call it a deletion. Note that since N is the number of words in the reference, the word error rate can be larger than 1.0, namely if the number of insertions I is larger than the number of correct words C. When reporting the performance of a speech recognition system, sometimes word accuracy (WAcc) is used instead: W A c c = 1 − W E R = N − S − D − I N = C − I N {\displaystyle {\mathit {WAcc}}=1-{\mathit {WER}}={\frac {N-S-D-I}{N}}={\frac {C-I}{N}}} Since the WER can be larger than 1.0, the word accuracy can be smaller than 0.0. == Experiments == It is commonly believed that a lower word error rate shows superior accuracy in recognition of speech, compared with a higher word error rate. However, at least one study has shown that this may not be true. In a Microsoft Research experiment, it was shown that, if people were trained under "that matches the optimization objective for understanding", (Wang, Acero and Chelba, 2003) they would show a higher accuracy in understanding of language than other people who demonstrated a lower word error rate, showing that true understanding of spoken language relies on more than just high word recognition accuracy. == Other metrics == One problem with using a generic formula such as the one above, however, is that no account is taken of the effect that different types of error may have on the likelihood of successful outcome, e.g. some errors may be more disruptive than others and some may be corrected more easily than others. These factors are likely to be specific to the syntax being tested. A further problem is that, even with the best alignment, the formula cannot distinguish a substitution error from a combined deletion plus insertion error. Hunt (1990) has proposed the use of a weighted measure of performance accuracy where errors of substitution are weighted at unity but errors of deletion and insertion are both weighted only at 0.5, thus: W E R = S + 0.5 D + 0.5 I N {\displaystyle {\mathit {WER}}={\frac {S+0.5D+0.5I}{N}}} There is some debate, however, as to whether Hunt's formula may properly be used to assess the performance of a single system, as it was developed as a means of comparing more fairly competing candidate systems. A further complication is added by whether a given syntax allows for error correction and, if it does, how easy that process is for the user. There is thus some merit to the argument that performance metrics should be developed to suit the particular system being measured. Whichever metric is used, however, one major theoretical problem in assessing the performance of a system is deciding whether a word has been “mis-pronounced,” i.e. does the fault lie with the user or with the recogniser. This may be particularly relevant in a system which is designed to cope with non-native speakers of a given language or with strong regional accents. The pace at which words should be spoken during the measurement process is also a source of variability between subjects, as is the need for subjects to rest or take a breath. All such factors may need to be controlled in some way. For text dictation it is generally agreed that performance accuracy at a rate below 95% is not acceptable, but this again may be syntax and/or domain specific, e.g. whether there is time pressure on users to complete the task, whether there are alternative methods of completion, and so on. The term "Single Word Error Rate" is sometimes referred to as the percentage of incorrect recognitions for each different word in the system vocabulary. == Edit distance == The word error rate may also be referred to as the length normalized edit distance. The normalized edit distance between X and Y, d( X, Y ) is defined as the minimum of W( P ) / L ( P ), where P is an editing path between X and Y, W ( P ) is the sum of the weights of the elementary edit operations of P, and L(P) is the number of these operations (length of P).
Flo (app)
Flo is a period-tracking app that provides menstrual cycle, ovulation and pregnancy tracking as well as perimenopause symptom tracking that was developed by Flo Health, Inc. It has over 380 million downloads worldwide and over 70 million monthly active users as of November 2024. In mid-2024, it reached unicorn status, and became Europe’s first femtech unicorn. The company has been accused of sharing users' sensitive health data with third parties without consent and misleading its users about data practices. == History == Flo Health, Inc. was co-founded in 2015 by Dmitry and Yuri Gurski, in Belarus. Their backgrounds helped build the first version of the software having experience in other fitness and health apps. Dmitry serves as the company's CEO. The company's development hubs are in London, Amsterdam and Vilnius. In 2016, the company raised $1 million in seed round funding from Flint Capital and Haxus Venture Fund. In 2017, Flo received an investment of $5 million from Flint Capital and model Natalia Vodianova with Vodianova helping develop an awareness campaign for the company. In 2018, Flo received an investment of $6 million from Mangrove Capital Partners, with participation from Flint Capital and Haxus, giving the company a valuation of $200 million. In mid-2019, Flo received an additional investment of $7.5 million led by Founders Fund. In 2020, the Federal Trade Commission alleged that Flo had misled users about its handling of health information to third parties including Google, Facebook, AppsFlyer, and Flurry since 2016. These allegations followed a 2019 report by The Wall Street Journal in reference to Facebook. The company reached a settlement in 2021 and was required to notify users of how their personal information was shared and obtain permission before any further information was shared. The agreement also required that Flo to undertake an independent privacy audit which it completed in March 2022. In early September 2021, Flo announced it closed $50M in a Series B financing, bringing the total capital raised to $65 million and company valuation to $800M led by VNV Global and Target Global. In March 2024, the Supreme Court of British Columbia certified a class action suit against Flo for sharing intimate data with Facebook and other third parties without user knowledge. In July 2024, Flo announced it raised more than $200M in Series C financing from General Atlantic bringing its valuation beyond $1 billion. As of November 2024, the app had over 380 million downloads world wide, and over 70 million monthly active users. In 2025, Flo adopted a data intelligence platform from Databricks to power its analytics and AI features, allowing users personalized cycle predictions. In 2025, a class action lawsuit in California was settled for $56 million with Flo paying $8 million and Google paying $48 million. == Features and privacy == Flo was initially created as a period and ovulation tracking application. It now provides reminders of upcoming menstrual cycles and a place to record various other health symptoms such as contraceptive methods, vaginal discharge (leukorrhea), water intake, pains, mood swings, and sexual activity. The application is available on iOS and Android. Flo is free to download and the free basic version gives you access to period and ovulation tracking and predictions, symptom tracking, cycle history, and anonymous mode. In Pregnancy mode, the app provides tracking features and educational material for pregnancy. In October 2023, Flo launched Flo for Partners, a feature that allows users to share their Flo data with their partner. In September 2022, as a response to Roe v. Wade being overturned, Flo sped up the release of a feature called "Anonymous Mode". Flo said this mode allows users to access the app without any personal identifiers such as name, email address, or technical identifiers being associated with their health data. Flo said it uses a technology called Oblivious HTTP to help protect user privacy in Anonymous Mode. == Recognition == Flo was named to Bloomberg’s Top 25 UK Startups to Watch for 2024. Flo's Anonymous Mode feature was recognized on both Fast Company's World Changing Ideas 2023 and TIME's Best Inventions List 2023. Flo is a CES 2019 Innovation Awards Honoree in the Software and Mobile Applications category.
Clubdjpro
ClubDJPro (often referred to as ClubDJ) is a DJ console and video mixing tool developed by Cube Software Solutions Inc. software. It was released in June 2005. == User interface == ClubDJPro has a GUI that was designed to allow aesthetic revisions via Skins. The skin engine that ClubDJPro uses allows for the ability to expand the software to take up the entire screen. As of 4.4.3.3 there are 3 user changeable skins included in the program which are changeable in the preferences tab. They are called 'AquaLung', 'Eleanor', and 'Grabber'. == Editions == ClubDJPro is available in two different editions, with separate features depending upon their target consumer group. DJ Edition - Can play audio files only. VJ Edition - Contains all of the features of the DJ Edition, in addition to support for video, karaoke, and visualizations. == Supported MIDI Controllers == Supported since version 2.0: Hercules Console Hercules Console MK2 Hercules Control MP3 PCDJ DAC-2 Controller == History == The initial "final release" of ClubDJPro was released on June 24, 2005. On June 26, 2009, the 4th iteration of the ClubDJPro software was released. The development of the software and website appears to have halted. As of March 2018 the website continues to show a new version "Coming Spring 2016".
Software durability
In software engineering, software durability means the solution ability of serviceability of software and to meet user's needs for a relatively long time. Software durability is important for user's satisfaction. For a software security to be durable, it must allow an organization to adjust the software to business needs that are constantly evolving, often in impulsive ways. Durability of software depends on four characteristics mainly; i.e. software trustworthiness, Human Trust for Serviceability, software dependability and software usability.
Direct voice input
Direct voice input (DVI), sometimes called voice input control (VIC), is a style of human–machine interaction "HMI" in which the user makes voice commands to issue instructions to the machine through speech recognition. In the field of military aviation, DVI has been introduced into the cockpits of several modern military aircraft, such as the Eurofighter Typhoon, the Lockheed Martin F-35 Lightning II, the Dassault Rafale, the KF-21 Boramae and the Saab JAS 39 Gripen. Such systems have also been used for various other purposes, including industry control systems and speech recognition assistance for impaired individuals. == Overview == DVI systems can be divided into two major categories of functionality: "user-dependent" or "user-independent". A user-dependent system requires that a personal voice template to be generated for a specific person; the template for this individual has to be loaded onto their assigned machine prior to use of the DVI system for it to function properly. In contrast, a user-independent system does not require any personal voice template, being intended to respond correctly to the voice of any user. They can also be categorised between "discrete recognition" and "continuous recognition". Users of a discrete recognition system must pause between each word so that the DVI system can identify the separations between each word, while a continuous speech recognition system is capable of understanding a normal rate of speech. During the mid-2000s, researchers at the National Aerospace Laboratory in the Netherlands examined the use of DVI in the "GRACE" simulator; a total of twelve pilots participated in the ensuing experiment. The tests performed reportedly revealed that, while the hardware itself functioned well, several improvements were desirable prior to real-world deployment on aircraft since DVI operations actually consumed more time in comparison to traditional existing methods. Recommendations for improvements included the adoption of simpler syntax, the achievement of a greater recognition rate, and a decrease in response times; all of the issues encountered were determined to be of a technological nature, and were deemed feasible to resolve. The researchers concluded that in cockpits, especially during emergencies where pilots have to operate entirely on their own, a DVI system could be highly relevant, but that it was not of crucial importance during most other conceivable scenarios. Around the same time, evaluations of DVI systems for civil aviation purposes were conducted within the framework of Project SafeSound, coordinated by the European Union. It involved the observation of pilot workloads in real-world cockpits and contrasting them against pilot activity in flight simulators using both conventional systems and DVI assistance. The project aimed to enhance aviation safety and to decrease the workload in both ground and flight operations via the application of enhanced audio functions. == Applications == === Aviation === Prior to its widespread deployment, a handful of conventional military aircraft were converted to trial DVI systems; examples include the Harrier AV-8B and F-16 VISTA. In another case, a General Dynamics F-16 Fighting Falcon simulator was modified with DVI for a voice control study that was undertaken by the Royal Netherlands Air Force. DVI trials have also been conducted on helicopters, including the Boeing AH-64 Apache, showing the potential to improve flight safety and mission effectiveness. Numerous modern fighter aircraft have been outfitted with DVI systems, often in combination with various other man-machine interface schemes, such as HOTAS-compliant controls and other advanced control technologies. The combination of Voice and HOTAS control schemes has sometimes been referred to as the "V-TAS" concept. A prominent fighter aircraft to be furnished with a V-TAS cockpit is the Eurofighter Typhoon. The Lockheed Martin F-35 Lightning II also features a DVI system, which was developed by Adacel. Other examples includes the Dassault Rafale and the Saab JAS 39 Gripen. Numerous aircraft have been planned to use DVI. At one stage, the United States Air Force had sought to integrate DVI upon the Lockheed Martin F-22 Raptor; however, the technology was eventually judged to pose too many technical risks at that point in time, and thus such efforts were abandoned. === Personal === By 1990, working prototypes of speech recognition systems were being demonstrated; these were being promoted for the purpose of providing an effective man-machine interface for individuals with impaired speech. Techniques employed included time-encoded digital speech and automatic token set selection. Investigations of these early DVI systems reportedly included the use of automatic diagnostic routines and limited-scale trials using volunteers. During the 2010s, various companies were offering voice recognition systems to the general public in the form of personal digital assistants. One example is the Google Voice service, which allows users to pose questions via a DVI package installed on either a personal computer, tablet, or mobile phone. Numerous digital assistants have been developed, such as Amazon Echo, Siri, and Cortana, that use DVI to interact with users. === Commercial === DVI technology has enabled automated telephone systems to be widely deployed. Many companies commonly use centralised phone systems that route callers to the correct department via such methods. Various car manufacturers have also furnished their road vehicles with DVI systems; these typically allow drivers to control infotainment systems and interact with mobile phones with more convenience than legacy methods. During the late 1980s, investigations into the use of DVI systems for controlling CNC machines and other manufacturing apparatus were underway. During the 2010s, such systems were being used for logistics and warehouse management purposes.