Miracle-dz/UniFAR-FTUs huggingface dataset:
An SDP Relaxation for the Sparse Integer Least Square Problem

In this paper, we study the polynomial approximability or solvability of sparse integer least square problem (SILS), which is the NP-hard variant of the least square problem, where we only consider sparse {0, +1, -1}-vectors. We propose an l1-based SDP relaxation to SILS, and introduce a randomized algorithm for SILS based on the SDP relaxation. In fact, the proposed randomized algorithm works for a broader class of binary quadratic program with cardinality constraint, where the objective function can be possibly non-convex. Moreover, when the sparsity parameter is fixed, we provide sufficient conditions for our SDP relaxation to solve SILS. The class of data input which guarantee that SDP solves SILS is broad enough to cover many cases in real-world applications, such as privacy preserving identification, and multiuser detection. To show this, we specialize our sufficient conditions to two special cases of SILS with relevant applications: the feature extraction problem and the integer sparse recovery problem. We show that our SDP relaxation can solve the feature extraction problem with sub-Gaussian data, under some weak conditions on the second moment of the covariance matrix. We also show that our SDP relaxation can solve the integer sparse recovery problem under some conditions that can be satisfied both in high and low coherence settings.
IDmUNet: A new image decomposition induced network for sparse feature segmentation

UNet and its variants are among the most popular methods for medical image segmentation. Despite their successes in task generality, most of them consider little mathematical modeling behind specific applications. In this paper, we focus on the sparse feature segmentation task and make a task-oriented network design, in which the target objects are sparsely distributed and the background is hard to be mathematically modeled. We start from an image decomposition model with sparsity regularization, and propose a deep unfolding network, namely IDNet, based on an iterative solver, scaled alternating direction method of multipliers (scaled-ADMM). The IDNet splits raw inputs into double feature layers. Then a new task-oriented segmentation network is constructed, dubbed as IDmUNet, based on the proposed IDNets and a mini-UNet. Because of the sparsity prior and deep unfolding method in the structure design, this IDmUNet combines the advantages of mathematical modeling and data-driven approaches. Firstly, our approach has mathematical interpretability and can achieve favorable performance with far fewer learnable parameters. Secondly, our IDmUNet is robust in a simple end-to-end training with explainable behaviors. In the experiments of retinal vessel segmentation (RVS), IDmUNet produces the state-of-the-art results with only 0.07m parameters, whereas SA-UNet, one of the latest variants of UNet, contains 0.54m and the original UNet 31.04m. Moreover, the training procedure of our network converges faster without overfitting phenomenon. This decomposition-based network construction strategy can be generalized to other problems with mathematically clear targets and complicated unclear backgrounds.
Prior-informed Uncertainty Modelling with Bayesian Polynomial Approximations

Orthogonal polynomial approximations form the foundation to a set of well-established methods for uncertainty quantification known as polynomial chaos. These approximations deliver models for emulating physical systems in a variety of computational engineering applications. In this paper, we describe a Bayesian formulation of polynomial approximations capable of incorporating uncertainties in input data. Through different priors in a hierarchical structure, this permits us to incorporate expert knowledge on the inference task via different approaches. These include beliefs of sparsity in the model; approximate knowledge of the polynomial coefficients (e.g. through low-fidelity estimates) or output mean, and correlated models that share similar functional and/or physical behaviours. We show that through a Bayesian framework, such prior knowledge can be leveraged to produce orthogonal polynomial approximations with enhanced predictive accuracy.
Pulsating B stars in the Scorpius–Centaurus Association with TESS

We study 119 B stars located in the Scorpius–Centaurus Association using data from NASA’s TESS Mission. We see pulsations in 81 stars (68%) across the full range of effective temperatures. In particular, we confirm previous reports of low-frequency pulsations in stars whose temperatures fall between the instability strips of SPB stars (slowly pulsating B stars) and δ Scuti stars. By taking the stellar densities into account, we conclude that these cannot be p modes and confirm previous suggestions that these are probably rapidly-rotating SPB stars. We also confirm that they follow two period–luminosity relations that are consistent with prograde sectoral g modes that are dipole (l = m = 1) and quadrupole (l = m = 2), respectively. One of the stars (ξ2 Cen) is a hybrid pulsator that shows regular spacings in both g and p modes. We confirm that α Cru has low-amplitude p-mode pulsations, making it one of the brightest β Cephei stars in the sky. We also find several interesting binaries, including a very short-period heartbeat star (HD 132094), a previously unknown eclipsing binary (π Lup), and an eclipsing binary with high-amplitude tidally driven pulsations (HR 5846). The results clearly demonstrate the power of TESS for studying variability in stellar associations.
Strong Determinism

What I’m really interested in is whether God could have made the world in a di ﬀ erent way; that is, whether the necessity of logical simplicity leaves any freedom at all. Abstract A strongly deterministic theory of physics is one that permits with exactly one possible history of the universe. In the words of Penrose (1989), "it is not just a matter of the future being determined by the past; the entire history of the universe is ﬁxed , according to some precise mathematical scheme, for all time. ” Such an extraordinary feature may appear unattainable in any realistic and simple theory of physics. In this paper, I propose a deﬁnition of strong determinism and contrast it with those of standard determinism and super-determinism. Next, I discuss its consequences for explanation, causation, prediction, fundamental properties, free will, and modality. Finally, I present the ﬁrst example of a realistic, simple, and strongly deterministic physical theory—the Everettian Wentaculus. As a consequence of physical laws, the history of the Everettian multiverse could not have been di ﬀ erent. If the Everettian Wentaculus is empirically equivalent to other quantum theories, we can never empirically ﬁnd out whether or not our world is strongly deterministic. Even if strong determinism fails to be true, it is closer to the actual world than we have presumed, with implications for some of the central topics in philosophy and foundations of physics.
Quantum Deep Learning for Mutant COVID-19 Strain Prediction

New COVID-19 epidemic strains like Delta and Omicron with increased transmissibility and pathogenicity emerge and spread across the whole world rapidly while causing high mortality during the pandemic period. Early prediction of possible variants (especially spike protein) of COVID-19 epidemic strains based on available mutated SARS-CoV-2 RNA sequences may lead to early prevention and treatment. Here, combining the advantage of quantum and quantum-inspired algorithms with the wide application of deep learning, we propose a development tool named DeepQuantum, and use this software to realize the goal of predicting spike protein variation structure of COVID-19 epidemic strains. In addition, this hybrid quantum-classical model for the first time achieves quantum-inspired blur convolution similar to classical depthwise convolution and also successfully applies quantum progressive training with quantum circuits, both of which guarantee that our model is the quantum counterpart of the famous style-based GAN. The results state that the fidelities of random generating spike protein variation structure are always beyond 96% for Delta, 94% for Omicron. The training loss curve is more stable and converges better with multiple loss functions compared with the corresponding classical algorithm. At last, evidences that quantum-inspired algorithms promote the classical deep learning and hybrid models effectively predict the mutant strains are strong.
Automatic Calibration Framework of Agent-based Models for Dynamic and Heterogeneous Parameters

Agent-based models (ABMs) highlight the importance of simulation validation, such as qualitative face validation and quantitative empirical validation. In particular, we focused on quantitative validation by adjusting simulation input parameters of the ABM. This study introduces an automatic calibration framework that combines the suggested dynamic and heterogeneous calibration methods. Specifically, the dynamic calibration fits the simulation results to the real-world data by automatically capturing suitable simulation time to adjust the simulation parameters. Meanwhile, the heterogeneous calibration reduces the distributional discrepancy between individuals in the simulation and the real world by adjusting agent related parameters cluster-wisely.
The Renovated Thacher Observatory and First Science Results

Located on the campus of the Thacher School in Southern California, the Thacher Observatory has a legacy of astronomy research and education that dates back to the late 1950s. In 2016, the observatory was fully renovated with upgrades including a new 0.7 m telescope, a research grade camera, and a slit dome with full automation capabilities. The low-elevation site is bordered by the Los Padres National Forest and therefore affords dark to very dark skies allowing for accurate and precise photometric observations. We present a characterization of the site including sky brightness, weather, and seeing, and we demonstrate the on-sky performance of the facility. Our primary research programs are based around our multi-band photometric capabilities and include photometric monitoring of variable sources, a nearby supernova search and followup program, a quick response transient followup effort, and exoplanet and eclipsing binary light curves. Select results from these programs are included in this work which highlight the broad range of science available to an automated observatory with a moderately sized telescope.
Adiabatic accretion onto black holes in Einstein-Maxwell-scalar theory

We study the adiabatic accretion process of ordinary baryonic gas onto spherically symmetric black holes in Einstein-Maxwell-scalar theory, with two parameters α and β in the coupling term. Especially, we demonstrate the range of the transonic points in terms of the charge-to-mass ratio squared and the dimensionless coordinate radius, in two important classes of black holes as examples. Further, we find that the two coupling parameters give modifications to the mass accretion rate at different orders of the sound speed at infinity. We also present their different effects on the temperature ratios of the accreted gas.
Quantum algorithms for grid-based variational time evolution

The simulation of quantum dynamics calls for quantum algorithms working in first quantized grid encodings. Here, we propose a variational quantum algorithm for performing quantum dynamics in first quantization. In addition to the usual reduction in circuit depth conferred by variational approaches, this algorithm also enjoys several advantages compared to previously proposed ones. For instance, variational approaches suffer from the need for a large number of measurements. However, the grid encoding of first quantized Hamiltonians only requires measuring in position and momentum bases, irrespective of the system size. Their combination with variational approaches is therefore particularly attractive. Moreover, heuristic variational forms can be employed to overcome the limitation of the hard decomposition of Trotterized first quantized Hamiltonians into quantum gates. We apply this quantum algorithm to the dynamics of several systems in one and two dimensions. Our simulations exhibit the previously observed numerical instabilities of variational time propagation approaches. We show how they can be significantly attenuated through subspace diagonalization at a cost of an additional O(MN2) 2-qubit gates where M is the number of dimensions and NM is the total number of grid points.
Trajectory convergence from coordinate-wise decrease of general convex energy functions

We consider arbitrary trajectories subject to a coordinate-wise energy decrease: the sign of the derivative of each entry is never the same as that of the corresponding entry of the gradient of some convex energy function. We show that this simple condition guarantees convergence to a point, to the minimum of the energy functions, or to a set where its Hessian has very specific properties. This extends and strengthens recent results that were restricted to quadratic energy functions.
Improved Search of Relevant Points for Nearest-Neighbor Classification

Given a training set $P \subset \mathbb{R}^d$, the nearest-neighbor classifier assigns any query point $q \in \mathbb{R}^d$ to the class of its closest point in $P$. To answer these classification queries, some training points are more relevant than others. We say a training point is relevant if its omission from the training set could induce the misclassification of some query point in $\mathbb{R}^d$. These relevant points are commonly known as border points, as they define the boundaries of the Voronoi diagram of $P$ that separate points of different classes. Being able to compute this set of points efficiently is crucial to reduce the size of the training set without affecting the accuracy of the nearest-neighbor classifier. Improving over a decades-long result by Clarkson, in a recent paper by Eppstein an output-sensitive algorithm was proposed to find the set of border points of $P$ in $O( n^2 + nk^2 )$ time, where $k$ is the size of such set. In this paper, we improve this algorithm to have time complexity equal to $O( nk^2 )$ by proving that the first steps of their algorithm, which require $O( n^2 )$ time, are unnecessary.
OverlapTransformer: An Efficient and Rotation-Invariant Transformer Network for LiDAR-Based Place Recognition

—Place recognition is an important capability for autonomously navigating vehicles operating in complex environments and under changing conditions. It is a key component for tasks such as loop closing in SLAM or global localization. In this paper, we address the problem of place recognition based on 3D LiDAR scans recorded by an autonomous vehicle. We propose a novel lightweight neural network exploiting the range image representation of LiDAR sensors to achieve fast execution with less than 4ms per frame. Based on that, we design a yaw-rotation-invariant architecture exploiting a transformer network, which boosts the place recognition performance of our method. We evaluate our approach on the KITTI and Ford Campus datasets. The experimental results show that our method can effectively detect loop closures compared to the state-of-the-art methods and generalizes well across different environments. To further evaluate long-term place recognition performance, we provide a novel challenging Haomo dataset, which contains LiDAR sequences recorded by a mobile robot in repetitive places across seasons. Both the implementation of our method and our new Haomo dataset are released here: https://github.com/haomo-ai/OverlapTransformer
Free Fock parafermions in the tight-binding model with dissipation

Parafermions that generalize (Majorana or usual) fermions appear as interacting quasi-particles because of their nature. Although attempts to develop models with free (non-interacting) parafermions have been undertaken, existing proposals require unphysical conditions such as realizing purely non-Hermitian systems. Here we present a way for the realization of free Fock parafermions in the tight-binding model with controlled dissipation of a very simple form. Introducing dissipation transforms an originally non-integrable quantum model to an exactly solvable classical one.
Efficient Two-Dimensional Self-Stabilizing Byzantine Clock Synchronization in WALDEN

For tolerating Byzantine faults of both the terminal and communication components in self-stabilizing clock synchronization, the two-dimensional self-stabilizing Byzantine-fault-tolerant clock synchronization problem is investigated and solved. By utilizing the time-triggered (TT) stage provided in the underlying networks as TT communication windows, the approximate agreement, hopping procedure, and randomized grandmasters are integrated into the overall solution. It is shown that with partitioning the communication components into 3 arbitrarily connected subnetworks, efficient synchronization can be achieved with one such subnetwork and less than 1/3 terminal components being Byzantine. Meanwhile, the desired stabilization can be reached for the specific networks in one or several seconds with high probabilities. This helps in developing various distributed hard-real-time systems with stringent time, resources, and safety requirements.
Enabling Automated Machine Learning for Model-Driven AI Engineering

Developing smart software services requires both Software Engineering and Artificial Intelligence (AI) skills. AI practitioners, such as data scientists often focus on the AI side, for example, creating and training Machine Learning (ML) models given a specific use case and data. They are typically not concerned with the entire software development life-cycle, architectural decisions for the system and performance issues beyond the predictive ML models (e.g., regarding the security, privacy, throughput, scalability, availability, as well as ethical, legal and regulatory compliance). In this manuscript, we propose a novel approach to enable Model-Driven Software Engineering and Model-Driven AI Engineering. In particular, we support Automated ML, thus assisting software engineers without deep AI knowledge in developing AI-intensive systems by choosing the most appropriate ML model, algorithm and techniques with suitable hyper-parameters for the task at hand. To validate our work, we carry out a case study in the smart energy domain.
A Transferable Legged Mobile Manipulation Framework Based on Disturbance Predictive Control

Due to their ability to adapt to different terrains, quadruped robots have drawn much attention in the research field of robot learning. Legged mobile manipulation, where a quadruped robot is equipped with a robotic arm, can greatly enhance the performance of the robot in various manipulation tasks. Several prior works have investigated legged mobile manipulation from the viewpoint of control theory. However, modeling a unified structure for various robotic arms and quadruped robots is a challenging task. In this paper, we propose a unified framework disturbance predictive control where a reinforcement learning scheme with a latent dynamic adapter is embedded into our proposed low-level controller. Our method can be well adapted to various types of robotic arms with a few random motion samples, and the experimental results demonstrate the effectiveness of our method.
Pizzetti formulae and the Radon Transform on the Sphere

In this paper, we obtain Pizzetti-type formulae on regions of the the unit sphere S of R, and study their applications to the problem of inverting the spherical Radon transform. In particular, we approach integration over pm ́2q-dimensional sub-spheres of S, pm ́1qdimensional sub-balls, and over pm ́ 1q-dimensional spherical caps as the action of suitable concentrated delta distributions. In turn, this leads to Pizzetti formulae that express such integrals in terms of the action of SOpm ́ 1q-invariant differential operators. In the last section of the paper, we use some of these expressions to derive the inversion formulae for the Radon transform on S in a direct way.
Divide and Conquer: Text Semantic Matching with Disentangled Keywords and Intents

Text semantic matching is a fundamental task that has been widely used in various scenarios, such as community question answering, information retrieval, and recommendation. Most state-of-the-art matching models, e.g., BERT, directly perform text comparison by processing each word uniformly. However, a query sentence generally comprises content that calls for different levels of matching granularity. Specifically, keywords represent factual information such as action, entity, and event that should be strictly matched, while intents convey abstract concepts and ideas that can be paraphrased into various expressions. In this work, we propose a simple yet effective training strategy for text semantic matching in a divide-and-conquer manner by disentangling keywords from intents. Our approach can be easily combined with pre-trained language models (PLM) without influencing their inference efficiency, achieving stable performance improvements against a wide range of PLMs on three benchmarks.
Deep Q-Learning Based Resource Allocation in 6G Interference Systems With Outage Constraints

This paper considers the resource allocation problem in the sixth generation (6G) wireless interference channel (IC) under link outage constraints. Since the optimization problem is non-convex in nature, existing approaches to find the optimal power allocation are computationally intensive. When it comes to internet of things (IoT) and massive machine-type communications (mMTC) in the emerging 6G, the computational complexity becomes practically infeasible. Recently, deep reinforcement learning has shown promising outcome in solving non-convex optimization problems with reduced complexity. In this paper, we utilize a deep Q-learning (DQL) approach which interacts with the wireless environment and learns the optimal power allocation of a wireless IC while maximizing overall sum-rate of the system and maintaining reliability requirement of each link. We have used two separate deep Q-networks to remove the inherent instability in learning process. Simulation results demonstrate that the proposed DQL approach outperforms existing geometric programming based solutions.
Bayesian Bilinear Neural Network for Predicting the Mid‐price Dynamics in Limit‐Order Book Markets

The prediction of financial markets is a challenging yet important task. In modern electronically-driven markets, traditional time-series econometric methods often appear incapable of capturing the true complexity of the multi-level interactions driving the price dynamics. While recent research has established the effectiveness of traditional machine learning (ML) models in financial applications, their intrinsic inability to deal with uncertainties, which is a great concern in econometrics research and real business applications, constitutes a major drawback. Bayesian methods naturally appear as a suitable remedy conveying the predictive ability of ML methods with the probabilistically-oriented practice of econometric research. By adopting a state-of-the-art second-order optimization algorithm, we train a Bayesian bilinear neural network with temporal attention, suitable for the challenging time-series task of predicting mid-price movements in ultra-high-frequency limit-order book markets. We thoroughly compare our Bayesian model with traditional ML alternatives by addressing the use of predictive distributions to analyze errors and uncertainties associated with the estimated parameters and model forecasts. Our results underline the feasibility of the Bayesian deep-learning approach and its predictive and decisional advantages in complex econometric tasks, prompting future research in this direction.