Miracle-dz/UniFAR-FTUs huggingface dataset:
Inverses of Matérn covariances on grids

We conduct a study of the aliased spectral densities of Matérn covariance functions on a regular grid of points, elucidating the properties of a popular approximation based on stochastic partial differential equations. While other researchers have shown that this approximation can work well for the covariance function, we find that it assigns too much power at high frequencies and does not provide increasingly accurate approximations to the inverse as the grid spacing goes to zero, except in the one-dimensional exponential covariance case.
Positively and Negatively Hydrated Counterions in Molecular Dynamics Simulations of DNA Double Helix

The DNA double helix is a polyanionic macromolecule that is neutralized in water solutions by metal ions (counterions). The property of counterions to stabilize the water network (positive hydration) or to make it friable (negative hydration) is important in terms of the physical mechanisms of stabilization of the DNA double helix. In the present research, the effects of positive hydration of Na+ counterions and negative hydration of K+ and Cs+ counterions incorporated into the hydration shell of the DNA double helix have been studied using molecular dynamics simulations. The results have shown that the dynamics of the hydration shell of counterions depends on the region of the double helix: minor groove, major groove, and outside the macromolecule. The longest average residence time has been observed for water molecules contacting with the counterions localized in the minor groove of the double helix (about 50 ps for Na+ and lower than 10 ps for K+ and Cs+). The estimated potentials of the mean force for the hydration shells of counterions show that the water molecules are constrained too strongly, and the effect of negative hydration for K+ and Cs+ counterions has not been observed in the simulations. The analysis has shown that the effects of counterion hydration can be described more accurately with water models having lower dipole moments.
CProp: Adaptive Learning Rate Scaling from Past Gradient Conformity

Most optimizers including stochastic gradient descent (SGD) and its adaptive gradient derivatives face the same problem where an effective learning rate during the training is vastly different. A learning rate scheduling, mostly tuned by hand, is usually employed in practice. In this paper, we propose CProp, a gradient scaling method, which acts as a second-level learning rate adapting throughout the training process based on cues from past gradient conformity. When the past gradients agree on direction, CProp keeps the original learning rate. On the contrary, if the gradients do not agree on direction, CProp scales down the gradient proportionally to its uncertainty. Since it works by scaling, it could apply to any existing optimizer extending its learning rate scheduling capability. We put CProp to a series of tests showing significant gain in training speed on both SGD and adaptive gradient method like Adam. Codes are available at this https URL .
DeGAN : Data-Enriching GAN for Retrieving Representative Samples from a Trained Classifier

In this era of digital information explosion, an abundance of data from numerous modalities is being generated as well as archived everyday. However, most problems associated with training Deep Neural Networks still revolve around lack of data that is rich enough for a given task. Data is required not only for training an initial model, but also for future learning tasks such as Model Compression and Incremental Learning. A diverse dataset may be used for training an initial model, but it may not be feasible to store it throughout the product life cycle due to data privacy issues or memory constraints. We propose to bridge the gap between the abundance of available data and lack of relevant data, for the future learning tasks of a given trained network. We use the available data, that may be an imbalanced subset of the original training dataset, or a related domain dataset, to retrieve representative samples from a trained classifier, using a novel Data-enriching GAN (DeGAN) framework. We demonstrate that data from a related domain can be leveraged to achieve state-of-the-art performance for the tasks of Data-free Knowledge Distillation and Incremental Learning on benchmark datasets. We further demonstrate that our proposed framework can enrich any data, even from unrelated domains, to make it more useful for the future learning tasks of a given network.
Multiple Pretext-Task for Self-Supervised Learning via Mixing Multiple Image Transformations

Self-supervised learning is one of the most promising approaches to learn representations capturing semantic features in images without any manual annotation cost. To learn useful representations, a self-supervised model solves a pretext-task, which is defined by data itself. Among a number of pretext-tasks, the rotation prediction task (Rotation) achieves better representations for solving various target tasks despite its simplicity of the implementation. However, we found that Rotation can fail to capture semantic features related to image textures and colors. To tackle this problem, we introduce a learning technique called multiple pretext-task for self-supervised learning (MP-SSL), which solves multiple pretext-task in addition to Rotation simultaneously. In order to capture features of textures and colors, we employ the transformations of image enhancements (e.g., sharpening and solarizing) as the additional pretext-tasks. MP-SSL efficiently trains a model by leveraging a Frank-Wolfe based multi-task training algorithm. Our experimental results show MP-SSL models outperform Rotation on multiple standard benchmarks and achieve state-of-the-art performance on Places-205.
Derandomized compressed sensing with nonuniform guarantees for 𝓁1 recovery

We extend the techniques of Hugel, Rauhut and Strohmer (Found. Comput. Math., 2014) to show that for every $\delta\in(0,1]$, there exists an explicit random $m\times N$ partial Fourier matrix $A$ with $m=s\operatorname{polylog}(N/\epsilon)$ and entropy $s^\delta\operatorname{polylog}(N/\epsilon)$ such that for every $s$-sparse signal $x\in\mathbb{C}^N$, there exists an event of probability at least $1-\epsilon$ over which $x$ is the unique minimizer of $\|z\|_1$ subject to $Az=Ax$. The bulk of our analysis uses tools from decoupling to estimate the extreme singular values of the submatrix of $A$ whose columns correspond to the support of $x$.
Minimax Semiparametric Learning With Approximate Sparsity

This paper is about the ability and means to root-n consistently and efficiently estimate linear, mean square continuous functionals of a high dimensional, approximately sparse regression. Such objects include a wide variety of interesting parameters such as the covariance between two regression residuals, a coefficient of a partially linear model, an average derivative, and the average treatment effect. We give lower bounds on the convergence rate of estimators of such objects and find that these bounds are substantially larger than in a low dimensional, semiparametric setting. We also give automatic debiased machine learners that are $1/\sqrt{n}$ consistent and asymptotically efficient under minimal conditions. These estimators use no cross-fitting or a special kind of cross-fitting to attain efficiency with faster than $n^{-1/4}$ convergence of the regression. This rate condition is substantially weaker than the product of convergence rates of two functions being faster than $1/\sqrt{n},$ as required for many other debiased machine learners.
Quantum Error Correction in Loop Quantum Gravity

Previous works (by Almiehri, Dong, Harlow, Pastakawski, Preskill, Yoshida and others) have established that quantum error correction plays an important role in understanding how the bulk degrees of freedom of an Anti-deSitter spacetime are encoded in the degrees of freedom of the boundary Conformal Field Theory. In previous work \cite{Vaid2013Elementary} I have argued that the Bilson-Thompson model \cite{Bilson-Thompson2006Quantum,Vaid2010Embedding} of elementary particles allows us to view elementary particles as gates for universal quantum computation. In the present work I show that the Bilson-Thompson model, where elementary particles are represented by elements of the framed braid group on three strands, provides an explicit model for the generation of qutrit (three-qubit) states which are the ingredients of Shor's quantum error correcting code. This allows, for the first time, to connect in a concrete manner the proposals of Almheiri, Pastawski, Preskill and others regarding the role of quantum error correction in quantum gravity, to a viable model of elementary particles. Loop Quantum Gravity (LQG), the theory of quantum gravity in which such topological excitations exist, can thus serve as the glue which can connect AdS/CFT based approaches to quantum gravity to the well understood physics of the Standard Model.
Evidence for Bosonization in a Three-Dimensional Gas of 
SU(N)
 Fermions

A multi-component Fermi gas with SU($N$) symmetry is expected to behave like spinless bosons in the large $N$ limit, where the large number of internal states weakens constraints from the Pauli exclusion principle. Whereas blurring the boundary between bosons and fermions lies at the heart of multiple disciplines, bosonization of SU($N$) fermions has been experimentally tested only in a one-dimensional (1D) system so far. Here, we report evidence for bosonization in a three-dimensional (3D) SU$(N)$ fermionic Ytterbium gas with tunable $N$. Using the column integrated momentum distribution, we measure contacts, the central quantity controlling dilute quantum gases, with a high signal-to-noise ratio in our system. We find that the contact per spin approaches a constant with a $1/N$ scaling in the low fugacity regime. This scaling signifies the vanishing role of the fermionic statistics in thermodynamics, and unfolds the intriguing nature of bosonization in 3D SU($N$) fermions. Our work suggests a new route of using contacts to explore multi-component quantum systems and their underlying symmetries.
Estimates of Bubbling Solutions of SU(3) Toda Systems at Critical Parameters. Part 1

For regular $SU(3)$ Toda systems defined on Riemann surface, we initiate the study of bubbling solutions if parameters $(\rho_1^k,\rho_2^k)$ are both tending to critical positions: $(\rho_1^k,\rho_2^k)\to (4\pi, 4\pi N)$ or $(4\pi N, 4\pi)$ ($N>0$ is an integer). We prove that there are at most three formations of bubbling profiles, and for each formation we identify leading terms of $\rho_1^k-4\pi$ and $\rho_2^k-4\pi N$, locations of blowup points and comparison of bubbling heights with sharp precision. The results of this article will be used as substantial tools for a number of degree counting theorems, critical point at infinity theory in the future.
Look, Listen, and Act: Towards Audio-Visual Embodied Navigation

A crucial ability of mobile intelligent agents is to integrate the evidence from multiple sensory inputs in an environment and to make a sequence of actions to reach their goals. In this paper, we attempt to approach the problem of Audio-Visual Embodied Navigation, the task of planning the shortest path from a random starting location in a scene to the sound source in an indoor environment, given only raw egocentric visual and audio sensory data. To accomplish this task, the agent is required to learn from various modalities, i.e., relating the audio signal to the visual environment. Here we describe an approach to audio-visual embodied navigation that takes advantage of both visual and audio pieces of evidence. Our solution is based on three key ideas: a visual perception mapper module that constructs its spatial memory of the environment, a sound perception module that infers the relative location of the sound source from the agent, and a dynamic path planner that plans a sequence of actions based on the audio-visual observations and the spatial memory of the environment to navigate toward the goal. Experimental results on a newly collected Visual-Audio-Room dataset using the simulated multi-modal environment demonstrate the effectiveness of our approach over several competitive baselines.
Electron Firehose Instabilities in High-β Intracluster Shocks

The preacceleration of electrons through reflection and shock drift acceleration (SDA) is essential for the diffusive shock acceleration of nonthermal electrons in collisionless shocks. Previous studies suggested that, in weak quasi-perpendicular (Q⊥) shocks in the high-β ( ) intracluster medium (ICM), the temperature anisotropy due to SDA-reflected electrons can drive the electron firehose instability, which excites oblique nonpropagating waves in the shock foot. In this paper, we investigate, through a linear analysis and particle-in-cell simulations, the firehose instabilities driven by an electron temperature anisotropy (ETAFI) and also by a drifting electron beam (EBFI) in β ∼ 100 ICM plasmas. The EBFI should be more relevant to describing the self-excitation of upstream waves in Q⊥-shocks, since backstreaming electrons in the shock foot behave more like an electron beam rather than an anisotropic bi-Maxwellian population. We find that the basic properties of the two instabilities, such as the growth rate, γ, and the wavenumber of fast-growing oblique modes, are similar in the ICM environment, with one exception; while the waves excited by the ETAFI are nonpropagating (ωr = 0), those excited by the EBFI have a nonzero frequency ( ). However, the frequency is small with ωr < γ. Thus, we conclude that the interpretation of previous studies for the nature of upstream waves based on the ETAFI remains valid in Q⊥-shocks in the ICM.
What could be the observational signature of dark matter in globular clusters?

Here we investigate the possibility that some globular clusters (GCs) harbor intermediate mass black holes (BH) in their centers and are also embedded in a low-mass dark matter (DM) halo. Up to date, there is no evidence on whether or not GCs have DM in their constitution. For standard cold DM cosmology, it is expected that GCs form with their own DM halos. Other studies investigate the possibility that GCs were initially embedded in massive DM halos that evolved during the cluster lifetime. An additional intriguing question is related to the existence of intermediate mass black holes (IMBH) in the GCs. The determination of whether GCs hold IMBHs would be able to answer important questions about GCs formation and the circumstances that gave rise to the IMBHs. DM & IMBH in the context of GCs are interesting subjects to be studied and we will perform such studies here, assuming the coexistence of both of them in some GCs. Having such information, we perform the study possible DM signals from GCs. One important subject to be studied is the DM density profile. In the inner regions of GCs, the DM density profile is still an open question of fundamental importance to DM studies, specially for the study of radio and γ-ray emission from DM annihilation in such regions. Here we consider the case of IMBHs in the inner regions of three GCs: 47 Tuc, NGC 6266 and ω Cen. The existence of a black hole (BH) directly affects the matter distribution in its vicinity. These effects are significant for IMBHs as well as supermassive black holes (SMBHs) and can lead to large DM overdensities called spikes. In this paper, we direct our studies to the radio synchrotron emission from DM annihilation with spike profiles around possible IMBHs in GCs. We present our results for synchrotron emission produced by DM annihilation via bb̄ channel. We use the best-fit DM mass of 34 GeV and annihilation channel in bb̄ used to explain the Galactic center “excess” and perform our analysis for the estimated radio flux. We direct our attention specially to the γ-ray emission from 47 Tuc. When considering a scenario wich includes a BH and the combined analysis of multi-wavelength studies, we conclude that some parameter choice as the annihilation cross section ⟨σ v⟩ used to fit the γ-ray excess differs by many orders of magnitude from the one necessary to fit the radio observations for this globular cluster if we consider the BH scenario.
Nuclear spin relaxation rate near the disorder-driven quantum critical point in Weyl fermion systems

Disorder such as impurities and dislocations in Weyl semimetals drives a quantum critical point (QCP) where the density of states at the Weyl point gains a nonzero value. Near the QCP, the asymptotic low-energy singularities of physical quantities are controlled by the critical exponents $\ensuremath{\nu}$ and $z$. The nuclear spin-lattice relaxation rate, which originates from the hyperfine coupling between a nuclear spin and long-range orbital currents in Weyl fermion systems, shows intriguing critical behavior. Based on the self-consistent Born approximation for impurities, we study the nuclear spin-lattice relaxation rate $1/{T}_{1}$ due to the orbital currents in disordered Weyl SMs. We find that ${({T}_{1}T)}^{\ensuremath{-}1}\ensuremath{\sim}{E}^{2/z}$ at the QCP where $E$ is the maximum of temperature $T$ and chemical potential $\ensuremath{\mu}(T)$ relative to the Weyl point. This scaling behavior of ${({T}_{1}T)}^{\ensuremath{-}1}$ is also confirmed by the self-consistent $T$-matrix approximation, where a remarkable temperature dependence of $\ensuremath{\mu}(T)$ could play an important role. We hope these results of ${({T}_{1}T)}^{\ensuremath{-}1}$ will serve as an impetus for exploration of the disorder-driven quantum criticality in Weyl materials.
Simultaneously determining the frequency sum and time difference of two photons through sum frequency generation

We propose, analyze and evaluate a technique for the joint measurement of time-frequency entanglement between two photons. In particular, we show that the frequency sum and time difference of two photons could be simultaneously measured through the sum-frequency generation process, without measuring the time or frequency of each individual photon. We demonstrate the usefulness of this technique by using it to design a time-frequency entanglement based continuous variable superdense coding and a quantum illumination protocol. Performance analysis of these two protocols suggests that the joint measurement of strong time-frequency entanglement of non-classical photon pairs can significantly enhance the performance of joint-measurement based quantum communication and metrology protocols.
Hysteresis and beating phenomena in loop quantum cosmology

Differences in pressure during expansion and contraction stages in cosmic evolution can result in a hysteresis-like phenomena in non-singular cyclic models sourced with scalar fields. We discuss this phenomena for spatially closed isotropic spacetime in loop quantum cosmology (LQC) for a quadratic and a cosh-like potential, with and without a negative cosmological constant using effective spacetime description of the underlying quantum geometry. Two inequivalent loop quantizations of this spacetime, one based on holonomies of the Ashtekar-Barbero connection using closed loops, and another based on the connection operator, are discussed. Due to quantum geometric effects, both models avoid classical singularities, but unlike the holonomy based quantization, connection based quantization results in two quantum bounces. In spite of differences in non-singular effective dynamics of both the models, the phenomena of hysteresis is found to be robust for the $\phi^2$ potential. Quasi-periodic beats exist for a cosh-like potential, irrespective of the nature of classical recollapse whether by spatial curvature, or a negative cosmological constant. An interplay of negative cosmological constant and spatial curvature in presence of potentials results in rich features such as islands of cluster of bounces separated by accelerated expansion, and a universe which either undergoes a step like expansion with multiple turnarounds or quasi-periodic beats depending on a "tuning" of the steepness parameter of the potential.
Concise and Effective Network for 3D Human Modeling from Orthogonal Silhouettes

In this paper, we revisit the problem of 3D human modeling from two orthogonal silhouettes of individuals (i.e., front and side views). Different from our prior work [Wang et al., 2003], a supervised learning approach based on convolutional neural network (CNN) is investigated to solve the problem by establishing a mapping function that can effectively extract features from two silhouettes and fuse them into coefficients in the shape space of human bodies. A new CNN structure is proposed in our work to exact not only the discriminative features of front and side views and also their mixed features for the mapping function. 3D human models with high accuracy are synthesized from coefficients generated by the mapping function. Existing CNN approaches for 3D human modeling usually learn a large number of parameters (from 8.5M to 355.4M) from two binary images. Differently, we investigate a new network architecture and conduct the samples on silhouettes as input. As a consequence, more accurate models can be generated by our network with only 2.4M coefficients. The training of our network is conducted on samples obtained by augmenting a publicly accessible dataset. Learning transfer by using datasets with a smaller number of scanned models is applied to our network to enable the function of generating results with gender-oriented (or geographical) patterns.
Revisiting turbulence small-scale behavior using velocity gradient triple decomposition

Turbulence small-scale behavior has been commonly investigated in literature by decomposing the velocity-gradient tensor (Aij) into the symmetric strain-rate (Sij) and anti-symmetric rotation-rate (Wij) tensors. To develop further insight, we revisit some of the key studies using a triple decomposition of the velocity-gradient tensor. The additive triple decomposition formally segregates the contributions of normal-strain-rate (Nij), pure-shear (Hij) and rigid-body-rotation-rate (Rij). The decomposition not only highlights the key role of shear, but it also provides a more accurate account of the influence of normal-strain and pure rotation on important small-scale features. First, the local streamline topology and geometry are described in terms of the three constituent tensors in velocity-gradient invariants’ space. Using direct numerical simulation (DNS) data sets of forced isotropic turbulence, the velocity-gradient and pressure field fluctuations are examined at different Reynolds numbers. At all Reynolds numbers, shear contributes the most and rigid-body-rotation the least toward the velocity-gradient magnitude (A2 ≡ AijAij). Especially, shear contribution is dominant in regions of high values of A2 (intermittency). It is shown that the high-degree of enstrophy intermittency reported in literature is due to the shear contribution toward vorticity rather than that of rigid-body-rotation. The study also provides an explanation for the non-intermittent nature of pressure-Laplacian, despite the strong intermittency of enstrophy and dissipation fields. The study further investigates the alignment of the rotation axis with normal strain-rate and pressure Hessian eigenvectors. Overall, it is demonstrated that triple decomposition offers unique and deeper understanding of velocity-gradient behavior in turbulence.
Some new results in random matrices over finite fields

In this note, we give various characterizations of random walks with possibly different steps that have relatively large discrepancy from the uniform distribution modulo a prime p , and use these results to study the distribution of the rank of random matrices over Fp and the equi‐distribution behavior of normal vectors of random hyperplanes. We also study the probability that a random square matrix is eigenvalue‐free, or when its characteristic polynomial is divisible by a given irreducible polynomial in the limit n→∞ in Fp . We show that these statistics are universal, extending results of Stong and Neumann‐Praeger beyond the uniform model.