Miracle-dz/UniFAR-FTUs huggingface dataset:
Experimental realization of an intrinsically error-protected superconducting qubit

Encoding a qubit in logical quantum states with wavefunctions characterized by disjoint support and robust energies can offer simultaneous protection against relaxation and pure dephasing. Using a circuit-quantum-electrodynamics architecture, we experimentally realize a superconducting $0-\pi$ qubit, which hosts protected states suitable for quantum-information processing. Multi-tone spectroscopy measurements reveal the energy level structure of the system, which can be precisely described by a simple two-mode Hamiltonian. We find that the parity symmetry of the qubit results in charge-insensitive levels connecting the protected states, allowing for logical operations. The measured relaxation (1.6 ms) and dephasing times (25 $\mu$s) demonstrate that our implementation of the $0-\pi$ circuit not only broadens the family of superconducting qubits, but also represents a promising candidate for the building block of a fault-tolerant quantum processor.
Koebe conjecture and the Weyl problem for convex surfaces in hyperbolic 3-space

We prove that the Koebe circle domain conjecture is equivalent to the Weyl type problem that every complete hyperbolic surface of genus zero is isometric to the boundary of the hyperbolic convex hull of the complement of a circle domain. It provides a new way to approach the Koebe's conjecture using convex geometry. Combining our result with the work of He-Schramm on the Koebe conjecture, one establishes that every simply connected non-compact polyhedral surface is discrete conformal to the complex plane or the open unit disk. The main tool we use is Schramm's transboundary extremal lengths.
Direct collapse to supermassive black hole seeds: the critical conditions for suppression of H2 cooling

Observations of high-redshift quasars imply the presence of supermassive black holes (SMBHs) already at $z$ ∼ 7.5. An appealing and promising pathway to their formation is the direct collapse scenario of a primordial gas in atomic-cooling haloes at $z$ ∼ 10–20, when the $\rm H_{2}$ formation is inhibited by a strong background radiation field, whose intensity exceeds a critical value, Jcrit. To estimate Jcrit, typically, studies have assumed idealized spectra, with a fixed ratio of $\rm H_{2}$ photodissociation rate $k_{\rm H_2}$ to the $\rm H^-$ photodetachment rate $k_{\rm H^-}$. This assumption, however, could be too narrow in scope as the nature of the background radiation field is not known precisely. In this work we argue that the critical condition for suppressing the H2 cooling in the collapsing gas could be described in a more general way by a combination of $k_{\rm H_2}$ and $k_{\rm H^-}$ parameters, without any additional assumptions about the shape of the underlying radiation spectrum. By performing a series of cosmological zoom-in simulations covering a wide range of relevant $k_{\rm H_2}$ and $k_{\rm H^-}$ parameters, we examine the gas flow by following evolution of basic parameters of the accretion flow. We test under what conditions the gas evolution is dominated by $\rm H_{2}$ and/or atomic cooling. We confirm the existence of a critical curve in the $k_{\rm H_2}{\! -\! }k_{\rm H^-}$ plane and provide an analytical fit to it. This curve depends on the conditions in the direct collapse, and reveals domains where the atomic cooling dominates over the molecular cooling. Furthermore, we have considered the effect of $\rm H_{2}$ self-shielding on the critical curve, by adopting three methods for the effective column density approximation in $\rm H_{2}$. We find that the estimate of the characteristic length scale for shielding can be improved by using λJeans25, which is 0.25 times that of the local Jeans length, which is consistent with previous one-zone modelling.
Precise measurement of quantum observables with neural-network estimators

The measurement precision of modern quantum simulators is intrinsically constrained by the limited set of measurements that can be efficiently implemented on hardware. This fundamental limitation is particularly severe for quantum algorithms where complex quantum observables are to be precisely evaluated. To achieve precise estimates with current methods, prohibitively large amounts of sample statistics are required in experiments. Here, we propose to reduce the measurement overhead by integrating artificial neural networks with quantum simulation platforms. We show that unsupervised learning of single-qubit data allows the trained networks to accommodate measurements of complex observables, otherwise costly using traditional post-processing techniques. The effectiveness of this hybrid measurement protocol is demonstrated for quantum chemistry Hamiltonians using both synthetic and experimental data. Neural-network estimators attain high-precision measurements with a drastic reduction in the amount of sample statistics, without requiring additional quantum resources.
Cross-correlation of the thermal Sunyaev–Zel’dovich effect and weak gravitational lensing: Planck and Subaru Hyper Suprime-Cam first-year data

Cross-correlation analysis of the thermal Sunyaev–Zel’dovich (tSZ) effect and weak gravitational lensing (WL) provides a powerful probe of cosmology and astrophysics of the intracluster medium. We present the measurement of the cross-correlation of tSZ and WL from Planck and Subaru Hyper-Suprime Cam. The combination enables us to study cluster astrophysics at high redshift. We use the tSZ-WL cross-correlation and the tSZ autopower spectrum measurements to place a tight constraint on the hydrostatic mass bias, which is a measure of the degree of non-thermal pressure support in galaxy clusters. With the prior on cosmological parameters derived from the analysis of the cosmic microwave background anisotropies by Planck and taking into account foreground contributions both in the tSZ autopower spectrum and the tSZ-WL cross-correlation, the hydrostatic mass bias is estimated to be $26.9^{+8.9}_{-4.4} {{\ \rm per\ cent}}$ ($68{{\ \rm per\ cent}}$ CL), which is consistent with recent measurements by mass calibration techniques.
Minimal warm inflation

Slow-roll inflation is a successful paradigm. However we find that even a small coupling of the inflaton to other light fields can dramatically alter the dynamics and predictions of inflation. As an example, the inflaton can generically have an axion-like coupling to gauge bosons. Even relatively small couplings will automatically induce a thermal bath during inflation. The thermal friction from this bath can easily be stronger than Hubble friction, significantly altering the usual predictions of any particular inflaton potential. Thermal effects suppress the tensor-to-scalar ratio r significantly, and predict unique non-gaussianities. This axion-like coupling provides a minimal model of warm inflation which avoids the usual problem of thermal backreaction on the inflaton potential. As a specific example, we find that hybrid inflation with this axion-like coupling can easily fit the current cosmological data.
Instance adaptive adversarial training: Improved accuracy tradeoffs in neural nets

Adversarial training is by far the most successful strategy for improving robustness of neural networks to adversarial attacks. Despite its success as a defense mechanism, adversarial training fails to generalize well to unperturbed test set. We hypothesize that this poor generalization is a consequence of adversarial training with uniform perturbation radius around every training sample. Samples close to decision boundary can be morphed into a different class under a small perturbation budget, and enforcing large margins around these samples produce poor decision boundaries that generalize poorly. Motivated by this hypothesis, we propose instance adaptive adversarial training -- a technique that enforces sample-specific perturbation margins around every training sample. We show that using our approach, test accuracy on unperturbed samples improve with a marginal drop in robustness. Extensive experiments on CIFAR-10, CIFAR-100 and Imagenet datasets demonstrate the effectiveness of our proposed approach.
Teaching Vehicles to Anticipate: A Systematic Study on Probabilistic Behavior Prediction Using Large Data Sets

By observing their environment as well as other traffic participants, humans are enabled to drive road vehicles safely. Vehicle passengers, however, perceive a notable difference between non-experienced and experienced drivers. In particular, they may get the impression that the latter ones anticipate what will happen in the next few moments and consider these foresights in their driving behavior. To make the driving style of automated vehicles comparable to the one of human drivers with respect to comfort and perceived safety, the aforementioned anticipation skills need to become a built-in feature of self-driving vehicles. This article provides a systematic comparison of methods and strategies to generate this intention for self-driving cars using machine learning techniques. To implement and test these algorithms we use a large data set collected over more than 30 000 km of highway driving and containing approximately 40 000 real-world driving situations. We further show that it is possible to classify driving maneuvers upcoming within the next 5 s with an Area Under the ROC Curve (AUC) above 0.92 for all defined maneuver classes. This enables us to predict the lateral position with a prediction horizon of 5 s with a median lateral error of less than 0.21 m.
Limit theorems for numbers of returns in arrays under $\phi$-mixing

We consider a $\phi$-mixing shift $T$ on a sequence space $\Om$ and study the number $\cN_N$ of returns $\{ T^{q_N(n)}\om\in A^a_n\}$ at times $q_N(n)$ to a cylinder $A^a_n$ constructed by a sequence $a\in\Om$ where $n$ runs either until a fixed integer $N$ or until a time $\tau_N$ of the first return $\{ T^{q_N(n)}\om\in A^b_m\}$ to another cylinder $A^b_m$ constructed by $b\in\Om$. Here $q_N(n)$ are certain functions of $n$ taking on nonnegative integer values when $n$ runs from 0 to $N$ and the dependence on $N$ is the main generalization here which requires certain conditions under which we obtain Poisson distributions limits of $\cN_N$ when counting is until $N$ as $N\to\infty$ and geometric distributions limits when counting is until $\tau_N$ as $N\to\infty$.
Annealed Denoising Score Matching: Learning Energy-Based Models in High-Dimensional Spaces

Energy-Based Models (EBMs) outputs unmormalized log-probability values given data samples. Such an estimation is essential in a variety of applications such as sample generation, denoising, sample restoration, outlier detection, Bayesian reasoning, and many more. However, standard maximum likelihood training is computationally expensive due to the requirement of sampling the model distribution. Score matching potentially alleviates this problem, and denoising score matching is a particularly convenient version. However, previous works do not produce models capable of high quality sample synthesis in high dimensional datasets from random initialization. We believe that is because the score is only matched over a single noise scale, which corresponds to a small set in high-dimensional space. To overcome this limitation, here we instead learn an energy function using denoising score matching over all noise scales. When sampled from random initialization using Annealed Langevin Dynamics and single-step denoising jump, our model produced high-quality samples comparable to state-of-the-art techniques such as GANs. The learned model also provide density information and set a new sample quality baseline in energy-based models. We further demonstrate that the proposed method generalizes well with an image inpainting task.
Toward Subject Invariant and Class Disentangled Representation in BCI via Cross-Domain Mutual Information Estimator

In recent, deep learning-based feature representation methods have shown a promising impact in electroencephalography (EEG)-based brain-computer interface (BCI). Nonetheless, due to high intra- and inter-subject variabilities, many studies on decoding EEG were designed in a subject-specific manner by using calibration samples, with no much concern on its less practical, time-consuming, and data-hungry process. To tackle this problem, recent studies took advantage of transfer learning, especially using domain adaptation techniques. However, there still remain two challenging limitations; i) most domain adaptation methods are designed for labeled source and unlabeled target domain whereas BCI tasks generally have multiple annotated domains. ii) most of the methods do not consider negatively transferable to disrupt generalization ability. In this paper, we propose a novel network architecture to tackle those limitations by estimating mutual information in high-level representation and low-level representation, separately. Specifically, our proposed method extracts domain-invariant and class-relevant features, thereby enhancing generalizability in classification across. It is also noteworthy that our method can be applicable to a new subject with a small amount of data via a fine-tuning, step only, reducing calibration time for practical uses. We validated our proposed method on a big motor imagery EEG dataset by showing promising results, compared to competing methods considered in our experiments.
On the Cauchy problem of 3D incompressible Navier-Stokes-Cahn-Hilliard system

In this paper, we are concerned with the Cauchy problem for 3D incompressible Navier-Stokes-Cahn-Hilliard equations. First, applying a refined pure energy method, assuming $\|u_0\|_{H^1}+\|\phi_0\|_{H^1}+\|\nabla\phi_0\|_{H^1}$ is sufficiently small, we obtain the global well-posedness of solutions. Moreover, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained, the $\dot{H}^{-s}$ ($0\leq s\leq\frac12$) negative Sobolev norms is shown to be preserved along time evolution and enhance the decay rates.
Phase diagram and dynamics of the 
SU(N)
 symmetric Kondo lattice model

In heavy-fermion systems, the competition between the local Kondo physics and intersite magnetic fluctuations results in unconventional quantum critical phenomena which are frequently addressed within the Kondo lattice model (KLM). Here we study this interplay in the SU($N$) symmetric generalization of the two-dimensional half-filled KLM by quantum Monte Carlo simulations with $N$ up to 8. While the long-range antiferromagnetic (AF) order in SU($N$) quantum spin systems typically gives way to spin-singlet ground states with spontaneously broken lattice symmetry, we find that the SU($N$) KLM is unique in that for each finite $N$ its ground-state phase diagram hosts only two phases -- AF order and the Kondo-screened phase. The absence of any intermediate phase between the $N=2$ and large-$N$ cases establishes adiabatic correspondence between both limits and confirms that the large-$N$ theory is a correct saddle point of the KLM fermionic path integral and a good starting point to include quantum fluctuations. In addition, we determine the evolution of the single-particle gap, quasiparticle residue of the doped hole at momentum $(\pi,\pi)$, and spin gap across the magnetic order-disorder transition. Our results indicate that increasing $N$ modifies the behavior of the coherence temperature: while it evolves smoothly across the magnetic transition at $N=2$ it develops an abrupt jump -- of up to an order of magnitude -- at larger but finite $N$. We discuss the magnetic order-disorder transition from a quantum-field-theoretic perspective and comment on implications of our findings for the interpretation of experiments on quantum critical heavy-fermion compounds.
A Deterministic Algorithm for Balanced Cut with Applications to Dynamic Connectivity, Flows, and Beyond

We consider the classical Minimum Balanced Cut problem: given a graph $G$, compute a partition of its vertices into two subsets of roughly equal volume, while minimizing the number of edges connecting the subsets. We present the first deterministic, almost-linear time approximation algorithm for this problem. Specifically, our algorithm, given an n-vertex $m$-edge graph $G$ and any parameter $1\leq r\leq O(\log n)$, computes a $(\log m)^{r^{2}}$-approximation for Minimum Balanced Cut in $G$, in time $O\left(m^{1+O(1/r)+o(1)}\cdot (\log m)^{O(r^{2})}\right)$. In particular, we obtain a $(\log m)^{1/\epsilon}$-approximation in time $m^{1+O(\sqrt{\epsilon})}$ for any constant $\epsilon > 0$, and a $(\log m)^{f(m)}$-approximation in time $m^{1+o(1)}$, for any slowly growing function $f(m)$. We obtain deterministic algorithms with similar guarantees for the Sparsest Cut and the Lowest-Conductance Cut problems. Our algorithm for the Minimum Balanced Cut problem in fact provides a stronger guarantee: it either returns a balanced cut whose value is close to a given target value, or it certifies that such a cut does not exist by exhibiting a large subgraph of $G$ that has high conductance. We use this algorithm to obtain deterministic algorithms for dynamic connectivity and minimum spanning forest, whose worst-case update time on an n-vertex graph is $n^{o(1)}$, thus resolving a major open problem in the area of dynamic graph algorithms. Our work also implies deterministic algorithms for a host of additional problems, whose time complexities match, up to subpolynomial in $n$ factors, those of known randomized algorithms. The implications include almost-linear time deterministic algorithms for solving Laplacian systems and for approximating maximum flows in undirected graphs.
The Role of Coded Side Information in Single-Server Private Information Retrieval

We study the role of coded side information in single-server Private Information Retrieval (PIR). An instance of the single-server PIR problem includes a server that stores a database of <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> independently and uniformly distributed messages, and a user who wants to retrieve one of these messages from the server. We consider settings in which the user initially has access to a coded side information which includes a linear combination of a subset of <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> messages in the database. We assume that the identities of the <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> messages that form the support set of the coded side information as well as the coding coefficients are initially unknown to the server. We consider two different models, depending on whether the support set of the coded side information includes the requested message or not. We also consider the following two privacy requirements: (i) the identities of both the demand and the support set of the coded side information need to be protected, or (ii) only the identity of the demand needs to be protected. For each model and for each of the privacy requirements, we consider the problem of designing a protocol for generating the user’s query and the server’s answer that enables the user to decode the message they need while satisfying the privacy requirement. We characterize the (scalar-linear) capacity of each setting, defined as the ratio of the number of information bits in a message to the minimum number of information bits downloaded from the server over all (scalar-linear) protocols that satisfy the privacy condition. Our converse proofs rely on new information-theoretic arguments—tailored to the setting of single-server PIR and different from the commonly-used techniques in multi-server PIR settings. We also present novel capacity-achieving scalar-linear protocols for each of the settings being considered.
Void halo mass function: A promising probe of neutrino mass

Cosmic voids, the underdense regions in the universe, are particularly sensitive to diffuse density components such as cosmic neutrinos. This sensitivity is enhanced by the match between void sizes and the free-streaming scale of massive neutrinos. Using the massive neutrino simulations \texttt{MassiveNuS}, we investigate the effect of neutrino mass on dark matter halos as a function of environment. We find that the halo mass function depends strongly on neutrino mass and that this dependence is more pronounced in voids than in high-density environments. An observational program that measured the characteristic mass of the most massive halos in voids should be able to place novel constraints on the sum of the masses of neutrinos $\sum m_\nu$. The neutrino mass effect in the simulations is quite strong: In a 512$^3$ $h^{-3}$ Mpc$^3$ survey, the mean mass of the 1000 most massive halos in the void interiors is $(4.82 \pm 0.11) \times 10^{12} h^{-1}M_{\odot}$ for $\sum m_\nu = 0.6$ eV and $(8.21 \pm 0.13) \times 10^{12} h^{-1}M_{\odot}$ for $\sum m_\nu = 0.1$ eV. Subaru (SuMIRe), Euclid and WFIRST will have both spectroscopic and weak lensing surveys. Covering volumes at least 50 times larger than our simulations, they should be sensitive probes of neutrino mass through void substructure.
Path Homologies of Deep Feedforward Networks

We provide a characterization of two types of directed homology for fully-connected, feedforward neural network architectures. These exact characterizations of the directed homology structure of a neural network architecture are the first of their kind. We show that the directed flag homology of deep networks reduces to computing the simplicial homology of the underlying undirected graph, which is explicitly given by Euler characteristic computations. We also show that the path homology of these networks is non-trivial in higher dimensions and depends on the number and size of the layers within the network. These results provide a foundation for investigating homological differences between neural network architectures and their realized structure as implied by their parameters.
On $\mu$-Dvoretzky random covering of the circle

In this paper, we study the Dvoretzky covering problem with non-uniformly distributed centers. When the probability law of the centers admits an absolutely continuous density which satisfies a regular condition on the set of essential infimum points, we give a necessary and sufficient condition for covering the circle. When the lengths of covering intervals are of the form $\ell_n = \frac{c}{n}$, we give a necessary and sufficient condition for covering the circle, without imposing any regularity on the density function.
Modeling magnetic evolution and exchange hardening in disordered magnets: The example of 
Mn1−xFexRu2Sn
 Heusler alloys

We demonstrate how exchange hardening can arise in a chemically disordered solid solution from a first-principles statistical mechanics approach. A general mixed-basis chemical and magnetic cluster expansion has been developed, and applied to the ${\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}{\mathrm{Ru}}_{2}\mathrm{Sn}$ Heusler alloy system; single-phase solid solutions between antiferromagnetic ${\mathrm{MnRu}}_{2}\mathrm{Sn}$ and ferromagnetic ${\mathrm{FeRu}}_{2}\mathrm{Sn}$ with disorder on the Mn/Fe sublattice that exhibit unexpected exchange hardening. Monte Carlo simulations applied to the cluster expansion are able to reproduce the experimentally measured magnetic transition temperatures and the bulk magnetization as a function of composition. The magnetic ordering around a site is shown to be dependent not only on bulk composition, but also on the identity of the site and the local composition around that site. The simulations predict that local antiferromagnetic orderings form inside a bulk ferromagnetic region at intermediate compositions that drives the exchange hardening. Furthermore, the antiferromagnetic regions disorder at a lower temperature than the ferromagnetic regions, providing an atomistic explanation for the experimentally observed decrease in exchange hardening with increasing temperature. These effects occur on a length scale too small to be resolved with previously used characterization techniques.