Miracle-dz/UniFAR-FTUs huggingface dataset:
Abelianization of some groups of interval exchanges

Let IET be the group of bijections from $\mathopen{[}0,1 \mathclose{[}$ to itself that are continuous outside a finite set, right-continuous and piecewise translations. The abelianization homomorphism $f: \text{IET} \to A$, called SAF-homomorphism, was described by Arnoux-Fathi and Sah. The abelian group $A$ is the second exterior power of the reals over the rationals. For every subgroup $\Gamma$ of $\mathbb{R/Z}$ we define $\text{IET}(\Gamma)$ as the subgroup of $\text{IET}$ consisting of all elements $f$ such that $f$ is continuous outside $\Gamma$. Let $\tilde{\Gamma}$ be the preimage of $\Gamma$ in $\mathbb{R}$. We establish an isomorphism between the abelianization of $\text{IET}(\Gamma)$ and the second skew-symmetric power of $\tilde{\Gamma}$ over $\mathbb{Z}$ denoted by ${}^\circleddash\! \! \bigwedge^2_{\mathbb{Z}} \tilde{\Gamma}$. This group often has non-trivial $2$-torsion, which is not detected by the SAF-homomorphism. We then define $\text{IET}^{\bowtie}$ the group of all interval exchange transformations with flips. Arnoux proved that this group is simple thus perfect. However for every subgroup $\text{IET}^{\bowtie}(\Gamma)$ we establish an isomorphism between its abelianization and $\langle \lbrace a \otimes a ~ [\text{mod}~2] \mid a \in \tilde{\Gamma} \rbrace \rangle \times \langle \lbrace \ell \wedge \ell ~ [\text{mod}~2] \mid \ell \in \tilde{\Gamma} \rbrace \rangle$ which is a $2$-elementary abelian subgroup of $\bigotimes^2_{\mathbb{Z}} \tilde{\Gamma} / (2\bigotimes^2_{\mathbb{Z}} \tilde{\Gamma}) \times {}^\circleddash\! \! \bigwedge^2_{\mathbb{Z}} \tilde{\Gamma} / (2 {}^\circleddash\! \! \bigwedge^2_{\mathbb{Z}} \tilde{\Gamma})$.
CoDEx: A Comprehensive Knowledge Graph Completion Benchmark

We present CoDEx, a set of knowledge graph completion datasets extracted from Wikidata and Wikipedia that improve upon existing knowledge graph completion benchmarks in scope and level of difficulty. In terms of scope, CoDEx comprises three knowledge graphs varying in size and structure, multilingual descriptions of entities and relations, and tens of thousands of hard negative triples that are plausible but verified to be false. To characterize CoDEx, we contribute thorough empirical analyses and benchmarking experiments. First, we analyze each CoDEx dataset in terms of logical relation patterns. Next, we report baseline link prediction and triple classification results on CoDEx for five extensively tuned embedding models. Finally, we differentiate CoDEx from the popular FB15K-237 knowledge graph completion dataset by showing that CoDEx covers more diverse and interpretable content, and is a more difficult link prediction benchmark. Data, code, and pretrained models are available at this https URL.
ChoreoNet: Towards Music to Dance Synthesis with Choreographic Action Unit

Dance and music are two highly correlated artistic forms. Synthesizing dance motions has attracted much attention recently. Most previous works conduct music-to-dance synthesis via directly music to human skeleton keypoints mapping. Meanwhile, human choreographers design dance motions from music in a two-stage manner: they firstly devise multiple choreographic dance units (CAUs), each with a series of dance motions, and then arrange the CAU sequence according to the rhythm, melody and emotion of the music. Inspired by these, we systematically study such two-stage choreography approach and construct a dataset to incorporate such choreography knowledge. Based on the constructed dataset, we design a two-stage music-to-dance synthesis framework ChoreoNet to imitate human choreography procedure. Our framework firstly devises a CAU prediction model to learn the mapping relationship between music and CAU sequences. Afterwards, we devise a spatial-temporal inpainting model to convert the CAU sequence into continuous dance motions. Experimental results demonstrate that the proposed ChoreoNet outperforms baseline methods (0.622 in terms of CAU BLEU score and 1.59 in terms of user study score).
Reconfigurable Intelligent Surface Assisted Massive MIMO with Antenna Selection

Antenna selection is capable of reducing the hardware complexity of massive multiple-input multiple-output (MIMO) networks at the cost of certain performance degradation. Reconfigurable intelligent surface (RIS) has emerged as a cost-effective technique that can enhance the spectrum-efficiency of wireless networks by reconfiguring the propagation environment. By employing RIS to compensate for the performance loss due to antenna selection, in this paper we propose a new network architecture, i.e., RIS-assisted massive MIMO system with antenna selection, to enhance the system performance while enjoying a low hardware cost. This is achieved by maximizing the channel capacity via joint antenna selection and passive beamforming while taking into account the cardinality constraint of active antennas and the unit-modulus constraints of all RIS elements. However, the formulated problem turns out to be highly intractable due to the non-convex constraints and coupled optimization variables, for which an alternating optimization framework is provided, yielding antenna selection and passive beamforming subproblems. The computationally efficient submodular optimization algorithms are developed to solve the antenna selection subproblem under different channel state information assumptions. The iterative algorithms based on block coordinate descent are further proposed for the passive beamforming design by exploiting the unique problem structures. Moreover, the proposed algorithms are feasible to any finite number of antennas, and thus can be applicable in both ordinary MIMO and massive MIMO settings. Experimental results will demonstrate the algorithmic advantages and desirable performance of the proposed algorithms for RIS-assisted massive MIMO systems with antenna selection.
Reusing a Pretrained Language Model on Languages with Limited Corpora for Unsupervised NMT

Using a language model (LM) pretrained on two languages with large monolingual data in order to initialize an unsupervised neural machine translation (UNMT) system yields state-of-the-art results. When limited data is available for one language, however, this method leads to poor translations. We present an effective approach that reuses an LM that is pretrained only on the high-resource language. The monolingual LM is fine-tuned on both languages and is then used to initialize a UNMT model. To reuse the pretrained LM, we have to modify its predefined vocabulary, to account for the new language. We therefore propose a novel vocabulary extension method. Our approach, RE-LM, outperforms a competitive cross-lingual pretraining model (XLM) in English-Macedonian (En-Mk) and English-Albanian (En-Sq), yielding more than +8.3 BLEU points for all four translation directions.
Retrofitting Structure-aware Transformer Language Model for End Tasks

We consider retrofitting structure-aware Transformer-based language model for facilitating end tasks by proposing to exploit syntactic distance to encode both the phrasal constituency and dependency connection into the language model. A middle-layer structural learning strategy is leveraged for structure integration, accomplished with main semantic task training under multi-task learning scheme. Experimental results show that the retrofitted structure-aware Transformer language model achieves improved perplexity, meanwhile inducing accurate syntactic phrases. By performing structure-aware fine-tuning, our model achieves significant improvements for both semantic- and syntactic-dependent tasks.
Joint Waveform and Beamforming Optimization for MIMO Wireless Power Transfer

In this paper, we study a multi-sine multiple-input multiple-output (MIMO) wireless power transfer (WPT) system with the objective to increase the output DC power. We jointly optimize the multi-sine waveform and beamforming accounting for the rectenna nonlinearity, and consider two combining schemes for the rectennas at the receiver, namely DC and RF combinings. For DC combining, the waveform and transmit beamforming are optimized, as a function of the channel state information (CSI). For RF combining, the optimal transmit and receive beamformings are provided in closed form and the waveform is optimized. We also consider a practical RF combining circuit using phase shifter and RF power combiner and optimize the waveform, transmit beamforming, and analog receive beamforming adaptive to the CSI. Two types of performance evaluations, based on the nonlinear rectenna model and accurate and realistic circuit simulations, are provided. The evaluations demonstrate that the joint waveform and beamforming design can increase the output DC power by leveraging the beamforming gain, the frequency diversity gain, and the rectenna nonlinearity. It also shows that the joint waveform and beamforming design provides a higher output DC power than the beamforming-only design with a relative gain of 180% in a two-transmit antenna sixteen-sinewave two-receive antenna setup.
Cosmological 3D H i Gas Map with HETDEX Lyα Emitters and eBOSS QSOs at z = 2: IGM−Galaxy/QSO Connection and a ∼40 Mpc Scale Giant H ii Bubble Candidate

We present cosmological (30−400 Mpc) distributions of neutral hydrogen (H i) in the intergalactic medium (IGM) traced by Lyα emitters (LAEs) and QSOs at z = 2.1–2.5, selected with the data of the ongoing Hobby–Eberly Telescope Dark Energy Experiment (HETDEX) and the eBOSS survey. Motivated by a previous study of Mukae et al., we investigate spatial correlations of LAEs and QSOs with H i tomography maps reconstructed from H i Lyα forest absorption in the spectra of background galaxies and QSOs obtained by the CLAMATO survey and this study, respectively. In the cosmological volume far from QSOs, we find that LAEs reside in regions of strong H i absorption, i.e., H i rich, which is consistent with results of previous galaxy−background QSO pair studies. Moreover, there is an anisotropy in the H i distribution plot of transverse and line-of-sight distances; on average the H i absorption peak is blueshifted by ∼200 km s−1 from the LAE Lyα redshift, reproducing the known average velocity offset between the Lyα emission redshift and the galaxy systemic redshift. We have identified a ∼40 Mpc scale volume of H i underdensity that is a candidate for a giant H ii bubble, where six QSOs and an LAE overdensity exist at . The coincidence of the QSO and LAE overdensities with the H i underdensity indicates that the ionizing photon radiation of the QSOs has created a highly ionized volume of multiple proximity zones in a matter overdensity. Our results suggest an evolutionary picture where H i gas in an overdensity of galaxies becomes highly photoionized when QSOs emerge in the galaxies.
Lower Bounds for Policy Iteration on Multi-action MDPs

Policy Iteration (PI) is a classical family of algorithms to compute an optimal policy for any given Markov Decision Problem (MDP). The basic idea in PI is to begin with some initial policy and to repeatedly update the policy to one from an improving set, until an optimal policy is reached. Different variants of PI result from the (switching) rule used for improvement. An important theoretical question is how many iterations a specified PI variant will take to terminate as a function of the number of states n and the number of actions k in the input MDP. While there has been considerable progress towards upper-bounding this number, there are fewer results on lower bounds. In particular, existing lower bounds primarily focus on the special case of k = 2 actions. We devise lower bounds for k≥3. Our main result is that a particular variant of PI can take Ω(kn/2) iterations to terminate. We also generalise existing constructions on 2-action MDPs to scale lower bounds by a factor of k for some common deterministic variants of PI, and by log(k) for corresponding randomised variants.
Duality Mapping for Schatten Matrix Norms

Abstract In this paper, we fully characterize the duality mapping over the space of matrices that are equipped with Schatten norms. Our approach is based on the analysis of the saturation of the Hölder inequality for Schatten norms. We prove in our main result that, for the duality mapping over the space of real-valued matrices with Schatten-p norm is a continuous and single-valued function and provide an explicit form for its computation. For the special case p = 1, the mapping is set-valued; by adding a rank constraint, we show that it can be reduced to a Borel-measurable single-valued function for which we also provide a closed-form expression.
C1QA and C1QC modify age‐at‐onset in familial amyloid polyneuropathy patients

Transthyretin (TTR) familial amyloid polyneuropathy (FAP) (OMIM 176300) shows a variable age‐at‐onset (AO), including within families. We hypothesized that variants in C1QA and C1QC genes, might also act as genetic modifiers of AO in TTR‐FAP Val30Met Portuguese patients.
Benchmarking quantum state transfer on quantum devices

Quantum state transfer (QST) provides a method to send arbitrary quantum states from one system to another. Such a concept is crucial for transmitting quantum information into the quantum memory, quantum processor, and quantum network. The standard criteria of QST are based on the fidelity between the prepared and received states. However, a non-vanishing fidelity is obtained even when the received quantum states are described using the classical model, called the local-hidden state (LHS) model. With the above definition of the classical QST process, in this work, we quantify the non-classicality of a QST process by measuring the spatio-temporal steerability. We show that the spatio-temporal steerability is preserved when the perfect QST process is successful. Otherwise, it decreases under imperfect QST processes. Therefore, the failure of the LHS model implies not only the achievement of spatio-temporal steering but also QST non-classicality. We then apply the spatio-temporal steerability measurement technique to benchmark quantum devices including the IBM quantum experience and QuTech quantum inspire under QST tasks. The experimental results show that the spatio-temporal steerability decreases as the circuit depth increases, and the reduction agrees with the noise model, which refers to the accumulation of errors during the QST process. Moreover, we show that the no-signaling in time condition could be violated because of the intrinsic non-Markovian effect of the devices.
On the Curse of Memory in Recurrent Neural Networks: Approximation and Optimization Analysis

We study the approximation properties and optimization dynamics of recurrent neural networks (RNNs) when applied to learn input-output relationships in temporal data. We consider the simple but representative setting of using continuous-time linear RNNs to learn from data generated by linear relationships. Mathematically, the latter can be understood as a sequence of linear functionals. We prove a universal approximation theorem of such linear functionals, and characterize the approximation rate and its relation with memory. Moreover, we perform a fine-grained dynamical analysis of training linear RNNs, which further reveal the intricate interactions between memory and learning. A unifying theme uncovered is the non-trivial effect of memory, a notion that can be made precise in our framework, on approximation and optimization: when there is long term memory in the target, it takes a large number of neurons to approximate it. Moreover, the training process will suffer from slow downs. In particular, both of these effects become exponentially more pronounced with memory - a phenomenon we call the "curse of memory". These analyses represent a basic step towards a concrete mathematical understanding of new phenomenon that may arise in learning temporal relationships using recurrent architectures.
Heterosis and Combining Ability Studies in Indian Mustard (Brassica juncea L.)

A study was made to estimate combining ability, heterosis over mid parents (MP) and better parent (BP) with ten diverse parents and their 45 F1s in half diallel mating design in Indian mustard for 13 quantitative and quality traits were made to derive the information on the extent of heterosis over economic parent and relative magnitude of general and specific combining ability effects. The present investigation was comprised of two inter-related experiments which were carried out during 2007–08 and 2008–09 at G.B. Pant University of Agriculture and Technology, Pantnagar. The objectives were to quantify combining ability and heterosis for all 13 quantitative characters including seed yield and oil content in Indian mustard (Brassica juncea L. Czern & Coss). The diallel analysis revealed the importance ofboth additive and nonadditive genetic variance for days to flowering, days to maturity, plant height, secondary branches/plant, length of main raceme, and seed yield/plant. The parents PWR9541, PRQ-2005, CS-609-B-10 and SKM-401 exhibited good GCA for seed yield/plant. For oil content PRQ-2005, RGN-142, PRB-2006-12 and Vardan were high GCA parents. The parent PRQ-2005 displayed desirable GCA effects for seven characters including seed yield and oil content. Similarly the strains CS-609-B-10, SKM-401 and PWR-9541 manifested desirable GCA effects for six, five and seven characters including seed yield, respectively. Based on desirable SCA effects, the crosses PRQ-2005 × PAB-9534, PRQ-2006-12 × Kanti, CS-609-B-10 × SKM401, CS-609-B-10 × Kanti, PRB-2006-12 × NDRE-4 and four others were found superior for seed yield/plant. Similarly, the crosses NDRE-4 × PWR-9541, CS-609-B10×Kanti, PRB-2006-12 × NDRE-4 and PRQ-2005 × NDRE-4 for earliness of flowering; and NDRE-4 × Kanti, SKM-401 × PAB-9534, Kanti × Vardan and PRQ-2005 × CS-609-B-10 for earliness of maturity appeared promising. Six crosses namely CS-609-B-10×NDRE-4 (170.50%), PRQ-2005×NDRE-4 (152.84%), RGN-142 × PRB-2006-12 (126.88%), CS-609-B-10 × Kanti (118.53%), PRB-2006-12 × Kanti (117.16%) and PAB9534 × Kanti (104.85%) exhibited high heterobeltiosis. These crosses also manifested significant heterosis over mid parent (MP) and standard variety (SV). Three crosses namely SKM-401×Vardan, PRB-2006-12×Vardan and NDRE-4×PWR-9541 manifested significant albeit low heterosis (upto 3.5% over BP, 3.3% over MP and 5.24% over SV) for oil content.
Domain Knowledge Empowered Structured Neural Net for End-to-End Event Temporal Relation Extraction

Extracting event temporal relations is a critical task for information extraction and plays an important role in natural language understanding. Prior systems leverage deep learning and pre-trained language models to improve the performance of the task. However, these systems often suffer from two short-comings: 1) when performing maximum a posteriori (MAP) inference based on neural models, previous systems only used structured knowledge that are assumed to be absolutely correct, i.e., hard constraints; 2) biased predictions on dominant temporal relations when training with a limited amount of data. To address these issues, we propose a framework that enhances deep neural network with distributional constraints constructed by probabilistic domain knowledge. We solve the constrained inference problem via Lagrangian Relaxation and apply it on end-to-end event temporal relation extraction tasks. Experimental results show our framework is able to improve the baseline neural network models with strong statistical significance on two widely used datasets in news and clinical domains.
Malicious Network Traffic Detection via Deep Learning: An Information Theoretic View

The attention that deep learning has garnered from the academic community and industry continues to grow year over year, and it has been said that we are in a new golden age of artificial intelligence research. However, neural networks are still often seen as a "black box" where learning occurs but cannot be understood in a human-interpretable way. Since these machine learning systems are increasingly being adopted in security contexts, it is important to explore these interpretations. We consider an Android malware traffic dataset for approaching this problem. Then, using the information plane, we explore how homeomorphism affects learned representation of the data and the invariance of the mutual information captured by the parameters on that data. We empirically validate these results, using accuracy as a second measure of similarity of learned representations. Our results suggest that although the details of learned representations and the specific coordinate system defined over the manifold of all parameters differ slightly, the functional approximations are the same. Furthermore, our results show that since mutual information remains invariant under homeomorphism, only feature engineering methods that alter the entropy of the dataset will change the outcome of the neural network. This means that for some datasets and tasks, neural networks require meaningful, human-driven feature engineering or changes in architecture to provide enough information for the neural network to generate a sufficient statistic. Applying our results can serve to guide analysis methods for machine learning engineers and suggests that neural networks that can exploit the convolution theorem are equally accurate as standard convolutional neural networks, and can be more computationally efficient.
Probing the Nature of High-redshift Weak Emission Line Quasars: A Young Quasar with a Starburst Host Galaxy

We present the discovery of PSO J083.8371+11.8482, a weak emission line quasar with extreme star formation rate at z = 6.3401. This quasar was selected from Pan-STARRS1, UHS, and unWISE photometric data. Gemini/GNIRS spectroscopy follow-up indicates a Mg ii-based black hole mass of M⊙ and an Eddington ratio of , in line with an actively accreting supermassive black hole (SMBH) at z ≳ 6. Hubble Space Telescope imaging sets strong constraint on lens boosting, showing no relevant effect on the apparent emission. The quasar is also observed as a pure point source with no additional emission component. The broad-line region (BLR) emission is intrinsically weak and not likely caused by an intervening absorber. We found rest-frame equivalent widths of EW , EW Å (3σ upper limit), and EW . A small proximity zone size ( pMpc) indicates a lifetime of only years from the last quasar phase ignition. ALMA shows extended [C ii] emission with a mild velocity gradient. The inferred far-infrared luminosity ( ) is one of the highest among all known quasar hosts at z ≳ 6. Dust and [C ii] emissions put a constraint on the star formation rate of SFR = 900– , similar to that of a hyperluminous infrared galaxy. Considering the observed quasar lifetime and BLR formation timescale, the weak-line profile in the quasar spectrum is most likely caused by a BLR that is not yet fully formed rather than by continuum boosting by gravitational lensing or a soft continuum due to super-Eddington accretion.