Miracle-dz/UniFAR-FTUs huggingface dataset:
X-ray detected AGN in SDSS dwarf galaxies

In this work we present a robust quantification of X-ray selected AGN in local ($z \leq 0.25$) dwarf galaxies ($M_\mathrm{*} \leq 3 \times 10^9 \mathrm{M_\odot}$). We define a parent sample of 4,331 dwarf galaxies found within the footprint of both the MPA-JHU galaxy catalogue (based on SDSS DR8) and 3XMM DR7, performed a careful review of the data to remove misidentifications and produced a sample of 61 dwarf galaxies that exhibit nuclear X-ray activity indicative of an AGN. We examine the optical emission line ratios of our X-ray selected sample and find that optical AGN diagnostics fail to identify 85% of the sources. We then calculated the growth rates of the black holes powering our AGN in terms of their specific accretion rates ($\propto L_\mathrm{X}/M_\mathrm{*}$, an approximate tracer of the Eddington ratio). Within our observed sample, we found a wide range of specific accretion rates. After correcting the observed sample for the varying sensitivity of 3XMM, we found further evidence for a wide range of X-ray luminosities and specific accretion rates, described by a power law. Using this corrected AGN sample we also define an AGN fraction describing their relative incidence within the parent sample. We found the AGN fraction increases with host galaxy mass (up to $\approx$ 6%) for galaxies with X-ray luminosities between $10^{39} \mathrm{erg/s}$ and $10^{42} \mathrm{erg/s}$, and by extrapolating the power law to higher luminosities, we found evidence to suggest the fraction of luminous AGN ($L_\mathrm{X} \geq 10^{42.4} \mathrm{erg/s}$) is constant out to $z \approx 0.7$.
Improved analysis of higher order random walks and applications

The motivation of this work is to extend the techniques of higher order random walks on simplicial complexes to analyze mixing times of Markov chains for combinatorial problems. Our main result is a sharp upper bound on the second eigenvalue of the down-up walk on a pure simplicial complex, in terms of the second eigenvalues of its links. We show some applications of this result in analyzing mixing times of Markov chains, including sampling independent sets of a graph and sampling common independent sets of two partition matroids.
Adaptive Stopping Rule for Kernel-based Gradient Descent Algorithms

In this paper, we propose an adaptive stopping rule for kernel-based gradient descent (KGD) algorithms. We introduce the empirical effective dimension to quantify the increments of iterations in KGD and derive an implementable early stopping strategy. We analyze the performance of the adaptive stopping rule in the framework of learning theory. Using the recently developed integral operator approach, we rigorously prove the optimality of the adaptive stopping rule in terms of showing the optimal learning rates for KGD equipped with this rule. Furthermore, a sharp bound on the number of iterations in KGD equipped with the proposed early stopping rule is also given to demonstrate its computational advantage.
Shallow Encoder Deep Decoder (SEDD) Networks for Image Encryption and Decryption

This paper explores a new framework for lossy image encryption and decryption using a simple shallow encoder neural network E for encryption, and a complex deep decoder neural network D for decryption. E is kept simple so that encoding can be done on low power and portable devices and can in principle be any nonlinear function which outputs an encoded vector. D is trained to decode the encodings using the dataset of image - encoded vector pairs obtained from E and happens independently of E. As the encodings come from E which while being a simple neural network, still has thousands of random parameters and therefore the encodings would be practically impossible to crack without D. This approach differs from autoencoders as D is trained completely independently of E, although the structure may seem similar. Therefore, this paper also explores empirically if a deep neural network can learn to reconstruct the original data in any useful form given the output of a neural network or any other nonlinear function, which can have very useful applications in Cryptanalysis. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the decoded images from D along with some limitations.
Bilateral synchronous mature ovarian teratoma and mucinous cystadenoma

Published reports of different synchronous tumours in both ovaries are scanty, and the few reported cases are mostly malignant. This report of synchronous benign tumors in both ovaries occurred in a 26 year old female who presented with one year history of painless abdominal swelling and two large multicystic masses on ultrasound scan. She had bilateral oophorectomy and histology revealed right sided benign cystic teratoma and left sided mucinous cystadenoma. Conclusion: Both tumours were benign and therefore potends no adverse consequences for the patient. Nonetheless, given the unusual presentation, she is being followed up.
A correlation between the number of satellites and the bulge-to-total baryonic mass ratio extending beyond the Local Group

Recent observations of the fields surrounding a few Milky-Way-like galaxies in the local Universe have become deep enough to enable investigations of the predictions of the standard LCDM cosmological model down to small scales outside the Local Group. Motivated by an observed correlation between the number of dwarf satellites (N_sat) and the bulge-to-total baryonic mass ratios (B/T) of the three main galaxies in the Local Group, i.e. the Milky Way, Andromeda, and Triangulum (M33), we use published data of three well-studied galaxies outside the Local Group, namely M81, Centaurus A, and M101, and their confirmed satellites, and we find a strong and significant correlation between N_sat and B/T. This presents itself in contradiction with the hitherto published results from cosmological simulations reporting an absence of a correlation between N_sat and B/T in the LCDM model. We conclude that, based on the current data, the N_sat vs. B/T correlation is no longer a property confined to only the Local Group.
Revisiting L2,1-Norm Robustness With Vector Outlier Regularization

In many real-world applications, data usually contain outliers. One popular approach is to use the <inline-formula> <tex-math notation="LaTeX">$L_{2,1}$ </tex-math></inline-formula>-norm function as a robust loss/error function. However, the robustness of the <inline-formula> <tex-math notation="LaTeX">$L_{2,1}$ </tex-math></inline-formula>-norm function is not well understood so far. In this brief, we propose a new vector outlier regularization (VOR) framework to understand and analyze the robustness of the <inline-formula> <tex-math notation="LaTeX">$L_{2,1}$ </tex-math></inline-formula>-norm function. Our VOR function defines a data point to be the outlier if it is outside a threshold with respect to a theoretical prediction, and regularizes it, i.e., pull it back to the threshold line. Thus, in the VOR function, how far an outlier lies away from its theoretical predicted value does not affect the final regularization and analysis results. One important aspect of the VOR function is that it has an equivalent continuous formulation, based on which we can prove that the <inline-formula> <tex-math notation="LaTeX">$L_{2,1}$ </tex-math></inline-formula>-norm function is the limiting case of the proposed VOR function. Based on this theoretical result, we thus provide a new and intuitive explanation for the robustness property of the <inline-formula> <tex-math notation="LaTeX">$L_{2,1}$ </tex-math></inline-formula>-norm function. As an example, we use the VOR function to matrix factorization and propose a VOR principal component analysis (PCA) (VORPCA). We show some benefits of VORPCA on data reconstruction and clustering tasks.
List Decoding for Oblivious Arbitrarily Varying MACs: Constrained and Gaussian

This paper provides inner and outer bounds on list sizes of list decoding for two-user oblivious arbitrarily varying multiple access channels (AVMACs). An oblivious AVMAC consists of two users who wish to transmit messages (without cooperation) to a remote receiver, a malicious jammer who only has access to the codebooks of both users (which are also known to every party), and a receiver who is required to decode the message pair sent by both users. The transmitters send codewords which encode messages subject to input constraints. The jammer, without knowing the transmitted codeword pair, injects adversarial noise subject to state constraints so as to actively corrupt the communication from both users to the receiver. It was left as an open question in [Cai16] to nail down the smallest list sizes for constrained AVMACs. Our inner and outer bounds are based on a judicious notion of symmetrizability for AVMACs introduced by [Cai16] with twists to incorporate input and state constraints. The analysis follows techniques by Csiszár and Narayan [CN88]. When no constraints are imposed,´ our bound collapse to prior results by Cai [Cai16] which characterized the list-decoding capacity region of unconstrained AVMACs. Techniques used in this paper can also be extended to the Gaussian case and we characterize the list-decoding capacity region of Gaussian AVMACs. The converse argument relies on a bounding technique recently used by Hosseinigoki and Kosut [HK19]. The full version of this paper is [Zha20].
Hypergraph Cuts with General Splitting Functions

The minimum $s$-$t$ cut problem in graphs is one of the most fundamental problems in combinatorial optimization, and graph cuts underlie algorithms throughout discrete mathematics, theoretical computer science, operations research, and data science. While graphs are a standard model for pairwise relationships, hypergraphs provide the flexibility to model multi-way relationships, and are now a standard model for complex data and systems. However, when generalizing from graphs to hypergraphs, the notion of a "cut hyperedge" is less clear, as a hyperedge's nodes can be split in several ways. Here, we develop a framework for hypergraph cuts by considering the problem of separating two terminal nodes in a hypergraph in a way that minimizes a sum of penalties at split hyperedges. In our setup, different ways of splitting the same hyperedge have different penalties, and the penalty is encoded by what we call a splitting function. Our framework opens a rich space on the foundations of hypergraph cuts. We first identify a natural class of cardinality-based hyperedge splitting functions that depend only on the number of nodes on each side of the split. In this case, we show that the general hypergraph $s$-$t$ cut problem can be reduced to a tractable graph $s$-$t$ cut problem if and only if the splitting functions are submodular. We also identify a wide regime of non-submodular splitting functions for which the problem is NP-hard. We also analyze extensions to multiway cuts with at least three terminal nodes and identify a natural class of splitting functions for which the problem can be reduced in an approximation-preserving way to the node-weighted multiway cut problem in graphs, again subject to a submodularity property. Finally, we outline several open questions on general hypergraph cut problems.
Unpaired Multi-Modal Segmentation via Knowledge Distillation

Multi-modal learning is typically performed with network architectures containing modality-specific layers and shared layers, utilizing co-registered images of different modalities. We propose a novel learning scheme for unpaired cross-modality image segmentation, with a highly compact architecture achieving superior segmentation accuracy. In our method, we heavily reuse network parameters, by sharing all convolutional kernels across CT and MRI, and only employ modality-specific internal normalization layers which compute respective statistics. To effectively train such a highly compact model, we introduce a novel loss term inspired by knowledge distillation, by explicitly constraining the KL-divergence of our derived prediction distributions between modalities. We have extensively validated our approach on two multi-class segmentation problems: i) cardiac structure segmentation, and ii) abdominal organ segmentation. Different network settings, i.e., 2D dilated network and 3D U-net, are utilized to investigate our method’s general efficacy. Experimental results on both tasks demonstrate that our novel multi-modal learning scheme consistently outperforms single-modal training and previous multi-modal approaches.
The bolometric quasar luminosity function at z = 0–7

In this paper, we provide updated constraints on the bolometric quasar luminosity function (QLF) from z = 0 to z = 7. The constraints are based on an observational compilation that includes observations in the rest-frame IR, B band, UV, soft, and hard X-ray in past decades. Our method follows Hopkins et al. with an updated quasar SED model and bolometric and extinction corrections. The new best-fitting bolometric quasar luminosity function behaves qualitatively different from the old Hopkins model at high redshift. Compared with the old model, the number density normalization decreases towards higher redshift and the bright-end slope is steeper at z ≳ 2. Due to the paucity of measurements at the faint end, the faint end slope at z ≳ 5 is quite uncertain. We present two models, one featuring a progressively steeper faint-end slope at higher redshift and the other featuring a shallow faint-end slope at z ≳ 5. Further multiband observations of the faint-end QLF are needed to distinguish between these models. The evolutionary pattern of the bolometric QLF can be interpreted as an early phase likely dominated by the hierarchical assembly of structures and a late phase likely dominated by the quenching of galaxies. We explore the implications of this model on the ionizing photon production by quasars, the CXB spectrum, the SMBH mass density, and mass functions. The predicted hydrogen photoionization rate contributed by quasars is subdominant during the epoch of reionization and only becomes important at z ≲ 3. The predicted CXB spectrum, cosmic SMBH mass density, and SMBH mass function are generally consistent with existing observations.
The TA Framework: Designing Real-time Teaching Augmentation for K-12 Classrooms

Recently, the HCI community has seen increased interest in the design of teaching augmentation (TA): tools that extend and complement teachers' pedagogical abilities during ongoing classroom activities. Examples of TA systems are emerging across multiple disciplines, taking various forms: e.g., ambient displays, wearables, or learning analytics dashboards. However, these diverse examples have not been analyzed together to derive more fundamental insights into the design of teaching augmentation. Addressing this opportunity, we broadly synthesize existing cases to propose the TA framework. Our framework specifies a rich design space in five dimensions, to support the design and analysis of teaching augmentation. We contextualize the framework using existing designs cases, to surface underlying design trade-offs: for example, balancing actionability of presented information with teachers' needs for professional autonomy, or balancing unobtrusiveness with informativeness in the design of TA systems. Applying the TA framework, we identify opportunities for future research and design.
Least squares binary quantization of neural networks

Quantizing weights and activations of deep neural networks results in significant improvement in inference efficiency at the cost of lower accuracy. A source of the accuracy gap between full precision and quantized models is the quantization error. In this work, we focus on the binary quantization, in which values are mapped to -1 and 1. We provide a unified framework to analyze different scaling strategies. Inspired by the pareto-optimality of 2-bits versus 1-bit quantization, we introduce a novel 2-bits quantization with provably least squares error. Our quantization algorithms can be implemented efficiently on the hardware using bitwise operations. We present proofs to show that our proposed methods are optimal, and also provide empirical error analysis. We conduct experiments on the ImageNet dataset and show a reduced accuracy gap when using the proposed least squares quantization algorithms.1
Role of the Unruh effect in Bremsstrahlung

An equivalence is demonstrated, by an explicit first order quantum calculation, between the Minkowski photon emission rate in the inertial frame for an accelerating charge moving on a Rindler trajectory with additional transverse drift motion and the combined Rindler photon emission and absorption rate of the same charge in the Rindler frame in the presence of the Davies-Unruh thermal bath. The equivalence also extends, for the Bremsstrahlung emitted by the same charge as calculated using the machinery of classical electrodynamics. The equivalence is shown to also hold for the case of accelerating charges moving on a Rindler trajectory with additional arbitrary transverse motion. Our results generalize those of Higuchi et al. (1992) and of Cozzella et al. (2017) for accelerated trajectories with circular transverse motion. Related issues and experimental implications are discussed.
Spherical Image Generation from a Single Normal Field of View Image by Considering Scene Symmetry

Spherical images taken in all directions (360 degrees) allow representing the surroundings of the subject and the space itself, providing an immersive experience to the viewers. Generating a spherical image from a single normal-field-of-view (NFOV) image is convenient and considerably expands the usage scenarios because there is no need to use a specific panoramic camera or take images from multiple directions; however, it is still a challenging and unsolved problem. The primary challenge is controlling the high degree of freedom involved in generating a wide area that includes the all directions of the desired plausible spherical image. On the other hand, scene symmetry is a basic property of the global structure of the spherical images, such as rotation symmetry, plane symmetry and asymmetry. We propose a method to generate spherical image from a single NFOV image, and control the degree of freedom of the generated regions using scene symmetry. We incorporate scene-symmetry parameters as latent variables into conditional variational autoencoders, following which we learn the conditional probability of spherical images for NFOV images and scene symmetry. Furthermore, the probability density functions are represented using neural networks, and scene symmetry is implemented using both circular shift and flip of the hidden variables. Our experiments show that the proposed method can generate various plausible spherical images, controlled from symmetric to asymmetric.
Quantum Poker -- a pedagogical tool to introduce the basic concepts of quantum computing and error mitigation techniques for NISQ devices

Quantum computers are on the verge of becoming a commercially available reality. They represent a paradigm shift in computing, with a steep learning gradient. The creation of games is a way to ease the transition for beginners. We present a game similar to the Poker variant Texas hold 'em with the intention to serve as an engaging pedagogical tool to learn the basics rules of quantum computing. The concepts of quantum states, quantum operations and measurement can be learned in a playful manner. The difference to the classical variant is that the community cards are replaced by a quantum register that is "randomly" initialized, and the cards for each player are replaced by quantum gates, randomly drawn from a set of available gates. Each player can create a quantum circuit with their cards, with the aim to maximize the number of 1's that are measured in the computational basis. The basic concepts of superposition, entanglement and quantum gates are employed. We provide a proof-of-concept implementation using Qiskit. A comparison of the results for the created circuits using a simulator and IBM machines is conducted, showing that error rates on contemporary quantum computers are still very high. For the success of noisy intermediate scale quantum (NISQ) computers, improvements on the error rates and error mitigation techniques are necessary, even for simple circuits. We show that quantum error mitigation (QEM) techniques can be used to improve expectation values of observables on real quantum devices.
Optimal control of perfect plasticity part I: Stress tracking

The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is to optimize the stress field by controlling the displacement at prescribed parts of the boundary. The control thus enters the system in the Dirichlet boundary conditions. Therefore, the safe load condition is automatically fulfilled so that the system admits a solution, whose stress field is unique. This gives rise to a well defined control-to-state operator, which is continuous but not Gateaux-differentiable. The control-to-state map is therefore regularized, first by means of the Yosida regularization and then by a second smoothing in order to obtain a smooth problem. The approximation of global minimizers of the original non-smooth optimal control problem is shown and optimality conditions for the regularized problem are established. A numerical example illustrates the feasibility of the smoothing approach.
On basic operations related to network induction of discrete convex functions

Discrete convex functions are used in many areas, including operations research, discrete-event systems, game theory, and economics. The objective of this paper is to investigate basic operations such as direct sum, splitting, and aggregation that are related to network induction of discrete convex functions as well as discrete convex sets. Various kinds of discrete convex functions in discrete convex analysis are considered such as integrally convex functions, L-convex functions, M-convex functions, multimodular functions, and discrete midpoint convex functions.