Hasil untuk "Folklore"

Robin Kouba, Vincent Neiger, Mohab Safey El Din

We provide a new complexity bound for the computation of grevlex Gröbner bases in the generic zero-dimensional case, relying on Moreno-Socías' conjecture. We first formalize a property of regular sequences that implies a well-known folklore consequence, which we call the increasing degree property. We then derive a new understanding of the selection of pairs in the F4 algorithm based on Moreno-Socías' conjecture. Moreover, we obtain an exact formula for the number of elements in the grevlex Gröbner basis of a given degree, for half of the relevant degrees. Combining these results, we derive a precise complexity formula for the F4 Tracer algorithm, together with its asymptotic behavior when the number of variables tends to infinity. These results yield an improvement over the state-of-the-art complexity bounds by a factor which is exponential in the number of variables.

Amey Bhangale, Arghya Chakraborty, Prahladh Harsha

Online bipartite matching is a classical problem in online algorithms and we know that both the deterministic fractional and randomized integral online matchings achieve the same competitive ratio of $1-\frac{1}{e}$. In this work, we study classes of graphs where the online degree is restricted to $2$. As expected, one can achieve a competitive ratio of better than $1-\frac{1}{e}$ in both the deterministic fractional and randomized integral cases, but surprisingly, these ratios are not the same. It was already known that for fractional matching, a $0.75$ competitive ratio algorithm is optimal. We show that the folklore \textsc{Half-Half} algorithm achieves a competitive ratio of $η\approx 0.717772\dots$ and more surprisingly, show that this is optimal by giving a matching lower-bound. This yields a separation between the two problems: deterministic fractional and randomized integral, showing that it is impossible to obtain a perfect rounding scheme.

Alex Henderson

As scholars such as Helena Bassil-Morozow have explored, the trickster character type—with its roots in mythology, folklore, and oral storytelling traditions—has been constantly reinvented and remixed in the context of contemporary literature and pop culture. The themes of liminality, marginality, shape-changing, and questioning authority with a playful and rebellious sense of humour, mean that the trickster may be especially at home in work aimed at adolescent readers, particularly those of marginalised identities. The emerging space of queer Young Adult (YA) literature is thus a vibrant storytelling landscape for trickster characters and trickster tales. This paper explores the queer trickster characteristics of Vanja, the anti-heroine of Margaret Owen’s Little Thieves. Vanja is a young, queer, marginal figure, her character arc concerned with agency and autonomy. She uses shapeshifting magic and clever subterfuge to impersonate nobility and steal from the rich, transgressing the borders of wealth and class, all while offering the reader a critique of the power structures and entitled individuals that support this social divide. Vanja’s liminality, humour, and eventual emergence as an (accidental) folk hero mark her as a queer teenage trickster protagonist and an effective example of the potential in this storytelling space.

Tohid Teymori

This study examines the trickster archetype within the narrative of Zāl and Simorgh in Ferdowsi’s Shahnameh. The trickster, a mythological figure characterized by ambivalence, shape-shifting, resourcefulness, and divine intervention, occupies a significant role across various cultural traditions. Drawing upon established theoretical frameworks, this research identifies Zāl and Simorgh as a trickster within Iranian mythology. The analysis focuses on key trickster attributes—including shapeshifting, wisdom, and the capacity to disrupt and reconstitute social order. Zāl, marked by his extraordinary birth and upbringing by Simorgh, embodies a liminal identity that facilitates intervention in pivotal events. Simorgh, in turn, functions as a supernatural guide and healer, contributing to the restoration of equilibrium and the revelation of hidden truths. A close reading of the Rostam and Esfandiar episode demonstrates how Zāl and Simorgh employ cunning and esoteric knowledge to challenge oppressive power structures and institute a renewed order. This study underscores the significance of the trickster archetype in Iranian mythic traditions and elucidates the roles of Zāl and Simorgh as agents of transformation and balance within the Persian cultural discourse. Keywords: Trickster, Zāl, Simorgh, Shahnameh, Mythology. IntroductionThe trickster archetype represents one of the most significant and beloved figures in world mythology, characterized by paradoxical qualities where positive attributes typically outweigh negative ones, though this balance varies across different mythological traditions. As liminal beings existing between worlds, tricksters challenge established laws, confront deities, and disrupt social and cultural norms. While often depicted as deceiving ordinary people, tricksters more importantly challenge those in positions of power, undermining the dominion of kings, heroes, and the powerful through cunning and artifice.This study examines the trickster archetype within the narrative framework of Zāl and Simorgh in Ferdowsi’s Shahnameh, positioning these figures within the broader context of Iranian mythology. The research addresses a significant gap in Iranian mythological studies, as the trickster concept, despite its prominence in global mythology, has remained largely unexplored in Persian literary scholarship. By applying established theoretical frameworks from folklore, psychoanalysis, mythology, and anthropology, this investigation seeks to illuminate the transformative roles of Zāl and Simorgh as agents of change and balance within Persian cultural discourse. Materials and MethodsThe methodological approach employs a comprehensive theoretical framework drawing primarily from the foundational works of Paul Radin and Carl Gustav Jung on the trickster archetype. Radin’s conception of the trickster as a “culture-bringer” who facilitates societal transformation from lower to higher levels of civilization provides a crucial analytical lens. Jung’s psychological interpretation, viewing the trickster as a representation of the collective unconscious and undifferentiated human consciousness retaining its animal nature, offers complementary insights into the archetype’s enduring significance.The analysis incorporates perspectives from various scholars, including Claude Lévi-Strauss’s structural approach to mythological dualities, Joseph Campbell’s hero archetype theory, and Mary Douglas’s anthropological insights on social order disruption. The study employs close textual reading of Shahnameh, focusing particularly on key episodes including Zāl’s birth and upbringing by Simorgh, and the pivotal Rostam and Esfandiar confrontation. Comparative analysis with trickster figures from other cultural traditions—including Loki from Norse mythology, Anansi from West African folklore, Coyote from Native American traditions, and Prometheus from Greek mythology—provides cross-cultural context for understanding the unique characteristics of the Iranian trickster manifestation. Research FindingsThe investigation reveals that Zāl and Simorgh collectively embody the essential characteristics of the trickster archetype within Iranian mythology. Key findings of the study include:Extraordinary Birth and Liminal Identity: Zāl’s albinism marks him as fundamentally different from birth, leading to his abandonment and subsequent raising by Simorgh. This unusual upbringing creates a liminal identity existing between human society and the supernatural realm, a defining characteristic of trickster figures.Shape-shifting and Duality: The relationship between Zāl and Simorgh demonstrates the trickster’s capacity for transformation and dual existence. Simorgh functions as both a physical being and Zāl’s spiritual essence, while Zāl himself bridges the animal, human, and divine realms.Wisdom and Problem-solving: Zāl’s renowned wisdom, acquired through Simorgh’s tutelage and his own dedicated study, enables him to serve as advisor and mediator in critical situations. His knowledge encompasses both earthly learning and supernatural wisdom, positioning him as a crucial problem-solver in times of crisis.Shamanic Attributes: Zāl exhibits shamanic characteristics through his ability to summon Simorgh via the ritual burning of the sacred feather, accessing supernatural assistance when confronting seemingly insurmountable challenges. This shamanic connection enables intervention in the natural order when necessary.Divine Intervention and Social Transformation: In the Rostam-Esfandiar episode, Zāl and Simorgh’s intervention challenges corrupt power structures represented by Goshtasp and Esfandiar’s ambitions, ultimately facilitating a restoration of proper governance and social order. Discussion of Results and ConclusionsThe findings demonstrate that Zāl and Simorgh function as a unified trickster entity, challenging oppressive power structures while maintaining cosmic and social balance. Unlike tricksters in other traditions who often act from self-interest, the Zāl-Simorgh complex operates primarily for societal benefit, distinguishing the Iranian trickster tradition. The Rostam-Esfandiar confrontation exemplifies the trickster’s role in exposing corruption and facilitating necessary social transformation. Esfandiar’s invulnerability, granted through Zoroastrian blessing, represents a sacred power corrupted by personal ambition. Zāl and Simorgh’s intervention—revealing the secret of targeting Esfandiar’s eyes with a double-headed arrow from the gaz tree—demonstrates the trickster’s function in challenging even sacred authority when it threatens social harmony. This episode reflects broader tensions between two political paradigms: the pre-Lohrasp tradition of balanced power between royal and heroic houses, and the Lohrasp-Goshtasp model concentrating all authority in the monarchy. The trickster’s intervention supports the restoration of balanced governance, suggesting Ferdowsi’s critique of absolute monarchical power. The comparative analysis reveals both universal and culturally specific aspects of the Iranian trickster. While sharing common features with global trickster figures—liminality, shape-shifting, wisdom, and social disruption—Zāl and Simorgh demonstrate unique characteristics rooted in Persian cultural values, particularly the emphasis on wisdom (kherad) and justice (dād).This study establishes Zāl and Simorgh as a distinctive trickster manifestation within Iranian mythology, contributing significantly to the theoretical understanding of the trickster archetype. The trickster archetype plays a vital but previously unrecognized role in Iranian mythological traditions, with Zāl and Simorgh embodying this function through their combined attributes and interventions. The Iranian trickster tradition emphasizes wisdom, justice, and societal benefit over the self-interested cunning often associated with tricksters in other cultures, reflecting core Persian cultural values. The Zāl-Simorgh complex serves as a mechanism for critiquing and transforming unjust power structures, particularly relevant to Ferdowsi’s historical context and his concerns about tyrannical rule. Recognition of the trickster pattern in Shahnameh opens new avenues for comparative mythological studies and a deeper understanding of Persian literary traditions. The study’s findings have implications beyond literary analysis, offering insights into mechanisms of cultural resistance, identity formation, and social transformation relevant to contemporary Iranian society. This research advances scholarship in Iranian mythology, comparative literature, and archetypal studies while demonstrating the continued relevance of ancient mythological patterns for understanding cultural dynamics and social change. Future research might explore trickster manifestations in other Persian literary works and examine the archetype’s evolution in modern Iranian literature and culture.

Nicola Gigli, Ivan Yuri Violo

The classical Reifenberg's theorem says that a set which is sufficiently well approximated by planes uniformly at all scales is a topological Hölder manifold. Remarkably, this generalizes to metric spaces, where the approximation by planes is replaced by the Gromov-Hausdorff distance. This fact was shown by Cheeger and Colding in an appendix of one of their celebrated works on Ricci limit spaces [8]. Given the recent interest around this statement in the growing field of analysis in metric spaces, in this note we provide a self contained and detailed proof of the Cheeger and Colding result. Our presentation substantially expands the arguments in [8] and makes explicit all the relevant estimates and constructions. As a byproduct we also shows a biLipschitz version of this result which, even if folklore among experts, was not present in the literature. This work is an extract from the doctoral dissertation of the second author.

Siqi He, Richard Wentworth, Boyu Zhang

This paper studies the relationship between an analytic compactification of the moduli space of flat $\mathrm{SL}_2(\mathbb{C})$ connections on a closed, oriented 3-manifold $M$ defined by Taubes, and the Morgan-Shalen compactification of the $\mathrm{SL}_2(\mathbb{C})$ character variety of the fundamental group of $M$. We exhibit an explicit correspondence between $\mathbb{Z}/2$ harmonic 1-forms, measured foliations, and equivariant harmonic maps to $\mathbb{R}$-trees, as initially proposed by Taubes. As an application, we prove that $\mathbb{Z}/2$ harmonic 1-forms exist on all Haken manifolds with respect to all Riemannian metrics. We also show that there exist manifolds that support singular $\mathbb{Z}/2$ harmonic 1-forms but have compact $\mathrm{SL}_2(\mathbb{C})$ character varieties, which resolves a folklore conjecture.

John A. Baldwin, Steven Sivek

The A-polynomial of a knot is defined in terms of SL(2,C) representations of the knot group, and encodes information about essential surfaces in the knot complement. In 2005, Dunfield-Garoufalidis and Boyer-Zhang proved that it detects the unknot using Kronheimer-Mrowka's work on the Property P conjecture. Here we use more recent results from instanton Floer homology to prove that a version of the A-polynomial detects whether a knot is a torus knot. We moreover completely determine which individual torus knots are detected by this A-polynomial. These results enable progress towards a folklore conjecture about boundary slopes of non-torus knots. Finally, we use similar ideas to prove that a knot in the 3-sphere admits infinitely many SL(2,C)-abelian Dehn surgeries if and only if it is a torus knot, affirming a variant of a conjecture due to Sivek-Zentner.

Tatiana Vladykina

Cosmogonic concepts of the Udmurt people can be detected through the names of stars, the nomination of which is usually based on mythological cognition. Additional and very significant information about space objects is contained in folklore texts. The images of stars are included in a stable triad of heavenly bodies along with the sun and the moon. Their constant feature is bright light, opposed to images of negative energy, forces of darkness – diseases or sorcerers. Therefore, images of stars are frequently used in conspiracy formulas, where they are presented as an insurmountable barrier to those who do evil. The stars, along with the sun and the moon, become metaphors and comparisons in the song culture of the Udmurt people. They are used as analogies in the characterization of family and kinship ties, testifying to the relationships within the clan. Stars/constellations as a symbol of unattainability and indivisibility are a kind of guarantor of the stability of the world.

Saajid Chowdhury, Hechen Hu, Matthew Romney et al.

We study the properties of $\text{CAT}(κ)$ surfaces: length metric spaces homeomorphic to a surface having curvature bounded above in the sense of satisfying the $\text{CAT}(κ)$ condition locally. The main facts about $\text{CAT}(κ)$ surfaces seem to be largely a part of mathematical folklore, and this paper is intended to rectify the situation. We provide a complete proof that $\text{CAT}(κ)$ surfaces have bounded (integral) curvature. This fact allows one to apply the established theory of surfaces of bounded curvature to derive further properties of $\text{CAT}(κ)$ surfaces. We also show that $\text{CAT}(κ)$ surfaces can be approximated by smooth Riemannian surfaces of Gaussian curvature at most $κ$. We do this by giving explicit formulas for smoothing the vertices of model polyhedral surfaces.

Tadashi Matsumoto, T. J. Sullivan

Gaussian processes (GPs) are widely-used tools in spatial statistics and machine learning and the formulae for the mean function and covariance kernel of a GP $T u$ that is the image of another GP $u$ under a linear transformation $T$ acting on the sample paths of $u$ are well known, almost to the point of being folklore. However, these formulae are often used without rigorous attention to technical details, particularly when $T$ is an unbounded operator such as a differential operator, which is common in many modern applications. This note provides a self-contained proof of the claimed formulae for the case of a closed, densely-defined operator $T$ acting on the sample paths of a square-integrable (not necessarily Gaussian) stochastic process. Our proof technique relies upon Hille's theorem for the Bochner integral of a Banach-valued random variable.

Erolova Yelis, Tsyryapkina Yulia

On 26 April 1986, the accident at the Chernobyl nuclear power plant in Soviet Ukraine led to a massive disaster, the consequences of which affected millions of people in northern and eastern Europe. Today, 35 years later, we recall it not only as one of the greatest catastrophes in the history of nuclear power but also as one of the main political preconditions or factors that led to the end of the USSR. This paper presents the initial stage of a comparative study on the memories of this disastrous event among Ukrainians, Belarusians, Russians, and Bulgarians living on the periphery of the affected zone. The aim is to trace diverse aspects of public reflection in connection with people’s awareness and the degree to which they were affected, the reactions to the disaster, its effects and consequences, the preparedness of the population, and the latter’s assessment of post-disaster management.

Yueyang Liu, Adithya M. Devraj, Benjamin Van Roy et al.

Assuming distributions are Gaussian often facilitates computations that are otherwise intractable. We study the performance of an agent that attains a bounded information ratio with respect to a bandit environment with a Gaussian prior distribution and a Gaussian likelihood function when applied instead to a Bernoulli bandit. Relative to an information-theoretic bound on the Bayesian regret the agent would incur when interacting with the Gaussian bandit, we bound the increase in regret when the agent interacts with the Bernoulli bandit. If the Gaussian prior distribution and likelihood function are sufficiently diffuse, this increase grows at a rate which is at most linear in the square-root of the time horizon, and thus the per-timestep increase vanishes. Our results formalize the folklore that so-called Bayesian agents remain effective when instantiated with diffuse misspecified distributions.

Haoxuan Wu, Jincheng Zhuang

The NP-hard problem of decoding random linear codes is crucial to both coding theory and cryptography. In particular, this problem underpins the security of many code based post-quantum cryptographic schemes. The state-of-art algorithms for solving this problem are the information syndrome decoding algorithm and its advanced variants. In this work, we consider syndrome decoding in the multiple instances setting. Two strategies are applied for different scenarios. The first strategy is to solve all instances with the aid of the precomputation technique. We adjust the current framework and distinguish the offline phase and online phase to reduce the amortized complexity. Further, we discuss the impact on the concrete security of some post-quantum schemes. The second strategy is to solve one out of many instances. Adapting the analysis for some earlier algorithm, we discuss the effectiveness of using advanced variants and confirm a related folklore conjecture.

Uladzimir Auseichyk

The article examines the historiography and the current state of research on the Old Believers in Northwestern Belarus. Four basic stages are distinguished in the history of studies on Old Believers in the region: second half of the 18th century – beginning of the 20th century; the interwar period (1920–1930 years); the Soviet period (1950–1980 years); the modern period (1990–2000 years). The characteristic of these stages is given, the methodology of conducted research is analyzed, the value of published works in this direction is revealed. The article analyzes research conducted from the second half of the 18th century to the last two decades of the 20th century. The main attention is given to the analysis of the works published during the second half of the of 19th century and the early 20th century.

Raivo Kalle, Andrea Pieroni, Ingvar Svanberg et al.

Presently, collecting data through citizen science (CS) is increasingly being used in botanical, zoological and other studies. However, until now, ethnobotanical studies have underused CS data collection methods. This study analyses the results of the appeal organized by the physician Dr. Mihkel Ostrov (1863–1940), which can be considered the first-ever internationally known systematic example of ethnopharmacological data collection involving citizens. We aim to understand what factors enhanced or diminished the success of the collaboration between Ostrov and the citizens of that time. The reliability of Ostrov’s collection was enhanced by the herbarium specimens (now missing) used in the identification of vernacular names. The collection describes the use of 65 species from 27 genera. The timing of its collection coincided with not only a national awakening and recently obtained high level of literacy but also the activation of civil society, people’s awareness of the need to collect folklore, the voluntary willingness of newspapers to provide publishing space and later to collect data, and the use of a survey method focusing on a narrow topic. While Ostrov’s only means of communication with the public was through newspapers, today, with electronic options, social media can also be used.

Olivier Biquard, Henri Guenancia

Let $X$ be a complex projective manifold and let $D\subset X$ be a smooth divisor. In this article, we are interested in studying limits when $β\to 0$ of Kähler-Einstein metrics $ω_β$ with a cone singularity of angle $2πβ$ along $D$. In our first result, we assume that $X\setminus D$ is a locally symmetric space and we show that $ω_β$ converges to the locally symmetric metric and further give asymptotics of $ω_β$ when $X\setminus D$ is a ball quotient. Our second result deals with the case when $X$ is Fano and $D$ is anticanonical. We prove a folklore conjecture asserting that a rescaled limit of $ω_β$ is the complete, Ricci flat Tian-Yau metric on $X\setminus D$. Furthermore, we prove that $(X,ω_β)$ converges to an interval in the Gromov-Hausdorff sense.

Kuuva, Sari

Wuokko, Maiju

Tässä katsausartikkelissa tarkastelen vapaa-ajan historiaa Suomessa. Analysoin työ- ja vapaa-aikaa toisistaan erottavien normien ja käytäntöjen kehitystä sekä eri aikoina vallinneita ristiriitoja periaatteen ja käytännön välillä. Keskityn siihen, millä tavoin työmarkkinalainsäädäntö ja -käytännöt ovat säädelleet vapaa-ajan viettoa ja erottaneet vapaa-aikaa työajasta. Katsausartikkelin aikajänne ulottuu teollistumisesta nykypäivään. Jaan tarkasteltavan ajanjakson kolmeen eri kauteen, jotka ovat 1) työaikalainsäädännön ja modernin vapaa-ajan varhaisvaiheet, 2) viisipäiväisen työviikon ja normaalivapaa-ajan lyhyt kukoistuskausi ja 3) vapaa-ajan eriytymisen ja epätasa-arvoistumisen aika. Hyödynnetty tutkimuskirjallisuus edustaa vapaa-aikaa tai työn ja vapaa-ajan erontekoa käsittelevää, etupäässä kotimaista sosiaali- ja kulttuurihistorian, työmarkkinahistorian, työelämän ja ajan sosiologian tutkimusta. Pohdin, mitä ydinteemoja eri aikakausia käsittelevä kirjallisuus nostaa esiin, mitkä teemat toistuvat eri aikakausien välillä ja millaiset kysymyksenasettelut olisivat tulevassa tutkimuksessa hedelmällisiä. Katsausartikkeli osoittaa, että historiallinen tarkastelu on tarpeen, jotta työn ja vapaa-ajan välisiin jännitteisiin niin menneisyydessä kuin nykyhetkessä pystytään pureutumaan syvällisesti ja ajan moninaiset ulottuvuudet tavoittaen.

Najmeh Hosseini Sarvari

Among the most popular oral stories are those about heroes and Ayyârân, which are often written long after the events they narrate occurred. "Abumuslemnama", "Hamzaname" and "Samak-e Ayyar" are some of the oldest stories, and "Hossein Kurd-e Shabestari" is almost the latest. The story of "Hossein Kurd-e Shabestari" was narrated during the Safavid era and is regarded as a continuation of the Ayyāri tradition and oral storytelling. The analysis of the story of "Hossein Kurd-e Shabestari" reveals that the character of Ayyār in this story differs significantly from those in previous stories on the surface and on the behavioral level. The purpose of this paper is to investigate these differences using descriptive and analytical methods. According to the results of this study, "Hossein Kurd" was a common, maverick hero who did not exhibit heroic behavioral delicacies like Samak that were characteristic of Ayyârân. "Hossein Kurd" is an illiterate hero who does not possess the privileges of acuteness, prudence or the skills of eloquence, as opposed to the previous Ayyâr heroes who were examples of conscious, educated, articulate, and knowledgeable heroes. The results of this study indicate that the character of a conscious hero is being replaced by an illiterate hero, who is devoid of any sense of awareness or rational thought.

Yasemin Uzun, Zeynep Türksever

Idioms and proverbs are taken an important place in teaching of Turkish to foreigners from B1 level. Proverbs and idioms play a big role in the conceptual skill gain that require abstract thinking. Idioms are the most concrete indicator of a nation's thinking system, emotions and perspective on the world. The meanings attributed to idioms also show how societies make sense of the world. In the study firstly, animal perception in Bosnian and Turkish idioms was tried to be determined. Especially in the idioms where the animal name is mentioned, many similarities have been found. Some animals have similar characteristics, while others have opposite meanings. In Bosnian, horses, donkeys or bulls have negative meanings. Although the donkey has a negative meaning in Turkish, there is no negative meaning attributed to the horse. This shows the importance of horse in Turkish society. Animals such as rat, turkey, rooster, parrot, panther and snail are included in Bosnian idioms and not in Turkish idioms dictionary. In the study firstly, the dictionary of Bosnian idioms was searched, idioms with the name of animals were identified, and then these animal names were searched in the Turkish idioms dictionary. This study is thought to be useful in teaching Turkish to Bosnians. In this study which is a qualitative research, document analysis was used. The data used in the study were obtained from the Bosnian idioms dictionary which was prepared by Şakir Bayhan and Turkish idioms dictionary which was prepared by Ömer Asım Aksoy.