Miracle-dz/UniFAR-FTUs huggingface dataset:
A survey of Elekes-R\'onyai-type problems

We give an overview of recent progress around a problem introduced by Elekes and Rónyai. The prototype problem is to show that a polynomial f ∈ R[x, y] has a large image on a Cartesian product A×B ⊂ R2, unless f has a group-related special form. We discuss this problem and a number of variants and generalizations. This includes the Elekes-Szabó problem, which generalizes the Elekes-Rónyai problem to a question about an upper bound on the intersection of an algebraic surface with a Cartesian product, and curve variants, where we ask the same questions for Cartesian products of finite subsets of algebraic curves. These problems lie at the crossroads of combinatorics, algebra, and geometry: They ask combinatorial questions about algebraic objects, whose answers turn out to have applications to geometric questions involving basic objects like distances, lines, and circles, as well as to sum-product-type questions from additive combinatorics. As part of a recent surge of algebraic techniques in combinatorial geometry, a number of quantitative and qualitative steps have been made within this framework. Nevertheless, many tantalizing open questions remain.
Algebras of quantum monodromy data and decorated character varieties

The Riemann-Hilbert correspondence is an isomorphism between the de Rham moduli space and the Betti moduli space, defined by associating to each Fuchsian system its monodromy representation class. In 1997 Hitchin proved that this map is a symplectomorphism. In this paper, we address the question of what happens to this theory if we extend the de Rham moduli space by allowing connections with higher order poles. In our previous paper arXiv:1511.03851, based on the idea of interpreting higher order poles in the connection as boundary components with bordered cusps (vertices of ideal triangles in the Poincar\'e metric) on the Riemann surface, we introduced the notion of decorated character variety to generalize the Betti moduli space. This decorated character variety is the quotient of the space of representations of the fundamental groupoid of arcs by a product of unipotent Borel sub-groups (one per bordered cusp). Here we prove that this representation space is endowed with a Poisson structure induced by the Fock--Rosly bracket and show that the quotient by unipotent Borel subgroups giving rise to the decorated character variety is a Poisson reduction. We deal with the Poisson bracket and its quantization simultaneously, thus providing a quantisation of the decorated character variety. In the case of dimension 2, we also endow the representation space with explicit Darboux coordinates. We conclude with a conjecture on the extended Riemann-Hilbert correspondence in the case of higher order poles.
Criteria for guaranteed breakdown in two-phase inhomogeneous bodies

Lower bounds are obtained on the maximum field strength in one or both phases in a body containing two-phases. These bounds only incorporate boundary data that can be obtained from measurements at the surface of the body, and thus may be useful for determining if breakdown has necessarily occurred in one of the phases, or that some other nonlinearities have occurred. It is assumed the response of the phases is linear up to the point of electric, dielectric, or elastic breakdown, or up to the point of the onset of nonlinearities. These bounds are calculated for conductivity, with one or two sets of boundary conditions, for complex conductivity (as appropriate at fixed frequency when the wavelength is much larger than the body, i.e. for quasistatics), and for two-dimensional elasticity. Sometimes the bounds are optimal when the field is constant in one of the phases, and using the algorithm of Kang, Kim, and Milton (2012) a wide variety of inclusion shapes having this property, for appropriately chosen bodies and appropriate boundary conditions, are numerically constructed. Such inclusions are known as EΩ-inclusions.
The dynamics of generic Kuperberg ﬂows

In this work, we study the dynamical properties of Krystyna Kuperberg's aperiodic flows on $3$-manifolds. We introduce the notion of a ``zippered lamination'', and with suitable generic hypotheses, show that the unique minimal set for such a flow is an invariant zippered lamination. We obtain a precise description of the topology and dynamical properties of the minimal set, including the presence of non-zero entropy-type invariants and chaotic behavior. Moreover, we show that the minimal set does not have stable shape, yet satisfies the Mittag-Leffler condition for homology groups.
Association between Sedentary Time and Falls among Middle-Aged Women in Japan

There are many reports on the risk of falls in older adults but none regarding the risk among middle-aged people. We aimed to determine fall risk factors among middle-aged women. The participants comprised 1421 women aged 40 to 64 years; anthropometric and other measurements were obtained, and lifestyle factors were examined using a self-administered questionnaire. The participants were categorized into two groups (No-fall and Fall/Almost-fall) based on their questionnaire responses. The No-fall and Fall/Almost-fall groups comprised 1114 and 307 participants, respectively. Body mass index, abdominal circumference measurements, and prevalence of dyslipidemia were significantly higher in the Fall/Almost-fall group. Additionally, those in the Fall/Almost-fall group had a shorter two-step test, experienced difficulty performing the 40 cm single-leg sit-to-stand test, and had higher 25-question Geriatric Locomotive Function Scale (GLFS-25) scores than those in the No-fall group. The results of the adjusted logistic regression analysis indicated that physical activity, higher GLFS-25 scores, and sedentary time of more than seven hours were all risk factors for falling or almost falling. Longer sedentary time is a new risk factor for falls among middle-aged women. It is necessary for people to be concerned with their sedentary behavior, such as by reducing or interrupting continuous sedentary time.
Seasonal Distribution of Nutrients in Water and Sediment of Three Coastal Region of Palk Bay Area, India

The present study was carried out to determine the seasonal distribution of nutrients in water and sediment of three coastal region of Thondi, Kottaipattinum and Sethubhavachatirum for a period of one year from January 2018 to December 2018. The analysis of different parameters such as nitrite, nitrate, ammonia, total nitrogen, inorganic phosphate, total phosphate, silicate, pH sediment, total phosphate, total nitrogen and total organic carbon were carried out using standard methods in water as well as in sediment. The nitrite values varied between 0.214 to 0.892 µm/l, 0.128 to 0.848 µm/l and 0.097 to 0.917 µm/l; nitrate values varied between 1.316 to 4.881 µm/l , 1.87 to 4.411 µm/l and 7.029 to 12.045 µm/l; ammonia values varied between 1.316 to 4.881 µm/l, 1.87 to 4.411 µm/l and 7.029 to 12.045 µm/l; total nitrogen values varied between 16.976 to 29.512 µm/l, 14.765 to 28.225 µm/l and 12.776 to 23.541 µm/l; inorganic phosphate values varied between 0.354 to 1.98 µm/l, 0.292 to 1.967 µm/l and 0.483 to 1.84 µm/l; total phosphorus values varied between 1.033 to 2. 508µm/l, 0.83 to 2.816 µm/l and 1.418 to 2.953 µm/l; silicate content values varied between 25.217 to 54.074 µm/l, 30.883 to 59.872 µm/l and 28.217 to 48.074 µm/l at Thondi, Kottaipattinum and Sethubhavachatirum, respectively. In sediment, pH varied between 8.0 to 8.20, 7.9 to 8.20 and 8.0 to 8.10; total phosphorus 0.15 to 2.61, 2.31 to 3.31 and 0.91 to 2.17; Total nitrogen 6.50 to 12.95 µg/g, 4.85 to 11.96 µg/g and 5.17 to 8.08 µg/g and the total organic carbon 1.57 to 5.36, 2.21 to 3.59 and 1.48 to 4.15 at the three stations
Conjugacy rigidity, cohomological triviality and barycentres of invariant measures

This thesis consists of three chapters and four appendices. Each chapter is a self-contained study of one topic in dynamical systems. Each chapter has its own notation. In chapter 1 we study conjugacies h between piecewise smooth conformal expanding Markov maps T1, T2. We prove that if h is piecewise continuous, satisfies an absolute continuity condition, and has essentially bounded partial derivatives, then it is as smooth as T1, T2. We use this result to give a new proof of part of Mostow's theorem on the rigidity of manifolds of constant negative curvature. In chapter 2 we study the cohomology of certain two-dimensional subshifts X with a semi-safe symbol. The simplest examples of such subshifts are the full shift and the golden mean shift. We prove the triviality of all locally constant co cycles on X taking values in a locally (residually finite) group. For real-valued cocycles we extend this result to the Holder category. In chapter 3 we consider the doubling map of the circle, and study the convex set n of barycentres of invariant measures. We prove that each interior point of n is the barycentre of an equilibrium state of a particular kind, and that this equilibrium state maximises entropy over all measures with this barycentre. We prove that any measure whose barycentre lies on the boundary an is not fully supported, and conjecture that its support has zero Hausdorff dimension. We conjecture further that an is non-differentiable at a countable dense set of points, the worst possible regularity for the boundary of a planar convex figure. Appendix A contains the proof of a technical lemma stated in section 1·3. Appendix B contains an alternative proof (due to de la Llave, Marco & Moriyon) of a theorem stated and proved in section 1·5. Appendix C contains numerical data to support the conjectures of chapter 3. Appendix D is a graphical plot of the data contained in Appendix C.
A piecewise linear FEM for an optimal control problem of fractional operators: error analysis on curved domains

We propose and analyze a new discretization technique for a linear-quadratic optimal control problem involving the fractional powers of a symmetric and uniformly elliptic second oder operator; control constraints are considered. Since these fractional operators can be realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic equation, we recast our problem as a nonuniformly elliptic optimal control problem. The rapid decay of the solution to this problem suggests a truncation that is suitable for numerical approximation. We propose a fully discrete scheme that is based on piecewise linear functions on quasi-uniform meshes to approximate the optimal control and first-degree tensor product functions on anisotropic meshes for the optimal state variable. We provide an a priori error analysis that relies on derived Holder and Sobolev regularity estimates for the optimal variables and error estimates for an scheme that approximates fractional diffusion on curved domains; the latter being an extension of previous available results. The analysis is valid in any dimension. We conclude by presenting some numerical experiments that validate the derived error estimates.
DDAD: Detachable Crowd Density Estimation Assisted Pedestrian Detection

Detecting pedestrians is a challenging computer vision task, especially in the intelligent transportation system. Mainstream pedestrian detection methods purely utilize information of bounding boxes, which overlooks the role of other valuable attributes (e.g., head, head-shoulders, and keypoints) of pedestrians and leads to sub-optimal solutions. Some works leveraged these valuable attributes with a minor performance improvement at the expense of increased computational complexity during the inference phase. To alleviate this dilemma, we propose a simple yet effective method, namely Detachable crowd Density estimation Assisted pedestrian Detection (DDAD), which leverages the crowd density attributes to assist pedestrian detection in the real-world scenes (e.g., crowded scenes and small-scale pedestrian scenes). The advantage of the crowd density estimation is that it allows the network to focus more on the human head and the small-scale pedestrians, which improves the features representation of pedestrians heavily occluded or far from cameras. Our DDAD works on a principle of multi-task learning and can be seamlessly applied to both one-stage and two-stage pedestrian detectors by equipping them with an extra detachable branch of crowd density estimation. The equipped crowd density estimation branch is trained with the annotations derived from the existing pedestrian bounding box annotations, occurring no extra annotation cost. Moreover, it can be removed during the inference phase without sacrificing the inference speed. Extensive experiments conducted on two challenging datasets, i.e., CrowdHuman and CityPersons, demonstrate that our proposed DDAD achieves a significant improvement upon the state-of-the-art methods. Code is available at https://github.com/SCUT-BIP-Lab/DDAD.
Hyperspectral Imaging Based Detection of PVC During Sellafield Repackaging Procedures

Traditionally, special nuclear material (SNM) at Sellafield has been stored in multilayered packages, consisting of metallic cans and an overlayer of plasticized polyvinyl chloride (PVC) as an intermediate layer when transitioning between areas of different radiological classification. However, it has been found that the plasticized PVC can break down in the presence of both radiation and heat, releasing hydrochloric acid, which can corrode these metallic containers. Therefore, internal repackaging procedures at Sellafield have focused recently on the removal of these PVC films from containers, where as much degraded and often adhered PVC as possible is manually removed based on visual inspection. This manual operation is time-consuming, and it is possible that residual fragments of PVC could remain, leading to corrosion-related issues in future. In this work, hyperspectral imaging (HSI) was evaluated as a new tool for detecting PVC on metallic surfaces. The Samples of stainless steel type 1.4404—also known as 316L, the same as is used to construct SNM cans—and PVC were imaged in our experiments, and support vector machine (SVM) classification models were used to generate detection maps. In these maps, pixels were classified into either PVC or 316L based on their spectral responses in the range 954–1700 nm of the electromagnetic spectrum. Results suggest that the HSI could be used for an effective automated detection and quantification of PVC during repackaging procedures, detection and quantification that could be extended to other similar applications.
Self Cycloaddition of o-Naphthoquinone Nitrosomethide to (±) Spiro{naphthalene(naphthopyranofurazan)}-one Oxide: An Insight into its Formation.

2-Hydroxy-1-naphthaldehyde oxime was oxidized by AgO (or Ag2 O), in presence of N-methyl morpholine N-oxide (NMMO), to the title spiro adduct-dimer (±)-Spiro{naphthalene-1(2H),4'-(naphtho[2',1':2,3]pyrano[4,5-c]furazan)}-2-one-11'-oxide by a Diels-Alder(D-A) type self-cycloaddition, through the agency of an o-naphthoquinone nitrosomethide (o-NQM). Moreover, 2-hydroxy-8-methoxy-1-naphthaldehyde oxime was prepared and subjected to the same oxidation conditions. Its sterically guided result, 9-methoxynaphtho[1,2-d]isoxazole, was isolated, instead of the expected spiro adduct. The peri intramolecular H bonding in the oxime is considered to have a key contribution to the outcome. Geometry and energy features of the oxidant- and stereo-guided selectivity of both oxidation outcomes have been explored by DFT, perturbation theory and coupled cluster calculations. The reaction free energy of the D-A intermolecular cycloaddition is calculated at -82.0 kcal/mol, indicating its predominance over the intramolecular cyclization of ca. -37.6 kcal/mol. The cycloaddition is facilitated by NMMO through dipolar interactions and hydrogen bonding with both metal complexes and o-NQM. The 8(peri)-OMe substitution of the reactant oxime sterically impedes formation of the spiro adduct, instead it undergoes a more facile cyclodehydration to the isoxazole structure by ca. 4.9 kcal/mol.
Sobolev Algebras Through a ‘Carré Du Champ’ Identity

Abstract We consider abstract Sobolev spaces of Bessel-type associated with an operator. In this work, we pursue the study of algebra properties of such functional spaces through the corresponding semigroup. As a follow-up to our previous work, we show that by making use of the property of a ‘carré du champ’ identity, this algebra property holds in a wider range than previously shown.
Torus knots and the rational DAHA

Author(s): Gorsky, E; Oblomkov, A; Rasmussen, J; Shende, V | Abstract: © 2014. We conjecturally extract the triply graded Khovanov-Rozansky homology of the (m;n) torus knot from the unique finite-dimensional simple representation of the rational DAHA of type A, rank n - 1, and central character m/n. The conjectural differentials of Gukov, Dunfield, and the third author receive an explicit algebraic expression in this picture, yielding a prescription for the doubly graded Khovanov-Rozansky homologies. We match our conjecture to previous conjectures of the first author relating knot homology to q; t-Catalan numbers and to previous conjectures of the last three authors relating knot homology to Hilbert schemes on singular curves.
Chaotically driven sigmoidal maps

We consider skew product dynamical systems $f:\Theta\times\mathbb{R}\to\Theta\times\mathbb{R}, f(\theta,y)=(T\theta,f_\theta(y))$ with a (generalized) baker transformation $T$ at the base and uniformly bounded increasing $C^3$ fibre maps $f_\theta$ with negative Schwarzian derivative. Under a partial hyperbolicity assumption that ensures the existence of strong stable fibres for $f$ we prove that the presence of these fibres restricts considerably the possible structures of invariant measures - both topologically and measure theoretically, and that this finally allows to provide a "thermodynamic formula" for the Hausdorff dimension of set of those base points over which the dynamics are synchronized, i.e. over which the global attractor consists of just one point.
A SIMPLICIAL APPROACH TO MULTIPLIER BIMONOIDS

Although multiplier bimonoids in general are not known to correspond to comonoids in any monoidal category, we classify them in terms of maps from the Catalan simplicial set to another suitable simplicial set; thus they can be regarded as (co)monoids in something more general than a monoidal category (namely, the simplicial set itself). We analyze the particular simplicial maps corresponding to that class of multiplier bimonoids which can be regarded as comonoids.
Matricial bridges for "Matrix algebras converge to the sphere"

In the high-energy quantum-physics literature one finds statements such as "matrix algebras converge to the sphere". Earlier I provided a general setting for understanding such statements, in which the matrix algebras are viewed as quantum metric spaces, and convergence is with respect to a quantum Gromov-Hausdorff-type distance. In the present paper, as preparation of discussing similar statements for convergence of "vector bundles" over matrix algebras to vector bundles over spaces, we introduce and study suitable matrix-norms for matrix algebras and spaces. Very recently Latremoliere introduced an improved quantum Gromov-Hausdorff-type distance between quantum metric spaces. We use it throughout this paper. To facilitate the calculations we introduce and develop a general notion of "bridges with conditional expectations".
Pelvic pain in transmasculine adolescents receiving testosterone therapy

Abstract Background: Pelvic pain is a common complaint among individuals assigned female at birth. However, few studies have explored pelvic pain among transmasculine patients on gender-affirming testosterone treatment, and most of these were performed in adult populations. Aims: The aim of our study was to investigate the prevalence, risk factors, nature and treatment of pelvic pain among trans adolescents on testosterone. Methods: A retrospective cohort study was performed on all trans adolescents started on gender-affirming testosterone treatment at our institution between 2007 and 2020. Results: Among 158 trans adolescents who were started on testosterone therapy and followed-up for at least six months, 37 (23.4%) reported pelvic pain, with a median interval between testosterone initiation and reported onset of pain of 1.6 months (range 0.3-6.4). The prevalence of pelvic pain was higher in patients who were receiving menstrual suppression (n = 36, 26.3%) compared to those who were not (n = 1, 4.8%), giving a risk difference of 21.5% (95% CI 9.8% to 33.2%, p = 0.028). The most common descriptive terms were “cramps” (n = 17, 45.9%) and “similar to previous period pain” (n = 8, 21.6%). A range of different pharmacological strategies were employed, including paracetamol, NSAIDs, danazol, norethisterone, medroxyprogesterone, etonogestrel implant, intra-uterine device, goserelin and pelvic floor physiotherapy, with variable outcomes. Conclusion: In conclusion, we report here – in what is to our knowledge the first time – the prevalence rate of pelvic pain in trans adolescents on gender-affirming testosterone treatment, and observe that a quarter of them described pelvic pain. Limitations of our study include its retrospective nature, which is likely to be associated with under-reporting of pelvic pain, and the limited documentation of the nature and likely causes of this pain within the medical records. Prospective longitudinal studies to better understand the nature, etiology and optimal management of testosterone-associated pelvic pain are therefore warranted.
A geometric Achlioptas process

The random geometric graph is obtained by sampling $n$ points from the unit square (uniformly at random and independently), and connecting two points whenever their distance is at most $r$, for some given $r=r(n)$. We consider the following variation on the random geometric graph: in each of $n$ rounds in total, a player is offered two random points from the unit square, and has to select exactly one of these two points for inclusion in the evolving geometric graph. We study the problem of avoiding a linear-sized (or "giant") component in this setting. Specifically, we show that for any $r\ll(n\log\log n)^{-1/3}$ there is a strategy that succeeds in keeping all component sizes sublinear, with probability tending to one as $n\to\infty$. We also show that this is tight in the following sense: for any $r\gg(n\log\log n)^{-1/3}$, the player will be forced to create a component of size $(1-o(1))n$, no matter how he plays, again with probability tending to one as $n\to\infty$. We also prove that the corresponding offline problem exhibits a similar threshold behaviour at $r(n)=\Theta(n^{-1/3})$. These findings should be compared to the existing results for the (ordinary) random geometric graph: there a giant component arises with high probability once $r$ is of order $n^{-1/2}$. Thus, our results show, in particular, that in the geometric setting the power of choices can be exploited to a much larger extent than in the classical Erd\H{o}s-R\'{e}nyi random graph, where the appearance of a giant component can only be delayed by a constant factor.
Eigenvalues, $K$ -theory and Minimal Flows

Abstract Let $(Y,\,T)$ be a minimal suspension flow built over a dynamical system $(X,\,S)$ and with (strictly positive, continuous) ceiling function $f:\,X\,\to \,\mathbb{R}$ . We show that the eigenvalues of $(Y,\,T)$ are contained in the range of a trace on the ${{K}_{0}}$ -group of $(X,\,S)$ . Moreover, a trace gives an order isomorphism of a subgroup of ${{K}_{0}}\left( C(X)\,{{\rtimes }_{S}}\,\mathbb{Z} \right)$ with the group of eigenvalues of $(Y,\,T)$ . Using this result, we relate the values of $t$ for which the time- $t$ map on the minimal suspension flow is minimal with the $K$ -theory of the base of this suspension.