Miracle-dz/UniFAR-FTUs huggingface dataset:
Subset Approach to Efficient Skyline Computation

Skyline query processing is essential to the database community. Many algorithms have been designed to perform efficient skyline computation, which can be generally categorized into sorting-based and partitioning-based by considering the different mechanisms to reduce the dominance tests. Sorting-based skyline algorithms first sort all points with respect to a monotone score function, for instance the sum of all values of a point, then the dominance tests can be bounded by the score function; partitioning-based algorithms create partitions from the dataset so that the dominance tests can be limited in partitions. On the other hand, the incomparability between points has been considered as an important property, that is, if two points are incomparable, then any dominance test between them is unnecessary. In fact, the state-of-the-art skyline algorithms effectively reduce the dominance tests by taking the incomparability into account. In this paper, we present a subset-based approach that allows to integrate subspace-based incomparability to existing sorting-based skyline algorithms and can therefore significantly reduce the total number of dominance tests in large multidimensional datasets. Our theoretical and experimental studies show that the proposed subset approach boosts existing sorting-based skyline algorithms and makes them comparable to the state-of-the-art algorithms and even faster with uniform independent data.
Classical field theory limit of 2D many-body quantum Gibbs states

Nonlinear Gibbs measures play an important role in many areas of mathematics, including nonlinear dispersive equations with random initial data and stochastic partial differential equations. In statistical physics, they are believed to emerge for some quantum systems at criticality. In space dimensions two or larger, the measures are concentrated on singular distributions and they have to be be appropriately this http URL this paper we provide the first rigorous derivation of these renormalized nonlinear Gibbs measures in two space dimensions, starting from a linear quantum system in a mean-field-type limit. More precisely, we consider the grand-canonical Gibbs state of a large 2D bosonic quantum system and prove that it converges to the renormalized Gibbs measure of a nonlinear Schr{o}dinger-type classical field theory. Reduced density matrices of the quantum Gibbs state converge to their classical analogues. The quantum system is well defined without any renormalization. By only tuning its chemical potential, we obtain a counter-term for the diverging repulsive interactions which provides the desired Wick renormalization of the limit classical theory.
Asymptotic Syzygies in the Setting of Semi-Ample Growth

We study the asymptotic non-vanishing of syzygies for products of projective spaces. Generalizing the monomial methods of Ein, Erman, and Lazarsfeld \cite{einErmanLazarsfeld16} we give an explicit range in which the graded Betti numbers of $\mathbb{P}^{n_1}\times \mathbb{P}^{n_2}$ embedded by $\mathcal{O}_{\mathbb{P}^{n_1}\times\mathbb{P}^{n_2}}(d_1,d_2)$ are non-zero. These bounds provide the first example of how the asymptotic syzygies of a smooth projective variety whose embedding line bundle grows in a semi-ample fashion behave in nuanced and previously unseen ways.
Some results on Multiplicity-free spaces

Let $(M,\omega)$ be a connected symplectic manifold on which a connected Lie group $G$ acts properly and in a Hamiltonian fashion with moment map $\mu:M \lra \mf g^*$. Our purpose is investigate multiplicity-free actions, giving criteria to decide a multiplicity freenes of the action. As an application we give the complete classification of multiplicity-free actions of compact Lie groups acting isometrically and in a Hamiltonian fashion on Hermitian symmetric spaces of noncompact type. Successively we make a connection between multiplicity-free actions on $M$ and multiplicity-free actions on the symplectic reduction and on the symplectic cut, which allow us to give new examples of multiplicity-free actions.
The generalized Lyapunov theorem and its application to quantum channels

We give a simple and physically intuitive necessary and sufficient condition for a map acting on a compact metric space to be mixing (i.e. infinitely many applications of the map transfer any input into a fixed convergency point). This is a generalization of the ‘Lyapunov direct method’. First we prove this theorem in topological spaces and for arbitrary continuous maps. Finally we apply our theorem to maps which are relevant in open quantum systems and quantum information, namely quantum channels. In this context, we also discuss the relations between mixing and ergodicity (i.e. the property that there exists only a single input state which is left invariant by a single application of the map) showing that the two are equivalent when the invariant point of the ergodic map is pure.
Weyl semimetal and superconductor designed in an orbital-selective superlattice

We propose two complementary design principles for engineering three-dimensional (3D) Weyl semimetals and superconductors in a layer-by-layer setup which includes even and odd parity orbitals in alternating layers - dubbed orbital selective superlattice. Such structure breaks mirror symmetry along the superlattice growth axis which, with the help of either a basal plane spin-orbit coupling or a spinless p+ip superconductivity, stabilizes a 3D Dirac node. To explore this idea, we develop a 3D generalization of Haldane model and a Bogoliubov-de-Gennes (BdG) Hamiltonian for the two cases, respectively, and show that a tunable single or multiple Weyl nodes with linear dispersion in all spatial directions can be engineered desirably in a widespread parameter space. We also demonstrate that a single helical Weyl band can be created at the $\Gamma$-point at the Fermi level in the superconducting case via gapping out either of the orbital state by violating its particle-hole symmetry but not any other symmetries. Finally, implications of our results for the realization of anomalous Hall effect and Majorana bound state are discussed.
K3 surfaces with a pair of commuting non-symplectic involutions

We study K3 surfaces with a pair of commuting involutions that are non-symplectic with respect to two anti-commuting complex structures that are determined by a hyper-K\"ahler metric. One motivation for this paper is the role of such $\mathbb{Z}^2_2$-actions for the construction of $G_2$-manifolds. We find a large class of smooth K3 surfaces with such pairs of involutions, but we also pay special attention to the case that the K3 surface has ADE-singularities. Therefore, we introduce a special class of non-symplectic involutions that are suitable for explicit calculations and find 320 examples of pairs of involutions that act on K3 surfaces with a great variety of singularities.
Metaplectic categories, gauging and property $F$

$N$-Metaplectic categories, unitary modular categories with the same fusion rules as $SO(N)_2$, are prototypical examples of weakly integral modular categories. As such, a conjecture of the second author would imply that images of the braid group representations associated with metaplectic categories are finite groups, i.e. have property $F$. While it was recently shown that $SO(N)_2$ itself has property $F$, proving property $F$ for the more general class of metaplectic modular categories is an open problem. We verify this conjecture for $N$-metaplectic modular categories when $N$ is odd, exploiting their classification and enumeration to relate them to $SO(N)_2$. In another direction, we prove that when $N$ is divisible by $8$ the $N$-metaplectic categories have $3$ non-trivial bosons, and the boson condensation procedure applied to 2 of these bosons yields $\frac{N}{4}$-metaplectic categories. Otherwise stated: any $8k$-metaplectic category is a $\mathbb{Z}_2$-gauging of a $2k$-metaplectic category, so that the $N$ even metaplectic categories lie towers of $\mathbb{Z}_2$-gaugings commencing with $2k$- or $4k$-metaplectic categories with $k$ odd.
SPM Bulletin 20

This issue contains announcements of articles on: The Pytkeev property; Partial order embeddings; Resolvability; Singular density; P(w)/fin and the Calkin algebra; Everywhere meagre and everywhere null sets; almost disjoint families; forcing axioms; Splitting families; Sacks Reals; unconditionally closed and algebraic sets in groups; Stratifiability; Dissipated Compacta; partition relations; pi-bases; covering by translates of a compact nullsets; and a new Problem of the Issue.
Topological Aspects of Matters and Langlands Program

In the framework of Langlands program, we offer a unified description of the integer and fractional quantum Hall effect as well as the fractal nature of energy spectra of 2d Bloch electrons. We categorify topological invariants on the Brillouin Zone and address the several dualities in a coherent manner where analogs of the classical Fourier transform provide an essential crux of the matter. Based on the Langlands philosophy, we elucidate the duality of topological computation and that of Ising models in the same context.
Traversing three-manifold triangulations and spines

A celebrated result concerning triangulations of a given closed 3-manifold is that any two triangulations with the same number of vertices are connected by a sequence of so-called 2-3 and 3-2 moves. A similar result is known for ideal triangulations of topologically finite non-compact 3-manifolds. These results build on classical work that goes back to Alexander, Newman, Moise, and Pachner. The key special case of 1-vertex triangulations of closed 3-manifolds was independently proven by Matveev and Piergallini. The general result for closed 3-manifolds can be found in work of Benedetti and Petronio, and Amendola gives a proof for topologically finite non-compact 3-manifolds. These results (and their proofs) are phrased in the dual language of spines. The purpose of this note is threefold. We wish to popularise Amendola's result; we give a combined proof for both closed and non-compact manifolds that emphasises the dual viewpoints of triangulations and spines; and we give a proof replacing a key general position argument due to Matveev with a more combinatorial argument inspired by the theory of subdivisions.
Spherical parking functions, uprooted trees, and yet another way to count $n^n$

Parking functions are a widely studied class of combinatorial objects, with connections to several branches of mathematics. The number of parking functions of length $n$ is given by $(n+1)^{n-1}$, which by Cayley's formula is equal to the number of spanning trees of the complete graph $K_n$. Parking functions can be identified with the standard monomials of $M_n$, a certain monomial ideal in the polynomial ring $S = K[x_1, \dots, x_n]$ with a set of generators indexed by the nonempty subsets of $[n] = \{1, 2, . , n\}$. In this note we study $M_n^{(n-2)}$, a subideal of $M_n$ obtained by allowing only generators corresponding to proper subsets of $[n]$. The set of standard monomials of $M_n^{(n-2)}$ consists of the usual parking functions as well as a collection of sequences we term `spherical parking functions' of length $n$, which we show has cardinality $(n-1)^{n-1}$. The proof is recursive and relies on known enumerative results regarding a certain class of `uprooted trees'. As a corollary we obtain a seemingly new combinatorial identity for $n^n$, reminiscent of a result of Benjamin and Juhnke. We discuss combinatorial refinements of our result and a conjectural relationship between the degree of spherical parking functions and inversions in uprooted trees.
Line arrangements and r-Stirling partitions

A set partition of $[n] := \{1, 2, \dots, n \}$ is called {\em $r$-Stirling} if the numbers $1, 2, \dots, r$ belong to distinct blocks. Haglund, Rhoades, and Shimozono constructed graded ring $R_{n,k}$ depending on two positive integers $k \leq n$ whose algebraic properties are governed by the combinatorics of ordered set partitions of $[n]$ with $k$ blocks. We introduce a variant $R_{n,k}^{(r)}$ of this quotient for ordered $r$-Stirling partitions which depends on three integers $r \leq k \leq n$. We describe the standard monomial basis of $R_{n,k}^{(r)}$ and use the combinatorial notion of the {\em coinversion code} of an ordered set partition to reprove and generalize some results of Haglund et. \ al.\ in a more direct way. Furthermore, we introduce a variety $X_{n,k}^{(r)}$ of line arrangements whose cohomology is presented as the integral form of $R_{n,k}^{(r)}$, generalizing results of Pawlowski and Rhoades.
Classical Influence Functionals: Rigorously Deducing Stochasticity From Deterministic Dynamics

The longstanding question of how stochastic behaviour arises from deterministic Hamiltonian dynamics is of great importance, and any truly holistic theory must be capable of describing this transition. Using the Koopman von-Neumann formulation of classical mechanics, we present here the Classical Influence Functional (CIF) -- a method to bridge the gap between deterministic and stochastic dynamics, and unify the formalisms describing these disparate behaviours. Using this new technique, we demonstrate how irreversible behaviour arises generically from the reduced microscopic dynamics of a system-environment amalgam. The classical influence functional is then used to rigorously derive a generalised Langevin equation from a microscopic Hamiltonian. In this method stochastic terms are not identified heuristically, but instead arise from an exact mapping only available in the path-integral formalism of classical mechanics. As a consequence of the CIF, we are also able to show that the proper classical limit of stochastic quantum dynamics corresponds to this Langevin equation, providing a further unifying link to quantum theories. These derivations highlight the utility of CIFs, and its potential as a tool in both fundamental and applied research.
Flabby and injective objects in toposes

We introduce a general notion of flabby objects in elementary toposes and study their basic properties. In the special case of localic toposes, this notion reduces to the common notion of flabby sheaves, yielding a site-independent characterization of flabby sheaves. Continuing a line of research started by Roswitha Harting, we use flabby objects to show that an internal notion of injective objects coincides with the corresponding external notion, in stark contrast with the situation for projective objects. We show as an application that higher direct images can be understood as internal cohomology, and we study flabby objects in the effective topos.
Linear scaling between microbial predator and prey densities in the global ocean

Abstract It has been proposed that microbial predator and prey densities are related through sublinear power laws. We revisited previously published biomass and abundance data and fitted Power‐law Biomass Scaling Relationships (PBSRs) between marine microzooplankton predators (Z) and phytoplankton prey (P), and marine viral predators (V) and bacterial prey (B). We analysed them assuming an error structure given by Type II regression models which, in contrast to the conventional Type I regression model, accounts for errors in both the independent and the dependent variables. We found that the data support linear relationships, in contrast to the sublinear relationships reported by previous authors. The scaling exponent yields an expected value of 1 with some spread in different datasets that was well‐described with a Gaussian distribution. Our results suggest that the ratios Z/P, and V/B are on average invariant, in contrast to the hypothesis that they systematically decrease with increasing P and B, respectively, as previously thought.
Deep null space learning for inverse problems: convergence analysis and rates

Recently, deep learning based methods appeared as a new paradigm for solving inverse problems. These methods empirically show excellent performance but lack of theoretical justification; in particular, no results on the regularization properties are available. In particular, this is the case for two-step deep learning approaches, where a classical reconstruction method is applied to the data in a first step and a trained deep neural network is applied to improve results in a second step. In this paper, we close the gap between practice and theory for a particular network structure in a two-step approach. For that purpose, we propose using so-called null space networks and introduce the concept of -regularization. Combined with a standard regularization method as reconstruction layer, the proposed deep null space learning approach is shown to be a -regularization method; convergence rates are also derived. The proposed null space network structure naturally preserves data consistency which is considered as key property of neural networks for solving inverse problems.
Cascaded noiseless linear amplification for single-photon state

Photon loss is one of the main obstacles in current long-distance quantum communications. The approach of noiseless linear amplification (NLA) is one of the powerful way to distill the single-photon state (SPS) from a mixed state, which comprises both the SPS and vacuum state. However, existing NLA protocol can only perform the amplification for one time. That is the fidelity of the SPS cannot be increased anymore. In this paper, We put forward an efficient cascaded NLA protocol for both the SPS and single-photon entanglement (SPE), respectively, with the help of some auxiliary single photons. By repeating this protocol for sever times, the fidelity of the SPS and SPE can reach near 100\%, which may make this protocol is extremely useful to close the detection loophole in quantum key distribution. Moreover, this protocol is based on the linear optics, which makes it feasible in current technology.
NKG2D‐mediated cytotoxicity improves after primary surgery for high‐grade serous ovarian cancer

Tumors compromise the patients’ immune system to promote their own survival. We have previously reported that HGSC exosomes play a central role, downregulating NKG2D cytotoxicity. Primary surgery's effect on tumor exosomes and NKG2D cytotoxicity in HGSC patients has not been studied before. The overall objective of this study was to explore the effect of surgery on the exosome‐induced impairment of NKG2D cytotoxicity in HGSC.
The Riemannian geometry of orbit spaces -- the metric, geodesics, and integrable systems

We investigate the rudiments of Riemannian geometry on orbit spaces $M/G$ for isometric proper actions of Lie groups on Riemannian manifolds. Minimal geodesic arcs are length minimising curves in the metric space $M/G$ and they can hit strata which are more singular only at the end points. This is phrased as convexity result. The geodesic spray, viewed as a (strata-preserving) vector field on $TM/G$, leads to the notion of geodesics in $M/G$ which are projections under $M\to M/G$ of geodesics which are normal to the orbits. It also leads to `ballistic curves' which are projections of the other geodesics. In examples (Hermitian and symmetric matrices, and more generally polar representations) we compute their equations by singular symplectic reductions and obtain generalizations of Calogero-Moser systems with spin.
Optimal indirect stability of a weakly damped elastic abstract system of second order equations coupled by velocities

In this paper, by means of the Riesz basis approach, we study the stability of a weakly damped system of two second order evolution equations coupled through the velocities (see (1.1)). If the fractional order damping becomes viscous and the waves propagate with equal speeds, we prove exponential stability of the system and, otherwise, we establish an optimal polynomial decay rate. Finally, we provide some illustrative examples.
Early surgery or conservative management for asymptomatic severe aortic stenosis: Meta‐analysis of RECOVERY and AVATAR

The standard practice for management for asymptomatic severe aortic stenosis with a normal left ventricular systolic function is conservative management with a few exceptions. This practice is challenged by two recent randomized controlled trials (RCT). All the prior data is observational. We performed a meta‐analysis of these 2 RCTs to determine if early surgical aortic valve replacement in this patient population is beneficial compared with the standard conservative therapy.
Aligned spins: orbital elements, decaying orbits, and last stable circular orbit to high post-Newtonian orders

In this paper, the quasi-Keplerian parameterization for the case that spins and orbital angular momentum in a compact binary system are aligned or anti-aligned with the orbital angular momentum vector is extended to 3PN point-mass, next-to-next-to-leading order spin–orbit, next-to-next-to-leading order spin(1)–spin(2) and next-to-leading order spin-squared dynamics in the conservative regime. In a further step, we use the expressions for the radiative multipole moments with spin to leading order linear and quadratic in both spins to compute radiation losses of the orbital binding energy and angular momentum. Orbital averaged expressions for the decay of energy and eccentricity are provided. An expression for the last stable circular orbit is given in terms of the angular velocity-type variable x.
Spectral Properties of Effective Dynamics from Conditional Expectations

The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective equations is the conditioning approach. In this paper, we are interested in the spectrum of the generator of the resulting effective dynamics, and how it compares to the spectrum of the full generator. We prove a new relative error bound in terms of the eigenfunction approximation error for reversible systems. We also present numerical examples indicating that, if Kramers–Moyal (KM) type approximations are used to compute the spectrum of the reduced generator, it seems largely insensitive to the time window used for the KM estimators. We analyze the implications of these observations for systems driven by underdamped Langevin dynamics, and show how meaningful effective dynamics can be defined in this setting.
Analysis of electromagnetic scattering from plasmonic inclusions at optical frequencies and applications

This paper is concerned with the analysis of time-harmonic electromagnetic scattering from plasmonic inclusions in the optical frequency regime. The electric permittivity and magnetic permeability in the inclusions are allowed to be negative-valued. Using layer potential techniques for the full Maxwell system, the scattering problem is reformulated into a system of integral equations. We derive the complete eigensystem of the involved matrix-valued integral operator within spherical geometry. As applications, we construct two types of plasmonic structures such that one can induce surface plasmon resonances at optical frequencies and the other one can produce invisibility cloaking. It is particularly noted that the cloaking effect is a newly found phenomenon and is of different nature from those existing ones for plasmonic structures in the literature. The surface plasmon resonance result may find applications in electromagnetic imaging.