Miracle-dz/UniFAR-FTUs huggingface dataset:
Jack-Hurwitz Number

Inspired by the algebraic expressions of [27] the Hurwitz numbers, which are mainly expressed by the elements of the transform matrix from the Schur functions s λ to the homogeneous symmetric power sum function p λ , and by the symplectic surgery theory of the relative GW-invariants [19], [14], using the elements of the transform matrix from the Jack function with two parameters [22] to the homogeneous symmetric power sum functions, we have constructed the Jack-Hurwitz numbers. As an application, we shall construct a series of newly genus-expanded cut-and-join diﬀerential operators, which can be thought of as the generalization of the Laplace-Beltrami operators and have the genus-expanded Jack function as their common eigenfunctions. Then we shall obtain some generating wave functions at the same level generated by the Jack-Hurwitz numbers, which can be expressed in terms of the newly cut-and-join diﬀerential operators. More important, our paper seems to reveal that there should exist a ( q, t ) -deformed relative Gromov-Witten theory.
Schur Multipliers of $C^*$-algebras, group-invariant compactification and applications to amenability and percolation

Let $\Gamma$ be a countable discrete group. Given any sequence $(f_n)_{n\geq 1}$ of $\ell^p$-normalized functions ($p\in [1,2)$), consider the associated positive definite matrix coefficients $\langle f_n, \rho(\cdot) f_n\rangle$ of the right regular representation $\rho$. We construct an orthogonal decomposition of the corresponding {\it Schur multipliers} on the reduced group $C^*$-algebra or the uniform Roe algebra of $\Gamma$. We identify this decomposition explicitly via the limit points of the orbits $(\widetilde f_n)_{n\geq 1}$ in the group-invariant compactification of the quotient space constructed by Varadhan and the first author in [14]. We apply this result and use positive-definiteness to provide two (quite different) characterizations of amenability of $\Gamma$ -- one via a variational approach and the other using group-invariant percolation on Cayley graphs constructed by Benjamini, Lyons, Peres and Schramm [1]. These results underline, from a new point of view to the best of our knowledge, the manner in which Schur multipliers capture geometric properties of the underlying group $\Gamma$.
Precise Asymptotics for Spectral Methods in Mixed Generalized Linear Models

In a mixed generalized linear model, the objective is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two statistically independent signals in a mixed generalized linear model with Gaussian covariates. Spectral methods are a popular class of estimators which output the top two eigenvectors of a suitable data-dependent matrix. However, despite the wide applicability, their design is still obtained via heuristic considerations, and the number of samples $n$ needed to guarantee recovery is super-linear in the signal dimension $d$. In this paper, we develop exact asymptotics on spectral methods in the challenging proportional regime in which $n, d$ grow large and their ratio converges to a finite constant. By doing so, we are able to optimize the design of the spectral method, and combine it with a simple linear estimator, in order to minimize the estimation error. Our characterization exploits a mix of tools from random matrices, free probability and the theory of approximate message passing algorithms. Numerical simulations for mixed linear regression and phase retrieval display the advantage enabled by our analysis over existing designs of spectral methods.
Looking for the left sneutrino LSP with displaced-vertex searches

We analyze a displaced dilepton signal expected at the LHC for a tau left sneutrino as the lightest supersymmetric particle with a mass in the range 45-100 GeV. The sneutrinos are pair produced via a virtual W, Z or γ in the s channel and, given the large value of the tau Yukawa coupling, their decays into two dileptons or a dilepton plus missing transverse energy from neutrinos can be significant. The discussion is carried out in the framework of the μνSSM, where the presence of R-parity violating couplings involving right-handed neutrinos solves the μ problem and can reproduce the neutrino data. To probe the tau left sneutrinos we compare the predictions of this scenario with the ATLAS search for long-lived particles using displaced lepton pairs in pp collisions at s=8 TeV, allowing us to constrain the parameter space of the model. We also consider an optimization of the trigger requirements used in existing displaced-vertex searches by means of a high level trigger that exploits tracker information. This optimization is generically useful for a light metastable particle decaying into soft charged leptons. The constraints on the sneutrino turn out to be more stringent. We finally discuss the prospects for the 13 TeV LHC searches as well as further potential optimizations. © 2018 authors. Published by the American Physical Society.
Monte Carlo simulation and large deviations theory for uniformly recurrent Markov chains

Importance sampling is a Monte Carlo simulation technique in which the simulation distribution is different from the true underlying distribution. In order to obtain an unbiased Monte Carlo estimate of the desired parameter, simulated events are weighted to reflect their true relative frequency. In this paper, we consider the estimation via simulation of certain large deviations probabilities for time-homogeneous Markov chains. We first demonstrate that when the simulation distribution is also a homogeneous Markov chain, the estimator variance will vanish exponentially as the sample size n tends to∞. We then prove that the estimator variance is asymptotically minimized by the same exponentially twisted Markov chain which arises in large deviation theory, and furthermore, this optimization is unique among uniformly recurrent homogeneous Markov chain simulation distributions.
Face Swapping as A Simple Arithmetic Operation

We propose a novel high-fidelity face swapping method called"Arithmetic Face Swapping"(AFS) that explicitly disentangles the intermediate latent space W+ of a pretrained StyleGAN into the"identity"and"style"subspaces so that a latent code in W+ is the sum of an"identity"code and a"style"code in the corresponding subspaces. Via our disentanglement, face swapping (FS) can be regarded as a simple arithmetic operation in W+, i.e., the summation of a source"identity"code and a target"style"code. This makes AFS more intuitive and elegant than other FS methods. In addition, our method can generalize over the standard face swapping to support other interesting operations, e.g., combining the identity of one source with styles of multiple targets and vice versa. We implement our identity-style disentanglement by learning a neural network that maps a latent code to a"style"code. We provide a condition for this network which theoretically guarantees identity preservation of the source face even after a sequence of face swapping operations. Extensive experiments demonstrate the advantage of our method over state-of-the-art FS methods in producing high-quality swapped faces. Our source code was made public at https://github.com/truongvu2000nd/AFS
Excitation of Molecular Hydrogen in the Orion Bar PhotodissociationRegion from a Deep Near-infrared IGRINS Spectrum

We present a deep near-infrared spectrum of the Orion Bar Photodissociation Region (PDR) taken with the Immersion Grating INfrared Spectrometer (IGRINS) on the 2.7 m telescope at the McDonald Observatory. IGRINS has high spectral resolution ( R ∼ 45,000 ) and instantaneous broad wavelength coverage (1.45–2.45 μm), enabling us to detect 87 emission lines from rovibrationally excited molecular hydrogen (H2) that arise from transitions out of 69 upper rovibration levels of the electronic ground state. These levels cover a large range of rotational and vibrational quantum numbers and excitation energies, making them excellent probes of the excitation mechanisms of H2 and physical conditions within the PDR. The Orion Bar PDR is thought to consist of cooler high density clumps or filaments ( T = 50 – 250 K, n H = 10 5 – 10 7 cm−3) embedded in a warmer lower density medium ( T = 250 – 1000 K, n H = 10 4 – 10 5 cm−3). We fit a grid of constant temperature and density Cloudy models, which recreate the observed H2 level populations well, to constrain the temperature to a range of 600–650 K and the density to n H = 2.5 × 10 3 – 10 4 cm−3. The best-fit model gives T = 625 K and n H = 5 × 10 3 cm−3. This well-constrained warm temperature is consistent with kinetic temperatures found by other studies for the Orion Bar’s lower density medium. However, the range of densities well fit by the model grid is marginally lower than those reported by other studies. We could be observing lower density gas than the surrounding medium, or perhaps a density-sensitive parameter in our models is not properly estimated.
Simple and Effective Augmentation Methods for CSI Based Indoor Localization

Indoor localization is a challenging task. Compared to outdoor environments where GPS is dominant, there is no robust and almost-universal approach. Recently, machine learning (ML) has emerged as the most promising approach for achieving accurate indoor localization. Nevertheless, its main challenge is requiring large datasets to train the neural networks. The data collection procedure is costly and laborious, requiring extensive measurements and labeling processes for different indoor environments. The situation can be improved by Data Augmentation (DA), a general framework to enlarge the datasets for ML, making ML systems more robust and increasing their generalization capabilities. This paper proposes two simple yet surprisingly effective DA algorithms for channel state information (CSI) based indoor localization motivated by physical considerations. We show that the number of measurements for a given accuracy requirement may be decreased by an order of magnitude. Specifically, we demonstrate the algorithms' effectiveness by experiments conducted with a measured indoor WiFi measurement dataset: As little as 10% of the original dataset size is enough to get the same performance as the original dataset. We also showed that if we further augment the dataset with the proposed techniques, test accuracy is improved more than three-fold.
Electromagnetic couplings in a collective model of the nucleon

We study the electromagnetic properties of the nucleon and its excitations in a collective model. In the ensuing algebraic treatment all results for helicity amplitudes and form factors can be derived in closed form in the limit of a large model space. We discuss nucleon form factors and transverse electromagnetic couplings in photo- and electroproduction, including transition form factors that can be measured at new electron facilities.
Understanding the Bystander Effect on Toxic Twitter Conversations

In this study, we explore the power of group dynamics to shape the toxicity of Twitter conversations. First, we examine how the presence of others in a conversation can potentially diffuse Twitter users' responsibility to address a toxic direct reply. Second, we examine whether the toxicity of the first direct reply to a toxic tweet in conversations establishes the group norms for subsequent replies. By doing so, we outline how bystanders and the tone of initial responses to a toxic reply are explanatory factors which affect whether others feel uninhibited to post their own abusive or derogatory replies. We test this premise by analyzing a random sample of more than 156k tweets belonging to ~9k conversations. Central to this work is the social psychological research on the"bystander effect"documenting that the presence of bystanders has the power to alter the dynamics of a social situation. If the first direct reply reaffirms the divisive tone, other replies may follow suit. We find evidence of a bystander effect, with our results showing that an increased number of users participating in the conversation before receiving a toxic tweet is negatively associated with the number of Twitter users who responded to the toxic reply in a non-toxic way. We also find that the initial responses to toxic tweets within conversations is of great importance. Posting a toxic reply immediately after a toxic comment is negatively associated with users posting non-toxic replies and Twitter conversations becoming increasingly toxic.
Air-Aided Communication between Ground Assets in a Poisson Forest

Ground assets deployed in a cluttered environment with randomized obstacles (e.g., a forest) may experience line of sight (LoS) obstruction due to those obstacles. Air assets can be deployed in the vicinity to aid the communication by establishing two-hop paths between the ground assets. Obstacles that are taller than a position-dependent critical height may still obstruct the LoS between a ground asset and an air asset. In this paper, we provide an analytical framework for computing the probability of obtaining a LoS path in a Poisson forest. Given the locations and heights of a ground asset and an air asset, we establish the critical height, which is a function of distance. To account for this dependence on distance, the blocking is modeled as an inhomogenous Poisson point process, and the LoS probability is its void probability. Examples and closed-form expressions are provided for two obstruction height distributions: uniform and truncated Gaussian. The examples are validated through simulation. Additionally, the end-to-end throughput is determined and shown to be a metric that balances communication distance with the impact of LoS blockage. Throughput is used to determine the range at which it is better to relay communications through the air asset, and, when the air asset is deployed, its optimal height.
Fused Lasso Nearly Isotonic Signal Approximation in General Dimensions

In this paper we introduce and study fused lasso nearly-isotonic signal approximation, which is a combination of fused lasso and generalized nearly-isotonic regression. We show how these three estimators relate to each other, derive solution to the general problem, show that it is computationally feasible and provides a trade-off between piecewise monotonicity, sparsity and goodness-of-fit. Also, we derive an unbiased estimator of the degrees of freedom of the approximator.
In-sample Curriculum Learning by Sequence Completion for Natural Language Generation

Curriculum learning has shown promising improvements in multiple domains by training machine learning models from easy samples to hard ones. Previous works which either design rules or train models for scoring the difficulty highly rely on task-specific expertise, and cannot generalize. Inspired by the “easy-to-hard” intuition, we propose to do in-sample curriculum learning for natural language generation tasks. Our learning strategy starts training the model to generate the last few words, i.e., do sequence completion, and gradually extends to generate the whole output sequence. Comprehensive experiments show that it generalizes well to different tasks and achieves significant improvements over strong baselines.
A Simple Spectroscopic Technique to Identify Rejuvenating Galaxies

Rejuvenating galaxies are unusual galaxies that fully quench and then subsequently experience a “rejuvenation” event to become star-forming once more. Rejuvenation rates vary substantially in models of galaxy formation: 10%–70% of massive galaxies are expected to experience rejuvenation by z = 0. Measuring the rate of rejuvenation is therefore important for calibrating the strength of star-formation feedback mechanisms. However, these observations are challenging because rejuvenating systems blend in with normal star-forming galaxies in broadband photometry. In this paper, we use the galaxy spectral energy distribution-fitting code Prospector to search for observational markers that distinguish normal star-forming galaxies from rejuvenating galaxies. We find that rejuvenating galaxies have smaller Balmer absorption line equivalent widths (EWs) than normal star-forming galaxies. This is analogous to the well-known “K+A” or post-starburst galaxies, which have strong Balmer absorption due to A-stars dominating the light: in this case, rejuvenating systems have a lack of A-stars, instead resembling “O—A” systems. We find star-forming galaxies that have Hβ, Hγ, and/or Hδ absorption EWs ≲3 Å corresponds to a highly pure selection of rejuvenating systems. Interestingly, while this technique is highly effective at identifying mild rejuvenation, “strongly” rejuvenating systems remain nearly indistinguishable from star-forming galaxies due to the well-known stellar outshining effect. We conclude that measuring Balmer absorption line EWs in star-forming galaxy populations is an efficient method to identify rejuvenating populations, and discuss several techniques to either remove or resolve the nebular emission which typically lies on top of these absorption lines.
Explaining (Sarcastic) Utterances to Enhance Affect Understanding in Multimodal Dialogues

Conversations emerge as the primary media for exchanging ideas and conceptions. From the listener’s perspective, identifying various affective qualities, such as sarcasm, humour, and emotions, is paramount for comprehending the true connotation of the emitted utterance. However, one of the major hurdles faced in learning these affect dimensions is the presence of figurative language, viz. irony, metaphor, or sarcasm. We hypothesize that any detection system constituting the exhaustive and explicit presentation of the emitted utterance would improve the overall comprehension of the dialogue. To this end, we explore the task of Sarcasm Explanation in Dialogues, which aims to unfold the hidden irony behind sarcastic utterances. We propose MOSES, a deep neural network which takes a multimodal (sarcastic) dialogue instance as an input and generates a natural language sentence as its explanation. Subsequently, we leverage the generated explanation for various natural language understanding tasks in a conversational dialogue setup, such as sarcasm detection, humour identification, and emotion recognition. Our evaluation shows that MOSES outperforms the state-of-the-art system for SED by an average of ∼2% on different evaluation metrics, such as ROUGE, BLEU, and METEOR. Further, we observe that leveraging the generated explanation advances three downstream tasks for affect classification – an average improvement of ~14% F1-score in the sarcasm detection task and ∼2% in the humour identification and emotion recognition task. We also perform extensive analyses to assess the quality of the results.
Higgs Cosmology and Dark Matter

Higgs vacuum stability has important consequences for cosmology. In particular, we argue that if the Higgs vacuum is metastable, then the dark matter cannot contain a single black hole of mass less than 1015g in our entire past light cone. In addition to being the destroyer microscopic black holes, it may be possible that Higgs vacuum decay is a source of primordial black holes during inflation.
NEW INTERPRETATION OF SKYRME THEORY

Based on the proposal that the Skyrme theory is a theory of monopole we provide a new interpretation of Skyrme theory, that the theory can also be viewed as an effective theory of strong interaction which is dual to QCD, where the monopoles (not the quarks) are confined through the Meissner effect. This dual picture leads us to predict the existence of a topological glueball in QCD, a chromoelectric knot which is dual to the chromomagnetic knot in Skyrme theory, whose mass and decay width are estimated to be around 60 GeV and 8 GeV. As importantly, the existence of the magnetic vortex and knot in Skyrme theory strongly indicates that the theory could also be interpreted to describe a very interesting low energy condensed matter physics in a completely different environment. These new interpretations of Skyrme theory puts the theory in a totally new perspective.
Reward is not Necessary: How to Create a Compositional Self-Preserving Agent for Life-Long Learning

We introduce a physiological model-based agent as proof-of-principle that it is possible to define a flexible self-preserving system that does not use a reward signal or reward-maximization as an objective. We achieve this by introducing the SelfPreserving Agent (SPA) with a physiological structure where the system can get trapped in an absorbing state if the agent does not solve and execute goal-directed polices. Our agent is defined using new class of Bellman equations called Operator Bellman Equations (OBEs), for encoding jointly non-stationary non-Markovian tasks formalized as a Temporal Goal Markov Decision Process (TGMDP). OBEs produce optimal goal-conditioned spatiotemporal transition operators that map an initial state-time to the final state-times of a policy used to complete a goal, and can also be used to forecast future states in multiple dynamic physiological statespaces. SPA is equipped with an intrinsic motivation function called the valence function, which quantifies the changes in empowerment (the channel capacity of a transition operator) after following a policy. Because empowerment is a function of a transition operator, there is a natural synergism between empowerment and OBEs: the OBEs create hierarchical transition operators, and the valence function can evaluate hierarchical empowerment change defined on these operators. The valence function can then be used for goal selection, wherein the agent chooses a policy sequence that realizes goal states which produce maximum empowerment gain. In doing so, the agent will seek freedom and avoid internal death-states that undermine its ability to control both external and internal states in the future, thereby exhibiting the capacity of predictive and anticipatory self-preservation. We argue that product-space valence maximization is a powerful single-objective multi-goal alternative to multi-objective RL because it avoids the problem of providing preference weights to select policies from a Pareto frontier, and that SPA registers the consequences of following a policy on many other state-spaces, which is necessary for performing sequential tasks. We also discuss how SPA is capable of high-level abstract symbolic reasoning when computing plans, and SPA’s capacity for life-long learning, where the agent learns new compositions of transition operators and prediction operator factorizations over time.
Open-quantum-systems approach to in-medium heavy quarkonium dynamics

Heavy quarkonium continues to play a central role in the study of nuclear matter under extremes of temperature and density in relativistic heavy-ion collisions. In this talk I report on recent developments in the theoretical description of quarkonium in-medium dynamics using the open-quantum systems approach. Not only does it provide a clear interpretation of the imaginary part of the complex heavy-quark potential but also reveals that a subtle interplay between screening and wavefunction decoherence is responsible for the melting of heavy quarkonium states.