Miracle-dz/UniFAR-FTUs huggingface dataset:
On the Generating Hypothesis in Noncommutative Stable Homotopy

Freyd's Generating Hypothesis is an important problem in topology with deep structural consequences for finite stable homotopy. Due to its complexity some recent work has examined analogous questions in various other triangulated categories. In this short note we analyze the question in noncommutative stable homotopy, which is a canonical generalization of finite stable homotopy. Along the way we also discuss Spanier-Whitehead duality in this extended setup.
YANG-MILLS HEATFLOW ON GAUGED HOLOMORPHIC MAPS

We study the gradient flow lines of a Yang-Mills-type functional on the space of gauged holomorphic maps $\mathcal{H}(P,X)$, where $P$ is a principal bundle on a Riemann surface $\Sigma$ and $X$ is a K\"ahler Hamiltonian $G$-manifold. For compact $\Sigma$, possibly with boundary, we prove long time existence of the gradient flow. The flow lines converge to critical points of the functional. So, there is a stratification on $\mathcal{H}(P,X)$ that is invariant under the action of the complexified gauge group. Symplectic vortices are the zeros of the functional we study. When $\Sigma$ has boundary, similar to Donaldson's result for the Hermitian Yang-Mills equations, we show that there is only a single stratum - any element of $\mathcal{H}(P,X)$ can be complex gauge transformed to a symplectic vortex. This is a version of Mundet's Hitchin-Kobayashi result on a surface with boundary.
CONVERGENT FLOWS AND LOW-VELOCITY SHOCKS IN DR21(OH)

DR21(OH) is a pc-scale massive, ∼7000 M☉ clump hosting three massive dense cores (MDCs) at an early stage of their evolution. We present a high angular resolution mosaic, covering ∼70″ × 100″, with the IRAM Plateau de Bure Interferometer at 3 mm to trace the dust continuum emission and the N2H+ (J = 1–0) and CH3CN (J = 5–4) molecular emission. The cold, dense gas traced by the compact emission in N2H+ is associated with the three MDCs and shows several velocity components toward each MDC. These velocity components reveal local shears in the velocity fields which are best interpreted as convergent flows. Moreover, we report the detection of weak extended emission from CH3CN at the position of the N2H+ velocity shears. We propose that this extended CH3CN emission is tracing warm gas associated with the low-velocity shocks expected at the location of convergence of the flows where velocity shears are observed. This is the first detection of low-velocity shocks associated with small (subparsec) scale convergent flows which are proposed to be at the origin of the densest structures and of the formation of (high-mass) stars. In addition, we propose that MDCs may be active sites of star formation for more than a crossing time as they continuously receive material from larger scale flows as suggested by the global picture of dynamical, gravity-driven evolution of massive clumps which is favored by the present observations.
A modified melting crystal model and the Ablowitz–Ladik hierarchy

This paper addresses the issue of integrable structure in a modified melting crystal model of topological string theory on the resolved conifold. The partition function can be expressed as the vacuum expectation value of an operator on the Fock space of 2D complex free fermion fields. The quantum torus algebra of fermion bilinears behind this expression is shown to have an extended set of ‘shift symmetries’. They are used to prove that the partition function (deformed by external potentials) is essentially a tau function of the 2D Toda hierarchy. This special solution of the 2D Toda hierarchy can also be characterized by a factorization problem of Z×Z? > matrices. The associated Lax operators turn out to be quotients of first-order difference operators. This implies that the solution of the 2D Toda hierarchy in question is actually a solution of the Ablowitz–Ladik (equivalently, the relativistic Toda) hierarchy. As a byproduct, the shift symmetries are shown to be related to matrix-valued quantum dilogarithmic functions.
Time-reversal and the adjoint method with an application in telecommunication

We establish a direct link between the time-reversal technique and the so-called adjoint method for imaging. Using this relationship, we derive new solution strategies for an inverse problem which arises in telecommunication. These strategies are all based on iterative time-reversal experiments, which try to solve the inverse problem experimentally instead of computationally. We will focus in particular on examples from underwater acoustic communication and wireless communication in a Multiple-Input Multiple-Output (MIMO) setup.
Betti Geometric Langlands

We introduce and survey a Betti form of the geometric Langlands conjecture, parallel to the de Rham form developed by Beilinson-Drinfeld and Arinkin-Gaitsgory, and the Dolbeault form of Donagi-Pantev, and inspired by the work of Kapustin-Witten in supersymmetric gauge theory. The conjecture proposes an automorphic category associated to a compact Riemann surface X and complex reductive group G is equivalent to a spectral category associated to the underlying topological surface S and Langlands dual group G^. The automorphic category consists of suitable C-sheaves on the moduli stack Bun_G(X) of G-bundles on X, while the spectral category consists of suitable O-modules on the character stack Loc_G^(S) of G^-local systems on S. The conjecture is compatible with and constrained by the natural symmetries of both sides coming from modifications of bundles and local systems. On the one hand, cuspidal Hecke eigensheaves in the de Rham and Betti sense are expected to coincide, so that one can view the Betti conjecture as offering a different "integration measure" on the same fundamental objects. On the other hand, the Betti spectral categories are more explicit than their de Rham counterparts and one might hope the conjecture is less challenging. The Betti program also enjoys symmetries coming from topological field theory: it is expected to extend to an equivalence of four-dimensional topological field theories, and in particular, the conjecture for closed surfaces is expected to reduce to the case of the thrice-punctured sphere. Finally, we also present ramified, quantum and integral variants of the conjecture, and highlight connections to other topics, including representation theory of real reductive groups and quantum groups.
SUPER-AGB–AGB EVOLUTION AND THE CHEMICAL INVENTORY IN NGC 2419

We follow the scenario of formation of second-generation stars in globular clusters by matter processed by hot bottom burning (HBB) in massive asymptotic giant branch (AGB) stars and super-AGB stars (SAGB). In the cluster NGC 2419 we assume the presence of an extreme population directly formed from the AGB and SAGB ejecta, so we can directly compare the yields for a metallicity Z = 0.0003 with the chemical inventory of the cluster NGC 2419. At such a low metallicity, the HBB temperatures (well above 108 K) allow a very advanced nucleosynthesis. Masses ∼6 M☉ deplete Mg and synthesize Si, going beyond Al, so this latter element is only moderately enhanced; sodium cannot be enhanced. The models are consistent with the observations, although the predicted Mg depletion is not as strong as in the observed stars. We predict that the oxygen abundance must be depleted by a huge factor (>50) in the Mg–poor stars. The HBB temperatures are close to the region where other p-capture reactions on heavier nuclei become possible. We show that high potassium abundance found in Mg-poor stars can be achieved during HBB by p-captures on the argon nuclei, if the relevant cross section(s) are larger than listed in the literature or if the HBB temperature is higher. Finally, we speculate that some calcium production is occurring owing to proton capture on potassium. We emphasize the importance of a strong effort to measure a larger sample of abundances in this cluster.
DISCOVERY OF AN ENERGETIC PULSAR ASSOCIATED WITH SNR G76.9+1.0

We report the discovery of PSR J2022+3842, a 24 ms radio and X-ray pulsar in the supernova remnant G76.9+1.0, in observations with the Chandra X-ray Observatory, the Robert C. Byrd Green Bank Radio Telescope, and the Rossi X-ray Timing Explorer (RXTE). The pulsar's spin-down rate implies a rotation-powered luminosity erg s−1, a surface dipole magnetic field strength Bs = 1.0 × 1012 G, and a characteristic age of 8.9 kyr. PSR J2022+3842 is thus the second-most energetic Galactic pulsar known, after the Crab pulsar, as well as the most rapidly rotating young, radio-bright pulsar known. The radio pulsations are highly dispersed and broadened by interstellar scattering, and we find that a large (δf/f ≈ 1.9 × 10−6) spin glitch must have occurred between our discovery and confirmation observations. The X-ray pulses are narrow (0.06 cycles FWHM) and visible up to 20 keV, consistent with magnetospheric emission from a rotation-powered pulsar. The Chandra X-ray image identifies the pulsar with a hard, unresolved source at the midpoint of the double-lobed radio morphology of G76.9+1.0 and embedded within faint, compact X-ray nebulosity. The spatial relationship of the X-ray and radio emissions is remarkably similar to the extended structure seen around the Vela pulsar. The combined Chandra and RXTE pulsar spectrum is well fitted by an absorbed power-law model with column density NH = (1.7 ± 0.3) × 1022 cm−2 and photon index Γ = 1.0 ± 0.2; this implies that the Chandra point-source flux is virtually 100% pulsed. For a distance of 10 kpc, the X-ray luminosity of PSR J2022+3842 is LX(2–10 keV) = 7.0 × 1033 erg s−1. Despite being extraordinarily energetic, PSR J2022+3842 lacks a bright X-ray wind nebula and has an unusually low conversion efficiency of spin-down power to X-ray luminosity, .
A Note on $\Gamma_n$-isometries

In this note we characterize the distinguished boundary of the symmetrized polydisc and thereby develop a model theory for $\Gamma_n$-isometries along the lines of \cite{AY}. We further prove that for invariant subspaces of $\Gamma_n$-isometries, similar to the case $n=2$ \cite{S}, Beurling-Lax-Halmos type representation holds.
Volume comparison with respect to scalar curvature

In this article, we investigate the volume comparison with respect to scalar curvature. In particular, we show volume comparison hold for small geodesic balls of metrics near $V$-static metrics. As for global results, we give volume comparison for metrics near Einstein metrics with certain restrictions. As an application, we recover a volume comparison result of compact hyperbolic manifolds due to Besson-Courtois-Gallot, which provides a partial answer to a conjecture of Schoen on volume of hyperbolic manifolds.
On the K‐theory of groups with finite decomposition complexity

It is proved that the assembly map in algebraic K ‐ and L ‐theory with respect to the family of finite subgroups is injective for groups Γ with finite quotient finite decomposition complexity (a strengthening of finite decomposition complexity introduced by Guentner, Tessera and Yu) that admit a finite‐dimensional model for E̲Γ and have an upper bound on the order of their finite subgroups. In particular, this applies to finitely generated linear groups over fields with characteristic zero with a finite‐dimensional model for E̲Γ .
Efficacy and safety of immune checkpoint inhibitors combined anti-angiogenic therapy in patients with unresectable hepatocellular carcinoma: A meta-analysis

Background: This study aimed to compare the efficacy and safety of immune checkpoint inhibitors (ICIs) combined with antiangiogenic agents in patients with unresectable hepatocellular carcinoma (HCC). Methods: We conducted a systematic literature search of articles published between the establishment of the database and February 2022. Data were extracted and analyzed using STATA 14.0. Results: Six randomized controlled trials (RCTs) (980 patients for combination therapy and 565 patients for monotherapy) and 5 single-arm studies (246 patients for ICIs combination therapy) were enrolled. The objective response rate (ORR) and disease control rate (DCR) were 26% and 70%, respectively, after ICIs combination therapy. Compared with monotherapy in RCTs, ICIs combination therapy resulted in higher progression-free survival (PFS) and overall survival (OS), but also increased the incidence of adverse events (AEs). Increased incidences of fatigue, hypertension, hyperbilirubinemia, proteinuria, and nausea were more common after ICIs combination therapy. Conclusion: The analysis results reveal that ICI-combined anti-angiogenesis therapy has higher efficacy than either ICIs or anti-angiogenesis options for unresectable HCC, but it is necessary to manage the AEs.
Thermodynamic formalism for Lorenz maps

For a 2-dimensional map representing an expanding geometric Lorenz at- tractor we prove that the attractor is the closure of a union of as long as possible unstable leaves with ending points. This allows to define the notion of good measures, those giving full measure to the union of these open leaves. Then, for any H\"older continuous potential we prove that there exists at most one relative equilibrium state among the set of good measures. Condition yielding existence are given.
A p-adic Eisenstein measure for vector-weight automorphic forms

We construct a p-adic Eisenstein measure with values in the space of vector-weight p-adic automorphic forms on certain unitary groups. This measure allows us to p-adically interpolate special values of certain vector-weight C-infinity automorphic forms, including Eisenstein series, as their weights vary. We also explain how to extend our methods to the case of Siegel modular forms and how to recover Nicholas Katz's p-adic families of Eisenstein series for Hilbert modular forms.
Criteria for generalized translation-invariant frames

This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower frame bound. Contrary to known conditions of a similar nature, the estimates take the phase of the generating functions in consideration and not only their modulus. The possibility of phase cancellations makes these estimates optimal for tight frames. The results on generalized translation-invariant systems will be proved in the setting of locally compact abelian groups, but even for euclidean space and the special case of (composite) wavelet systems the results are new.
Periodic approximation of exceptional Lyapunov exponents for semi-invertible operator cocycles

We prove that for semi-invertible and H\"older continuous linear cocycles $A$ acting on an arbitrary Banach space and defined over a base space that satisfies the Anosov Closing Property, all exceptional Lyapunov exponents of $A$ with respect to an ergodic invariant measure for base dynamics can be approximated with Lyapunov exponents of $A$ with respect to ergodic measures supported on periodic orbits. Our result is applicable to a wide class of infinite-dimensional dynamical systems.
ON THE STATIC SPACETIME OF A SINGLE POINT CHARGE

Among all electromagnetic theories which (a) are derivable from a Lagrangian, (b) satisfy the dominant energy condition, and (c) in the weak field limit coincide with classical linear electromagnetics, we identify a certain subclass with the property that the corresponding spherically symmetric, asymptotically flat, electrostatic spacetime metric has the mildest possible singularity at its center, namely, a conical singularity on the time axis. The electric field moreover has a point defect on the time axis, its total energy is finite, and is equal to the ADM mass of the spacetime. By an appropriate scaling of the Lagrangian, one can arrange the total mass and total charge of these spacetimes to have any chosen values. For small enough mass-to-charge ratio, these spacetimes have no horizons and no trapped null geodesics. We also prove the uniqueness of these solutions in the spherically symmetric class, and we conclude by performing a qualitative study of the geodesics and test-charge trajectories of these spacetimes.
SMOOTH BIMODULES AND COHOMOLOGY OF II1 FACTORS

We prove that, under rather general conditions, the 1-cohomology of a von Neumann algebra $M$ with values in a Banach $M$ -bimodule satisfying a combination of smoothness and operatorial conditions vanishes. For instance, we show that, if $M$ acts normally on a Hilbert space ${\mathcal{H}}$ and ${\mathcal{B}}_{0}\subset {\mathcal{B}}({\mathcal{H}})$ is a norm closed $M$ -bimodule such that any $T\in {\mathcal{B}}_{0}$ is smooth (i.e., the left and right multiplications of $T$ by $x\in M$ are continuous from the unit ball of $M$ with the $s^{\ast }$ -topology to ${\mathcal{B}}_{0}$ with its norm), then any derivation of $M$ into ${\mathcal{B}}_{0}$ is inner. The compact operators are smooth over any $M\subset {\mathcal{B}}({\mathcal{H}})$ , but there is a large variety of non-compact smooth elements as well.
Error term improvements for van der Corput transforms

We improve the error term in the van der Corput transform for exponential sums \sum_{a \le n \le b} g(n) exp(2\pi i f(n)). For many functions g and f, we can extract the next term in the asymptotic, showing that previous results, such as those of Karatsuba and Korolev, are sharp. Of particular note, the methods of this paper avoid the use of the truncated Poisson formula, and thus can be applied to much longer intervals [a,b] with far better results. We provide a detailed analysis of the error term in the case g(x)=1 and f(x)=(x/3)^{3/2}.
Size bias for one and all

Size bias occurs famously in waiting-time paradoxes, undesirably in sampling schemes, and unexpectedly in connection with Stein's method, tightness, analysis of the lognormal distribution, Skorohod embedding, infinite divisibility, and number theory. In this paper we review the basics and survey some of these unexpected connections.
Universal Cycles of Restricted Words

A connected digraph in which the in-degree of any vertex equals its out-degree is Eulerian, this baseline result is used as the basis of existence proofs for universal cycles (also known as generalized deBruijn cycles or U-cycles) of several combinatorial objects. We extend the body of known results by presenting new results on the existence of universal cycles of monotone, "augmented onto", and Lipschitz functions in addition to universal cycles of certain types of lattice paths and random walks.
On non-degeneracy of Riemannian Schwarzschild-anti de Sitter metrics

We prove that the $TT$-gauge-fixed linearised Einstein operator is non-degenerate for Riemannian Kottler ("Schwarzschild-anti de Sitter") metrics with dimension- and topology-dependent ranges of mass parameter. We provide evidence that this remains true for all such metrics except the spherical ones with a critical mass.
Proof of Grothendieck--Serre conjecture on principal bundles over regular local rings containing a finite field

Let R be a regular local ring, containing a finite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R. In other words, if K is the fraction field of R, then the map of non-abelian cohomology pointed sets H ét(R,G) → H 1 ét(K,G), induced by the inclusion of R into K, has a trivial kernel. If the regular local ring R contains an infinite field this result is proved in [FP]. Thus the conjecture holds for regular local rings containing a field.
Rigidity of the saddle connection complex

For a half‐translation surface (S,q)$(S,q)$ , the associated saddle connection complex A(S,q)$\mathcal {A}(S,q)$ is the simplicial complex where vertices are the saddle connections on (S,q)$(S,q)$ , with simplices spanned by sets of pairwise disjoint saddle connections. This complex can be naturally regarded as an induced subcomplex of the arc complex. We prove that any simplicial isomorphism ϕ:A(S,q)→A(S′,q′)$\phi \colon \mathcal {A}(S,q) \rightarrow \mathcal {A}(S^{\prime },q^{\prime })$ between saddle connection complexes is induced by an affine diffeomorphism F:(S,q)→(S′,q′)$F \colon (S,q) \rightarrow (S^{\prime },q^{\prime })$ . In particular, this shows that the saddle connection complex is a complete invariant of affine equivalence classes of half‐translation surfaces. Throughout our proof, we develop several combinatorial criteria of independent interest for detecting various geometric objects on a half‐translation surface.
Search trees: Metric aspects and strong limit theorems

We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces converge with probability 1. This is then used to obtain almost sure convergence for various tree functionals, together with representations of the respective limit random variables as functions of the limit tree.
Topological equivalence for discontinuous random dynamical systems and applications

After defining non-Gaussian L\'evy processes for two-sided time, stochastic differential equations with such L\'evy processes are considered. Solution paths for these stochastic differential equations have countable jump discontinuities in time. Topological equivalence (or conjugacy) for such an It\^o stochastic differential equation and its transformed random differential equation is established. Consequently, a stochastic Hartman-Grobman theorem is proved for the linearization of the It\^o stochastic differential equation. Furthermore, for Marcus stochastic differential equations,this topological equivalence is used to prove existence of global random attractors.
Diophantine approximation with nonsingular integral transformations

Let $\Gamma$ be the multiplicative semigroup of all $n\times n$ matrices with integral entries and positive determinant. Let $1\leq p \leq n-1$ and $V=\R^n\oplus \cdots \oplus \R^n$ ($p$ copies). We consider the componentwise action of $\Gamma$ on $V$. Let $\bx\in V$ be such that $\Gamma \bx$ is dense in $V$. We discuss the effectiveness of the approximation of any target point $\by \in V$ by the orbit $\{ \gamma \bx \mid \gamma \in \Gamma\}$, in terms of $\norm \gamma \norm$, and prove in particular that for all $\bx$ in the complement of a specific null set described in terms of a certain Diophantine condition, the exponent of approximation is $(n-p)/p$; that is, for any $\rho<(n-p)/p$, $\norm \gamma \bx - \by \norm < \norm \gamma \norm^{-\rho}$ for infinitely many $\gamma$.
ON THE METRIC ENTROPY OF THE BANACH–MAZUR COMPACTUM

We study the metric entropy of the metric space $B_n$ of all n-dimensional Banach spaces (the so-called Banach-Mazur compactum) equipped with the Banach-Mazur (multiplicative) "distance" $d$. We are interested either in estimates independent of the dimension or in asymptotic estimates when the dimension tends to $\infty$. For instance, we prove that, if $N({B_n},d, 1+\varepsilon)$ is the smallest number of "balls" of "radius" $1+\varepsilon$ that cover $ B_n$, then for any $\varepsilon>0$ we have $$0<\liminf_{n\to \infty}n^{-1} \log\log N(B_n,d,1+\varepsilon)\le \limsup_{n\to \infty}n^{-1} \log\log N(B_n,d,1+\varepsilon)<\infty. $$ We also prove an analogous result for the metric entropy of the set of n-dimensional operator spaces equipped with the distance $d_N$ naturally associated to $N\times N$-matrices with operator entries. In that case $N$ is arbitrary but our estimates are valid independently of $N$. In the Banach space case (i.e.N=1) the above upper bound is part of the folklore, and the lower bound is at least partially known (but apparently has not appeared in print). While we follow the same approach in both cases, the matricial case requires more delicate ingredients, namely estimates (from our previous work) on certain $n$-tuples of $N\times N$ unitary matrices known as "quantum expanders".