Miracle-dz/UniFAR-FTUs huggingface dataset:
The Structure of the Density-Potential Mapping. Part II: Including Magnetic Fields

The Hohenberg–Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just one-body particle density. In this Part II of a series of two articles, we aim at clarifying the status of this theorem within different extensions of DFT including magnetic fields. We will in particular discuss current-density-functional theory (CDFT) and review the different formulations known in the literature, including the conventional paramagnetic CDFT and some nonstandard alternatives. For the former, it is known that the Hohenberg–Kohn theorem is no longer valid due to counterexamples. Nonetheless, paramagnetic CDFT has the mathematical framework closest to standard DFT and, just like in standard DFT, nondifferentiability of the density functional can be mitigated through Moreau–Yosida regularization. Interesting insights can be drawn from both Maxwell–Schrödinger DFT and quantum-electrodynamic DFT, which are also discussed here.
Gaussian Universality of Perceptrons with Random Labels

While classical in many theoretical settings - and in particular in statistical physics-inspired works - the assumption of Gaussian i.i. d. input data is often perceived as a strong limitation in the context of statistics and machine learning. In this study, we redeem this line of work in the case of generalized linear classification, a.k. a. the perceptron model, with random labels. We argue that there is a large universality class of high-dimensional input data for which we obtain the same minimum training loss as for Gaussian data with corresponding data covariance. In the limit of vanishing regularization, we further demonstrate that the training loss is independent of the data covariance. On the theoretical side, we prove this universality for an arbitrary mixture of homogeneous Gaussian clouds. Empirically, we show that the universality holds also for a broad range of real datasets.
DAVA: Disentangling Adversarial Variational Autoencoder

The use of well-disentangled representations offers many advantages for downstream tasks, e.g. an increased sample efficiency, or better interpretability. However, the quality of disentangled interpretations is often highly dependent on the choice of dataset-specific hyperparameters, in particular the regularization strength. To address this issue, we introduce DAVA, a novel training procedure for variational auto-encoders. DAVA completely alleviates the problem of hyperparameter selection. We compare DAVA to models with optimal hyperparameters. Without any hyperparameter tuning, DAVA is competitive on a diverse range of commonly used datasets. Underlying DAVA, we discover a necessary condition for unsupervised disentanglement, which we call PIPE. We demonstrate the ability of PIPE to positively predict the performance of downstream models in abstract reasoning. We also thoroughly investigate correlations with existing supervised and unsupervised metrics. The code is available at https://github.com/besterma/dava.
Cardinality Estimation over Knowledge Graphs with Embeddings and Graph Neural Networks

Cardinality Estimation over Knowledge Graphs (KG) is crucial for query optimization, yet remains a challenging task due to the semi-structured nature and complex correlations of data in typical KGs. In this work, we propose GNCE, a novel approach that leverages knowledge graph embeddings and Graph Neural Networks (GNN) to accurately predict the cardinality of conjunctive queries over KGs. GNCE first creates semantically meaningful embeddings for all entities in the KG, which are then used to learn a representation of a query using a GNN to estimate the cardinality of the query. We evaluate GNCE on several KGs in terms of q-Error and demonstrate that it outperforms state-of-the-art approaches based on sampling, summaries, and (machine) learning in terms of estimation accuracy while also having a low execution time and few parameters. Additionally, we show that GNCE performs similarly well on real-world queries and can inductively generalize to unseen entities, making it suitable for use in dynamic query processing scenarios. Our proposed approach has the potential to significantly improve query optimization and related applications that rely on accurate cardinality estimates of conjunctive queries.
Self-Improving Robots: End-to-End Autonomous Visuomotor Reinforcement Learning

In imitation and reinforcement learning, the cost of human supervision limits the amount of data that robots can be trained on. An aspirational goal is to construct self-improving robots: robots that can learn and improve on their own, from autonomous interaction with minimal human supervision or oversight. Such robots could collect and train on much larger datasets, and thus learn more robust and performant policies. While reinforcement learning offers a framework for such autonomous learning via trial-and-error, practical realizations end up requiring extensive human supervision for reward function design and repeated resetting of the environment between episodes of interactions. In this work, we propose MEDAL++, a novel design for self-improving robotic systems: given a small set of expert demonstrations at the start, the robot autonomously practices the task by learning to both do and undo the task, simultaneously inferring the reward function from the demonstrations. The policy and reward function are learned end-to-end from high-dimensional visual inputs, bypassing the need for explicit state estimation or task-specific pre-training for visual encoders used in prior work. We first evaluate our proposed algorithm on a simulated non-episodic benchmark EARL, finding that MEDAL++ is both more data efficient and gets up to 30% better final performance compared to state-of-the-art vision-based methods. Our real-robot experiments show that MEDAL++ can be applied to manipulation problems in larger environments than those considered in prior work, and autonomous self-improvement can improve the success rate by 30-70% over behavior cloning on just the expert data. Code, training and evaluation videos along with a brief overview is available at: https://architsharma97.github. io/self-improving-robots/
Ego-Noise Reduction of a Mobile Robot Using Noise Spatial Covariance Matrix Learning and Minimum Variance Distortionless Response

The performance of speech and events recognition systems significantly improved recently thanks to deep learning methods. However, some of these tasks remain challenging when algorithms are deployed on robots due to the unseen mechanical noise and electrical interference generated by their actuators while training the neural networks. Ego-noise reduction as a preprocessing step therefore can help solve this issue when using pre-trained speech and event recognition algorithms on robots. In this paper, we propose a new method to reduce ego-noise using only a microphone array and less than two minute of noise recordings. Using Principal Component Analysis (PCA), the best covariance matrix candidate is selected from a dictionary created online during calibration and used with the Minimum Variance Distortionless Response (MVDR) beamformer. Results show that the proposed method runs in real-time, improves the signal-to-distortion ratio (SDR) by up to 10 dB, decreases the word error rate (WER) by 55% in some cases and increases the Average Precision (AP) of event detection by up to 0.2.
The Impact of Data Persistence Bias on Social Media Studies

Social media studies often collect data retrospectively to analyze public opinion. Social media data may decay over time and such decay may prevent the collection of the complete dataset. As a result, the collected dataset may differ from the complete dataset and the study may suffer from data persistence bias. Past research suggests that the datasets collected retrospectively are largely representative of the original dataset in terms of textual content. However, no study analyzed the impact of data persistence bias on social media studies such as those focusing on controversial topics. In this study, we analyze the data persistence and the bias it introduces on the datasets of three types: controversial topics, trending topics, and framing of issues. We report which topics are more likely to suffer from data persistence among these datasets. We quantify the data persistence bias using the change in political orientation, the presence of potentially harmful content and topics as measures. We found that controversial datasets are more likely to suffer from data persistence and they lean towards the political left upon recollection. The turnout of the data that contain potentially harmful content is significantly lower on non-controversial datasets. Overall, we found that the topics promoted by right-aligned users are more likely to suffer from data persistence. Account suspensions are the primary factor contributing to data removals, if not the only one. Our results emphasize the importance of accounting for the data persistence bias by collecting the data in real time when the dataset employed is vulnerable to data persistence bias.
One-dimensional direct current resistivity due to strong turbulence

Strong Langmuir turbulence acts to generate localized spiky fields and ion cavities. It is shown that these cavities generate potential barriers that can trap a significant fraction of the electrons. For example, a 20% cavity traps 50% of the electrons. This can seriously change the direct current properties of a collisionless plasma and lead to the appearance of anomalous dc resistivity.
Small sample performance of robust estimators of tail parameters for pareto and exponential models

Robust estimation of tail index parameters is treated for (equivalent) two-parameter Pareto and exponential models. These distributions arise as parametric models in actuarial science, economics, telecommunications, and reliability, for example, as well as in semiparametric modeling of upper observations in samples from distributions which are regularly varying or in the domain of attraction of extreme value distributions. In a recent previous paper, new estimators of "generalized median" (GM) type were introduced and shown to provide more favorable trade-offs between efficiency and robustness than several well-established estimators, including those corresponding to methods of maximum likelihood, trimming, and quantiles. Here we establish-via simulation-that the superiority of the GM type estimators remains valid even for small sample sizes n=10 and 25. To bridge between "small" and "large" sample sizes, we also include the cases n=50 and 100. Further, we arrive at guidelines for selection of a particlar GM estimator in practice, depending upon the sample size, upon whether protection is desired against upper outliers onlu, or against both upper and lower outliers, and upon whether the level of possible contamination by outliers is high or low. Comparisons of estimators are made on the basis of relative efficiency with respect to the maximum likelihood estimator, breakdown points, and premium-protection plots.
Penalising the biases in norm regularisation enforces sparsity

Controlling the parameters' norm often yields good generalisation when training neural networks. Beyond simple intuitions, the relation between regularising parameters' norm and obtained estimators remains theoretically misunderstood. For one hidden ReLU layer networks with unidimensional data, this work shows the parameters' norm required to represent a function is given by the total variation of its second derivative, weighted by a $\sqrt{1+x^2}$ factor. Notably, this weighting factor disappears when the norm of bias terms is not regularised. The presence of this additional weighting factor is of utmost significance as it is shown to enforce the uniqueness and sparsity (in the number of kinks) of the minimal norm interpolator. Conversely, omitting the bias' norm allows for non-sparse solutions. Penalising the bias terms in the regularisation, either explicitly or implicitly, thus leads to sparse estimators.
Choosing Public Datasets for Private Machine Learning via Gradient Subspace Distance

Differentially private stochastic gradient descent privatizes model training by injecting noise into each iteration, where the noise magnitude increases with the number of model parameters. Recent works suggest that we can reduce the noise by leveraging public data for private machine learning, by projecting gradients onto a subspace prescribed by the public data. However, given a choice of public datasets, it is not a priori clear which one may be most appropriate for the private task. We give an algorithm for selecting a public dataset by measuring a low-dimensional subspace distance between gradients of the public and private examples. We provide theoretical analysis demonstrating that the excess risk scales with this subspace distance. This distance is easy to compute and robust to modifications in the setting. Empirical evaluation shows that trained model accuracy is monotone in this distance.
Lusternik-Schnirelmann category of spaces with free fundamental group

The Lusternik–Schnirelmann category cat.X / of a topological space X is the least integer n for which X has an open cover X DU0[U1[ [Un where each inclusion map Uk ,! X is nullhomotopic. Lusternik and Schnirelmann introduced this invariant in the 1930s for use in their study of critical points of smooth functions on manifolds. We refer to the book by Cornea, Lupton, Oprea and Tanre [1] for standard results on L–S category and to Whitehead [4] for background on homotopy theory.
An Improved Iem Model for Bistatic Scattering From Rough Surfaces

In the development of the IEM model for surface single scattering a simplifying assumption was applied to the phase of the Green's function in the average power calculation leading to a surface scattering model in algebraic form. In this paper we remove this simplifying assumption yielding a more complex model but still in algebraic form. We shall show that the assumption used in the past does not cause an appreciable difference when the incident and scattered angles are close to each other. However, for different incident and scatter angles there is a noticeable difference especially when the surface roughness is small and scattering is weak. For surfaces with large scale roughness the difference between the original IEM and the improved IEM is generally negligible. Bistatically, the improved IEM is in good agreement with the standard small perturbation model in the low frequency region and with the standard Kirchhoff model in the high frequency region. A recent publication extending the original IEM model along a different direction is shown to be a more restrictive surface scattering model in terms of applicability to moist rough surfaces.
Flow and heat transfer in rectangular enclosures using a new block-implicit numerical method

This work reports a numerical investigation on buoyancy-induced flows occurring in enclosures of small aspect ratio and inclined with respect to the horizontal direction. The numerical method used consists of the control-volume approach and a new block-implicit error-smoothing operator. Governing equations are written in terms of primitive variables and are recast into a general form. In the proposed method, all governing equation are relaxed locally, in contrast with commonly used segregated schemes. The effects of Rayleigh number, aspect ratio, and cavity inclination on temperature and velocity patterns are discussed. It is expected that more advanced parallel computer architectures can benefit from the error-smoothing operator described here.
Modified dynamics (MOND) as a dark halo

We propose a form for dark haloes that embodies the fundamental aspect of Milgrom's modified dynamics (MOND): the discrepancy between the visible mass and the Newtonian dynamical mass appears below a critical acceleration. This is a halo having a density distribution, at least to several tens of kpc, of the form Sigma(0)/r, where Sigma(0), is a constant of surface density which does not vary from galaxy to galaxy. To avoid rising rotation curves, such a density distribution must obviously steepen beyond some radius, and we have chosen the Hernquist model in which the density falls as 1/r(4) beyond a characteristic scale. We show that, assuming that the visible (baryonic) matter is some constant fraction of the dark matter, spiral galaxies with such haloes exhibit a Tully-Fisher law of the observed form. In a sample of 10 spiral galaxies with well-determined extended rotation curves this halo, combined with the observable matter, can successfully model the observed curves. Moreover, in the seven most luminous galaxies, the best-fitting models have about the same value of Sigma(0) and are effectively one-parameter fits as in MOND (mass-to-light of the visible disc). The one-parameter description, however, does break down for the three dwarf galaxies in the sample with the lowest internal accelerations.
Inference and diagnostics in skew scale mixtures of normal regression models

Skew scale mixtures of normal distributions are often used for statistical procedures involving asymmetric data and heavy-tailed. The main virtue of the members of this family of distributions is that they are easy to simulate from and they also supply genuine expectation-maximization (EM) algorithms for maximum likelihood estimation. In this paper, we extend the EM algorithm for linear regression models and we develop diagnostics analyses via local influence and generalized leverage, following Zhu and Lee's approach. This is because Cook's well-known approach cannot be used to obtain measures of local influence. The EM-type algorithm has been discussed with an emphasis on the skew Student-t-normal, skew slash, skew-contaminated normal and skew power-exponential distributions. Finally, results obtained for a real data set are reported, illustrating the usefulness of the proposed method.
Estimation for Location-Scale Models with Censored Data

This article considers a class of estimators for the location and scale parameters in the location-scale model based on ‘synthetic data’ when the observations are randomly censored on the right. The asymptotic normality of the estimators is established using counting process and martingale techniques when the censoring distribution is known and unknown, respectively. In the case when the censoring distribution is known, we show that the asymptotic variances of this class of estimators depend on the data transformation and have a lower bound which is not achievable by this class of estimators. However, in the case that the censoring distribution is unknown and estimated by the Kaplan–Meier estimator, this class of estimators has the same asymptotic variance and attains the lower bound for variance for the case of known censoring distribution. This is different from censored regression analysis, where asymptotic variances depend on the data transformation. Our method has three valuable advantages over the method of maximum likelihood estimation. First, our estimators are available in a closed form and do not require an iterative algorithm. Second, simulation studies show that our estimators being moment-based are comparable to maximum likelihood estimators and outperform them when sample size is small and censoring rate is high. Third, our estimators are more robust to model misspecification than maximum likelihood estimators. Therefore, our method can serve as a competitive alternative to the method of maximum likelihood in estimation for location-scale models with censored data. A numerical example is presented to illustrate the proposed method.
Solid/liquid phase change heat transfer in porous media (Effects of fins on the solidification process)

Numerical calculations on the solidification process in a porous medium surrounded by a finned surface were performed using a simple quasi-steady model as well as an accurate finite-difference method, and their results were compared with experimental data. Calculations for the case without fins were also performed for comparison. In addition, the effects of important parameters appearing the governing equations on the solidification process were systematically examined using the finite-difference method. As a result, the finite-difference solutions were in excellent agreement with the experimental ones over a wide range of conditions. The quasi-steady model gives fairly accurate solutions for the case without fins, but the solutions were not sufficiently accurate for the case with fins, especially under conditions for which the solidification rate was large. Among parameters appearing in the governing equations, both the porosity of the porous medium and the ratio of the thermal conductivity of the porous particles to that of ice did not largely affect the solidification process and the fin effectiveness. They were largely affected by changes in the Stefan number and the aspect ratio of the considered region.
Natural convection in an inclined enclosure

The effect of inclination on laminar natural convection in a square cavity is studied numerically for inclination angles ranging from 40° to 160°, Rayleigh numbers between 103 and 106 and Prandtl numbers from 0.02 to 4,000. Contours of stream functions and temperature are presented in order to provide a new insight and a better understanding of the flow and heat transfer characteristics in a square cavity. Finds computed local and mean Nusselt numbers at the hot wall in satisfactory agreement with experimental and other numerical results. Finds the mean heat flux at the hot wall as well as the distribution of the local heat flux along the heated wall are found to depend on the inclination angle, the Rayleigh number and the Prandtl number. Such a dependence is significant for angles greater than 90°, while for smaller angles the effect of the inclination angle on the Nusselt‐Rayleigh correlation is weaker.
Experimental results of GaInP/sub 2//GaAs/Ge triple junction cell development for space power systems

This paper describes the successful demonstration of high efficiency, large area monolithic triple-junction, n-on-p, GaInP/sub 2//GaAs/Ge cells. The highest cell efficiency (cell size: 2 cm/spl times/2 cm) measured to date is 25.7%, under 1 sun, AM0 illumination. A very uniform distribution of cell efficiency across a 3" diameter wafer is also achieved. The average efficiency of 164, 2 cm/spl times/2 cm triple junction cells and 52 cell-interconnect-cover (CIC) assemblies are 22.6% and 21.9%, respectively. The results of temperature coefficient, 1 MeV electron irradiation and thermal cycle measurements (for CICs) are also reported.