Miracle-dz/UniFAR-FTUs huggingface dataset:
Symbolic powers of monomial ideals

Let $A = K[X_1,\ldots, X_d]$ and let $I$, $J$ be monomial ideals in $A$. Let $I_n(J) = (I^n \colon J^\infty)$ be the $n^{th}$ symbolic power of $I$ \wrt \ $J$. It is easy to see that the function $f^I_J(n) = e_0(I_n(J)/I^n)$ is of quasi-polynomial type, say of period $g$ and degree $c$. For $n \gg 0$ say \[ f^I_J(n) = a_c(n)n^c + a_{c-1}(n)n^{c-1} + \text{lower terms}, \] where for $i = 0, \ldots, c$, $a_i \colon \mathbb{N} \rt \mathbb{Z}$ are periodic functions of period $g$ and $a_c \neq 0$. In an earlier paper we (together with Herzog and Verma) proved that $\dim I_n(J)/I^n$ is constant for $n \gg 0$ and $a_c(-)$ is a constant. In this paper we prove that if $I$ is generated by some elements of the same degree and height $I \geq 2$ then $a_{c-1}(-)$ is also a constant.
Modelling depletion by re-accretion of gas from a dusty disc in post-AGB stars

Many disc-type post-asymptotic giant branch (post-AGB) stars are chemically peculiar, showing underabundances of refractory elements in their photospheres that correlate with condensation temperature. The aim of this paper is to investigate how accretion from a circumbinary disc can cause this phenomenon of depletion and how this impacts the evolution of post-AGB stars. We used the MESA code to evolve stars in the post-AGB phase, while including accretion of metal-poor gas. We compared the models to a sample of 58 observed disc-type post-AGB stars with chemical abundance data. For each of these stars, we estimated the luminosity and the mass using the Gaia distance. We modelled the accretion rate onto the binary from a viscously evolving disc for a range of initial accretion rates and disc masses. We find that large initial accretion rates (≳3 × 10−7 M⊙ yr−1) and large initial disc masses (∼10−2 M⊙) are needed to reproduce the observed depleted post-AGB stars. Based on these high accretion rates, the evolution timescale of post-AGB stars can be significantly extended by a factor between two and five. We distinguish depletion patterns that are unsaturated (plateau profile) from those that are saturated, and we expect that post-red giant branch (post-RGB) stars are much more likely to show an unsaturated abundance pattern compared to post-AGB stars. Finally, because of the slower evolution of the low-mass post-RGB stars, we find that these systems can become depleted at lower effective temperatures (<5000 K). We conclude that accretion from a circumbinary disc successfully accounts for the chemical peculiarity of post-AGB stars.
Three-dimensional universality class of the Ising model with power-law correlated critical disorder

We use large-scale Monte Carlo simulations to test the Weinrib-Halperin criterion that predicts new universality classes in the presence of sufficiently slowly decaying power-law-correlated quenched disorder. While new universality classes are reasonably well established, the predicted exponents are controversial. We propose a method of growing such correlated disorder using the three-dimensional Ising model as benchmark systems both for generating disorder and studying the resulting phase transition. Critical equilibrium configurations of a disorder-free system are used to define the two-value distributed random bonds with a small power-law exponent given by the pure Ising exponent. Finite-size scaling analysis shows a new universality class with a single phase transition, but the critical exponents $\nu_d=1.13(5), \eta_d=0.48(3)$ differ significantly from theoretical predictions. We find that depending on details of the disorder generation, disorder-averaged quantities can develop peaks at two temperatures for finite sizes. Finally, a layer model with the two values of bonds spatially separated to halves of the system genuinely has multiple phase transitions and thermodynamic properties can be flexibly tuned by adjusting the model parameters.
Generalised Zero-Shot Learning with a Classifier Ensemble over Multi-Modal Embedding Spaces

Generalised zero-shot learning (GZSL) methods aim to classify previously seen and unseen visual classes by leveraging the semantic information of those classes. In the context of GZSL, semantic information is non-visual data such as a text description of both seen and unseen classes. Previous GZSL methods have utilised transformations between visual and semantic embedding spaces, as well as the learning of joint spaces that include both visual and semantic information. In either case, classification is then performed on a single learned space. We argue that each embedding space contains complementary information for the GZSL problem. By using just a visual, semantic or joint space some of this information will invariably be lost. In this paper, we demonstrate the advantages of our new GZSL method that combines the classification of visual, semantic and joint spaces. Most importantly, this ensembling allows for more information from the source domains to be seen during classification. An additional contribution of our work is the application of a calibration procedure for each classifier in the ensemble. This calibration mitigates the problem of model selection when combining the classifiers. Lastly, our proposed method achieves state-of-the-art results on the CUB, AWA1 and AWA2 benchmark data sets and provides competitive performance on the SUN data set.
Addressing multiple bit/symbol errors in DRAM subsystem

As DRAM technology continues to evolve towards smaller feature sizes and increased densities, faults in DRAM subsystem are becoming more severe. Current servers mostly use CHIPKILL based schemes to tolerate up-to one/two symbol errors per DRAM beat. Such schemes may not detect multiple symbol errors arising due to faults in multiple devices and/or data-bus, address bus. In this article, we introduce Single Symbol Correction Multiple Symbol Detection (SSCMSD)—a novel error handling scheme to correct single-symbol errors and detect multi-symbol errors. Our scheme makes use of a hash in combination with Error Correcting Code (ECC) to avoid silent data corruptions (SDCs). We develop a novel scheme that deploys 32-bit CRC along with Reed-Solomon code to implement SSCMSD for a ×4 based DDR4 system. Simulation based experiments show that our scheme effectively guards against device, data-bus and address-bus errors only limited by the aliasing probability of the hash. Our novel design enabled us to achieve this without introducing additional READ latency. We need 19 chips per rank, 76 data bus-lines and additional hash-logic at the memory controller.
Classification of Hand Movements From EEG Using a Deep Attention-Based LSTM Network

Classifying limb movements using brain activity is an important task in Brain-computer Interfaces (BCI) that has been successfully used in multiple application domains, ranging from human-computer interaction to medical and biomedical applications. This paper proposes a novel solution for classification of left/right hand movement by exploiting a Long Short-Term Memory (LSTM) network with attention mechanism to learn the electroencephalogram (EEG) time-series information. To this end, a wide range of time and frequency domain features are extracted from the EEG signals and used to train an LSTM network to perform the classification task. We conduct extensive experiments with the EEG Movement dataset and show that our proposed solution our method achieves improvements over several benchmarks and state-of-the-art methods in both intra-subject and cross-subject validation schemes. Moreover, we utilize the proposed framework to analyze the information as received by the sensors and monitor the activated regions of the brain by tracking EEG topography throughout the experiments.
Predictive Generalized Graph Fourier Transform for Attribute Compression of Dynamic Point Clouds

As 3D scanning devices and depth sensors advance, dynamic point clouds have attracted increasing attention as a format for 3D objects in motion, with applications in various fields such as immersive telepresence, navigation for autonomous driving and gaming. Nevertheless, the tremendous amount of data in dynamic point clouds significantly burden transmission and storage. To this end, we propose a complete compression framework for attributes of 3D dynamic point clouds, focusing on optimal inter-coding. Firstly, we derive the optimal inter-prediction and predictive transform coding assuming the Gaussian Markov Random Field model with respect to a spatio-temporal graph underlying the attributes of dynamic point clouds. The optimal predictive transform proves to be the Generalized Graph Fourier Transform in terms of spatio-temporal decorrelation. Secondly, we propose refined motion estimation via efficient registration prior to inter-prediction, which searches the temporal correspondence between adjacent frames of irregular point clouds. Finally, we present a complete framework based on the optimal inter-coding and our previously proposed intra-coding, where we determine the optimal coding mode from rate-distortion optimization with the proposed offline-trained $\lambda $ -Q model. Experimental results show that we achieve around 17% bit rate reduction on average over competitive dynamic point cloud compression methods.
Multi-turn Dialogue Response Generation with Autoregressive Transformer Models

Neural dialogue models, despite their successes, still suffer from lack of relevance, diversity, and in many cases coherence in their generated responses. These issues have been attributed to reasons including (1) short-range model architectures that capture limited temporal dependencies, (2) limitations of the maximum likelihood training objective, (3) the concave entropy profile of dialogue datasets resulting into short and generic responses, and (4) out-of-vocabulary problem leading to generation of a large number of $<$UNK$>$ tokens. Autoregressive transformer models such as GPT-2, although trained with the maximum likelihood objective, do not suffer from the out-of-vocabulary problem and have demonstrated an excellent ability to capture long-range structures in language modeling tasks. In this paper, we examine the use of autoregressive transformer models for multi-turn dialogue response generation. In our experiments, we employ small and medium GPT-2 models (with publicly available pretrained language model parameters) on the open-domain Movie Triples dataset and the closed-domain Ubuntu Dialogue dataset. The models (with and without pretraining) achieve significant improvements over the baselines for multi-turn dialogue response generation. They also produce state-of-the-art performance on the two datasets based on several metrics, including BLEU, ROGUE, and distinct n-gram.
Consistent radial velocities of classical Cepheids from the cross-correlation technique

Context. Accurate radial velocities (vrad) of Cepheids are mandatory within the context of Cepheid distance measurements using the Baade-Wesselink technique. The most common vrad derivation method consists in cross-correlating the observed stellar spectra with a binary template and measuring a velocity on the resulting mean profile. Nevertheless, for Cepheids and other pulsating stars, the spectral lines selected within the template as well as the way of fitting the cross-correlation function (CCF) have a direct and significant impact on the measured vrad. Aims. Our first aim is to detail the steps to compute consistent CCFs and vrad of Cepheids. Next, this study aims at characterising the impact of Cepheid spectral properties and vrad computation methods on the resulting line profiles and vrad time series. Methods. We collected more than 3900 high-resolution spectra from seven different spectrographs of 64 Classical Milky Way (MW) Cepheids. These spectra were normalised and standardised using a single custom-made process on pre-defined wavelength ranges. We built six tailored correlation templates selecting unblended spectral lines of different depths based on a synthetic Cepheid spectrum, on three different wavelength ranges from 3900 to 8000 Å. Each observed spectrum was cross-correlated with these templates to build the corresponding CCFs, adopted as the proxy for the spectrum mean line profile. We derived a set of line profile observables as well as three different vrad measurements from each CCF and two custom proxies for the CCF quality and amount of signal. Results. This study presents a large catalogue of consistent Cepheid CCFs and vrad time series. It confirms that each step of the process has a significant impact on the deduced vrad: the wavelength, the template line depth and width, and the vrad computation method. The way towards more robust Cepheid vrad time series seems to go through steps that minimise the asymmetry of the line profile and its impact on the vrad. Centroid or first-moment vrad, that exhibit slightly smaller amplitudes but significantly smaller scatter than Gaussian or biGaussian vrad, should therefore be favoured. Stronger or deeper spectral lines also tend to be less asymmetric and lead to more robust vrad than weaker lines.
Adversarially Trained End-to-end Korean Singing Voice Synthesis System

In this paper, we propose an end-to-end Korean singing voice synthesis system from lyrics and a symbolic melody using the following three novel approaches: 1) phonetic enhancement masking, 2) local conditioning of text and pitch to the super-resolution network, and 3) conditional adversarial training. The proposed system consists of two main modules; a mel-synthesis network that generates a mel-spectrogram from the given input information, and a super-resolution network that upsamples the generated mel-spectrogram into a linear-spectrogram. In the mel-synthesis network, phonetic enhancement masking is applied to generate implicit formant masks solely from the input text, which enables a more accurate phonetic control of singing voice. In addition, we show that two other proposed methods -- local conditioning of text and pitch, and conditional adversarial training -- are crucial for a realistic generation of the human singing voice in the super-resolution process. Finally, both quantitative and qualitative evaluations are conducted, confirming the validity of all proposed methods.
Few-Shot Object Detection With Attention-RPN and Multi-Relation Detector

Conventional methods for object detection typically require a substantial amount of training data and preparing such high-quality training data is very labor-intensive. In this paper, we propose a novel few-shot object detection network that aims at detecting objects of unseen categories with only a few annotated examples. Central to our method are our Attention-RPN, Multi-Relation Detector and Contrastive Training strategy, which exploit the similarity between the few shot support set and query set to detect novel objects while suppressing false detection in the background. To train our network, we contribute a new dataset that contains 1000 categories of various objects with high-quality annotations. To the best of our knowledge, this is one of the first datasets specifically designed for few-shot object detection. Once our few-shot network is trained, it can detect objects of unseen categories without further training or fine-tuning. Our method is general and has a wide range of potential applications. We produce a new state-of-the-art performance on different datasets in the few-shot setting. The dataset link is https://github.com/fanq15/Few-Shot-Object-Detection-Dataset.
Floating Phases in One-Dimensional Rydberg Ising Chains

We report on the quantitative ground state phase diagram of a van der Waals interacting chain of Rydberg atoms. These systems are known to host crystalline phases locked to the underlying lattice as well as a gapped, disordered phase. We locate and characterize a third type of phase, the so called floating phase, which can be seen as a one-dimensional 'crystalline' phase which is not locked to the lattice. These phases have been theoretically predicted to exist in the phase diagram, but were not reported so far. Our results have been obtained using state-of-the-art numerical tensor network techniques and pave the way for the experimental exploration of floating phases with existing Rydberg quantum simulators.
Model Agnostic Defence Against Backdoor Attacks in Machine Learning

Machine learning (ML) has automated a multitude of our day-to-day decision-making domains, such as education, employment, and driving automation. The continued success of ML largely depends on our ability to trust the model we are using. Recently, a new class of attacks called backdoor attacks have been developed. These attacks undermine the user’s trust in ML models. In this article, we present Neo, a model agnostic framework to detect and mitigate such backdoor attacks in image classification ML models. For a given image classification model, our approach analyzes the inputs it receives and determines if the model is backdoored. In addition to this feature, we also mitigate these attacks by determining the correct predictions of the poisoned images. We have implemented Neo and evaluated it against three state-of-the-art poisoned models. In our evaluation, we show that Neo can detect $\approx$88% of the poisoned inputs on average and it is as fast as 4.4 ms per input image. We also compare our Neo approach with the state-of-the-art defence methodologies proposed for backdoor attacks. Our evaluation reveals that despite being a blackbox approach, Neo is more effective in thwarting backdoor attacks than the existing techniques. Finally, we also reconstruct the exact poisoned input for the user to effectively test their systems.
A Long-term Photometric Variability and Spectroscopic Study of Luminous Blue Variable AF And in M31

We present a photometric and spectroscopic analysis of the Hubble–Sandage variable star AF And in M31. The data have been taken under the Nainital Microlensing Survey during 1998–2002, and follow-up observations were carried out until 2011. During this period, photometric observations in Cousins R and I bands were obtained for 169 nights spanning about 5000 days. AF And showed a prominent outburst around 1999 mid-January, followed by a gradual decrease in brightness of about 1.5 mag in the next 3 yr with a declining rate of ∼0.0015 mag day−1, leading to a quiescent phase at the end of 2001. After lying low for about 9 yr, AF And again went through a secondary outburst phase in late 2010 with an amplitude of 0.44 mag, where it lasted for one year before fading back to its quiescent phase. Spectroscopic observations of AF And show prominent Balmer and He i emission lines along with the comparatively weaker Fe ii and [Fe ii] emissions. Asymmetric emission line profiles in its spectrum imply a mass-loss rate of about 2.2 × 10−4 M⊙ yr−1 through the stellar winds in the photosphere. Using spectral energy distribution fitting, we find a photospheric temperature of 33,000 ± 3000 K during the visual minimum. Using a weak P Cygni profile of the He i emission line, the wind terminal velocity for AF And is found to be around 280–300 km s−1.
HIGHER-DIMENSIONAL SHRINKING TARGET PROBLEM FOR BETA DYNAMICAL SYSTEMS

Abstract We consider the two-dimensional shrinking target problem in beta dynamical systems (for general $\beta>1$ ) with general errors of approximation. Let $f, g$ be two positive continuous functions. For any $x_0,y_0\in [0,1]$ , define the shrinking target set $$ \begin{align*}E(T_\beta, f,g):=\left\{(x,y)\in [0,1]^2: \begin{array}{@{}ll@{}} \lvert T_{\beta}^{n}x-x_{0}\rvert <e^{-S_nf(x)}\\[1ex] \lvert T_{\beta}^{n}y-y_{0}\rvert < e^{-S_ng(y)} \end{array} \ {\text{for infinitely many}} \ n\in \mathbb N \right\}, \end{align*} $$ where $S_nf(x)=\sum _{j=0}^{n-1}f(T_\beta ^jx)$ is the Birkhoff sum. We calculate the Hausdorff dimension of this set and prove that it is the solution to some pressure function. This represents the first result of this kind for the higher-dimensional beta dynamical systems.
Symmetries of the Hydrogen Atom

We exhibit a new type of symmetry in the Schrodinger equation for the hydrogen atom that uses algebraic families of groups. We prove that the regular solutions of the Schrodinger equation carry the structure of an algebraic family of Harish-Chandra modules, and we characterize this family. We show that the spectrum of the Schrodinger operator and the spaces of definite energy states, as they are calculated in physics, may be obtained from these purely algebraic considerations, the latter via a Jantzen filtration. Finally, we compare the algebraic family of regular solutions with the direct integral decomposition that is obtained from the Schrodinger equation by Hilbert space spectral theory.
Neural Blind Deconvolution Using Deep Priors

Blind deconvolution is a classical yet challenging low-level vision problem with many real-world applications. Traditional maximum a posterior (MAP) based methods rely heavily on fixed and handcrafted priors that certainly are insufficient in characterizing clean images and blur kernels, and usually adopt specially designed alternating minimization to avoid trivial solution. In contrast, existing deep motion deblurring networks learn from massive training images the mapping to clean image or blur kernel, but are limited in handling various complex and large size blur kernels. To connect MAP and deep models, we in this paper present two generative networks for respectively modeling the deep priors of clean image and blur kernel, and propose an unconstrained neural optimization solution to blind deconvolution. In particular, we adopt an asymmetric Autoencoder with skip connections for generating latent clean image, and a fully-connected network (FCN) for generating blur kernel. Moreover, the SoftMax nonlinearity is applied to the output layer of FCN to meet the non-negative and equality constraints. The process of neural optimization can be explained as a kind of ''zero-shot" self-supervised learning of the generative networks, and thus our proposed method is dubbed SelfDeblur. Experimental results show that our SelfDeblur can achieve notable quantitative gains as well as more visually plausible deblurring results in comparison to state-of-the-art blind deconvolution methods on benchmark datasets and real-world blurry images. The source code is publicly available at https://github.com/csdwren/SelfDeblur
Designing an All-Carbon Membrane for Water Desalination

We design an all-carbon membrane for the filtration and desalination of water. A unique layered assembly of carbon nanostructures including graphite oxide (GO), buckypaper consisting of carbon nanotubes, and a strong carbon fabric provides high mechanical strength and thermal stability, resilience to harsh chemical cleaning agents and electrical conductivity, thus addressing major shortcomings of commercial reverse osmosis membranes. We use ab initio density functional theory calculations to obtain atomic-level insight into the permeation of water molecules in-between GO layers and across in-layer vacancy defects. Our calculations elucidate the reason for selective rejection of solvated Na$^+$ ions in an optimized GO membrane that is structurally stabilized in a sandwich arrangement in-between layers of buckypaper, which are protected on both sides by strong carbon fabric layers.