Miracle-dz/UniFAR-FTUs huggingface dataset:
Good for Games Automata: From Nondeterminism to Alternation

A word automaton recognizing a language $L$ is good for games (GFG) if its composition with any game with winning condition $L$ preserves the game's winner. While all deterministic automata are GFG, some nondeterministic automata are not. There are various other properties that are used in the literature for defining that a nondeterministic automaton is GFG, including "history-deterministic", "compliant with some letter game", "good for trees", and "good for composition with other automata". The equivalence of these properties has not been formally shown. We generalize all of these definitions to alternating automata and show their equivalence. We further show that alternating GFG automata are as expressive as deterministic automata with the same acceptance conditions and indices. We then show that alternating GFG automata over finite words, and weak automata over infinite words, are not more succinct than deterministic automata, and that determinizing Buchi and co-Buchi alternating GFG automata involves a $2^{\Theta(n)}$ state blow-up. We leave open the question of whether alternating GFG automata of stronger acceptance conditions allow for doubly-exponential succinctness compared to deterministic automata.
An Approach for Reviewing Security-Related Aspects in Agile Requirements Specifications of Web Applications

Defects in requirements specifications can have severe consequences during the software development lifecycle. Some of them result in overall project failure due to incorrect or missing quality characteristics such as security. There are several concerns that make security difficult to deal with; for instance, (1) when stakeholders discuss general requirements in meetings, they are often unaware that they should also discuss security-related topics, and (2) they typically do not have enough expertise in security. This often leads to unspecified or ill-defined security-related aspects. These concerns become even more challenging in agile contexts, where lightweight documentation is typically involved. The goal of this paper is to design and evaluate an approach for reviewing security-related aspects in agile requirements specifications of web applications. The approach considers user stories and security specifications as input and relates those user stories to security properties via Natural Language Processing. Based on the related security properties, our approach then identifies high-level security requirements from the Open Web Application Security Project to be verified and generates a reading technique to support reviewers in detecting defects. We evaluate our approach via two controlled experiment trials. We compare the effectiveness and efficiency of novice inspectors verifying security aspects in agile requirements using our approach against using the complete list of high-level security requirements. The (statistically significant) results indicate that using our approach has a positive impact (with large effect size) on the performance of inspectors in terms of effectiveness and efficiency.
Indications for Dzyaloshinskii-Moriya interaction at the Pd/Fe interface studied by 
in situ
 polarized neutron reflectometry

Using \textit{in situ} polarized neutron reflectometry, the depth resolved evolution of the magnetism and structure in a Pd/Fe/Pd trilayer thin-film is measured during growth. The initial film structure of Pd/Fe shows a small proximity induced magnetism in the underlayer and a magnetization in the Fe layer of $\approx1.6$\,$\mu_{\text{B}}$ per Fe atom, less than the expected bulk value of $2.2$\,$\mu_{\text{B}}$. Deposition of the Pd capping layer initially follows an island-like growth mode with subsequent coalescence. With increasing Pd deposition the Fe moment and the proximity-induced magnetism in the Pd capping layer decrease. After final deposition of the Pd capping layer, the magnetic profile is structurally and magnetically symmetric across the Fe layer, with magnetism induced in Pd up to 0.92 \,nm from the interface. Throughout the Pd deposition the Pd/Fe/Pd trilayer structure is becoming increasingly symmetric, a fact which points to a Dzyaloshinskii-Moriya interaction as a likely cause of the observed magnetic behavior.
Nobeyama 45 m mapping observations toward Orion A. III. Multi-line observations toward an outflow-shocked region, Orion Molecular Cloud 2 FIR 4

We present the results of mapping observations toward an outflow-shocked region, OMC-2 FIR 4, using the Nobeyama 45 m telescope. We observed the area in 13CO (J = 1–0), C18O (J = 1–0), N2H+ (J = 1–0), CCS (JN = 87–76), HCO+ (J = 1–0), H13CO+ (J = 1–0), HN13C (J = 1–0), H13CN (J = 1–0), DNC (J = 1–0), N2D+ (J = 1–0), and DC3N (J = 9–8). We detected a dense molecular clump that contains FIR 4/5. We also detected, in the 13CO line, blueshifted and redshifted components driven presumably by protostellar outflows in this region. The axes of the FIR 3 and VLA 13 outflows, projected on the plane of the sky, appear to point to the FIR 4 clump, suggesting that it may be compressed by protostellar outflows from Class I sources, FIR 3 and VLA 13. Applying a hyperfine fit of N2H+ lines, we estimated the excitation temperature to be ∼20 K. The high excitation temperature is consistent with the fact that the clump contains protostars. CCS emission was detected in this region for the first time. Its abundance is estimated to be a few × 10−12, indicating that the region is chemically evolved at ∼105 yr, which is comparable to the typical lifetime of Class I protostars. This timescale is consistent with the scenario that star formation in FIR 4 is triggered by dynamical compression of the protostellar outflows. The [HNC]/[HCN] ratio was evaluated to be ∼0.5 in the dense clump and the outflow lobes, whereas it is somewhat larger in the envelope of the dense clump. The small [HNC]/[HCN] ratio indicates that HNC formation was prevented due to high temperatures. Such high temperatures seem to be consistent with the scenario that either protostellar radiation, or outflow compression, or both affected the thermal properties of this region.
Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves

A new type of wave–mean flow interaction is identified and studied in which a small-amplitude, linear, dispersive modulated wave propagates through an evolving, nonlinear, large-scale fluid state such as an expansion (rarefaction) wave or a dispersive shock wave (undular bore). The Korteweg–de Vries (KdV) equation is considered as a prototypical example of dynamic wavepacket–mean flow interaction. Modulation equations are derived for the coupling between linear wave modulations and a nonlinear mean flow. These equations admit a particular class of solutions that describe the transmission or trapping of a linear wavepacket by an unsteady hydrodynamic state. Two adiabatic invariants of motion are identified that determine the transmission, trapping conditions and show that wavepackets incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves exhibit so-called hydrodynamic reciprocity recently described in Maiden et al. (Phys. Rev. Lett., vol. 120, 2018, 144101) in the context of hydrodynamic soliton tunnelling. The modulation theory results are in excellent agreement with direct numerical simulations of full KdV dynamics. The integrability of the KdV equation is not invoked so these results can be extended to other nonlinear dispersive fluid mechanic models.
Can Neutron-star Mergers Explain the r-process Enrichment in Globular Clusters?

Star-to-star dispersion of r-process elements has been observed in a significant number of old, metal-poor globular clusters (GCs). We investigate early-time neutron-star mergers as the mechanism for this enrichment. Through both numerical modeling and analytical arguments, we show that neutron-star mergers cannot be induced through dynamical interactions early in the history of the cluster, even when the most liberal assumptions about neutron-star segregation are assumed. Therefore, if neutron-star mergers are the primary mechanism for r-process dispersion in GCs, they likely result from the evolution of isolated, primordial binaries in the clusters. Through population modeling of double neutron-star progenitors, we find that most enrichment candidates are fast-merging systems that undergo a phase of mass transfer involving a naked He-star donor. Only models where a significant number of double neutron-star progenitors proceed through this evolutionary phase give rise to moderate fractions of GCs with enrichment; under various assumptions for the initial properties of GCs, a neutron-star merger with the potential for enrichment will occur in ∼15%–60% (∼30%–90%) of GCs if this phase of mass transfer proceeds stably (unstably). The strong anti-correlation between the pre-supernova orbital separation and post-supernova systemic velocity due to mass loss in the supernova leads to efficient ejection of most enrichment candidates from their host clusters. Thus, most enrichment events occur shortly after the double neutron stars are born. This Requires star-forming gas that can absorb the r-process ejecta to be present in the globular cluster 30–50 Myr after the initial burst of star formation. If scenarios for redistributing gas in GCs cannot act on these timescales, the number of neutron-star merger enrichment candidates drops severely, and it is likely that another mechanism, such as r-process enrichment from collapsars, is at play.
ZN graded discrete integrable systems and Darboux transformations

We present the Darboux transformations for a novel class of two-dimensional discrete integrable systems named as graded discrete integrable systems, which were firstly proposed by Fordy and Xenitidis within the framework of graded discrete Lax pairs very recently. In this paper, the graded discrete equations in the coprime case and their corresponding Lax pairs are derived from the discrete Gel’fand–Dikii hierarchy by applying a transformation of the independent variables. The construction of the Darboux tranformations is realised by considering the associated linear problems in the bilinear formalism for the graded lattice equations. We show that all these graded equations share a unified solution structure in our scheme.
Global manifold structure of a continuous-time heterodimensional cycle

A heterodimensional cycle consists of a pair of heteroclinic connections between two saddle periodic orbits with unstable manifolds of different dimensions. Recent theoretical work on chaotic dynamics beyond the uniformly hyperbolic setting has shown that heterodimensional cycles may occur robustly in diffeomorphisms of dimension at least three. We study a concrete example of a heterodimensional cycle in the continuous-time setting, specifically in a four-dimensional vector field model of intracellular calcium dynamics. By employing advanced numerical techniques, Zhang, Krauskopf and Kirk [Discr. Contin. Dynam. Syst. A 32(8) 2825--2851 (2012)] found that a heterodimensional cycle exists in this model. We investigate the geometric structure of the associated stable and unstable manifolds in the neighbourhood of this heterodimensional cycle, consisting of a single connecting orbit of codimension one and an entire cylinder of structurally stable connecting orbits between two saddle periodic orbits. We employ a boundary-value problem set-up to compute their stable and unstable manifolds, which we visualize in different projections of phase space and as intersection sets with a suitable three-dimensional Poincare section. We show that, locally near the intersection set of the heterodimensional cycle, the manifolds interact as described by the theory for three-dimensional diffeomorphisms. On the other hand, their global structure is more intricate, which is due to the fact that it is not possible to find a Poincare section that is transverse to the flow everywhere. Our results show that the abstract concept of a heterodimensional cycle arises and can be studied in continuous-time models from applications.
Rerandomization and regression adjustment

Randomization is a basis for the statistical inference of treatment effects without strong assumptions on the outcome‐generating process. Appropriately using covariates further yields more precise estimators in randomized experiments. R. A. Fisher suggested blocking on discrete covariates in the design stage or conducting analysis of covariance in the analysis stage. We can embed blocking in a wider class of experimental design called rerandomization, and extend the classical analysis of covariance to more general regression adjustment. Rerandomization trumps complete randomization in the design stage, and regression adjustment trumps the simple difference‐in‐means estimator in the analysis stage. It is then intuitive to use both rerandomization and regression adjustment. Under the randomization inference framework, we establish a unified theory allowing the designer and analyser to have access to different sets of covariates. We find that asymptotically, for any given estimator with or without regression adjustment, rerandomization never hurts either the sampling precision or the estimated precision, and, for any given design with or without rerandomization, our regression‐adjusted estimator never hurts the estimated precision. Therefore, combining rerandomization and regression adjustment yields better coverage properties and thus improves statistical inference. To quantify these statements theoretically, we discuss optimal regression‐adjusted estimators in terms of the sampling precision and the estimated precision, and then measure the additional gains of the designer and the analyser. We finally suggest the use of rerandomization in the design and regression adjustment in the analysis followed by the Huber–White robust standard error.
Discrete scattering by a pair of parallel defects

Scattering of a time-harmonic anti-plane shear wave due to either a pair of crack tips or a pair of rigid constraint tips on square lattice is considered. The two problems correspond to the so-called zero-offset case of scattering due to a pair of identical Sommerfeld screens. The peculiar structural symmetry allows the reduction of coupled equations to two scalar Wiener–Hopf equations and a total of four geometrically reduced problems on lattice half-plane. Exact solution of each problem for incidence from the bulk lattice, as well as from an associated lattice waveguide, is constructed. A suitable superposition of the four expressions is used to construct the solution of the main problem. The discrete paradigm involving the wave mode incident from the waveguide is relevant for modern applications where an investigation of mechanisms of electronic and thermal transport at nanoscale remains an interesting problem. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.
ournal of C osmology and A stroparticle hysics Baryon Acoustic Oscillations and the Hubble constant: past, present and future

We investigate constraints on the Hubble constant ( H 0 ) using Baryon Acoustic Oscillations (BAO) and baryon density measurements from Big Bang Nucleosynthesis (BBN). We start by investigating the tension between galaxy BAO measurements and those using the Lyman- α forest, within a Bayesian framework. Using the latest results from eBOSS DR14 we ﬁnd that the probability of this tension being statistical is (cid:39) 6 . 3% assuming ﬂat ΛCDM. We measure H 0 = 67 . 6 ± 1 . 1 km s − 1 Mpc − 1 , with a weak dependence on the BBN prior used, in agreement with results from Planck Cosmic Microwave Background (CMB) results and in strong tension with distance ladder results. Finally, we forecast the future of BAO + BBN measurements of H 0 , using the Dark Energy Spectroscopic Instrument (DESI). We ﬁnd that the choice of BBN prior will have a signiﬁcant impact when considering future BAO measurements from DESI.
On uniqueness of solutions to viscous HJB equations with a subquadratic nonlinearity in the gradient

Abstract Uniqueness of positive solutions to viscous Hamilton–Jacobi–Bellman (HJB) equations of the form , with f a coercive function and λ a constant, in the subquadratic case, that is, , appears to be an open problem. Barles and Meireles [Comm. Partial Differential Equations 41 (2016)] show uniqueness in the case that and for some , essentially matching earlier results of Ichihara, who considered more general Hamiltonians but with better regularity for f. Without enforcing this assumption, to our knowledge, there are no results on uniqueness in the literature. In this short article, we show that the equation has a unique positive solution for any locally Lipschitz continuous, coercive f which satisfies for some positive constant κ. Since , this assumption imposes very mild restrictions on the growth of the potential f. We also show that this solution fully characterizes optimality for the associated ergodic problem. Our method involves the study of an infinite dimensional linear program for elliptic equations for measures, and is very different from earlier approaches. It also applies to the larger class of Hamiltonians studied by Ichihara, and we show that it is well suited to provide optimality results for the associated ergodic control problem, even in a pathwise sense, and without resorting to the parabolic problem.
Confinement and Effective Mass of Test Particles in Thick Branes Coupled Non Minimally With the Dilatonic Field

In this manuscript we study the confinement of test particles in smooth Randall-Sundrum models. It is a known fact that free test particles can not be localized neither in thin or thick branes. Recently a coupling of the particle to a scalar field has been used to localize a limited range of masses. It is found that the threshold mass depends on the specific model chosen. Up to now, no mechanism has been found that can trap test particles of any mass to the brane. In order to solve this problem, we first find a general expression for the effective mass observed on the brane. Next we show that by coupling the particle to the dilaton we obtain the trapping of particles of any mass. We further show the fact that this result is valid for any smooth version which recover the RS model asymptotically. For this, we just need of general aspects of the field equations of motion. As an example, we apply the method to the specific cases of deformed and undeformed topological defects.
Variational inequalities and mean-field approximations for partially observed systems of queueing networks

Queueing networks are systems of theoretical interest that find widespread use in the performance evaluation of interconnected resources. In comparison to counterpart models in genetics or mathematical biology, the stochastic (jump) processes induced by queueing networks have distinctive coupling and synchronization properties. This has prevented the derivation of variational approximations for conditional representations of transient dynamics, which rely on simplifying independence assumptions. Here, we present a model augmentation to a multivariate counting process for interactions across service stations, and we enable the variational evaluation of mean-field measures for partially-observed multi-class networks. We also show that our framework offers an efficient and improved alternative for inference tasks, where existing variational or numerically intensive solutions do not work.
Nearest Neighbors for Matrix Estimation Interpreted as Blind Regression for Latent Variable Model

We consider the setup of nonparametric <italic>blind regression</italic> for estimating the entries of a large <inline-formula> <tex-math notation="LaTeX">${m} \times {n}$ </tex-math></inline-formula> matrix, when provided with a small, random fraction of noisy measurements. We assume that all rows <inline-formula> <tex-math notation="LaTeX">${u} \in [{m}]$ </tex-math></inline-formula> and columns <inline-formula> <tex-math notation="LaTeX">${i} \in [{n}]$ </tex-math></inline-formula> of the matrix are associated to latent features <inline-formula> <tex-math notation="LaTeX">${x}_{\text {row}}({{u}})$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">${x}_{\text {col}}({{i}})$ </tex-math></inline-formula> respectively, and the <inline-formula> <tex-math notation="LaTeX">$({\it{ u, i}})$ </tex-math></inline-formula>-th entry of the matrix, <inline-formula> <tex-math notation="LaTeX">${A}({\it{ u, i}})$ </tex-math></inline-formula> is equal to <inline-formula> <tex-math notation="LaTeX">${f}({x}_{\text {row}}({{u}}), {x}_{\text {col}}({{i}}))$ </tex-math></inline-formula> for a latent function <inline-formula> <tex-math notation="LaTeX">$f$ </tex-math></inline-formula>. Given noisy observations of a small, random subset of the matrix entries, our goal is to estimate the unobserved entries of the matrix as well as to “de-noise” the observed entries. As the main result of this work, we introduce a nearest-neighbor-based estimation algorithm, and establish its consistency when the underlying latent function <inline-formula> <tex-math notation="LaTeX">$f$ </tex-math></inline-formula> is Lipschitz, the underlying latent space is a bounded diameter Polish space, and the random fraction of observed entries in the matrix is at least <inline-formula> <tex-math notation="LaTeX">$\max \big ({m}^{-1 + \delta }, {n}^{-1/2 + \delta } \big)$ </tex-math></inline-formula>, for any <inline-formula> <tex-math notation="LaTeX">$\delta > 0$ </tex-math></inline-formula>. As an important byproduct, our analysis sheds light into the performance of the classical collaborative filtering algorithm for matrix completion, which has been widely utilized in practice. Experiments with the MovieLens and Netflix datasets suggest that our algorithm provides a principled improvement over basic collaborative filtering and is competitive with matrix factorization methods. Our algorithm has a natural extension to the setting of tensor completion via flattening the tensor to matrix. When applied to the setting of image in-painting, which is a 3-order tensor, we find that our approach is competitive with respect to state-of-art tensor completion algorithms across benchmark images.
Morphological Irregularity Correlates with Frequency

We present a study of morphological irregularity. Following recent work, we define an information-theoretic measure of irregularity based on the predictability of forms in a language. Using a neural transduction model, we estimate this quantity for the forms in 28 languages. We first present several validatory and exploratory analyses of irregularity. We then show that our analyses provide evidence for a correlation between irregularity and frequency: higher frequency items are more likely to be irregular and irregular items are more likely be highly frequent. To our knowledge, this result is the first of its breadth and confirms longstanding proposals from the linguistics literature. The correlation is more robust when aggregated at the level of whole paradigms—providing support for models of linguistic structure in which inflected forms are unified by abstract underlying stems or lexemes.