Miracle-dz/UniFAR-FTUs huggingface dataset:
Functions on surfaces and constructions of
 manifolds in dimensions three, four and five

We offer a new proof that two closed oriented 4–manifolds are cobordant if their signatures agree, in the spirit of Lickorish’s proof [6] that all closed oriented 3–manifolds bound 4–manifolds. Where Lickorish uses Heegaard splittings we use trisections. In fact we begin with a subtle recasting of Lickorish’s argument: Instead of factoring the gluing map for a Heegaard splitting as a product of Dehn twists, we encode each handlebody in a Heegaard splitting in terms of a Morse function on the surface and build the 4–manifold from a generic homotopy between the two functions. This extends up a dimension by encoding a trisection of a closed 4–manifold as a triangle (circle) of functions and constructing an associated 5– manifold from an extension to a 2–simplex (disk) of functions. This borrows ideas from Hatcher and Thurston’s proof [3] that the mapping class group of a surface is finitely presented.
Twisted Hilbert modular L-functions and spectral theory

These are notes for four lectures given at the 2010 CIMPA Research School "Automorphic Forms and L-functions" in Weihai, China. The lectures focused on a Burgess-like subconvex bound for twisted Hilbert modular L-functions published jointly with Valentin Blomer in the same year. They discussed the proof in some detail, especially how spectral theory can be used to estimate the relevant shifted convolution sums efficiently. They also discussed briefly an application for the number of representations by a totally positive ternary quadratic form over a totally real number field.
Evaluation of real-life data on the use of inhaler devices, including satisfaction and adherence to treatment, by community pharmacists in partnership with pulmonary disease specialists

Abstract Objective The use of inhaler device (UID) and the satisfaction and adherence of patients to treatment were evaluated by Istanbul city community pharmacists to obtain real-life data from patients with asthma or chronic obstructive pulmonary disease (COPD). Methods Pharmacists educated by pulmonary disease specialists asked patients who combined medications with inhaler devices to fill out a questionnaire prepared by the specialists. Each patient’s UID was checked, and their errors were corrected by showing them the already prepared standard video of their inhaler device. Afterward, the UID was repeated and rechecked. The visual analog scale (VAS), feeling of satisfaction with the inhaler (FSI-10) questionnaire, and the Morisky Green Levine (MGL) scale were used for symptom control, satisfaction, and adherence, respectively. Then, we compared the results of three different types of inhalers: metered dose inhalers (MDI), dry powder inhalers (DPI), and dry powder inhalation capsules (DPI Caps). Results Twenty-seven (19.3%) patients used MDI, 42 (30%) used DPI caps, and 71 (50.7%) used DPI. UID before training was better in patients with DPI than in those with MDI and DPI Cap (p < 0.001). After training, the UID increased in all three groups (p < 0.001). The VAS scores were high in the DPI Caps group than the other groups (p < 0.001). The FSI-10 score was not significantly different among the groups (p > 0.05). Full-adherence was observed in 36.8% of the MDI group, 39.1% of the DPI Caps group, and 21.7% of the DPI groups (p > 0.05). Conclusion The partnership between community pharmacists and pulmonary disease specialists improved patients’ UID.
The Moduli Space of Totally Marked Degree Two Rational Maps

A rational map $\phi: \mathbb{P}^1 \to \mathbb{P}^1$ along with an ordered list of fixed and critical points is called a totally marked rational map. The space of totally marked degree two rational maps, $Rat^{tm}_2$ can be parametrized by an affine open subset of $(\mathbb{P}^1)^5$. We consider the natural action of $SL_2$ on $Rat^{tm}_2$ induced from the action of $SL_2$ on $(\mathbb{P}^1)^5$ and prove that the quotient space $Rat^{tm}_2/SL_2$ exists as a scheme. The quotient is isomorphic to a Del Pezzo surface with the isomorphism being defined over $\mathbb{Z}[1/2]$.
Health behaviors, psychosocial factors, and academic engagement in youth with autism spectrum disorder: A latent class analysis

The purpose of this study was to identify behavioral and health‐related profiles of children with autism spectrum disorder (ASD), based on the 2016 National Survey of Children's Health. A sample of 894 children with ASD (weighted sample N = 768,181) were included in the analysis. All data were parent‐reported and included measures on current diagnosis of ASD, general child health, weight status, physical activity (PA), screen time (ST), sleep duration, academic engagement, and social engagement. Latent class analysis, estimated with Mplus v. 8.4, was used to identify latent profiles of children with ASD. A three‐profile solution was the best fitting model, per model fit criteria. Children in profile 1 had overall more positive attributes (better health and weight, PA, more engaged in school, little difficulty in making friends, and modest ST) relative to children in either profiles 2 or 3. Children in profile 2 had distinctly increased ST and more difficulty in making friends when compared with children in either other profile. A greater proportion of children in profiles 2 and 3 were receiving behavioral treatment compared to profile 1; however, no differences were observed among profiles according to ASD severity, medication status, or additional health conditions. Studies should examine causal mechanisms among health behaviors, academic achievement, and social engagement in youth with ASD.
Foliation-based quantization and black hole information

We extend the foliation-based quantization scheme of Park (2015 Eur. Phys. J. C 75 459) to arbitrary asymptotically flat backgrounds including those that are time- and position- dependent. One of the ingredients to accomplishing the extension is imposition of a Neumann-type boundary condition. The quantization procedure, especially the gauge-fixing-induced reduction, provides a new insight into the black hole information paradox. The hypersurface degrees of freedom in the asymptotic region—whose dynamics should be responsible for part of the ‘hair’—as well as transitions among various excitations play a central role in the global formulation of the information and proposed solution of the information paradox. In retrospect, the quantization scheme reveals the origin of the difficulty of the information problem: the problem’s ties with the quantization of gravity and subtle boundary dynamics as well as the multilayered techniques required for its setup and study. We also comment on the implications of the asymptotic symmetries for the present quantization framework.
DIFFUSION LIMITS FOR A MARKOV MODULATED BINOMIAL COUNTING PROCESS

In this paper, we study limit behavior for a Markov-modulated binomial counting process, also called a binomial counting process under regime switching. Such a process naturally appears in the context of credit risk when multiple obligors are present. Markov-modulation takes place when the failure/default rate of each individual obligor depends on an underlying Markov chain. The limit behavior under consideration occurs when the number of obligors increases unboundedly, and/or by accelerating the modulating Markov process, called rapid switching. We establish diffusion approximations, obtained by application of (semi)martingale central limit theorems. Depending on the specific circumstances, different approximations are found.
18‐year follow‐up of enzyme‐replacement therapy in two siblings with attenuated mucopolysaccharidosis I

Mucopolysaccharidosis type I (MPS I) is an autosomal recessive disorder caused by the deficiency of α‐L‐iduronidase and characterized by a progressive course with multisystem involvement. Clinically, MPS I is divided into two forms: (1) severe (Hurler syndrome), which presents in infancy and is characterized by rapid progressive neurological involvement; (2) attenuated (Hurler/Scheie and Scheie syndromes), which displays a slower progression and absent to mild nervous system involvement. The specific treatment for attenuated MPS I consists of enzyme‐replacement therapy with laronidase (human recombinant α‐L‐iduronidase, Aldurazyme). We present updated data after 18 years of laronidase treatment in two siblings affected by the attenuated form of MPS I who started therapy at 5 months and 5 years of age, respectively. Clinical and laboratory data of the siblings show that long‐term enzyme replacement therapy may improve/stabilize many symptoms already present at the time of the diagnosis and reduce the disease progression. This study confirms that early diagnosis and early initiation of enzyme‐replacement therapy are essential to modify positively the natural history of the attenuated form of MPS I.
Hierarchical domain structures associated with oxygen octahedra tilting patterns in lead-free (Bi1/2Na1/2)TiO3

Hierarchical domain structures associated with oxygen octahedra tilting patterns were observed in lead-free (Bi1/2Na1/2)TiO3 ceramics using aberration-corrected high-resolution transmission electron microscopy (HRTEM). Three types of domains are induced by distinct mechanisms: the ‘orientation-domain’ is induced at micrometer scale formed by different tilting orientations of the oxygen octahedra, the ‘meso-chemical-domain’ occurs at a few tens of nanometer scale by chemical composition variation on the A-site in the ABO3 perovskite structure, and the ‘nano-cluster-region’ runs across several unit-cells with apparent A-site cation segregation with oxygen vacancies clustering around Na cations. Based on HRTEM amplitude contrast imaging (ACI), the correlation between the oxygen octahedral tilting pattern and compositional non-stoichiometry was established. The role of the hierarchical domain structure associated with the tilting patterns of the oxygen octahedra on the ferroelectric behavior of (Bi1/2Na1/2)TiO3 is also discussed.
Reidemeister Torsion in Floer--Novikov Theory and Counting pseudo-holomorphic tori, II

This is the first part of an article in two parts, which builds the foundation of a Floer-theoretic invariant, (I_F). (See math.DG/0505013 for part II). The Floer homology can be trivial in many variants of the Floer theory; it is therefore interesting to consider more refined invariants of the Floer complex. We consider one such instance--the Reidemeister torsion (\tau_F) of the Floer-Novikov complex of (possibly non-hamiltonian) symplectomorphisms. (\tau_F) turns out NOT to be invariant under hamiltonian isotopies, but this failure may be fixed by introducing certain ``correction term'': We define a Floer-theoretic zeta function (\zeta_F), by counting perturbed pseudo-holomorphic tori in a way very similar to the genus 1 Gromov invariant. The main result of this article states that under suitable monotonicity conditions, the product (I_F:=\tau_F\zeta_F) is invariant under hamiltonian isotopies. In fact, (I_F) is invariant under general symplectic isotopies when the underlying symplectic manifold (M) is monotone. Because the torsion invariant we consider is not a homotopy invariant, the continuation method used in typical invariance proofs of Floer theory does not apply; instead, the detailed bifurcation analysis is worked out. This is the first time such analysis appears in the Floer theory literature in its entirety. Applications of (I_F), and the construction of (I_F) in different versions of Floer theories are discussed in sequels to this article.
Combined Effect of Layered Double Hydroxides and Nano silver on Bacterial Inhibition and Gas Barrier Properties of Chitosan Grafted Polyacrylonitrile Nanocomposites

ABSTRACT Herein, chitosan-grafted-poly(acrylonitrile) (CS-g-PAN) nanocomposites are prepared by emulsifier-free emulsion polymerization technique with dispersion of layered double hydroxides(LDHs) and nano silver(AgNPs). The interactions of AgNPs and LDH with co-polymeric matrix are investigated by FTIR and XRD. It is noticed that LDH platelets are intercalated and partially exfoliated within the copolymeric matrices. Dispersion of fillers creates tortuous path which enhances the gas barrier properties up to seven folds. Antibacterial behavior of nanocomposites is achieved due to incorporation of silver nanoparticles and LDH. Thermal stability, chemical resistance and biodegradable properties of the synthesized material are also increased due to combined effect of LDH and AgNPs. Graphical Abstract
The bulk-edge correspondence for continuous dislocated systems

We study topological aspects of defect modes for a family of operators $\{\mathscr{P}(t)\}_{t \in [0,2\pi]}$ on $L^2(\mathbb{R})$. $\mathscr{P}(t)$ is a periodic Schrodinger operator $P_0$ perturbed by a dislocated potential. This potential is periodic on the left and on the right, but acquires a phase defect $t$ from $-\infty$ relative to $+\infty$. When $t=\pi$ and the dislocation is small and adiabatic, Fefferman, Lee-Thorp and Weinstein showed in previous work that Dirac points of $P_0$ (degeneracies in the band spectrum of $P_0$) bifurcate to defect modes of $\mathscr{P}(\pi)$. We show that these modes are topologically protected at the level of the family $\{\mathscr{P}(t)\}_{t \in [0,2\pi]}$. This means that local perturbations cannot remove these states for all values of $t$, even outside the small adiabatic regime studied by Fefferman$-$Lee-Thorp$-$Weinstein. We define two topological quantities: an edge index (the signed number of eigenvalues crossing an energy gap as $t$ runs from $0$ to $2\pi$) and a bulk index (the Chern number of a Bloch eigenbundle for the periodic operator near $+\infty$). We prove that these indexes are equal to the same odd winding number. This shows the bulk-edge correspondence for the family $\{\mathscr{P}(t)\}_{t \in [0,2\pi]}$. We express this winding number in terms of the asymptotic shape of the dislocation and of the Dirac point Bloch modes. We illustrate the topological depth of our model via the computation of the bulk/edge index on a few examples.
Validation of the Steinberg Parenting Styles Scale in Peruvian adolescents

Abstract Introduction: There are numerous scales of parenting styles adapted for Peruvian adolescents. In addition, some report a structural model that does not match the model of the original version. Objective: Evaluate the psychometric properties of the Steinberg’s Parenting Styles Scale in Peruvian adolescents. Method: The sample included 563 students. A model of relationships in three dimensions is conﬁrmed: involvement, psychological autonomy, and parental supervision. Results: The analysis suggested the elimination of ﬁve items. The resulting scale shows a good ﬁt: χ 2 = 469.051, df = 184, χ 2 /df = 2.54, CFI = . 95, TLI = . 94, RMSEA = . 053, SRMR = . 063. Likewise, it shows an optimal internal consistency determined by the McDonald’s omega index. Conclusion: The internal structure of the questionnaire was similar to the original questionnaire and presented adequate reliability and construct validity. however, additional studies with larger age range samples and diﬀerent Peruvian subcultures are required to achieve its generalization.
Coordinates on the augmented moduli space of convex RP2 structures

Let S be an orientable, finite‐type surface with negative Euler characteristic. The augmented moduli space of convex real projective structures on S was first defined and topologized by the first author. In this paper, we give an explicit description of this topology using explicit coordinates. More precisely, given every point in this augmented moduli space, we find explicit continuous coordinates on the quotient of a suitable open neighborhood about this point by a suitable subgroup of the mapping class group of S . Using this, we give a simpler proof of the fact that the augmented moduli space of convex real projective structures on S is homeomorphic to the orbifold vector bundle of regular cubic differentials over the Deligne–Mumford compactification of the moduli space of Riemann surfaces homeomorphic to S .
Counting cusp forms by analytic conductor

The universal family is the set of cuspidal automorphic representations of bounded analytic conductor on ${\rm GL}_n$ over a number field. We prove an asymptotic for the universal family, under a spherical assumption at the archimedean places when $n\geqslant 3$. We interpret the leading term constant geometrically and conjecturally determine the underlying Sato--Tate measure. Our methods naturally provide uniform Weyl laws with explicit level savings and strong quantitative bounds on the non-tempered discrete spectrum for ${\rm GL}_n$.
Caveolae and Bin1 form ring-shaped platforms for T-tubule initiation

Excitation-contraction coupling requires a highly specialized membrane structure, the triad, composed of a plasma membrane invagination, the T-tubule, surrounded by two sarcoplasmic reticulum terminal cisternae. Although the precise mechanisms governing T-tubule biogenesis and triad formation remain largely unknown, studies have shown that caveolae participate in T-tubule formation and mutations of several of their constituents induce muscle weakness and myopathies. Here, we demonstrate that, at the plasma membrane, caveolae composed of caveolin-3 and Bin1 assemble into ring-like structures from which emerge tubes enriched in the dihydropyridine receptor. Overexpression of Bin1 lead to the formation of both rings and tubes and we show that Bin1 forms scaffolds on which caveolae accumulate to form the initial T-tubule. Cav3 deficiency caused by either gene silencing or pathogenic mutations cause defective ring formation and perturbed Bin1-mediated tubulation that may explain defective T-tubule organization in mature muscles. Our results uncover new pathophysiological mechanisms that may prove relevant to myopathies caused by Cav3 or Bin1.
Overflow of Working Memory from an Easily Accessible Active State

Working memory is a system that realizes short-term memory retention and is essential to everyday activities. Recently, it has been suggested that working memory items can be maintained in both an active state with sustained neural activity and a latent state without any explicit neural activity. However, how easily we can retrieve memories in each state and how much information can be retained in the active state remains unknown. Here, we addressed these questions by adopting a novel experimental paradigm for measuring the reaction time required to recall a letter of the alphabet when presented with a corresponding color, based on memorized color/letter pairs. The results demonstrated that when participants retained only two pairs of items, they could recall both pairs similarly quickly. However, when there were two or more memorized pairs, the most recent or internally attended pairs were recalled more quickly than the other pairs. These results suggest that memories in the “active” state are accessed first and memories that have overflowed into the “latent” state are accessed afterward. Additionally, the capacity of the easily accessible active state is extremely limited (to approximately two chunks of information) compared with the traditionally considered working memory capacity (four to seven chunks). These results provide robust behavioral support for the co-existence of multiple states in working memory and underscore the need for a more detailed classification of the working memory capacity. SIGNIFICANCE STATEMENT We sometimes cannot quickly retrieve what we are sure we remember. Regarding working memory retrieval, we observed a phenomenon that the most recently encoded memory was retrieved quickly whereas others were retrieved afterward, showing an “overflow” of memory items from an easily accessible active state. This observation has two critical implications: 1) when maintaining multiple items in working memory, not all items are functionally the same, and there is a dissociation between easily accessible active items and items that have overflowed to a latent state; 2) the number of items that can be maintained in the active state is two, which is remarkably smaller than the traditionally considered working memory capacity of four, necessitating the update of working memory models.
On rational maps from the product of two general curves

This paper treats the dominant rational maps from the product of two very general curves to nonsingular projective surfaces. Combining the result by Bastianelli and Pirola, we prove that the product of two very general curves of genus $g\geq 7$ and $g'\geq 3$ does not admit dominant rational maps of degree $> 1$ if the image surface is non-ruled. We also treat the case of the 2-symmetric product of a curve.
Room-temperature crystallography reveals altered binding of small-molecule fragments to PTP1B

Much of our current understanding of how small-molecule ligands interact with proteins stems from X-ray crystal structures determined at cryogenic (cryo) temperature. For proteins alone, room-temperature (RT) crystallography can reveal previously hidden, biologically relevant alternate conformations. However, less is understood about how RT crystallography may impact the conformational landscapes of protein-ligand complexes. Previously we showed that small-molecule fragments cluster in putative allosteric sites using a cryo crystallographic screen of the therapeutic target PTP1B (Keedy*, Hill*, 2018). Here we have performed two RT crystallographic screens of PTP1B using many of the same fragments, representing the largest RT crystallographic screens of a diverse library of ligands to date, and enabling a direct interrogation of the effect of data collection temperature on protein-ligand interactions. We show that at RT, fewer ligands bind, and often more weakly -- but with a variety of temperature-dependent differences, including unique binding poses, changes in solvation, new binding sites, and distinct protein allosteric conformational responses. Overall, this work suggests that the vast body of existing cryogenic-temperature protein-ligand structures may provide an incomplete picture, and highlights the potential of RT crystallography to help complete this picture by revealing distinct conformational modes of protein-ligand systems. Our results may inspire future use of RT crystallography to interrogate the roles of protein-ligand conformational ensembles in biological function.
Higher string topology on general spaces

In this paper, I give a generalized analogue of the string topology results of Chas and Sullivan, and of Cohen and Jones. For a finite simplicial complex X and k ⩾ 1, I construct a spectrum Maps(Sk, X)S(X), which is obtained by taking a generalization of the Spivak bundle on X (which however is not a stable sphere bundle unless X is a Poincaré space), pulling back to Maps(Sk, X) and quotienting out the section at infinity. I show that the corresponding chain complex is naturally homotopy equivalent to an algebra over the (k + 1)‐dimensional unframed little disk operad Ck + 1. I also prove a conjecture of Kontsevich, which states that the Quillen cohomology of a based Ck‐algebra (in the category of chain complexes) is equivalent to a shift of its Hochschild cohomology, as well as prove that the operad C*Ck is Koszul‐dual to itself up to a shift in the derived category. This gives one a natural notion of (derived) Koszul dual C*Ck‐algebras. I show that the cochain complex of X and the chain complex of Ωk X are Koszul dual to each other as C*Ck‐algebras, and that the chain complex of Maps(Sk, X)S(X) is naturally equivalent to their (equivalent) Hochschild cohomology in the category of C* Ck‐algebras. 2000 Mathematics Subject Classification 55P48 (primary), 16E40, 55N45, 18D50 (secondary).