Miracle-dz/UniFAR-FTUs huggingface dataset:
Poisson Algebra of Differential Forms

We give a natural definition of a Poisson differential algebra. Consistency conditions are formulated in geometrical terms. It is found that one can often locally put the Poisson structure on the differential calculus in a simple canonical form by a coordinate trans-formation. This is in analogy with the standard Darboux's theorem for symplectic geometry. For certain cases there exists a realization of the exterior derivative through a certain canonical one-form. All the above are carried out similarly for the case of a complex Poisson differential algebra. The case of one complex dimension is treated in detail and interesting features are noted. Conclusions are made in the last section.
Parabolic Lp Dirichlet boundary value problem
and VMO-type time-varying domains

We prove the solvability of the parabolic $L^p$ Dirichlet boundary value problem for $1 < p \leq \infty$ for a PDE of the form $u_t = \mbox{div} (A \nabla u) + B \cdot \nabla u$ on time-varying domains where the coefficients $A= [a_{ij}(X, t)]$ and $B=[b_i]$ satisfy a certain natural small Carleson condition. This result brings the state of affairs in the parabolic setting up to the elliptic standard. Furthermore, we establish that if the coefficients of the operator $A,\,B$ satisfy a vanishing Carleson condition and the time-varying domain is of VMO type then the parabolic $L^p$ Dirichlet boundary value problem is solvable for all $1 < p \leq \infty$. This result is related to results in papers by Mazýa, Mitrea and Shaposhnikova, and Hofmann, Mitrea and Taylor where the fact that boundary of domain has normal in VMO or near VMO implies invertibility of certain boundary operators in $L^p$ for all $1 < p \leq \infty$ which then (using the method of layer potentials) implies solvability of the $L^p$ boundary value problem in the same range for certain elliptic PDEs. Our result does not use the method of layer potentials, since the coefficients we consider are too rough to use this technique but remarkably we recover $L^p$ solvability in the full range of $p$'s as the two papers mentioned above.
Plato’s cave and differential forms

In the 1970s and again in the 1990s, Gromov gave a number of theorems and conjectures motivated by the notion that the real homotopy theory of compact manifolds and simplicial complexes influences the geometry of maps between them. The main technical result of this paper supports this intuition: we show that maps of differential algebras are closely shadowed, in a technical sense, by maps between the corresponding spaces. As a concrete application, we prove the following conjecture of Gromov: if $X$ and $Y$ are finite complexes with $Y$ simply connected, then there are constants $C(X,Y)$ and $p(X,Y)$ such that any two homotopic $L$-Lipschitz maps have a $C(L+1)^p$-Lipschitz homotopy (and if one of the maps is a constant, $p$ can be taken to be $2$.) We hope that it will lead more generally to a better understanding of the space of maps from $X$ to $Y$ in this setting.
‘What price do you put on your health?’: Medical cannabis, financial toxicity and patient perspectives on medication access in advanced cancer

Following 2016 legislation permitting limited access to cannabis for research and medicinal purposes, the number of randomized clinical trials (RCTs) investigating the effectiveness of medicinal cannabis (MC) on symptom burden relief in cancer contexts has increased in Australia. This study aimed to understand the perceptions, hopes and concerns of people with advanced cancer regarding the future availability and regulation of MC in Australia.
Cusp forms on the exceptional group of type $E_{7}$

Let $\mathbf{G}$ be the connected reductive group of type $E_{7,3}$ over $\mathbb{Q}$ and $\mathfrak{T}$ be the corresponding symmetric domain in $\mathbb{C}^{27}$. Let ${\rm\Gamma}=\mathbf{G}(\mathbb{Z})$ be the arithmetic subgroup defined by Baily. In this paper, for any positive integer $k\geqslant 10$, we will construct a (non-zero) holomorphic cusp form on $\mathfrak{T}$ of weight $2k$ with respect to ${\rm\Gamma}$ from a Hecke cusp form in $S_{2k-8}(\text{SL}_{2}(\mathbb{Z}))$. We follow Ikeda’s idea of using Siegel’s Eisenstein series, their Fourier–Jacobi expansions, and the compatible family of Eisenstein series.
Teriparatide Followed by Denosumab in Premenopausal Idiopathic Osteoporosis: Bone Microstructure and Strength by HR‐pQCT

Premenopausal women with idiopathic osteoporosis (PreMenIOP) have marked deficits in skeletal microstructure. We have reported that sequential treatment with teriparatide and denosumab improves central skeletal bone mineral density (BMD) by dual‐energy X‐ray absorptiometry and central QCT in PreMenIOP. We conducted preplanned analyses of high‐resolution peripheral quantitative computed tomography (HR‐pQCT) scans from teriparatide and denosumab extension studies to measure effects on volumetric BMD (vBMD), microarchitecture, and estimated strength at the distal radius and tibia. Of 41 women enrolled in the parent teriparatide study (20 mcg daily), 34 enrolled in the HR‐pQCT study. HR‐pQCT participants initially received teriparatide (N = 24) or placebo (N = 10) for 6 months; all then received teriparatide for 24 months. After teriparatide, 26 enrolled in the phase 2B denosumab extension (60 mg q6M) for 24 months. Primary outcomes were percentage change in vBMD, microstructure, and stiffness after teriparatide and after denosumab. Changes after sequential teriparatide and denosumab were secondary outcomes. After teriparatide, significant improvements were seen in tibial trabecular number (3.3%, p = 0.01), cortical area and thickness (both 2.7%, p < 0.001), and radial trabecular microarchitecture (number: 6.8%, thickness: 2.2%, separation: −5.1%, all p < 0.02). Despite increases in cortical porosity and decreases in cortical density, whole‐bone stiffness and failure load increased at both sites. After denosumab, increases in total (3.5%, p < 0.001 and 3.3%, p = 0.02) and cortical vBMD (1.7% and 3.2%; both p < 0.01), and failure load (1.1% and 3.6%; both p < 0.05) were seen at tibia and radius, respectively. Trabecular density (3.5%, p < 0.001) and number (2.4%, p = 0.03) increased at the tibia, while thickness (3.0%, p = 0.02) increased at the radius. After 48 months of sequential treatment, significant increases in total vBMD (tibia: p < 0.001; radius: p = 0.01), trabecular microstructure (p < 0.05), cortical thickness (tibia: p < 0.001; radius: p = 0.02), and whole bone strength (p < 0.02) were seen at both sites. Significant increases in total vBMD and bone strength parameters after sequential treatment with teriparatide followed by denosumab support the use of this regimen in PreMenIOP. © 2022 American Society for Bone and Mineral Research (ASBMR).
Teaching Broad Reasoning Skills for Multi-Step QA by Generating Hard Contexts

Question-answering datasets require a broad set of reasoning skills. We show how to use question decompositions to teach language models these broad reasoning skills in a robust fashion. Specifically, we use widely available QDMR representations to programmatically create hard-to-cheat synthetic contexts for real questions in six multi-step reasoning datasets. These contexts are carefully designed to avoid common reasoning shortcuts prevalent in real contexts that prevent models from learning the right skills. This results in a pretraining dataset, named TeaBReaC, containing 525K multi-step questions (with associated formal programs) covering about 900 reasoning patterns. We show that pretraining standard language models (LMs) on TeaBReaC before fine-tuning them on target datasets improves their performance by up to 13 F1 points across 4 multi-step QA datasets, with up to 21 point gain on more complex questions. The resulting models also demonstrate higher robustness, with a 5-8 F1 point improvement on two contrast sets. Furthermore, TeaBReaC pretraining substantially improves model performance and robustness even when starting with numerate LMs pretrained using recent methods (e.g., PReasM, POET). Our work thus shows how to effectively use decomposition-guided contexts to robustly teach multi-step reasoning.
Leveraging Statistical Shape Priors in GAN-Based ECG Synthesis

Electrocardiogram (ECG) data collection during emergency situations is challenging, making ECG data generation an efficient solution for dealing with highly imbalanced ECG training datasets. In this paper, we propose a novel approach for ECG signal generation using Generative Adversarial Networks (GANs) and statistical ECG data modeling. Our approach leverages prior knowledge about ECG dynamics to synthesize realistic signals, addressing the complex dynamics of ECG signals. To validate our approach, we conducted experiments using ECG signals from the MIT-BIH arrhythmia database. Our results demonstrate that our approach, which models temporal and amplitude variations of ECG signals as 2-D shapes, generates more realistic signals compared to state-of-the-art GAN based generation baselines. Our proposed approach has significant implications for improving the quality of ECG training datasets, which can ultimately lead to better performance of ECG classification algorithms. This research contributes to the development of more efficient and accurate methods for ECG analysis, which can aid in the diagnosis and treatment of cardiac diseases.
Hardware/Software Co-Design With ADC-Less In-Memory Computing Hardware for Spiking Neural Networks

Spiking Neural Networks (SNNs) are bio-plausible models that hold great potential for realizing energy-efficient implementations of sequential tasks on resource-constrained edge devices. However, commercial edge platforms based on standard GPUs are not optimized to deploy SNNs, resulting in high energy and latency. While analog In-Memory Computing (IMC) platforms can serve as energy-efficient inference engines, they are accursed by the immense energy, latency, and area requirements of high-precision ADCs (HP-ADC), overshadowing the benefits of in-memory computations. We propose a hardware/software co-design methodology to deploy SNNs into an ADC-Less IMC architecture using sense-amplifiers as 1-bit ADCs replacing conventional HP-ADCs and alleviating the above issues. Our proposed framework incurs minimal accuracy degradation by performing hardware-aware training and is able to scale beyond simple image classification tasks to more complex sequential regression tasks. Experiments on complex tasks of optical flow estimation and gesture recognition show that progressively increasing the hardware awareness during SNN training allows the model to adapt and learn the errors due to the non-idealities associated with ADC-Less IMC. Also, the proposed ADC-Less IMC offers significant energy and latency improvements, <inline-formula><tex-math notation="LaTeX">$2-7\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>2</mml:mn><mml:mo>-</mml:mo><mml:mn>7</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="apolinario-ieq1-3316121.gif"/></alternatives></inline-formula> and <inline-formula><tex-math notation="LaTeX">$8.9-24.6\times$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>8</mml:mn><mml:mo>. </mml:mo><mml:mn>9</mml:mn><mml:mo>-</mml:mo><mml:mn>24</mml:mn><mml:mo>. </mml:mo><mml:mn>6</mml:mn><mml:mo>×</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="apolinario-ieq2-3316121.gif"/></alternatives></inline-formula>, respectively, depending on the SNN model and the workload, compared to HP-ADC IMC.
Improving Adversarial Robustness to Sensitivity and Invariance Attacks with Deep Metric Learning

Intentionally crafted adversarial samples have effectively exploited weaknesses in deep neural networks. A standard method in adversarial robustness assumes a framework to defend against samples crafted by minimally perturbing a sample such that its corresponding model output changes. These sensitivity attacks exploit the model's sensitivity toward task-irrelevant features. Another form of adversarial sample can be crafted via invariance attacks, which exploit the model underestimating the importance of relevant features. Previous literature has indicated a tradeoff in defending against both attack types within a strictly L-p bounded defense. To promote robustness toward both types of attacks beyond Euclidean distance metrics, we use metric learning to frame adversarial regularization as an optimal transport problem. Our preliminary results indicate that regularizing over invariant perturbations in our framework improves both invariant and sensitivity defense.
Distributed Linear Bandits under Communication Constraints

We consider distributed linear bandits where $M$ agents learn collaboratively to minimize the overall cumulative regret incurred by all agents. Information exchange is facilitated by a central server, and both the uplink and downlink communications are carried over channels with fixed capacity, which limits the amount of information that can be transmitted in each use of the channels. We investigate the regret-communication trade-off by (i) establishing information-theoretic lower bounds on the required communications (in terms of bits) for achieving a sublinear regret order; (ii) developing an efficient algorithm that achieves the minimum sublinear regret order offered by centralized learning using the minimum order of communications dictated by the information-theoretic lower bounds. For sparse linear bandits, we show a variant of the proposed algorithm offers better regret-communication trade-off by leveraging the sparsity of the problem.
No Agreement Without Loss: Learning and Social Choice in Peer Review

In peer review systems, reviewers are often asked to evaluate various features of submissions, such as technical quality or novelty. A score is given to each of the predefined features and based on these the reviewer has to provide an overall quantitative recommendation. It may be assumed that each reviewer has her own mapping from the set of features to a recommendation, and that different reviewers have different mappings in mind. This introduces an element of arbitrariness known as commensuration bias. In this paper we discuss a framework, introduced by Noothigattu, Shah and Procaccia, and then applied by the organizers of the AAAI 2022 conference. Noothigattu, Shah and Procaccia proposed to aggregate reviewer's mapping by minimizing certain loss functions, and studied axiomatic properties of this approach, in the sense of social choice theory. We challenge several of the results and assumptions used in their work and report a number of negative results. On the one hand, we study a trade-off between some of the axioms proposed and the ability of the method to properly capture agreements of the majority of reviewers. On the other hand, we show that dropping a certain unrealistic assumption has dramatic effects, including causing the method to be discontinuous.
Holomorphic Cohomological Convolution and Hadamard Product

In this article, we explain the link between Pohlen's extended Hadamard product and the holomorphic cohomological convolution on $\mathbb{C}^*$. For this purpose, we introduce a generalized Hadamard product, which is defined even if the holomorphic functions do not vanish at infinity, as well as a notion of strongly convolvable sets.
Self-Adapting Noise-Contrastive Estimation for Energy-Based Models

Training energy-based models (EBMs) with noise-contrastive estimation (NCE) is theoretically feasible but practically challenging. Effective learning requires the noise distribution to be approximately similar to the target distribution, especially in high-dimensional domains. Previous works have explored modelling the noise distribution as a separate generative model, and then concurrently training this noise model with the EBM. While this method allows for more effective noise-contrastive estimation, it comes at the cost of extra memory and training complexity. Instead, this thesis proposes a self-adapting NCE algorithm which uses static instances of the EBM along its training trajectory as the noise distribution. During training, these static instances progressively converge to the target distribution, thereby circumventing the need to simultaneously train an auxiliary noise model. Moreover, we express this self-adapting NCE algorithm in the framework of Bregman divergences and show that it is a generalization of maximum likelihood learning for EBMs. The performance of our algorithm is evaluated across a range of noise update intervals, and experimental results show that shorter update intervals are conducive to higher synthesis quality.
Acoustic power absorption and enhancement generated by slow and fast MHD waves

We used long duration, high quality, unresolved (Sun-as-a star) observations collected by the ground based network BiSON and by the instruments GOLF and VIRGO on board the ESA/NASA SOHO satellite to search for solar-cycle-related changes in mode characteristics in velocity and continuum intensity for the frequency range between 2.5mHz < nu < 6.8mHz. Over the ascending phase of solar cycle 23 we found a suppression in the p-mode amplitudes both in the velocity and intensity data between 2.5mHz <nu< 4.5mHz with a maximum suppression for frequencies in the range between 2.5mHz <nu< 3.5mHz. The size of the amplitude suppression is 13+-2 per cent for the velocity and 9+-2 per cent for the intensity observations. Over the range 4.5mHz <nu< 5.5mHz the findings hint within the errors to a null change both in the velocity and intensity amplitudes. At still higher frequencies, in the so called High-frequency Interference Peaks (HIPs) between 5.8mHz <nu < 6.8mHz, we found an enhancement in the velocity amplitudes with the maximum 36+-7 per cent occurring for 6.3mHz <nu< 6.8mHz. However, in intensity observations we found a rather smaller enhancement of about 5+-2 per cent in the same interval. There is evidence that the frequency dependence of solar-cycle velocity amplitude changes is consistent with the theory behind the mode conversion of acoustic waves in a non-vertical magnetic field, but there are some problems with the intensity data, which may be due to the height in the solar atmosphere at which the VIRGO data are taken.
Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae

In this paper, we calibrate the Amati relation (the E p–E iso correlation) of gamma-ray bursts (GRBs) in a cosmology-independent way. By using a Gaussian process to reconstruct the smoothed luminosity distance from the Pantheon type Ia supernovae sample, we utilize the reconstructed results to calibrate the E p–E iso correlation with the Markov Chain Monte Carlo method and construct a Hubble diagram with the A220 GRB data, in which there are A118 GRB data with the higher qualities appropriate for cosmological purposes. With 98 GRBs at 1.4 < z ≤ 8.2 in the A118 sample and the observed Hubble data, we obtain Ωm = 0.346−0.069+0.048 , h = 0.677−0.029+0.029 for the flat ΛCDM model, and Ωm = 0.314−0.055+0.072 , h = 0.705−0.069+0.055 , w = −1.23−0.64+0.33 for the flat wCDM model, which are consistent with those from fitting the coefficients of the Amati relation and the cosmological parameters simultaneously.
Quantum state transfer on a class of circulant graphs

ABSTRACT We study the existence of quantum state transfer on non-integral circulant graphs. We find that continuous-time quantum walks on quantum networks based on certain circulant graphs with vertices exhibit pretty good state transfer when there is no external dynamic control over the system. We generalize a few previously known results on pretty good state transfer on circulant graphs, and this way we re-discover all integral circulant graphs on vertices exhibiting perfect state transfer.
Spectral quantization for ancient asymptotically cylindrical flows

We study ancient mean curvature flows in Rn+1 whose tangent flow at −∞ is a shrinking cylinder R × S( √ 2(n− k)|t|), where 1 ≤ k ≤ n − 1. We prove that the cylindrical profile function u of these flows have the asymptotics u(y, ω, τ) = (yQy − 2tr(Q))/|τ | + o(|τ |−1) as τ → −∞, where the cylindrical matrix Q is a constant symmetric k × k matrix whose eigenvalues are quantized to be either 0 or − √ 2(n−k) 4 . Compared with the bubble-sheet quantization theorem in R4 obtained by Haslhofer and the first author, this theorem has full generality in the sense of removing noncollapsing condition and being valid for all dimensions. In addition, we establish symmetry improvement theorem which generalizes the corresponding results of Brendle-Choi and the second author to all dimensions. Finally, we give some geometric applications of the two theorems. In particular, we obtain the asymptotics, compactness and O(n− k+ 1) symmetry of k-ovals in Rn+1 which are ancient noncollapsed flows in Rn+1 satisfying full rank condition that rk(Q) = k, and we also obtain the classification of ancient noncollapsed flows in Rn+1 satisfying vanishing rank condition that rk(Q) = 0.
Distinguishability-based genuine nonlocality with genuine multipartite entanglement

A set of orthogonal multipartite quantum states is said to be distinguishability-based genuinely nonlocal (also genuinely nonlocal, for abbreviation) if the states are locally indistinguishable across any bipartition of the subsystems. This form of multipartite nonlocality, although more naturally arising than the recently popular"strong nonlocality"in the context of local distinguishability, receives much less attention. In this work, we study the distinguishability-based genuine nonlocality of a typical type of genuine multipartite entangled states -- the d-dimensional GHZ states, featuring systems with local dimension not limited to 2. In the three-partite case, we find the existence of small genuinely nonlocal sets consisting of these states: we show that the cardinality can at least scale down to linear in the local dimension d, with the linear factor l = 1. Specifically, the method we use is semidefinite program and the GHZ states to construct these sets are special ones which we call"GHZ-lattices". This result might arguably suggest a significant gap between the strength of strong nonlocality and the distinguishability-based genuine nonlocality. Moreover, we put forward the notion of (s,n)-threshold distinguishability and utilizing a similar method, we successfully construct (2,3)-threshold sets consisting of GHZ states in three-partite systems.
Thermal bottomonium suppression

I discuss recent calculations of the thermal suppression of bottomonium states in relativistic heavy ion collisions. I present results for the inclusive Υ(1s) and Υ(2s) suppression as a function of centrality. I compare with the most recent CMS preliminary data available at central rapidities and make predictions at forward rapidities which are within the acceptance of the ALICE dimuon spectrometer.
Exact replica treatment of non-Hermitean complex random matrices

Recently discovered exact integrability of zero-dimensional replica field theories [E. Kanzieper, Phys. Rev. Lett. 89, 250201 (2002)] is examined in the context of Ginibre Unitary Ensemble of non-Hermitean random matrices (GinUE). In particular, various nonperturbative fermionic replica partition functions for this random matrix model are shown to belong to a positive, semi-infinite Toda Lattice Hierarchy which,
A 3D-Shape Similarity-based Contrastive Approach to Molecular Representation Learning

Molecular shape and geometry dictate key biophysical recognition processes, yet many graph neural networks disregard 3D information for molecular property prediction. Here, we propose a new contrastive-learning procedure for graph neural networks, Molecular Contrastive Learning from Shape Similarity (MolCLaSS), that implicitly learns a three-dimensional representation. Rather than directly encoding or targeting three-dimensional poses, MolCLaSS matches a similarity objective based on Gaussian overlays to learn a meaningful representation of molecular shape. We demonstrate how this framework naturally captures key aspects of three-dimensionality that two-dimensional representations cannot and provides an inductive framework for scaffold hopping.