Miracle-dz/UniFAR-FTUs huggingface dataset:
The Sun’s Magnetic (Hale) Cycle and 27 Day Recurrences in the aa Geomagnetic Index

We construct a new solar cycle phase clock which maps each of the last 18 solar cycles onto a single normalized epoch for the approximately 22 yr Hale (magnetic polarity) cycle, using the Hilbert transform of daily sunspot numbers (SSNs) since 1818. The occurrences of solar maxima show almost no discernible Hale cycle dependence, consistent with the clock being synchronized to polarity reversals. We reengineer the Sargent R27 index and combine it with our epoch analysis to obtain a high time resolution parameter for 27 day recurrence in aa, 〈acv(27)〉. This reveals that the transition to recurrence, that is, to an ordered solar wind dominated by high-speed streams, is fast, with an upper bound of a few solar rotations. It resolves an extended late declining phase which is approximately twice as long on even Schwabe cycles as odd. Galactic cosmic ray flux rises in step with 〈acv(27)〉 but then stays high. Our analysis also identifies a slow-timescale trend in SSN that simply tracks the Gleissberg cycle. We find that this trend is in phase with the slow-timescale trend in the modulus of sunspot latitudes, and in antiphase with that of the R27 index.
Black Hole Mergers from Star Clusters with Top-heavy Initial Mass Functions

Recent observations of globular clusters (GCs) provide evidence that the stellar initial mass function (IMF) may not be universal, suggesting specifically that the IMF grows increasingly top-heavy with decreasing metallicity and increasing gas density. Noncanonical IMFs can greatly affect the evolution of GCs, mainly because the high end determines how many black holes (BHs) form. Here we compute a new set of GC models, varying the IMF within observational uncertainties. We find that GCs with top-heavy IMFs lose most of their mass within a few gigayears through stellar winds and tidal stripping. Heating of the cluster through BH mass segregation greatly enhances this process. We show that, as they approach complete dissolution, GCs with top-heavy IMFs can evolve into “dark clusters” consisting of mostly BHs by mass. In addition to producing more BHs, GCs with top-heavy IMFs also produce many more binary BH (BBH) mergers. Even though these clusters are short-lived, mergers of ejected BBHs continue at a rate comparable to, or greater than, what is found for long-lived GCs with canonical IMFs. Therefore, these clusters, though they are no longer visible today, could still contribute significantly to the local BBH merger rate detectable by LIGO/Virgo, especially for sources with higher component masses well into the BH mass gap. We also report that one of our GC models with a top-heavy IMF produces dozens of intermediate-mass black holes (IMBHs) with masses , including one with . Ultimately, additional gravitational wave observations will provide strong constraints on the stellar IMF in old GCs and the formation of IMBHs at high redshift.
Cosmological Constant as a Finite Temperature Effect

The cosmological constant problem is examined by taking an Einstein--scalar with a Higgs-type potential and scrutinizing the infrared structure induced by finite temperature effects. A variant optimal perturbation theory is implemented in the recently proposed quantum-gravitational framework. The optimized renormalized mass, i.e., the renormalized mass determined by the variant optimal perturbation theory, of the scalar field turns out to be on the order of the temperature. This shifts the cosmological constant problem to compatibility of the consequent perturbative analysis. The compatibility is guaranteed essentially by renormalization group invariance of physical quantities. We point out the resummation behind the invariance.
Modal Logic With Non-Deterministic Semantics: Part II - Quantified Case

In the first part of this paper we analyzed finite non-deterministic matrix semantics for propositional non-normal modal logics as an alternative to the standard Kripke possible world semantics. This kind of modal system characterized by finite non-deterministic matrices was originally proposed by Ju. Ivlev in the 70s. The aim of this second paper is to introduce a formal non-deterministic semantical framework for the quantified versions of some Ivlev-like non-normal modal logics. It will be shown that several well-known controversial issues of quantified modal logics, relative to the identity predicate, Barcan’s formulas and de re and de dicto modalities, can be tackled from a new angle within the present framework.
First-order algorithms for robust optimization problems via convex-concave saddle-point Lagrangian reformulation

Robust optimization (RO) is one of the key paradigms for solving optimization problems affected by uncertainty. Two principal approaches for RO, the robust counterpart method and the adversarial approach, potentially lead to excessively large optimization problems. For that reason, first order approaches, based on online-convex-optimization, have been proposed (Ben-Tal et al. (2015), Kilinc-Karzan and Ho-Nguyen (2018)) as alternatives for the case of large-scale problems. However, these methods are either stochastic in nature or involve a binary search for the optimal value. We propose deterministic first-order algorithms based on a saddle-point Lagrangian reformulation that avoids both of these issues. Our approach recovers the other approaches' O(1/epsilon^2) convergence rate in the general case, and offers an improved O(1/epsilon) rate for problems with constraints which are affine both in the decision and in the uncertainty. Experiment involving robust quadratic optimization demonstrates the numerical benefits of our approach.
Data Poisoning Attacks to Deep Learning Based Recommender Systems

Recommender systems play a crucial role in helping users to find their interested information in various web services such as Amazon, YouTube, and Google News. Various recommender systems, ranging from neighborhood-based, association-rule-based, matrix-factorization-based, to deep learning based, have been developed and deployed in industry. Among them, deep learning based recommender systems become increasingly popular due to their superior performance. In this work, we conduct the first systematic study on data poisoning attacks to deep learning based recommender systems. An attacker's goal is to manipulate a recommender system such that the attacker-chosen target items are recommended to many users. To achieve this goal, our attack injects fake users with carefully crafted ratings to a recommender system. Specifically, we formulate our attack as an optimization problem, such that the injected ratings would maximize the number of normal users to whom the target items are recommended. However, it is challenging to solve the optimization problem because it is a non-convex integer programming problem. To address the challenge, we develop multiple techniques to approximately solve the optimization problem. Our experimental results on three real-world datasets, including small and large datasets, show that our attack is effective and outperforms existing attacks. Moreover, we attempt to detect fake users via statistical analysis of the rating patterns of normal and fake users. Our results show that our attack is still effective and outperforms existing attacks even if such a detector is deployed.
Safety-Oriented Pedestrian Motion and Scene Occupancy Forecasting

In this paper, we address the important problem in self-driving of forecasting multi-pedestrian motion and their shared scene occupancy map, critical for safe navigation. Our contributions are two-fold. First, we advocate for predicting both the individual motions as well as the scene occupancy map in order to effectively deal with missing detections caused by postprocessing, e.g., confidence thresholding and non-maximum suppression. Second, we propose a Scene-Actor Graph Neural Network (SA-GNN) which preserves the relative spatial information of pedestrians via 2D convolution, and captures the interactions among pedestrians within the same scene, including those that have not been detected, via message passing. On two large-scale real-world datasets, nuScenes and ATG4D, we showcase that our scene-occupancy predictions are more accurate and better calibrated than those from state-of-the-art motion forecasting methods, while also matching their performance in pedestrian motion forecasting metrics.
Free energy screening of small ligands binding to an artificial protein cavity

The λ-dynamics simulation method was used to study the binding of 10 five-member ring heterocycle derivatives to an artificial cavity created inside cytochrome C peroxidase by mutagenesis. Application of λ dynamics using a multiple topology approach resulted in trapping in local minima. To extend the method to these cases, a new restraining potential was devised and added to the extended Hamiltonian. Two approximations were introduced in order to estimate the binding free energy within small simulation times using this potential: (a) The entropy terms related to the restraining potential are assumed to cancel, due to the similarity of the ligands. (b) The restraining potential calculated from the coordinates of the environmental atoms during a λ-dynamics simulation is assumed to be equal to that of the average coordinates. Relatively short λ-dynamics simulations with this restraining potential successfully yielded reasonable estimates of the binding affinity of the ligands as compared with both experiment.
Fertilization Effects on Soil Solution Chemistry in Three Eucalypt Plantations

Concentrations of nutrients in soil solution may by important indicators of nutrient availability for forest plantations, but we were unaware of the extent to which these concentrations varied temporally and were affected by fertilizer treatments at various sites. The effect of fertilizing eucalypt plantations on the concentrations of NH 4 , NO 3 , and inorganic phosphate (Pi), and on electrical conductivity (EC) and pH in paste extracts was assessed at three sites in Tasmania, Australia. Nitrogen and P fertilizers were broadcast at elemental rates in the range 0 to 600 kg ha -1 as (NH 4 ) 2 SO 4 and triple super-phosphate within 2 mo of planting, and again at 26 mo at two of the sites. Nutrient concentrations in undiluted soil solution were inferred by adjusting for the effects of dilution and buffering. Both fertilization events decreased pH by up to one-half a unit, and increased conductivity and the concentrations of NH 4 and P i by up to 10-fold in the 0- to 60-cm depth at all sites. Even at the highest rate of application, values of all parameters generally returned to unfertilized values before the second application of fertilizer. Rates of decrease in concentrations of NH 4 and P l after fertilization were unaffected by the age of the crop. When broadcast, applications of fertilizers may be needed at 2- to 4-yr intervals to maintain high nutrient availability. A single application of (NH 4 ) 2 SO 4 to these soils at a typical rate of 200 kg N ha -1 will have minimal effect on pH, but multiple applications could decrease pH and adversely affect Ca, K, and Mg availability.
Algebraic localization implies exponential localization in non-periodic insulators

Exponentially-localized Wannier functions are a basis of the Fermi projection of a Hamiltonian consisting of functions which decay exponentially quickly in space. In two and three spatial dimensions, it is well understood for periodic insulators that exponentially-localized Wannier functions exist if and only if there exists an orthonormal basis for the Fermi projection with finite second moment (i.e. all basis elements satisfy $\int |\boldsymbol{x}|^2 |w(\boldsymbol{x})|^2 \,\text{d}{\boldsymbol{x}} 0$ then there also exists an orthonormal basis for the Fermi projection which decays exponentially quickly in space. This result lends support to the Localization Dichotomy Conjecture for non-periodic systems recently proposed by Marcelli, Monaco, Moscolari, and Panati.
SDP Achieves Exact Minimax Optimality in Phase Synchronization

We study the phase synchronization problem with noisy measurements <inline-formula> <tex-math notation="LaTeX">$Y=z^{*}z^{* { \mathrm {\scriptscriptstyle H} }}+\sigma W\in \mathbb {C}^{n\times n}$ </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">$z^{*}$ </tex-math></inline-formula> is an <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>-dimensional complex unit-modulus vector and <inline-formula> <tex-math notation="LaTeX">$W$ </tex-math></inline-formula> is a complex-valued Gaussian random matrix. It is assumed that each entry <inline-formula> <tex-math notation="LaTeX">$Y_{jk}$ </tex-math></inline-formula> is observed with probability <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula>. We prove that an SDP relaxation of the MLE achieves the error bound <inline-formula> <tex-math notation="LaTeX">$(1+o(1))\frac {\sigma ^{2}}{2np}$ </tex-math></inline-formula> under a normalized squared <inline-formula> <tex-math notation="LaTeX">$\ell _{2}$ </tex-math></inline-formula> loss. This result matches the minimax lower bound of the problem, and even the leading constant is sharp. The analysis of the SDP is based on an equivalent non-convex programming whose solution can be characterized as a fixed point of the generalized power iteration lifted to a higher dimensional space. This viewpoint unifies the proofs of the statistical optimality of three different methods: MLE, SDP, and generalized power method. The technique is also applied to the analysis of the SDP for <inline-formula> <tex-math notation="LaTeX">$\mathbb {Z}_{2}$ </tex-math></inline-formula> synchronization, and we achieve the minimax optimal error <inline-formula> <tex-math notation="LaTeX">$\exp \left ({-(1-o(1))\frac {np}{2\sigma ^{2}}}\right)$ </tex-math></inline-formula> with a sharp constant in the exponent.
A Deterministic Parallel APSP Algorithm and its Applications

In this paper we show a deterministic parallel all-pairs shortest paths algorithm for real-weighted directed graphs. The algorithm has $\tilde{O}(nm+(n/d)^3)$ work and $\tilde{O}(d)$ depth for any depth parameter $d\in [1,n]$. To the best of our knowledge, such a trade-off has only been previously described for the real-weighted single-source shortest paths problem using randomization [Bringmann et al., ICALP'17]. Moreover, our result improves upon the parallelism of the state-of-the-art randomized parallel algorithm for computing transitive closure, which has $\tilde{O}(nm+n^3/d^2)$ work and $\tilde{O}(d)$ depth [Ullman and Yannakakis, SIAM J. Comput. '91]. Our APSP algorithm turns out to be a powerful tool for designing efficient planar graph algorithms in both parallel and sequential regimes. One notable ingredient of our parallel APSP algorithm is a simple deterministic $\tilde{O}(nm)$-work $\tilde{O}(d)$-depth procedure for computing $\tilde{O}(n/d)$-size hitting sets of shortest $d$-hop paths between all pairs of vertices of a real-weighted digraph. Such hitting sets have also been called $d$-hub sets. Hub sets have previously proved especially useful in designing parallel or dynamic shortest paths algorithms and are typically obtained via random sampling. Our procedure implies, for example, an $\tilde{O}(nm)$-time deterministic algorithm for finding a shortest negative cycle of a real-weighted digraph. Such a near-optimal bound for this problem has been so far only achieved using a randomized algorithm [Orlin et al., Discret. Appl. Math. '18].
Can RNNs learn Recursive Nested Subject-Verb Agreements?

One of the fundamental principles of contemporary linguistics states that language processing requires the ability to extract recursively nested tree structures. However, it remains unclear whether and how this code could be implemented in neural circuits. Recent advances in Recurrent Neural Networks (RNNs), which achieve near-human performance in some language tasks, provide a compelling model to address such questions. Here, we present a new framework to study recursive processing in RNNs, using subject-verb agreement as a probe into the representations of the neural network. We trained six distinct types of RNNs on a simplified probabilistic context-free grammar designed to independently manipulate the length of a sentence and the depth of its syntactic tree. All RNNs generalized to subject-verb dependencies longer than those seen during training. However, none systematically generalized to deeper tree structures, even those with a structural bias towards learning nested tree (i.e., stack-RNNs). In addition, our analyses revealed primacy and recency effects in the generalization patterns of LSTM-based models, showing that these models tend to perform well on the outerand innermost parts of a center-embedded tree structure, but poorly on its middle levels. Finally, probing the internal states of the model during the processing of sentences with nested tree structures, we found a complex encoding of grammatical agreement information (e.g. grammatical number), in which all the information for multiple words nouns was carried by a single unit. Taken together, these results indicate how neural networks may extract bounded nested tree structures, without learning a systematic recursive rule. These authors contributed equally to this work. ar X iv :2 10 1. 02 25 8v 1 [ cs . C L ] 6 J an 2 02 1 A PREPRINT JANUARY 8, 2021
Adaptive Group Testing on Networks with Community Structure

Since the inception of the group testing problem in World War II, one of the prevailing assumptions in the probabilistic variant of the problem has been that individuals in the population are infected by a disease independently. However, this assumption rarely holds in practice, as diseases typically spread through interactions between individuals and therefore cause infections to be correlated. Inspired by characteristics of COVID-19 and similar diseases, we consider an infection model over networks which generalizes the traditional i.i. d. model from probabilistic group testing. Under this infection model, we ask whether knowledge of the network structure can be leveraged to perform group testing more efficiently, focusing specifically on community-structured graphs drawn from the stochastic block model. We prove that when the network and infection parameters are conducive to “strong community structure;” our proposed adaptive, graph-aware algorithm outperforms the baseline binary splitting algorithm, and is even order-optimal in certain parameter regimes. A full version of this paper is accessible at http://arxiv.org/abs/2101.0240S. Omitted proofs and numerical experiments are provided in the full version
Finite-temperature photoemission in the extended Falicov-Kimball model: a case study for Ta$_2$NiSe$_5$

Utilizing the unbiased time-dependent density-matrix renormalization group technique, we examine the photoemission spectra in the extended Falicov-Kimball model at zero and finite temperatures, particularly with regard to the excitonic insulator state most likely observed in the quasi-one-dimensional material Ta$_2$NiSe$_5$. Working with infinite boundary conditions, we are able to simulate all dynamical correlation functions directly in the thermodynamic limit. For model parameters best suited for Ta$_2$NiSe$_5$ the photoemission spectra show a weak but clearly visible two-peak structure, around the Fermi momenta $k\simeq\pm k_{\rm F}$, which suggests that Ta$_2$NiSe$_5$ develops an excitonic insulator of BCS-like type. At higher temperatures, the leakage of the conduction-electron band beyond the Fermi energy becomes distinct, which provides a possible explanation for the bare non-interacting band structure seen in time- and angle-resolved photoemission spectroscopy experiments.
Identification of Latent Variables From Graphical Model Residuals

Graph-based causal discovery methods aim to capture conditional independencies consistent with the observed data and differentiate causal relationships from indirect or induced ones. Successful construction of graphical models of data depends on the assumption of causal sufficiency: that is, that all confounding variables are measured. When this assumption is not met, learned graphical structures may become arbitrarily incorrect and effects implied by such models may be wrongly attributed, carry the wrong magnitude, or mis-represent direction of correlation. Wide application of graphical models to increasingly less curated "big data" draws renewed attention to the unobserved confounder problem. We present a novel method that aims to control for the latent space when estimating a DAG by iteratively deriving proxies for the latent space from the residuals of the inferred model. Under mild assumptions, our method improves structural inference of Gaussian graphical models and enhances identifiability of the causal effect. In addition, when the model is being used to predict outcomes, it un-confounds the coefficients on the parents of the outcomes and leads to improved predictive performance when out-of-sample regime is very different from the training data. We show that any improvement of prediction of an outcome is intrinsically capped and cannot rise beyond a certain limit as compared to the confounded model. We extend our methodology beyond GGMs to ordinal variables and nonlinear cases. Our R package provides both PCA and autoencoder implementations of the methodology, suitable for GGMs with some guarantees and for better performance in general cases but without such guarantees.
A Comprehensive Study on Optimization Strategies for Gradient Descent In Deep Learning

One of the most important parts of Artificial Neural Networks is minimizing the loss functions which tells us how good or bad our model is. To minimize these losses we need to tune the weights and biases. Also to calculate the minimum value of a function we need gradient. And to update our weights we need gradient descent. But there are some problems with regular gradient descent ie. it is quite slow and not that accurate. This article aims to give an introduction to optimization strategies to gradient descent. In addition, we shall also discuss the architecture of these algorithms and further optimization of Neural Networks in general
FLGUARD: Secure and Private Federated Learning

—Recently, a number of backdoor attacks against Fed-erated Learning (FL) have been proposed. In such attacks, an adversary injects poisoned model updates into the federated model aggregation process with the goal of manipulating the aggregated model to provide false predictions on speciﬁc adversary-chosen inputs. A number of defenses have been proposed but none of them can effectively protect the FL process also against so-called multi-backdoor attacks in which multiple different backdoors are injected by the adversary simultaneously without severely impacting the benign performance of the aggregated model. To overcome this challenge, we introduce FLG UARD , a poisoning defense framework that is able to defend FL against state-of-the-art backdoor attacks while simultaneously maintaining the benign performance of the aggregated model. Moreover, FL is also vulnerable to inference attacks , in which a malicious aggregator can infer information about clients’ training data from their model updates. To thwart such attacks, we augment FLG UARD with state-of-the-art secure computation techniques that securely evaluate the FLG UARD algorithm. We provide formal argumentation for the effectiveness of our FLG UARD and extensively evaluate it against known backdoor attacks on several datasets and applications (including image classiﬁcation, word prediction, and IoT intrusion detection) demonstrating that FLG UARD can entirely remove backdoors with a negligible effect on accuracy. We also show that private FLG UARD achieves practical runtimes.