Miracle-dz/UniFAR-FTUs huggingface dataset:
Robust and efficient CMB lensing power spectrum from polarization surveys

Deep surveys of the CMB polarization have more information on the lensing signal than the quadratic estimators (QE) can capture. We showed in a recent work that a CMB lensing power spectrum built from a single optimized CMB lensing mass map, working in close analogy to state-of-the-art QE techniques, can result in an essentially optimal spectrum estimator at reasonable numerical cost. We extend this analysis here to account for real-life non-idealities including masking and realistic instrumental noise maps. As in the QE case, it is necessary to include small corrections to account for the estimator response to these anisotropies, which we demonstrate can be estimated easily from simulations. The realization-dependent debiasing of the spectrum remains robust, allowing unbiased recovery of the band powers even in cases where the statistical model used for the lensing map reconstruction is grossly wrong. This allows now robust and at the same time optimal CMB lensing constraints from CMB data, on all scales relevant for the inference of the neutrino mass, or other parameters of our cosmological model.
On exceptionality of dimension three in terms of lattice angles

In this study, we investigate the lattice angle, which is defined as the angle between two vectors whose components are integers. We focus on the set of angles between a fixed integer vector and other integer vectors. For non-three-dimensional lattices, we proved that this set contains all lattice angles, irrespective of the fixed vector choice. In contrast, for the three-dimensional lattice, we proved that this set of angles cannot cover all lattice angles, for any fixed vector. Thus, only the three-dimensional lattice is an exception. We further provide the condition for a given three-dimensional integer vector to intersect another integer vector at a given angle, which involves a number-theoretic property of the squared norm of the given vector and the squared tangent of the given angle.
Real moments of the logarithmic derivative of characteristic polynomials in random matrix ensembles

We prove asymptotics for real moments of the logarithmic derivative of characteristic polynomials evaluated at $1-\frac{a}{N}$ in unitary, even orthogonal, and symplectic ensembles, where $a>0$ and $a=o(1)$ as the size $N$ of the matrix goes to infinity. Previously, such asymptotics were known only for integer moments (in the unitary ensemble by the work of Bailey, Bettin, Blower, Conrey, Prokhorov, Rubinstein and Snaith, and in orthogonal and symplectic ensembles by the work of Alvarez and Snaith), except that in the odd orthogonal ensemble real moments asymptotics were obtained by Alvarez, Bousseyroux and Snaith. Our proof is new and does not make use of the aforementioned integer moments results, and is different from the method in the work of Alvarez et al for the odd orthogonal ensemble.
Controle do crescimento de mudas de morangueiro Camarosa cultivadas em substrato comercial pela aplicação de Proexadione cálcio

O objetivo do trabalho foi avaliar o efeito do proexadione calcio (ProCa) no controle do crescimento de mudas de morangueiro para producao em substrato comercial. O experimento foi realizado em casa de vegetacao com mudas da cultivar Camarosa produzidas por enraizamento de estoloes e mantidas em bandejas de 72 celulas. Os tratamentos consistiram de sete concentracoes do regulador de crescimento vegetal ProCa (0, 25, 50, 100, 200, 400 e 800 mg L-1). Sendo realizadas avaliacoes de crescimento vegetativo e resposta fisiologica. O delineamento foi inteiramente casualizado com quatro repeticoes de 12 plantas. Observou-se que aplicacoes de doses de ProCa a partir de 200 mg L-1 (200, 400 e 800 mg L-1), reduzem o crescimento vegetativo, assim como, aumentam a concentracao de clorofila e a atividade fotossintetica de mudas de morangueiro ‘Camarosa’
Dynamic Point Fields

Recent years have witnessed significant progress in the field of neural surface reconstruction. While extensive focus was put on volumetric and implicit approaches, a number of works have shown that explicit graphics primitives, such as point clouds, can significantly reduce computational complexity without sacrificing the reconstructed surface quality. However, less emphasis has been put on modeling dynamic surfaces with point primitives. In this work, we present a dynamic point field model that combines the representational benefits of explicit point-based graphics with implicit deformation networks to allow efficient modeling of non-rigid 3D surfaces. Using explicit surface primitives also allows us to easily incorporate well-established constraints such as isometric-as-possible regularization. While learning this deformation model is prone to local optima when trained in a fully unsupervised manner, we propose to also leverage semantic information, such as keypoint correspondence, to guide the deformation learning. We demonstrate how this approach can be used for creating an expressive animatable human avatar from a collection of 3D scans. Here, previous methods mostly rely on variants of the linear blend skinning paradigm, which fundamentally limits the expressivity of such models when dealing with complex cloth appearances, such as long skirts. We show the advantages of our dynamic point field framework in terms of its representational power, learning efficiency, and robustness to out-of-distribution novel poses. The code for the project is publicly available 1.
Noncommutative Derivation of the Planck's Radiation Law

The Planck's radiation law for the blackbody radiation spectrum was capable to explain the experimentally-measured blackbody spectrum. In order to get this result, Planck proposed his radiation law in a two-fold way: 1) by an \textit{ad hoc} modification of the assumed connection between energy and entropy for thermal radiation; 2) by assuming that the calculation of the entropy of an oscillator in thermal equilibrium with radiation is carried out by discrete units of energy. As a consequence, the energy quantization, linear in frequency, was thus introduced into physics. However, the energy quantization of the simple harmonic oscillator was originally postulated by Planck in an incomplete way, i.e., the ground state energy was not assumed to be null. Of course, this issue has been solved in different ways over time. Despite of this, we propose an alternative way to fix this issue by describing harmonic oscillators at noncommutative(NC) framework, where the non-null ground state energy naturally arises as a NC contribution. With this approach, the Planck's quantum theory is updated and, consequently, becomes compatible with the quantum mechanics inaugurated in 1925.
2 1 O ct 2 01 4 A NEW SIMPLE PROOF OF THE AZTEC DIAMOND

The Aztec diamond of order n is the union of lattice squares in the plane intersecting the square |x| + |y| < n. The Aztec diamond theorem states that the number of domino tilings of this shape is 2n(n+1)/2. It was first proved by Elkies, Kuperberg, Larsen and Propp in 1992. We give a new simple proof of this theorem. A domino is a 1 × 2 rectangle in the plane whose corners are lattice points, i.e. have integer coordinates. A domino tiling of a subset S of the plane is a covering of S by a set of dominoes whose interiors are disjoint. The problem of counting the number of domino tilings (or tilings, for short) of a given set S has received much attention in the last 50 years, partly because of its significance in physics, but also because of the many beautiful mathematical structures that have appeared in its study. For example, the number of domino tilings of a 2 × n rectangle is the nth Fibonacci number, and there is a rather non-trivial formula for the number of domino tilings of an m×n-rectangle due to Kasteleyn [5], Fisher and Temperley [9], which for even m = n reads 2 /2 n/2
High-energy spin waves in the spin-1 square-lattice antiferromagnet 
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Inelastic neutron scattering is used to study the magnetic excitations of the $S=1$ square-lattice antiferromagnet La$_2$NiO$_4$. We find that the spin waves cannot be described by a simple classical (harmonic) Heisenberg model with only nearest-neighbor interactions. The spin-wave dispersion measured along the antiferromagnetic Brillouin-zone boundary shows a minimum energy at the $(1/2,0)$ position as is observed in some $S=1/2$ square-lattice antiferromagnets. Thus, our results suggest that the quantum dispersion renormalization effects or longer-range exchange interactions observed in cuprates and other $S=1/2$ square-lattice antiferromagnets are also present in La$_2$NiO$_4$. We also find that the overall intensity of the spin-wave excitations is suppressed relative to linear spin-wave theory indicating that covalency is important. Two-magnon scattering is also observed.
Modeling Compact Objects with EFT II: The Post-Newtonian Expansion

Part 2 of 3 from master's thesis: Modeling Compact Objects with Effective Field Theory. Using the Effective Field Theory framework for extended objects, we build the effective theory of a binary system made up of the most general compact objects in a theory of gravity as General Relativity with electrodynamics, objects which are described by their mass, spin, charge and their finite-size structure. We obtain the leading order post-Newtonian expansion to each of the relevant terms in the effective action that have been derived using the coset construction, where the covariant building blocks to build up the tower of invariant operators are derived from symmetry principles. Having matched the coefficients of the theory from the literature, we show the predictivity of our theory by obtaining well known post-Newtonian results on spinning extended objects, as well as on charged objects. Then, we bring new results on the polarizability and dissipation of charged spinning compact objects.
Knowledge Combination to Learn Rotated Detection without Rotated Annotation

Rotated bounding boxes drastically reduce output ambiguity of elongated objects, making it superior to axis-aligned bounding boxes. Despite the effectiveness, rotated detectors are not widely employed. Annotating rotated bounding boxes is such a laborious process that they are not provided in many detection datasets where axis-aligned annotations are used instead. In this paper, we propose a framework that allows the model to predict precise rotated boxes only requiring cheaper axis-aligned annotation of the target dataset 1. To achieve this, we leverage the fact that neural networks are capable of learning richer representation of the target domain than what is utilized by the task. The under-utilized representation can be exploited to address a more detailed task. Our framework combines task knowledge of an out-of-domain source dataset with stronger annotation and domain knowledge of the target dataset with weaker annotation. A novel assignment process and projection loss are used to enable the cotraining on the source and target datasets. As a result, the model is able to solve the more detailed task in the target domain, without additional computation overhead during inference. We extensively evaluate the method on various target datasets including fresh-produce dataset, HRSC2016 and SSDD. Results show that the proposed method consistently performs on par with the fully supervised approach.
On creating new essential spectrum by self-adjoint extension of gapped operators

Given a densely defined and gapped symmetric operator with infinite deficiency index, it is shown how self-adjoint extensions admitting arbitrarily prescribed portions of the gap as essential spectrum are identified and constructed within a general extension scheme. The emergence of new spectrum in the gap by self-adjoint extension is a problem with a long history and recent deep understanding, and yet it remains topical in several recent applications. Whereas it is already an established fact that, in case of infinite deficiency index, any kind of spectrum inside the gap can be generated by a suitable self-adjoint extension, the present discussion has the virtue of showing the clean and simple operator-theoretic mechanism of emergence of such extensions.
A non-backtracking method for long matrix completion

We consider the problem of rectangular matrix completion in the regime where the matrix M of size n × m is “long”, i.e., the aspect ratio m/n diverges to inﬁnity. Such matrices are of particular interest in the study of tensor completion, where they arise from the unfolding of an odd-order low-rank tensor. In the case where the sampling probability is d √ mn , we propose a new algorithm for recovering the singular values and left singular vectors of the original matrix based on a variant of the standard non-backtracking operator of a suitably deﬁned bipartite graph. We show that when d is above a Kesten-Stigum-type sampling threshold, our algorithm recovers a correlated version of the singular value decomposition of M with quantiﬁable error bounds. This is the ﬁrst result in the regime of bounded d for weak recovery and the ﬁrst result for weak consistency when d → ∞ arbitrarily slowly without any polylog factors.
How well do Large Language Models perform in Arithmetic tasks?

Large language models have emerged abilities including chain-of-thought to answer math word problems step by step. Solving math word problems not only requires abilities to disassemble problems via chain-of-thought but also needs to calculate arithmetic expressions correctly for each step. To the best of our knowledge, there is no work to focus on evaluating the arithmetic ability of large language models. In this work, we propose an arithmetic dataset MATH 401 to test the latest large language models including GPT-4, ChatGPT, InstrctGPT, Galactica, and LLaMA with various arithmetic expressions and provide a detailed analysis of the ability of large language models. MATH 401 and evaluation codes are released at \url{https://github.com/GanjinZero/math401-llm}.
Self-Distillation for Gaussian Process Regression and Classification

We propose two approaches to extend the notion of knowledge distillation to Gaussian Process Regression (GPR) and Gaussian Process Classification (GPC); data-centric and distribution-centric. The data-centric approach resembles most current distillation techniques for machine learning, and refits a model on deterministic predictions from the teacher, while the distribution-centric approach, re-uses the full probabilistic posterior for the next iteration. By analyzing the properties of these approaches, we show that the data-centric approach for GPR closely relates to known results for self-distillation of kernel ridge regression and that the distribution-centric approach for GPR corresponds to ordinary GPR with a very particular choice of hyperparameters. Furthermore, we demonstrate that the distribution-centric approach for GPC approximately corresponds to data duplication and a particular scaling of the covariance and that the data-centric approach for GPC requires redefining the model from a Binomial likelihood to a continuous Bernoulli likelihood to be well-specified. To the best of our knowledge, our proposed approaches are the first to formulate knowledge distillation specifically for Gaussian Process models.
Metrics and properties of optimal gauges in multimode cavity QED

Multi-mode cavity quantum electrodynamics (QED) describes, for example, the coupling between an atom and a multi-mode electromagnetic resonator. The gauge choice is important for practical calculations in truncated Hilbert spaces, because the exact gauge-invariance is recovered only in the whole space. An optimal gauge can be defined as the one predicting the most accurate observables for the same number of atomic levels and modes. Different metrics quantifying the gauge performance can be introduced depending on the observable of interest. In this work we demonstrate that the optimal choice is generally mode-dependent, i.e., a different gauge is needed for each cavity mode. While the choice of gauge becomes more important for increasing light-matter interaction, we also show that the optimal gauge does not correspond to the situation where the entanglement between light and matter is the smallest.
Modules Satisfying the S-Noetherian Property and S-ACCR

Let R be a commutative ring with unity, S a multiplicative subset of R, and M an R-module. In this article, we investigate S-Noetherian modules. We give an S-version of Eakin–Nagata–Formanek Theroem [7], in the case where S is finite. We prove that if M is an S-finite R-module and any increasing chain of extended submodules of M is S-stationary then M is S-Noetherian. In the second part of this article, we define S-accr modules. An R-module M is said to satisfy S-accr if any ascending chain of residuals of the form (N: B) ⊆ (N: B2) ⊆ (N: B3) ⊆ … is S-stationary where N is a submodule of M and B is a finitely generated ideal of R. We investigate the class of such modules M, and we generalize some known results of P. C. Lu ([5], [6]).
A Comprehensive Mass Flux Scheme for Cumulus Parameterization in Large-Scale Models

Abstract Observational studies indicate that a mass flux approach may provide a realistic framework for cumulus parameterization in large-scale models, but this approach, through the introduction of a spectral cloud ensemble, leads normally to rather complex schemes. In this paper the question is addressed whether much simpler schemes can already provide realistic values of the thermal forcing by convection under various synoptic conditions. This is done through verifying such a scheme first on data from field experiments for periods of tropical penetrative convection (GATE, Marshall Islands), tradewind cumuli (ATEX, BOMEX) and extratropical organized convection (SESAME-79) and then in a NWP model. The scheme considers a population of clouds where the cloud ensemble is described by a one-dimensional bulk model as earlier applied by Yanai et al. in a diagnostic study of tropical convection. Cumulus scale downdrafts are included. Various types of convection are represented, i.e., penetrative convection in c.
A note on the classification of positive solutions to the critical p-Laplace equation in $\mathbb{R}^n$

In this note, we obtain a classification result for positive solutions to the critical p-Laplace equation in $\mathbb{R}^n$ with $n\ge4$ and $p>p_n$ for some number $p_n\in\left(\frac{n}{3},\frac{n+1}{3}\right)$ such that $p_n\sim\frac{n}{3}+\frac{1}{n}$, which slightly improves upon a similar result recently obtained by Ou under the condition $p\ge\frac{n+1}{3}$.
Van der Waals Nanoantennas on Gold as Hosts for Hybrid Mie-Plasmonic Resonances

Dielectric nanoresonators have been shown to circumvent the heavy optical losses associated with plasmonic devices, however they suffer from less confined resonances. By constructing a hybrid system of both dielectric and metallic materials, one can retain the low losses of dielectric resonances, whilst gaining additional control over the tuning of the modes with the metal, and achieving stronger mode confinement. In particular, multi-layered van der Waals materials are emerging as promising candidates for integration with metals owing to their weak attractive forces, which enable deposition onto such substrates without the requirement of lattice matching. Here we use layered, high refractive index WS$_2$ exfoliated on gold, to fabricate and optically characterize a hybrid nanoantenna-on-gold system. We experimentally observe a hybridization of Mie resonances, Fabry-P\'erot modes, and surface plasmon-polaritons launched from the nanoantennas into the substrate. We achieve experimental quality factors of Mie-plasmonic modes of up to 20 times that of Mie resonances in nanoantennas on silica, and observe signatures of a supercavity mode with a Q factor of 263 $\pm$ 28, resulting from strong mode coupling between a higher-order anapole and Fabry-P\'erot-plasmonic mode. We further simulate WS$_2$ nanoantennas on gold with an hBN spacer, resulting in calculated electric field enhancements exceeding 2600, and a Purcell factor of 713. Our results demonstrate dramatic changes in the optical response of dielectric nanophotonic structures placed on gold, opening new possibilities for nanophotonics and sensing with simple-to-fabricate devices.
Scalable quantum photonic devices emitting indistinguishable photons in the telecom C-band

Epitaxial semiconductor quantum dots (QDs) are a promising resource for quantum light generation and the realization of non-linear quantum photonic elements operating at the single-photon level. Their random spatial distribution resulting from their self-organized nature, however, restrains the fabrication yield of quantum devices with the desired functionality. As a solution, the QDs can be imaged and localized, enabling deterministic device fabrication. Due to the significant electronic noise of camera sensors operating in the telecommunication C-band, $1530-1560~\mathrm{nm}$, this technique remained challenging. In this work, we report on the imaging of QDs epitaxially grown on InP with emission wavelengths in the telecom C-band demonstrating a localization accuracy of $80~\mathrm{nm}$. This is enabled by the hybrid integration of QDs in a planar sample geometry with a bottom metallic reflector to enhance the out-of-plane emission. To exemplify our approach, we successfully fabricate circular Bragg grating cavities around single pre-selected QDs with an overall cavity placement uncertainty of $90~\mathrm{nm}$. QD-cavity coupling is demonstrated by a Purcell enhancement up to $\sim5$ with an estimated photon extraction efficiency of $(16.6\pm2.7)\%$ into a numerical aperture of $0.4$. We demonstrate triggered single-photon emission with $g^{(2)}(0)=(3.2\pm0.6)\times10^{-3}$ and record-high photon indistinguishability associated with two-photon interference visibilities of $V = (19.3\pm2.6)\%$ and $V_{\mathrm{PS}} = 99.8^{+0.2}_{-2.6}\%$ without and with temporal postselection, respectively. While the performance of our devices readily enables proof-of-principle experiments in quantum information, further improvements in the yield and coherence may enable the realization of non-linear devices at the single photon level and advanced quantum networks at the telecom wavelength.
On the graph theory of majority illusions

The popularity of an opinion in one's direct circles is not necessarily a good indicator of its popularity in one's entire community. For instance, when confronted with a majority of opposing opinions in one's circles, one might get the impression that one belongs to a minority. From this perspective, network structure makes local information about global properties of the group potentially inaccurate. However, the way a social network is wired also determines what kind of information distortion can actually occur. In this paper, we discuss which classes of networks allow for a majority of agents to have the wrong impression about what the majority opinion is, that is, to be in a 'majority illusion'.
On Armendariz Rings of Inverse Skew Laurent Series Type

Let R be a ring equipped with an automorphism α and an α-derivation δ. We study Armendariz rings of inverse (α,δ)-skew Laurent series type ((α,δ)-𝙸𝙻𝙰 rings) as a generalization of the standard Armendariz condition from polynomials to inverse skew Laurent series. We resolve the structure of (α,δ)-𝙸𝙻𝙰 rings and obtain various necessary or sufficient conditions for a ring to be (α,δ)-𝙸𝙻𝙰, unifying and generalizing a number of known Armendariz-like conditions. Also, we study relations between the set of annihilators in R and the set of annihilators in the inverse skew Laurent series ring R((x-1;α,δ)). For an α-compatible (α,δ)-𝙸𝙻𝙰 ring R, we prove that several properties transfer between R and R((x-1;α,δ)). Moreover, the radical of R((x-1;α,δ)) is determined in an α-compatible (α,δ)-𝙸𝙻𝙰 ring R.