Miracle-dz/UniFAR-FTUs huggingface dataset:
Zeros of large degree Vorob'ev-Yablonski polynomials via a Hankel determinant identity

In the present paper we derive a new Hankel determinant representation for the square of the Vorob'ev-Yablonski polynomial $\mathcal{Q}_n(x),x\in\mathbb{C}$. These polynomials are the major ingredients in the construction of rational solutions to the second Painleve equation $u_{xx}=xu+2u^3+\alpha$. As an application of the new identity, we study the zero distribution of $\mathcal{Q}_n(x)$ as $n\rightarrow\infty$ by asymptotically analyzing a certain collection of (pseudo) orthogonal polynomials connected to the aforementioned Hankel determinant. Our approach reproduces recently obtained results in the same context by Buckingham and Miller \cite{BM}, which used the Jimbo-Miwa Lax representation of PII equation and the asymptotical analysis thereof.
Highly incidental patterns on a quadratic hypersurface in $\mathbb{R}^4$

In [Sharir and Solomon 2015], Sharir and Solomon showed that the number of incidences between $m$ distinct points and $n$ distinct lines in $\mathbb R^4$ is $$O^*\left(m^{2/5}n^{4/5}+ m^{1/2}n^{1/2}q^{1/4} + m^{2/3}n^{1/3}s^{1/3} + m + n\right),$$ provided that no 2-flat contains more than $s$ lines, and no hyperplane or quadric contains more than $q$ lines, where the $O^*$ hides a multiplicative factor of $2^{c\sqrt {\log m}}$ for some absolute constant $c$. In this paper we prove that, for integers $m,n,$ satisfying $n^{9/8}<m<n^{3/2}$, there exist $m$ points and $n$ lines on the quadratic hypersurface in $\mathbb{R}^4$ $$ \{(x_1,x_2,x_3,x_4)\in \mathbb R^4 \mid x_1 = x_2^2 + x_3^2 - x_4^2\}, $$ such that (i) at most $s=O(1)$ lines lie on any 2-flat, (ii) at most $q=O(n/m^{1/3})$ lines lie on any hyperplane, and (iii) the number of incidences between the points and the lines is $\Theta(m^{2/3}n^{1/2})$, which is asymptotically larger than the upper bound in~(\ref{fourdimbound}). This shows that the assumption that no quadric contains more than $q$ lines (in the above mentioned theorem of Sharir and Solomon is necessary.
Existence of solution to a critical equation with variable exponent

In this paper we study the existence problem for the p(x)−Laplacian operator with a nonlinear critical source. We find a local condition on the exponents ensuring the existence of a nontrivial solution that shows that the Pohozaev obstruction does not holds in general in the variable exponent setting. The proof relies on the Concentration–Compactness Principle for variable exponents and the Mountain Pass Theorem.
Enhanced momentum feedback from clustered supernovae

Young stars typically form in star clusters, so the supernovae (SNe) they produce are clustered in space and time. This clustering of SNe may alter the momentum per SN deposited in the interstellar medium (ISM) by affecting the local ISM density, which in turn affects the cooling rate. We study the effect of multiple SNe using idealized 1D hydrodynamic simulations which explore a large parameter space of the number of SNe, and the background gas density and metallicity. The results are provided as a table and an analytic fitting formula. We find that for clusters with up to ~100 SNe the asymptotic momentum scales super-linearly with the number of SNe, resulting in a momentum per SN that can be an order of magnitude larger than for a single SN, with a maximum efficiency for clusters with 10-100 SNe. We argue that additional physical processes not included in our simulations -- self-gravity, breakout from a galactic disk, and galactic shear -- can slightly reduce the momentum enhancement from clustering, but the average momentum per SN still remains a factor of 4 larger than the isolated SN value when averaged over a realistic cluster mass function for a star-forming galaxy. We conclude with a discussion of the possible role of mixing between hot and cold gas, induced by multi-dimensional instabilities or preexisting density variations, as a limiting factor in the buildup of momentum by clustered SNe, and suggest future numerical experiments to explore these effects.
On hypersemigroups

Abstract Two well known results on semigroups, one of them clue to Calais, the other to Lajos, are generalized in case of hypersemigroups in the way indicated in the present paper. We prove that a nonempty subset B of a regular hypersemigroup H is a bi-ideal of H if and only if it is represented in the form B = A * C where A is a right ideal and C a left ideal of H. We also show that an hyper semigroup H is regular if and only if the right and the left ideals of H are idempotent, and for every right ideal A and every left ideal B of H, the product A * B is a quasi-ideal of H.
Groupoids, Loop Spaces and Quantization of 2-PLECTIC Manifolds

We describe the quantization of 2-plectic manifolds as they arise in the context of the quantum geometry of M-branes and non-geometric flux compactifications of closed string theory. We review the groupoid approach to quantizing Poisson manifolds in detail, and then extend it to the loop spaces of 2-plectic manifolds, which are naturally symplectic manifolds. In particular, we discuss the groupoid quantization of the loop spaces of ℝ3, 𝕋3 and S3, and derive some interesting implications which match physical expectations from string theory and M-theory.
Identifying galaxy candidates in WSRT H i imaging of ultra-compact high velocity clouds

Ultra-compact high velocity clouds (UCHVCs) were identified in the Arecibo Legacy Fast ALFA (ALFALFA) H i survey as potential gas-bearing dark matter halos. Here we present higher resolution neutral hydrogen (H i) observations of twelve UCHVCS with the Westerbork Synthesis Radio Telescope (WSRT). The UCHVCs were selected based on a combination of size, isolation, large recessional velocity and high column density as the best candidate dark matter halos. The WSRT data were tapered to image the UCHVCs at 210′′ (comparable to the Arecibo resolution) and 105′′ angular resolution. In a comparison of the single-dish to interferometer data, we find that the integrated line flux recovered in the WSRT observations is generally comparable to that from the single-dish ALFALFA data. In addition, any structure seen in the ALFALFA data is reproduced in the WSRT maps at the same angular resolution. At 210′′ resolution all the sources are generally compact with a smooth H i morphology, as expected from their identification as UCHVCs. At the higher angular resolution, a majority of the sources break into small clumps contained in a diffuse envelope. These UCHVCs also have no ordered velocity motion and are most likely Galactic halo clouds. We identify two UCHVCs, AGC 198606 and AGC 249525, as excellent galaxy candidates based on maintaining a smooth H i morphology at higher angular resolution and showing ordered velocity motion consistent with rotation. A third source, AGC 249565, lies between these two populations in properties and is a possible galaxy candidate. If interpreted as gas-bearing dark matter halos, the three candidate galaxies have rotation velocities of 8–15 km s -1 , H i masses of 0.6–50 × 10 5 M ⊙ , H i radii of 0.3–2 kpc, and dynamical masses of 2–20 × 10 7 M ⊙ for a range of plausible distances. These are the UCHVCs with the highest column density values in the ALFALFA H i data and we suggest this is the best way to identify further candidates.
Quantum symmetry groups of C*‐algebras equipped with orthogonal filtrations

Motivated by the work of Goswami on quantum isometry groups of non‐commutative manifolds, we define the quantum symmetry group of a unital C*‐algebra A equipped with an orthogonal filtration as the universal object in the category of compact quantum groups acting on A in a filtration‐preserving fashion. The existence of such a universal object is proved and several examples discussed. In particular, we study the universal quantum group acting on the dual of the free group and preserving both the word length and the block length.
MOLECULAR GAS, CO, AND STAR FORMATION IN GALAXIES: EMERGENT EMPIRICAL RELATIONS, FEEDBACK, AND THE EVOLUTION OF VERY GAS-RICH SYSTEMS

We use time-varying models of the coupled evolution of the H i, H2 gas phases and stars in galaxy-sized numerical simulations to (1) test for the emergence of the Kennicutt–Schmidt (K–S) and the H2–pressure relation, (2) explore a realistic H2-regulated star formation recipe which brings forth a neglected and potentially significant SF-regulating factor, and (3) go beyond typical galactic environments (for which these galactic empirical relations are deduced) to explore the early evolution of very gas-rich galaxies. In this work, we model low-mass galaxies (Mbaryon ⩽ 109 M☉), while incorporating an independent treatment of CO formation and destruction, the most important tracer molecule of H2 in galaxies, along with that for the H2 gas itself. We find that both the K–S and the H2–pressure empirical relations can robustly emerge in galaxies after a dynamic equilibrium sets in between the various interstellar medium (ISM) states, the stellar component and its feedback (T ≳ 1 Gyr). The only significant dependence of these relations seems to be for the CO-derived (and thus directly observable) ones, which show a strong dependence on the ISM metallicity. The H2-regulated star formation recipe successfully reproduces the morphological and quantitative aspects of previous numerical models while doing away with the star formation efficiency parameter. Most of the H i → H2 mass exchange is found taking place under highly non-equilibrium conditions necessitating a time-dependent treatment even in typical ISM environments. Our dynamic models indicate that the CO molecule can be a poor, nonlinear, H2 gas tracer. Finally, for early evolutionary stages (T ≲ 0.4 Gyr), we find significant and systematic deviations of the true star formation from that expected from the K–S relation, which are especially pronounced and prolonged for metal-poor systems. The largest such deviations occur for the very gas-rich galaxies, where deviations of a factor ∼3–4 in global star formation rate (SFR) can take place with respect to those expected from the CO-derived K–S relation. This is particularly important since gas-rich systems at high redshifts could appear as having unusually high SFRs with respect to their CO-bright H2 gas reservoirs. This points to a possibly serious deficiency of K–S relations as elements of the sub-grid physics of star formation in simulations of structure formation in the early universe.
Density stability for some L\'evy-driven Stochastic Differential Equations

We consider a Stochastic Differential Equation driven by a L\'evy process whose L\'evy measure satisfy a tempered stable domination. We study how a perturbation of the coefficients reflects on the density of the solution. We quantify the distance between the densities in term of the proximity of the coefficients. This extend to the stable case the works of [KKM15], where the noise is Gaussian.
Partially hyperbolic dynamics in dimension 3

Partial hyperbolicity appeared in the sixties as a natural generaliza- tion of hyperbolicity. In the last 20 years in this area there has been great activity. Here we survey the state of the art in some topics, focusing especially in partial hyperbolicity in dimension 3. The reason for this is not only that it is the smallest dimension in which non-degenerate partial hyperbolicity can occur, but also that the topology of 3-manifolds influences this dynamics in revealing ways.
Second Order Necessary Conditions for Optimal Control Problems on Riemannian Manifolds

This work is concerned with an optimal control problem on a Riemannian manifold, for which two typical cases are considered. The first case is when the endpoint is free. For this case, the control set is assumed to be a separable metric space. By introducing suitable dual equations, which depend on the curvature tensor of the manifold, we establish the second order necessary and sufficient optimality conditions of integral form. In particular, when the control set is a Polish space, the second order necessary condition is reduced to a pointwise form. As a key preliminary result and also an interesting byproduct, we derive a geometric lemma, which may have some independent interest. The second case is when the endpoint is fixed. For this more difficult case, the control set is assumed to be open in an Euclidian space. We obtain the second order necessary and sufficient optimality conditions, in which the curvature tensor also appears explicitly. Our optimality conditions can be used to recover the following famous geometry result: Any geodesic connecting two fixed points on a Riemannian manifold satisfies the second variation of energy; while the existing optimality conditions in control literatures fail to give the same result.
NEW ESTIMATORS OF BLACK HOLE MASS IN ACTIVE GALACTIC NUCLEI WITH HYDROGEN PASCHEN LINES

More than 50% of active galactic nuclei (AGNs) are suspected to be red and affected by dust obscuration. Meanwhile, popular spectral diagnostics of AGNs are based on optical or ultraviolet light, making dust obscuration the primary concern for understanding the general nature of AGNs and the supermassive black holes residing in them. To provide a method for investigating properties of dusty AGNs, we derive new black hole (BH) mass estimators based on velocity widths and luminosities of near-infrared (NIR) hydrogen emission lines such as Pα and Pβ, and also investigate the line ratios of these hydrogen lines. To derive the BH mass (MBH) estimators, we used a sample of 37 unobscured type 1 AGNs with an MBH range of 106.8–109.4 M☉, where MBH comes from either the reverberation mapping method or single-epoch measurement method using Balmer lines. Our work shows that MBH can be estimated from the Paschen line luminosities and velocity widths to an accuracy of 0.18–0.24 dex (rms scatter). We also show that the mean line ratios of the Paschen lines and the Balmer lines are , , which are consistent with case B recombination under a typical AGN broad-line region (BLR) environment. These ratios can be used as reference points when estimating the amount of dust extinction over the BLR for red AGNs. We expect the future application of the new BH mass estimators on red, dusty AGNs to provide a fresh view of obscured AGNs.
A new approach toward boundedness in a two‐dimensional parabolic chemotaxis system with singular sensitivity

We consider the parabolic chemotaxis model ut=Δu−χ∇·uv∇vvt=Δv−v+u in a smooth, bounded, convex two‐dimensional domain and show global existence and boundedness of solutions for χ∈(0,χ0) for some χ0>1, thereby proving that the value χ = 1 is not critical in this regard.
Phase diagram for a copolymer in a micro-emulsion

In this paper we study a model describing a copolymer in a micro-emulsion. The copolymer consists of a random concatenation of hydrophobic and hydrophilic monomers, the micro-emulsion consists of large blocks of oil and water arranged in a percolation-type fashion. The interaction Hamiltonian assigns energy $-\alpha$ to hydrophobic monomers in oil and energy $-\beta$ to hydrophilic monomers in water, where $\alpha,\beta$ are parameters that without loss of generality are taken to lie in the cone $\{(\alpha,\beta) \in\mathbb{R}^2\colon\,\alpha \geq |\beta|\}$. Depending on the values of these parameters, the copolymer either stays close to the oil-water interface (localization) or wanders off into the oil and/or the water (delocalization). Based on an assumption about the strict concavity of the free energy of a copolymer near a linear interface, we derive a variational formula for the quenched free energy per monomer that is column-based, i.e., captures what the copolymer does in columns of different type. We subsequently transform this into a variational formula that is slope-based, i.e., captures what the polymer does as it travels at different slopes, and we use the latter to identify the phase diagram in the $(\alpha,\beta)$-cone. There are two regimes: supercritical (the oil blocks percolate) and subcritical (the oil blocks do not percolate). The supercritical and the subcritical phase diagram each have two localized phases and two delocalized phases, separated by four critical curves meeting at a quadruple critical point. The different phases correspond to the different ways in which the copolymer can move through the micro-emulsion. The analysis of the phase diagram is based on three hypotheses of percolation-type on the blocks. We show that these three hypotheses are plausible, but do not provide a proof.
Newman-Rivlin asymptotics for partial sums of power series

We discuss analogues of Newman and Rivlin's formula concerning the ratio of a partial sum of a power series to its limit function and present a new general result of this type for entire functions with a certain asymptotic character. The main tool used in the proof is a Riemann-Hilbert formulation for the partial sums introduced by Kriecherbauer et al. This new result makes some progress on verifying a part of the Saff-Varga Width Conjecture concerning the zero-free regions of these partial sums.
Langlands-Shahidi $L$-functions for $GSpin$ groups and the generic Arthur packet conjecture

We prove that $L$-functions from Langlands-Shahidi method in the case of $GSpin$ groups over a non-Archimedean local field of characteristic zero are Artin $L$-functions through the local Langlands correspondence. It has an application on the proof of a weak version of the generic Arthur packet conjecture. Furthermore, we study and describe a local $L$-packet that contains a generic member in the case of $GSpin$ groups. Using this description of a local $L$-packet, we strengthen a weak version of the generic Arthur packet conjecture in those cases (local version of the generalized Ramanujan conjecture).
Derived class of m-cluster tilted algebras of type 𝔸̃

In this paper, we characterize all the finite-dimensional algebras that are derived equivalent to an [Formula: see text]-cluster tilted algebras of type [Formula: see text]. This generalizes a result of Bobiński and Buan [The algebras derived equivalent to gentle cluster tilted algebras, J. Algebra Appl. 11(1) (2012), Article ID:1250012, 26 pp.].
OPE Convergence in Conformal Field Theory

We clarify questions related to the convergence of the OPE and conformal block decomposition in unitary Conformal Field Theories (for any number of spacetime dimensions). In particular, we explain why these expansions are convergent in a finite region. We also show that the convergence is exponentially fast, in the sense that the operators of dimension above ∆ contribute to correlation functions at most exp(−a∆). Here the constant a > 0 depends on the positions of operator insertions and we compute it explicitly. August 2012 ar X iv :1 20 8. 64 49 v1 [ he pth ] 3 1 A ug 2 01 2
Algorithmic Recommendations and Human Discretion

Human decision-makers frequently override the recommendations generated by predictive algorithms, but it is unclear whether these discretionary overrides add valuable private information or reintroduce human biases and mistakes. We develop new quasi-experimental tools to measure the impact of human discretion over an algorithm on the accuracy of decisions, even when the outcome of interest is only selectively observed, in the context of bail decisions. We find that 90% of the judges in our setting underperform the algorithm when they make a discretionary override, with most making override decisions that are no better than random. Yet the remaining 10% of judges outperform the algorithm in terms of both accuracy and fairness when they make a discretionary override. We provide suggestive evidence on the behavior underlying these differences in judge performance, showing that the high-performing judges are more likely to use relevant private information and are less likely to overreact to highly salient events compared to the low-performing judges.
On the overlap distribution of Branching Random Walks

In this paper, we study the overlap distribution and Gibbs measure of the Branching Random Walk with Gaussian increments on a binary tree. We first prove that the Branching Random Walk is 1 step Replica Symmetry Breaking and give a precise form for its overlap distribution, verifying a prediction of Derrida and Spohn. We then prove that the Gibbs measure of this system satisfies the Ghirlanda-Guerra identities. As a consequence, the limiting Gibbs measure has Poisson-Dirichlet statistics. The main technical result is a proof that the overlap distribution for the Branching Random Walk is supported on the set {0, 1}.
Heavy subsets and non-contractible trajectories

Entov and Polterovich defined heaviness for closed subsets of a symplectic manifold by using the Hamiltonian Floer theory on contractible trajectories. Heavy subsets are known to be non-displaceable. In the present paper, we define a relative symplectic capacity $C(M,X,R;e)$ for a symplectic manifold $(M,\omega)$ and its subset $X$ which measures the existence of non-contractible trajectories of Hamiltonian isotopies on the product with annulus. We prove that $C(M,X,R;e)$ is finite if $(M,\omega)$ is monotone and $X$ is a heavy subset. We also prove that $C(M,X,R;e)$ is infinite if $X$ is a displaceable compact subset.
Expanding maps and non-trivial self-covers on infra-nilmanifolds

Every expanding map on a closed manifold is topologically conjugate to an expanding map on an infra-nilmanifold, but not every infra-nilmanifold admits an expanding map. In this article we give a complete algebraic characterization of the infra-nilmanifolds admitting an expanding map. We show that, just as in the case of Anosov diffeomorphisms, the existence of an expanding map depends only on the rational holonomy representation of the infra-nilmanifold. A similar characterization is also given for the infra-nilmanifolds with a non-trivial self-cover, which corresponds to determining which almost-Bieberbach groups are co-Hopfian. These results provide many new examples of infra-nilmanifolds without non-trivial self-covers or expanding maps.
On the vanishing of relative negative K-theory

In this paper, we study the relative negative [Formula: see text]-groups [Formula: see text] of a map [Formula: see text] of schemes. We prove a relative version of Weibel’s conjecture; i.e. if [Formula: see text] is a smooth affine map of Noetherian schemes with [Formula: see text], then [Formula: see text] for [Formula: see text] and the natural map [Formula: see text] is an isomorphism for all [Formula: see text] and [Formula: see text] We also prove a vanishing result for relative negative [Formula: see text]-groups of a subintegral map.
Geometry and Temperature Chaos in Mixed Spherical Spin Glasses at Low Temperature: The Perturbative Regime

We study the Gibbs measure of mixed spherical p‐spin glass models at low temperature, in (part of) the 1‐RSB regime, including, in particular, models close to pure in an appropriate sense. We show that the Gibbs measure concentrates on spherical bands around deep critical points of the (extended) Hamiltonian restricted to the sphere of radius Nρ* , where ρ*2 is the rightmost point in the support of the overlap distribution. We also show that the relevant critical points are pairwise orthogonal for two different low temperatures. This allows us to explain why temperature chaos occurs for those models, in contrast to the pure spherical models. © 2019 Wiley Periodicals, Inc.