Miracle-dz/UniFAR-FTUs huggingface dataset:
Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformization

Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling intrinsically discrete data, such as language and graphs. This is achieved by formulating both the forward noising process and the corresponding reversed process as Continuous Time Markov Chains (CTMCs). In this paper, we investigate the theoretical properties of the discrete diffusion model. Specifically, we introduce an algorithm leveraging the uniformization of continuous Markov chains, implementing transitions on random time points. Under reasonable assumptions on the learning of the discrete score function, we derive Total Variation distance and KL divergence guarantees for sampling from any distribution on a hypercube. Our results align with state-of-the-art achievements for diffusion models in $\mathbb{R}^d$ and further underscore the advantages of discrete diffusion models in comparison to the $\mathbb{R}^d$ setting.
A Distributional Analogue to the Successor Representation

This paper contributes a new approach for distributional reinforcement learning which elucidates a clean separation of transition structure and reward in the learning process. Analogous to how the successor representation (SR) describes the expected consequences of behaving according to a given policy, our distributional successor measure (SM) describes the distributional consequences of this behaviour. We formulate the distributional SM as a distribution over distributions and provide theory connecting it with distributional and model-based reinforcement learning. Moreover, we propose an algorithm that learns the distributional SM from data by minimizing a two-level maximum mean discrepancy. Key to our method are a number of algorithmic techniques that are independently valuable for learning generative models of state. As an illustration of the usefulness of the distributional SM, we show that it enables zero-shot risk-sensitive policy evaluation in a way that was not previously possible.
Totally geodesic submanifolds and polar actions on Stiefel manifolds

We classify totally geodesic submanifolds of the real Stiefel manifolds of orthogonal two-frames. We also classify polar actions on these Stiefel manifolds, specifically, we prove that the orbits of polar actions are lifts of polar actions on the corresponding Grassmannian. In the case of cohomogeneity-one actions we are able to obtain a classification for all real, complex and quaternionic Stiefel manifolds of $k$-frames.
Representations of a quantum-deformed Lorentz algebra, Clebsch-Gordan map, and Fenchel-Nielsen representation of quantum complex flat connections at level-$k$

A family of infinite-dimensional irreducible $\star$-representations on $\mathcal{H}\simeq L^2(\mathbb{R})\otimes\mathbb{C}^k$ is defined for a quantum-deformed Lorentz algebra $U_\mathbf{q}(sl_2)\otimes U_{\tilde{\mathbf{q}}}(sl_2)$, where $\mathbf{q}=\exp[\frac{2\pi i}{k}(1+b^2)]$ and $\tilde{\mathbf{q}}=\exp[\frac{2\pi i}{k}(1+b^{-2})]$ with $k\in\mathbb{Z}_+$ and $|b|=1$. The representations are constructed with the irreducible representation of quantum torus algebra at level-$k$, which is developed from the quantization of $\mathrm{SL}(2,\mathbb{C})$ Chern-Simons theory. We study the Clebsch-Gordan decomposition of the tensor product representation, and we show that it reduces to the same problem as diagonalizing the complex Fenchel-Nielson length operators in quantizing $\mathrm{SL}(2,\mathbb{C})$ flat connections on 4-holed sphere. Finally, the spectral decomposition of the complex Fenchel-Nielson length operators results in the direct-integral representation of the Hilbert space $\mathcal{H}$, which we call the Fenchel-Nielson representation.
On the Submultiplicativity of Matrix Norms Induced by Random Vectors

In a recent article, Ch\'avez, Garcia and Hurley introduced a new family of norms $\|\cdot\|_{\mathbf{X},d}$ on the space of $n \times n$ complex matrices which are induced by random vectors $\mathbf{X}$ having finite $d$-moments. Therein, the authors asked under which conditions the norms induced by a scalar multiple of $\mathbf{X}$ are submultiplicative. In this paper, this question is completely answered by proving that this is always the case, as long as the entries of $\mathbf{X}$ have finite $p$-moments for $p=\max\{2+\varepsilon,d\}$.
CMA-R: Causal Mediation Analysis for Explaining Rumour Detection

We apply causal mediation analysis to explain the decision-making process of neural models for rumour detection on Twitter.Interventions at the input and network level reveal the causal impacts of tweets and words in the model output.We find that our approach CMA-R – Causal Mediation Analysis for Rumour detection – identifies salient tweets that explain model predictions and show strong agreement with human judgements for critical tweets determining the truthfulness of stories.CMA-R can further highlight causally impactful words in the salient tweets, providing another layer of interpretability and transparency into these blackbox rumour detection systems. Code is available at: https://github.com/ltian678/cma-r.
EFFECTS OF SOME SOIL TREATED PESTICIDES ON GROWTH CHARACTERISTICS OF FABA BEAN AND WHEAT PLANTS

The present study was conducted during December 1 st , 2009 to October 1 st 2010 to determine the effects of Treflan, Glyphosate, Ridomil and Cyrin C, on germination, vegetative growth characteristics, nodulation (in faba bean), and nutrient status as well as pesticide residues in Wheat (Triticum aestivum L.) and Faba bean (Vicia faba) plants. Results showed that Treflan caused significant decrease in number of nodules per plant, number of branches, plant height, shoot fresh and dry weight in bean plants, and significantly reduced plant contents of potassium, sodium, zinc, manganese and calcium of bean plants. Treflan also reduced the number of tillers per plant, plant height, shoot fresh and dry weight, root dry weight and plant contents of total nitrogen, phosphorus, potassium, sodium, iron, zinc and manganese in wheat plants significantly. Cyrin C reduced the plant contents of nitrogen and manganese in bean plants. Ridomil decreased number of branches per plant in bean, root dry weights of both beans and wheat plants, and reduced the plant contents of nitrogen, sodium and manganese in bean plants and increase phosphorus, and manganese contents of wheat plants significantly. Glyphosate caused significant decrease in number of tillers per plant, plant height, shoot fresh and dry weight in bean and wheat plants and increased the contents of N, P, Na and decrease Fe contents significantly in wheat plants. Treflan was reduced the wheat seed germination percentage significantly and delayed the germination to 15 days. Cyrin C caused reduction in wheat seed germination, but Ridomil and Glyphosate were increased wheat seed germination percentages. All pesticide treatments delayed bean seed germination. After three months of pesticide treatments, residues of Metalaxyl (Ridomil) and chlorpyrifos were detected in samples of bean and wheat plants. Keywords— Wheat, faba bean, Pesticides, Plant Growth.
Detecting Low-Degree Truncation

We consider the following basic, and very broad, statistical problem: Given a known high-dimensional distribution ${\cal D}$ over $\mathbb{R}^n$ and a collection of data points in $\mathbb{R}^n$, distinguish between the two possibilities that (i) the data was drawn from ${\cal D}$, versus (ii) the data was drawn from ${\cal D}|_S$, i.e. from ${\cal D}$ subject to truncation by an unknown truncation set $S \subseteq \mathbb{R}^n$. We study this problem in the setting where ${\cal D}$ is a high-dimensional i.i. d. product distribution and $S$ is an unknown degree-$d$ polynomial threshold function (one of the most well-studied types of Boolean-valued function over $\mathbb{R}^n$). Our main results are an efficient algorithm when ${\cal D}$ is a hypercontractive distribution, and a matching lower bound: $\bullet$ For any constant $d$, we give a polynomial-time algorithm which successfully distinguishes ${\cal D}$ from ${\cal D}|_S$ using $O(n^{d/2})$ samples (subject to mild technical conditions on ${\cal D}$ and $S$); $\bullet$ Even for the simplest case of ${\cal D}$ being the uniform distribution over $\{+1, -1\}^n$, we show that for any constant $d$, any distinguishing algorithm for degree-$d$ polynomial threshold functions must use $\Omega(n^{d/2})$ samples.
On the Resurgence of Recurrent Models for Long Sequences - Survey and Research Opportunities in the Transformer Era

A longstanding challenge for the Machine Learning community is the one of developing models that are capable of processing and learning from very long sequences of data. The outstanding results of Transformers-based networks (e.g., Large Language Models) promotes the idea of parallel attention as the key to succeed in such a challenge, obfuscating the role of classic sequential processing of Recurrent Models. However, in the last few years, researchers who were concerned by the quadratic complexity of self-attention have been proposing a novel wave of neural models, which gets the best from the two worlds, i.e., Transformers and Recurrent Nets. Meanwhile, Deep Space-State Models emerged as robust approaches to function approximation over time, thus opening a new perspective in learning from sequential data, followed by many people in the field and exploited to implement a special class of (linear) Recurrent Neural Networks. This survey is aimed at providing an overview of these trends framed under the unifying umbrella of Recurrence. Moreover, it emphasizes novel research opportunities that become prominent when abandoning the idea of processing long sequences whose length is known-in-advance for the more realistic setting of potentially infinite-length sequences, thus intersecting the field of lifelong-online learning from streamed data.
On the asymptotic density of $k$-tuples of positive integers with pairwise non-coprime components

We use the convolution method for arithmetic functions of several variables to deduce an asymptotic formula for the number of $k$-tuples of positive integers with components which are pairwise non-coprime and $\le x$. More generally, we obtain asymptotic formulas on the number of $k$-tuples $(n_1,\ldots,n_k)\in {\Bbb N}^k$ such that at least $r$ pairs $(n_i,n_j)$, respectively exactly $r$ pairs are coprime. Our results answer the questions raised by Moree (2005, 2014), and generalize and refine related results obtained by Heyman (2014) and Hu (2014).
UGMAE: A Unified Framework for Graph Masked Autoencoders

Generative self-supervised learning on graphs, particularly graph masked autoencoders, has emerged as a popular learning paradigm and demonstrated its efficacy in handling non-Euclidean data. However, several remaining issues limit the capability of existing methods: 1) the disregard of uneven node significance in masking, 2) the underutilization of holistic graph information, 3) the ignorance of semantic knowledge in the representation space due to the exclusive use of reconstruction loss in the output space, and 4) the unstable reconstructions caused by the large volume of masked contents. In light of this, we propose UGMAE, a unified framework for graph masked autoencoders to address these issues from the perspectives of adaptivity, integrity, complementarity, and consistency. Specifically, we first develop an adaptive feature mask generator to account for the unique significance of nodes and sample informative masks (adaptivity). We then design a ranking-based structure reconstruction objective joint with feature reconstruction to capture holistic graph information and emphasize the topological proximity between neighbors (integrity). After that, we present a bootstrapping-based similarity module to encode the high-level semantic knowledge in the representation space, complementary to the low-level reconstruction in the output space (complementarity). Finally, we build a consistency assurance module to provide reconstruction objectives with extra stabilized consistency targets (consistency). Extensive experiments demonstrate that UGMAE outperforms both contrastive and generative state-of-the-art baselines on several tasks across multiple datasets.
Leveraging Digital Cousins for Ensemble Q-Learning in Large-Scale Wireless Networks

Optimizing large-scale wireless networks, including optimal resource management, power allocation, and throughput maximization, is inherently challenging due to their non-observable system dynamics and heterogeneous and complex nature. Herein, a novel ensemble <inline-formula><tex-math notation="LaTeX">$Q$</tex-math></inline-formula>-learning algorithm that addresses the performance and complexity challenges of the traditional <inline-formula><tex-math notation="LaTeX">$Q$</tex-math></inline-formula>-learning algorithm for optimizing wireless networks is presented. Ensemble learning with synthetic Markov Decision Processes is tailored to wireless networks via new models for approximating large state-space observable wireless networks. In particular, <italic>digital cousins</italic> are proposed as an extension of the traditional digital twin concept wherein multiple <inline-formula><tex-math notation="LaTeX">$Q$</tex-math></inline-formula>-learning algorithms on multiple synthetic Markovian environments are run in parallel and their outputs are fused into a single <inline-formula><tex-math notation="LaTeX">$Q$</tex-math></inline-formula>-function. Convergence analyses of key statistics and <inline-formula><tex-math notation="LaTeX">$Q$</tex-math></inline-formula>-functions and derivations of upper bounds on the estimation bias and variance are provided. Numerical results across a variety of real-world wireless networks show that the proposed algorithm can achieve up to 50% less average policy error with up to 40% less runtime complexity than the state-of-the-art reinforcement learning algorithms. It is also shown that theoretical results properly predict trends in the experimental results.
Gravitational Magnus effect from scalar dark matter

In fluid dynamics, the Magnus effect is the force perpendicular to the motion of a spinning object as it moves through a medium. In general relativity, an analogous effect exists for a spinning compact object moving through matter, purely as a result of gravitational interactions. In this work we consider a Kerr black hole moving at relativistic velocities through scalar dark matter that is at rest. We simulate the system numerically and extract the total spin-curvature force on the black hole perpendicular to its motion. We confirm that the force scales linearly with the dimensionless spin parameter $a/M$ of the black hole up to $a/M = 0.99$, and measure its dependence on the speed $v$ of the black hole in the range $0.1 \le v \le 0.55$ for a fixed spin. Compared to previous analytic work applicable at small $v$, higher-order corrections in the velocity are found to be important: the total force is nonzero, and the dependence is not linear in $v$. We find that in all cases the total force is in the opposite direction to the hydrodynamical analogue, although at low speeds it appears to approach the expectation that the Weyl and Magnus components cancel. Spin-curvature effects may leave an imprint on gravitational wave signals from extreme mass-ratio inspirals, where the secondary black hole has a nonnegligible spin and moves in the presence of a dark matter cloud. We hope that our simulations can be used to support and extend the limits of analytic results, which are necessary to better quantify such effects in the relativistic regime.
The Limits of Price Discrimination Under Privacy Constraints

We consider a producer's problem of selling a product to a continuum of privacy-conscious consumers, where the producer can implement third-degree price discrimination, offering different prices to different market segments. In the absence of privacy constraints, Bergemann, Brooks, and Morris [2015] characterize the set of all possible consumer-producer utilities, showing that it is a triangle. We consider a privacy mechanism that provides a degree of protection by probabilistically masking each market segment, and we establish that the resultant set of all consumer-producer utilities forms a convex polygon, characterized explicitly as a linear mapping of a certain high-dimensional convex polytope into $\mathbb{R}^2$. This characterization enables us to investigate the impact of the privacy mechanism on both producer and consumer utilities. In particular, we establish that the privacy constraint always hurts the producer by reducing both the maximum and minimum utility achievable. From the consumer's perspective, although the privacy mechanism ensures an increase in the minimum utility compared to the non-private scenario, interestingly, it may reduce the maximum utility. Finally, we demonstrate that increasing the privacy level does not necessarily intensify these effects. For instance, the maximum utility for the producer or the minimum utility for the consumer may exhibit nonmonotonic behavior in response to an increase of the privacy level.
Inevitability of Polarization in Geometric Opinion Exchange

Polarization and unexpected correlations between opinions on diverse topics (including in politics, culture and consumer choices) are an object of sustained attention. However, numerous theoretical models do not seem to convincingly explain these phenomena. This paper is motivated by a recent line of work, studying models where polarization can be explained in terms of biased assimilation and geometric interplay between opinions on various topics. The agent opinions are represented as unit vectors on a multidimensional sphere and updated according to geometric rules. In contrast to previous work, we focus on the classical opinion exchange setting, where the agents update their opinions in discrete time steps, with a pair of agents interacting randomly at every step. The opinions are updated according to an update rule belonging to a general class. Our findings are twofold. First, polarization appears to be ubiquitous in the class of models we study, requiring only relatively modest assumptions reflecting biased assimilation. Second, there is a qualitative difference between two-dimensional dynamics on the one hand, and three or more dimensions on the other. Accordingly, we prove almost sure polarization for a large class of update rules in two dimensions. Then, we prove polarization in three and more dimensions in more limited cases and try to shed light on central difficulties that are absent in two dimensions.
Preferred left-handed conformations of glycyls with pathogenic variants protect against aggregation

Due to the lack of Cβ atom, the glycyl residues can exhibit left-handed Ramachandran conformations that are mostly disallowed for L-amino acids. The structural and functional significance of distinct glycyl conformations remains under-appreciated. Through systematic analyses of various datasets, we show that: i) the left-handed glycyl residues are over-represented at disease-associated sites and are evolutionarily conserved. ii) The mutations of L-disallowed Gly tend to destabilize the native folding as assessed through the change in free energies. An independent analysis of folding nuclei further corroborates the findings. iii) L-disallowed Gly are enriched at the aggregation gatekeepers, more significantly so in thermophiles, and the mutations thereof reduce the protein solubility. (iv) The positive Φ dihedral angle of L-disallowed Gly disorients its Cα atom out of the phase of alternating pleats of β-strand, conforming a crescent that is incompatible to further pair with other β-strands, and thus discourages the inter-molecular aggregation of β-strands during protein folding. v) L-disallowed conformation of Gly holds predictive power to identify sites having pathogenic variants. Altogether, our observations highlight that the L-disallowed conformations of glycyls are evolutionarily selected to endow protein stability and protection against aggregation. Apart from enhancing the existing knowledge, the findings have implications in prioritizing the genetic lesions implicated in diseases, and in designing proteins with greater stability and solubility.
Single molecule imaging of the central dogma reveals myosin-2A gene expression is regulated by contextual translational buffering

While protein homeostasis is a hallmark of gene regulation, unraveling the hidden regulatory mechanisms that maintain homeostasis is difficult using traditional methods. To confront this problem, we CRISPR engineered a human cell line with multiple tags in the endogenous MYH9 gene, which encodes the essential and ubiquitous myosin-2A cytoskeletal motor. Using these cells, we imaged MYH9 transcription, translation, and mature mRNA and protein in distinct colors, enabling a full dissection of the central dogma. Our data show that MYH9 transcription is upregulated in an SRF-dependent manner in response to cytoskeletal cues and that MYH9 translation can either buffer or match the transcriptional response depending on context. Upon knockdown of actin-depolymerizing proteins like cofilin, translation efficiency drops by a factor of two to buffer strong transcriptional upregulation, likely to help prevent excessive myosin activity. In contrast, following serum stimulation, translation matches the transcriptional response to readily reestablish steady state. Our results identify contextual translational buffering as an important regulatory mechanism driving stable MYH9 expression. They also demonstrate the power and broad applicability of our cell line, which can now be used to accurately quantify central dogma dynamics in response to diverse forms of cellular perturbations.
Endothelial fatty acid-binding proteins contribute to the pathogenesis of pulmonary hypertension

Background Pulmonary arterial hypertension (PAH) is a devastating disease characterized by obliterative vascular remodeling and persistent increase of vascular resistance, leading to right heart failure and premature death. Understanding the cellular and molecular mechanisms will help develop novel therapeutic approaches for PAH patients. Recent studies showed that FABP4 and FABP5 were expressed in ECs across multiple tissues and circulating FABP4 level was elevated in the PAH patients. However, the role of endothelial FABP4/5 in the pathogenesis of PAH remains undetermined. Methods FABP4/5 expression was examined in pulmonary arterial endothelial cells (PAECs) and lung tissues from patients with idiopathic PAH (IPAH) and pulmonary hypertension (PH) rat models. Plasma proteome analysis was performed in human PAH samples. Echocardiography, hemodynamics, histology, and immunostaining were performed to evaluate the lung and heart PH phenotypes in Egln1Tie2Cre (CKO) mice and Egln1Tie2Cre/Fabp4-5-/- (TKO) mice. Bulk RNA sequencing (RNA-seq) and single-cell RNA-seq (scRNA-seq) analysis were performed to understand the cellular and molecular mechanisms of endothelial FABP4/5 mediated PAH pathogenesis. Results Both FABP4 and FABP5 were highly induced in ECs of CKO mice and PAECs from IPAH patients, and in whole lungs of PH rats. Plasma levels of FABP4/5 were upregulated in IPAH patients and directly correlated with severity of hemodynamics and biochemical parameters. Genetic deletion of both Fabp4 and 5 in CKO mice caused a reduction of right ventricular systolic pressure (RVSP) and RV hypertrophy, attenuated pulmonary vascular remodeling and prevented the right heart failure. Fabp4/5 deletion also normalized EC glycolysis, reduced ROS and HIF-2α expression, and decreased aberrant EC proliferation in CKO lungs. Conclusions PH causes aberrant expression of FABP4/5 in pulmonary ECs which leads to enhanced ECs glycolysis and hyperproliferation, contributing to the accumulation of arterial ECs and vascular remodeling and exacerbating the disease.