Miracle-dz/UniFAR-FTUs huggingface dataset:
Belief, knowledge and evidence

We present a logical system that combines the well-known classical epistemic concepts of belief and knowledge with a concept of evidence such that the intuitive principle \textit{`evidence yields belief and knowledge'} is satisfied. Our approach relies on previous works of the first author \cite{lewjlc2, lewigpl, lewapal} who introduced a modal system containing $S5$-style principles for the reasoning about intutionistic truth (i.e. \textit{proof}) and, inspired by \cite{artpro}, combined that system with concepts of \textit{intuitionistic} belief and knowledge. We consider that combined system and replace the constructive concept of \textit{proof} with a classical notion of \textit{evidence}. This results in a logic that combines modal system $S5$ with classical epistemic principles where $\square\varphi$ reads as `$\varphi$ is evident' in an epistemic sense. Inspired by \cite{lewapal}, and in contrast to the usual possible worlds semantics found in the literature, we propose here a relational, frame-based semantics where belief and knowledge are not modeled via accessibility relations but directly as sets of propositions (sets of sets of worlds).
Anomalies of $(1+1)D$ categorical symmetries

We present a general approach for detecting when a fusion category symmetry is anomalous, based on the existence of a special kind of Lagrangian algebra of the corresponding Drinfeld center. The Drinfeld center of a fusion category $\mathcal{A}$ describes a $(2+1)D$ topological order whose gapped boundaries enumerate all $(1+1)D$ gapped phases with the fusion category symmetry, which may be spontaneously broken. There always exists a gapped boundary, given by the \emph{electric} Lagrangian algebra, that describes a phase with $\mathcal{A}$ fully spontaneously broken. The symmetry defects of this boundary can be identified with the objects in $\mathcal{A}$. We observe that if there exists a different gapped boundary, given by a \emph{magnetic} Lagrangian algebra, then there exists a gapped phase where $\mathcal{A}$ is not spontaneously broken at all, which means that $\mathcal{A}$ is not anomalous. In certain cases, we show that requiring the existence of such a magnetic Lagrangian algebra leads to highly computable obstructions to $\mathcal{A}$ being anomaly-free. As an application, we consider the Drinfeld centers of $\mathbb{Z}_N\times\mathbb{Z}_N$ Tambara-Yamagami fusion categories and recover known results from the study of fiber functors.
Gaussian model for closed curves

Gaussian Mixture Models (GMM) do not adapt well to curved and strongly nonlinear data. However, we can use Gaussians in the curvilinear coordinate systems to solve this problem. Moreover, such a solution allows for the adaptation of clusters to the complicated shapes defined by the family of functions. But still, it is challenging to model clusters as closed curves (e.g., circles, ellipses, etc.). In this work, we propose a density representation of the closed curve, which can be used to detect the complicated templates in the data. For this purpose, we define a new probability distribution to model closed curves. Then we construct a mixture of such distributions and show that it can be effectively trained in the case of the one-dimensional closed curves.
Reconstructing star formation rate for compact binary populations with Einstein telescope

Einstein Telescope (ET) is a proposed third generation, wide-band gravitational wave (GW) detector. Given its improved detection sensitivity in comparison to the second generation detectors, it will be capable of exploring the universe with GWs up to very high redshifts. In this paper we present the algorithm to answer three main questions regarding the star formation rate density (SFR) (i) when did the formation terminate? , (ii) at what redshift does the SFR peak? , and finally (iii) what is the functional form of SFR at high redshift? for a given population. We present an algorithm to infer the functional form of SFR for different populations of compact binaries originating in stars from Population (Pop) I+II and Pop III, using ET as a single instrument. We show that the reconstruction of SFR is essentially independent of the time delay distributions up to $z \sim 14$ and the accuracy of the reconstruction strongly depends on the time delay distribution only at high redshifts of $z\gtrsim 14$. We define the termination redshift as the redshift where the SFR drops to 1\% of its peak value. In this analysis we constrain the peak of the SFR as a function of redshift and show that ET as a single instrument can distinguish the termination redshifts of different SFRs. The accurate estimate of the termination redshift depends on correctly modelling the tail of the time delay distribution representing delay time $\gtrsim 8$ Gyr.
Effects of exit Mach number and temperature on mean-flow and turbulence characteristics in round jets

This paper describes mean-flow and turbulence measurements conducted in a round jet over a range of Mach numbers from 0·3 to 1·7 and jet-exit static temperatures from −40 to over 400 °C. It is a continuation of an earlier work, reported by Lau, Morris & Fisher (1979), to try to map the distribution of the various flow characteristics in the jet flow field and to observe the effects of changing jet exit conditions. In the earlier study, the effort was confined to isothermal jets at a limited number of exit Mach numbers, and the laser velocimeter proved to be a particularly useful instrument, especially in situations where the more severe flow conditions made it impossible to extract fluctuating-velocity data by any other means. The present effort capitalizes on this aspect of the velocimeter and also its ability to measure mean velocities accurately; and the extended range and detail of jet conditions chosen for this study is intended to provide a clearer understanding of the effects of systematically changing the jet conditions. Corresponding Pitot and total temperature measurements are also carried out under a representative set of jet conditions specifically to try to shed light on the effect of jet heating. Based on the various axial and radial distributions which are obtained, a picture is constructed of the changing boundaries of the shear layer with changing jet conditions.
Maxwell's Demon for Emergent Page Curve and Split Property

Seeking for the proper situation of Emergent Gravity, we recent reveal that the entropic mechanism only happens when extremal surfaces are varied, which is similar to the non-gravitational-bath-coupled setup of the island development. In this paper, we consider perturbing thin shell state outside horizon during equilibrating, to find the evolution of these Euclidean states requires an external force to be $ F_{ex}\propto T_{H}\delta A(\mu_a)$, proportional to area variation of the apparent horizon which could transform into the actual event horizon as extremal surface. We analogize the falling tendency to the 2nd law tendency, and then explore the potential tendency violation of Hawking radiation. This analogy recalls the role of Maxwell's Demon to interpret the mechanism of the bath for the Page curve to emerge in a close universe. It could reconcile the Split Problem concerning quantum gravity raised by Raju.
SAT Requires Exhaustive Search

In this paper, by constructing extremely hard examples of CSP (with large domains) and SAT (with long clauses), we prove that such examples cannot be solved without exhaustive search, which is stronger than P $\neq$ NP. This constructive approach for proving impossibility results is very different (and missing) from those currently used in computational complexity theory, but is similar to that used by Kurt G\"{o}del in proving his famous logical impossibility results. Just as shown by G\"{o}del's results that proving formal unprovability is feasible in mathematics, the results of this paper show that proving computational hardness is not hard in mathematics. Specifically, proving lower bounds for many problems, such as 3-SAT, can be challenging because these problems have various effective strategies available for avoiding exhaustive search. However, in cases of extremely hard examples, exhaustive search may be the only viable option, and proving its necessity becomes more straightforward. Consequently, it makes the separation between SAT (with long clauses) and 3-SAT much easier than that between 3-SAT and 2-SAT. Finally, the main results of this paper demonstrate that the fundamental difference between the syntax and the semantics revealed by G\"{o}del's results also exists in CSP and SAT.
An Inverse Scattering Problem

In this paper we give an elementary method to study an inverse scattering problem for a pair of Hamiltonians (H(h), H0(h)) on L 2 (IR n ), where H0(h) = - h 2 ∆, H(h) = H0(h) + V, and V is a short-range potential. We show that, in dimension  ] , ( ); (
Fine-tuning of explainable CNNs for skin lesion classification based on dermatologists' feedback towards increasing trust

In this paper, we propose a CNN fine-tuning method which enables users to give simultaneous feedback on two outputs: the classification itself and the visual explanation for the classification. We present the effect of this feedback strategy in a skin lesion classification task and measure how CNNs react to the two types of user feedback. To implement this approach, we propose a novel CNN architecture that integrates the Grad-CAM technique for explaining the model's decision in the training loop. Using simulated user feedback, we found that fine-tuning our model on both classification and explanation improves visual explanation while preserving classification accuracy, thus potentially increasing the trust of users in using CNN-based skin lesion classifiers.
Synthesis of Opacity-Enforcing Winning Strategies Against Colluded Opponent

This paper studies language-based opacity enforcement in a two-player, zero-sum game on a graph. In this game, player 1 (P1) wins if he can achieve a secret temporal goal described by the language of a finite automaton, no matter what strategy the opponent player 2 (P2) selects. In addition, P1 aims to win while making its goal opaque to a passive observer with imperfect information. However, P2 colludes with the observer to reveal P1's secret whenever P2 cannot prevent P1 from achieving its goal, and therefore, opacity must be enforced against P2. We show that a winning and opacity-enforcing strategy for P1 can be computed by reducing the problem to solving a reachability game augmented with the observer's belief states. Furthermore, if such a strategy does not exist, winning for P1 must entail the price of revealing his secret to the observer. We demonstrate our game-theoretic solution of opacity-enforcement control through a small illustrative example and in a robot motion planning problem.
Communication of Statistics and Evidence in Times of Crisis

This review provides an overview of concepts relating to the communication of statistical and empirical evidence in times of crisis, with a special focus on COVID-19. In it, we consider topics relating to both the communication of numbers, such as the role of format, context, comparisons, and visualization, and the communication of evidence more broadly, such as evidence quality, the influence of changes in available evidence, transparency, and repeated decision-making. A central focus is on the communication of the inherent uncertainties in statistical analysis, especially in rapidly changing informational environments during crises. We present relevant literature on these topics and draw connections to the communication of statistics and empirical evidence during the COVID-19 pandemic and beyond. We finish by suggesting some considerations for those faced with communicating statistics and evidence in times of crisis. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 11 is March 2024. Please see http://www.annualreviews. org/page/journal/pubdates for revised estimates.
Is ChatGPT a Highly Fluent Grammatical Error Correction System? A Comprehensive Evaluation

ChatGPT, a large-scale language model based on the advanced GPT-3.5 architecture, has shown remarkable potential in various Natural Language Processing (NLP) tasks. However, there is currently a dearth of comprehensive study exploring its potential in the area of Grammatical Error Correction (GEC). To showcase its capabilities in GEC, we design zero-shot chain-of-thought (CoT) and few-shot CoT settings using in-context learning for ChatGPT. Our evaluation involves assessing ChatGPT's performance on five official test sets in three different languages, along with three document-level GEC test sets in English. Our experimental results and human evaluations demonstrate that ChatGPT has excellent error detection capabilities and can freely correct errors to make the corrected sentences very fluent, possibly due to its over-correction tendencies and not adhering to the principle of minimal edits. Additionally, its performance in non-English and low-resource settings highlights its potential in multilingual GEC tasks. However, further analysis of various types of errors at the document-level has shown that ChatGPT cannot effectively correct agreement, coreference, tense errors across sentences, and cross-sentence boundary errors.
Moving Obstacle Collision Avoidance via Chance-Constrained MPC with CBF

Model predictive control (MPC) with control barrier functions (CBF) is a promising solution to address the moving obstacle collision avoidance (MOCA) problem. Unlike MPC with distance constraints (MPC-DC), this approach facilitates early obstacle avoidance without the need to increase prediction horizons. However, the existing MPC-CBF method is deterministic and fails to account for perception uncertainties. This paper proposes a generalized MPC-CBF approach for stochastic scenarios, which maintains the advantages of the deterministic method for addressing the MOCA problem. Specifically, the chance-constrained MPC-CBF (CC-MPC-CBF) technique is introduced to ensure that a user-defined collision avoidance probability is met by utilizing probabilistic CBFs. However, due to the potential empty intersection between the reachable set and the safe region confined by CBF constraints, the CC-MPC-CBF problem can pose challenges in achieving feasibility. To address this issue, we propose a sequential implementation approach that involves solving a standard MPC optimization problem followed by a predictive safety filter optimization, which leads to improved feasibility. Furthermore, we introduce an iterative convex optimization scheme to further expedite the resolution of the predictive safety filter, which results in an efficient approach to tackling the non-convex CC-MPC-CBF problem. We apply our proposed algorithm to a 2-D integrator system for MOCA, and we showcase its resilience to obstacle measurement uncertainties and favorable feasibility properties.
Divided Attention: Unsupervised Multi-Object Discovery with Contextually Separated Slots

We introduce a method to segment the visual field into independently moving regions, trained with no ground truth or supervision. It consists of an adversarial conditional encoder-decoder architecture based on Slot Attention, modified to use the image as context to decode optical flow without attempting to reconstruct the image itself. In the resulting multi-modal representation, one modality (flow) feeds the encoder to produce separate latent codes (slots), whereas the other modality (image) conditions the decoder to generate the first (flow) from the slots. This design frees the representation from having to encode complex nuisance variability in the image due to, for instance, illumination and reflectance properties of the scene. Since customary autoencoding based on minimizing the reconstruction error does not preclude the entire flow from being encoded into a single slot, we modify the loss to an adversarial criterion based on Contextual Information Separation. The resulting min-max optimization fosters the separation of objects and their assignment to different attention slots, leading to Divided Attention, or DivA. DivA outperforms recent unsupervised multi-object motion segmentation methods while tripling run-time speed up to 104FPS and reducing the performance gap from supervised methods to 12% or less. DivA can handle different numbers of objects and different image sizes at training and test time, is invariant to permutation of object labels, and does not require explicit regularization.
Randomized Adversarial Style Perturbations for Domain Generalization

We propose a novel domain generalization technique, referred to as Randomized Adversarial Style Perturbation (RASP), which is motivated by the observation that the characteristics of each domain are captured by the feature statistics corresponding to style. The proposed algorithm perturbs the style of a feature in an adversarial direction towards a randomly selected class, and makes the model learn against being misled by the unexpected styles observed in unseen target domains. While RASP is effective to handle domain shifts, its naive integration into the training procedure might degrade the capability of learning knowledge from source domains because it has no restriction on the perturbations of representations. This challenge is alleviated by Normalized Feature Mixup (NFM), which facilitates the learning of the original features while achieving robustness to perturbed representations via their mixup during training. We evaluate the proposed algorithm via extensive experiments on various benchmarks and show that our approach improves domain generalization performance, especially in large-scale benchmarks.
Magnetohydrodynamic turbulence in the solar wind

Recent work in describing the solar wind as an MHD turbulent fluid has shown that the magnetic fluctuations are adequately described as time stationary and to some extent as spatially homogeneous. Spectra of the three rugged invariants of incompressible MHD are the principal quantities used to characterize the velocity and magnetic field fluctuations. Unresolved issues concerning the existence of actively developing turbulence are discussed.
Independent Vector Extraction Constrained on Manifold of Half-Length Filters

Independent Vector Analysis (IVA) is a popular extension of Independent Component Analysis (ICA) for joint separation of a set of instantaneous linear mixtures, with a direct application in frequency-domain speaker separation or extraction. The mixtures are parameterized by mixing matrices, one matrix per mixture. This means that the IVA mixing model does not account for any relationships between parameters across the mixtures/frequencies. The separation proceeds jointly only through the source model, where statistical dependencies of sources across the mixtures are taken into account. In this paper, we propose a mixing model for joint blind source extraction where the mixing model parameters are linked across the frequencies. This is achieved by constraining the set of feasible parameters to the manifold of half-length separating filters, which has a clear interpretation and application in frequency-domain speaker extraction.
OrienterNet: Visual Localization in 2D Public Maps with Neural Matching

Humans can orient themselves in their 3D environments using simple 2D maps. Differently, algorithms for visual localization mostly rely on complex 3D point clouds that are expensive to build, store, and maintain over time. We bridge this gap by introducing OrienterNet, the first deep neural network that can localize an image with sub-meter accuracy using the same 2D semantic maps that humans use. OrienterNet estimates the location and orientation of a query image by matching a neural Bird's-Eye View with open and globally available maps from OpenStreetMap, enabling anyone to localize anywhere such maps are available. OrienterNet is supervised only by camera poses but learns to perform semantic matching with a wide range of map elements in an end-to-end manner. To enable this, we introduce a large crowd-sourced dataset of images captured across 12 cities from the diverse viewpoints of cars, bikes, and pedestrians. OrienterNet generalizes to new datasets and pushes the state of the art in both robotics and AR scenarios. The code is available at github.com/facebookresearch/OrienterNet.
On the Prime Number Divisibility by Deep Learning

Certain tasks such as determining whether a given integer can be divided by 2, 3, or other prime numbers may be trivial for human beings, but can be less straightforward for computers in the absence of pre-speciﬁed algorithms. In this paper, we tested multiple deep learning architectures and feature engineering approaches, and evaluated the scenario of determining divisibility of large ﬁnite integers (up to 2 32 ) by small prime numbers. It turns out that, regardless of the network frameworks or the complexity of the network structures (CNN, RNN, Transformer, etc.), the ability to predict the prime number divisibility critically depends on the feature space fed into the deep learning models. We also evaluated commercially available Automated Machine Learning (AutoML) pipelines from Amazon, Google and Microsoft, and demonstrated that they failed to address this issue unless appropriately engineered features were provided. We further proposed a closed form solution to the problem using the ordinary linear regression on Fourier series basis vectors, and showed its success. Finally, we evaluated prompt-based learning using ChatGPT and demonstrated its success on small primes and apparent failures on larger primes. We conclude that feature engineering remains an important task to improve the performance, increase the interpretability, and reduce the complexity of machine learning/deep learning models, even in the era of AutoML and large-language models (LLMs).
Abnormal Event Detection via Hypergraph Contrastive Learning

Abnormal event detection, which refers to mining unusual interactions among involved entities, plays an important role in many real applications. Previous works mostly over-simplify this task as detecting abnormal pair-wise interactions. However, real-world events may contain multi-typed attributed entities and complex interactions among them, which forms an Attributed Heterogeneous Information Network (AHIN). With the boom of social networks, abnormal event detection in AHIN has become an important, but seldom explored task. In this paper, we firstly study the unsupervised abnormal event detection problem in AHIN. The events are considered as star-schema instances of AHIN and are further modeled by hypergraphs. A novel hypergraph contrastive learning method, named AEHCL, is proposed to fully capture abnormal event patterns. AEHCL designs the intra-event and inter-event contrastive modules to exploit self-supervised AHIN information. The intra-event contrastive module captures the pair-wise and multivariate interaction anomalies within an event, and the inter-event module captures the contextual anomalies among events. These two modules collaboratively boost the performance of each other and improve the detection results. During the testing phase, a contrastive learning-based abnormal event score function is further proposed to measure the abnormality degree of events. Extensive experiments on three datasets in different scenarios demonstrate the effectiveness of AEHCL, and the results improve state-of-the-art baselines up to 12.0% in Average Precision (AP) and 4.6% in Area Under Curve (AUC) respectively.