Roc
The Roc is an enormous legendary bird of prey central to Middle Eastern folklore, characterized by its colossal size enabling it to hunt and carry off full-grown elephants as prey.[1][2] Originating from the Arabic rukhkh and Persian rukh, the creature embodies exaggerated tales of predatory power, with descriptions emphasizing wings spanning dozens of yards and feathers resembling palm fronds.[1][3] The Roc gained prominence in the One Thousand and One Nights collection, especially through Sinbad the Sailor's voyages, where it transports the mariner via its leg or devastates vessels by hurling massive rocks from aloft.[4] These narratives, rooted in pre-Islamic oral traditions blending Persian, Indian, and Arab elements, portray the bird nesting on remote islands amid diamond valleys or mountainous realms, guarding vast eggs that marauders exploit for survival.[3][5] European awareness of the Roc spread via medieval travelers' reports, including Marco Polo's 13th-century accounts linking it to Madagascar, where oversized feathers—likely from the extinct elephant bird Aepyornis—may have fueled the myth through misidentified relics.[2][3] While purely mythical, the legend reflects causal observations of outsized avian fossils or rare megafauna encounters, underscoring humanity's pattern of amplifying natural phenomena into symbols of awe and peril.[2][5]Mythology and folklore
The legendary bird
The Roc is a gigantic mythical bird of prey central to medieval Persian-Arabic folklore, depicted as capable of seizing and devouring elephants by lifting them aloft and dashing them against mountains.[2] Its name derives from the Arabic rukhkh (رُخّ), a term of Persian origin referring to this colossal avian predator.[1] Descriptions emphasize its prodigious scale, with wingspans reported up to 48 feet and feathers resembling palm fronds in length, enabling feats beyond any known avian physiology.[5] The creature features most prominently in the frame narrative of Sinbad the Sailor within One Thousand and One Nights, a compilation of tales from the Islamic Golden Age dating to the 8th–14th centuries CE. In Sinbad's second voyage, the merchant shipwrecks on an island harboring a Roc's egg the size of a domed pavilion; Sinbad chisels into it, prompting the parent bird's return, after which he binds himself to its leg with his turban and is transported to a diamond-strewn valley teeming with serpents.[6] In the fifth voyage, a pair of Rocs retaliates against intruders by hurling boulders the size of millstones from the sky, pulverizing Sinbad's vessel and scattering its crew.[7] These episodes portray the Roc not merely as a monster but as a guardian of remote, perilous domains, embodying the perils of exploration in pre-modern cosmography. The legend gained wider currency through 13th-century Venetian explorer Marco Polo's Travels, where he recounts hearsay from Madagascar locals about the rukh: a bird of elephantine girth with plumage yielding 10–12-foot feathers used as sails or tents.[2] Polo locates its habitat amid the Comoros and Madagascar, regions then harboring megafaunal remnants. Paleontological hypotheses link the myth to Aepyornis maximus, the elephant bird—a flightless ratite endemic to Madagascar that reached 3 meters in height, weighed up to 500 kilograms, and produced eggs with 7–9 liter volumes, surpassing those of any extant species.[8][9] Extinct by around 1000 CE from human overhunting and habitat loss, subfossil bones and intact eggshells discovered by Arab and later European mariners likely amplified oral traditions into the hyperbolized Roc, conflating grounded ratites with predatory raptors.[10] This rationalization aligns with patterns in folklore where megafauna fossils inspire chimeric beasts, though direct causation remains speculative absent textual attestations predating Aepyornis extinction.Science and mathematics
Receiver operating characteristic (ROC) curve
The receiver operating characteristic (ROC) curve is a graphical representation used to evaluate the performance of binary classifiers by plotting the true positive rate (TPR, or sensitivity) against the false positive rate (FPR, or 1-specificity) at various threshold settings.[11] This plot illustrates the trade-off between correctly identifying positive instances and incorrectly classifying negatives as positives, independent of any specific decision threshold.[12] Originating from signal detection theory during World War II, the ROC framework was developed to assess radar systems' ability to distinguish signals from noise, with early formalization in the 1950s by researchers including Peterson, Birdsall, and Fox, who analyzed discriminator systems for radio signal detection.[13][14] To construct an ROC curve, a classifier's output scores for positive and negative instances are ranked, and thresholds are varied across the score range; for each threshold, TPR (TP / (TP + FN)) and FPR (FP / (FP + TN)) are calculated, where TP denotes true positives, FN false negatives, FP false positives, and TN true negatives.[11] Points are plotted connecting these (FPR, TPR) pairs, forming a curve from (0,0) to (1,1); a random classifier yields the diagonal line (AUC = 0.5), while perfect discrimination reaches the upper-left corner (AUC = 1.0).[15] The area under the curve (AUC) quantifies overall discriminative ability, representing the probability that a randomly selected positive instance scores higher than a randomly selected negative one, with values above 0.7 often indicating acceptable performance in diagnostic contexts.[15][16] In applications, ROC curves assess diagnostic tests in medicine, such as evaluating biomarker accuracy for disease detection by comparing tests or selecting optimal thresholds that balance sensitivity and specificity.[11] In machine learning, they evaluate classifiers across domains like pattern recognition, where AUC serves as a threshold-invariant metric for model comparison, though it assumes balanced class costs.[16] Advantages include comprehensive visualization of performance across thresholds and insensitivity to prevalence shifts, aiding fair comparisons.[11] Limitations arise in imbalanced datasets, where high AUC may mask poor positive-class prediction, and it overlooks clinical costs or decision impacts, prompting alternatives like net benefit analysis or Matthews correlation coefficient for more balanced evaluation.[17][18]Named individuals
Surname and stage name bearers
Patricia Roc (1915–2003), born Felicia Miriam Ursula Herold, was an English actress who rose to prominence in post-war British cinema, ranking among the top female stars in popularity polls by the Motion Picture Herald and appearing in Gainsborough melodramas such as Madonna of the Seven Moons (1945).[19] Her career spanned over 50 films from the late 1930s to the 1950s, often portraying strong-willed heroines in period dramas.[20] Agustí Roc Amador (born August 28, 1971), a Catalan athlete, achieved success as a ski mountaineer and long-distance runner, securing three consecutive Skyrunner World Series titles from 2002 to 2004 and dominating European trail running events in the early 2000s alongside figures like Ricardo Mejia.[21] Roc Marciano (born Rahkeim Calief Meyer, February 11, 1978), an American rapper and producer from Hempstead, New York, is recognized for pioneering underground hip-hop with albums like Marcberg (2010) and intricate, sparse production styles influenced by his early work with groups such as UN.[22][23] Tay Roc (born Donte Richardson), a Baltimore-based battle rapper, has competed in over 60 documented battles since starting at age 16, gaining prominence in platforms like Ultimate Rap League (URL) for aggressive delivery and schemes, with notable matchups against opponents including Daylyt and Murda Mook.[24][25] Kele Le Roc, a British urban contemporary singer active in the late 1990s and early 2000s, released hits like "My Love" (1999), which peaked at number 8 on the UK Singles Chart, blending R&B with dance elements before shifting to independent releases.[26]Geographical locations
Settlements and regions
Roč is a small village in Istria County, northwestern Croatia, administratively belonging to the municipality of Buzet. It had a population of 187 residents according to the 2021 census.[27] The settlement covers an area characterized by hilly terrain typical of inland Istria, with historical significance tied to medieval fortifications and Glagolitic heritage sites.[28] Le Roc is a commune in the Lot department of south-western France, within the Occitanie region and the arrondissement of Gourdon. Its population was recorded at 213 inhabitants, with a density of about 30 per square kilometer across roughly 7 square kilometers of land.[29] The area features rural landscapes along the Dordogne Valley, supporting agriculture and small-scale tourism.[30]Organizations and companies
Commercial brands
RoC Skincare is a dermatologist-recommended brand specializing in anti-aging products, particularly those featuring stabilized retinol, hyaluronic acid, and vitamin C formulations. Founded in 1957 by French pharmacist Dr. Jean-Charles Lissarrague at Pharmacie Rogé Cavaillès in Paris, it pioneered the first hypoallergenic skincare product and broad-spectrum UV protection in 1960, emphasizing clinical efficacy through collaborations with dermatologists.[31] [32] Key offerings include the RETINOL CORREXION line for wrinkle reduction, such as the Deep Wrinkle Night Cream and Line Smoothing Eye Cream, distributed through mass retailers like Walmart, Target, and Ulta.[31] In January 2024, private equity firm Bridgepoint acquired the brand, building on its legacy previously under Johnson & Johnson ownership.[32] Rocawear, stylized as Roc-A-Fear, is an urban apparel brand targeting hip-hop and streetwear audiences with clothing, footwear, and accessories. Launched in 1999 by Roc-A-Fella Records co-founders Damon Dash and Shawn "Jay-Z" Carter, it expanded rapidly into a lifestyle line reflecting the era's hip-hop culture, achieving peak revenues exceeding $300 million annually by the mid-2000s.[33] [34] In 2007, Jay-Z sold his majority stake to Iconix Brand Group for $204 million, after which the brand continued licensing deals for products like jeans, outerwear, and jewelry, maintaining distribution in department stores and urban outlets.[33] Despite shifts in ownership, Rocawear has sustained relevance through revivals emphasizing durable, grind-oriented designs for men aged 18-35.[35]Non-commercial entities
ROC USA, a national nonprofit social enterprise founded in 2008, assists residents of manufactured home communities in forming limited equity cooperatives to achieve collective ownership of their parks, thereby enhancing economic stability and preventing evictions by corporate landlords.[36] By 2023, ROC USA and its affiliates had facilitated the conversion of over 300 communities across 21 states, leveraging financing from subsidiaries like ROC USA Capital, a Community Development Financial Institution.[37] The Roc Solid Foundation, a 501(c)(3) tax-exempt organization with EIN 26-4082283, supports children battling cancer and their families by constructing therapeutic play structures at hospitals and distributing "Ready Bags" containing essential items during treatment.[38] Established to provide emotional relief through play, the foundation has delivered hundreds of playsets and bags since its inception, focusing on long-term hope rather than medical funding. ROC United (Restaurant Opportunities Centers United), a worker-led nonprofit founded in 2001, advocates for improved wages, working conditions, and career advancement in the restaurant sector, representing over 20,000 members through policy campaigns, training programs, and legal support. Operating chapters in multiple U.S. cities, it has influenced legislation on fair pay and anti-harassment measures, drawing on direct testimony from low-wage employees to challenge industry exploitation.[39] ROC the Future, a Rochester, New York-based nonprofit alliance launched in 2012, coordinates early childhood education initiatives to boost kindergarten readiness and long-term academic outcomes for local children, partnering with over 100 organizations to address systemic gaps in underserved communities.[40] Its data-driven efforts include cradle-to-career tracking and family engagement programs, with evaluations showing improved school preparedness metrics among participants.Media and entertainment
Television
Roc is an American comedy-drama television series that aired on the Fox network from August 25, 1991, to May 10, 1994.[41] The program centers on Roc Emerson, a Baltimore sanitation worker portrayed by Charles S. Dutton, who navigates family dynamics, workplace challenges, and urban life alongside his wife Eleanor (Ella Joyce), younger brother Joey (Rocky Carroll), and father Andrew "Pop" Emerson (Carl Gordon).[41] Created by Stan Daniels, the series blends humor with dramatic elements drawn from working-class experiences, often addressing themes such as racial tensions, economic struggles, and interpersonal conflicts.[42] The show produced 72 episodes across three seasons, with the second season notable for being performed live before audiences, a format that heightened its raw, improvisational feel and contributed to its authenticity.[43] Principal recurring cast included Alexis Fields as Roc's niece, with guest appearances by actors like Richard Roundtree and Garrett Morris enhancing storylines involving community issues and personal growth.[44] Episodes typically ran 22-30 minutes, focusing on self-contained narratives like neighborhood disputes or family milestones, while maintaining a grounded portrayal of African American family life without relying on stereotypes.[45] Critically, Roc received a 7.4/10 rating on IMDb based on over 2,000 user votes, with Season 1 earning an 88% approval on Rotten Tomatoes from eight reviews, praised for its heartfelt storytelling and Dutton's commanding performance.[41] The series concluded after its third season amid shifting network priorities, though it remains cited for pioneering live sitcom elements post-I Love Lucy era and for its unvarnished depiction of blue-collar resilience.[46] Streaming availability includes platforms like Pluto TV and Apple TV, preserving its episodes for modern audiences.[47][45]Music
Roc-A-Fella Records, a hip-hop label, was established in 1994 by Shawn "Jay-Z" Carter, Damon Dash, and Kareem "Biggs" Burke as an independent venture to release Jay-Z's debut album after rejections from major labels.[48][49] The label's name derived from "Rockefeller," symbolizing ambitions of wealth and influence akin to the Rockefeller family, with "Roc" becoming a core motif in its branding, including the diamond hand gesture formed by connecting thumbs and index fingers.[50] Initially distributed through Priority Records, Roc-A-Fella gained prominence with Jay-Z's Reasonable Doubt in 1996, which sold over 420,000 copies in its first week via independent promotion.[51] In 1997, Roc-A-Fella sold 50% equity to Def Jam Recordings for $1.5 million, enabling expansion while retaining operational control; this partnership facilitated signings like Beanie Sigel, Cam'ron, Freeway, and later Kanye West, whose 2004 debut The College Dropout achieved multi-platinum status under the imprint.[51] The label's roster emphasized East Coast rap, producing hits such as Jay-Z's "Hard Knock Life (Ghetto Anthem)" in 1998, which peaked at number 15 on the Billboard Hot 100 and drove over 5 million album sales.[48] Internal disputes led to its effective dissolution by 2009, with Jay-Z acquiring full ownership amid conflicts with Dash and Burke over management and finances.[51][52] ROC Nation, founded by Jay-Z in 2008, evolved from Roc-A-Fella into a broader entertainment entity incorporating a music label focused on artist management, publishing, and recordings in hip-hop and pop genres.[53] Unlike the street-oriented Roc-A-Fella, ROC Nation prioritized diversified ventures, signing acts including Rihanna, whose 2009 album Rated R was released under its distribution deal with Def Jam, and later Megan Thee Stallion and A$AP Rocky.[54] By 2023, ROC Nation managed over 20 recording artists, emphasizing long-term career development over short-term hits, with Jay-Z retaining creative oversight.[54] The "Roc" branding persists in ROC Nation's logo and artist affiliations, symbolizing continuity from the original label's legacy.[50]Games and literature
The roc, a colossal bird of prey from Middle Eastern mythology, features prominently in the collection One Thousand and One Nights, particularly in the tales of Sinbad the Sailor, where it is depicted as capable of carrying off elephants and laying eggs the size of small hills on remote islands.[7] These stories, compiled between the 8th and 14th centuries, portray the roc as a fearsome predator inhabiting isolated mountains and islands, with Sinbad encountering its massive egg and fledglings during his voyages.[55] The creature's immense scale—wingspans estimated in folklore to exceed hundreds of feet—serves as a symbol of untamed natural power and peril in these narratives, influencing later Western adaptations like Marco Polo's accounts of similar giant birds in Madagascar.[56] In tabletop role-playing games, the roc appears as a high-level monstrosity in Dungeons & Dragons (D&D), first detailed in the 1974 original edition and persisting through editions like 5th edition (2014), where it is classified as a Gargantuan beast with a challenge rating of 11, capable of multiattacks including beak strikes (4d8+9 piercing damage) and talon grapples to snatch prey up to Large size before dropping them from heights.[57] Rocs in D&D lore nest in remote mountains, preying on giant creatures like elephants or whales, and are often used by dungeon masters as aerial threats or guardians, with variants like the arbor roc in campaigns such as Critical Role emphasizing their role in large-scale combats.[58] Video games have incorporated the roc as both a creature and thematic element; in Age of Mythology (2002), it serves as a flying myth unit for Egyptian players advancing to the Heroic Age under gods like Sobek, functioning as a transport that can carry ground units into battle while dealing melee damage.[59] Other titles, such as the arcade platformer Roc'n Rope (1983) by Konami, evoke the mythical bird through its title and exploratory mechanics involving swinging on ropes to collect gems in monster-filled environments, though the gameplay centers on human protagonists rather than the creature itself. Independent projects like Roc's Odyssey (announced 2025) feature the roc as a playable character in an action-RPG blending combat and platforming, drawing directly from the mythological archetype for its narrative of epic journeys.[60]Economics and finance
Financial metrics
Return on capital (ROC) is a key profitability ratio in corporate finance that measures the earnings generated per unit of capital invested in a firm's operating assets, reflecting the efficiency of capital allocation across both debt and equity providers. It provides insight into whether management is utilizing invested capital to create value beyond the cost of financing.[61] The standard formula for ROC is: ROC = \frac{\text{Operating Income}t \times (1 - \text{tax rate})}{\text{Book Value of Invested Capital}{t-1}} where operating income is typically EBIT (earnings before interest and taxes), adjusted for taxes to yield NOPAT (net operating profit after taxes), and invested capital comprises the book value of debt plus equity minus excess non-operating cash, using the prior period's value to mitigate circularity in calculations.[61] Adjustments may be applied for items like capitalized research and development expenses or operating leases to better approximate economic capital invested.[61] ROC differs from return on equity (ROE), which uses net income divided by book equity and focuses only on equity returns, making it more susceptible to leverage effects; ROC offers a broader operational perspective by incorporating all capital sources. It is often used interchangeably with return on invested capital (ROIC), though ROIC may emphasize capital tied to specific projects excluding non-operating items.[61] A ROC exceeding the firm's weighted average cost of capital (WACC) signals value creation through excess returns, while a lower ROC indicates potential value destruction; this comparison underpins economic value added (EVA) frameworks. In valuation practice, analysts forecast sustainable ROC levels—often converging to industry averages for mature firms, around 2-3% above WACC—to project free cash flows and compute terminal values in discounted cash flow models.[61] Limitations include reliance on accounting book values, which may not capture market realities or intangible assets, necessitating judgment in adjustments for cross-firm comparisons.[61]Transportation
Vehicle models
The Volkswagen T-Roc is a subcompact crossover SUV produced by the German automaker Volkswagen. Launched in 2017, the model has sold more than two million units worldwide as of 2025.[62] It is manufactured at Volkswagen's facility in Palmela, Portugal.[62] A second-generation T-Roc premiered on August 27, 2025, incorporating a redesigned exterior, advanced driver assistance systems, and optional mild-hybrid technology for improved efficiency.[63][64] Powertrain options span petrol and diesel engines, with power outputs from 115 PS in base mild-hybrid variants to 300 PS in the performance-oriented T-Roc R model equipped with all-wheel drive.[65][62] Fuel consumption for the 1.5 eTSI mild-hybrid variant ranges from 5.6 to 6.0 liters per 100 km under combined cycle testing, with CO₂ emissions between 128 and 136 g/km.[62] Trim levels for the T-Roc include entry-level options focused on functionality, such as Life and Trend, alongside more equipped variants like Style and sporty R-Line, which add features like matrix LED headlights, digital cockpits, and enhanced chassis tuning.[66][65] The lineup emphasizes modular equipment packages for customization, with pricing starting at approximately £29,650 in the UK market for 2025 models.[65] A cabriolet body style was added to the range in 2020, marking Volkswagen's return to the convertible SUV segment after a two-year hiatus.[67] Key specifications for representative second-generation models are summarized below:| Variant | Engine | Power (PS) | Transmission | Drive | Combined Fuel Consumption (l/100 km) | CO₂ Emissions (g/km) |
|---|---|---|---|---|---|---|
| 1.5 eTSI Mild-Hybrid | 1.5L Turbo Petrol | 150 | 7-speed DSG | Front-Wheel | 5.6-6.0 | 128-136 |
| T-Roc R | 2.0L Turbo Petrol | 300 | 7-speed DSG | All-Wheel | Not specified in base data | Not specified in base data |