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English: The investigation in this paper targets the design and the evaluation of jamming intrusion detection based on Fuzzy Logic in wireless mesh IoT Networks in a distributed manner. Our approach uses information collected at local nodes and from the sink as input to the fuzzy logic controller. In order to find th...
English: The detection of gravitational waves (GW) with an electromagnetic counterpart enabled the first Hubble Constant $H_0$ measurement through the standard siren method. Current constraints suggest that $\sim 20-30\%$ of LIGO/Virgo/KAGRA (LVK) Binary Black Hole (BBH) mergers might occur in Active Galactic Nuclei ...
English: Sensing and aggregation of noisy observations should not be considered as separate issues. The quality of collective estimation involves a difficult tradeoff between sensing quality which increases by increasing the number of sensors, and aggregation quality which typically decreases if the number of sensors...
English: In this work, we use the liquid ammonia method to successfully intercalate potassium atoms into ZrTe5 single crystal, and find a transition from semimetal to semiconductor at low temperature in the intercalated ZrTe5. The resistance anomalous peak is gradually suppressed and finally disappears with increasin...
English: A key contribution to X-ray dark-field (XDF) is X-ray diffusion by sample structures smaller than the imaging system's spatial resolution. However, some XDF techniques report that resolvable sample edges also generate XDF. Speckle-based X-ray imaging (SBXI) extracts XDF by analyzing sample-imposed changes to...
English: Existing photorealistic relightable hand models require extensive identity-specific observations in different views, poses, and illuminations, and face challenges in generalizing to natural illuminations and novel identities. To bridge this gap, we present URHand, the first universal relightable hand model t...
English: We study an extension of the classical Paley-Wiener space structure, which is based on bilinear expansions of integral kernels into biorthogonal sequences of functions. The structure includes both sampling expansions and Fourier-Neumann type series as special cases, and it also provides a bilinear expansion ...
English: In large-scale recommendation systems, the vast array of items makes it infeasible to obtain accurate user preferences for each product, resulting in a common issue of missing labels. Typically, only items previously recommended to users have associated ground truth data. Although there is extensive research...
English: We present wide-field multiband photometry of globular cluster (GC) systems in NGC 1399, NGC 1404, and NGC 1387 located at the central region of the Fornax galaxy cluster. Observation was carried out through U, B, V, and I bands, which marks one of the widest and deepest U-band studies on extragalactic GC sy...
English: Consider a random vector (X, T), where X is d-dimensional and T is one-dimensional. We suppose that the random variable T is subject to random right censoring and satisfies the $\alpha$-mixing property. The aim of this paper is to study the behavior of the kernel estimator of the relative error regression an...
English: We study decay properties for solutions to the initial value problem associated with the one-dimensional Zakharov-Rubenchik/Benney-Roskes system. We prove time-integrability in growing compact intervals of size $t^{r}$, $r<2/3$, centered on some characteristic curves coming from the underlying transport equa...
English: Diffusion Transformers (DiTs) dominate video generation but their high computational cost severely limits real-world applicability, usually requiring tens of minutes to generate a few seconds of video even on high-performance GPUs. This inefficiency primarily arises from the quadratic computational complexit...
English: The process by which a system of non-luminous bodies form around a star is fundamental to understanding the origins of our own solar system and how it fits into the context of other systems we have begun to study around other stars. Some basics of solar system formation have emerged to describe the process b...
English: The equation of state and composition of the inner crust of neutron stars at zero temperature are calculated, using the T = 0 version of the TETFSI (temperature-dependent extended Thomas-Fermi plus Strutinsky integral) method, for each of a family of three functionals based on Skyrme-type forces BSk19, BSk20...
English: Microwave photonics (MWP) is an emerging field in which radio frequency (RF) signals are generated, distributed, processed and analyzed using the strength of photonic techniques. It is a technology that enables various functionalities which are not feasible to achieve only in the microwave domain. A particul...
English: Active galaxies are the most powerful engines in the Universe for converting gravitational energy into radiation, and their study at all epochs of evolution is therefore important. Powerful radio-loud quasars and radio galaxies have the added advantage that, since their radio jets need X-ray-emitting gas as ...
English: The high tunability of the density of states of graphene makes it an ideal probe of quantum transport in different regimes. In particular, the supercurrent that can flow through a non-superconducting (N) material connected to two superconducting electrodes, crucially depends on the lenghth of the N relative ...
English: The structural and magnetic properties of spinel compounds $CoB_2O_4$ (B=Cr,Mn and Fe) are studied using the DFT+U method and generalized gradient approximation (GGA). We concentrate on understanding the trends in the properties of these materials as the B cation changes, in terms of relative strengths of cr...
English: In this paper we present our system design and methodology for making absolute quantum efficiency (QE) measurements through the vacuum ultraviolet (VUV) and verify the system with delta-doped silicon CCDs. Delta-doped detectors provide an excellent platform to validate measurements through the VUV due to the...
English: In this paper we investigate the resonant electron-plasmon interactions in a drifting electron gas of arbitrary degeneracy. The kinetic corrected quantum hydrodyanmic model is transformed into the effective Schr\"{o}dinger-Poisson model and driven coupled pseudoforce system is obtained via the separation of ...
English: Riemann sums, a classical method for approximating the definite integral of a function, have been extensively studied in the past. However, their monotonic properties, while still of great importance, particularly in approximation theory and interpolation theory, remain somewhat obscure. This paper is dedica...
English: We consider single cell multi-user OFDMA downlink resource allocation on a flat-fading channel such that average supply power is minimized while fulfilling a set of target rates. Available degrees of freedom are transmission power and duration. This paper extends our previous work on power optimal resource a...
English: The notion of mid $p$-summable sequences was introduced by Karn and Sinha in 2014 and recently explored and expanded by Botelho, Campos and Santos in 2017. In this paper we design a theory of mid summable sequences in the anisotropic setting defining a new more general space called space of mid $(q,p)$-summa...
English: In this work we are interested in extreme vortex states leading to the maximum possible growth of palinstrophy in 2D viscous incompressible flows on periodic domains. This study is a part of a broader research effort motivated by the question about the finite-time singularity formation in the 3D Navier-Stoke...
English: Superbursts are thought to be powered by the unstable ignition of a carbon-enriched layer formed from the burning of accreted hydrogen and helium. As shown by Cumming & Bildsten, the short recurrence time hinges on the crust being sufficiently hot at densities > 1.0e9 g/cc. In this Letter, we self-consistent...
English: We present a practical approach for computing the sandwich variance estimator in two-stage regression model settings. As a motivating example for two-stage regression, we consider regression calibration, a popular approach for addressing covariate measurement error. The sandwich variance approach has been ra...
English: We surveyed the 25 Ori association for direct-imaging companions. This association has an age of only few million years. Among other targets, we observed CVSO 30, which has recently been identified as the first T Tauri star found to host a transiting planet candidate. We report on photometric and spectroscop...
English: Until recently, it has been possible only for nearby galaxies to study the scaling relations between central black hole and host galaxy in detail. Because of the small number densities at low redshift, (luminous) AGN are underrepresented in such detailed studies. The advent of adaptive optics (AO) at large t...
English: Multi-modal word semantics aims to enhance embeddings with perceptual input, assuming that human meaning representation is grounded in sensory experience. Most research focuses on evaluation involving direct visual input, however, visual grounding can contribute to linguistic applications as well. Another mo...
English: Parabolic almost conformally symplectic structures were introduced in the first part of this series of articles as a class of geometric structures which have an underlying almost conformally symplectic structure. If this underlying structure is conformally symplectic, then one obtains a PCS-structure. In the...
English: We present HST/STIS observations and analysis of two prominent nebular structures around the central source of Eta Carinae, the knots C and D. The former is brighter than the latter for emission lines from intermediate or high ionization potential ions. The brightness of lines from intermediate and high ioni...
English: This thesis deals with the general problem of determining when the heart $\mathcal{H}$ of a t-structure in a triangulated category $\mathcal{D}$ is a Grothendieck or a module category. As preliminaries, we study Grothendieck conditions AB3-AB5 for $\mathcal{H}$ in a very general setting. We then concentrate ...
English: A new method for the design of linear-phase robust far-field broadband beamformers using constrained optimization is proposed. In the method, the maximum passband ripple and minimum stopband attenuation are ensured to be within prescribed levels, while at the same time maintaining a good linear-phase charact...
English: We develop a framework and unified, compact notation to include neutrino direct interaction effects with neutrino oscillations for a wide class of low-energy, effective four-Fermi interactions. Modest flavor-violating interaction strengths can make significant changes in the boundaries in $\Delta M^2 \leftri...
English: We show that manifolds of fixed points, which are generated by exactly marginal operators, are common in N=1 supersymmetric gauge theory. We present a unified and simple prescription for identifying these operators, using tools similar to those employed in two-dimensional N=2 supersymmetry. In particular we ...
English: Looking into the inside of radiative corrections is an interesting subject as a deeper study of the standard electroweak theory after its remarkable success in the precision analyses. I will discuss here a test of ``structure" of the EW radiative corrections to the weak-boson masses, and show that we can now...
English: We apply parquet-diagram summation methods for the calculation of the superfluid gap in $S$-wave pairing in neutron matter for realistic nucleon-nucleon interactions such as the Argonne $v_6$ and the Reid $v_6$ potentials. It is shown that diagrammatic contributions that are outside the parquet class play an...
English: Despite the recent advances in the so-called "cold start" generation from text prompts, their needs in data and computing resources, as well as the ambiguities around intellectual property and privacy concerns pose certain counterarguments for their utility. An interesting and relatively unexplored alternati...
English: We generated an event catalog with an automated detection algorithm based on the entire EUVI image database observed with the two Solar Terrestrial Relations Observatory STEREO-A and -B spacecraft over the first six years of the mission (2006\,--\,2012). The event catalog includes the heliographic positions ...
English: We tackle the "relative" Lehmer problem on algebraic subvarieties of a multiplicative torus. Generalizing a theorem of F. Amoroso and U. Zannier, we give a lower bound for the normalized height of a non torsion hypersurface in terms of its obstruction index over $\Q^{ab}$, the maximal abelian extension of $\...
English: Context: Molecular hydrogen ($\rm{H_2}$) is crucial in galaxy formation and evolution, serving as the main fuel for star formation (SF). In metal-enriched environments, $\rm{H_2}$ primarily forms on interstellar dust grain surfaces. However, due to the complexities of modelling this process, SF in cosmologic...
English: Conservation laws in the form of elliptic and parabolic partial differential equations (PDEs) are fundamental to the modeling of many problems such as heat transfer and flow in porous media. Many of such PDEs are stochastic due to the presence of uncertainty in the conductivity field. Based on the relation b...
English: Multimodal large language models (MLLMs) have achieved significant success in the general field of image processing. Their emerging task generalization and freeform conversational capabilities can greatly facilitate medical diagnostic assistance, helping patients better understand their conditions and enhanc...
English: We report the discovery of coherent radio emission from the young, rapidly-rotating magnetic Bp star HD 133880 at a frequency of 610 MHz with the Giant Metrewave Radio Telescope (GMRT). This is only the second magnetic star in which coherent radio emission has been detected. In our observations of HD 133880 ...
English: Most existing text-to-image generation methods adopt a multi-stage modular architecture which has three significant problems: 1) Training multiple networks increases the run time and affects the convergence and stability of the generative model; 2) These approaches ignore the quality of early-stage generator...
English: The application of deep neural networks to remote sensing imagery is often constrained by the lack of ground-truth annotations. Adressing this issue requires models that generalize efficiently from limited amounts of labeled data, allowing us to tackle a wider range of Earth observation tasks. Another challe...
English: In 2009, J. Wood proved that Frobenius bimodules have the extension property for symmetrized weight compositions. More generally, it was later shown that having a cyclic socle is sufficient for satisfying the property, while the necessity remained an open question. In this thesis, a partial converse is prove...
English: The study of excited hadron spectra using Lattice QCD is currently evolving. An important step toward obtaining resonance parameters from Lattice QCD is the calculation of finite volume energy spectra. Somewhat more rigorous studies of finite volume spectra are currently possible and should be completed in t...
English: We compare the predictions of a range of existing models based on the Vector Meson Dominance hypothesis with data on e^+ e^- -> pi^+ pi^$ and e^+ e^- -> mu^+ mu^- cross-sections and the phase and near-threshold behavior of the timelike pion form factor, with the aim of determining which (if any) of these mod...
English: The goal of the study is to determine the underlying processes leading to the observed collaborator distribution in modern scientific fields, with special attention to non-power law behavior. Nanoscience is used as a case study of a modern interdisciplinary field, and its coauthorship network for 2000-04 per...
English: Let G be a finite group of order n and V an irreducible representation over the complex numbers of dimension d. For some nonnegative number e, we have n=d(d+e). If e is small, then the character of V has unusually large degree. We fix e and attempt to classify such groups. For e<=3 we give a complete classif...
English: We discuss a new completely integrable case of the time-dependent Schroedinger equation in $R^n$ with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator recently considered by Meiler, Cordero-Soto, and Suslov. A second pair o...
English: New particles coupled to the Standard Model can equilibrate in stellar cores if they are sufficiently heavy and strongly coupled. In this work, we investigate the astrophysical consequences of such a scenario for massive stars by incorporating new contributions to the equation of state into a state of the ar...
English: In this work, a study on Variable Neighborhood Search algorithms for multi-depot dial-a-ride problems is presented. In dial-a-ride problems patients need to be transported from pre-specified pickup locations to pre-specified delivery locations, under different considerations. The addressed problem presents s...
English: We present the first inelastic neutron scattering study of the short wavelength dynamics in a phospholipid bilayer. We show that inelastic neutron scattering using a triple-axis spectrometer at the high flux reactor of the ILL yields the necessary resolution and signal to determine the dynamics of model memb...
English: We theoretically studied the thermally assisted spin torque switching of a synthetic free layer and showed that the switching time is minimized if the condition H_J=\|H_s\|/(2 alpha) is satisfied, where H_J, H_s and alpha are the coupling field of two ferromagnetic layers, the amplitude of the spin torque, and...
English: Many imaging systems are used to estimate a vector of parameters associated with the object being imaged. In many cases there are other parameters in the model for the imaging data that are not of interest for the task at hand. We refer to these as nuisance parameters and use them to form the components of t...
English: Decoding for many NLP tasks requires an effective heuristic algorithm for approximating exact search since the problem of searching the full output space is often intractable, or impractical in many settings. The default algorithm for this job is beam search -- a pruned version of breadth-first search. Quite...
English: Online recommender systems should be always aligned with users' current interest to accurately suggest items that each user would like. Since user interest usually evolves over time, the update strategy should be flexible to quickly catch users' current interest from continuously generated new user-item inte...
English: As essential aerial platforms, unmanned aerial vehicles (UAVs) play an increasingly important role in broad wireless connectivity and high-data-rate transmission for future communication systems. Notably, various communication scenarios are involved in UAV communications, such as intercommunications between ...
English: Generalized quantum cluster algebras introduced in [1] are quantum deformation of generalized cluster algebras of geometric types. In this paper, we prove that the Laurent phenomenon holds in these generalized quantum cluster algebras. We also show that upper bounds coincide with the corresponding generalize...
English: In spite of the great success of deep learning technologies, training and delivery of a practically serviceable model is still a highly time-consuming process. Furthermore, a resulting model is usually too generic and heavyweight, and hence essentially goes through another expensive model compression phase t...
English: This work aims to design a cellular network for maximal energy efficiency (EE). In particular, we consider the uplink with multi-antenna base stations and assume that zero- forcing (ZF) combining is used for data detection with imperfect channel state information. Using stochastic geometry and a new lower bo...
English: We study the Chern-Simons number diffusion rate in the (1+1)-dimensional latticeAbelian Higgs model at temperatures much higher than, as well as comparable to, the sphaleron energy. It is found that in the high-temperature limit the rate is likely to grow as power 2/3 of the temperature. In the intermediate-...
English: It is shown that the evidence asserted in the Comment [arXiv:1205.6418] on the chemical composition data published by Carpinteri et al. [Strain 47 (Suppl. 2), 282 (2011)]-that the data "cannot be the result of independent measurements as claimed by the authors" -may be not necessarily true. A simpler fact co...
English: Currency note recognition is a critical accessibility need for blind individuals, as identifying banknotes accurately can impact their independence and security in financial transactions. Several traditional and technological initiatives have been taken to date. Nevertheless, these approaches are less user-f...
English: We explore the thermodynamics and phase structure of the Polyakov loop-extended two flavor chiral quark--meson (PQM) model beyond the mean-field approximation at imaginary chemical potential. Our approach is based on the functional renormalization group (FRG) method. At finite temperature and imaginary chemi...
English: We investigated the evolutionary stages and disk properties of 211 Young stellar objects (YSOs) across the Perseus cloud by modeling the broadband optical to mid-infrared (IR) spectral energy distribution (SED). By exploring the relationships among the turnoff wave bands lambda_turnoff (longward of which sig...
English: Adhesion of bacteria to liquid-liquid interfaces can play a role in the biodegradation of dispersed hydrocarbons and in biochemical and bioprocess engineering. Whereas thermodynamic factors underpinning adhesion are well studied, the role of bacterial activity on adhesion is less explored.Here, we show that ...
English: We have analized a sample of 327 clusters of galaxies spanning the range 0.06-0.70 in redshift. Strong constraints on their mean intracluster emission by dust have been obtained using maps and catalogs from the HERSCHEL HerMES project; within a radius of 5 arcmin centered in each cluster, the 95% C.L. limits...
English: Non-convex quadratically constrained quadratic programming (QCQP) problems have numerous applications in signal processing, machine learning, and wireless communications, albeit the general QCQP is NP-hard, and several interesting special cases are NP-hard as well. This paper proposes a new algorithm for gen...
English: In the first Born approximation we study the reactions $K\phi\to\pi K$, $\rho K$, $\pi K^$, and $\rho K^$ with quark-antiquark annihilation and creation. Transition amplitudes are derived with the development in spherical harmonics of the relative-motion wave functions of the two initial mesons and of the ...
English: The aims of this work are 1) to sketch a proof that there are such parameterizations of the local frame and canonical connection structures when the gravitational field equations in f(R,T)-modified gravity, MG, can be integrated in generic off-diagonal forms with metrics depending on all spacetime coordinate...
English: We report the discovery of a radio transient VLA 232937.2-235553, coincident with the proposed X-ray afterglow for the gamma-ray burst GRB 981226. This GRB has the highest ratio of X-ray to gamma-ray fluence of all the GRBs detected by BeppoSAX so far and yet no corresponding optical transient was detected. ...
English: We extend Douglas' solution of the problem of finding minimal surfaces to anti-de Sitter space. The case of a circle as a boundary contour is elaborated. We discuss applications to ${\cal N}=4$ super Yang-Mills: a circular Wilson loop and the Schwinger process, where we calculate the $1/\sqrt{\lambda}$ corre...
English: We discuss a box model of migration in channels of networks with possible application for modelling motion of migrants in migration networks. The channel consists of nodes of the network (nodes may be considered as boxes representing countries) and edges that connect these nodes and represent possible ways f...
English: This paper deals with quadratic irrationals of the form $m/q+\sqrt v$ for fixed positive integers $v$ and $q$, $v$ not a square, and varying integers $m$, $(m,q)=1$. Two numbers $m/q+\sqrt v$, $n/q+\sqrt v$ of this kind are equivalent (in a classical sense) if their continued fraction expansions can be writt...
English: We consider a simple initial-boundary-value problem for the shallow water equations in one space dimension. We discretize the problem in space by the standard Galerkin finite element method on a quasiuniform mesh and in time by the classical 4-stage, 4th order, explicit Runge-Kutta scheme. Assuming smoothnes...
English: Stable Set and Graph Coloring belong to the class of NP-hard optimization problems on graphs. It is well known that even near-optimal solutions for these problems are difficult to find in polynomial time. The Lov\'asz theta function, introduced by Lov\'asz in the late 1970s, provides a powerful tool in the s...
English: The fullerene C$_{60}$, one of the largest molecules identified in the interstellar medium (ISM), has been proposed to form top-down through the photo-chemical processing of large (more than 60 C-atoms) polycyclic aromatic hydrocarbon (PAH) molecules. In this article, we focus on the opposite process, invest...
English: We formulate, solve computationally and study experimentally the problem of collecting solar energy in three dimensions(1-5). We demonstrate that absorbers and reflectors can be combined in the absence of sun tracking to build three-dimensional photovoltaic (3DPV) structures that can generate measured energy...
English: Numerical security proofs offer a versatile approach for evaluating the secret-key generation rate of quantum key distribution (QKD) protocols. However, existing methods typically require perfect source characterization, which is unrealistic in practice due to the presence of inevitable encoding imperfection...
English: In this paper, we arrive at the notion of equivalence classes of a non-commutative field exploring some ideas by Soloviev to nonlocal quantum fields. Specifically, an equivalence relation between non-commutative fields is formulated by replacing the weak relative locality condition by a weak relative asympto...
English: Motivated by recent experiments searching for Majorana zero modes in tripartite semiconductor nanowires with epitaxial superconductor and ferromagnetic-insulator layers, we explore the emergence of topological superconductivity in such devices for paradigmatic arrangements of the three constituents. Accounti...
English: We study semiparametric inference in some linear regression models with time-varying coefficients, dependent regressors and dependent errors. This problem, which has been considered recently by Zhang and Wu (2012) under the functional dependence measure, is interesting for parsimony reasons or for testing st...
English: An exact solution for a high speed deterministic traffic model with open boundaries and synchronous update rule is presented. Because of the strong correlations in the model, the qualitative structure of the stationary state can be described for general values of the maximum speed. It is shown in the case of...
English: X-ray photoelectron diffraction is used to directly probe the intra-cell polar atomic distortion and tetragonality associated with ferroelectricity in ultrathin epitaxial PbTiO3 films. Our measurements, combined with ab-initio calculations, unambiguously demonstrate non-centro-symmetry in films a few unit ce...
English: The sliding window model of computation captures scenarios in which data are continually arriving in the form of a stream, and only the most recent $w$ items are used for analysis. In this setting, an algorithm needs to accurately track some desired statistics over the sliding window using a small space. Whe...
English: This paper explores zero-label learning in Natural Language Processing (NLP), whereby no human-annotated data is used anywhere during training and models are trained purely on synthetic data. At the core of our framework is a novel approach for better leveraging the powerful pretrained language models. Speci...
English: In recent years, sensors from smart consumer devices have shown great diagnostic potential in movement disorders. In this context, data modalities such as electronic questionnaires, hand movement and voice captures have successfully captured biomarkers and allowed discrimination between Parkinson's disease (...
English: In recent years, there has been a surge of interest in research on automatic mental health detection (MHD) from social media data leveraging advances in natural language processing and machine learning techniques. While significant progress has been achieved in this interdisciplinary research area, the vast ...
English: The emergence of mental states from neural states by partitioning the neural phase space is analyzed in terms of symbolic dynamics. Well-defined mental states provide contexts inducing a criterion of structural stability for the neurodynamics that can be implemented by particular partitions. This leads to di...
English: It is well known that azimuthal spin wave modes of magnetic vortex state in permalloy nanodisks have circular symmetry. Intuitively, magnetic materials having magnetocrystalline anisotropy is not compatible with the circular symmetry of the azimuthal modes. In this article, however, we report cubic azimuthal...
English: This paper presents a novel approach for enhancing the multiple sets of acoustic patterns automatically discovered from a given corpus. In a previous work it was proposed that different HMM configurations (number of states per model, number of distinct models) for the acoustic patterns form a two-dimensional...
English: We present some new results on searches for new physics at the Tevatron Run 1 (1992 -- 1996). The topics covered are searches for R-Parity violating and conserving mSUGRA, large extra dimensions in di-photon and monojet channels, leptoquark in jets + missing Et channel, and two model independent searches. Al...
English: In unsupervised learning, an unbiased uniform sampling strategy is typically used, in order that the learned features faithfully encode the statistical structure of the training data. In this work, we explore whether active example selection strategies - algorithms that select which examples to use, based on...
English: Lattice QCD calculations of baryon forces are performed for the first time with (almost) physical quark masses. $N_f = 2+1$ dynamical clover fermion gauge configurations are generated at the lattice spacing of $a \simeq 0.085$ fm on a $(96 a)^4 \simeq (8.2 {\rm fm})^4$ lattice with quark masses corresponding...
English: Millimeter-wave has become an integral part of 5G networks to meet the ever-increasing demand for user data throughput. Employing higher carrier frequencies introduces new challenges for the propagation channel such as higher path loss and rapid signal degradations. On the other hand, higher frequencies allo...
English: We present a formalism for jointly fitting pre- and post-reconstruction redshift-space clustering (RSD) and baryon acoustic oscillations (BAO) plus gravitational lensing (of the CMB) that works directly with the observed 2-point statistics. The formalism is based upon (effective) Lagrangian perturbation theo...