Miracle-dz/UniFAR-FTUs huggingface dataset:
Pseudo Numerical Methods for Diffusion Models on Manifolds

Denoising Diffusion Probabilistic Models (DDPMs) can generate high-quality samples such as image and audio samples. However, DDPMs require hundreds to thousands of iterations to produce final samples. Several prior works have successfully accelerated DDPMs through adjusting the variance schedule (e.g., Improved Denoising Diffusion Probabilistic Models) or the denoising equation (e.g., Denoising Diffusion Implicit Models (DDIMs)). However, these acceleration methods cannot maintain the quality of samples and even introduce new noise at a high speedup rate, which limit their practicability. To accelerate the inference process while keeping the sample quality, we provide a fresh perspective that DDPMs should be treated as solving differential equations on manifolds. Under such a perspective, we propose pseudo numerical methods for diffusion models (PNDMs). Specifically, we figure out how to solve differential equations on manifolds and show that DDIMs are simple cases of pseudo numerical methods. We change several classical numerical methods to corresponding pseudo numerical methods and find that the pseudo linear multi-step method is the best in most situations. According to our experiments, by directly using pre-trained models on Cifar10, CelebA and LSUN, PNDMs can generate higher quality synthetic images with only 50 steps compared with 1000-step DDIMs (20x speedup), significantly outperform DDIMs with 250 steps (by around 0.4 in FID) and have good generalization on different variance schedules. Our implementation is available at https://github.com/luping-liu/PNDM.
Characterizing the aerosol atmosphere above the Observatorio del Roque de los Muchachos by analyzing seven years of data taken with an GaAsP HPD-readout, absolutely calibrated elastic LIDAR

We present a new elastic LIDAR concept, based on a bi-axially mounted Nd:YAG laser and a telescope with HPD readout, combined with fast FADC signal digitization and offline pulse analysis. The LIDAR return signals have been extensively quality checked and absolutely calibrated. We analyse seven years of quasi-continuous LIDAR data taken during those nights when the MAGIC telescopes were operating. Characterization of the nocturnal ground layer yields zenith and azimuth angle dependent aerosol extinction scale heights for clear nights. We derive aerosol transmission statistics for light emitted from various altitudes throughout the year and separated by seasons. We find further seasonal dependencies of cloud base and top altitudes, but none for the LIDAR ratios of clouds. Finally, the night sky background light is characterized using the LIDAR photon backgrounds.
LIDAR data based Segmentation and Localization using Open Street Maps for Rural Roads

Accurate pose estimation is a fundamental ability that all mobile robots must posses in order to traverse robustly in a given environment. Much like a human, this ability is dependent on the robot's understanding of a given scene. For Autonomous Vehicles (AV's), detailed 3D maps created beforehand are widely used to augment the perceptive abilities and estimate pose based on current sensor measurements. This approach however is less suited for rural communities that are sparsely connected and cover large areas. To deal with the challenge of localizing a vehicle in a rural setting, this paper presents a data-set of rural road scenes, along with an approach for fast segmentation of roads using LIDAR point clouds. The segmented point cloud in concert with road network information from Open Street Maps (OSM) is used for pose estimation. We propose two measurement models which are compared with state of the art methods for localization on OSM for tracking as well as global localization. The results show that the proposed algorithm is able to estimate pose within a 2 sq. km area with mean accuracy of 6.5 meters.
Amplification of gravitationally induced entanglement

Observation of gravitationally induced entanglement between two massive particles can be viewed as imply-ing the existence of the nonclassical nature of gravity. However, weak interaction in the gravitational ﬁeld is extremely small so that gravitationally induced entanglement is exceptionally challenging to test in practice. For addressing this key challenge, here we propose a criterion based on the logical contradictions of weak entanglement, which may boost the sensitivity of the signal due to the gravitationally induced entanglement. Speciﬁcally, we make use of the weak-value scenario and Einstein-Podolsky-Rosen (EPR) steering. We prove that it is impossible for a classical mediator to act on two local quantum objects to simulate ampliﬁed-weak-value phenomenon in two-setting EPR steering. Our approach can amplify the signal of gravitationally induced entanglement that were previously impossible to observe, by any desired factor that depends on the magnitude of the weak value. Our results not only open up the possibility of exploring nonclassical nature of gravity in the near future, but also pave the way for weak entanglement criterion of a more general nature.
Tight Wavelet Filter Banks with Prescribed Directions

Constructing tight wavelet filter banks with prescribed directions is challenging. This paper presents a systematic method for designing a tight wavelet filter bank, given any prescribed directions. There are two types of wavelet filters in our tight wavelet filter bank. One type is entirely determined by the prescribed information about the directionality and makes the wavelet filter bank directional. The other type helps the wavelet filter bank to be tight. In addition to the flexibility in choosing the directions, our construction method has other useful properties. It works for any multidimension, and it allows the user to have any prescribed number of vanishing moments along the chosen directions. Furthermore, our tight wavelet filter banks have fast algorithms for analysis and synthesis. Concrete examples are given to illustrate our construction method and properties of resulting tight wavelet filter banks.
SRL-SOA: Self-Representation Learning with Sparse 1D-Operational Autoencoder for Hyperspectral Image Band Selection

The band selection in the hyperspectral image (HSI) data processing is an important task considering its effect on the computational complexity and accuracy. In this work, we propose a novel framework for the band selection problem: Self-Representation Learning (SRL) with Sparse 1D-Operational Autoencoder (SOA). The proposed SLR-SOA approach introduces a novel autoencoder model, SOA, that is designed to learn a representation domain where the data are sparsely represented. Moreover, the network composes of 1D-operational layers with the non-linear neuron model. Hence, the learning capability of neurons (filters) is greatly improved with shallow architectures. Using compact architectures is especially crucial in autoencoders as they tend to overfit easily because of their identity mapping objective. Overall, we show that the proposed SRL-SOA band selection approach outperforms the competing methods over two HSI data including Indian Pines and Salinas-A considering the achieved land cover classification accuracies. The software implementation of the SRL-SOA approach is shared publicly1.
Effect of Contact Angle on Capillary Pressure and Liquid Recovery from Angular Pore Channels

We predict the volume of liquid recovered from diﬀerent-shaped prismatic channels following gas displacement. This recovery factor depends strongly on the contact angle at which the gas-liquid interfaces meet the walls of the channel. We show that scaling the contact angle by a critical value, dependent on the channel shape, leads to a master curve for the recovery factor. Our numerical simulations with the Surface Evolver are supported by theoretical calculations for the capillary entry pressure in a channel with a triangular or rectangular cross-section and for the interface shape in a “scalloped” triangular channel formed between three parallel cylinders.
ESCAPE to Precaution against Leader Failures

Leader-based consensus protocols must undergo a view-change phase to elect a new leader when the current leader fails. The new leader often comes from a candidate server that collects votes from a quorum of servers. However, voting-based election mechanisms intrinsically incite competition in leadership candidacy since candidates may collect only partial votes. This split-vote scenario can result in no leadership winner and thus prolongs the undesired view-change period. In this paper, we investigate a case study of Raft’s leader election and propose a new leader election protocol, called ESCAPE, that fundamentally solves split votes by prioritizing servers based on their log responsiveness. ESCAPE dynamically distributes configurations that offer different priorities to servers through periodic heartbeats. In each assignment, ESCAPE assigns configurations that are more inclined to win an election to servers that have more up-to-date log responsiveness, thereby preparing a pool of prioritized candidates. Consequently, when the next election takes place, the candidate with the highest priority can defeat its counterparts and becomes the next leader without competition. The evaluation results show that ESCAPE progressively reduces the leader election time when the cluster scales up, and the improvement becomes more significant under message loss.
Analyzing Adaptive Scaffolds that Help Students Develop Self-Regulated Learning Behaviors

Providing adaptive scaffolds to help learners develop self-regulated learning (SRL) processes has been an important goal for intelligent learning environments. Adaptive scaffolding is especially important in open-ended learning environments (OELE), where novice learners often face difficulties in completing their learning tasks. This paper presents a systematic framework for adaptive scaffolding in Betty's Brain, a learning-by-teaching OELE for middle school science, where students construct a causal model to teach a virtual agent, generically named Betty. We evaluate the adaptive scaffolding framework and discuss its implications on the development of more effective scaffolds for SRL in OELEs. We detect key cognitive/metacognitive inflection points, i.e., instances where students' behaviors and performance change as they work on their learning tasks. At such inflection points, Mr. Davis (a mentor agent) or Betty (the teachable agent) provide conversational feedback, focused on strategies to help students become productive learners. We conduct a classroom study with 98 middle schoolers to analyze the impact of adaptive scaffolds on students' learning behaviors and performance. Adaptive scaffolding produced mixed results, with some scaffolds (viz., strategic hints that supported debugging and assessment of causal models) being generally more useful to students than others (viz., encouragement prompts). We also note differences in learning behaviors of High and Low performers after receiving scaffolds. Overall, our findings suggest how adaptive scaffolding in OELEs like Betty's Brain can be further improved to narrow the gap between High and Low performers.
Study of final-state interactions of protons in neutrino-nucleus scattering with INCL and NuWro cascade models

The modeling of neutrino-nucleus interactions constitutes a challenging source of systematic uncertainty for the extraction of precise values of neutrino oscillation parameters in long-baseline accelera-tor neutrino experiments. To improve such modeling and minimize the corresponding uncertainties, a new generation of detectors is being developed, which aim to measure the complete ﬁnal state of particles resulting from neutrino interactions. In order to fully beneﬁt from the improved detector capabilities, precise simulations of the nuclear eﬀects on the ﬁnal-state nucleons are needed. This article presents the study of the in-medium propagation of knocked-out protons, i.e., ﬁnal-state interactions (FSI), comparing the NuWro and INCL cascade models. The INCL model is used here for the ﬁrst time to predict exclusive ﬁnal states in measured neutrino interaction cross sections. This study of INCL in the framework of neutrino interactions features various novelties, including the production of nuclear clusters (e.g., deuterons, α particles) in the ﬁnal state. The paper includes a complete characterization of the ﬁnal state after FSI, comparisons to available measurements of single transverse variables, and an assessment of the observability of nuclear clusters.
Beyond the Erd\H{o}s discrepancy problem in function fields

We characterize the limiting behavior of partial sums of multiplicative functions $f:\mathbb{F}_q[t]\to S^1$. In contrast to the number field setting, the characterization depends crucially on whether the notion of discrepancy is defined using long intervals, short intervals, or lexicographic intervals. Concerning the notion of short interval discrepancy, we show that a completely multiplicative $f:\mathbb{F}_q[t]\to\{-1,+1\}$ with $q$ odd has bounded short interval sums if and only if $f$ coincides with a"modified"Dirichlet character to a prime power modulus. This confirms the function field version of a conjecture over $\mathbb{Z}$ that such modified characters are extremal with respect to the growth rate of partial sums. Regarding the lexicographic discrepancy, we prove that the discrepancy of a completely multiplicative sequence is always infinite if we define it using a natural lexicographic ordering of $\mathbb{F}_{q}[t]$. This answers a question of Liu and Wooley. Concerning the long sum discrepancy, it was observed by the Polymath 5 collaboration that the Erd\H{o}s discrepancy problem admits infinitely many completely multiplicative counterexamples on $\mathbb{F}_q[t]$. Nevertheless, we are able to classify the counterexamples if we restrict to the class of modified Dirichlet characters. In this setting, we determine the precise growth rate of the discrepancy, which is still unknown for the analogous problem over the integers.
Multi-Channel FFT Architectures Designed via Folding and Interleaving

Computing the FFT of a single channel is well understood in the literature. However, computing the FFT of multiple channels in a systematic manner has not been fully addressed. This paper presents a framework to design a family of multi-channel FFT architectures using folding and interleaving. Three distinct multi-channel FFT architectures are presented in this paper. These architectures differ in the input and output preprocessing steps and are based on different folding sets, i.e., different orders of execution.
Real-time Emotion Appraisal with Circumplex Model for Human-Robot Interaction

Emotions are the intrinsic or extrinsic representations of our experiences. The importance of emotions during a human-human interaction is immense as it formulates the basis of our interaction framework. There are several approaches in psychology to evaluate emotional states in humans based on the perceived stimuli. However, the topic has been less explored as far as human-robot interaction is concerned. This paper uses an appropriate emotion appraisal mechanism from psychology, generating an emotional state in a humanoid robot on-the-fly during human-robot interaction. Since the exhibition of only six basic emotions is not sufficient to cater to diverse situations, the use of the Circumplex Model in this work has allowed the life-sized robot called ROBIN to experience 28 emotional states in different interaction scenarios. Realistic robot behaviour has been generated based on the proposed appraisal system in various interaction scenarios.
Configuration of Magnetotail Current Sheet Prior to Magnetic Reconnection Onset

The magnetotail current sheet configuration determines magnetic reconnection properties that control the substorm onset, one of the most energetic phenomena in the Earth’s magnetosphere. The quiet‐time current sheet is often approximated as a two‐dimensional (2D) magnetic field configuration balanced by isotropic plasma pressure gradients. However, reconnection onset is preceded by the current sheet thinning and the formation of a nearly one‐dimensional (1D) magnetic field configuration. In this study, using particle‐in‐cell simulations, we investigate the force balance of such thin current sheets when they are driven by plasma inflow. We demonstrate that the magnetic field configuration transitions from 2D to 1D thanks to the formation of plasma pressure nongyrotropy and reveal its origin in the nongyrotropic terms of the ion distributions. We show that substorm onset may be controlled by the instability and dynamics of such nongyrotropic current sheets, having properties much different from the most commonly investigated 2D isotropic configuration.
Identifying the Adoption or Rejection of Misinformation Targeting COVID-19 Vaccines in Twitter Discourse

Although billions of COVID-19 vaccines have been administered, too many people remain hesitant. Misinformation about the COVID-19 vaccines, propagating on social media, is believed to drive hesitancy towards vaccination. However, exposure to misinformation does not necessarily indicate misinformation adoption. In this paper we describe a novel framework for identifying the stance towards misinformation, relying on attitude consistency and its properties. The interactions between attitude consistency, adoption or rejection of misinformation and the content of microblogs are exploited in a novel neural architecture, where the stance towards misinformation is organized in a knowledge graph. This new neural framework is enabling the identification of stance towards misinformation about COVID-19 vaccines with state-of-the-art results. The experiments are performed on a new dataset of misinformation towards COVID-19 vaccines, called CoVaxLies, collected from recent Twitter discourse. Because CoVaxLies provides a taxonomy of the misinformation about COVID-19 vaccines, we are able to show which type of misinformation is mostly adopted and which is mostly rejected.
Four classic problems

In this work we survey four classic problems: Borsuk’s partition problem, Tarski’s plank problem, the Kneser–Poulsen problem on the monotonicity of the union of balls under a contraction of their centers, and the Hadwiger–Levi problem on covering convex bodies by their smaller positively homothetic copies 1. The Borsuk problem Borsuk [1933] asked the question whether every bounded set in n-dimensional space can be partitioned into n + 1 subsets of smaller diameter. Although Borsuk did not suggest a positive solution of the problem, for a long while there was general belief that the answer is yes, so, the problem became known as Borsuk’s conjecture. The truth of the conjecture for n = 2 follows easily by the theorem of Pál [1920] stating that every set of unit diameter can be covered by a regular hexagon of side length 1/ √ 3. Dissecting the hexagon into three pentagons yields the sharp upper bound √ 3/2 for the diameter of the pieces. The same upper bound was obtained by Gale [1953], who obtained it by dissecting a suitable truncation of an equilateral triangle of side-length √ 3. For sets of constant width some stronger theorems were proved. For a convex disk K, let d(K) denote the smallest number with the property that K can be covered by three sets of diameter d(K). Lenz [1956b] proved that for a set K of constant width 1 the inequality √ 3 − 1 ≤ d(K) ≤ √ 3/2 holds, where equality is reached in the upper bound only for the circle, and in the lower bound only for the Reuleaux triangle. Let l(K) and L(K) denote the side-length of the largest equilateral triangle inscribed in K and the side-length of the smallest equilateral triangle circumscribed about K, respectively. Melzak [1963] proved that a set K of constant width 1 can be covered by three sets of diameter at most min{l(K), √ 3 − l(K)} and Schopp [1977] proved that it can be covered by three circular disks of diameter L(K)/2. Schopp also proved that √ 12 − 2 ≤ L(K) ≤ √ 3 for every set of constant width 1. In a theorem of Chakerian and Sallee [1969] the roles of disks is changed to the opposite: They proved that every convex disk of unit diameter can be covered by three copies of any set of constant width 0.9101. Eggleston [1955] settled the three-dimensional case of Borsuk’s conjecture by a rather complicated analytic argument. Simpler proofs were given by Grünbaum The English translation of the book “Lagerungen in der Ebene, auf der Kugel und im Raum” by László Fejes Tóth will be published by Springer in the book series Grundlehren der mathematischen Wissenschaften under the title “Lagerungen—Arrangements in the Plane, on the Sphere and in Space”. Besides detailed notes to the original text the English edition contains eight self-contained new chapters surveying topics related to the subject of the book but not contained in it. This is a preprint of one of the new chapters.
SYSTEMATIC METHOD TO GENERATE NEW IDEAS IN FUZZY FRONT END USING TRIZ

The obstacle for idea generation in fuzzy fi'ont end (FFE) is difficult to apply knowledge in different fields for designers.Theory of inventive problem solving TRIZ and computer-aided innovation systems (CAIs) which are TRIZ-base software systems with a knowledge base provide a framework for knowledge application in different fields.The major methods in TRIZ are selected, which have four types.The problems to be solved for each method are summarized and mapping from the problems to the methods is given.Systematic method with eight paths to integrate the methods and problems is formed.A case study shows the idea generation in FFE using the integrated method step by step.
Higher dimensional CFTs as 2D conformally-equivariant topological field theories

Two and three-point functions of primary fields in four dimensional CFT have a simple space-time dependences factored out from the combinatoric structure which enumerates the fields and gives their couplings. This has led to the formulation of two dimensional topological field theories with SO(4, 2) equivariance which are conjectured to be equivalent to higher dimensional conformal field theories. We review this CFT4/TFT2 construction in the simplest possible setting of a free scalar field, which gives an algebraic construction of the correlators in terms of an infinite dimensional so(4, 2) equivariant algebra with finite dimensional subspaces at fixed scaling dimension. Crossing symmetry of the CFT4 is related to associativity of the algebra. This construction is then extended to describe perturbative CFT4, by making use of deformed co-products. Motivated by the Wilson-Fisher CFT we outline the construction of U(so(d,2)) equivariant TFT2 for non-integer d, in terms of diagram algebras and their representations. Robert de Mello Koch School of Science, Huzhou University, Huzhou 313000, China and Mandelstam Institute for Theoretical Physics, University of Witwatersrand, Wits, 2050, South Africa, e-mail: robert@neo.phys.wits.ac. za Sanjaye Ramgoolam Centre for Theoretical Physics, Department of Physics and Astronomy, Queen Mary University of London, London E1 4NS, United Kingdom and Mandelstam Institute for Theoretical Physics, University of Witwatersrand, Wits, 2050, South Africa, e-mail: s.ramgoolam@qmul.ac. uk Written version of the talk given by SR at XIV International Workshop LIE THEORY AND ITS APPLICATIONS IN PHYSICS, Sofia