A Comparison between Term-Independence Retrieval Models for Ad Hoc Retrieval

In Information Retrieval, numerous retrieval models or document ranking functions have been developed in the quest for better retrieval effectiveness. Apart from some formal retrieval models formulated on a theoretical basis, various recent works have applied heuristic constraints to guide the derivation of document ranking functions. While many recent methods are shown to improve over established and successful models, comparison among these new methods under a common environment is often missing. To address this issue, we perform an extensive and up-to-date comparison of leading term-independence retrieval models implemented in our own retrieval system. Our study focuses on the following questions: (RQ1) Is there a retrieval model that consistently outperforms all other models across multiple collections; (RQ2) What are the important features of an effective document ranking function? Our retrieval experiments performed on several TREC test collections of a wide range of sizes (up to the terabyte-sized Clueweb09 Category B) enable us to answer these research questions. This work also serves as a reproducibility study for leading retrieval models. While our experiments show that no single retrieval model outperforms all others across all tested collections, some recent retrieval models, such as MATF and MVD, consistently perform better than the common baselines.

Asymptotic and numerical analysis of slowly varying two-dimensional quantum waveguides

The work is devoted to the asymptotic and numerical analysis of the wave function propagating in two-dimensional quantum waveguides with confining potentials supported on slowly varying tubes. The leading term of the asymptotics of the wave function is determined by an adiabatic approach and the WKB approximation. Unlike other similar studies, in the present work we consider arbitrary bounded potentials and obtain exact solutions for the thresholds, and for the transverse modes in the form of power series of the spectral parameter. Our approach leads to an effective numerical method for the analysis of such quantum waveguides and for the tunnel effect observed in sections of the waveguide that shrink or widen too much. Several examples of interest show the applicability of the method.

Holographic thermal correlators revisited

We study 2-point correlation functions for scalar operators in position space through holography including bulk cubic couplings as well as higher curvature couplings to the square of the Weyl tensor. We focus on scalar operators with large conformal dimensions. This allows us to use the geodesic approximation for propagators. In addition to the leading order contribution, captured by geodesics anchored at the insertion points of the operators on the boundary and probing the bulk geometry thoroughly studied in the literature, the first correction is given by a Witten diagram involving both the bulk cubic coupling and the higher curvature couplings. As a result, this correction is proportional to the VEV of a neutral operator Ok and thus probes the interior of the black hole exactly as in the case studied by Grinberg and Maldacena [13]. The form of the correction matches the general expectations in CFT and allows to identify the contributions of TnOk (being Tn the general contraction of n energy-momentum tensors) to the 2-point function. This correction is actually the leading term for off-diagonal correlators (i.e. correlators for operators of different conformal dimension), which can then be computed holographically in this way.

Forces in Schwarzschild, Vaidya and generalized Vaidya spacetimes

In this paper we investigate how the leading term in the geodesic equation in Schwarzschild spacetime changes under the coordinate transformation to Eddington-Finkelstein coordinates. This term corresponds to the Newton force of attraction. Also we consider this term when we add the energy-momentum tensor of the form of the null dust and the null perfect fluid into right-hand side of the Einstein equation. We estimate the value of this force in Vaidya spacetime when the naked singularity formation occurs. Also we give conditions in generalized Vaidya spacetime when this force of attraction is replaced by the force of repulsion.

Algebraic Lq-norms and complexity-like properties of Jacobi polynomials-Degree and parameter asymptotics

The Jacobi polynomials $\hat{P}_n^{(\alpha,\beta)}(x)$ conform the canonical family of hypergeometric orthogonal polynomials (HOPs) with the two-parameter weight function $(1-x)^\alpha (1+x)^\beta, \alpha,\beta>-1,$ on the interval $[-1,+1]$. The spreading of its associated probability density (i.e., the Rakhmanov density) over the orthogonality support has been quantified, beyond the dispersion measures (moments around the origin, variance), by the algebraic $\mathfrak{L}_{q}$-norms (Shannon and R\’enyi entropies) and the monotonic complexity-like measures of Cram\’er-Rao, Fisher-Shannon and LMC (L\’opez-Ruiz, Mancini and Calbet) types. These quantities, however, have been often determined in an analytically highbrow, non-handy way; specially when the degree or the parameters $(\alpha,\beta)$ are large. In this work, we determine in a simple, compact form the leading term of the entropic and complexity-like properties of the Jacobi polynomials in the two extreme situations: ($n\rightarrow \infty$; fixed $\alpha,\beta$) and ($\alpha\rightarrow \infty$; fixed $n,\beta$). These two asymptotics are relevant \textit{per se} and because they control the physical entropy and complexity measures of the high energy (Rydberg) and high dimensional (pseudoclassical) states of many exactly, conditional exactly and quasi-exactly solvable quantum-mechanical potentials which model numerous atomic and molecular systems.

Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models

We consider the problem of the decomposition of the Rényi entanglement entropies in theories with a non-abelian symmetry by doing a thorough analysis of Wess-Zumino-Witten (WZW) models. We first consider SU(2)k as a case study and then generalise to an arbitrary non-abelian Lie group. We find that at leading order in the subsystem size L the entanglement is equally distributed among the different sectors labelled by the irreducible representation of the associated algebra. We also identify the leading term that breaks this equipartition: it does not depend on L but only on the dimension of the representation. Moreover, a log log L contribution to the Rényi entropies exhibits a universal prefactor equal to half the dimension of the Lie group.

MHV gluon scattering amplitudes from celestial current algebras

We show that the Mellin transform of an n-point tree level MHV gluon scattering amplitude, also known as the celestial amplitude in pure Yang-Mills theory, satisfies a system of (n−2) linear first order partial differential equations corresponding to (n−2) positive helicity gluons. Although these equations closely resemble Knizhnik-Zamoldochikov equations for SU(N) current algebra there is also an additional “correction” term coming from the subleading soft gluon current algebra. These equations can be used to compute the leading term in the gluon-gluon OPE on the celestial sphere. Similar equations can also be written down for the momentum space tree level MHV scattering amplitudes. We also propose a way to deal with the non closure of subleading current algebra generators under commutation. This is then used to compute some subleading terms in the mixed helicity gluon OPE.

Moisture and the Persistence of Annular Modes

Annular modes are the leading mode of variability in extratropical atmospheres, and a key source of predictability at mid-latitudes. Previous studies of annular modes have primarily used dry atmospheric models, so that moisture’s role in annular mode dynamics is still unclear. In this study, a moist two-layer quasi-geostrophic channel model is used to study the effects of moisture on annular mode persistence. Using a channel model allows moisture’s direct effects to be studied, rather than changes in persistence due to geometric effects associated with shifts in jet latitude on the sphere. Simulations are performed in which the strength of latent heat release is varied, to investigate how annular mode persistence responds as precipitation becomes a leading term in the thermodynamic budget. At short lags (<20 model days ≈ 4 Earth days), moisture increases annular mode persistence, reflecting weaker eddy activity that is less effective at disrupting zonal-mean wind anomalies. Comparisons to dry simulations with weaker mean flows demonstrate that moisture is particularly effective at damping high frequency eddies, further enhancing short lag persistence. At long lags (>20 model days), moisture weakly increases persistence, though it decreases the amplitudes of low frequency annular mode anomalies. In the most realistic simulation, the greater short-lag persistence increases the e-folding time of the zonal index by 21 model days (≈4 Earth days). Moisture also causes a transition to propagating variability, though this does not seem to affect the leading mode’s persistence.

Mutual information superadditivity and unitarity bounds

We derive the property of strong superadditivity of mutual information arising from the Markov property of the vacuum state in a conformal field theory and strong subadditivity of entanglement entropy. We show this inequality encodes unitarity bounds for different types of fields. These unitarity bounds are precisely the ones that saturate for free fields. This has a natural explanation in terms of the possibility of localizing algebras on null surfaces. A particular continuity property of mutual information characterizes free fields from the entropic point of view. We derive a general formula for the leading long distance term of the mutual information for regions of arbitrary shape which involves the modular flow of these regions. We obtain the general form of this leading term for two spheres with arbitrary orientations in spacetime, and for primary fields of any tensor representation. For free fields we further obtain the explicit form of the leading term for arbitrary regions with boundaries on null cones.

Singular matrix conjugacy problem with rapidly oscillating off-diagonal entries. Asymptotics of the solution in the case when a diagonal entry vanishes at a stationary point

The ( 2 × 2 ) (2\times 2) matrix conjugacy problem (the Riemann–Hilbert problem) with rapidly oscillating off-diagonal entries and quadratic phase function is considered, specifically, the case when one of the diagonal entries vanishes at a stationary point. For solutions of this problem, the leading term of the asymptotics is found. However, the method allows us to construct complete expansions in power orders. These asymptotics can be used, for example, to construct the asymptotics of solutions of the Cauchy problem for the nonlinear Schrödinger equation for large times in the case of the so-called collisionless shock region.