Miracle-dz/UniFAR-FTUs huggingface dataset:
On Manifold Hypothesis: Hypersurface Submanifold Embedding Using Osculating Hyperspheres

Consider a set of n data points in the Euclidean space R. This set is called dataset in machine learning and data science. Manifold hypothesis states that the dataset lies on a low-dimensional submanifold with high probability. All dimensionality reduction and manifold learning methods have the assumption of manifold hypothesis. In this paper, we show that the dataset lies on an embedded hypersurface submanifold which is locally (d− 1)-dimensional. Hence, we show that the manifold hypothesis holds at least for the embedding dimensionality d− 1. Using an induction in a pyramid structure, we also extend the embedding dimensionality to lower embedding dimensionalities to show the validity of manifold hypothesis for embedding dimensionalities {1, 2, . , d− 1}. For embedding the hypersurface, we first construct the d nearest neighbors graph for data. For every point, we fit an osculating hypersphere Sd−1 using its neighbors where this hypersphere is osculating to a hypothetical hypersurface. Then, using surgery theory, we apply surgery on the osculating hyperspheres to obtain n hyper-caps. We connect the hyper-caps to one another using partial hyper-cylinders. By connecting all parts, the embedded hypersurface is obtained as the disjoint union of these elements. We discuss the geometrical characteristics of the embedded hypersurface, such as having boundary, its topology, smoothness, boundedness, orientability, compactness, and injectivity. Some discussion are also provided for the linearity and structure of data. This paper is the intersection of several fields of science including machine learning, differential geometry, and algebraic topology.
Causal Inference Through the Structural Causal Marginal Problem

We introduce an approach to counterfactual inference based on merging information from multiple datasets. We consider a causal reformulation of the statistical marginal problem: given a collection of marginal structural causal models (SCMs) over distinct but overlapping sets of variables, determine the set of joint SCMs that are counterfactually consistent with the marginal ones. We formalise this approach for categorical SCMs using the response function formulation and show that it reduces the space of allowed marginal and joint SCMs. Our work thus highlights a new mode of falsifiability through additional variables, in contrast to the statistical one via additional data.
Generalizability of Machine Learning Models: Quantitative Evaluation of Three Methodological Pitfalls

Purpose To investigate the impact of the following three methodological pitfalls on model generalizability: (a) violation of the independence assumption, (b) model evaluation with an inappropriate performance indicator or baseline for comparison, and (c) batch effect. Materials and Methods The authors used retrospective CT, histopathologic analysis, and radiography datasets to develop machine learning models with and without the three methodological pitfalls to quantitatively illustrate their effect on model performance and generalizability. F1 score was used to measure performance, and differences in performance between models developed with and without errors were assessed using the Wilcoxon rank sum test when applicable. Results Violation of the independence assumption by applying oversampling, feature selection, and data augmentation before splitting data into training, validation, and test sets seemingly improved model F1 scores by 71.2% for predicting local recurrence and 5.0% for predicting 3-year overall survival in head and neck cancer and by 46.0% for distinguishing histopathologic patterns in lung cancer. Randomly distributing data points for a patient across datasets superficially improved the F1 score by 21.8%. High model performance metrics did not indicate high-quality lung segmentation. In the presence of a batch effect, a model built for pneumonia detection had an F1 score of 98.7% but correctly classified only 3.86% of samples from a new dataset of healthy patients. Conclusion Machine learning models developed with these methodological pitfalls, which are undetectable during internal evaluation, produce inaccurate predictions; thus, understanding and avoiding these pitfalls is necessary for developing generalizable models. Keywords: Random Forest, Diagnosis, Prognosis, Convolutional Neural Network (CNN), Medical Image Analysis, Generalizability, Machine Learning, Deep Learning, Model Evaluation Supplemental material is available for this article. Published under a CC BY 4.0 license.
The High Fraction of Thin Disk Galaxies Continues to Challenge ΛCDM Cosmology

Any viable cosmological framework has to match the observed proportion of early- and late-type galaxies. In this contribution, we focus on the distribution of galaxy morphological types in the standard model of cosmology (Lambda cold dark matter, ΛCDM). Using the latest state-of-the-art cosmological ΛCDM simulations known as Illustris, IllustrisTNG, and EAGLE, we calculate the intrinsic and sky-projected aspect ratio distribution of the stars in subhalos with stellar mass M * > 1010 M ⊙ at redshift z = 0. There is a significant deficit of intrinsically thin disk galaxies, which however comprise most of the locally observed galaxy population. Consequently, the sky-projected aspect ratio distribution produced by these ΛCDM simulations disagrees with the Galaxy And Mass Assembly (GAMA) survey and Sloan Digital Sky Survey at ≥12. 52σ (TNG50-1) and ≥14. 82σ (EAGLE50) confidence. The deficit of intrinsically thin galaxies could be due to a much less hierarchical merger-driven build-up of observed galaxies than is given by the ΛCDM framework. It might also arise from the implemented sub-grid models, or from the limited resolution of the above-mentioned hydrodynamical simulations. We estimate that an 85 times better mass resolution realization than TNG50-1 would reduce the tension with GAMA to the 5. 58σ level. Finally, we show that galaxies with fewer major mergers have a somewhat thinner aspect ratio distribution. Given also the high expected frequency of minor mergers in ΛCDM, the problem may be due to minor mergers. In this case, the angular momentum problem could be alleviated in Milgromian dynamics because of a reduced merger frequency arising from the absence of dynamical friction between extended dark matter halos.
HECO: Automatic Code Optimizations for Efficient Fully Homomorphic Encryption

In recent years, Fully Homomorphic Encryption (FHE) has undergone several breakthroughs and advancements leading to a leap in performance. Today, performance is no longer a major barrier to adoption. Instead, it is the complexity of developing an efﬁcient FHE application that currently limits deploying FHE in practice and at scale. Several FHE compilers have emerged recently to ease FHE development. However, none of these answer how to automatically transform imperative programs to secure and efﬁcient FHE implementations. This is a fundamental issue that needs to be addressed before we can realistically expect broader use of FHE. Au-tomating these transformations is challenging because the restrictive set of operations in FHE and their non-intuitive performance characteristics require programs to be drastically transformed to achieve efﬁciency. In addition, existing tools are monolithic and focus on individual optimizations. Therefore, they fail to fully address the needs of end-to-end FHE development. In this paper, we present HECO, a new end-to-end design for FHE compilers that takes high-level imperative programs and emits efﬁcient and secure FHE implementations. In our design, we take a broader view of FHE development, extending the scope of optimizations beyond the cryptographic challenges existing tools focus on.
Around Smale's 14th problem

We consider the Lorenz equations, a system of three dimensional ordinary differential equations modeling atmospheric convection. As the equations are chaotic and hard to study, a simpler “geometric model” has been introduced in the seventies. One of the classical problems in dynamical systems is to relate the original equations to the simplified geometric model. This has been achieved numerically by Tucker [24]. Here we show that for a different parameter we can prove the relation to the geometric model analytically, by elementary geometric
Investigation of Torque Ripple in Voltage Source Inverter driven Induction Motor Drive operated with Space Vector based Harmonic Elimination Pulse Width Modulation Scheme

The lower order harmonic elimination using the space vector pulse width modulation (SVPWM) technique is possible by introducing the dwell time-division coefficient ’k’ in the space vector. In this paper, torque ripple analysis is carried out for the space vector-based harmonic elimination (SVHE) scheme. The obtained results are compared with the existing schemes, such as conventional and advanced bus clamping SVPWM schemes. Further, the obtained results are validated through simulation results. The SVHE scheme gives a lower torque ripple than the conventional and advance bus clamping schemes at higher modulation indices.
Minimal Length of Nontrivial Solutions of the Isometry Equation and MacWilliams Extension Property with Respect to Weighted Poset Metric

For $R \triangleq Ma{t_m}({\mathbb{F}})$, the ring of all m × m matrices over the finite field ${\mathbb{F}}$ with $|{\mathbb{F}}| = q$, and the left R-module $A \triangleq Ma{t_{m,k}}({\mathbb{F}})$ with m + 1 ⩽ k, by deriving the minimal length of solutions of the related isometry equation, Dyshko has proved in [3], [4] that the minimal code length n for An not satisfying the MacWilliams extension property (MEP) with respect to Hamming weight is equal to $\prod\nolimits_{i = 1}^m {\left( {{q^i} + 1} \right)}$. In this paper, using the Möbius functions, we derive the minimal length of nontrivial solutions of the isometry equation for a finite lattice. For the finite vector space ${\mathbf{H}} \triangleq \prod\nolimits_{i \in \Omega } {{{\mathbb{F}}^{{k_i}}}}$, a poset P = (Ω, ≼P) and a map ω: Ω → ℝ+ give rise to the (P, ω)-weight on H, which has been proposed by Hyun, Kim and Park in [18]. For such a weight, we study the relations between the MEP and other properties including admitting MacWilliams identity, Fourier-reflexivity of involved partitions and the Unique Decomposition Property (UDP) defined for (P, ω). We give necessary and sufficient conditions for H to satisfy the MEP with the additional assumption that either P is hierarchical or ω is identically 1, i.e., (P, ω)-weight coincides with P-weight, which further allow us to partly answer a conjecture proposed by Machado and Firer in [22].
The Madelung constant in N dimensions

We introduce two convergent series expansions (direct and recursive) in terms of Bessel functions and the number of representations of an integer as a sum of squares for N-dimensional Madelung constants, MN(s), where s is the exponent of the Madelung series (usually chosen as s=1/2). The convergence of the Bessel function expansion is discussed in detail. Values for MN(s) for s=12,32,3 and 6 for dimension up to N=20 are presented. This work extends Zucker’s original analysis on N-dimensional Madelung constants for even dimensions up to N=8.
Constructing knots with specified geometric limits

It is known that any tame hyperbolic 3-manifold with infinite volume and a single end is the geometric limit of a sequence of finite volume hyperbolic knot complements. Purcell and Souto showed that if the original manifold embeds in the 3-sphere, then such knots can be taken to lie in the 3-sphere. However, their proof was nonconstructive; no examples were produced. In this paper, we give a constructive proof in the geometrically finite case. That is, given a geometrically finite, tame hyperbolic 3-manifold with one end, we build an explicit family of knots whose complements converge to it geometrically. Our knots lie in the (topological) double of the original manifold. The construction generalises the class of fully augmented links to a Kleinian groups setting.
For the splitting method of the nonlinear heat equation with initial datum in W^1, q

In this paper, we analyze an operator splitting scheme of the nonlinear heat equation in Ω ⊂ R (d ≥ 1): { ∂tu = ∆u+ λ|u| u in Ω× (0,∞), u = 0 in ∂Ω× (0,∞), u(x, 0) = φ(x) in Ω, where λ ∈ {−1, 1} and φ ∈ W (Ω) ∩ L∞(Ω) with 2 ≤ p < ∞ and d(p − 1)/2 < q < ∞. We establish the well-posedness of the approximation of u in L-space (r ≥ q), and furthermore, we derive its convergence rate of order O(τ) for a time step τ > 0. Finally, we give some numerical examples to confirm the reliability of the analyzed result.
Feasibility of Interactive 3D Map for Remote Sighted Assistance

Remote sighted assistance (RSA) has emerged as a conversational assistive technology, where remote sighted workers, i.e., agents, provide real-time assistance to users with vision impairments via video-chat-like communication. Researchers found that agents' lack of environmental knowledge, the difficulty of orienting users in their surroundings, and the inability to estimate distances from users' camera feeds are key challenges to sighted agents. To address these challenges, researchers have suggested assisting agents with computer vision technologies, especially 3D reconstruction. This paper presents a high-fidelity prototype of such an RSA, where agents use interactive 3D maps with localization capability. We conducted a walkthrough study with thirteen agents and one user with simulated vision impairment using this prototype. The study revealed that, compared to baseline RSA, the agents were significantly faster in providing navigational assistance to users, and their mental workload was significantly reduced -- all indicate the feasibility and prospect of 3D maps in RSA.
ASR-Aware End-to-End Neural Diarization

We present a Conformer-based end-to-end neural diarization (EEND) model that uses both acoustic input and features derived from an automatic speech recognition (ASR) model. Two categories of features are explored: features derived directly from ASR output (phones, position-in-word and word boundaries) and features derived from a lexical speaker change detection model, trained by finetuning a pretrained BERT model on the ASR output. Three modifications to the Conformer-based EEND architecture are proposed to incorporate the features. First, ASR features are concatenated with acoustic features. Second, we propose a new attention mechanism called contextualized self-attention that utilizes ASR features to build robust speaker representations. Finally, multi-task learning is used to train the model to minimize classification loss for the ASR features along with diarization loss. Experiments on the two-speaker English conversations of Switchboard+SRE data sets show that multi-task learning with position-in-word information is the most effective way of utilizing ASR features, reducing the diarization error rate (DER) by 20% relative to the baseline.
Skeleton-Based Action Segmentation With Multi-Stage Spatial-Temporal Graph Convolutional Neural Networks

The ability to identify and temporally segment fine-grained actions in motion capture sequences is crucial for applications in human movement analysis. Motion capture is typically performed with optical or inertial measurement systems, which encode human movement as a time series of human joint locations and orientations or their higher-order representations. State-of-the-art action segmentation approaches use multiple stages of temporal convolutions. The main idea is to generate an initial prediction with several layers of temporal convolutions and refine these predictions over multiple stages, also with temporal convolutions. Although these approaches capture long-term temporal patterns, the initial predictions do not adequately consider the spatial hierarchy among the human joints. To address this limitation, we recently introduced multi-stage spatial-temporal graph convolutional neural networks (MS-GCN). Our framework replaces the initial stage of temporal convolutions with spatial graph convolutions and dilated temporal convolutions, which better exploit the spatial configuration of the joints and their long-term temporal dynamics. Our framework was compared to four strong baselines on five tasks. Experimental results demonstrate that our framework is a strong baseline for skeleton-based action segmentation.
Optimized Potential Initialization for Low-latency Spiking Neural Networks

Spiking Neural Networks (SNNs) have been attached great importance due to the distinctive properties of low power consumption, biological plausibility, and adversarial robustness. The most effective way to train deep SNNs is through ANN-to-SNN conversion, which have yielded the best performance in deep network structure and large-scale datasets. However, there is a trade-off between accuracy and latency. In order to achieve high precision as original ANNs, a long simulation time is needed to match the firing rate of a spiking neuron with the activation value of an analog neuron, which impedes the practical application of SNN. In this paper, we aim to achieve high-performance converted SNNs with extremely low latency (fewer than 32 time-steps). We start by theoretically analyzing ANN-to-SNN conversion and show that scaling the thresholds does play a similar role as weight normalization. Instead of introducing constraints that facilitate ANN-to-SNN conversion at the cost of model capacity, we applied a more direct way by optimizing the initial membrane potential to reduce the conversion loss in each layer. Besides, we demonstrate that optimal initialization of membrane potentials can implement expected error-free ANN-to-SNN conversion. We evaluate our algorithm on the CIFAR-10 dataset and CIFAR-100 dataset and achieve state-of-the-art accuracy, using fewer time-steps. For example, we reach top-1 accuracy of 93.38% on CIFAR-10 with 16 time-steps. Moreover, our method can be applied to other ANN-SNN conversion methodologies and remarkably promote performance when the time-steps is small.
Harmony: Overcoming the hurdles of GPU memory capacity to train massive DNN models on commodity servers

Deep neural networks (DNNs) have grown exponentially in size over the past decade, leaving only those who have massive datacenter-based resources with the ability to develop and train such models. One of the main challenges for the long tail of researchers who might have only limited resources (e.g., a single multi-GPU server) is limited GPU memory capacity compared to model size. The problem is so acute that the memory requirement of training massive DNN models can often exceed the aggregate capacity of all available GPUs on a single server; this problem only gets worse with the trend of ever-growing model sizes. Current solutions that rely on virtualizing GPU memory (by swapping to/from CPU memory) incur excessive swapping overhead. In this paper, we present a new training framework, Harmony, and advocate rethinking how DNN frameworks schedule computation and move data to push the boundaries of training massive models efficiently on a single commodity server. Across various massive DNN models, Harmony is able to reduce swap load by up to two orders of magnitude and obtain a training throughput speedup of up to 7.6x over highly optimized baselines with virtualized memory.
Formulating bulk viscosity for neutron star simulations

In order to extract the precise physical information encoded in the gravitational and electromagnetic signals from powerful neutron-star merger events, we need to include as much of the relevant physics as possible in our numerical simulations. This presents a severe challenge, given that many of the involved parameters are poorly constrained. In this paper we focus on the role of nuclear reactions. Combining a theoretical discussion with an analysis connecting to state-of-the-art simulations, we outline multiple arguments that lead to a reactive system being described in terms of a bulk viscosity. The results demonstrate that in order to properly account for nuclear reactions, future simulations must be able to handle different regimes where rather different assumptions/approximations are appropriate. We also touch upon the link to models based on the large-eddy-strategy required to capture turbulence.
The REBELS ALMA Survey: cosmic dust temperature evolution out to z $\sim$ 7

ALMA observations have revealed the presence of dust in the first generations of galaxies in the Universe. However, the dust temperature $T_d$ remains mostly unconstrained due to the few available FIR continuum data at redshift $z>5$. This introduces large uncertainties in several properties of high-$z$ galaxies, namely their dust masses, infrared luminosities, and obscured fraction of star formation. Using a new method based on simultaneous [CII] 158$\mu$m line and underlying dust continuum measurements, we derive $T_ d$ in the continuum and [CII] detected $z\approx 7$ galaxies in the ALMA Large Project REBELS sample. We find $39\ \mathrm{K}<T_d<58\ \mathrm{K}$, and dust masses in the narrow range $M_d = (0.9-3.6)\times 10^7 M_{\odot}$. These results allow us to extend for the first time the reported $T_d(z)$ relation into the Epoch of Reionization. We produce a new physical model that explains the increasing $T_ d(z)$ trend with the decrease of gas depletion time, $t_{dep}=M_g/\mathrm{SFR}$, induced by the higher cosmological accretion rate at early times; this hypothesis yields $T_d \propto (1+z)^{0.4}$. The model also explains the observed $T_d$ scatter at a fixed redshift. We find that dust is warmer in obscured sources, as a larger obscuration results in more efficient dust heating. For UV-transparent (obscured) galaxies, $T_d$ only depends on the gas column density (metallicity), $T_d \propto N_H^{1/6}$ ($T_d \propto Z^{-1/6}$). REBELS galaxies are on average relatively transparent, with effective gas column densities around $N_H \simeq (0.03-1)\times 10^{21} \mathrm{cm}^{-2}$. We predict that other high-$z$ galaxies (e.g. MACS0416-Y1, A2744-YD4), with estimated $T_d \gg 60$ K, are significantly obscured, low-metallicity systems. In fact $T_d$ is higher in metal-poor systems due to their smaller dust content, which for fixed $L_{ IR}$ results in warmer temperatures.
SDEX: Monte Carlo Simulation of Stochastic Differential Equations on Memristor Crossbars

Here we present stochastic differential equations (SDEs) on a memristor crossbar, where the source of gaussian noise is derived from the random conductance due to ion drift in the devices during programming. We examine the effects of line resistance on the generation of normal random vectors, showing the skew and kurtosis are within acceptable bounds. We then show the implementation of a stochastic differential equation solver for the Black-Scholes SDE, and compare the distribution with the analytic solution. We determine that the random number generation works as intended, and calculate the energy cost of the simulation.
A Method for Electric Power Equipment Remote Control Based on IEC 61850

The remote control of electric power equipment is an important approach to solving the problem of safety and steady operation of the power grid.IEC 61850 makes a new requirement on remote control for electric power equipment.Based on an analysis of the finite state machine of select before operate(SBO) with enhanced security,a new remote control model for power telecontrol system is proposed on the basis of IEC 61850.Moreover,considering the actual needs of the power telecontrol system,a telecontrol interface based on IEC 61850 is designed to control the intelligent electronic device and to open or close the circuit breakers.A prototype system based on the above-mentioned methods has been developed and gone through field-testing and trial operation in a subtransmission network,which proves that the models and methods proposed are satisfactory and feasible.