Miracle-dz/UniFAR-FTUs huggingface dataset:
Causal Inference in Directed, Possibly Cyclic, Graphical Models

We consider the problem of learning a directed graph $G^\star$ from observational data. We assume that the distribution which gives rise to the samples is Markov and faithful to the graph $G^\star$ and that there are no unobserved variables. We do not rely on any further assumptions regarding the graph or the distribution of the variables. In particular, we allow for directed cycles in $G^\star$ and work in the fully non-parametric setting. Given the set of conditional independence statements satisfied by the distribution, we aim to find a directed graph which satisfies the same $d$-separation statements as $G^\star$. We propose a hybrid approach consisting of two steps. We first find a partially ordered partition of the vertices of $G^\star$ by optimizing a certain score in a greedy fashion. We prove that any optimal partition uniquely characterizes the Markov equivalence class of $G^\star$. Given an optimal partition, we propose an algorithm for constructing a graph in the Markov equivalence class of $G^\star$ whose strongly connected components correspond to the elements of the partition, and which are partially ordered according to the partial order of the partition. Our algorithm comes in two versions -- one which is provably correct and another one which performs fast in practice.
Scheme-Theoretic Approach to Computational Complexity. IV. A New Perspective on Hardness of Approximation

We provide a new approach for establishing hardness of approximation results, based on the theory recently introduced by the author. It allows one to directly show that approximating a problem beyond a certain threshold requires super-polynomial time. To exhibit the framework, we revisit two famous problems in this paper. The particular results we prove are: MAX-3-SAT$(1,\frac{7}{8}+\epsilon)$ requires exponential time for any constant $\epsilon$ satisfying $\frac{1}{8} \geq \epsilon>0$. In particular, the gap exponential time hypothesis (Gap-ETH) holds. MAX-3-LIN-2$(1-\epsilon, \frac{1}{2}+\epsilon)$ requires exponential time for any constant $\epsilon$ satisfying $\frac{1}{4} \geq \epsilon>0$.
Algorithms as Social-Ecological-Technological Systems: an Environmental Justice Lens on Algorithmic Audits

This paper reframes algorithmic systems as intimately connected to and part of social and ecological systems, and proposes a first-of-its-kind methodology for environmental justice-oriented algorithmic audits. How do we consider environmental and climate justice dimensions of the way algorithmic systems are designed, developed, and deployed? These impacts are inherently emergent and can only be understood and addressed at the level of relations between an algorithmic system and the social (including institutional) and ecological components of the broader ecosystem it operates in. As a result, we claim that in absence of an integral ontology for algorithmic systems, we cannot do justice to the emergent nature of broader environmental impacts of algorithmic systems and their underlying computational infrastructure. Furthermore, an integral lens provides many lessons from the history of environmental justice that are of relevance in current day struggles for algorithmic justice. We propose to define algorithmic systems as ontologically indistinct from Social-Ecological-Technological Systems (SETS), framing emergent implications as couplings between social, ecological, and technical components of the broader fabric in which algorithms are integrated and operate. We draw upon prior work on SETS analysis as well as emerging themes in the literature and practices of Environmental Justice (EJ) to conceptualize and assess algorithmic impact. We then offer three policy recommendations to help establish a SETS-based EJ approach to algorithmic audits: (1) broaden the inputs and open-up the outputs of an audit, (2) enable meaningful access to redress, and (3) guarantee a place-based and relational approach to the process of evaluating impact. We operationalize these as a qualitative framework of questions for a spectrum of stakeholders. Doing so, this article aims to inspire stronger and more frequent interactions across policymakers, researchers, practitioners, civil society, and grassroots communities. https://arxiv.org/abs/2305.05733.
High-fidelity transport of trapped-ion qubits in a multilayer array

A variety of physical platforms are investigated for quantum control of many particles, and techniques are extended to access multiple dimensions. Here, we present our experimental study of shuttling single Mg$^+$ ions within a scalable trap-array architecture that contains up to thirteen trapping sites in a three-dimensional arrangement. We shuttle ions from a dedicated loading hub to multiple sites with a success rate of larger than $0.99999$. In a prototype application, we demonstrate the preservation of the coherence of superposition states of a hyperfine qubit during inter-site shuttling. Our findings highlight the potential of these techniques for use in future large-scale architectures.
Joint Falsification and Fidelity Settings Optimization for Validation of Safety-Critical Systems: A Theoretical Analysis

Safety validation is a crucial component in the development and deployment of autonomous systems, such as self-driving vehicles and robotic systems. Ensuring safe operation necessitates extensive testing and verification of control policies, typically conducted in simulation environments. High-fidelity simulators accurately model real-world dynamics but entail high computational costs, limiting their scalability for exhaustive testing. Conversely, low-fidelity simulators offer efficiency but may not capture the intricacies of high-fidelity simulators, potentially yielding false conclusions. We propose a joint falsification and fidelity optimization framework for safety validation of autonomous systems. Our mathematical formulation combines counterexample searches with simulator fidelity improvement, facilitating more efficient exploration of the critical environmental configurations challenging the control system. Our contributions encompass a set of theorems addressing counterexample sensitivity analysis, sample complexity, convergence, the interplay between the outer and inner optimization loops, and regret bound analysis. The proposed joint optimization approach enables a more targeted and efficient testing process, optimizes the use of available computational resources, and enhances confidence in autonomous system safety validation.
Fast Teammate Adaptation in the Presence of Sudden Policy Change

In cooperative multi-agent reinforcement learning (MARL), where an agent coordinates with teammate(s) for a shared goal, it may sustain non-stationary caused by the policy change of teammates. Prior works mainly concentrate on the policy change during the training phase or teammates altering cross episodes, ignoring the fact that teammates may suffer from policy change suddenly within an episode, which might lead to miscoordination and poor performance as a result. We formulate the problem as an open Dec-POMDP, where we control some agents to coordinate with uncontrolled teammates, whose policies could be changed within one episode. Then we develop a new framework, fast teammates adaptation (Fastap), to address the problem. Concretely, we first train versatile teammates' policies and assign them to different clusters via the Chinese Restaurant Process (CRP). Then, we train the controlled agent(s) to coordinate with the sampled uncontrolled teammates by capturing their identifications as context for fast adaptation. Finally, each agent applies its local information to anticipate the teammates' context for decision-making accordingly. This process proceeds alternately, leading to a robust policy that can adapt to any teammates during the decentralized execution phase. We show in multiple multi-agent benchmarks that Fastap can achieve superior performance than multiple baselines in stationary and non-stationary scenarios.
Calculation of the hyperfine structure of Er and Fm

A version of the configuration interaction method, which has been recently developed to deal with large number of valence electrons, has been used to calculate magnetic dipole and electric quadrupole hyperfine structure constants for a number of states of erbium and fermium. Calculations for fermium are done for extracting nuclear moments of Fm isotopes from recent and future measurements. Calculations for erbium, which has electronic structure similar to those of fermium, are done to study the accuracy of the method.
Fine-tuning Language Models with Generative Adversarial Feedback

Reinforcement Learning with Human Feedback (RLHF) has been demonstrated to signiﬁcantly enhance the performance of large language models (LLMs) by aligning their outputs with desired human values. However, RLHF is constrained by the expertise and productivity limitations of human evaluators. In this study, we investigate an alternative approach: Reinforcement Learning with Generative Adversarial Feedback (RLGAF) to RLHF. Our preliminary ﬁndings indicate that RLGAF can help align LLMs outputs while not suﬀering from the inherent restrictions of RLHF, suggesting promising avenues for further research on automating AI alignment.
Hadwiger's Conjecture for some graphs with independence number two

Let $h(G)$ denote the largest $t$ such that $G$ contains $K_t$ as a minor, $\chi(G)$ the chromatic number of $G$ respectively. In 1943, Hadwiger conjectured that $h(G) \geq \chi(G)$ for any graph $G$. In this paper, we will prove Hadwiger's Conjecture holds for $H$-free graphs with independence number two, where $H$ is any one of some given graphs.
Foray into the topology of poly‐bi‐[8]‐annulenylene

Analyzing phase transitions using the inherent geometrical attributes of a system has garnered enormous interest over the past few decades. The usual candidate often used for investigation is graphene—the most celebrated material among the family of tri‐coordinated graphed lattices. We show in this report that other inhabitants of the family demonstrate equally admirable structural and functional properties that at its core are controlled by their topology. Two interesting members of the family are cyclooctatrene (COT) and COT‐based polymer: poly‐bi‐[8]‐annulenylene, both in one and two dimensions that have been investigated by polymer chemists over a period of 50 years for its possible application in batteries exploiting its conducting properties. A single COT unit is demonstrated herein to exhibit topological solitons at sites of a broken bond similar to an open one‐dimensional Su–Schrieffer–Heeger (SSH) chain. We observe that poly‐bi‐[8]‐annulenylene in one dimension mimics two coupled SSH chains in the weak coupling limit, thereby showing the presence of topological edge modes. In the strong coupling limit, we investigate the different parameter values of our system for which we observe zero‐energy modes. Further, the application of an external magnetic field and its effects on the band flattening of the energy bands has also been studied. In two dimensions, poly‐bi‐[8]‐annulenylene forms a square‐octagon lattice which upon breaking time‐reversal symmetry goes into a topological phase forming noise‐resilient edge modes. We hope our analysis would pave the way for synthesizing such topological materials and exploiting their properties for promising applications in optoelectronics, photovoltaics, and renewable energy sources. We show in this paper tri‐coordinated lattice systems: cylooctatrene (COT) and COT‐based polymer: poly‐bi‐[8]‐annulenylene exhibit exotic topological properties. Flat bands are generated upon application of tailored magnetic flux for poly‐bi‐[8]‐annulenylene in one dimension. Insights from this paper open the possibility of using these polymers as an experimental ground to observe many flat‐band and topology‐related phenomena.
Robust Multigrid Methods for Discontinuous Galerkin Discretizations of an Elliptic Optimal Control Problem

We consider discontinuous Galerkin methods for an elliptic distributed optimal control problem, and we propose multigrid methods to solve the discretized system. We prove that the 𝑊-cycle algorithm is uniformly convergent in the energy norm and is robust with respect to a regularization parameter on convex domains. Numerical results are shown for both 𝑊-cycle and 𝑉-cycle algorithms.
Private Product Computation Using Quantum Entanglement

In this article, we show that a pair of entangled qubits can be used to compute a product privately. More precisely, two participants with a private input from a finite field can perform local operations on a shared, Bell-like quantum state, and when these qubits are later sent to a third participant, the third participant can determine the product of the inputs, but without learning more about the individual inputs. We give a concrete way to realize this product computation for arbitrary finite fields of prime order.
Towards a unitary formulation of quantum field theory in curved spacetime I: the case of de Sitter spacetime

Before we ask what is the theory of quantum gravity, it is a legitimate quest to formulate a robust quantum field theory in curved spacetime (QFTCS). Several conceptual problems have raised concerns over several decades, mainly because no S-matrix formulation is yet found in QFTCS. We argue that the institutional thinking of fixing a spacetime geometry, observers, light-cones and then quantizing the fields in that"intuitively", or"classically", fixed spacetime is the origin of the problem. In this paper, acknowledging the fact that"time"is a parameter in quantum theory, which is different from its status in the context of General Relativity (GR), we start with a"quantum first approach"and propose new formulation for QFTCS based on the discrete spacetime transformations ($\mathcal{C}\mathcal{P}\mathcal{T}$). Our framework for a QFTCS is built on a refined understanding of standard QFT S-matrix that explicitly reflects the $\mathcal{C}\mathcal{P}\mathcal{T}$ invariance of scattering amplitudes. We rewrite the standard QFT equipped with a direct-sum Fock space structure, that is explicitly $\mathcal{C}\mathcal{P}\mathcal{T}$ invariant. Applying this framework to QFTCS, in the context of de Sitter (dS) spacetime (in the flat FLRW coordinates), we elucidate how one can define a consistent S-matrix that is analogous to the QFT S-matrix in Minkowski spacetime. We discuss how this approach to quantization complies with the observer complementarity principle. We also comment on extending our quantization scheme to dS spacetime expressed in the closed FLRW coordinates. Furthermore, we discuss briefly the implications of our QFTCS approach for quantum gravity.
The Unified Framework for Modelling Credit Cycles with Marshall-Walras Price Formation Process And Systemic Risk Assessment

Systemic risk is a rapidly developing area of research. Classical financial models often do not adequately reflect the phenomena of bubbles, crises, and transitions between them during credit cycles. To study very improbable events, systemic risk methodologies utilise advanced mathematical and computational tools, such as complex systems, chaos theory, and Monte Carlo simulations. In this paper, a relatively simple mathematical formalism is applied to provide a unified framework for modeling credit cycles and systemic risk assessment. The proposed model is analyzed in detail to assess whether it can reflect very different states of the economy. Basing on those results, measures of systemic risk are constructed to provide information regarding the stability of the system. The formalism is then applied to describe the full credit cycle with the explanation of causal relationships between the phases expressed in terms of parameters derived from real-world quantities. The framework can be naturally interpreted and understood with respect to different economic situations and easily incorporated into the analysis and decision-making process based on classical models, significantly enhancing their quality and flexibility.
Autonomous Stabilization of Retinal Videos for Streamlining Assessment of Spontaneous Venous Pulsations

Spontaneous retinal Venous Pulsations (SVP) are rhythmic changes in the caliber of the central retinal vein and are observed in the optic disc region (ODR) of the retina. Its absence is a critical indicator of various ocular or neurological abnormalities. Recent advances in imaging technology have enabled the development of portable smartphone-based devices for observing the retina and assessment of SVPs. However, the quality of smartphone-based retinal videos is often poor due to noise and image jitting, which in return, can severely obstruct the observation of SVPs. In this work, we developed a fully automated retinal video stabilization method that enables the examination of SVPs captured by various mobile devices. Specifically, we first propose an ODR Spatio-Temporal Localization (ODR-STL) module to localize visible ODR and remove noisy and jittering frames. Then, we introduce a Noise-Aware Template Matching (NATM) module to stabilize high-quality video segments at a fixed position in the field of view. After the processing, the SVPs can be easily observed in the stabilized videos, significantly facilitating user observations. Furthermore, our method is cost-effective and has been tested in both subjective and objective evaluations. Both of the evaluations support its effectiveness in facilitating the observation of SVPs. This can improve the timely diagnosis and treatment of associated diseases, making it a valuable tool for eye health professionals.
Yquilibrium: A Theory for (Non-) Convex Economies

General equilibrium, the cornerstone of modern economics and finance, rests on assumptions many markets do not meet. Spectrum auctions, electricity markets, and cap-and-trade programs for resource rights often feature non-convexities in preferences or production that can cause non-existence of Walrasian equilibrium and render general equilibrium vacuous. Yquilibrium complements general equilibrium with an optimization approach to (non-) convex economies that does not require perfect competition. Yquilibrium coincides with Walrasian equilibrium when the latter exists. Yquilibrium exists even if Walrasian equilibrium ceases to and produces optimal allocations subject to linear, anonymous, and (approximately) utility-clearing prices.
First measurement of the $|t|$-dependence of incoherent J/$\psi$ photonuclear production

The first measurement of the cross section for incoherent photonuclear production of J/$\psi$ vector meson as a function of the Mandelstam $|t|$ variable is presented. The measurement was carried out with the ALICE detector at midrapidity, $|y|<0.8$, using ultra-peripheral collisions of Pb nuclei at a centre-of-mass energy per nucleon pair $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV. This rapidity interval corresponds to a Bjorken-$x$ range $(0.3$$-$$1.4)\times 10^{-3}$. Cross sections are reported in five $|t|$ intervals in the range $0.04<|t|<1$~GeV$^2$ and compared to the predictions of different models. Models that ignore quantum fluctuations of the gluon density in the colliding hadron predict a $|t|$-dependence of the cross section much steeper than in data. The inclusion of such fluctuations in the same models provides a better description of the data.
Orthogonal Transforms in Neural Networks Amount to Effective Regularization

We consider applications of neural networks in nonlinear system identification and formulate a hypothesis that adjusting general network structure by incorporating frequency information or other known orthogonal transform, should result in an efficient neural network retaining its universal properties. We show that such a structure is a universal approximator and that using any orthogonal transform in a proposed way implies regularization during training by adjusting the learning rate of each parameter individually. We empirically show in particular, that such a structure, using the Fourier transform, outperforms equivalent models without orthogonality support.
Tight information bounds for spontaneous-emission-lifetime resolution of quantum sources with varied spectral purity

We generalize the theory of resolving a mixture of two closely spaced spontaneous emission lifetimes to include pure dephasing contributions to decoherence, leading to the resurgence of Rayleigh's Curse at small lifetime separations. Considerable resolution enhancement remains possible when lifetime broadening is more significant than that due to pure dephasing. In the limit that lifetime broadening dominates, one can achieve super-resolution either by a tailored one-photon measurement or Hong-Ou-Mandel interferometry. We describe conditions for which either choice is superior.
Reference-based OCT Angiogram Super-resolution with Learnable Texture Generation

Optical coherence tomography angiography (OCTA) is a new imaging modality to visualize retinal microvasculature and has been readily adopted in clinics. High-resolution OCT angiograms are important to qualitatively and quantitatively identify potential biomarkers for different retinal diseases accurately. However, one significant problem of OCTA is the inevitable decrease in resolution when increasing the field-of-view given a fixed acquisition time. To address this issue, we propose a novel reference-based super-resolution (RefSR) framework to preserve the resolution of the OCT angiograms while increasing the scanning area. Specifically, textures from the normal RefSR pipeline are used to train a learnable texture generator (LTG), which is designed to generate textures according to the input. The key difference between the proposed method and traditional RefSR models is that the textures used during inference are generated by the LTG instead of being searched from a single reference image. Since the LTG is optimized throughout the whole training process, the available texture space is significantly enlarged and no longer limited to a single reference image, but extends to all textures contained in the training samples. Moreover, our proposed LTGNet does not require a reference image at the inference phase, thereby becoming invulnerable to the selection of the reference image. Both experimental and visual results show that LTGNet has superior performance and robustness over state-of-the-art methods, indicating good reliability and promise in real-life deployment. The source code will be made available upon acceptance.
Merging Rate of Opinions via Optimal Transport on Random Measures

The Dirichlet process has been pivotal to the development of Bayesian nonparametrics, allowing one to learn the law of the observations through closed-form expressions. Still, its learning mechanism is often too simplistic and many generalizations have been proposed to increase its flexibility, a popular one being the class of normalized completely random measures. Here we investigate a simple yet fundamental matter: will a different prior actually guarantee a different learning outcome? To this end, we develop a new framework for assessing the merging rate of opinions based on three leading pillars: i) the investigation of identifiability of completely random measures; ii) the measurement of their discrepancy through a novel optimal transport distance; iii) the establishment of general techniques to conduct posterior analyses, unravelling both finite-sample and asymptotic behaviour of the distance as the number of observations grows. Our findings provide neat and interpretable insights on the impact of popular Bayesian nonparametric priors, avoiding the usual restrictive assumptions on the data-generating process.