Miracle-dz/UniFAR-FTUs huggingface dataset:
Gopakumar–Vafa invariants and wall-crossing

In this paper, we generalize a mathematical definition of Gopakumar-Vafa (GV) invariants on Calabi-Yau 3-folds introduced by Maulik and the author, using an analogue of BPS sheaves introduced by Davison-Meinhardt on the coarse moduli spaces of one dimensional twisted semistable sheaves with arbitrary holomorphic Euler characteristics. We show that our generalized GV invariants are independent of twisted stability conditions, and conjecture that they are also independent of holomorphic Euler characteristics, so that they define the same GV invariants. As an application, we will show the flop transformation formula of GV invariants.
Effects of non-thermal atmospheric plasma on human periodontal ligament mesenchymal stem cells

Here we investigate the influences of non-thermal atmospheric plasma on human mesenchymal stem cells isolated from periodontal ligament (hPDL-MSCs). A specially redesigned plasma needle was used as the source of low-temperature plasma and its effects on different hPDL-MSC functions were investigated. Cell cultures were obtained from extracted normal impacted third molars and characterized for their phenotype and multi-potential differentiation. The hPDL-MSCs possessed all the typical MSC properties, including clonogenic ability, high proliferation rate, specific phenotype and multilineage differentiation. The data regarding the interaction of plasma with hPDL-MSCs demonstrated that plasma treatment inhibited the migration of hPDL-MSCs and induced some detachment, while not affecting their viability. Additionally, plasma significantly attenuated hPDL-MSCs' proliferation, but promoted their osteogenic differentiation. The results of this study indicated that a non-thermal plasma offers specific activity with non-destructive properties that can be advantageous for future dental applications.
Grothendieck duality under Spec Z

We define the derived category of a concrete category in a way which extends the usual definition of the derived category of a ring, and we prove that the bounded-below derived category of $\Spec \mathbb{M}_0$ (an approximation, used by e.g. Connes and Consani, to "$\Spec$ of the field with one element") is the stable homotopy category of connective spectra. We also describe some basic features of Grothendieck duality for the map from $\Spec \mathbb{Z}$ to $\Spec \mathbb{M}_0$, or, what comes to the same thing, the map from $\Spec \mathbb{Z}$ to $\Spec$ of the sphere spectrum; these basic features include a computation of the homology of the dualizing complex $f^! (S)$ of abelian groups associated to the sphere spectrum.
The Toda conjecture

We study the Toda conjecture of Eguchi and Yang for the Gromov-Witten invariants of CP^1,using the bihamiltonian method of the formal calculus of variations. We also study its relationship to the Virasoro conjecture for CP^1, recently proved by Givental (math.AG/0108100).
Abelian Chern–Simons theory. I. A topological quantum field theory

We give a construction of the Abelian Chern–Simons gauge theory from the point of view of a 2+1-dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas that have been previously explored in connection to the non-Abelian Chern–Simons theory [J. Diff. Geom. 33, 787–902 (1991); Topology 32, 509–529 (1993)]. We formulate the topological quantum field theory in terms of the category of extended 2- and 3-manifolds introduced in a preprint by Walker in 1991 and prove that it satisfies the axioms of unitary topological quantum field theories formulated by Atiyah [Publ. Math. Inst. Hautes Etudes Sci. Pans 68, 175–186 (1989)].
The Role of Potential Vorticity Generation in Tropical Cyclone Rainbands

Abstract The implied heating and potential vorticity generation in tropical cyclone rainbands is derived from observed vertical motion profiles. High levels of potential vorticity generation are found in the stratiform rain regions, sufficient to generate substantial wind maxima along the bands within a couple of hours. Such generation may represent a significant source of potential vorticity for the system as a whole and may have implications for cyclone intensity.
Abelian right perpendicular subcategories in module categories

We show that an abelian category can be exactly, fully faithfully embedded into a module category as the right perpendicular subcategory to a set of modules or module morphisms if and only if it is a locally presentable abelian category with a projective generator, or in other words, the category of models of an additive algebraic theory of possibly infinite bounded arity. This includes the categories of contramodules over topological rings and other examples. Various versions of the definition of the right perpendicular subcategory are considered, all leading to the same class of abelian categories. We also discuss sufficient conditions under which the natural forgetful functors from the categories of contramodules to the related categories of modules are fully faithful.
Lagrangian cobordism. I

This paper discusses the cobordism of Lagrangian submanifolds (in the monotone setting) and structures it as a category that is related in a functorial way to an appropriate (derived) Fukaya category. Are also discussed obstructions to cobordism based on properties of Lagrangian quantum homology, relations to Lagrangian surgery, as well as examples of non-isotopic but cobordant Lagrangians. This is a revision of our earlier preprint from September 2011.
Accurate device simulations through CD-SEM-based edge-contour extraction

A new methodology to predict changes in device performances due to systematic lithography and etch effects is described in this paper. Our methodology consists on Automatic Edge-Contour-Extraction (ECE) on Poly Over Active Layer, taking along the manufacturing variability. In general, the AMAT SEM (Scanning Electron Microscopy) ECE algorithm is based on CAD (GDS) to SEM pattern recognition, followed by CD based 2D edge extraction. Device modeling (using SPICE simulation) is used, to predict the nominal values as well as the device performances variability of the transistors drive current (Ion) and leakage current (Ioff). We used our method to compare a classical (simple rectangular) transistors and "U-Shape AA" transistors, both manufactured using Tower TS013LL (0.13um Low-Leakage) Platform. It was found, as predicted, that U-shape transistors have larger W distribution. However, "U-shape" also showed much tighter L distribution and the overall Ion spread is lower comparing to classical transistors. Also, U-Shape transistors found to have lower Lstdev (gate length distribution of each individual transistor). We also used the ECE methodology, to compare transistors of single side dog-bone to double-side dog-bone. Based on our work, we can predict that single-side dog-bone transistors, will have higher and larger Ioff distributions, and the overall Ioff speared along the wafer, will go up to a factor of x2.5.
Graphical representations of Ising and Potts models

Statistical physics seeks to explain macroscopic properties of matter in terms of microscopic interactions. Of particular interest is the phenomenon of phase transition: the sudden changes in macroscopic properties as external conditions are varied. Two models in particular are of great interest to mathematicians, namely the Ising model of a magnet and the percolation model of a porous solid. These models in turn are part of the unifying framework of the random-cluster representation, a model for random graphs which was first studied by Fortuin and Kasteleyn in the 1970’s. The random-cluster representation has proved extremely useful in proving important facts about the Ising model and similar models. In this work we study the corresponding graphical framework for two related models. The first model is the transverse field quantum Ising model, an extension of the original Ising model which was introduced by Lieb, Schultz and Mattis in the 1960’s. The second model is the space–time percolation process, which is closely related to the contact model for the spread of disease. In Chapter 2 we define the appropriate space–time random-cluster model and explore a range of useful probabilistic techniques for studying it. The space– time Potts model emerges as a natural generalization of the quantum Ising model. The basic properties of the phase transitions in these models are treated in this chapter, such as the fact that there is at most one unbounded fk-cluster, and the resulting lower bound on the critical value in Z. In Chapter 3 we develop an alternative graphical representation of the quantum Ising model, called the random-parity representation. This representation is based on the random-current representation of the classical Ising model, and allows us to study in much greater detail the phase transition and critical behaviour. A major aim of this chapter is to prove sharpness of the phase transition in the quantum Ising model—a central issue in the theory— and to establish bounds on some critical exponents. We address these issues by using the random-parity representation to establish certain differential inequalities, integration of which gives the results. In Chapter 4 we explore some consequences and possible extensions of the results established in Chapters 2 and 3. For example, we determine the critical point for the quantum Ising model in Z and in ‘star-like’ geometries.
Fourier multipliers in $\mathrm{SL}_n(\mathbf{R})$

We establish precise regularity conditions for $L_p$-boundedness of Fourier multipliers in the group algebra of $SL_n(\mathbf{R})$. Our main result is inspired by Hormander-Mikhlin criterion from classical harmonic analysis, although it is substantially and necessarily different. Locally, we get sharp growth rates of Lie derivatives around the singularity and nearly optimal regularity order. The asymptotics also match Mikhlin formula for a exponentially growing metric with respect to the word length. Additional decay comes imposed by this growth and Mikhlin condition for high order terms. Lafforgue/de la Salle's rigidity theorem fits here. The proof includes a new relation between Fourier and Schur $L_p$-multipliers for nonamenable groups. In $SL_n(\mathbf{R})$, this holds in terms of Harish-Chandra's almost $L_2$ matrix coefficients. By transference, matters are reduced to a rather nontrivial $RC_p$-inequality for $SL_n(\mathbf{R})$-twisted forms of Riesz transforms associated to fractional laplacians. Our second result gives a new and much stronger rigidity theorem for radial multipliers in $SL_n(\mathbf{R})$. More precisely, additional regularity and Mikhlin type conditions are proved to be necessary up to an order $\sim |\frac12 - \frac1p| (n-1)$ for large enough $n$ in terms of $p$. Locally, necessary and sufficient growth rates match up to that order. Asymptotically, extra decay for the symbol and its derivatives imposes more accurate and additional rigidity in a wider range of $L_p$-spaces. This rigidity increases with the rank, so we can construct radial generating functions satisfying our Hormander-Mikhlin sufficient conditions in rank $n$ and failing the rigidity conditions for ranks $m >> n$. We also prove automatic regularity and rigidity estimates for first and higher order derivatives of $\mathrm{K}$-biinvariant multipliers in the rank 1 groups $SO(n,1)$.
On a generalized Appell system and monogenic power series

Recently Appell systems of monogenic polynomials in ℝ3 were constructed by several authors. Main purpose of this paper is the description of another Appell system that is complete in the space of square integrable quaternion‐valued functions. A new Taylor‐type series expansion based on the Appell polynomials is presented, which can be related to the corresponding Fourier series analogously as in the complex one‐dimensional case. These results find applications in the description of the hypercomplex derivative, the monogenic primitive of a monogenic function and the characterization of functions from the monogenic Dirichlet space. Copyright © 2009 John Wiley & Sons, Ltd.
The relationship between gross profit, operating profit and net income and future returns in Brazil BETWEEN GROSS PROFIT, OPERATING PROFIT AND NET INCOME AND FUTURE RETURNS IN

Objective: The objective of this study was to verify which of the profit definitions (gross profit, operating profit or net profit) performs better in explaining the future behavior of returns in the Brazilian market, and whether these results are maintained when forming portfolios combining profitability, book-to-market indexes and BrF_Score. Method: To this end, the Fama and MacBeth two-stage regressions, Hotelling's T2 test and Fama and French's three-factor model are used, in addition to the analysis of the excess returns of the portfolios built. The periodicity of the study is monthly, covering the period from January 2010 to June 2019, totaling 15,577 observations from 200 firms. Results: The results show that net income and operating income produce the profitability metrics with the greatest explanatory powers for one-month forward returns, and produce the portfolios with the highest excess returns compared to profitability metrics based on gross profit. Contributions: Therefore, the contribution of the paper was to show that net income explains future returns better in the Brazilian market, while in the American market, there is evidence that gross profit plays this role, and these differences are due to the different macroeconomic influences suffered by such markets. that all increases in explanatory power are statistically significant, indicating that all profitability to the model, confirming the usefulness of taking into account the profitability when designing an investment strategy.
Time for Pragmatism Huw

: Are the passage of time and the distinction between past and future features of the world in itself, or manifestations of the human perspective? The latter view has much in common with pragmatism, though few of its proponents think of themselves as pragmatists, and pragmatists are often unaware of this congenial application of their methodology. This link between time and pragmatism only scratches the surface of the deep two-way dependencies between these two topics. The human temporal perspective turns out to be deeply implicated not merely in our temporal notions themselves, but in many other conceptual categories – arguably, in fact, in all of them, and in the nature of language and thought. In this way, reflection on our own temporal character vindicates James’ famous slogan for global pragmatism: ‘The trail of the human serpent is thus over everything. ’
On the nonlinear impulsive ψ-Hilfer fractional differential equations

In this paper, we consider the nonlinear Ψ-Hilfer impulsive fractional differential equation. Our main objective is to derive the formula for the solution and examine the existence and uniqueness of solutions. The acquired results are extended to the nonlocal Ψ-Hilfer impulsive fractional differential equation. We gave an applications to the outcomes we obtained. Further, examples are provided in support of the results we got.
When Schools Do Not Like Students: Direct and Spillover Effects of Cream-Skimming

Cream skimming occurs when private or charter schools attract the best students from public schools, draining the latter of higher performing students. This paper studies the effect of school-side student selection on this pattern and its direct and spillover effects on students’ outcomes. Using rich administrative data from Chile, we document strong evidence of school-side selection in publicly subsidized private schools, explaining up to 20 percent of the performance gap with respect to public schools. Leveraging centralized admission lotteries to simulate the distribution of potential classroom compositions, we estimate the impact of this screening on students’ academic performance, college enrollment, and behavioral outcomes. While we document value-added benefits of attending selective schools, we find no difference between effects on low and high income students. These findings oppose school-student fit as the major driver for screening. In contrast, we find support for sizeable peer effects in classrooms that received lottery-induced shocks to their class composition, which potentially explains schools’ implementation of screening practices. ∗Escobar Salce and Mart́ınez: Harris School of Public Policy, University of Chicago. Emails: descobarsalce@uchicago.edu; mariaadelaidamc@uchicago.edu. All remaining errors are ours.
Vafa-Witten invariants for projective surfaces II: semistable case.

On a polarised surface, solutions of the Vafa-Witten equations correspond to certain polystable Higgs pairs. When stability and semistability coincide, the moduli space admits a symmetric obstruction theory and a $\mathbb C^*$ action with compact fixed locus. Applying virtual localisation we define invariants constant under deformations. When the vanishing theorem of Vafa-Witten holds, the result is the (signed) Euler characteristic of the moduli space of instantons. In general there are other, rational, contributions. Calculations of these on surfaces with positive canonical bundle recover the first terms of modular forms predicted by Vafa and Witten.
Fault-ignorant quantum search

We investigate the problem of quantum searching on a noisy quantum computer. Taking a fault-ignorant approach, we analyze quantum algorithms that solve the task for various different noise strengths, which are possibly unknown beforehand. We prove lower bounds on the runtime of such algorithms and thereby find that the quadratic speedup is necessarily lost (in our noise models). However, for low but constant noise levels the algorithms we provide (based on Groverʼs algorithm) still outperform the best noiseless classical search algorithm.
Non-Gravity Trade – Globalization Institute Working Paper No. 388 – Dallas Fed

This paper examines the relationship between countries’ bilateral trade with the United States that is not due to gravity (non-gravity trade) and the distribution of income within countries. In countries where only a small share of the population is educated, an increase in non-gravity trade is associated with a significant increase in income inequality. As education of the population increases, the correlation between non-gravity trade and income inequality becomes smaller. Non-gravity trade has no significant effect on income inequality in countries that are world leaders in education.
of Biogeography Disease biogeography: spatial and temporal analyses of infectious disease burden at the country-level scale provides new insights and challenges

In a recent study, Wood et al. (2017 Phil. Trans. Roy. Soc. B 372, 20160122) utilized a novel set of spatial and temporal analyses to identify which factors were most strongly correlated with changes in human infectious disease burdens from 1990 to 2010 in 60 countries. Using the statistical analyses and findings of this article as a framework, I have identified three important insights and challenges that this research presents for disease biogeography moving forward. First, the main factor still limiting disease biogeography research progress is underreported or absent data – particularly in the case of neglected tropical diseases. Second, the use of disability-adjusted life years instead of indirect measures of disease burden should be a focal point of disease biogeography research since it allows for comparisons of lethal and non-lethal diseases. Finally, disease biogeography studies that utilize country-level statistical analyses may be better at identifying demographic and economic drivers than environmental or biological drivers.
On unconventional limit sets of contractive functions on $\mathbb Z_p$

In the present paper, we are going to study metric properties of unconventional limit set of a semigroup $G$ generated by contractive functions $\{f_{i}\}_{i=1}^N$ on the unit ball $\mathbb Z_p$ of $p$-adic numbers. Namely, we prove that the unconventional limit set is compact, perfect and uniformly disconnected. Moreover, we provide an example of two contractions for which the corresponding unconventional limiting set is quasi-symmetrically equivalent to the symbolic Cantor set.
Observational Constraints on Interstellar Grain Alignment

We present new multicolor photopolarimetry of stars behind the Southern Coalsack. Analyzed together with multiband polarization data from the literature, probing the Chamaeleon I, Musca, ρ Opiuchus, R CrA, and Taurus clouds, we show that the wavelength of maximum polarization (λmax) is linearly correlated with the radiation environment of the grains. Using far-infrared emission data, we show that the large scatter seen in previous studies of λmax as a function of AV is primarily due to line-of-sight effects causing some AV measurements to not be a good tracer of the extinction (radiation field strength) seen by the grains being probed. The derived slopes in λmax versus AV, for the individual clouds, are consistent with a common value, while the zero intercepts scale with the average values of the ratios of total to selective extinction (RV) for the individual clouds. Within each cloud we do not find direct correlations between λmax and RV. The positive slope is consistent with recent developments in theory and indicating alignment driven by the radiation field. The present data cannot conclusively differentiate between direct radiative torques and alignment driven by H2 formation. However, the small values of λmax(AV = 0), seen in several clouds, suggest a role for the latter, at least at the cloud surfaces. The scatter in the λmax versus AV relation is found to be associated with the characteristics of the embedded YSOs in the clouds. We propose that this is partially due to locally increased plasma damping of the grain rotation caused by X-rays from the YSOs.
Examining User Preferences based on Personality Factors in Graphical User Interface Design

Individual differences play a major role in human-computer interaction. In particular, personality shapes how we process and act on the world, and how users perceive and accept technology. Nevertheless, there is limited evidence on the effect of different personality types in graphical user interface design preferences. Weighting how personality affects perception, we leverage in-depth synergies between personality variables and design preferences for graphical user interface elements to study whether it is possible to formulate a novel set of design guidelines that allow the creation of user interfaces customized to psychological variables. A clustering approach of the subjects (N=65) yielded three different personality profiles based on the personality variables of the Five-Factor Model. Then, an association rules algorithm produced a set of rules from which we created a set of design guidelines. We discuss the study implications and future work opportunities.