Miracle-dz/UniFAR-FTUs huggingface dataset:
Neural Posterior Regularization for Likelihood-Free Inference

A simulation is useful when the phenomenon of interest is either expensive to regenerate or irreproducible with the same context. Recently, Bayesian inference on the distribution of the simulation input parameter has been implemented sequentially to minimize the required simulation budget for the task of simulation validation to the real-world. However, the Bayesian inference is still challenging when the ground-truth posterior is multi-modal with a high-dimensional simulation output. This paper introduces a regularization technique, namely Neural Posterior Regularization (NPR), which enforces the model to explore the input parameter space e ﬀ ectively. Afterward, we provide the closed-form solution of the regularized optimization that enables analyzing the e ﬀ ect of the regularization. We empirically validate that NPR attains the statistically signiﬁcant gain on benchmark performances for diverse simulation tasks.
An anomaly detector with immediate feedback to hunt for planets of Earth mass and below by microlensing

The discovery of OGLE 2005-BLG-390Lb, the first cool rocky/i cy exoplanet, impressively demonstrated the sensitivity of the microlensing technique to extra-solar planets below 10 M�. A planet of 1 Minstead of the expected 5 Mfor OGLE 2005-BLG-390Lb (with an uncertainty factor of two) in the same spot would have provided a detectable deviation with an amplitude of � 3 per cent and a duration of � 12 h. While a standard sampling interval of 1.5 to 2.5 hours for microlensing follow-up observations appears to be insuffi- cient for characterizing such light curve anomalies and thereby claiming the discovery of the planets that caused these, an early detection of a deviation could trigger higher-cadence sam- pling which would have allowed the discovery of an Earth-mass planet in this case. Here, we describe the implementation of an automated anomaly detector, embedded into the eSTAR system, that profits from immediate feedback provided by the robotic telescopes that form the RoboNet-1.0 network. It went into operation for the 2007 microlensing observing season. As part of our discussion about an optimal strategy for planet detection, we shed some new light on whether concentrating on highly-magnified events i s promising and planets in the 'resonant' angular separation equal to the angular Einstei n radius are revealed most easily. Given that sub-Neptune mass planets can be considered being common around the host stars probed by microlensing (preferentially M- and K-dwarfs), the higher number of events that can be monitored with a network of 2m telescopes and the increased detection efficiency for planets below 5 Marising from an optimized strategy gives a common effort of current mi- crolensing campaigns a fair chance to detect an Earth-mass planet (from the ground) ahead of the COROT or Kepler missions. The detection limit of gravitational microlensing extends even below 0.1 M�, but such planets are not very likely to be detected from current cam- paigns. However, these will be within the reach of high-cadence monitoring with a network of wide-field telescopes or a space-based telescope.
A Note on Free Idempotent Generated Semigroups over the Full Monoid of Partial Transformations

Recently, Gray and Ru\v skuc proved that if e is a rank k idempotent transformation of the set {1,…, n} to itself and k ≤ n − 2, then the maximal subgroup of the free idempotent generated semigroup over the full transformation monoid 𝒯 n containing e is isomorphic to the symmetric group 𝒮 k . We prove that the same holds when 𝒯 n is replaced by 𝒫𝒯 n , the full monoid of partial transformations on {1,…, n}.
The averaged characteristic polynomial for the Gaussian and chiral Gaussian ensembles with a source

In classical random matrix theory the Gaussian and chiral Gaussian random matrix models with a source are realized as shifted mean Gaussian, and chiral Gaussian, random matrices with real (β = 1), complex (β = 2) and real quaternion (β = 4) elements. We use the Dyson Brownian motion model to give a meaning for general β > 0. In the Gaussian case a further construction valid for β > 0 is given, as the eigenvalue PDF of a recursively defined random matrix ensemble. In the case of real or complex elements, a combinatorial argument is used to compute the averaged characteristic polynomial. The resulting functional forms are shown to be special cases of duality formulas due to Desrosiers. New derivations of the general case of Desrosiers' dualities are given. A soft edge scaling limit of the averaged characteristic polynomial is identified, and an explicit evaluation in terms of so-called incomplete Airy functions is obtained.
Nonlinear perturbations of a p(x) ‐Laplacian equation with critical growth in RN

We prove the existence of solution for a class of p(x) ‐Laplacian equations where the nonlinearity has a critical growth. Here, we consider two cases: the first case involves the situation where the variable exponents are periodic functions. The second one involves the case where the variable exponents are nonperiodic perturbations.
Partial separatrices and local Brunella's alternative

Here we state a conjecture concerning a local version of Brunella's alternative: any codimension one foliation in $({\mathbb C}^3,0)$ without germ of invariant surface has a neighborhood of the origin formed by leaves containing a germ of analytic curve at the origin. We prove the conjecture for the class of codimension one foliations whose reduction of singularities is obtained by blowing-up points and curves of equireduction and such that the final singularities are free of saddle-nodes. The concept of "partial separatrix" for a given reduction of singularities has a central role in our argumentations, as well as the quantitative control of the generic Camacho-Sad index in dimension three. The "nodal components" are the only possible obstructions to get such germs of analytic curves. We use the partial separatrices to push the leaves near a nodal component towards compact diacritical divisors, finding in this way the desired analytic curves.
On mixed multiplicities of ideals

Let R be the local ring of a point on a variety X over an algebraically closed field k. We make a connection between the notion of mixed (Samuel) multiplicity of m-primary ideals in R and intersection theory of subspaces of rational functions on X which deals with the number of solutions of systems of equations. From this we readily deduce several properties of mixed multiplicities. In particular, we prove a (reverse) Alexandrov-Fenchel inequality for mixed multiplicities due to Teissier and Rees-Sharp. As an application in convex geometry we obtain a proof of a (reverse) Alexandrov-Fenchel inequality for covolumes of convex bodies inscribed in a convex cone.
GLOBULAR CLUSTERS IN THE OUTER GALACTIC HALO: AM-1 AND PALOMAR 14

AM-1, at ∼120 kpc, and Palomar 14 (Pal 14), at ∼70 kpc, are two of the most distant Galactic globular clusters (GCs) known. We present Hubble Space Telescope Wide Field Planetary Camera 2 photometry of AM-1 and Pal 14 that reveals unprecedented depth and detail in the color–magnitude diagrams of these two clusters. Absolute and relative age measurements confirm that both are younger than the inner halo GC M 3 by 1.5–2 Gyr assuming all three clusters have similar compositions. Thus AM-1 and Pal 14 join Pal 3, Pal 4, and Eridanus as distant GCs with red horizontal branches (HBs) and young ages relative to the inner halo. Within the context of the entire body of research on the ages of second parameter GCs, the observed correlation between age and HB morphology suggests that age is the best candidate for the second parameter. However, this conclusion is tempered by the lack of precise chemical abundance determinations for a significant fraction of second parameter GCs.
Characterization of the structural, oxidative, and immunological features of testis tissue from Zucker diabetic fatty rats

Abstract The purpose of this study was to characterize the testicular profile of Zucker diabetic fatty (ZDF) rats presenting with type 2 diabetes mellitus (DM2) in the absence or presence of obesity. To achieve this, testes were collected from 270-day-old male Wistar (n = 15), ZDF nonobese (n = 15), and ZDF obese rats (n = 16). Changes to the testicular structure were quantified morphometrically, while immunocytochemistry was employed to assess caspase-3 activity. Reactive oxygen species (ROS) production, fluctuations of major antioxidant molecules, and the extent of damage to the proteins and lipids were assessed in tissue lysates. Levels of selected interleukins (ILs) were determined by enzyme-linked immunosorbent assay. The results reveal significant alterations to the testicular structure accompanied by caspase-3 overexpression, particularly in ZDF obese rats. The most notable disruption of the oxidative balance, characterized by ROS overproduction, antioxidant deficiency, protein, and lipid deterioration was recorded in ZDF rats suffering from both DM2 and obesity. Accordingly, the highest concentrations of pro-inflammatory IL-1, IL-6, and IL-18 accompanied by reduced levels of the anti-inflammatory IL-10 were found in testicular tissue collected from ZDF obese rats. This study highlights the vulnerability of male gonads to pathophysiological changes caused by hyperglycemia, which are further exacerbated by excessive adipose tissue.
On Borel hull operations

We show that some set-theoretic assumptions (for example Martin's Axiom) imply that there is no translation invariant Borel hull operation on the family of Lebesgue null sets and on the family of meager sets in (in R^n). We also prove that if the meager ideal admits a monotone Borel hull operation, then there is also a monotone Borel hull operation on the sigma-algebra of sets with the property of Baire.
Computing the entropy of a large matrix

Given a large real symmetric, positive semidefinite matrix, the goal of this paper is to show how a numerical approximation of the von Neumann entropy of the matrix can be computed in an efficient way, without relying on matrix diagonalization. An application from quantum optics dealing with the entanglement between photons illustrates the new algorithm.
How reliable are Coupled Model Intercomparison Project Phase 6 models in representing the Asian summer monsoon anticyclone?

We assess the Asian summer monsoon anticyclone (ASMA) in Coupled Model Intercomparison Project Phase 6 (CMIP6) models for the historical period (1850–2014). The ASMA is a quasi‐stationary warm anticyclone during the boreal summer monsoon season, centred around Tibet. It is a prominent circulation feature that affects trace species transport, stratosphere–troposphere exchange, along with strong feedbacks to weather and climate. The study is a novel attempt to quantify the performance of models participating in the CMIP6 consortium and understand long‐term variability and teleconnections of the ASMA. We note that CMIP6 models capture the mean ASMA features reasonably well, albeit with some differences around the edges. For most of the models, interannual variations are not in phase with the reanalysis and show sharper increasing trend in the ASMA strength. There is about a twofold increase in the trends during the recent period (1980–2014) as compared to the 1950–2014 period. A multimodel mean (MME) chosen based upon the statistical metrics (mean, standard deviation, mean absolute error and root‐mean‐square error), target diagram, and density distributions is further used to examine the prominent modes of variability. Our results suggest that the signals of significant periodicity, particularly the 2–4 years signal, and the SST correlations in MME are inconsistent with observations. In CMIP6 models, we note stronger upper level divergence over the western and eastern Pacific but convergence over the Indian ocean, South Asia and the central Pacific. The streamfunction and rotational winds also show strong highs north of 20°N. Overall, it is seen that basic features such as spatial extent and evolution of ASMA are reasonably captured, but the strength and interannual variations are dissonant across the CMIP6 models. These findings are useful for studies focusing on regional meteorology, transportation of atmospheric tracers and climate change projections over the region involving the ASMA.
Symmetry results for stable and monotone solutions to fibered systems of PDEs

We study the symmetry properties for solutions of elliptic systems of the type where x ∈ ℝm with 1 ≤ m < N, X = (x, y) ∈ ℝm × ℝN-m, and F1,…,Fn are the derivatives with respect to ξ1,…,ξn of some F = F(x,ξ1,…,ξn) such that for any i = 1,…,n and any fixed (x,ξ1,…,ξi-1,ξi+1,…,ξn) ∈ ℝm × ℝn-1 the map ξi → F(x,ξ1,…,ξi,…,ξn) belongs to C2(ℝ). We obtain a Poincare-type formula for the solutions of the system and we use it to prove a symmetry result both for stable and for monotone solutions.
Multiple populations in ω Centauri: a cluster analysis of spectroscopic data

ω Centauri, the largest globular cluster of the Milky Way, is composed of several stellar populations, which can be seen in both photometry and spectroscopy. The history of how these different populations assembled will allow us to reconstruct the evolution of this complex object. In particular, understanding the detailed chemical evolution will be particularly illuminating. However, this is not easy because of the errors intrinsic to abundance determinations. We performed a statistical cluster analysis on the large data set of accurate abundances recently provided for about 800 red giant branch stars. We find that stars in ω Cen divide into three main groups. The metal-poor group includes about a third of the total. It shows a moderate O-Na anticorrelation, and similar to other clusters, the O-poor second generation stars are more centrally concentrated than the O-rich first generation ones. This whole population is La-poor, with a pattern of abundances for n-capture elements that is very close to a scaled r-process one. The metal-intermediate group includes the majority of the cluster stars. This is a much more complex population, with an internal spread in the abundances of most elements. It shows an extreme O-Na anticorrelation, with a very numerous population of extremely O-poor and He-rich second generation stars. This second generation is very centrally concentrated. This whole population is La-rich, with a pattern of the abundances of n-capture elements that shows a strong contribution by the s-process. The spread in metallicity within this metalintermediate population is not very large, and we can attribute it either to non-uniformities of an originally very extended star-forming region, or to some ability to retain a fraction of the ejecta of the core-collapse SNe that exploded first, or both. As previously noticed, the metal-rich group has an Na-O correlation rather than anticorrelation. There is evidence for the contribution of both massive stars ending their life as core-collapse SNe, and intermediate/low mass stars, producing the s-capture elements. Kinematics of this population suggests that it formed within the cluster rather than being accreted.
The Divisor Function in Arithmetic Progressions to Smooth Moduli

By using the $q$-analogue of van der Corput's method we study the divisor function in an arithmetic progression to modulus $q$. We show that the expected asymptotic formula holds for a larger range of $q$ than was previously known, provided that $q$ has a certain factorisation.
TRACER: Signature-based Static Analysis for Detecting Recurring Vulnerabilities

Similar software vulnerabilities recur because developers reuse existing vulnerable code, or make similar mistakes when implementing the same logic. Recently, various analysis techniques have been proposed to find syntactically recurring vulnerabilities via code reuse. However, limited attention has been devoted to semantically recurring ones that share the same vulnerable behavior in different code structures. In this paper, we present a general analysis framework, called TRACER, for detecting such recurring vulnerabilities. TRACER is based on a taint analysis that can detect various types of vulnerabilities. For a given set of known vulnerabilities, the taint analysis extracts vulnerable traces and establishes a signature database of them. When a new unseen program is analyzed, TRACER compares all potentially vulnerable traces reported by the analysis with the known vulnerability signatures. Then, TRACER reports a list of potential vulnerabilities ranked by the similarity score. We evaluate TRACER on 273 Debian packages in C/C++. Our experiment results demonstrate that TRACER is able to find 281 previously unknown vulnerabilities with 6 CVE identifiers assigned.
Vertex operator algebras associated to modular invariant representations for $A_1 ^{(1)}$

We investigate vertex operator algebras $L(k,0)$ associated with modular-invariant representations for an affine Lie algebra $A_1 ^{(1)}$ , where k is 'admissible' rational number. We show that VOA $L(k,0)$ is rational in the category $\cal O$ and find all irreducible representations in the category of weight modules.
A general approach to Read's type constructions of operators without non‐trivial invariant closed subspaces

We present a general method for constructing operators without non‐trivial invariant closed subsets on a large class of non‐reflexive Banach spaces. In particular, our approach unifies and generalizes several constructions due to Read of operators without non‐trivial invariant subspaces on the spaces ℓ1 , c0 or ⨁ℓ2J , and without non‐trivial invariant subsets on ℓ1 . We also investigate how far our methods can be extended to the Hilbertian setting, and construct an operator on a quasi‐reflexive dual Banach space which has no non‐trivial w* ‐closed invariant subspace.
Towards Automated Safety Vetting of Smart Contracts in Decentralized Applications

We propose VetSC, a novel UI-driven, program analysis guided model checking technique that can automatically extract contract semantics in DApps so as to enable targeted safety vetting. To facilitate model checking, we extract business model graphs from contract code that capture its intrinsic business and safety logic. To automatically determine what safety specifications to check, we retrieve textual semantics from DApp user interfaces. To exclude untrusted UI text, we also validate the UI-logic consistency and detect any discrepancies. We have implemented VetSC and applied it to 34 real-world DApps. Experiments have demonstrated that VetSC can accurately interpret smart contract code, enable autonomous safety vetting, and discover safety risks in real-world Dapps. Using our tool, we have successfully discovered 19 new safety risks in the wild, such as expired lottery tickets and double voting.
Feature Inference Attack on Shapley Values

As a solution concept in cooperative game theory, Shapley value is highly recognized in model interpretability studies and widely adopted by the leading Machine Learning as a Service (MLaaS) providers, such as Google, Microsoft, and IBM. However, as the Shapley value-based model interpretability methods have been thoroughly studied, few researchers consider the privacy risks incurred by Shapley values, despite that interpretability and privacy are two foundations of machine learning (ML) models. In this paper, we investigate the privacy risks of Shapley value-based model interpretability methods using feature inference attacks: reconstructing the private model inputs based on their Shapley value explanations. Specifically, we present two adversaries. The first adversary can reconstruct the private inputs by training an attack model based on an auxiliary dataset and black-box access to the model interpretability services. The second adversary, even without any background knowledge, can successfully reconstruct most of the private features by exploiting the local linear correlations between the model inputs and outputs. We perform the proposed attacks on the leading MLaaS platforms, i.e., Google Cloud, Microsoft Azure, and IBM aix360. The experimental results demonstrate the vulnerability of the state-of-the-art Shapley value-based model interpretability methods used in the leading MLaaS platforms and highlight the significance and necessity of designing privacy-preserving model interpretability methods in future studies. To our best knowledge, this is also the first work that investigates the privacy risks of Shapley values.
Gap Detection in Pairs of Ultrasound Mid-air Vibrotactile Stimuli

Ultrasound mid-air haptic (UMH) devices are a novel tool for haptic feedback, capable of providing localized vibrotactile stimuli to users at a distance. UMH applications largely rely on generating tactile shape outlines on the users’ skin. Here we investigate how to achieve sensations of continuity or gaps within such two-dimensional curves by studying the perception of pairs of amplitude-modulated focused ultrasound stimuli. On the one hand, we aim to investigate perceptual effects that may arise from providing simultaneous UMH stimuli. On the other hand, we wish to provide perception-based rendering guidelines for generating continuous or discontinuous sensations of tactile shapes. Finally, we hope to contribute toward a measure of the perceptually achievable resolution of UMH interfaces. We performed a user study to identify how far apart two focal points need to be to elicit a perceptual experience of two distinct stimuli separated by a gap. Mean gap detection thresholds were found at 32.3-mm spacing between focal points, but a high within- and between-subject variability was observed. Pairs spaced below 15 mm were consistently (>95%) perceived as a single stimulus, while pairs spaced 45 mm apart were consistently (84%) perceived as two separate stimuli. To investigate the observed variability, we resort to acoustic simulations of the resulting pressure fields. These show a non-linear evolution of actual peak pressure spacing as a function of nominal focal point spacing. Beyond an initial threshold in spacing (between 15 and 18 mm), which we believe to be related to the perceived size of a focal point, the probability of detecting a gap between focal points appears to linearly increase with spacing. Our work highlights physical interactions and perceptual effects to consider when designing or investigating the perception of UMH shapes.
Batching, Aggregation, and Zero-Knowledge Proofs in Bilinear Accumulators

An accumulator is a cryptographic primitive that allows a prover to succinctly commit to a set of values while being able to provide proofs of (non-)membership. A batch proof is an accumulator proof that can be used to prove (non-)membership of multiple values simultaneously. In this work, we present a zero-knowledge batch proof with constant proof size and constant verification in the Bilinear Pairings (BP) setting. Our scheme is 16x to 42x faster than state-of-the-art SNARK-based zero-knowledge batch proofs in the RSA setting. Additionally, we propose protocols that allow a prover to aggregate multiple individual non-membership proofs, in the BP setting, into a single batch proof of constant size. Our construction for aggregation satisfies a strong soundness definition - one where the accumulator value can be chosen arbitrarily. We evaluate our techniques and systematically compare them with RSA-based alternatives. Our evaluation results showcase several scenarios for which BP accumulators are clearly preferable and can serve as a guideline when choosing between the two types of accumulators.
On the heights of totally p-adic numbers

Bombieri and Zannier established lower and upper bounds for the limit infimum of the Weil height in fields of totally p-adic numbers and generalizations thereof. In this paper, we use potential theoretic techniques to generalize the upper bounds from their paper and, under the assumption of integrality, to improve slightly upon their bounds.