Miracle-dz/UniFAR-FTUs huggingface dataset:
Isometric embedding of the n-point spaces into the space of spaces for $n \leq 4$

In [The Space of Spaces: Curvature Bounds and Gradient Flows on the Space of Metric Measure Spaces. Memoirs of the American Mathematical Society. American Mathematical Society, 2023], Sturm studied the space of all metric measure spaces up to isomorphism which he called The space of spaces. He also introduced for a natural number n the space of all n-points metric spaces. The aim of this article is to study if the embedding of this space in the space of spaces is isometric. Using results from [Haggai Maron and Yaron Lipman. (probably) concave graph matching. Advances in Neural Information Processing Systems, 31, 2018] and [Hiroshi Maehara. Euclidean embeddings of finite metric spaces. Discrete Mathematics, 2013], we prove that it is the case for $n \leq 4$ and for Euclidean metric spaces.
Extracting the Luttinger parameter from a single wave function

The low-energy physics of Tomonaga-Luttinger liquids (TLLs) is controlled by the Luttinger parameter. We demonstrate that this parameter can be extracted from a single wave function for one-component TLLs with periodic boundary condition. This method relies on the fact that TLLs are described by conformal field theory in which crosscap states can be constructed. The overlaps between the crosscap states and the ground state as well as some excited states are proved to be universal numbers that directly reveal the Luttinger parameter. In microscopic lattice models, crosscap states are formed by putting each pair of antipodal sites into a maximally entangled state. Analytical and numerical calculations are performed in a few representative models to substantiate the conformal field theory prediction. The extracted Luttinger parameters are generally quite accurate in finite-size systems with moderate lengths, so there is no need to perform data fitting and/or finite-size scaling.
A generalised Nehari manifold method for a class of non-linear Schrödinger systems in ℝ3

We study the existence of positive solutions of a particular elliptic system in $\mathbb{R}^3$ composed of two coupled non linear stationary Schr\"odinger equations (NLSEs), that is $-\epsilon^2 \Delta u + V(x) u= h_v(u,v), - \epsilon^2 \Delta v + V(x) v=h_u (u,v)$. Under certain hypotheses on the potential $V$ and the non linearity $h$, we manage to prove that there exists a solution $(u_\epsilon,v_\epsilon)$ that decays exponentially with respect to local minima points of the potential and whose energy tends to concentrate around these points, as $\epsilon \to 0$. We also estimate this energy in terms of particular ground state energies. This work follows closely what is done in https://doi.org/10.1007/s00526-007-0103-z , although here we consider a more general non linearity and we restrict ourselves to the case where the domain is $\mathbb{R}^3$.
Probing Two-body Bound States in the Continuum and Nonlinear Breathers Using Intensity Correlations

We study Hanbury Brown-Twiss spatial intensity correlations in femtosecond laser-fabricated photonic Su-Schrieffer-Heeger lattices. We first probe edge bound states in the continuum (BICs) of two indistinguishable bosons by mapping the intensity correlations to the two-body bosonic quantum walk. These two-body edge BICs show remarkable robustness in the presence of disorder. The localization of intensity correlation, observed in the linear regime, persists at weak nonlinearity due to the formation of {\it long-lived breathers} and solitons on the edge of the lattice. For stronger nonlinearities, the light tends to be delocalized from the edge site into the bulk, destroying the localization of the intensity correlation. Our results show the interplay of band structure, initial state, and nonlinearity influencing transport and intensity correlations.
Multimode Interferometers: an Analytical Method for Determining the Accumulated Phase Difference Between the Fundamental Mode and One Arbitrary High-Order Mode

In multimode interferometers, the interaction between several modes brings a high level of complexity to the interpretation of its light patterns. With recent advances, it is possible to selectively excite only a couple of modes inside the device. This paper presents an analytical method for determining the phase difference between two propagating modes in the multimode interferometer, in an effort to simplify the usage and expand the range of applications for this type of optical devices.
Development of Context-Sensitive Formulas to Obtain Constant Luminance Perception for a Foreground Object in Front of Backgrounds of Varying Luminance

In this article, we present a framework for developing context-sensitive luminance correction formulas that can produce constant luminance perception for foreground objects. Our formulas make the foreground object slightly translucent to mix with the blurred version of the background. This mix can quickly produce any desired illusion of luminance in foreground objects based on the luminance of the background. The translucency formula has only one parameter; the relative size of the foreground object, which is a number between zero and one. We have identified the general structure of the translucency formulas as a power function of the relative size of the foreground object. We have implemented a web-based interactive program in Shadertoy. Using this program, we determined the coefficients of the polynomial exponents of the power function. To intuitively control the coefficients of the polynomial functions, we have used a B\'{e}zier form. Our final translucency formula uses a quadratic polynomial and requires only three coefficients. We also identified a simpler affine formula, which requires only two coefficients. We made our program publicly available in Shadertoy so that anyone can access and improve it. In this article, we also explain how to intuitively change the polynomial part of the formula. Using our explanation, users change the polynomial part of the formula to obtain their own perceptively constant luminance. This can be used as a crowd-sourcing experiment for further improvement of the formula.
Predicting machine failures from multivariate time series: an industrial case study

Non-neural Machine Learning (ML) and Deep Learning (DL) models are often used to predict system failures in the context of industrial maintenance. However, only a few researches jointly assess the effect of varying the amount of past data used to make a prediction and the extension in the future of the forecast. This study evaluates the impact of the size of the reading window and of the prediction window on the performances of models trained to forecast failures in three data sets concerning the operation of (1) an industrial wrapping machine working in discrete sessions, (2) an industrial blood refrigerator working continuously, and (3) a nitrogen generator working continuously. The problem is formulated as a binary classification task that assigns the positive label to the prediction window based on the probability of a failure to occur in such an interval. Six algorithms (logistic regression, random forest, support vector machine, LSTM, ConvLSTM, and Transformers) are compared using multivariate telemetry time series. The results indicate that, in the considered scenarios, the dimension of the prediction windows plays a crucial role and highlight the effectiveness of DL approaches at classifying data with diverse time-dependent patterns preceding a failure and the effectiveness of ML approaches at classifying similar and repetitive patterns preceding a failure.
Quanto Option Pricing on a Multivariate Levy Process Model with a Generative Artificial Intelligence

In this study, we discuss a machine learning technique to price exotic options with two underlying assets based on a non-Gaussian Levy process model. We introduce a new multivariate Levy process model named the generalized normal tempered stable (gNTS) process, which is defined by time-changed multivariate Brownian motion. Since the gNTS process does not provide a simple analytic formula for the probability density function (PDF), we use the conditional real-valued non-volume preserving (CRealNVP) model, which is a type of flow-based generative network. Then, we discuss the no-arbitrage pricing on the gNTS model for pricing the quanto option, whose underlying assets consist of a foreign index and foreign exchange rate. We present the training of the CRealNVP model to learn the PDF of the gNTS process using a training set generated by Monte Carlo simulation. Next, we estimate the parameters of the gNTS model with the trained CRealNVP model using the empirical data observed in the market. Finally, we provide a method to find an equivalent martingale measure on the gNTS model and to price the quanto option using the CRealNVP model with the risk-neutral parameters of the gNTS model.
Separate and Conquer: Decoupling Co-occurrence via Decomposition and Representation for Weakly Supervised Semantic Segmentation

Weakly supervised semantic segmentation (WSSS) with image-level labels aims to achieve segmentation tasks without dense annotations. However, attributed to the frequent coupling of co-occurring objects and the limited supervision from image-level labels, the challenging co-occurrence problem is widely present and leads to false activation of objects in WSSS. In this work, we devise a 'Separate and Conquer' scheme SeCo to tackle this issue from dimensions of image space and feature space. In the image space, we propose to 'separate' the co-occurring objects with image decomposition by subdividing images into patches. Importantly, we assign each patch a category tag from Class Activation Maps (CAMs), which spatially helps remove the co-context bias and guide the subsequent representation. In the feature space, we propose to 'conquer' the false activation by enhancing semantic representation with multi-granularity knowledge contrast. To this end, a dual-teacher-single-student architecture is designed and tag-guided contrast is conducted, which guarantee the correctness of knowledge and further facilitate the discrepancy among co-contexts. We streamline the multi-staged WSSS pipeline end-to-end and tackle this issue without external supervision. Extensive experiments are conducted, validating the efficiency of our method and the superiority over previous single-staged and even multi-staged competitors on PASCAL VOC and MS COCO. Code is available at https://github.com/zwyang6/SeCo.git.
SINR-Aware Deep Reinforcement Learning for Distributed Dynamic Channel Allocation in Cognitive Interference Networks

We consider the problem of dynamic channel allocation (DCA) in cognitive communication networks with the goal of maximizing a global signal-to-interference-plus-noise ratio (SINR) measure under a specified target quality of service (QoS)-SINR for each network. The shared bandwidth is partitioned into K channels with frequency separation. In contrast to the majority of existing studies that assume perfect orthogonality or a one- to-one user-channel allocation mapping, this paper focuses on real-world systems experiencing inter-carrier interference (ICI) and channel reuse by multiple large-scale networks. This realistic scenario significantly increases the problem dimension, rendering existing algorithms inefficient. We propose a novel multi-agent reinforcement learning (RL) framework for distributed DCA, named Channel Allocation RL To Overlapped Networks (CARLTON). The CARLTON framework is based on the Centralized Training with Decentralized Execution (CTDE) paradigm, utilizing the DeepMellow value-based RL algorithm. To ensure robust performance in the interference-laden environment we address, CARLTON employs a low-dimensional representation of observations, generating a QoS-type measure while maximizing a global SINR measure and ensuring the target QoS-SINR for each network. Our results demonstrate exceptional performance and robust generalization, showcasing superior efficiency compared to alternative state-of-the-art methods, while achieving a marginally diminished performance relative to a fully centralized approach.
Generation of skill-specific maps from graph world models for robotic systems

With the increase in the availability of Building Information Models (BIM) and (semi-) automatic tools to generate BIM from point clouds, we propose a world model architecture and algorithms to allow the use of the semantic and geometric knowledge encoded within these models to generate maps for robot localization and navigation. When heterogeneous robots are deployed within an environment, maps obtained from classical SLAM approaches might not be shared between all agents within a team of robots, e.g. due to a mismatch in sensor type, or a difference in physical robot dimensions. Our approach extracts the 3D geometry and semantic description of building elements (e.g. material, element type, color) from BIM, and represents this knowledge in a graph. Based on queries on the graph and knowledge of the skills of the robot, we can generate skill-specific maps that can be used during the execution of localization or navigation tasks. The approach is validated with data from complex build environments and integrated into existing navigation frameworks.
PETROLEUM SYSTEMS OF THE PETREL SUB-BASIN-AN INTEGRATED APPROACH TO BASIN ANALYSIS AND IDENTIFICATION OF HYDROCARBON EXPLORATION OPPORTUNITIES

A petroleum system evaluation of the Petrel Sub-basin in the Bonaparte Gulf, northwest Australia, suggests that the wells drilled in the area have not fully evaluated the petroleum potential. Some of the lowest risk plays in the basin have not been tested adequately or have not been assessed in probable economic fairways. Several important discoveries have highlighted the existence of at least three petroleum systems in the Petrel Sub-basin; Larapintine, Transitional and Gondwanan. Best known are the Gondwanan gas discoveries at Petrel, Tern and most recently Fishburn, where hydrocarbons are reservoired in Late Permian sandstones and are probably sourced from Permian deltaic sequences. Kurt her inshore, oil has been recovered from Carboniferous and Early Permian reservoirs at Turtle and Barnett. The source of the oil is considered to be Carboniferous anoxic marine shales of a distinct petroleum system transitional between the Gondwanan and Larapintine systems (Milligans Formation source rock and Late Carboniferous to Permian reservoirs). Onshore, there is a gas discovery at Gariinala-1 and significant oil shows in Ningbing-1, in Late Devonian Larapintine system rocks. Geochemical analysis of the oil shows it to be sourced from a carbonate marine source rock, different from the clastic derived oils obtained from Turtle and Barnett. Recent discoveries in the Timor Sea have provoked a re-assessment of the very similar, largely untested, Mesozoic, Westralian petroleum system in the outer part of the Petrel Sub-basin. The prospective Mesozoic play fairway occurs in the northern part of the Petrel Sub-basin, extending into Area B of the Zone of Cooperation.
Misalignment-Robust Frequency Distribution Loss for Image Transformation

This paper aims to address a common challenge in deep learning-based image transformation methods, such as image enhancement and super-resolution, which heavily rely on precisely aligned paired datasets with pixel-level alignments. However, creating precisely aligned paired images presents significant challenges and hinders the advancement of methods trained on such data. To overcome this challenge, this paper introduces a novel and simple Frequency Distribution Loss (FDL) for computing distribution distance within the frequency domain. Specifically, we transform image features into the frequency domain using Discrete Fourier Transformation (DFT). Subsequently, frequency components (amplitude and phase) are processed separately to form the FDL loss function. Our method is empirically proven effective as a training constraint due to the thoughtful utilization of global information in the frequency domain. Extensive experimental evaluations, focusing on image enhancement and super-resolution tasks, demonstrate that FDL outperforms existing misalignment-robust loss functions. Furthermore, we explore the potential of our FDL for image style transfer that relies solely on completely misaligned data. Our code is available at: https://github.com/eezkni/FDL
Generative AI and Copyright: A Dynamic Perspective

The rapid advancement of generative AI is poised to disrupt the creative industry. Amidst the immense excitement for this new technology, its future development and applications in the creative industry hinge crucially upon two copyright issues: 1) the compensation to creators whose content has been used to train generative AI models (the fair use standard); and 2) the eligibility of AI-generated content for copyright protection (AI-copyrightability). While both issues have ignited heated debates among academics and practitioners, most analysis has focused on their challenges posed to existing copyright doctrines. In this paper, we aim to better understand the economic implications of these two regulatory issues and their interactions. By constructing a dynamic model with endogenous content creation and AI model development, we unravel the impacts of the fair use standard and AI-copyrightability on AI development, AI company profit, creators income, and consumer welfare, and how these impacts are influenced by various economic and operational factors. For example, while generous fair use (use data for AI training without compensating the creator) benefits all parties when abundant training data exists, it can hurt creators and consumers when such data is scarce. Similarly, stronger AI-copyrightability (AI content enjoys more copyright protection) could hinder AI development and reduce social welfare. Our analysis also highlights the complex interplay between these two copyright issues. For instance, when existing training data is scarce, generous fair use may be preferred only when AI-copyrightability is weak. Our findings underscore the need for policymakers to embrace a dynamic, context-specific approach in making regulatory decisions and provide insights for business leaders navigating the complexities of the global regulatory environment.
The Logarithmic Random Bidding for the Parallel Roulette Wheel Selection with Precise Probabilities

The roulette wheel selection is a critical process in heuristic algorithms, enabling the probabilistic choice of items based on assigned fitness values. It selects an item with a probability proportional to its fitness value. This technique is commonly employed in ant-colony algorithms to randomly determine the next city to visit when solving the traveling salesman problem. Our study focuses on parallel algorithms designed to select one of multiple processors, each associated with fitness values, using random wheel selection. We propose a novel approach called logarithmic random bidding, which achieves an expected runtime logarithmic to the number of processors with non-zero fitness values, using the CRCW-PRAM model with a shared memory of constant size. Notably, the logarithmic random bidding technique demonstrates efficient performance, particularly in scenarios where only a few processors are assigned non-zero fitness values.
Breaking the Black-Box: Confidence-Guided Model Inversion Attack for Distribution Shift

Model inversion attacks (MIAs) seek to infer the private training data of a target classifier by generating synthetic images that reflect the characteristics of the target class through querying the model. However, prior studies have relied on full access to the target model, which is not practical in real-world scenarios. Additionally, existing black-box MIAs assume that the image prior and target model follow the same distribution. However, when confronted with diverse data distribution settings, these methods may result in suboptimal performance in conducting attacks. To address these limitations, this paper proposes a \textbf{C}onfidence-\textbf{G}uided \textbf{M}odel \textbf{I}nversion attack method called CG-MI, which utilizes the latent space of a pre-trained publicly available generative adversarial network (GAN) as prior information and gradient-free optimizer, enabling high-resolution MIAs across different data distributions in a black-box setting. Our experiments demonstrate that our method significantly \textbf{outperforms the SOTA black-box MIA by more than 49\% for Celeba and 58\% for Facescrub in different distribution settings}. Furthermore, our method exhibits the ability to generate high-quality images \textbf{comparable to those produced by white-box attacks}. Our method provides a practical and effective solution for black-box model inversion attacks.
Six-Point Method for Multi-Camera Systems with Reduced Solution Space

Relative pose estimation using point correspondences (PC) is a widely used technique. A minimal configuration of six PCs is required for generalized cameras. In this paper, we present several minimal solvers that use six PCs to compute the 6DOF relative pose of a multi-camera system, including a minimal solver for the generalized camera and two minimal solvers for the practical configuration of two-camera rigs. The equation construction is based on the decoupling of rotation and translation. Rotation is represented by Cayley or quaternion parametrization, and translation can be eliminated by using the hidden variable technique. Ray bundle constraints are found and proven when a subset of PCs relate the same cameras across two views. This is the key to reducing the number of solutions and generating numerically stable solvers. Moreover, all configurations of six-point problems for multi-camera systems are enumerated. Extensive experiments demonstrate that our solvers are more accurate than the state-of-the-art six-point methods, while achieving better performance in efficiency.
Data augmentation method for modeling health records with applications to clopidogrel treatment failure detection

We present a novel data augmentation method to address the challenge of data scarcity in modeling longitudinal patterns in Electronic Health Records (EHR) of patients using natural language processing (NLP) algorithms. The proposed method generates augmented data by rearranging the orders of medical records within a visit where the order of elements are not obvious, if any. Applying the proposed method to the clopidogrel treatment failure detection task enabled up to 5.3% absolute improvement in terms of ROC-AUC (from 0.908 without augmentation to 0.961 with augmentation) when it was used during the pre-training procedure. It was also shown that the augmentation helped to improve performance during fine-tuning procedures, especially when the amount of labeled training data is limited.
Real-time scattering in the lattice Schwinger model

Tensor network methods have demonstrated their suitability for the study of equilibrium properties of lattice gauge theories, even close to the continuum limit. We use them in an out-of-equilibrium scenario, much less explored so far, by simulating the real-time collisions of composite mesons in the lattice Schwinger model. Constructing wave-packets of vector mesons at different incoming momenta, we observe the opening of the inelastic channel in which two heavier mesons are produced and identify the momentum threshold. To detect the products of the collision in the strong coupling regime we propose local quantitites that could be measured in current quantum simulation platforms.