Miracle-dz/UniFAR-FTUs huggingface dataset:
Systolic geometry and simplicial complexity for groups

Abstract Twenty years ago Gromov asked about how large is the set of isomorphism classes of groups whose systolic area is bounded from above. This article introduces a new combinatorial invariant for finitely presentable groups called simplicial complexity that allows to obtain a quite satisfactory answer to his question. Using this new complexity, we also derive new results on systolic area for groups that specify its topological behaviour.
Gas cooling in semi-analytic models and smoothed particle hydrodynamics simulations: are results consistent?: Gas cooling in SAMs and SPH simulations

We present a detailed comparison between the galaxy populations within a massive cluster, as predicted by hydrodynamical smoothed particle hydrodynamics (SPH) simulations and by a semi-analytic model (SAM) of galaxy formation. Both models include gas cooling and a simple prescription of star formation, which consists in transforming instantaneously any cold gas available into stars, while neglecting any source of energy feedback. This simplified comparison is thus not meant to be compared with observational data, but is aimed at understanding the level of agreement, at the stripped-down level considered, between two techniques that are widely used to model galaxy formation in a cosmological framework and which present complementary advantages and disadvantages. We find that, in general, galaxy populations from SAMs and SPH have similar statistical properties, in agreement with previous studies. However, when comparing galaxies on an object-by-object basis, we find a number of interesting differences: (i) the star formation histories of the brightest cluster galaxies (BCGs) from SAM and SPH models differ significantly, with the SPH BCG exhibiting a lower level of star formation activity at low redshift, and a more intense and shorter initial burst of star formation with respect to its SAM counterpart; (ii) while all stars associated with the BCG were formed in its progenitors in the SAM used here, this holds true only for half of the final BCG stellar mass in the SPH simulation, the remaining half being contributed by tidal stripping of stars from the diffuse stellar component associated with galaxies accreted on the cluster halo; (iii) SPH satellites can lose up to 90 per cent of their stellar mass at the time of accretion, due to tidal stripping, a process not included in the SAM used in this paper; (iv) in the SPH simulation, significant cooling occurs on the most massive satellite galaxies and this lasts for up to 1 Gyr after accretion. This physical process is not included in the SAM used in this paper, as well as in most of the models discussed in the recent literature. Our results identify specific directions of improvements for our methods to study galaxy formation in a hierarchical universe.
Family of bound entangled states on the boundary of the Peres set

Bound entangled (BE) states are strange in nature: non-zero amount of free entanglement is required to create them but no free entanglement can be distilled from them under local operations and classical communication (LOCC). Even though usefulness of such states has been shown in several information processing tasks, there exists no simple method to characterize all these states for an arbitrary composite quantum system. Here we present a $(d-3)/2$-parameter family of BE states each with positive partial transpose (PPT). This family of PPT-BE states is introduced by constructing an unextendible product basis (UPB) in $\mathbb{C}^d\otimes\mathbb{C}^d$ with $d$ odd and $d\ge 5$. We also provide the `tile structure' corresponding to these UPBs. The range of each such PPT-BE state is contained in a $2(d-1)$ dimensional entangled subspace whereas the associated UPB-subspace is of dimension $(d-1)^2+1$. We further show that each of these PPT-BE states can be written as a convex combination of $(d-1)/2$ number of rank-4 PPT-BE states. Moreover, we prove that these rank-4 PPT-BE states are extreme points of the convex compact set $\mathcal{P}$ of all PPT states in $\mathbb{C}^d\otimes\mathbb{C}^d$, namely the {\it Peres} set. An interesting geometric implication of our result is that the convex hull of these rank-4 PPT-BE extreme points -- the $(d-3)/2$-simplex -- is sitting on the boundary between the set $\mathcal{P}$ and the set of non-PPT states. We also discuss consequences of our construction in the context of quantum state discrimination by LOCC.
Dyadic cubes in spaces of homogeneous type

The system of Euclidean dyadic cubes used in harmonic analysis can be generalized to more abstract spaces. In this text, we present Michael Christ’s construction of dyadic cubes in a space of homogeneous type, i.e. a quasi-metric space with a doubling measure. The essential properties of the dyadic cubes are that they form a tree structure such that any two of them are either disjoint or one is contained in the other, and that each generation of cubes covers the whole space excluding a possible set of measure zero. In addition, dyadic cubes are not too far away from balls in the sense that they are bounded by balls of the same magnitude from inside and outside.
"Pudding mold" band drives large thermopower in NaxCoO2

In the present study, we pin down the origin of the coexistence of the large thermopower and the low resistivity in Na x CoO 2 . It is revealed that not just the density of states (DOS), the effective mass, nor the band width, but the peculiar shape of the a 1 g band referred to as the “pudding mold” type, which consists of a dispersive portion and a somewhat flat portion, is playing an important role in this phenomenon. The present study provides a new guiding principle for designing good thermoelectric materials.
Genus Two Stable Maps, Local Equations and Modular Resolutions

We geometrically describe a canonical sequence of modular blowups of the relative Picard stack of the Artin stack of pre-stable genus two curves. The final blowup stack locally diagonalizes certain tautological derived objects. This implies a resolution of the primary component of the moduli space of genus two stable maps to projective space and meanwhile makes the whole moduli space admit only normal crossing singularities. Our approach should extend to higher genera.
Time dependent quantum scattering theory on complete manifolds with a corner of codimension 2

We show the existence and orthogonality of wave operators naturally associated to a compatible Laplacian on a complete manifold with a corner of codimension 2. In fact, we prove asymptotic completeness i.e. that the image of these wave operators is equal to the space of absolutely continuous states of the compatible Laplacian. We achieve this last result using time dependent methods coming from many-body Schr\"odinger equations.
A Description of Totally Reflexive Modules for a Class of non-Gorenstein Rings

We consider local non-Gorenstein rings of the form $(S_i,\mathfrak{n}_i)=k[X, Y_1, \ldots ,Y_i]/\left(X^2, (Y_1, \ldots, Y_i)^2\right), $ where $i\geq 2. $ We show that every totally reflexive $S_i$-module has a presentation matrix of the form $I x + \sum_{j=1}^i B_j y_j, $ where $I$ is the identity matrix and $B_j$ is an square matrix with entries in the residue field, $k$. From there, we prove that there exists a bijection between the set of isomorphism classes of totally reflexive modules (without projective summands) over $S_i$ which are minimal generated by $n$ elements and the set of $i$-tuples of $n \times n$ matrices with entries in $k$ modulo a certain equivalence relation.
Veto Interval Graphs and Variations

We introduce a variation of interval graphs, called veto interval (VI) graphs. A VI graph is represented by a set of closed intervals, each containing a point called a veto mark. The edge $ab$ is in the graph if the intervals corresponding to the vertices $a$ and $b$ intersect, and neither contains the veto mark of the other. We find families of graphs which are VI graphs, and prove results towards characterizing the maximum chromatic number of a VI graph. We define and prove similar results about several related graph families, including unit VI graphs, midpoint unit VI (MUVI) graphs, and single and double approval graphs. We also highlight a relationship between approval graphs and a family of tolerance graphs.
Classical scale-invariance, the electroweak scale and vector dark matter

We consider a classically scale-invariant extension of the standard model in which a dark, non-Abelian gauge symmetry is spontaneously broken via the Coleman-Weinberg mechanism. Higgs portal couplings between the dark and standard model sectors provide an origin for the Higgs mass squared parameter and, hence, the electroweak scale. We find that choices for model parameters exist in which the dark gauge multiplet is viable as dark matter.
A new $\operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$-invariant of dessins d'enfants

We study the action of $\operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ on the category of Belyi functions (finite, \'{e}tale covers of $\mathbb{P}^1_{\overline{\mathbb{Q}}}\setminus \{0,1,\infty\}$). We describe a new combinatorial $\operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$-invariant for whose monodromy cycle types above $0$ and $\infty$ are the same. We use a version of our invariant to prove that $\operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ acts faithfully on the set of Belyi functions whose monodromy cycle types above 0 and $\infty$ are the same; the proof of this result involves a version of Belyi's Theorem for odd degree morphisms. Using our invariant, we obtain that for all $k < 2^{\sqrt{\frac{2}{3}}}$ and all positive integers $N$, there is an $n \le N$ such that the set of degree $n$ Belyi functions of a particular rational Nielsen class must split into at least $\Omega\left(k^{\sqrt{N}}\right)$ Galois orbits.
Linearized internal functionals for anisotropic conductivities

This paper concerns the reconstruction of an anisotropic conductivity tensor in an elliptic second-order equation from knowledge of the so-called power density functionals. This problem finds applications in several coupled-physics medical imaging modalities such as ultrasound modulated electrical impedance tomography and impedance-acoustic tomography. We consider the linearization of the nonlinear hybrid inverse problem. We find sufficient conditions for the linearized problem, a system of partial differential equations, to be elliptic and for the system to be injective. Such conditions are found to hold for a lesser number of measurements than those required in recently established explicit reconstruction procedures for the nonlinear problem.
Two-colour atom guide and 1D optical lattice using evanescent fields of high-order transverse modes

We propose a two-colour scheme of atom guide and 1D optical lattice using evanescent light fields of TE00 and TE01 transverse modes in an optical waveguide. The optical waveguide carries red-detuned light and blue-detuned light, with both modes far from resonance. The atom guide and 1D optical lattice potentials can be transformed to each other by using a Mach–Zehnder interferometer to accurately control mode transformation. This might provide a new approach to realize flexible transition between the guiding and trapping states of atoms.
On self-avoiding polygons and walks: counting, joining and closing

For d at least two and integer n, let c_n = c_n(d) denote the number of length n self-avoiding walks beginning at the origin in the integer lattice Z^d, and, for even n, let p_n = p_n(d) denote the number of length n self-avoiding polygons in Z^d up to translation. Then the probability under the uniform law W_n on self-avoiding walks Gamma of any given odd length n beginning at the origin that Gamma closes -- i.e., that Gamma's endpoint is a neighbour of the origin -- is given by W_n ( Gamma closes ) = 2(n+1) p_{n+1}/c_n. The polygon and walk cardinalities share a common exponential growth: lim_n c_n^{1/n} = lim_{n even} p_n^{1/n} = mu (where the common value mu is called the connective constant). Madras [26] has shown that p_n is at most C n^{-1/2} mu^n in dimension d=2, while the closing probability was recently shown in [12] to satisfy W_n ( Gamma closes ) is at most n^{-1/4 + o(1)} in any dimension d at least two. Here we establish that (1) W_n ( Gamma closes ) is at most n^{-1/2 + o(1)} for any d at least two; (2) W_n ( Gamma closes ) is at most n^{-4/7 + o(1)} for a subsequence of odd n, if d = 2; and (3) p_n is at most n^{-3/2 + o(1)} mu^n for a set of even n of full density when d=2. We also argue that the closing probability is bounded above by n^{-(1 - 1/d) + o(1)} on a full density set when d is at least three for a certain variant of self-avoiding walk.
Representation Complexity of Semi-algebraic Graphs

The representation complexity of a bipartite graph $G=(P,Q)$ is the minimum size $\sum_{i=1}^s (|A_i|+|B_i|)$ over all possible ways to write $G$ as a (not necessarily disjoint) union of complete bipartite subgraphs $G=\cup_{i=1}^s A_i\times B_i$ where $A_i\subset P, B_i\subset Q$ for $i=1,\dots, s$. In this paper we prove that if $G$ is \emph{semi-algebraic}, i.e. when $P$ is a set of $m$ points in $\mathbb{R}^{d_1}$, $Q$ is a set of $n$ points in $\mathbb{R}^{d_2}$ and the edges are defined by some semi-algebraic relations, the representation complexity of $G$ is $O( m^{\frac{d_1d_2-d_2}{d_1d_2-1}+\varepsilon} n^{\frac{d_1d_2-d_1}{d_1d_2-1}+\varepsilon}+m^{1+\varepsilon}+n^{1+\varepsilon})$ for arbitrarily small positive $\varepsilon$. This generalizes results by Apfelbaum-Sharir and Solomon-Sharir. As a consequence, when $G$ is $K_{u,u}$-free for some positive integer $u$, its number of edges is $O(u m^{\frac{d_1d_2-d_2}{d_1d_2-1}+\varepsilon} n^{\frac{d_1d_2-d_1}{d_1d_2-1}+\varepsilon}+ u m^{1+\varepsilon}+u n^{1+\varepsilon})$. This bound is stronger than that of Fox, Pach, Sheffer, Suk and Zahl when the first term dominates and $u$ grows with $m,n$. Another consequence is that we can find a large complete bipartite subgraph in a semi-algebraic graph when the number of edges is large. Similar results hold for semi-algebraic hypergraphs.
Within-object element ambiguity allows for a strange illusion of alternating facial expression and structure

COPYRIGHT © 2022 Bachmann. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Within-object element ambiguity allows for a strange illusion of alternating facial expression and structure
Batch and sampling time exert a larger influence on the fungal community than gastrointestinal location in model animals: A meaningful case study

Fungi play a fundamental role in the intestinal ecosystem and health, but our knowledge of fungal composition and distribution in the whole gastrointestinal tract (GIT) is very limited. The physiological similarity between humans and pigs in terms of digestive and associated metabolic processes places, the pig in a superior position over other non-primate models. Here, we aimed to characterize the diversity and composition of fungi in the GIT of pigs. Using high-throughput sequencing, we evaluated the fungal community in different locations of GIT of 11 pigs with 128.41 ± 1.25 kg body weight acquired successively. Among them, five pigs are sacrificed in April 2019 (Batch 1) and the other six are sacrificed in January 2020 (Batch 2). All subjects with similar genetic backgrounds, housing, management, and diet. Finally, no significant difference is found in the α-diversity (Richness) of the fungal community among all intestinal segments. Basidiomycota and Ascomycota are the two predominant fungal phyla, but Batch 1 harbored a notably high abundance of Basidiomycota and Batch 2 harbored a high abundance of Ascomycota. Moreover, the two batches harbored completely different fungal compositions and core fungal genera. FUNGuild (Fungal Functional Guild) analysis revealed that most of the fungal species present in the GIT are saprotroph, plant pathogen, and animal endosymbiont. Our study is the first to report that even under the same condition, large variations in fungal composition in the host GIT still occur from batch-to-batch and sampling time. The implications of our observations serve as references to the development of better models of the human gut.
Calcium handling maturation and adaptation to increased substrate stiffness in human iPSC-derived cardiomyocytes: The impact of full-length dystrophin deficiency

Cardiomyocytes differentiated from human induced Pluripotent Stem Cells (hiPSC- CMs) are a unique source for modelling inherited cardiomyopathies. In particular, the possibility of observing maturation processes in a simple culture dish opens novel perspectives in the study of early-disease defects caused by genetic mutations before the onset of clinical manifestations. For instance, calcium handling abnormalities are considered as a leading cause of cardiomyocyte dysfunction in several genetic-based dilated cardiomyopathies, including rare types such as Duchenne Muscular Dystrophy (DMD)-associated cardiomyopathy. To better define the maturation of calcium handling we simultaneously measured action potential and calcium transients (Ca-Ts) using fluorescent indicators at specific time points. We combined micropatterned substrates with long-term cultures to improve maturation of hiPSC-CMs (60, 75 or 90 days post-differentiation). Control-(hiPSC)-CMs displayed increased maturation over time (90 vs 60 days), with longer action potential duration (APD), increased Ca-T amplitude, faster Ca-T rise (time to peak) and Ca-T decay (RT50). The progressively increased contribution of the SR to Ca release (estimated by post-rest potentiation or Caffeine-induced Ca-Ts) appeared as the main determinant of the progressive rise of Ca-T amplitude during maturation. As an example of severe cardiomyopathy with early onset, we compared hiPSC-CMs generated from a DMD patient (DMD-ΔExon50) and a CRISPR-Cas9 genome edited cell line isogenic to the healthy control with deletion of a G base at position 263 of the DMD gene (c.263delG-CMs). In DMD-hiPSC-CMs, changes of Ca-Ts during maturation were less pronounced: indeed, DMD cells at 90 days showed reduced Ca-T amplitude and faster Ca-T rise and RT50, as compared with control hiPSC-CMs. Caffeine-Ca-T was reduced in amplitude and had a slower time course, suggesting lower SR calcium content and NCX function in DMD vs control cells. Nonetheless, the inotropic and lusitropic responses to forskolin were preserved. CRISPR-induced c.263delG-CM line recapitulated the same developmental calcium handling alterations observed in DMD-CMs. We then tested the effects of micropatterned substrates with higher stiffness. In control hiPSC-CMs, higher stiffness leads to higher amplitude of Ca-T with faster decay kinetics. In hiPSC-CMs lacking full-length dystrophin, however, stiffer substrates did not modify Ca-Ts but only led to higher SR Ca content. These findings highlighted the inability of dystrophin-deficient cardiomyocytes to adjust their calcium homeostasis in response to increases of extracellular matrix stiffness, which suggests a mechanism occurring during the physiological and pathological development (i.e. fibrosis).
A calculus for the moduli space of
 curves

This article accompanies my lecture at the 2015 AMS summer institute in algebraic geometry in Salt Lake City. I survey the recent advances in the study of tautological classes on the moduli spaces of curves. After discussing the Faber-Zagier relations on the moduli spaces of nonsingular curves and the kappa rings of the moduli spaces of curves of compact type, I present Pixton's proposal for a complete calculus of tautological classes on the moduli spaces of stable curves. Several open questions are discussed. An effort has been made to condense a great deal of mathematics into as few pages as possible with the hope that the reader will follow through to the end.
Changes in root chemical diversity along an elevation gradient of Changbai Mountain, China

Root chemical traits play a critical role in plant resource use strategies and ecosystem nutrient cycling; however, the chemical diversity of multiple elements of fine root and community chemical assembly belowground are poorly understood. Here, we measured 13 elements (C, N, K, Ca, Mg, S, P, Al, Fe, Na, Mn, Zn, and Cu) in the fine roots of 204 plant species along elevational transect from 540 to 2357 m of Changbai Mountain, China to explore the variation, diversity, and community assembly of root chemical traits. At the species level, the concentrations of macronutrients (N, K, Ca, Mg, S, and P) decreased, whereas the trace metals (Fe, Mn, and Zn) increased with elevation. Root chemical traits at the community level systematically shifted along elevational gradients showing a pattern similar to that at the species level, which were mainly influenced by climate and soil rather than species diversity. In general, the interactions of climate and soil were the main drivers of root chemical assembly for woody layers, whereas soil factors played significant role for root chemical assembly for herb layer. The chemical assembly of rock-derived element P was mainly driven by soil factors. Meanwhile, root chemical diversities were mainly regulated by species diversity, the interactions of climate and soil, and soil factors in the tree, shrub, and herb layers, respectively. A better understanding of plant root chemical diversity and community chemical assembly will help to reveal the role of chemical traits in ecosystem functioning.
Contractive idempotents on locally compact quantum groups

A general form of contractive idempotent functionals on coamenable locally compact quantum groups is obtained, generalising the result of Greenleaf on contractive measures on locally compact groups. The image of a convolution operator associated to a contractive idempotent is shown to be a ternary ring of operators. As a consequence a one-to-one correspondence between contractive idempotents and a certain class of ternary rings of operators is established.
Environmentally specific servant leadership and voluntary pro-environmental behavior in the context of green operations: A serial mediation path

Green operations of organizations and enhancement of corporate social responsibility hinges upon leaders. This study investigated the influential role performed by environmentally specific servant leadership in provoking voluntary pro-environmental behavior of employees. The findings illuminate a serial chain mediation model that originates as a result of environmentally specific servant leadership and leads toward psychological empowerment, and organizational identity, ultimately leading toward voluntary pro-environmental behavior. Data from the textile sector of Pakistan uncovered that environmentally specific servant leadership prompted the voluntary pro-environmental behavior of employees. Moreover, environmentally specific servant leadership was significantly linked with voluntary pro-environmental behavior through psychological empowerment. The study supports the serial mediation of psychological empowerment and organizational identity in stirring voluntary pro-environmental behavior. An organizational psychological mechanism has been unraveled that can help organizations achieve a high level of sustainability and can serve as a catalyst for organizational green operations.