Miracle-dz/UniFAR-FTUs huggingface dataset:
Injective modules over the Jacobson algebra 
$K\langle X, Y \ | \ XY=1\rangle $

Abstract For a field K, let $\mathcal {R}$ denote the Jacobson algebra $K\langle X, Y \ | \ XY=1\rangle $ . We give an explicit construction of the injective envelope of each of the (infinitely many) simple left $\mathcal {R}$ -modules. Consequently, we obtain an explicit description of a minimal injective cogenerator for $\mathcal {R}$ . Our approach involves realizing $\mathcal {R}$ up to isomorphism as the Leavitt path K-algebra of an appropriate graph $\mathcal {T}$ , which thereby allows us to utilize important machinery developed for that class of algebras.
A Decade of Multiwavelength Observations of the TeV Blazar 1ES 1215+303: Extreme Shift of the Synchrotron Peak Frequency and Long-term Optical–Gamma-Ray Flux Increase

Blazars are known for their variability on a wide range of timescales at all wavelengths. Most studies of TeV gamma-ray blazars focus on short timescales, especially during flares. With a decade of observations from the Fermi-LAT and VERITAS, we present an extensive study of the long-term multiwavelength radio-to-gamma-ray flux-density variability, with the addition of a couple of short-time radio-structure and optical polarization observations of the blazar 1ES 1215+303 (z = 0.130), with a focus on its gamma-ray emission from 100 MeV to 30 TeV. Multiple strong GeV gamma-ray flares, a long-term increase in the gamma-ray and optical flux baseline, and a linear correlation between these two bands are observed over the ten-year period. Typical HBL behaviors are identified in the radio morphology and broadband spectrum of the source. Three stationary features in the innermost jet are resolved by Very Long Baseline Array at 43.1, 22.2, and 15.3 GHz. We employ a two-component synchrotron self-Compton model to describe different flux states of the source, including the epoch during which an extreme shift in energy of the synchrotron peak frequency from infrared to soft X-rays is observed.
Fine-grained Uncertainty Modeling in Neural Networks

Existing uncertainty modeling approaches try to detect an out-of-distribution point from the in-distribution dataset. We extend this argument to detect finer-grained uncertainty that distinguishes between (a). certain points, (b). uncertain points but within the data distribution, and (c). out-of-distribution points. Our method corrects overconfident NN decisions, detects outlier points and learns to say ``I don't know'' when uncertain about a critical point between the top two predictions. In addition, we provide a mechanism to quantify class distributions overlap in the decision manifold and investigate its implications in model interpretability. Our method is two-step: in the first step, the proposed method builds a class distribution using Kernel Activation Vectors (kav) extracted from the Network. In the second step, the algorithm determines the confidence of a test point by a hierarchical decision rule based on the chi-squared distribution of squared Mahalanobis distances. Our method sits on top of a given Neural Network, requires a single scan of training data to estimate class distribution statistics, and is highly scalable to deep networks and wider pre-softmax layer. As a positive side effect, our method helps to prevent adversarial attacks without requiring any additional training. It is directly achieved when the Softmax layer is substituted by our robust uncertainty layer at the evaluation phase.
Tidal heating of quantum black holes and their imprints on gravitational waves

The characteristic difference between a black hole and other exotic compact objects (ECOs) is the presence of the horizon. The horizon of a classical black hole acts as a one-way membrane. Due to this nature, any perturbation on the black hole must satisfy ingoing boundary conditions at the horizon. For an ECO either the horizon is replaced or modified with a surface with non zero reflectivity. This results in a modification of the boundary condition of the perturbation around such systems. In this work, we study how tidal heating of an ECO gets modified due to the presence of a reflective surface and what implication it brings for the gravitational wave observations.
Task-Based Quantization with Application to MIMO Receivers

Multiple-input multiple-output (MIMO) systems are required to communicate reliably at high spectral bands using a large number of antennas, while operating under strict power and cost constraints. In order to meet these constraints, future MIMO receivers are expected to operate with low resolution quantizers, namely, utilize a limited number of bits for representing their observed measurements, inherently distorting the digital representation of the acquired signals. The fact that MIMO receivers use their measurements for some task, such as symbol detection and channel estimation, other than recovering the underlying analog signal, indicates that the distortion induced by bit-constrained quantization can be reduced by designing the acquisition scheme in light of the system task, i.e., by {\em task-based quantization}. In this work we survey the theory and design approaches to task-based quantization, presenting model-aware designs as well as data-driven implementations. Then, we show how one can implement a task-based bit-constrained MIMO receiver, presenting approaches ranging from conventional hybrid receiver architectures to structures exploiting the dynamic nature of metasurface antennas. This survey narrows the gap between theoretical task-based quantization and its implementation in practice, providing concrete algorithmic and hardware design principles for realizing task-based MIMO receivers.
Graph Convolutional Gaussian Processes For Link Prediction

Link prediction aims to reveal missing edges in a graph. We address this task with a Gaussian process that is transformed using simplified graph convolutions to better leverage the inductive bias of the domain. To scale the Gaussian process model to large graphs, we introduce a variational inducing point method that places pseudo inputs on a graph-structured domain. We evaluate our model on eight large graphs with up to thousands of nodes and report consistent improvements over existing Gaussian process models as well as competitive performance when compared to state-of-the-art graph neural network approaches.
Black Hole Superradiant Instability from Ultralight Spin-2 Fields.

Ultralight bosonic fields are compelling dark-matter candidates and arise in a variety of beyond standard model scenarios. These fields can tap energy and angular momentum from spinning black holes through superradiant instabilities, during which a macroscopic bosonic condensate develops around the black hole. Striking features of this phenomenon include gaps in the spin-mass distribution of astrophysical black holes and a continuous gravitational-wave (GW) signal emitted by the condensate. So far these processes have been studied in great detail for scalar fields and, more recently, for vector fields. Here we take an important step forward in the black hole superradiance program by computing, analytically, the instability timescale, direct GW emission, and stochastic background, in the case of massive tensor (i.e., spin-2) fields. Our analysis is valid for any black hole spin and for small boson masses. The instability of massive spin-2 fields shares some properties with the scalar and vector cases, but its phenomenology is much richer, for example, there exist multiple modes with comparable instability timescales, and the dominant GW signal is hexadecapolar rather than quadrupolar. Electromagnetic and GW observations of spinning black holes in the mass range M∈(1,10^{10}) M_{⊙} can constrain the mass of a putative spin-2 field in the range 10^{-22}≲m_{b} c^{2}/eV≲10^{-10} . For 10^{-17}≲m_{b} c^{2}/eV≲10^{-15} , the space mission LISA could detect the continuous GW signal for sources at redshift z=20, or even larger.
Decisions, Counterfactual Explanations and Strategic Behavior

As data-driven predictive models are increasingly used to inform decisions, it has been argued that decision makers should provide explanations that help individuals understand what would have to change for these decisions to be beneficial ones. However, there has been little discussion on the possibility that individuals may use the above counterfactual explanations to invest effort strategically and maximize their chances of receiving a beneficial decision. In this paper, our goal is to find policies and counterfactual explanations that are optimal in terms of utility in such a strategic setting. We first show that, given a pre-defined policy, the problem of finding the optimal set of counterfactual explanations is NP-hard. Then, we show that the corresponding objective is nondecreasing and satisfies submodularity and this allows a standard greedy algorithm to enjoy approximation guarantees. In addition, we further show that the problem of jointly finding both the optimal policy and set of counterfactual explanations reduces to maximizing a non-monotone submodular function. As a result, we can use a recent randomized algorithm to solve the problem, which also offers approximation guarantees. Finally, we demonstrate that, by incorporating a matroid constraint into the problem formulation, we can increase the diversity of the optimal set of counterfactual explanations and incentivize individuals across the whole spectrum of the population to self improve. Experiments on synthetic and real lending and credit card data illustrate our theoretical findings and show that the counterfactual explanations and decision policies found by our algorithms achieve higher utility than several competitive baselines.
ALMA Reveals the Molecular Gas Properties of Five Star-forming Galaxies across the Main Sequence at 3

We present the detection of CO (5−4) with signal-to-noise ratio (S/N) > 7–13 and a lower CO transition with S/N > 3 (CO (4−3) for four galaxies, and CO (3−2) for one) with the Atacama Large Millimeter/submillimeter Array in bands 3 and 4 in five main-sequence (MS) star-forming galaxies with stellar masses (3–6) × 1010M⊙ at 3 < z < 3.5. We find a good correlation between the total far-infrared luminosity LFIR and the luminosity of the CO (5−4) transition , where increases with star formation rate (SFR), indicating that CO (5−4) is a good tracer of the obscured SFR in these galaxies. The two galaxies that lie closer to the star-forming MS have CO spectral line energy distribution (SLED) slopes that are comparable to other star-forming populations, such as local submillimeter galaxies and BzK star-forming galaxies; the three objects with higher specific star formation rates have far steeper CO SLEDs, which possibly indicates a more concentrated episode of star formation. By exploiting the CO SLED slopes to extrapolate the luminosity of the CO (1−0) transition and using a classical conversion factor for MS galaxies of , we find that these galaxies are very gas-rich, with molecular gas fractions between 60% and 80% and quite long depletion times, between 0.2 and 1 Gyr. Finally, we obtain dynamical masses that are comparable to the sum of stellar and gas mass (at least for four out of five galaxies), allowing us to put a first constraint on the αCO parameter for MS galaxies at an unprecedented redshift.
Dynamically Generated Inflationary ΛCDM

Our primary objective is to construct a plausible, unified model of inflation, dark energy and dark matter from a fundamental Lagrangian action first principle, wherein all fundamental ingredients are systematically dynamically generated starting from a very simple model of modified gravity interacting with a single scalar field employing the formalism of non-Riemannian spacetime volume-elements. The non-Riemannian volume element in the initial scalar field action leads to a hidden, nonlinear Noether symmetry which produces an energy-momentum tensor identified as the sum of a dynamically generated cosmological constant and dust-like dark matter. The non-Riemannian volume-element in the initial Einstein–Hilbert action upon passage to the physical Einstein-frame creates, dynamically, a second scalar field with a non-trivial inflationary potential and with an additional interaction with the dynamically generated dark matter. The resulting Einstein-frame action describes a fully dynamically generated inflationary model coupled to dark matter. Numerical results for observables such as the scalar power spectral index and the tensor-to-scalar ratio conform to the latest 2018 PLANCK data.
Smoothness and Stability in GANs

Generative adversarial networks, or GANs, commonly display unstable behavior during training. In this work, we develop a principled theoretical framework for understanding the stability of various types of GANs. In particular, we derive conditions that guarantee eventual stationarity of the generator when it is trained with gradient descent, conditions that must be satisfied by the divergence that is minimized by the GAN and the generator's architecture. We find that existing GAN variants satisfy some, but not all, of these conditions. Using tools from convex analysis, optimal transport, and reproducing kernels, we construct a GAN that fulfills these conditions simultaneously. In the process, we explain and clarify the need for various existing GAN stabilization techniques, including Lipschitz constraints, gradient penalties, and smooth activation functions.
Fundamental Tradeoffs between Invariance and Sensitivity to Adversarial Perturbations

Adversarial examples are malicious inputs crafted to induce misclassification. Commonly studied sensitivity-based adversarial examples introduce semantically-small changes to an input that result in a different model prediction. This paper studies a complementary failure mode, invariance-based adversarial examples, that introduce minimal semantic changes that modify an input's true label yet preserve the model's prediction. We demonstrate fundamental tradeoffs between these two types of adversarial examples. We show that defenses against sensitivity-based attacks actively harm a model's accuracy on invariance-based attacks, and that new approaches are needed to resist both attack types. In particular, we break state-of-the-art adversarially-trained and certifiably-robust models by generating small perturbations that the models are (provably) robust to, yet that change an input's class according to human labelers. Finally, we formally show that the existence of excessively invariant classifiers arises from the presence of overly-robust predictive features in standard datasets.
SN 2010kd: Photometric and Spectroscopic Analysis of a Slow-decaying Superluminous Supernova

This paper presents data and analysis of SN 2010kd, a low-redshift (z = 0.101) H-deficient superluminous supernova (SLSN), based on ultraviolet/optical photometry and optical spectroscopy spanning between −28 and +194 days relative to B-band maximum light. The B-band light-curve comparison of SN 2010kd with a subset of well-studied SLSNe I at comparable redshifts indicates that it is a slow-decaying PTF12dam-like SLSN. Analytical light-curve modeling using the Minim code suggests that the bolometric light curve of SN 2010kd favors circumstellar matter interaction for the powering mechanism. SYNAPPS modeling of the early-phase spectra does not identify broad H or He lines, whereas the photospheric-phase spectra are dominated by O i, O ii, C ii, C iv, and Si ii, in particular the presence of both low- and high-velocity components of O ii and Si ii lines. The nebular-phase spectra of SN 2010kd are dominated by O i and Ca ii emission lines similar to those seen in other SLSNe I. The line velocities in SN 2010kd exhibit flatter evolution curves similar to SN 2015bn but with comparatively higher values. SN 2010kd shows a higher single-zone local thermodynamic equilibrium temperature in comparison to PTF12dam and SN 2015bn, and it has an upper O i ejected mass limit of ∼10 M⊙. The host of SN 2010kd is a dwarf galaxy with a high star formation rate (∼0.18 ± 0.04 M⊙ yr−1) and extreme emission lines.
Synthetic spectroscopic indices for identifying multiple stellar populations in globular clusters

We present an investigation of synthetic spectroscopic indices that can plausibly help in identifying the presence of multiple stellar populations in globular clusters. The study is based on a new grid of stellar model atmospheres and high-resolution (R=500,000) synthetic spectra, that consider chemical partitions that have been singled out in Galactic globular clusters. The database is composed of 3472 model atmospheres and theoretical spectra calculated with the collection of Fortran codes DFSYNTHE, ATLAS9 and SYNTHE, developed by Robert L. Kurucz. They cover a range of effective temperature from 4300 to 7000 K, surface gravity from 2.0 to 5.0 dex and four different chemical compositions. A set of 19 spectroscopic indices were calculated from a degraded version (R=2500) of the theoretical spectra dataset. The set includes five indices previously used in the context of globular clusters analyses and 14 indices that we have newly defined by maximizing the capability of differentiating the chemical compositions. We explored the effects of atmospheric parameters on the index values and identified the optimal spectral diagnostics that allow to trace the signatures of objects of different stellar populations, located in the main sequence, the red giant branch and the horizontal branch. We found a suitable set of indices, that mostly involve molecular bands (in particular NH, but also CH and CN), that are very promising for spectroscopically identifying multiple stellar populations in globular clusters.
Modular polymer representations of the Weyl algebra

One of the key conceptual challenges in quantum gravity is to understand how quantum theory should modify the very notion of spacetime. One way to investigate this question is to study the alternatives to Schrodinger quantum mechanics. The polymer representation, inspired by loop quantum gravity, can be understood as capturing features of discrete spatial geometry. The modular representation, on the other hand, has a built-in unification of position and momentum polarizations via a length scale. In this paper, we introduce the modular polymer representations of the Weyl algebra, in which neither position nor momentum exists as a well-defined operator. As inequivalent representations, they are candidates for describing new physics. We illustrate this by studying the dynamics of the harmonic oscillator as an example, with the prospect of eventually applying this representation to quantum cosmology.
Area Spectral Efficiency and SINR Scaling Laws in Multi-Antenna Cellular Networks

We study the scaling laws of the signal-to-interference-plus-noise ratio (SINR) and area spectral efficiency (ASE) in multi-antenna cellular networks, where the number of antennas scales with the base station (BS) spatial density $\lambda$. We start with the MISO case having $N_t(\lambda)$ transmit antennas and a single receive antenna and prove that the average SINR scales as $\frac{N_t(\lambda)}{\lambda}$ and the average ASE scales as $\lambda\log\left(1+\frac{N_t(\lambda)}{\lambda}\right)$. For the MIMO case with single-stream eigenbeamforming and $N_r(\lambda) \leq N_t(\lambda)$ receive antennas, we prove that the scaling laws of the conditional SINR and ASE are exactly the same as the MISO case, i.e. not dependent on $N_r(\lambda)$. We also show that coordinated beamforming amongst $K\leq N_t(\lambda)$ neighboring BSs does not improve the scaling laws regardless of $K$. From a system design perspective, our results suggest that deploying multi-antenna BSs can help maintain the per-user throughput and the linear increase in the ASE with BS density, while the number of antennas at the user equipment and the use of BS cooperation do not matter much.
Turbo-Aggregate: Breaking the Quadratic Aggregation Barrier in Secure Federated Learning

Federated learning is a distributed framework for training machine learning models over the data residing at mobile devices, while protecting the privacy of individual users. A major bottleneck in scaling federated learning to a large number of users is the overhead of secure model aggregation across many users. In particular, the overhead of the state-of-the-art protocols for secure model aggregation grows quadratically with the number of users. In this article, we propose the first secure aggregation framework, named Turbo-Aggregate, that in a network with <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> users achieves a secure aggregation overhead of <inline-formula> <tex-math notation="LaTeX">$O(N\log {N})$ </tex-math></inline-formula>, as opposed to <inline-formula> <tex-math notation="LaTeX">$O(N^{2})$ </tex-math></inline-formula>, while tolerating up to a user dropout rate of 50%. Turbo-Aggregate employs a multi-group circular strategy for efficient model aggregation, and leverages additive secret sharing and novel coding techniques for injecting aggregation redundancy in order to handle user dropouts while guaranteeing user privacy. We experimentally demonstrate that Turbo-Aggregate achieves a total running time that grows almost linear in the number of users, and provides up to <inline-formula> <tex-math notation="LaTeX">$40\times $ </tex-math></inline-formula> speedup over the state-of-the-art protocols with up to <inline-formula> <tex-math notation="LaTeX">$N=200$ </tex-math></inline-formula> users. Our experiments also demonstrate the impact of model size and bandwidth on the performance of Turbo-Aggregate.
Multiplicities of irreducible theta divisors

Let $(A,\Theta)$ be a principally polarized abelian variety of dimension $g\geq 4$. Based on vanishing theorems, differentiation techniques and intersection theory, we show that whenever the theta divisor $\Theta$ is irreducible, its multiplicity at any point is at most $g-2$. This improves work of Kollar, Smith-Varley, and Ein-Lazarsfeld. We also introduce some new ideas to study the same type of questions for pluri-theta divisors.
Community Detection on Mixture Multi-layer Networks via Regularized Tensor Decomposition

We study the problem of community detection in multi-layer networks, where pairs of nodes can be related in multiple modalities. We introduce a general framework, i.e., mixture multi-layer stochastic block model (MMSBM), which includes many earlier models as special cases. We propose a tensor-based algorithm (TWIST) to reveal both global/local memberships of nodes, and memberships of layers. We show that the TWIST procedure can accurately detect the communities with small misclassification error as the number of nodes and/or the number of layers increases. Numerical studies confirm our theoretical findings. To our best knowledge, this is the first systematic study on the mixture multi-layer networks using tensor decomposition. The method is applied to two real datasets: worldwide trading networks and malaria parasite genes networks, yielding new and interesting findings.