Miracle-dz/UniFAR-FTUs huggingface dataset:
Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie

Since the seminal work of Venkatakrishnan et al. [89] in 2013, Plug & Play (PnP) methods have become ubiquitous in Bayesian imaging. These methods derive Minimum Mean Square Error (MMSE) or Maximum A Posteriori (MAP) estimators for inverse problems in imaging by combining an explicit likelihood function with a prior that is implicitly defined by an image denoising algorithm. The PnP algorithms proposed in the literature mainly differ in the iterative schemes they use for optimisation or for sampling. In the case of optimisation schemes, some recent works guarantee the convergence to a fixed point, albeit not necessarily a MAP estimate. In the case of sampling schemes, to the best of our knowledge, there is no known proof of convergence. There also remain important open questions regarding whether the underlying Bayesian models and estimators are well defined, well-posed, and have the basic regularity properties required to support these numerical schemes. To address these limitations, this paper develops theory, methods, and provably convergent algorithms for performing Bayesian inference with PnP priors. We introduce two algorithms: 1) PnPULA (Plug & Play Unadjusted Langevin Algorithm) for Monte Carlo sampling and MMSE inference; and 2) PnP-SGD (Plug & Play Stochastic Gradient Descent) for MAP inference. Using recent results on the quantitative convergence of Markov chains, we establish detailed convergence guarantees for these two algorithms under realistic assumptions on the denoising operators used, with special attention to denoisers based on deep neural networks. We also show that these algorithms approximately target a decision-theoretically optimal Bayesian model that is well-posed. The proposed algorithms are demonstrated on several canonical problems such as image deblurring, inpainting, and denoising, where they are used for point estimation as well as for uncertainty visualisation and quantification. ∗VDB was partially supported by EPSRC grant EP/R034710/1. RL was partially supported by grants from Région Ile-De-France. AD acknowledges support of the Lagrange Mathematical and Computing Research Center. MP was partially supported by EPSRC grant EP/T007346/1. JD and AA acknowledge support from the French Research Agency through the PostProdLEAP project (ANR-19-CE23-0027-01). Computer experiments for this work ran on a Titan Xp GPU donated by NVIDIA, as well as on HPC resources from GENCI-IDRIS (Grant 2020-AD011011641). †These authors contributed equally ‡Université de Paris, MAP5 UMR 8145, F-75006 Paris, France §Department of Statistics University of Oxford 24-29 St Giles OX1 3LB, Oxford United Kingdom ¶Institut Universitaire de France (IUF) ‖Centre Borelli, UMR 9010, École Normale Supérieure Paris-Saclay ∗∗School of Mathematical and Computer Sciences, Heriot-Watt University & Maxwell Institute for Mathematical Sciences, Edinburgh, United Kingdom 1 ar X iv :2 10 3. 04 71 5v 4 [ st at . M E ] 1 9 M ar 2 02 1
High-sensitivity electrochemical dual-QCM for reliable three-electrode measurements

Electrochemical quartz crystal microbalance (EC-QCM) is a versatile gravimetric technique that allows for parallel characterization of mass deposition and electrochemical properties. Despite its broad applicability, simultaneous characterization of two electrodes remains challenging due to practical difficulties posed by the dampening from fixture parasitics and the dissipative medium. In this study, we present a dual electrochemical QCM (dual EC-QCM) that is employed in a three-electrode configuration to enable consequent monitoring of mass deposition and viscous loading on two crystals, the working electrode (WE) and the counter electrode (CE). A novel cor-rection approach along with a three standard complex impedance calibration is employed to overcome the effect of dampening while keeping high spectral sensitivity. Separation of viscous loading and rigid mass deposition is achieved by robust characterization
Analysis of the ultraviolet absorption cross sections of six isotopically substituted nitrous oxide species using 3D wave packet propagation

The ultraviolet absorption cross sections of six isotopically substituted nitrous oxide species ( 1 4 N 1 4 N 1 6 O, 1 4 N 1 4 N 1 7 O, 1 4 N 1 4 N 1 8 O, 1 4 N 1 5 N 1 6 O, 1 5 N 1 4 N 1 6 O, and 1 5 N 1 5 N 1 6 O) were computed using the wave packet propagation technique to explore the influence of excited-state dynamics, transition dipole surface, and initial vibrational state. Three-dimensional potential energy surfaces for the electronic states of N 2 O related to the experimentally observed photoabsorption between 170 and 220 nm were calculated using the ab initio molecular orbital configuration interaction method. The transition dipole moment surfaces between these states were also calculated. Numerous wave packet simulations were carried out and used to calculate the temperature-dependent photodissociation cross sections of the six isotopically substituted species. The photolytic isotopic fractionation constants determined using the calculated cross sections are in good agreement with recent experiments. The results show that, in addition to the effect of the changed shape of the ground-state vibrational wave function with isotopic substitution, photodissociation dynamics play a central role in determining isotopic fractionation constants.
Classification of minimal Z2×Z2-graded Lie (super)algebras and some applications

This paper presents the classification, over the fields of real and complex numbers, of the minimal Z2 × Z2-graded Lie algebras and Lie superalgebras spanned by 4 generators and with no empty graded sector. The inequivalent graded Lie (super)algebras are obtained by solving the constraints imposed by the respective graded Jacobi identities. A motivation for this mathematical result is to systematically investigate the properties of dynamical systems invariant under graded (super)algebras. Recent works only paid attention to the special case of the one-dimensional Z2×Z2-graded Poincaré superalgebra. As applications, we are able to extend certain constructions originally introduced for this special superalgebra to other listed Z2 × Z2-graded (super)algebras. We mention, in particular, the notion of Z2 × Z2-graded superspace and of invariant dynamical systems (both classical worldline sigma models and quantum Hamiltonians). As a further byproduct we point out that, contrary to Z2 × Z2graded superalgebras, a theory invariant under a Z2×Z2-graded algebra implies the presence of ordinary bosons and three different types of exotic bosons, with exotic bosons of different types anticommuting among themselves.
Estimating Lifetimes of UV-selected Massive Galaxies at 0.5 ≤ z ≤ 2.5 in the COSMOS/UltraVISTA Field through Clustering Analyses

To investigate the lifetimes of red sequence (RS), blue cloud (BC), and green valley (GV) galaxies, we derive their lifetimes using clustering analyses at 0.5 ≤ z ≤ 2.5 in the COSMOS/UltraVISTA field. Several essentials that may influence the lifetime estimation have been explored, including the dark matter (DM) halo mass function (HMF), the width of the redshift bin, the growth of DM halos within each redshift bin, and the stellar mass. We find that the HMF difference results in scatters of ∼0.2 dex on the lifetime estimation, adopting a redshift bin width of Δz = 0.5 is good enough to estimate the lifetime, and no significant effect on lifetime estimation is found due to the growth of DM halos within each redshift bin. The galaxy subsamples with higher stellar masses generally have shorter lifetimes, but the lifetimes in different subsamples at z > 1.5 tend to be independent of stellar mass. Consistently, the clustering-based lifetime for each galaxy subsample agrees well with that inferred using the spectral energy distribution modeling. Moreover, the lifetimes of the RS and BC galaxies also coincide well with their typical gas-depletion timescales attributed to the consumption of star formation. Interestingly, the distinct lifetime behaviors of the GV galaxies at z ≤ 1.5 and z > 1.5 cannot be fully accounted for by their gas-depletion timescales. Instead, this discrepancy between the lifetimes and gas-depletion timescales of the GV galaxies suggests that there are additional physical processes, such as feedback of active galactic nuclei, which accelerates the quenching of GV galaxies at high redshifts.
Strong Approximate Consensus Halving and the Borsuk-Ulam Theorem

In the consensus halving problem we are given n agents with valuations over the interval $[0,1]$. The goal is to divide the interval into at most $n+1$ pieces (by placing at most n cuts), which may be combined to give a partition of $[0,1]$ into two sets valued equally by all agents. The existence of a solution may be established by the Borsuk-Ulam theorem. We consider the task of computing an approximation of an exact solution of the consensus halving problem, where the valuations are given by distribution functions computed by algebraic circuits. Here approximation refers to computing a point that $\varepsilon$-close to an exact solution, also called strong approximation. We show that this task is polynomial time equivalent to computing an approximation to an exact solution of the Borsuk-Ulam search problem defined by a continuous function that is computed by an algebraic circuit. The Borsuk-Ulam search problem is the defining problem of the complexity class BU. We introduce a new complexity class BBU to also capture an alternative formulation of the Borsuk-Ulam theorem from a computational point of view. We investigate their relationship and prove several structural results for these classes as well as for the complexity class FIXP.
Discovering Multiple Phases of Dynamics by Dissecting Multivariate Time Series

We proposed a data-driven approach to dissect multivariate time series in order to discover multiple phases underlying dynamics of complex systems. This computing approach is developed as a multiple-dimension version of Hierarchical Factor Segmentation(HFS) technique. This expanded approach proposes a systematic protocol of choosing various extreme events in multi-dimensional space. Upon each chosen event, an empirical distribution of event-recurrence, or waiting time between the excursions, is fitted by a geometric distribution with time-varying parameters. Iterative fittings are performed across all chosen events. We then collect and summarize the local recurrent patterns into a global dynamic mechanism. Clustering is applied for partitioning the whole time period into alternating segments, in which variables are identically distributed. Feature weighting techniques are also considered to compensate for some drawbacks of clustering. Our simulation results show that this expanded approach can even detect systematic differences when the joint distribution varies. In real data experiments, we analyze the relationship from returns, trading volume, and transaction number of a single, as well as of multiple stocks in S&P500. We can successfully not only map out volatile periods but also provide potential associative links between stocks.
Stochasticity helps to navigate rough landscapes: comparing gradient-descent-based algorithms in the phase retrieval problem

In this paper we investigate how gradient-based algorithms such as gradient descent (GD), (multi-pass) stochastic GD, its persistent variant, and the Langevin algorithm navigate non-convex loss-landscapes and which of them is able to reach the best generalization error at limited sample complexity. We consider the loss landscape of the high-dimensional phase retrieval problem as a prototypical highly non-convex example. We observe that for phase retrieval the stochastic variants of GD are able to reach perfect generalization for regions of control parameters where the GD algorithm is not. We apply dynamical mean-field theory from statistical physics to characterize analytically the full trajectories of these algorithms in their continuous-time limit, with a warm start, and for large system sizes. We further unveil several intriguing properties of the landscape and the algorithms such as that the GD can obtain better generalization properties from less informed initializations.
Assessment of leachates from a Cuban municipal solid waste landfill: characterisation and treatment

Calle 100 landfill receives 75% of the solid waste of Havana. In this work, the physical-chemical and microbiological evaluation and the treatment of its leachates was carried out. The study of the elimination of pollutants was carried out at laboratory scale. The characterisation showed an important content in organic substances of high molecular weight, fulvic and humic acids that have a toxic character. The use of anaerobic filter at low organic charge (3 kg/m3.day) allows fulfilling the Cuban discharge guideline, but at high organic charge the filter is unable to eliminate the organic pollution. In the case of the use of ozone, there was an increase of the biodegradability because BOD5/COD ratio increases from 0.30 up to 0.45; ozonation also allows a material solubilisation process. The best results were obtained when advanced primary treatment followed by ozonation and anaerobic filter was used. This treatment scheme allows a reduction of 60% in turbidity, colour, optical density at 254 nm and chemical oxygen demand and a decrease higher than 99.99% for coliforms. The economic estimate shows a cost of 1.4 USD/m3.
Semianalyitcal synthesis scheme for multifunctional metasurfaces on demand

We propose a comprehensive field-based semianalytical method for designing fabrication-ready multifunctional periodic metasurfaces (MSs). Harnessing recent work on multielement metagratings based on capacitively-loaded strips, we have extended our previous meta-atom design formulation to generate realistic substrate-supported printed-circuit-board layouts for anomalous refraction MSs. Subsequently, we apply a greedy algorithm for iteratively optimizing individual scatterers across the entire macroperiod to achieve multiple design goals for corresponding multiple incidence angles with a single MS structure. As verified with commercial solvers, the proposed semianalytical scheme, properly accounting for near-field coupling between the various scatterers, can reliably produce highly efficient multifunctional MSs on demand, without requiring time-consuming full-wave optimization.
Active-Set Identification with Complexity Guarantees of an Almost Cyclic 2-Coordinate Descent Method with Armijo Line Search

In this paper, it is established finite active-set identification of an almost cyclic 2-coordinate descent method for problems with one linear coupling constraint and simple bounds. First, general active-set identification results are stated for non-convex objective functions. Then, under convexity and a quadratic growth condition (satisfied by any strongly convex function), complexity results on the number of iterations required to identify the active set are given. In our analysis, a simple Armijo line search is used to compute the stepsize, thus not requiring exact minimizations or additional information.
Robust noncoplanar magnetism in band-filling-tuned (
Nd1−xCax)2Mo2O7

In the metallic pyrochlore Nd2Mo2O7, the conducting Molybdenum sublattice adopts canted, yet nearly collinear ferromagnetic order with nonzero scalar spin chirality. The chemical potential may be controlled by replacing Nd3+ with Ca2+, while introducing only minimal additional disorder to the conducting states. Here, we demonstrate the stability of the canted ferromagnetic state, including the tilting angle of Molybdenum spins, in (Nd1−xCax)2Mo2O7 (NCMO) with x ≤ 0.15 using magnetic susceptibility measurements. Mo-Mo and Mo-Nd magnetic couplings both change sign above x = 0.22, where the canted ferromagnetic state gives way to a spin-glass metallic region. Contributions to the Curie-Weiss law from two magnetic sublattices are separated systematically. ∗ hirschberger@ap.t. u-tokyo.ac. jp 1 ar X iv :2 10 3. 04 29 5v 1 [ co nd -m at . m tr lsc i] 7 M ar 2 02 1
A H\"ormander-Mikhlin multiplier theory for free groups and amalgamated free products of von Neumann algebras

Abstract. We establish a platform to transfer Lp-completely bounded maps on tensor products of von Neumann algebras to Lp-completely bounded maps on the corresponding amalgamated free products. As a consequence, we obtain a Hörmander-Mikhlin multiplier theory for free products of groups. Let F∞ be a free group on infinite generators {g1, g2, · · · }. Given d ≥ 1 and a bounded symbol m on Z satisfying the classical Hörmander-Mikhlin condition, the linear map Mm : C[F∞] → C[F∞] defined by λ(g) 7→ m(k1, · · · , kd)λ(g) for g = g k1 i1 · · · gn in ∈ F∞ in reduced form (with kl = 0 in m(k1, · · · , kd) for l > n), extends to a complete bounded map on Lp(F̂∞) for all 1 < p < ∞, where F̂∞ is the group von Neumann algebra of F∞. A similar result holds for any free product of discrete groups.
T-Miner: A Generative Approach to Defend Against Trojan Attacks on DNN-based Text Classification

Deep Neural Network (DNN) classifiers are known to be vulnerable to Trojan or backdoor attacks, where the classifier is manipulated such that it misclassifies any input containing an attacker-determined Trojan trigger. Backdoors compromise a model's integrity, thereby posing a severe threat to the landscape of DNN-based classification. While multiple defenses against such attacks exist for classifiers in the image domain, there have been limited efforts to protect classifiers in the text domain. We present Trojan-Miner (T-Miner) -- a defense framework for Trojan attacks on DNN-based text classifiers. T-Miner employs a sequence-to-sequence (seq-2-seq) generative model that probes the suspicious classifier and learns to produce text sequences that are likely to contain the Trojan trigger. T-Miner then analyzes the text produced by the generative model to determine if they contain trigger phrases, and correspondingly, whether the tested classifier has a backdoor. T-Miner requires no access to the training dataset or clean inputs of the suspicious classifier, and instead uses synthetically crafted "nonsensical" text inputs to train the generative model. We extensively evaluate T-Miner on 1100 model instances spanning 3 ubiquitous DNN model architectures, 5 different classification tasks, and a variety of trigger phrases. We show that T-Miner detects Trojan and clean models with a 98.75% overall accuracy, while achieving low false positives on clean models. We also show that T-Miner is robust against a variety of targeted, advanced attacks from an adaptive attacker.
Student-Teacher Feature Pyramid Matching for Unsupervised Anomaly Detection

Anomaly detection is a challenging task and usually formulated as an unsupervised learning problem for the unex-pectedness of anomalies. This paper proposes a simple yet powerful approach to this issue, which is implemented in the student-teacher framework for its advantages but substantially extends it in terms of both accuracy and efﬁciency. Given a strong model pre-trained on image classiﬁcation as the teacher, we distill the knowledge into a single student network with the identical architecture to learn the distribution of anomaly-free images and this one-step transfer preserves the crucial clues as much as possible. Moreover, we integrate the multi-scale feature matching strategy into the framework, and this hierarchical feature alignment enables the student network to receive a mixture of multi-level knowledge from the feature pyramid under better supervision, thus allowing to detect anomalies of various sizes. The difference between feature pyramids generated by the two networks serves as a scoring function indicating the probability of anomaly occurring. Due to such operations, our approach achieves accurate and fast pixel-level anomaly detection. Very competitive results are delivered on three major benchmarks, signiﬁcantly superior to the state of the art ones. In addition, it makes inferences at a very high speed (with 100 FPS for images of the size at 256 × 256), at least dozens of times faster than the latest counterparts.
Multicolour photometry and Gaia EDR3 astrometry of two couples of binary clusters (NGC 5617 and Trumpler 22) and (NGC 3293 and NGC 3324)

This paper presents a comprehensive analysis of two pairs of binary clusters (NGC 5617 and Trumpler 22) and (NGC 3293 and NGC 3324) located in the fourth quadrant of our Galaxy. For this purpose we use different data taken from VVV survey, WISE, VPHAS, APASS, GLIMPSE along with Gaia~EDR3 astrometric data. We identified 584, 429, 692 and 273 most probable cluster members with membership probability higher than 80 % towards the region of clusters NGC 5617, Trumpler 22, NGC 3293 and NGC 3324. We estimated the value of R as ~ 3.1 for clusters NGC 5617 and Trumpler 22, which indicates normal extinction law. The value of R ~ 3.8 and 1.9 represent the abnormal extinction law towards the clusters NGC 3293 and NGC 3324. Our Kinematical analysis show that all these clusters have circular orbits. Ages are found to be 90\pm10 and 12\pm3 Myr for the cluster pairs (NGC 5617 and Trumpler 22) and (NGC 3293 and NGC 3324), respectively. The distances of 2.43\pm0.08, 2.64\pm0.07, 2.59\pm0.1 and 2.80\pm0.2 kpc estimated using parallax are alike to the values calculated by using the distance modulus. We have also identified 18 and 44 young stellar object candidates present in NGC 5617 and Trumpler 22, respectively. Mass function slopes are found to be in fair agreement with the Salpeter's value. The dynamical study of these objects shows a lack of faint stars in their inner regions, which leads to the mass-segregation effect. Our study indicates that NGC 5617 and Trumpler 22 are dynamically relaxed but the other pair of clusters are not. Orbital alongwith the physical parameters show that the clusters in both pairs are physically connected.
Noisy Label Learning for Large-scale Medical Image Classification

The classiﬁcation accuracy of deep learning models depends not only on the size of their training sets, but also on the quality of their labels. In medical image classiﬁcation, large-scale datasets are becoming abundant, but their labels will be noisy when they are automatically extracted from radiology reports using natural language processing tools. Given that deep learning models can easily overﬁt these noisy-label samples, it is important to study training approaches that can handle label noise. In this paper, we adapt a state-of-the-art (SOTA) noisy-label multi-class training approach to learn a multi-label classiﬁer for the dataset Chest X-ray14, which is a large scale dataset known to contain label noise in the training set. Given that this dataset also has label noise in the testing set, we propose a new theoretically sound method to estimate the performance of the model on a hidden clean testing data, given the result on the noisy testing data. Using our clean data performance estimation, we notice that the majority of label noise on Chest X-ray14 is present in the class ’No Finding’, which is intuitively correct because this is the most likely class to contain one or more of the 14 diseases due to labelling mistakes.