Hasil untuk "Folklore"

R. Bauman

Ivano Basile, Grant N. Remmen, Georgina Staudt

We employ multiparticle factorization to constrain deformations of tree-level open string amplitudes. Assuming minimal degeneracy among intermediate states of the same spin up through the second excited level, we find that the Regge intercept among all amplitudes of the Koba-Nielsen type can be uniquely fixed using seven-point factorization, precisely matching the bosonic string. Moreover, we produce novel constraints on deformations of the worldsheet integrand. We then turn to deformations of superstrings, with massless external states and arbitrary spectral degeneracy, using soft kinematics. Accounting for the infinite tower of higher-spin resonances, we obtain novel multipositivity bounds to leading and subleading order in the large-level limit. We apply these bounds to the simplest factorizable satellite deformation in the family of amplitudes found by Gross, showing that any deformation of four-point string amplitudes of this type is forbidden by unitarity. Our results reinforce the folklore that the higher-spin tower of string excitations is dramatically more rigid than any finite number of species.

Martino Stefanini, Aleksandra A. Ziolkowska, Dmitry Budker et al.

The Lindblad master equation is a foundational tool for modeling the dynamics of open quantum systems. As its use has extended far beyond its original domain, the boundaries of its validity have grown opaque. In particular, the rise of new research areas including open quantum many-body systems, non-equilibrium condensed matter, and the possibility to test its limits in driven-open quantum simulators, call for a critical revision of its regimes of applicability. In this pedagogical review, we re-examine the folklore surrounding its three standard approximations (Born, Markov, and Rotating Wave Approximation), as we build our narrative by employing a series of examples and case studies accessible to any reader with a solid background on the fundamentals of quantum mechanics. As a synthesis of our work, we offer a checklist that contrasts common lore with refined expectations, offering a practical guideline for assessing the breakdown of the Lindblad framework in the problem at hand.

Nathaël Da Costa, Marvin Pförtner, Jon Cockayne

Conditioning, the central operation in Bayesian statistics, is formalised by the notion of disintegration of measures. However, due to the implicit nature of their definition, constructing disintegrations is often difficult. A folklore result in machine learning conflates the construction of a disintegration with the restriction of probability density functions onto the subset of events that are consistent with a given observation. We provide a comprehensive set of mathematical tools which can be used to construct disintegrations and apply these to find densities of disintegrations on differentiable manifolds. Using our results, we provide a disturbingly simple example in which the restricted density and the disintegration density drastically disagree. Motivated by applications in approximate Bayesian inference and Bayesian inverse problems, we further study the modes of disintegrations. We show that the recently introduced notion of a "conditional mode" does not coincide in general with the modes of the conditional measure obtained through disintegration, but rather the modes of the restricted measure. We also discuss the implications of the discrepancy between the two measures in practice, advocating for the utility of both approaches depending on the modelling context.

Raphael Yuster

For a digraph $G$, let $f(G)$ be the maximum chromatic number of an acyclic subgraph of $G$. For an $n$-vertex digraph $G$ it is proved that $f(G) \ge n^{5/9-o(1)}s^{-14/9}$ where $s$ is the bipartite independence number of $G$, i.e., the largest $s$ for which there are two disjoint $s$-sets of vertices with no edge between them. This generalizes a result of Fox, Kwan and Sudakov, who proved this for the case $s=0$ (i.e., tournaments and semicomplete digraphs). Consequently, if $s=n^{o(1)}$, then $f(G) \ge n^{5/9-o(1)}$ which polynomially improves the folklore bound $f(G) \ge n^{1/2-o(1)}$. As a corollary, with high probability, all orientations of the random $n$-vertex graph with edge probability $p=n^{-o(1)}$ (in particular, constant $p$, hence almost all $n$-vertex graphs) satisfy $f(G) \ge n^{5/9-o(1)}$. Our proof uses a theorem of Gallai and Milgram that together with several additional ideas, essentially reduces to the proof of Fox, Kwan and Sudakov.

Mark Sellke, Steven Yin

The property of learning-curve monotonicity, highlighted in a recent series of work by Loog, Mey and Viering, describes algorithms which only improve in average performance given more data, for any underlying data distribution within a given family. We establish the first nontrivial monotonicity guarantees for the maximum likelihood estimator in a variety of well-specified parametric settings. For sequential prediction with log loss, we show monotonicity (in fact complete monotonicity) of the forward KL divergence for Gaussian vectors with unknown covariance and either known or unknown mean, as well as for Gamma variables with unknown scale parameter. The Gaussian setting was explicitly highlighted as open in the aforementioned works, even in dimension 1. Finally we observe that for reverse KL divergence, a folklore trick yields monotonicity for very general exponential families. All results in this paper were derived by variants of GPT-5.2 Pro. Humans did not provide any proof strategies or intermediate arguments, but only prompted the model to continue developing additional results, and verified and transcribed its proofs.

Jnaneshwar Baslingker, Manjunath Krishnapur, Mokshay Madiman

We prove log-concavity of the lengths of the top rows of Young diagrams under Poissonized Plancherel measure. This is the first known positive result towards a 2008 conjecture of Chen that the length of the top row of a Young diagram under the Plancherel measure is log-concave. This is done by showing that the ordered elements of several discrete ensembles have log-concave distributions. In particular, we show the log-concavity of passage times in last passage percolation with geometric weights, using their connection to Meixner ensembles. In the continuous setting, distributions of the maximal elements of beta ensembles with convex potentials on the real line are shown to be log-concave. As a result, log-concavity of the Tracy-Widom distributions for all parameters $β>0$ follows, confirming a folklore conjecture that was partially proved by Deift for $β=2$. Furthermore, we also obtain log-concavity and positive association for the joint distribution of the $k$ smallest eigenvalues of the stochastic Airy operator. Our methods also show the log-concavity of the Airy-2 process and the Airy distribution. A log-concave distribution with full-dimensional support must have density, a fact that was apparently not known for some of these examples.

Satoshi Matsuoka, Jens Domke, Mohamed Wahib et al.

In this thought-provoking article, we discuss certain myths and legends that are folklore among members of the high-performance computing community. We gathered these myths from conversations at conferences and meetings, product advertisements, papers, and other communications such as tweets, blogs, and news articles within and beyond our community. We believe they represent the zeitgeist of the current era of massive change, driven by the end of many scaling laws such as Dennard scaling and Moore's law. While some laws end, new directions are emerging, such as algorithmic scaling or novel architecture research. Nevertheless, these myths are rarely based on scientific facts, but rather on some evidence or argumentation. In fact, we believe that this is the very reason for the existence of many myths and why they cannot be answered clearly. While it feels like there should be clear answers for each, some may remain endless philosophical debates, such as whether Beethoven was better than Mozart. We would like to see our collection of myths as a discussion of possible new directions for research and industry investment.

Maya Febrianti, Khairil Anwar, Zurmailis Zurmailis

The legend of the Orang Kayo Hitam is a folk tale from Jambi. The legend of the Orang Kayo Hitam develops between spoken and written. The legend of the Orang Kayo Hitam is considered a historical story or folklore that has meaningful values in life. This paper will discuss the existence of the Legend of the Orang Kayo Hitam in Jambi with the aim of describing the existence of the Legend of the Orang Kayo Hitam in society and the existence of the Legend of the Orang Kayo Hitam in literary works. The research method is a qualitative descriptive method using explanations. Data analysis was done by rereading interview data and story books to get results that are close to the problem formulation. The result of this paper is the existence of the Legend of the Orang Kayo Hitam seen from the community, the author continues to work by himself by the Legend of the Orang Kayo Hitam. For the people of the Legend of the Orang Kayo Hitam, it is very influential in social life, besides that people easily tell briefly the Legend of the Orang Kayo Hitam, some relics of the Orang Kayo Hitam are still used as icons in Jambi. While in literary works, the author describes the Legend of Orang Kayo Hitam fairly, the work used in this paper has a long period of publication and has differences in the title and content of the story text. The message conveyed was that Jambi had a firm leader during his reign, Orang Kayo Hitam had an influence in the creation of new works.

Teresa Sordé-Martí, Adnan Abdul Ghani, Bilal Almobarak et al.

Abstract A growing body of literature suggests that involving end-users in intervention research, including design, implementation, and evaluation, is associated with numerous positive outcomes. These outcomes include improved intervention efficacy, sustainability, and psychological growth among collaborators. The value of this approach and the recommendation for researchers to embrace co-creation in implementation and policies have also been recognised within the EU Framework of Research Innovation. Furthermore, it has been suggested that this approach may be particularly relevant for working with individuals from marginalised groups, whose voices are often absent from research and policy discussions. However, there has been limited attention given to how co-creation unfolds in practice. In this article, we provide a review of the methodological framework implemented by the H2020 REFUGE-ED (2021–2023), which was conducted in collaboration with migrant, refugee, and asylum-seeking communities. The project implemented the 'REFUGE-ED Dialogic Co-Creation Process (RDCP)' in 46 educational settings across six European countries. Considering the need for evidence-based approaches in education and mental health and psychosocial support practices, we suggest that the RDCP has the potential for sustainability and replicability in diverse contexts.

Toni Karvonen, Chris J. Oates

Gaussian process regression underpins countless academic and industrial applications of machine learning and statistics, with maximum likelihood estimation routinely used to select appropriate parameters for the covariance kernel. However, it remains an open problem to establish the circumstances in which maximum likelihood estimation is well-posed, that is, when the predictions of the regression model are insensitive to small perturbations of the data. This article identifies scenarios where the maximum likelihood estimator fails to be well-posed, in that the predictive distributions are not Lipschitz in the data with respect to the Hellinger distance. These failure cases occur in the noiseless data setting, for any Gaussian process with a stationary covariance function whose lengthscale parameter is estimated using maximum likelihood. Although the failure of maximum likelihood estimation is part of Gaussian process folklore, these rigorous theoretical results appear to be the first of their kind. The implication of these negative results is that well-posedness may need to be assessed post-hoc, on a case-by-case basis, when maximum likelihood estimation is used to train a Gaussian process model.

Kristina Perkola

This article takes into consideration the specific period of ethnomusicological and musicological publications from after World War II to the late 1980s, when political turbulences severely damaged social processes and diverted the normal flow of cultural and scientific developments in Kosovo. As a consequence of historical, political and social circumstances, the trajectory of art in Kosovo has followed its own specific history in which classical music (in written form) was completely unknown until the second part of the 20th century, since before then musical tradition had been transmitted only in oral form. The most important and abundant part of this tradition is the rich musical folklore. The first studies in the field of ethnomusicology and the publications by different authors are presented in this article. The Albanian folklore from Kosovo, both collected and studied, was the main promoter in the development of ethnomusicology and musicology. Such research was begun by foreign scholars in the first part of the 20th century and then was continued by scholars from Kosovo in the second part of the same century. Lorenc Antoni’s work presents the first most important trace of ethnomusicological work done by a local Kosovo author, followed subsequently by others. While studies in the field of ethnomusicology (within the Folklore Branch at the Albanological Institute in Prishtina) have reached a certain level of quality during the last half century, historical musicology failed to follow the course of the primary compositional and artistic activities. Consequently, it has not as yet reached the same level as the other musical areas.

Radvan Markus

Clément L. Canonne

The goal of this short note is to provide simple proofs for the "folklore facts" on the sample complexity of learning a discrete probability distribution over a known domain of size $k$ to various distances $\varepsilon$, with error probability $δ$.

Zakarias Sjöström Dyrefelt

We prove continuity results for new stability thresholds related to uniform K-stability and deduce that uniform K-stability is an open condition in the Kähler cone of any compact Kähler manifold, thus establishing an algebro-geometric counterpart to a classical result of LeBrun-Simanca for constant scalar curvature (cscK) metrics. This settles a folklore conjecture in the field, and in particular implies openness of uniform K-stability for smooth polarized varieties. Moreover, it strengthens evidence supporting the uniform version of the Yau-Tian-Donaldson conjecture for arbitrary polarizations, including the case of irrational polarizations and non-projective Kähler manifolds. As a key tool we introduce a new norm on test configurations and establish estimates for non-archimedean energy functionals in terms of this norm. This leads to new characterizations of uniform K-stability by restricting to test configurations that satisfy certain uniform bounds. As a byproduct we obtain continuity results for a stability threshold related to non-archimedean entropy and deduce openness of uniform J-stability, as well as openness of J-stability in the projective case.

Nazlı Gündüz

Since ancient times, hunger, drought, animosity or the search for better education caused people to leave their lands and go to other places or other countries. Inevitably, these types of moves bring the phenomenon of culture to the fore. This article discusses how the Zaza /Alevi born Dutch writer Murat Işık, who witnessed emigration from Turkey to The Netherlands, deals with the factors of internal migration in his novel Verloren Grond (Lost Ground), which bears traces of his family’s biography. In the work, migration of the Uslu family brings to the agenda feelings, hopes and disappointments of family members. The novel is examined with the aid of both the push-pull model of migration and pushing and pulling factors leading to migration. The most important pushing factor in the novel is the father’s leg amputation. The ground inherited from his father is thought to be the only pulling factor for the family because it will provide them with economic salvation. The phenomenon of land is very important for human beings because it represents ancestral heritage, belongingness, identity and freedom. The second important pushing factor is an earthquake, which triggers the idea of going to the big city as a pulling factor. After the migrations, the members of the family experience various types of social and cultural adaptation problems. Thus, through the novel we realize that the phenomena of migration are economically, socially and culturally important for the Uslu family, and consequently have positive and negative results for each individual.

Enrique JIMÉNEZ VAQUERIZO

The present article is born with the intention of showing a retrospective vision of the traditional games and sports, rooted in the oral tradition, of a province like Segovia with a lot of historical weight within the Iberian Peninsula.<br />The first line of research shows us how the practice, culture and folklore related to these practices have a common link: Be part of a wide network of royal canyons, Cañada Segoviana and the Occidental Cañada Leonesa, both communicated in the «Vera de la Sierra» canyon.<br />The second line of research would be around the economy of the Mesta, the transhumance and the marketing of cloth. As a source of cultural transmission on a peninsular level.<br />We will finish with a classification and reflection on the pedagogical resources that can facilitate us the teaching work from the school and its federated sport as the true exposition of what was and should be its practice.

Sebastiano Vigna

When the Mersenne Twister made his first appearance in 1997 it was a powerful example of how linear maps on $\mathbf F_2$ could be used to generate pseudorandom numbers. In particular, the easiness with which generators with long periods could be defined gave the Mersenne Twister a large following, in spite of the fact that such long periods are not a measure of quality, and they require a large amount of memory. Even at the time of its publication, several defects of the Mersenne Twister were predictable, but they were somewhat obscured by other interesting properties. Today the Mersenne Twister is the default generator in C compilers, the Python language, the Maple mathematical computation system, and in many other environments. Nonetheless, knowledge accumulated in the last $20$ years suggests that the Mersenne Twister has, in fact, severe defects, and should never be used as a general-purpose pseudorandom number generator. Many of these results are folklore, or are scattered through very specialized literature. This paper surveys these results for the non-specialist, providing new, simple, understandable examples, and it is intended as a guide for the final user, or for language implementors, so that they can take an informed decision about whether to use the Mersenne Twister or not.

Atanas Stoychev Orachev

The available database from the Thracian lands allows us to understand how the prehistoric civilizational models began and how the principles of interacting between their two main structures — the village and the city have crystalized. Nowhere else in Europe it is possible to trace better the peculiarities throughout thousands of past years and outline the essential differences between rural and urban culture. And to understand the fundamental differences in worldviews, to look at the differences in everyday stereotypes and the ways in which peasants and citizens conceive, perceive and strive to organize the world. This is also illustrated by the available written information and monuments about one of the most ancient cultural heroes — Orpheus, which should not be associated with the Thracian Orphism postulates in Thracology. In fact, for the Thracian cattle-breeding community, the invention of agriculture, the cleansing of wicked deeds, the remedies for diseases and the redemption of God’s wrath were most important in order to ensure fertility of flocks, fields and people. It is significant that in the Bogomil Books and Legends, in the Bulgarian apocryphal works and folklore there are many Orpheus notions: about Good and Evil and the corresponding anthem-prayers; data on medicines, divinations and prayers; substances for the remission of sins; fortune-telling; and last but not least, prayers and blessings for fertility.

Jonas Stelzig

We study consequences and applications of the folklore statement that every double complex over a field decomposes into so-called squares and zigzags. This result makes questions about the associated cohomology groups and spectral sequences easy to understand. We describe a notion of `universal' quasi-isomorphism, investigate the behaviour of the decomposition under tensor product and compute the Grothendieck ring of the category of bounded double complexes over a field with finite cohomologies up to such quasi-isomorphism (and some variants). Applying the theory to the double complexes of smooth complex valued forms on compact complex manifolds, we obtain a Poincaré duality for higher pages of the Frölicher spectral sequence, construct a functorial three-space decomposition of the middle cohomology, give an example of a map between compact complex manifolds which does not respect the Hodge filtration strictly, compute the Bott-Chern and Aeppli cohomology for Calabi-Eckmann manifolds, introduce new numerical bimeromorphic invariants, show that the non-Kählerness degrees are not bimeromorphic invariants in dimensions higher than three and that the $\partial\overline{\partial}$-lemma and some related properties are bimeromorphic invariants if, and only if, they are stable under restriction to complex submanifolds.