Miracle-dz/UniFAR-FTUs huggingface dataset:
Courant-sharp Robin eigenvalues for the square: The case of negative Robin parameter

We consider the cases where there is equality in Courant’s nodal domain theorem for the Laplacian with a Robin boundary condition on the square. In our previous two papers, we treated the cases where the Robin parameter h > 0 is large, small respectively. In this paper we investigate the case where h < 0.
Set System Blowups

We prove that given a constant $k \ge 2$ and a large set system $\mathcal{F}$ of sets of size at most $w$, a typical $k$-tuple of sets $(S_1, \cdots, S_k)$ from $\mathcal{F}$ can be blown up in the following sense: for each $1 \le i \le k$, we can find a large subfamily $\mathcal{F}_i$ containing $S_i$ so that for $i \neq j$, if $T_i \in \mathcal{F}_i$ and $T_j \in \mathcal{F}_j$ , then $T_i \cap T_j=S_i \cap S_j$. This greatly improves the bounds in an old result of Furedi.
Data-consistent neural networks for solving nonlinear inverse problems

Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical reconstruction method and then apply a neural network to improve its solution. Empirical evidence shows that plain two-step methods provide high-quality reconstructions, but they lack a convergence analysis as known for classical regularization methods. In this paper we formalize the use of such two-step approaches in the context of classical regularization theory. We propose data-consistent neural networks that can be combined with classical regularization methods. This yields a data-driven regularization method for which we provide a convergence analysis with respect to noise. Numerical simulations show that compared to standard two-step deep learning methods, our approach provides better stability with respect to out of distribution examples in the test set, while performing similarly on test data drawn from the distribution of the training set. Our method provides a stable solution approach to inverse problems that beneficially combines the known nonlinear forward model with available information on the desired solution manifold in training data.
From rest-frame luminosity functions to observer-frame colour distributions: tackling the next challenge in cosmological simulations

Galaxy spectral energy distributions (SEDs) remain among the most challenging yet informative quantities to reproduce in simulations due to the large and complex mixture of physical processes that shape the radiation output of a galaxy. With the increasing number of surveys utilising broadband colours as part of their target selection criteria, the production of realistic SEDs in simulations is necessary for assisting in survey design and interpretation of observations. The recent success in reproducing the observed luminosity functions (LF) from far-UV to far-IR, using the state-of-the-art semi-analytic model \shark\ and the SED generator \prospect, represents a critical step towards better galaxy colour predictions. We show that with \shark\ and \prospect\ we can closely reproduce the optical colour distributions observed in the panchromatic GAMA survey. The treatment of feedback, star formation, central-satellite interactions and radiation re-processing by dust are critical for this achievement. The first three processes create a bimodal distribution, while dust attenuation defines the location and shape of the blue and red populations. While a naive comparison between observation and simulations displays the known issue of over-quenching of satellite galaxies, the introduction of empirically-motivated observational errors and classification from the same group finder used in GAMA greatly reduces this tension. The introduction of random re-assignment of $\sim 15\%$ of centrals/satellites as satellites/centrals on the simulation classification closely resembles the outcome of the group finder, providing a computationally less intensive method to compare simulations with observations.
Topology and adjunction in promise constraint satisfaction

The approximate graph colouring problem concerns colouring a $k$-colourable graph with $c$ colours, where $c\geq k$. This problem naturally generalises to promise graph homomorphism and further to promise constraint satisfaction problems. Complexity analysis of all these problems is notoriously difficult. In this paper, we introduce two new techniques to analyse the complexity of promise CSPs: one is based on topology and the other on adjunction. We apply these techniques, together with the previously introduced algebraic approach, to obtain new NP-hardness results for a significant class of approximate graph colouring and promise graph homomorphism problems.
Inverse magnetic catalysis -- how much do we know about?

Some of the advances made in the literature to understand the phase transitions of quark matter in the presence of strong magnetic field and finite temperature (zero quark chemical potential) are reviewed. We start by discussing the physics behind the Magnetic catalysis (MC) at zero/finite temperature and then focus on the lattice predictions for inverse magnetic catalysis (IMC) at high temperature and strong magnetic fields. Possible explanations for the IMC are covered as well. Finally, we discuss recent efforts to modify QCD (quantum chromodynamics) effective models in order to reproduce the IMC observed on the lattice simulations. We emphasize the fact that applying thermo-magnetic effects on the coupling constant of the NJL model significantly improve the effectiveness of the NJL model to obtain a reasonable physical description of hot and magnetized quark matter being in agreement with lattice results.
Spectra of perfect state transfer Hamiltonians on fractal-like graphs

In this paper we study the spectral features, on fractal-like graphs, of Hamiltonians which exhibit the special property of perfect quantum state transfer (PQST): the transmission of quantum states without dissipation. The essential goal is to develop the theoretical framework for understanding the interplay between PQST, spectral properties, and the geometry of the underlying graph, in order to design novel protocols for applications in quantum information science. We present a new lifting and gluing construction, and use this to prove results concerning an inductive spectral structure, applicable to a wide variety of fractal-like graphs. We illustrate this construction with explicit examples for several classes of diamond graphs.
The Milky Way’s bar structural properties from gravitational waves

The Laser Interferometer Space Antenna (LISA) will enable Galactic gravitational wave (GW) astronomy by individually resolving $ > 10^4$ signals from double white dwarf (DWD) binaries throughout the Milky Way. In this work we assess for the first time the potential of LISA data to map the Galactic stellar bar and spiral arms, since GWs are unaffected by stellar crowding and dust extinction unlike optical observations of the bulge region. To achieve this goal we combine a realistic population of Galactic DWDs with a high-resolution N-Body simulation a galaxy in good agreement with the Milky Way. We then model GW signals from our synthetic DWD population and reconstruct the structure of the simulated Galaxy from mock LISA observations. Our results show that while the low signal contrast between the background disc and the spiral arms hampers our ability to characterise the spiral structure, the stellar bar will instead clearly appear in the GW map of the bulge. The bar length and bar width derived from these synthetic observations are underestimated, respectively within $1\sigma$ and at a level greater than $2\sigma$, but the resulting axis ratio agrees to well within $1\sigma$, while the viewing angle is recovered to within one degree. These are competitive constraints compared to those from electromagnetic tracers, and they are obtained with a completely independent method. We therefore foresee that the synergistic use of GWs and electromagnetic tracers will be a powerful strategy to map the bar and the bulge of the Milky Way.
A Unified Object Motion and Affinity Model for Online Multi-Object Tracking

Current popular online multi-object tracking (MOT) solutions apply single object trackers (SOTs) to capture object motions, while often requiring an extra affinity network to associate objects, especially for the occluded ones. This brings extra computational overhead due to repetitive feature extraction for SOT and affinity computation. Meanwhile, the model size of the sophisticated affinity network is usually non-trivial. In this paper, we propose a novel MOT framework that unifies object motion and affinity model into a single network, named UMA, in order to learn a compact feature that is discriminative for both object motion and affinity measure. In particular, UMA integrates single object tracking and metric learning into a unified triplet network by means of multi-task learning. Such design brings advantages of improved computation efficiency, low memory requirement and simplified training procedure. In addition, we equip our model with a task-specific attention module, which is used to boost task-aware feature learning. The proposed UMA can be easily trained end-to-end, and is elegant – requiring only one training stage. Experimental results show that it achieves promising performance on several MOT Challenge benchmarks.
Analog MIMO RoC Passive Relay for Indoor Deployments of Wireless Networks

Most of the indoor coverage issues arise from network deployments that are usually planned for outdoor scenarios. Moreover, the ever-growing number of devices with different Radio Access Technologies (RATs), expected for new 5G scenarios and to maintain compatibility with older cellular standards (mostly 3G/4G), worsen this situation thus calling for novel bandwidth-efficient, low-latency and cost-effective solutions for indoor coverage. To solve this problem, Centralized Radio Access Network (C-RAN) architectures have been proposed to provide dense and controlled coverage inside buildings. However, all-digital C-RAN solutions are complex and expensive when indoor layout constraints and device costs are considered. We discuss here an analog C-RAN architecture, referred to as Analog MIMO Radio-over-Copper (A-MIMO-RoC), that aims at distributing RF signals indoors over distances in the order of 50 m. The all-analog passive-only design presented here proves the feasibility of analog relaying of MIMO radio signals over LAN cables at frequency bandwidth values up to 400 MHz for multi-RAT applications. After asserting the feasibility of the A-MIMO-RoC platform, we present some experimental results obtained with the proposed architecture. These preliminary results show that the A-MIMO-RoC system is a valid solution towards the design of dedicated 4G/5G indoor wireless systems for the billions of buildings which nowadays still suffer from severe indoor coverage issues.
Coverage-Guided Testing for Recurrent Neural Networks

Recurrent neural networks (RNNs) have been applied to a broad range of applications, including natural language processing, drug discovery, and video recognition. Their vulnerability to input perturbation is also known. Aligning with a view from software defect detection, this article aims to develop a coverage-guided testing approach to systematically exploit the internal behavior of RNNs, with the expectation that such testing can detect defects with high possibility. Technically, the long short-term memory network (LSTM), a major class of RNNs, is thoroughly studied. A family of three test metrics are designed to quantify not only the values but also the temporal relations (including both stepwise and bounded-length) exhibited when LSTM processing inputs. A genetic algorithm is applied to efficiently generate test cases. The test metrics and test case generation algorithm are implemented into a tool testRNN, which is then evaluated on a set of LSTM benchmarks. Experiments confirm that testRNN has advantages over the state-of-the-art tool DeepStellar and attack-based defect detection methods, owing to its working with finer temporal semantics and the consideration of the naturalness of input perturbation. Furthermore, testRNN enables meaningful information to be collected and exhibited for users to understand the testing results, which is an important step toward interpretable neural network testing.
Quantification of model uncertainty on path-space via goal-oriented relative entropy

Quantifying the impact of parametric and model-form uncertainty on the predictions of stochastic models is a key challenge in many applications. Previous work has shown that the relative entropy rate is an effective tool for deriving path-space uncertainty quantification (UQ) bounds on ergodic averages. In this work we identify appropriate information-theoretic objects for a wider range of quantities of interest on path-space, such as hitting times and exponentially discounted observables, and develop the corresponding UQ bounds. In addition, our method yields tighter UQ bounds, even in cases where previous relative-entropy-based methods also apply, e.g., for ergodic averages. We illustrate these results with examples from option pricing, non-reversible diffusion processes, stochastic control, semi-Markov queueing models, and expectations and distributions of hitting times.
Lattice Boltzmann simulations capture the multiscale physics of soft flowing crystals

The study of the underlying physics of soft flowing materials depends heavily on numerical simulations, due to the complex structure of the governing equations reflecting the competition of concurrent mechanisms acting at widely disparate scales in space and time. A full-scale computational modelling remains a formidable challenge since it amounts to simultaneously handling six or more spatial decades in space and twice as many in time. Coarse-grained methods often provide a viable strategy to significantly mitigate this issue, through the implementation of mesoscale supramolecular forces designed to capture the essential physics at a fraction of the computational cost of a full-detail description. Here, we review some recent advances in the design of a lattice Boltzmann mesoscale approach for soft flowing materials, inclusive of near-contact interactions (NCIs) between dynamic interfaces, as they occur in high packing-fraction soft flowing crystals. The method proves capable of capturing several aspects of the rheology of soft flowing crystals, namely, (i) a 3/2 power-law dependence of the dispersed phase flow rate on the applied pressure gradient, (ii) the structural transition between an ex-two and ex-one (bamboo) configurations with the associated drop of the flow rate, (iii) the onset of interfacial waves once NCI is sufficiently intense. This article is part of the theme issue ‘Fluid dynamics, soft matter and complex systems: recent results and new methods’.
FastPay: High-Performance Byzantine Fault Tolerant Settlement

FastPay allows a set of distributed authorities, some of which are Byzantine, to maintain a high-integrity and availability settlement system for pre-funded payments. It can be used to settle payments in a native unit of value (crypto-currency), or as a financial side-infrastructure to support retail payments in fiat currencies. FastPay is based on Byzantine Consistent Broadcast as its core primitive, foregoing the expenses of full atomic commit channels (consensus). The resulting system has low-latency for both confirmation and payment finality. Remarkably, each authority can be sharded across many machines to allow unbounded horizontal scalability. Our experiments demonstrate intra-continental confirmation latency of less than 100ms, making FastPay applicable to point of sale payments. In laboratory environments, we achieve over 80,000 transactions per second with 20 authorities---surpassing the requirements of current retail card payment networks, while significantly increasing their robustness.
Efficient generation of extreme terahertz harmonics in three-dimensional Dirac semimetals

Frequency multiplication of terahertz signals on a solid state platform is highly sought-after for the next generation of high-speed electronics and the creation of frequency combs. Solutions to efficiently generate extreme harmonics (up to the $31^{\rm{st}}$ harmonic and beyond) of a terahertz signal with modest input intensities, however, remain elusive. Using fully nonperturbative simulations and complementary analytical theory, we show that 3D Dirac semimetals (DSMs) have enormous potential as compact sources of extreme terahertz harmonics, achieving energy conversion efficiencies beyond $10^{-5}$ at the $31^{\rm{st}}$ harmonic with input intensities on the order of $10$ MW/cm$^2$, over $10^5$ times lower than in conventional THz high harmonic generation systems. Our theory also reveals a fundamental feature in the nonlinear optics of 3D DSMs: a distinctive regime where higher-order optical nonlinearity vanishes, arising as a direct result of the extra dimensionality in 3D DSMs compared to 2D DSMs. Our findings should pave the way to the development of efficient platforms for high-frequency terahertz light sources and optoelectronics based on 3D DSMs.
The Relationship Between Attachment Styles and Parental Attitudes in High School Students

Abstract The purpose of this study is to investigate the attitudes of the parents of the students studying in various high schools and the relationships between attachment styles. The study sample consisted of 206 students. The data was collected through the Parental Attitudes Scale (PAS) and Relationship Scales Questionnaire (RSQ). Test data was analyzed by correlation analysis. As a result of the study, fearful binding affinities were found to be lessened with the increasing trends of secure attachment. Among the students who were included in the study, those who were not shown any interest by their families can be interpreted as those who go through the perception of pressure. As the reduction of the democratic attitude observed, the authoritarian attitude and protective attitude had increased among the participants.
Diffusive photospheres in gamma-ray bursts

Photospheric emission may originate from relativistic outflows in two qualitatively different regimes: last scattering of photons inside the outflow at the photospheric radius or radiative diffusion to the boundary of the outflow. In this work, the measurement of temperature and flux of the thermal component in the early afterglows of several gamma-ray bursts along with the total flux in the prompt phase is used to determine initial radii of the outflow as well as its Lorentz factors. Results indicate that in some cases the outflow has relatively low Lorentz factors (Γ < 10), favouring cocoon interpretation, while in other cases Lorentz factors are larger (Γ > 10), indicating diffusive photospheric origin of the thermal component, associated with an ultrarelativistic outflow.
Probabilistic Counters for Privacy Preserving Data Aggregation

Probabilistic counters are well known tools often used for space-efficient set cardinality estimation. In this paper we investigate probabilistic counters from the perspective of preserving privacy. We use standard, rigid differential privacy notion. The intuition is that the probabilistic counters do not reveal too much information about individuals, but provide only general information about the population. Thus they can be used safely without violating privacy of individuals. It turned out however that providing a precise, formal analysis of privacy parameters of probabilistic counters is surprisingly difficult and needs advanced techniques and a very careful approach. We demonstrate also that probabilistic counters can be used as a privacy protecion mechanism without any extra randomization. That is, the inherit randomization from the protocol is sufficient for protecting privacy, even if the probabilistic counter is used many times. In particular we present a specific privacy-preserving data aggregation protocol based on a probabilistic counter. Our results can be used for example in performing distributed surveys.
Adversarial Multi-Binary Neural Network for Multi-class Classification

Multi-class text classification is one of the key problems in machine learning and natural language processing. Emerging neural networks deal with the problem using a multi-output softmax layer and achieve substantial progress, but they do not explicitly learn the correlation among classes. In this paper, we use a multi-task framework to address multi-class classification, where a multi-class classifier and multiple binary classifiers are trained together. Moreover, we employ adversarial training to distinguish the class-specific features and the class-agnostic features. The model benefits from better feature representation. We conduct experiments on two large-scale multi-class text classification tasks and demonstrate that the proposed architecture outperforms baseline approaches.
An Implicit Representation of Swept Volumes based on Local Shapes and Movements

We introduce a new way to implicitly represent swept volumes in 3D. We first implicitize the base volume and then apply the time-dependent rigid transformation to build an implicit representation of the swept volume. This way, we build a fitting representation, where geometric details generated by the rigid transformation and details of the base volume itself are both taken into account. This representation relies on a partition of a boundary box of the swept volume according to portions of the space related either to parts of the base volume or to time span of the transformation.
Logarithmic Regret Bound in Partially Observable Linear Dynamical Systems

We study the problem of system identification and adaptive control in partially observable linear dynamical systems. Adaptive and closed-loop system identification is a challenging problem due to correlations introduced in data collection. In this paper, we present the first model estimation method with finite-time guarantees in both open and closed-loop system identification. Deploying this estimation method, we propose adaptive control online learning (AdaptOn), an efficient reinforcement learning algorithm that adaptively learns the system dynamics and continuously updates its controller through online learning steps. AdaptOn estimates the model dynamics by occasionally solving a linear regression problem through interactions with the environment. Using policy re-parameterization and the estimated model, AdaptOn constructs counterfactual loss functions to be used for updating the controller through online gradient descent. Over time, AdaptOn improves its model estimates and obtains more accurate gradient updates to improve the controller. We show that AdaptOn achieves a regret upper bound of $\text{polylog}\left(T\right)$, after $T$ time steps of agent-environment interaction. To the best of our knowledge, AdaptOn is the first algorithm that achieves $\text{polylog}\left(T\right)$ regret in adaptive control of unknown partially observable linear dynamical systems which includes linear quadratic Gaussian (LQG) control.